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There are several types of this isomerism frequently encountered in coordination chemistry and the following represents some of them. Isomers that contain the same number of atoms of each kind but differ in which atoms are bonded to one another are called structural isomers, which differ in structure or bond type. For inorganic complexes, there are three types of structural isomers: ionization, coordination, and linkage and two types of stereoisomers: geometric and optical.
19.08: Isomerism in d-block Metal Complexes
Coordination isomerism is a form of structural isomerism in which the composition of the complex ion varies. In a coordination isomer the total ratio of ligand to metal remains the same, but the ligands attached to a specific metal ion change. Ionization isomers can be thought of as occurring because of the formation of different ions in solution.
Introduction
Ionization isomers are identical except for a ligand has exchanged places with an anion or neutral molecule that was originally outside the coordination complex. The central ion and the other ligands are identical. For example, an octahedral isomer will have five ligands that are identical, but the sixth will differ. The non-matching ligand in one compound will be outside of the coordination sphere of the other compound. Because the anion or molecule outside the coordination sphere is different, the chemical properties of these isomers is different.
The difference between the ionization isomers can be viewed within the context of the ions generated when each are dissolved in solution.
For example, when pentaaquabromocobaltate(II)chloride is dissolved in water, $Cl^-$ ions are generated:
$CoBr(H_2O)_5Cl {(s)} \rightarrow CoBr(H_2O)^+_{5} (aq) + Cl^+ (aq) \nonumber$
whereas when pentaaquachlorocobaltate(II)bromide is dissolved, $Br^-$ ions are generated:
$CoCl(H_2O)_5Br {(s)} \rightarrow CoCl(H_2O)^+_{5} (aq) + Br^+ (aq). \nonumber$
Note
If one dissolved $[PtBr(NH_3)_3]NO_2$ and $[Pt(NO_2)(NH_3)_3]Br$ into solution, then two different set of ions will be general.
• Dissolving $[Pt(NO_2)(NH_3)_3]Br$ in aqueous solution would have the following reaction
$[PtBr(NH_3)_3]NO_2 (s) \rightarrow [PtBr(NH_3)_3]^+ (aq) + NO_2^- (aq) \label{R1}$
• Dissolving of $[Pt(NO_2)(NH_3)_3]Br$ in aqueous solution would be
$[Pt(NO_2)(NH_3)_3]Br (s) \rightarrow [Pt(NO_2)(NH_3)_3]^+ (aq) + Br^- (aq) \label{R2}$
Notice that these two ionization isomers differ in that one ion is directly attached to the central metal, but the other is not.
Equations $\ref{R1}$ and $\ref{R2}$ are valid under the assumption that the platinum-ligand bonds of the complexes are stable (i.e., not labile). Otherwise, they may break and other ligands (e.g., water) may bind.
Example $1$
Are $\ce{[Cr(NH3)5(OSO3)]Br}$ and $\ce{[Cr(NH3)5Br]SO4}$ coordination isomers?
Solution
First, we need confirm that each compound has the same number of atoms of the respective elements (this requires viewing both cations and anions of each compound).
Element number of atoms in $\ce{[Cr(NH3)5(OSO3)]Br}$ number of atoms in $\ce{[Cr(NH3)5Br]SO4}$
$\ce{Cr}$ 1 1
$\ce{N}$ 5 5
$\ce{H}$ 15 15
$\ce{O}$ 4 4
$\ce{S}$ 1 1
$\ce{Br}$ 1 1
Now, let's look at what these two compounds look like (Figure $2$). The sulfate group is a ligand with a dative bond to the chromium atom and the bromide counter ion ($\ce{[Cr(NH3)5(OSO3)]Br}$). For $\ce{[Cr(NH3)5Br]SO4}$, this is the the reverse.
Yes, $\ce{[Cr(NH3)5(OSO3)]Br}$ and $\ce{[Cr(NH3)5Br]SO4}$ are coordination isomers.
Exercise $1$
Are [Co(NH3)5(SO4)]Br and [Co(NH3)5Br]SO4 ionization isomers?
Solution
In the first isomer, SO4 is attached to the Cobalt and is part of the complex ion (the cation), with Br as the anion. In the second isomer, Br is attached to the cobalt as part of the complex and SO4 is acting as the anion.
A hydrate isomer is a specific kind of ionization isomer where a water molecule is one of the molecules that exchanges places.
Solvate or Hydrate Isomerization: A Special kind of Ionization Isomer
A very similar type of isomerism results from replacement of a coordinated group by a solvent molecule (Solvate Isomerism). In the case of water, this is called Hydrate isomerism. The best known example of this occurs for chromium chloride "CrCl3.6H2O" which may contain 4, 5, or 6 coordinated water molecules.
• $[CrCl_2(H_2O)_4]Cl \cdot 2H_2O$: bright-green colored
• $[CrCl(H_2O)_5]Cl_2 \cdot H_2O$: grey-green colored
• $[Cr(H_2O)_6]Cl_3$: violet colored
These isomers have very different chemical properties and on reaction with $AgNO_3$ to test for $Cl^-$ ions, would find 1, 2, and 3 $Cl^-$ ions in solution respectively.
Contributors and Attributions
• The Department of Chemistry, University of the West Indies) | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/19%3A_d-Block_Metal_Chemistry_-_General_Considerations/19.08%3A_Isomerism_in_d-block_Metal_Complexes/19.8A%3A_Structural_Isomerism_-_Ionization_Isomers.txt |
A very similar type of isomerism results from replacement of a coordinated group by a solvent molecule (Solvate Isomerism), which in the case of water is called Hydrate Isomerism. The best known example of this occurs for chromium chloride ($CrCl_3 \cdot 6H_2O$) which may contain 4, 5, or 6 coordinated water molecules (assuming a coordination number of 6). The dot here is used essentially as an expression of ignorance to indicate that, though the parts of the molecule separated by the dot are bonded to one another in some fashion, the exact structural details of that interaction are not fully expressed in the resulting formula. Using Alfred Werner’s coordination theory that indicates that several of the water molecules are actually bonded directly (via coordinate covalent bonds) to the central chromium ion. In fact, there are several possible compounds that use the brackets to signify bonding in the complex and the the dots to signify "water molecules that are not bound to the central metal, but are part of the lattice:
• $[CrCl_2(H_2O)_4]Cl \cdot 2H_2O$: bright-green colored
• $[CrCl(H_2O)_5]Cl_2 \cdot H_2O$: grey-green colored
• $[Cr(H_2O)_6]Cl_3$: violet colored
These isomers have very different chemical properties and on reaction with $AgNO_3$ to test for $Cl^-$ ions, would find 1, 2, and 3 $Cl^-$ ions in solution, respectively.
Upon crystallization from water, many compounds incorporate water molecules in their crystalline frameworks. These "waters of crystallization" refers to water that is found in the crystalline framework of a metal complex or a salt, which is not directly bonded to the metal cation. In the first two hydrate isomers, there are water molecules that are artifacts of the crystallization and occur inside crystals. These water of crystallization is the total weight of water in a substance at a given temperature and is mostly present in a definite (stoichiometric) ratio.
The $[Cr(H_2O)_6]Cl_3$ hydrate isomer (left) is violet colored and the $[CrCl(H_2O)_5]Cl_2 \cdot H_2O$ hydrate isomer is green-grey colored.
What are "Waters of Crystallization"?
A compound with associated water of crystallization is known as a hydrate. The structure of hydrates can be quite elaborate, because of the existence of hydrogen bonds that define polymeric structures. For example, consider the aquo complex $NiCl_2 \cdot 6H_2O$ that consists of separated trans-[NiCl2(H2O)4] molecules linked more weakly to adjacent water molecules. Only four of the six water molecules in the formula are bound to the nickel (II) cation, and the remaining two are waters of crystallization as the crystal structure resolves.
Structure of $NiCl_2 \cdot 6H_2O$ salt with chlorine atoms (green), water molecules (red), and Ni metals (blue) indicated. (CC BY-SA 4.0; Smokefoot).
Water is particularly common solvent to be found in crystals because it is small and polar. But all solvents can be found in some host crystals. Water is noteworthy because it is reactive, whereas other solvents such as benzene are considered to be chemically innocuous.
19.8C: Structural Isomerism - Coordination Isomerism
Coordination isomerism occurs in compounds containing complex anionic and cationic parts and can be viewed as the interchange of one or more ligands between the cationic complex ion and the anionic complex ion. For example, \(\ce{[Co(NH3)6][Cr(CN)6]}\) is a coordination isomer with \(\ce{[Cr(NH3)6][Co(CN)6]}\). Alternatively, coordination isomers may be formed by switching the metals between the two complex ions like \(\ce{[Zn(NH3)4][CuCl4]}\) and \(\ce{[Cu(NH3)4][ZnCl4]}\).
Exercise \(1\)
Are \(\ce{[Cu(NH3)4][PtCl4]}\) and \(\ce{[Pt(NH3)4][CuCl4]}\) coordination isomers?
Solution
Here, both the cation and anion are complex ions. In the first isomer, \(\ce{NH3}\) is attached to the copper and the \(\ce{Cl^{-}}\) are attached to the platinum. In the second isomer, they have swapped.
Yes, they are coordination isomers.
Exercise \(2\)
What is one coordination isomer of \(\ce{[Co(NH3)6] [Cr(C2O4)3]}\)?
Solution
Coordination isomers involve swapping the species from the inner coordination sphere to one metal (e.g, cation) to inner coordination sphere of a different metal (e.g., the anion) in the compound. One isomer is completely swapping the ligand sphere, e.g, \(\ce{[Co(C2O4)3] [Cr(NH3)6]}\).
Alternative coordination isomers are \(\ce{ [Co(NH3)4(C2O4)] [Cr(NH3)2(C2O4)2]}\) and \(\ce{ [Co(NH3)2(C2O4)2] [Cr(NH3)4(C2O4)]}\).
Contributors and Attributions
• The Department of Chemistry, University of the West Indies)
19.8D: Structural Isomerism - Linkage Isomerism
Linkage isomerism occurs with ambidentate ligands that are capable of coordinating in more than one way. The best known cases involve the monodentate ligands: \(SCN^- / NCS^-\) and \(NO_2^- / ONO^-\). The only difference is what atoms the molecular ligands bind to the central ion. The ligand(s) must have more than one donor atom, but bind to ion in only one place. For example, the (NO2-) ion is a ligand can bind to the central atom through the nitrogen or the oxygen atom, but cannot bind to the central atom with both oxygen and nitrogen at once, in which case it would be called a polydentate rather than an ambidentate ligand.
The names used to specify the changed ligands are changed as well. For example, the (NO2-) ion is called nitro when it binds with the N atom and is called nitrito when it binds with the O atom.
Example \(1\): Nitro- vs. Nitrito- Linkage Isomers
The cationic cobalt complex [Co(NH3)5(NO2)]Cl2 exists in two separable linkage isomers of the complex ion: (NH3)5(NO2)]2+.
(left) The nitro isomer (Co-NO2) and (right) the nitrito isomer (Co-ONO)
When donation is from nitrogen to a metal center, the complex is known as a nitro- complex and when donation is from one oxygen to a metal center, the complex is known as a nitrito- complex. An alternative formula structure to emphasize the different coordinate covalent bond for the two isomers
• \([Co(ONO)(NH_3)_5]Cl\): the nitrito isomer -O attached
• \([Co(NO_2)(NH_3)_5]Cl\): the nitro isomer - N attached.
The formula of the complex is unchanged, but the properties of the complex may differ.
Another example of an ambidentate ligans is thiocyanate, SCN, which can attach at either the sulfur atom or the nitrogen atom. Such compounds give rise to linkage isomerism. Polyfunctional ligands can bond to a metal center through different ligand atoms to form various isomers. Other ligands that give rise to linkage isomers include selenocyanate, SeCN – isoselenocyanate, NCSeand sulfite, SO32.
Exercise \(1\)
Are [FeCl5(NO2)]3– and [FeCl5(ONO)]3– linkage isomers?
Solution
Here, the difference is in how the ligand bonds to the metal. In the first isomer, the ligand bonds to the metal through an electron pair on the nitrogen. In the second isomer, the ligand bonds to the metal through an electron pair on one of the oxygen atoms. It's easier to see it:
Contributors and Attributions
• The Department of Chemistry, University of the West Indies) | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/19%3A_d-Block_Metal_Chemistry_-_General_Considerations/19.08%3A_Isomerism_in_d-block_Metal_Complexes/19.8B%3A_Structural_Isomerism_-_Hydration_Isomers.txt |
Isomers are classified into 1) stereoisomers which have different spatial orientations, and 2) constitutional isomers where atoms are connected in different orders. There are two types of stereoisomers: enantiomers and diastereomers.
Enantiomers
One of the stereoisomeric types is enantiomers where two compounds look like mirror images, but those are not superimposable. It is a kind of mirror-image stereoisomers, but the image and mirror images are not superimposable like left and right hand. For this reason, such structures are also called chiral molecules. On the other hand, there are superimposable structures which are called achiral molecules. As shown in Figure 2, an enantiomeric compound pair is non-superimposable and therefore two are not identical.
Like the figure above, chiral molecules have a centric atom called a stereocenter or an asymmetric atom in their structures. For instance, the example in Figure 2 has an asymmetric carbon in its center and it is connected to other substituent groups. Due to the symmetry of enantiomers, an enantiomer pair has most chemical and physical properties such as melting and boiling points, densities, and energy contents.
Diastereomers
Diastereomers are non-enantiomeric where two compounds of the same stereoisomers do not look like mirror images. Figure 2 shows an example of diastereomers. Unlike enantiomeric compounds, two compounds of a diastereomer pair have different chemical and physical properties.
The existence of coordination compounds with the same formula but different arrangements of the ligands was crucial in the development of coordination chemistry. Two or more compounds with the same formula but different arrangements of the atoms are called isomers. Because isomers usually have different physical and chemical properties, it is important to know which isomer we are dealing with if more than one isomer is possible. Recall that in many cases more than one structure is possible for organic compounds with the same molecular formula; examples discussed previously include n-butane versus isobutane and cis-2-butene versus trans-2-butene. As we will see, coordination compounds exhibit the same types of isomers as organic compounds, as well as several kinds of isomers that are unique.
Planar Isomers
Metal complexes that differ only in which ligands are adjacent to one another (cis) or directly across from one another (trans) in the coordination sphere of the metal are called geometrical isomers. They are most important for square planar and octahedral complexes.
Because all vertices of a square are equivalent, it does not matter which vertex is occupied by the ligand B in a square planar MA3B complex; hence only a single geometrical isomer is possible in this case (and in the analogous MAB3 case). All four structures shown here are chemically identical because they can be superimposed simply by rotating the complex in space:
For an MA2B2 complex, there are two possible isomers: either the A ligands can be adjacent to one another (cis), in which case the B ligands must also be cis, or the A ligands can be across from one another (trans), in which case the B ligands must also be trans. Even though it is possible to draw the cis isomer in four different ways and the trans isomer in two different ways, all members of each set are chemically equivalent:
Because there is no way to convert the cis structure to the trans by rotating or flipping the molecule in space, they are fundamentally different arrangements of atoms in space. Probably the best-known examples of cis and trans isomers of an MA2B2 square planar complex are cis-Pt(NH3)2Cl2, also known as cisplatin, and trans-Pt(NH3)2Cl2, which is actually toxic rather than therapeutic.
The anticancer drug cisplatin and its inactive trans isomer. Cisplatin is especially effective against tumors of the reproductive organs, which primarily affect individuals in their 20s and were notoriously difficult to cure. For example, after being diagnosed with metastasized testicular cancer in 1991 and given only a 50% chance of survival, Lance Armstrong was cured by treatment with cisplatin.
Square planar complexes that contain symmetrical bidentate ligands, such as [Pt(en)2]2+, have only one possible structure, in which curved lines linking the two N atoms indicate the ethylenediamine ligands:
Octahedral Isomers
Octahedral complexes also exhibit cis and trans isomers. Like square planar complexes, only one structure is possible for octahedral complexes in which only one ligand is different from the other five (MA5B). Even though we usually draw an octahedron in a way that suggests that the four “in-plane” ligands are different from the two “axial” ligands, in fact all six vertices of an octahedron are equivalent. Consequently, no matter how we draw an MA5B structure, it can be superimposed on any other representation simply by rotating the molecule in space. Two of the many possible orientations of an MA5B structure are as follows:
If two ligands in an octahedral complex are different from the other four, giving an MA4B2 complex, two isomers are possible. The two B ligands can be cis or trans. Cis- and trans-[Co(NH3)4Cl2]Cl are examples of this type of system:
Replacing another A ligand by B gives an MA3B3 complex for which there are also two possible isomers. In one, the three ligands of each kind occupy opposite triangular faces of the octahedron; this is called the fac isomer (for facial). In the other, the three ligands of each kind lie on what would be the meridian if the complex were viewed as a sphere; this is called the mer isomer (for meridional):
Example \(1\)
Draw all the possible geometrical isomers for the complex [Co(H2O)2(ox)BrCl], where ox is O2CCO2, which stands for oxalate.
Given: formula of complex
Asked for: structures of geometrical isomers
Solution
This complex contains one bidentate ligand (oxalate), which can occupy only adjacent (cis) positions, and four monodentate ligands, two of which are identical (H2O). The easiest way to attack the problem is to go through the various combinations of ligands systematically to determine which ligands can be trans. Thus either the water ligands can be trans to one another or the two halide ligands can be trans to one another, giving the two geometrical isomers shown here:
In addition, two structures are possible in which one of the halides is trans to a water ligand. In the first, the chloride ligand is in the same plane as the oxalate ligand and trans to one of the oxalate oxygens. Exchanging the chloride and bromide ligands gives the other, in which the bromide ligand is in the same plane as the oxalate ligand and trans to one of the oxalate oxygens:
This complex can therefore exist as four different geometrical isomers.
Exercise \(1\)
Draw all the possible geometrical isomers for the complex [Cr(en)2(CN)2]+.
Answer
Two geometrical isomers are possible: trans and cis.
Summary
Many metal complexes form isomers, which are two or more compounds with the same formula but different arrangements of atoms. Structural isomers differ in which atoms are bonded to one another, while geometrical isomers differ only in the arrangement of ligands around the metal ion. Ligands adjacent to one another are cis, while ligands across from one another are trans. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/19%3A_d-Block_Metal_Chemistry_-_General_Considerations/19.08%3A_Isomerism_in_d-block_Metal_Complexes/19.8E%3A_Stereoisomerism_-_Diastereomers.txt |
Optical activity refers to whether or not a compound has optical isomers. A coordinate compound that is optically active has optical isomers and a coordinate compound that is not optically active does not have optical isomers. As we will discuss later, optical isomers have the unique property of rotating light. When light is shot through a polarimeter, optical isomers can rotate the light so it comes out in a different direction on the other end. Armed with the knowledge of symmetry and mirror images, optical isomers should not be very difficult. There are two ways optical isomers can be determined: using mirror images or using planes of symmetry.
Optical isomers do not exhibit symmetry and do not have identical mirror images. Let's go through a quick review of symmetry and mirror images. A mirror image of an object is that object flipped or the way the object would look in front of a mirror. For example, the mirror image of your left hand would be your right hand. Symmetry on the other hand refers to when an object looks exactly the same when sliced in a certain direction with a plane. For example imagine the shape of a square. No matter in what direction it is sliced, the two resulting images will be the same.
Method 1: The "Mirror Image Method"
The mirror images method uses a mirror image of the molecule to determined whether optical isomers exist or not. If the mirror image can be rotated in such a way that it looks identical to the original molecule, then the molecule is said to be superimposable and has no optical isomers. On the other hand, if the mirror image cannot be rotated in any way such that it looks identical to the original molecule, then the molecule is said to be non-superimposable and the molecule has optical isomers. Once again, if the mirror image is superimposable, then no optical isomers but if the mirror image is non-superimposable, then optical isomers exist.
Definition: Non-superimposable
Non-superimposable means the structure cannot be rotated in a way that one can be put on top of another. This means that no matter how the structure is rotated, it cannot be put on top of another with all points matching. An example of this is your hands. Both left and right hands are identical, but they cannot be put on top of each other with all points matching.
The examples you are most likely to need occur in octahedral complexes which contain bidentate ligands - ions like \([Ni(NH_2CH_2CH_2NH_2)_3]^{2+}\) or \([Cr(C_2O_4)_3]^{3-}\). The diagram below shows a simplified view of one of these ions. Essentially, they all have the same shape - all that differs is the nature of the "headphones".
A substance with no plane of symmetry is going to have optical isomers - one of which is the mirror image of the other. One of the isomers will rotate the plane of polarization of plane polarised light clockwise; the other rotates it counter-clockwise. In this case, the two isomers are:
You may be able to see that there is no way of rotating the second isomer in space so that it looks exactly the same as the first one. As long as you draw the isomers carefully, with the second one a true reflection of the first, the two structures will be different.
Method 2: The "Plane of Symmetry Method"
The plane of symmetry method uses symmetry, as it's name indicates, to identify optical isomers. In this method, one tries to see if such a plane exists which when cut through the coordinate compound produces two exact images. In other words, one looks for the existence of a plane of symmetry within the coordinate compound. If a plane of symmetry exists, then no optical isomers exist. On the other hand, if there is no plane of symmetry, the coordinate compound has optical isomers. Furthermore, if a plane of symmetry exists around the central atom, then that molecule is called achiral but if a plane of symmetry does not exist around the central molecule, then that molecule has chiral center.
Example \(1\): CHBrClF
Consider the tetrahedral molecule, CHBrClF (note the color scheme: grey=carbon, white=hydrogen, green=chlorine, blue=fluorine, red=bromine)
Is this molecule optically active? In other words, does this molecule have optical isomers?
Solution
First take the Mirror-image method. The mirror image of the molecule is:
Note that this mirror image is not superimposable. In other words, the mirror image above cannot be rotated in any such way that it looks identical to the original molecule. Remember, if the mirror image is not superimposable, then optical isomers exist. Thus we know that this molecule has optical isomers.
Let's try approaching this problem using the symmetry method. If we take the original molecule and draw an axis or plane of symmetry down the middle, this is what we get:
Since the left side is not identical to the right, this molecule does not have a symmetrical center and thus can be called chiral.Additionally, because it does not have a symmetrical center, we can conclude that this molecule has optical isomers. In general, when dealing with a tetrahedral molecule that has 4 different ligands, optical isomers will exist most of the time.
No matter which method you use, the answer will end up being the same.
Optical isomers because they have no plane of symmetry. In the organic case, for tetrahedral complexes, this is fairly easy to recognize the possibility of this by looking for a center atom with four different things attached to it. Unfortunately, this is not quite so easy with more complicated geometries!
Example \(1\): \(\ce{PFeCl3F3}\)
This time we will be analyzing the octahedral compound FeCl3F3. Is this molecule optically active?
(note the color scheme: orange=iron, blue=fluorine, green=chlorine):
Solution
If we try to attempt this problem using the mirror image method, we notice that the mirror image is essentially identical to the original molecule. In other words, the mirror image can be placed on top of the original molecule and is thus superimposable. Since the mirror image is superimposable, this molecule does not have any optical isomers. Let's attempt this same problem using the symmetry method. If we draw an axis or plane of symmetry, this is what we get:
Since the left side is identical to the right side, this molecule has a symmetrical center and is an achiral molecule. Thus, it has no optical isomers.
What is a Polarimeter?
A polarimeter is a scientific instrument used to measure the angle of rotation caused by passing polarized light through an optically active substance. Some chemical substances are optically active, and polarized (uni-directional) light will rotate either to the left (counter-clockwise) or right (clockwise) when passed through these substances. The amount by which the light is rotated is known as the angle of rotation. The angle of rotation is basically known as observed angle.
The polarimeter is made up of a polarizer (#3 on Figure \(1\)) and an analyzer (#7 on Figure \(1\)). The polarizer allows only those light waves which move in a single plane. This causes the light to become plane polarized. When the analyzer is also placed in a similar position it allows the light waves coming from the polarizer to pass through it. When it is rotated through the right angle no waves can pass through the right angle and the field appears to be dark. If now a glass tube containing an optically active solution is placed between the polarizer and analyzer the light now rotates through the plane of polarization through a certain angle, the analyzer will have to be rotated in same angle.
Nomenclature of Optical Isomers
Various methods have been used to denote the absolute configuration of optical isomers such as R or S, Λ or Δ, or C and A. The IUPAC rules suggest that for general octahedral complexes C/A scheme is convenient to use and that for bis and tris bidentate complexes the absolute configuration be designated Lambda Λ (left-handed) and Delta Δ (right-handed).
Priorities are assigned for mononuclear coordination systems based on the standard sequence rules developed for enantiomeric carbon compounds by Cahn, Ingold and Prelog (CIP rules). These rules use the coordinating atom to arrange the ligands into a priority order such that the highest atomic number gives the highest priority number (smallest CIP number). For example the hypothetical complex [Co Cl Br I NH3 NO2 SCN]2- would assign the I- as 1, Br as 2, Cl as 3, SCN as 4, NO2 as 5 and NH3 as 6.
Figure \(2\): Here is one isomer where the I and Cl, and Br and NO2 were found to be trans- to each other.
The reference axis for an octahedral center is that axis containing the ligating atom of CIP priority 1 and the trans ligating atom of lowest possible priority (highest numerical value). The atoms in the coordination plane perpendicular to the reference axis are viewed from the ligand having that highest priority (CIP priority 1) and the clockwise and anticlockwise sequences of priority numbers are compared. The structure is assigned the symbol C or A, according to whether the clockwise (C) or anticlockwise (A) sequence is lower at the first point of difference. In the example shown above this would be C.
The two optical isomers of [Co(en)3]3+ have identical chemical properties and just denoting their absolute configuration does NOT give any information regarding the direction in which they rotate plane-polarised light. This can ONLY be determined from measurement and then the isomers are further distinguished by using the prefixes (-) and (+) depending on whether they rotate left or right.
To add to the confusion, when measured at the sodium D line (589 nm), the tris(1,2-diaminoethane)M(III) complexes (M= Rh(III) and Co(III)) with IDENTICAL absolute configuration, rotate plane polarized light in OPPOSITE directions! The left-handed (Λ)-[Co(en)3]3+ isomer gives a rotation to the right and therefore corresponds to the (+) isomer. Since the successful resolution of an entirely inorganic ion (containing no C atoms) (hexol) only a handful of truly inorganic complexes have been isolated as their optical isomers e.g. (NH4)2Pt(S5)3.2H2O.
For tetrahedral complexes, R and S would be used in a similar method to tetrahedral Carbon species and although it is predicted that tetrahedral complexes with 4 different ligands should be able to give rise to optical isomers, in general they are too labile and can not be isolated.
Contributors and Attributions
• The Department of Chemistry, University of the West Indies)
• Jim Clark (Chemguide.co.uk) | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/19%3A_d-Block_Metal_Chemistry_-_General_Considerations/19.08%3A_Isomerism_in_d-block_Metal_Complexes/19.8F%3A_Stereoisomerism_-_Enantiomers.txt |
A consequence of Crystal Field Theory is that the distribution of electrons in the d orbitals may lead to net stabilization (decrease in energy) of some complexes depending on the specific ligand field geometry and metal d-electron configurations. It is a simple matter to calculate this stabilization since all that is needed is the electron configuration and knowledge of the splitting patterns.
Definition: Crystal Field Stabilization Energy
The Crystal Field Stabilization Energy is defined as the energy of the electron configuration in the ligand field minus the energy of the electronic configuration in the isotropic field.
$CFSE=\Delta{E}=E_{\text{ligand field}} - E_{\text{isotropic field}} \label{1}$
The CSFE will depend on multiple factors including:
For an octahedral complex, an electron in the more stable $t_{2g}$ subset is treated as contributing $-2/5\Delta_o$ whereas an electron in the higher energy $e_g$ subset contributes to a destabilization of $+3/5\Delta_o$. The final answer is then expressed as a multiple of the crystal field splitting parameter $\Delta_o$. If any electrons are paired within a single orbital, then the term $P$ is used to represent the spin pairing energy.
Example $1$: CFSE for a high Spin $d^7$ complex
What is the Crystal Field Stabilization Energy for a high spin $d^7$ octahedral complex?
Solution
The splitting pattern and electron configuration for both isotropic and octahedral ligand fields are compared below.
The energy of the isotropic field $(E_{\text{isotropic field}}$) is
$E_{\text{isotropic field}}= 7 \times 0 + 2P = 2P \nonumber$
The energy of the octahedral ligand field $E_{\text{ligand field}}$ is
$E_{\text{ligand field}} = (5 \times -2/5 \Delta_o ) + (2 \times 3/5 \Delta_o) + 2P = -4/5 \Delta_o + 2P \nonumber$
So via Equation \ref{1}, the CFSE is
\begin{align} CFSE &=E_{\text{ligand field}} - E_{\text{isotropic field}} \nonumber \[4pt] &=( -4/5\Delta_o + 2P ) - 2P \nonumber \[4pt] &=-4/5 \Delta_o \nonumber \end{align} \nonumber
Notice that the Spin pairing Energy falls out in this case (and will when calculating the CFSE of high spin complexes) since the number of paired electrons in the ligand field is the same as that in isotropic field of the free metal ion.
Example $2$: CFSE for a Low Spin $d^7$ complex
What is the Crystal Field Stabilization Energy for a low spin $d^7$ octahedral complex?
Solution
The splitting pattern and electron configuration for both isotropic and octahedral ligand fields are compared below.
The energy of the isotropic field is the same as calculated for the high spin configuration in Example 1:
$E_{\text{isotropic field}}= 7 \times 0 + 2P = 2P \nonumber$
The energy of the octahedral ligand\) field $E_{\text{ligand field}}$ is
\begin{align} E_{\text{ligand field}} &= (6 \times -2/5 \Delta_o ) + (1 \times 3/5 \Delta_o) + 3P \nonumber \[4pt] &= -9/5 \Delta_o + 3P \nonumber \end{align} \nonumber
So via Equation \ref{1}, the CFSE is
\begin{align} CFSE&=E_{\text{ligand field}} - E_{\text{isotropic field}} \nonumber \[4pt] &=( -9/5 \Delta_o + 3P ) - 2P \nonumber \[4pt] &=-9/5 \Delta_o + P \nonumber \end{align} \nonumber
Adding in the pairing energy since it will require extra energy to pair up one extra group of electrons. This appears more a more stable configuration than the high spin $d^7$ configuration in Example $1$, but we have then to take into consideration the Pairing energy $P$ to know definitely, which varies between $200-400\; kJ\; mol^{-1}$ depending on the metal.
Table $1$: Crystal Field Stabilization Energies (CFSE) for high and low spin octahedral complexes
Total d-electrons Isotropic Field Octahedral Complex Crystal Field Stabilization Energy
High Spin Low Spin
$E_{\text{isotropic field}}$ Configuration $E_{\text{ligand field}}$ Configuration $E_{\text{ligand field}}$ High Spin Low Spin
d0 0 $t_{2g}$0$e_g$0 0 $t_{2g}$0$e_g$0 0 0 0
d1 0 $t_{2g}$1$e_g$0 -2/5 $\Delta_o$ $t_{2g}$1$e_g$0 -2/5 $\Delta_o$ -2/5 $\Delta_o$ -2/5 $\Delta_o$
d2 0 $t_{2g}$2$e_g$0 -4/5 $\Delta_o$ $t_{2g}$2$e_g$0 -4/5 $\Delta_o$ -4/5 $\Delta_o$ -4/5 $\Delta_o$
d3 0 $t_{2g}$3$e_g$0 -6/5 $\Delta_o$ $t_{2g}$3$e_g$0 -6/5 $\Delta_o$ -6/5 $\Delta_o$ -6/5 $\Delta_o$
d4 0 $t_{2g}$3$e_g$1 -3/5 $\Delta_o$ $t_{2g}$4$e_g$0 -8/5 $\Delta_o$ + P -3/5 $\Delta_o$ -8/5 $\Delta_o$ + P
d5 0 $t_{2g}$3$e_g$2 0 $\Delta_o$ $t_{2g}$5$e_g$0 -10/5 $\Delta_o$ + 2P 0 $\Delta_o$ -10/5 $\Delta_o$ + 2P
d6 P $t_{2g}$4$e_g$2 -2/5 $\Delta_o$ + P $t_{2g}$6$e_g$0 -12/5 $\Delta_o$ + 3P -2/5 $\Delta_o$ -12/5 $\Delta_o$ + P
d7 2P $t_{2g}$5$e_g$2 -4/5 $\Delta_o$ + 2P $t_{2g}$6$e_g$1 -9/5 $\Delta_o$ + 3P -4/5 $\Delta_o$ -9/5 $\Delta_o$ + P
d8 3P $t_{2g}$6$e_g$2 -6/5 $\Delta_o$ + 3P $t_{2g}$6$e_g$2 -6/5 $\Delta_o$ + 3P -6/5 $\Delta_o$ -6/5 $\Delta_o$
d9 4P $t_{2g}$6$e_g$3 -3/5 $\Delta_o$ + 4P $t_{2g}$6$e_g$3 -3/5 $\Delta_o$ + 4P -3/5 $\Delta_o$ -3/5 $\Delta_o$
d10 5P $t_{2g}$6$e_g$4 0 $\Delta_o$ + 5P $t_{2g}$6$e_g$4 0 $\Delta_o$ + 5P 0 0
$P$ is the spin pairing energy and represents the energy required to pair up electrons within the same orbital. For a given metal ion P (pairing energy) is constant, but it does not vary with ligand and oxidation state of the metal ion).
Octahedral Preference
Similar CFSE values can be constructed for non-octahedral ligand field geometries once the knowledge of the d-orbital splitting is known and the electron configuration within those orbitals known, e.g., the tetrahedral complexes in Table $2$. These energies geoemtries can then be contrasted to the octahedral CFSE to calculate a thermodynamic preference (Enthalpy-wise) for a metal-ligand combination to favor the octahedral geometry. This is quantified via a Octahedral Site Preference Energy defined below.
Definition: Octahedral Site Preference Energies
The Octahedral Site Preference Energy (OSPE) is defined as the difference of CFSE energies for a non-octahedral complex and the octahedral complex. For comparing the preference of forming an octahedral ligand field vs. a tetrahedral ligand field, the OSPE is thus:
$OSPE = CFSE_{(oct)} - CFSE_{(tet)} \label{2}$
The OSPE quantifies the preference of a complex to exhibit an octahedral geometry vs. a tetrahedral geometry.
Note: the conversion between $\Delta_o$ and $\Delta_t$ used for these calculations is:
$\Delta_t \approx \dfrac{4}{9} \Delta_o \label{3}$
which is applicable for comparing octahedral and tetrahedral complexes that involve same ligands only.
Table $2$: Octahedral Site Preference Energies (OSPE)
Total d-electrons CFSE(Octahedral) CFSE(Tetrahedral) OSPE (for high spin complexes)**
High Spin Low Spin Configuration Always High Spin*
d0 0 $\Delta_o$ 0 $\Delta_o$ e0 0 $\Delta_t$ 0 $\Delta_o$
d1 -2/5 $\Delta_o$ -2/5 $\Delta_o$ e1 -3/5 $\Delta_t$ -6/45 $\Delta_o$
d2 -4/5 $\Delta_o$ -4/5 $\Delta_o$ e2 -6/5 $\Delta_t$ -12/45 $\Delta_o$
d3 -6/5 $\Delta_o$ -6/5 $\Delta_o$ e2t21 -4/5 $\Delta_t$ -38/45 $\Delta_o$
d4 -3/5 $\Delta_o$ -8/5 $\Delta_o$ + P e2t22 -2/5 $\Delta_t$ -19/45 $\Delta_o$
d5 0 $\Delta_o$ -10/5 $\Delta_o$ + 2P e2t23 0 $\Delta_t$ 0 $\Delta_o$
d6 -2/5 $\Delta_o$ -12/5 $\Delta_o$ + P e3t23 -3/5 $\Delta_t$ -6/45 $\Delta_o$
d7 -4/5 $\Delta_o$ -9/5 $\Delta_o$ + P e4t23 -6/5 $\Delta_t$ -12/45 $\Delta_o$
d8 -6/5 $\Delta_o$ -6/5 $\Delta_o$ e4t24 -4/5 $\Delta_t$ -38/45 $\Delta_o$
d9 -3/5 $\Delta_o$ -3/5 $\Delta_o$ e4t25 -2/5 $\Delta_t$ -19/45 $\Delta_o$
d10 0 0 e4t26 0 $\Delta_t$ 0 $\Delta_o$
$P$ is the spin pairing energy and represents the energy required to pair up electrons within the same orbital.
Tetrahedral complexes are always high spin since the splitting is appreciably smaller than $P$ (Equation \ref{3}).
After conversion with Equation \ref{3}. The data in Tables $1$ and $2$ are represented graphically by the curves in Figure $1$ below for the high spin complexes only. The low spin complexes require knowledge of $P$ to graph.
Figure $1$: Crystal Field Stabilization Energies for both octahedral fields ($CFSE_{oct}$) and tetrahedral fields ($CFSE_{tet}$). Octahedral Site Preference Energies (OSPE) are in yellow. This is for high spin complexes.
From a simple inspection of Figure $1$, the following observations can be made:
• The OSPE is small in $d^1$, $d^2$, $d^5$, $d^6$, $d^7$ complexes and other factors influence the stability of the complexes including steric factors
• The OSPE is large in $d^3$ and $d^8$ complexes which strongly favor octahedral geometries
Applications
The "double-humped" curve in Figure $1$ is found for various properties of the first-row transition metals, including Hydration and Lattice energies of the M(II) ions, ionic radii as well as the stability of M(II) complexes. This suggests that these properties are somehow related to Crystal Field effects.
In the case of Hydration Energies describing the complexation of water ligands to a bare metal ion:
$M^{2+} (g) + H_2O \rightarrow [M(OH_2)_6]^{2+} (aq) \nonumber$
Table $3$ and Figure $1$ shows this type of curve. Note that in any series of this type not all the data are available since a number of ions are not very stable in the M(II) state.
Table $3$: Hydration energies of $M^{2+}$ ions
M ΔH°/kJmol-1 M ΔH°/kJmol-1
Ca -2469 Fe -2840
Sc no stable 2+ ion Co -2910
Ti -2729 Ni -2993
>V -2777 Cu -2996
Cr -2792 Zn -2928
Mn -2733
Graphically the data in Table 2 can be represented by:
Figure $2$: hydration energies of $M^{2+}$ ions
Contributors and Attributions
• The Department of Chemistry, University of the West Indies) | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/20%3A_d-Block_Metal_Chemistry_-_Coordination_Complexes/20.03%3A_Crystal_Field_Theory/20.3B%3A_Crystal_Field_Stabilization_Energy_-_High-_and_Low-spin_Octahedral_C.txt |
Ligand Field Theory can be considered an extension of Crystal Field Theory such that all levels of covalent interactions can be incorporated into the model. Treatment of the bonding in LFT is generally done using Molecular Orbital Theory. A qualitative approach that can be used for octahedral metal complexes is given in the following 3 diagrams.
In the first diagram, the 3d, 4s and 4p metal ion atomic orbitals are shown together with the ligand group orbitals that would have the correct symmetry to be able to overlap with them. The symmetry adapted linear comination of ligand orbitals are generated by taking 6 sigma orbitals from the ligands, designated as σx, σ-x, σy, σ-y, σz, σ-z and then combining them to make 6 ligand group orbitals. (labelled eg, a1g, t1u)
In the second diagram only sigma bonding is considered and it shows the combination of the metal 3d, 4s and 4p orbitals with OCCUPIED ligand group orbitals (using 1 orbital from each ligand). The result is that that the metal electrons would be fed into t2g and eg* molecular orbitals which is similar to the CFT model except that the eg orbital is now eg*.
For example: B - [M(II)I6]4- A - [M(II)(H2O)6]2+ C - [M(II)(CN)6]4-
In the third diagram, π (pi) bonding is considered. In general π bonds are weaker than σ (sigma) bonds and so the effect is to modify rather than dramatically alter the description. 2 orbitals from each ligand are combined to give a total of 12 which are subdivided into four sets with three ligand group orbitals in each set. These are labelled t1g, t1u, t2g and t2u. The metal t2g orbital is the most suitable for interaction and this is shown in the 2 cases above.
Case A is the same as above, ignoring π interactions.
• For case B, the ligand π orbitals are full and at lower energy than the metal t2g. This causes a decrease in the size of Δ.
• For case C, the ligand π orbitals are empty and at higher energy than the metal t2g. This causes an increase in the size of Δ.
Returning to the problem of correctly placing ligands in the Spectrochemical series, the halides are examples of case A and groups like CN- and CO are examples of case B. It is possible then to explain the Spectrochemical series once covalent effects are considered.
Some convincing arguments for covalency and effects on Δ come from a study of the IR spectra recorded for simple carbonyl compounds e.g. M(CO)6.
• The CO molecule has a strong triple bond which in the IR gives rise to a strong absorption at ~2140 cm-1. For the series [Mn(CO)6]+, [Cr(CO)6] and [V(CO)6]-, which are isoelectronic, the IR bands for the CO have shifted to 2090, 2000 and 1860 cm-1 respectively. Despite the fact that the metals have the same number of electrons (isoelectronic) the frequency of force constant of the CO bond is seen to vary Mn+ > Cr > V-.
• This can not be explained on an ionic basis but is consistent with the π bonding scheme since the greater the positive charge on the metal, the less readily the metal can delocalize electrons back into the π* orbitals of the CO group.
Note that the IR values we are dealing with relate to the CO bond and not the M-C so when the CO frequency gets less then it is losing triple bond character and becoming more like a double bond. This is expected if electrons are pushed back from the metal into what were empty π* antibonding orbitals.
Contributors and Attributions
• The Department of Chemistry, University of the West Indies) | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/20%3A_d-Block_Metal_Chemistry_-_Coordination_Complexes/20.05%3A_Ligand_Field_Theory.txt |
Learning Objectives
• Compate two spin-orbit coupling schemes that couple the total spin angular momenta and total orbital angular momenta of a multi-electron spectra
We need to be able to identify the electronic states that result from a given electron configuration and determine their relative energies. An electronic state of an atom is characterized by a specific energy, wavefunction (including spin), electron configuration, total angular momentum, and the way the orbital and spin angular momenta of the different electrons are coupled together. There are two descriptions for the coupling of angular momentum. One is called j-j coupling, and the other is called L-S coupling. The j-j coupling scheme is used for heavy elements (z > 40) and the L-S coupling scheme is used for the lighter elements. Only L-S coupling is discussed below.
L-S Coupling of Angular Momenta
L-S coupling also is called R-S or Russell-Saunders coupling. In L-S coupling, the orbital and spin angular momenta of all the electrons are combined separately
$L = \sum _i l_i \label{8.11.3}$
$S = \sum _i s_i \label{8.11.4}$
The total angular momentum vector then is the sum of the total orbital angular momentum vector and the total spin angular momentum vector.
$J = L + S \label{8.11.5}$
The total angular momentum quantum number parameterizes the total angular momentum of a given particle, by combining its orbital angular momentum and its intrinsic angular momentum (i.e., its spin). Due to the spin-orbit interaction in the atom, the orbital angular momentum no longer commutes with the Hamiltonian, nor does the spin.
However the total angular momentum $J$ does commute with the Hamiltonian and so is a constant of motion (does not change in time). The relevant definitions of the angular momenta are:
Orbital Angular Momentum
$|\vec{L}| = \hbar \sqrt{\ell(\ell+1)} \nonumber$
with its projection on the z-axis $L_z = m_\ell \hbar \nonumber$
Spin Angular Momentum
$|\vec{S}| = \hbar \sqrt{s(s+1)} \nonumber$
with its projection on the z-axis $S_z = m_s \hbar \nonumber$
Total Angular Momentum
$|\vec{J}| = \hbar \sqrt{j(j+1)} \nonumber$
with its projection on the z-axis $J_z = m_j \hbar \nonumber$
where
• $l$ is the azimuthal quantum number of a single electron,
• $s$ is the spin quantum number intrinsic to the electron,
• $j$ is the total angular momentum quantum number of the electron,
The quantum numbers take the values:
\begin{align} & m_\ell \in \{ -\ell, -(\ell-1) \cdots \ell-1, \ell \} , \quad \ell \in \{ 0,1 \cdots n-1 \} \& m_s \in \{ -s, -(s-1) \cdots s-1, s \} , \& m_j \in \{ -j, -(j-1) \cdots j-1, j \} , \& m_j=m_\ell+m_s, \quad j=|\ell+s|\\end{align} \nonumber
and the magnitudes are:
\begin{align} & |\textbf{J}| = \hbar\sqrt{j(j+1)} \& |\textbf{J}_1| = \hbar\sqrt{j_1(j_1+1)} \& |\textbf{J}_2| = \hbar\sqrt{j_2(j_2+1)} \\end{align} \nonumber
in which
$j \in \{ |j_1 - j_2|, |j_1 - j_2| - 1 \cdots j_1 + j_2 - 1, j_1 + j_2 \} \,\! \nonumber$
This process may be repeated for a third electron, then the fourth etc. until the total angular momentum has been found.
The result of these vector sums is specified in a code that is called a Russell-Saunders term symbol, and each term symbol identifies an energy level of the atom. Consequently, the energy levels also are called terms. A term symbol has the form $^{2s+1} L_J$ where the code letter that is used for the total orbital angular momentum quantum number L = 0, 1, 2, 3, 4, 5 is S, P, D, F, G, H, respectively. Note how this code matches that used for the atomic orbitals. The superscript $2S+1$ gives the spin multiplicity of the state, where S is the total spin angular momentum quantum number. The spin multiplicity is the number of spin states associated with a given electronic state. In order not to confuse the code letter S for the orbital angular momentum with the spin quantum number S, you must examine the context in which it is used carefully. In the term symbol, the subscript J gives the total angular momentum quantum number. Because of spin-orbit coupling, only $J$ and $M_j$ are valid quantum numbers, but because the spin-orbit coupling is weak $L$, $M_l$, $S$, and $m_s$ still serve to identify and characterize the states for the lighter elements.
For example, the ground state, i.e. the lowest energy state, of the hydrogen atom corresponds to the electron configuration in which the electron occupies the 1s spatial orbital and can have either spin $\alpha$ or spin $\beta$. The term symbol for the ground state is $^2 S_{1/2}$, which is read as “doublet S 1/2”. The spin quantum number is 1/2 so the superscript 2S+1 = 2, which gives the spin multiplicity of the state, i.e. the number of spin states equals 2 corresponding to $\alpha$ and $\beta$. The S in the term symbol indicates that the total orbital angular momentum quantum number is 0 (For the ground state of hydrogen, there is only one electron and it is in an s-orbital with $l = 0$ ). The subscript ½ refers to the total angular momentum quantum number. The total angular momentum is the sum of the spin and orbital angular momenta for the electrons in an atom. In this case, the total angular momentum quantum number is just the spin angular momentum quantum number, ½, since the orbital angular momentum is zero. The ground state has a degeneracy of two because the total angular momentum can have a z-axis projection of $+\frac {1}{2} \hbar$ or $-\frac {1}{2} \hbar$, corresponding to $m_J$ = +1/2 or -1/2 resulting from the two electron spin states $\alpha$ and $\beta$. We also can say, equivalently, that the ground state term or energy level is two-fold degenerate.
Exercise 8.9.1
Write the term symbol for a state that has 0 for both the spin and orbital angular momentum quantum numbers.
Exercise 8.9.2
Write the term symbol for a state that has 0 for the spin and 1 for the orbital angular momentum quantum numbers | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/20%3A_d-Block_Metal_Chemistry_-_Coordination_Complexes/20.06%3A_Decribing_Electrons_in_Multi-Electron_Systems/20.6D%3A_The_Quantum_Numbers_%28J%29_and_%28M_J%29.txt |
We have already looked at Transition metal ion complexes with D ground states which accounts for the d1, d4, d6 and d9 configurations.
We turn now to d2, d3, d7 and d8 configurations for which the ground state of the free ions are given by Russell-Saunders F terms.
In octahedral and tetrahedral crystal fields, the F state is split into A2(g), T1(g) and T2(g) terms, while the P term generates an additional T1(g) term. Once again we can make use of the analogy to the splitting of orbitals in a crystal field so in this case we can look at how the f-orbitals lose their 7-fold degeneracy in an octahedral field.
It should be noted that whenever the ground state is an F term there will be a P term found at higher energy with the same spin multiplicity. The separation of these terms in the free ion is measured in terms of the B Racah parameter and is equivalent to 15B (where B is usually around 1000 cm-1).
Once again, one approach taken to aid in the interpretation of these spectra is to use an Orgel diagram. The relevant Orgel diagram for the F ground state is given below:
oct d3,d8 tet d2,d7 ←-----------------------------------→ oct d2,d7 tet d3,d8
ν1 = Δ (T2g←A2g) ν1= 4/5 Δ + x (T2g←T1g)
ν2 = 9/5 Δ - x (T1g←A2g) ν2 = 9/5 Δ + x (A2g←T1g) OR ν2 = 3/5 Δ + 15B + 2x (T1g(P)←T1g)
ν3 = 6/5 Δ + 15B + x (T1g(P)←A2g) ν3 = 3/5 Δ + 15B + 2x (T1g(P)←T1g) OR ν3 = 9/5 Δ + x (A2g←T1g)
The lines showing the A2 and T2 terms are linear and depend solely on Δ. The "non-crossing rule" results in the lines for the two T1 terms being curved to avoid each other and as a result this introduces a "configuration interaction" in the transition energy equations.
That is, whenever there are lines with equivalent Russell-Saunders terms on the Orgel diagram they are not allowed to cross and are found to diverge. All other lines are expected to be linear.
Visible spectra of some Cr(III) complexes
For Cr(III) complexes, we would start by writing the free ion electronic configuration as d3 and in an octahedral crystal field this would be described as t2g3 eg0.
The Russell-Saunders scheme that takes into account the electron-electron interactions would be described by a free ion ground state of 4F. To decide which side of the F Orgel diagram should be applied to the interpretation can be quickly determined by looking at the electronic configuration and noting that the ground state is singly degenerate (i.e. we need the left-hand-side where the lowest term is A2).
It is expected then that there should be 3 absorption bands found in the electronic spectrum. The energy of the first transition corresponds directly to Δ and the transition is written as 4T2g ← 4A2g.
If we now consider the d2 electronic configuration, then the Russell-Saunders free ion ground term state is a 3F. For an octahedral complex, the lowest energy state is a triplet which tells us that we need to be using the right-hand-side of the F Orgel diagram.
The first transition is written as 3T2g ← 3T1g and the energy of this transition does NOT correspond directly to Δ. It should be carefully noted that when using this side of the F-Orgel diagram none of the expected transitions correspond exactly to Δ . Interpretation of d2 spectra are made even more complicated since as we increase the size of Δ we note that at some point the 3T1g(P) and 3A2g lines cross. To determine the sequence of the transitions (that is whether we are on the left-hand-side or right-hand-side of the intersection) normally requires that all 3 absorption bands can be observed. This is often not the case and an alternative approach to interpretation of these spectra is needed. One such approach makes use of what are known as Tanabe-Sugano diagrams. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/20%3A_d-Block_Metal_Chemistry_-_Coordination_Complexes/20.06%3A_Decribing_Electrons_in_Multi-Electron_Systems/20.6F%3A_The_d_Configuration.txt |
Crystal Field Theory copes reasonably well for d1 (d9) systems but not for multi-electron systems, which are the more common. To deal with these systems we need to introduce a new concept, that of the electronic state. Electronic configurations refer to the way in which the electrons occupy the d orbitals, so for Ti(III) we write an electronic configuration of [Ar] 3d1 and in an octahedral crystal field the lowest energy configuration would be written as t2g1 eg0.
The electronic state refers to energy levels available to a group of electrons. This is much more complex than the single electron case since not only is it necessary to consider the crystal field effects of the repulsion of the metal electrons by the ligand electrons, but it is necessary to include the interactions between the electrons themselves.
When describing electronic configurations, lower case letters are used, thus t2g1 etc.
For electronic states, upper case (CAPITAL) letters are used and by analogy, a T state is triply degenerate. Subscripts 1 and 2 are used to distinguish states of like degeneracy and g and u subscripts indicate the presence of a center of symmetry eg. T1g, T2g, T1u and T2u.
These symbols are further modified to show the spin multiplicity of the electronic state using the Russell-Saunders Notation.
If we consider the Ti(III) case, the electronic configuration is d1. In an octahedral crystal field this would give rise to a t2g1 arrangement and the excitation of the low lying electron to the higher level would then give an eg1 arrangement.
Only one d-d transition is expected and this roughly corresponds to what is observed for Ti(III) complexes, although it is somewhat more complicated due to Jahn-Teller considerations. At the high energy end of the spectrum, the presence of a charge transfer band should be noted as well. The origin of this will not be covered in detail in this course.
One approach taken when we consider the Russell-Saunders scheme with the various electronic states makes use of what are called Orgel diagrams. The relevant Orgel diagram for the D ground state is given below:
oct 4,9 tet 1,6 <-------------------------------------------> oct 1,6 tet 4,9
For a Fe(II) high spin octahedral complex we would write the free ion electronic configuration as d6 and in the octahedral crystal field it would be described as t2g4 eg2.
The Russell-Saunders scheme that takes into account the electron-electron interactions would be described by a free ion ground state of 5D. In octahedral and tetrahedral crystal fields, this D state is split into E(g) and T2(g) terms. To decide which side of the D Orgel diagram should be applied to the interpretation can be quickly determined by looking at the electronic configuration and noting that the ground state is triply degenerate and the excited state is doubly degenerate (i.e. we must use the right-hand-side).
It is expected then that there should be 1 absorption band found in the electronic spectrum and that the energy of the transition corresponds directly to Δ. The transition is written in a notation that is read from right to left, which in this case is 5Eg ← 5T2g.
Contributors and Attributions
The Department of Chemistry, University of the West Indies) | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/20%3A_d-Block_Metal_Chemistry_-_Coordination_Complexes/20.07%3A_Electronic_Spectra_-_Absorption/20.7A%3A_Spectral_Features.txt |
For ALL octahedral complexes, except high spin d5, simple CFT would predict that only 1 band should appear in the electronic spectrum and that the energy of this band should correspond to the absorption of energy equivalent to Δ. In practice, ignoring spin-forbidden lines, this is only observed for those ions with D free ion ground terms i.e., d1, d9 as well as d4, d6.
The observation of 2 or 3 peaks in the electronic spectra of d2, d3, d7 and d8 high spin octahedral complexes requires further treatment involving electron-electron interactions. Using the Russell-Saunders (LS) coupling scheme, these free ion configurations give rise to F free ion ground states which in octahedral and tetrahedral fields are split into terms designated by the symbols A2(g), T2(g) and T1(g).
To derive the energies of these terms and the transition energies between them is beyond the needs of introductory level courses and is not covered in general textbooks[10,11]. A listing of some of them is given here as an Appendix. What is necessary is an understanding of how to use the diagrams, created to display the energy levels, in the interpretation of spectra.
In the laboratory component of the course we will measure the absorption spectra of some typical chromium(III) complexes and calculate the spectrochemical splitting factor, Δ. This corresponds to the energy found from the first transition below and as shown in Table 1 is generally between 15,000 cm-1 (for weak field complexes) and 27,000 cm-1 (for strong field complexes).
For the d3 octahedral case, 3 peaks can be predicted and these would correspond to the following transitions and energies:
1. 4T2g4A2g transition energy = Δ
2. 4T1g(F) ← 4A2g transition energy = 9/5 * Δ - C.I.
3. 4T1g(P) ← 4A2g transition energy = 6/5 * Δ + 15B' + C.I.
where C.I. is the configuration interaction arising from the "non-crossing rule".
Table 1. Peak positions for some octahedral Cr(III) complexes (in cm-1).
Complex
ν1
ν2
ν3
ν2/ ν1
ν1/ ν2
Δ/B
Ref
Cr3+ in emerald
16260
23700
37740
1.46
0.686
20.4
13
K2NaCrF6
16050
23260
35460
1.45
0.690
21.4
13
[Cr(H2O)6]3+
17000
24000
37500
1.41
0.708
24.5
This work
Chrome alum
17400
24500
37800
1.36
0.710
29.2
4
[Cr(C2O4)3]3-
17544
23866
?
1.37
0.735
28.0
This work
[Cr(NCS)6]3-
17800
23800
?
1.34
0.748
31.1
4
[Cr(acac)3]
17860
23800
?
1.33
0.752
31.5
This work
[Cr(NH3)6]3+
21550
28500
?
1.32
0.756
32.6
4
[Cr(en)3]3+
21600
28500
?
1.32
0.758
33.0
4
[Cr(CN)6]3-
26700
32200
?
1.21
0.829
52.4
4
For octahedral Ni(II) complexes the transitions would be:
1. 3T2g3A2g transition energy = Δ
2. 3T1g(F) ← 3A2g transition energy = 9/5 * Δ - C.I.
3. 3T1g(P) ← 3A2g transition energy = 6/5 * Δ + 15B' + C.I.
where C.I. again is the configuration interaction and as before the first transition corresponds exactly to Δ.
For M(II) the size of Δ is much less than for M(III) and typical values for Ni(II) are 6500 to 13000 cm-1 as shown in Table 2.
Table 2. Peak positions for some octahedral Ni(II) complexes (in cm-1).
Complex
ν1
ν2
ν3
ν1
ν1/ ν2
Δ/B
Ref
NiBr2
6800
11800
20600
1.74
0.576
5
13
[Ni(H2O)6]2+
8500
13800
25300
1.62
0.616
11.6
13
[Ni(gly)3]-
10100
16600
27600
1.64
0.608
10.6
13
[Ni(NH3)6]2+
10750
17500
28200
1.63
0.614
11.2
13
[Ni(en)3]2+
11200
18350
29000
1.64
0.610
10.6
3
[Ni(bipy)3]2+
12650
19200
?
1.52
0.659
17
3
For d2 octahedral complexes, few examples have been published. One such is V3+ doped in Al2O3 where the vanadium ion is generally regarded as octahedral, Table 3.
Table 3. Peak positions for some octahedral V(III) complexes (in cm-1).
Complex
ν1
ν2
ν3
ν2/ ν1
ν1/ν2
Δ/B
Ref
V3+ in Al2O3
17400
25200
34500
1.448
0.6906
30.90
13
[VCl3(MeCN)3]
14400
21400
?
1.486
0.6729
28.68
4
K3[VF6]
14800
23250
?
1.571
0.6365
24.78
4
Interpretation of the spectrum highlights the difficulty of using the right-hand side of the Orgel diagram as previously noted. For d2 cases where none of the transitions correspond exactly to Δ often only 2 of the 3 transitions are clearly observed and hence the calculations will have three unknowns (Δ, B and C.I.) but only 2 energies to use in the the analysis.
The first transition can be unambiguously assigned as:
3T2g3T1g transition energy = 4/5 * Δ + C.I.
But, depending on the size of the ligand field ( Δ) the second transition may be due to:
3A2g3T1g transition energy = 9/5 * Δ + C.I.
for a weak field or
3T1g(P) ← 3T1g transition energy = 3/5 * Δ + 15B' + 2 * C.I.
for a strong field.
The transition energies of these terms are clearly different and it is often necessary to calculate (or estimate) values of B, Δ and C.I. for both arrangements and then evaluate the answers to see which fits better.
The difference between the 3A2g and the 3T2g (F) lines should give Δ. In this case Δ is equal to either:
25200 - 17400 = 7800 cm-1
or 34500 - 17400 = 17100 cm-1.
Given that we expect Δ to be greater than 15000 cm-1 then we must interpret the second transition as to the 3T2g(P) and the third to 3A2g. Further evaluation of the expressions then gives C.I. as 3720 cm-1 and B' as 567 cm-1.
Solving the equations like this for the three unknowns can ONLY be done if the three transitions are observed. When only two transitions are observed, a series of equations[14] have been determined that can be used to calculate both B and Δ. This approach still requires some evaluation of the numbers to ensure a valid fit. For this reason, Tanabe-Sugano diagrams become a better method for interpreting spectra of d2 octahedral complexes.
Using Tanabe-Sugano diagrams
The use of Orgel diagrams allows a qualitative description of the spin-allowed electronic transitions expected for states derived from D and F ground terms. Only 2 diagrams are needed for high spin d2-d9 and both tetrahedral and octahedral ions are covered.
Tanabe-Sugano diagrams were developed in the 1950's to give a semi-quantitative approach and include both high and low spin ions and not only the spin-allowed transitions are shown but the spin-forbidden transitions are displayed as well.
At first glance they can appear quite daunting, but in practice they are much easier to use for interpreting spectra and provide much more information. The obvious differences are the presence of the additional lines and that the ground state is shown as the base line along the X axis rather than as a straight line or curve originating from the Y axis.
On the X axis Δ/B' is plotted while on the Y axis E/B' is plotted, where B' is the modified Racah B parameter that exists in the complex.
A separate diagram is needed for each electronic configuration d2-d9 and for the d4-d7 cases both the high spin and low spin electronic configurations are shown. The high spin is on the left-hand-side of the vertical line on the diagram.
For the d2 case where it is difficult to use an Orgel diagram, the TS diagram is shown below. The ground state is 3T1g which is plotted along the base line.
Note that the transitions that occur are dependent on the sizes of Δ and B and the A2g term may be either higher or lower than the T1g (P) term (depending on whether Δ/B' is greater than about 15).
For the V(III) aqua ion, transitions are observed at 17,200 and 25,600 cm-1 which are assigned to the 3T2g ← 3T1g and 3T1g(P) ← 3T1g (F) respectively.
Interpretation requires taking the ratio of these frequencies and then finding the position on the diagram where the height of the 3T1g(P) / 3T2g exactly matches that ratio.
For a ratio of 1.49, this is found on the diagram below at Δ/B' of 28.0.
Reading off the position on the Y axis for the three spin-allowed lines gives E/B' values of 25.9, 38.6 and 53 (3T2g, 3T1g and 3A2g)
To determine the value of Δ and B' is now relatively straightforward since from the first transition energy of 17,200 cm-1 and the value of E/B' of 25.9 we can equate B' as:
B' = 17,200/ 25.9 or B' = 665 cm-1
Alternatively from the second transition energy of 25,600 cm-1 and the value of E/B' of 38.6 we can equate B' as:
B' = 25,600/ 38.6 or B' = 663 cm-1 which is in excellent agreement with the value found from the first transition.
The value of Δ can then be determined from the Δ/B' ratio of 28.0 and the value just calculated for B' of 665 cm-1.
This gives Δ as 28.0 x 665 = 18,600 cm-1
The transition 3A2g ← 3T1g would be predicted to occur at 53 x 665 that is 35,245 cm-1 (or 284 nm) which is in the UV region and not observed. (Possibly obscured by charge transfer bands).
The values of Δ and B' can be compared to similar V(III) complexes and it should be noted that in general for M(III) ions the Δ value is often about 3/2 times the value expected for M(II) ions.
The free ion value of B for a V(III) ion is 860 cm-1 and the reduction of this value noted for the observed B' is a measure of what is described as the Nephelauxetic Effect.
The Nephelauxetic Effect
The Racah repulsion parameters for a metal complex vary as the ligand is changed
• As the complex becomes more covalent the electrons are to some extent spread over the ligands so the electron-electron repulsion is reduced
• This reduction in repulsion as covalency increases is called the nephelauxetic effect (literally "cloud expanding")
A nephelauxetic series can be set up based on the variation of the Racah parameter.
A large reduction in B (free ion) indicates a strong Nephelauxetic Effect.
{B(free ion)- B'(Complex)} / B(free ion)
The Nephelauxetic Series is given by:
``` F- < H2O < urea < NH3 < en ~ C2O42- < NCS- < Cl- ~ CN- < Br- < S2- ~ I-
```
This series is consistent with fluoride complexes being the most ionic and giving a small reduction in B while covalently bonded ligands such as I- give a large reduction of B.
N.B. The order of the nephelauxetic series is NOT the same as the spectrochemical series as one is an indication of B and the other of Δ
As an example of a Cr(III) complex, using the observed peaks found for [Cr(NH3)6]3+ in Table 1 above, namely ν1 = 21550 cm-1 and ν2 = 28500 cm-1 the ratio of ν21 = 1.32.
The value of Δ is obtained directly from the first transition so Δ/B' is equal to ν1/B' and finding B' is now relatively straightforward since from the first transition energy of 21,550 cm-1 and the value of Δ/B' (ν1/B') of 32.6 we get:
B' = 21,550/ 32.6 or B' = 661 cm-1
The third peak can then be predicted to occur at 69.64 * 661 = 46030 cm-1 or 217 nm (well in the UV region and probably hidden by charge transfer or solvent bands).
It is important to remember that for spectra recorded in solution the width of the peaks may be as large as 1-2000 cm-1 so as long as it is possible to unambiguously assign peaks, the techniques are valuable.
high-spin octahedral d5 case and low-spin complexes
For Mn(II) and other d5 cases, the ground state is 6S and higher states include, 4G, 4D, 4P 4F etc.
It is expected that since there are NO spin-allowed transitions possible, the electronic spectrum should only contain very weak bands. For the other electronic configurations spin-forbidden bands are rarely observed since they are hidden by the more intense spin-allowed transitions. Since there are now no spin-allowed transitions, by amplifying the signal and using concentrated solutions, a number of weak peaks can be seen.
The Tanabe-Sugano diagram can be used to interpret these bands by once again calculating the ratio of the energies of 2 peaks and finding that position on the diagram. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/20%3A_d-Block_Metal_Chemistry_-_Coordination_Complexes/20.07%3A_Electronic_Spectra_-_Absorption/20.7F%3A_Interpretation_of_Electronic_Absorption_Spectra_-_Tanabe-.txt |
To make use of the Tanabe-Sugano diagrams provided in textbooks, it would be expected that they should at least be able to cope with typical spectra for d3, d8 octahedral and d2, d7 tetrahedral systems since these are predicted to be the most favoured from Crystal Field Stabilisation calculations. This is not the case. All the diagrams presented are impractical, being far too small and for chromium(III) actually stop before the region of interest of many simple coordination complexes.
If we ignore spin-forbidden transitions, where the energy of the states depend on both the B and C Racah parameter, then it should be possible to use the dn, d10-n relationship between octahedral and tetrahedral for interpretation of the spin-allowed transitions. This is because, for example, the d3 octahedral and d7 tetrahedral states have the same energy dependencies on Δ/B. When using the Tanabe-Sugano diagram in this way the major difference is that the size of Δ tetrahedral is only roughly 4/9 times that of Δ octahedral and so all complexes are high spin and the area of interest is moved closer to the left hand side of the diagram.
Procedure
• Record the UV/Vis spectrum of your sample.
• Tabulate peak information in wavelengths (nm) and convert to wavenumbers (cm-1), {ν = 107 / λ}
• calculate the extinction coefficients based on the concentration
• calculate the experimental ratio of v2 / v1
• use the appropriate Tanabe-Sugano diagram to locate where the ratio of the second to first peak matches that of the experimental value above.
For d2 (oct), d8 (tet) and d3, d8 (oct) d2, d7 (tet) JAVA applets and spreadsheets are available which perform these calculations.
• Tabulate the values of v1 / B', v2 / B', v3 / B' from the Y-intercepts and Δ/B' from the X-intercept.
• Using your experimental values of v1 and v2 (v3 if seen), calculate an average value of B' from these Y intercept values.
• Calculate Δ based on your value of Δ/B'.
• Assign all the spin-allowed transitions you observed.
• Comment on the size of the experimental B' compared to the free-ion value.
• Do you observe any peaks that might be spin-forbidden transitions? If so, can you assign them?
• Comment on the size of your calculated extinction coefficients and relate this to the relevant selection rules.
• The expected values should be compared to the following rough guide.
• For M2+ complexes, expect Δ= 7500 - 12500 cm-1.
• For M3+ complexes, expect Δ= 14000 - 25000 cm-1.
B for first-row transition metal free ions is around 1000 cm-1. Depending on the position of the ligand in the nephelauxetic series, this can be reduced to as low as 60% in the complex. Extinction coefficients for octahedral complexes are expected to be around 50-100 times smaller than for tetrahedral complexes. For a typical spin-allowed but Laporte (orbitally) forbidden transition in an octahedral complex, expect ε < 10 m2mol-1.
Example \(1\):
For an octahedral Ni(II) complex, three peaks were observed at 8000, 13200 and 22800 cm-1. From the ratio v2/v1 of 1.65 this gives a value of Δ/B' of 10.0. This can be shown in the following diagram.
Since v1= Δ in this case (and equals 8000 cm-1) then B' can be evaluated to be 800 cm-1. The spin-forbidden lines that would be between v2 and v3 in energy are not observed in the spectrum nor are any lines seen at higher energy. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/20%3A_d-Block_Metal_Chemistry_-_Coordination_Complexes/20.07%3A_Electronic_Spectra_-_Absorption/20.7G%3A_Help_on_using_Tanabe-Sugano_diagrams.txt |
Overview
• To introduce the concept of absorption and emission line spectra and describe the Balmer equation to describe the visible lines of atomic hydrogen.
The first person to realize that white light was made up of the colors of the rainbow was Isaac Newton, who in 1666 passed sunlight through a narrow slit, then a prism, to project the colored spectrum on to a wall. This effect had been noticed previously, of course, not least in the sky, but previous attempts to explain it, by Descartes and others, had suggested that the white light became colored when it was refracted, the color depending on the angle of refraction. Newton clarified the situation by using a second prism to reconstitute the white light, making much more plausible the idea that the white light was composed of the separate colors. He then took a monochromatic component from the spectrum generated by one prism and passed it through a second prism, establishing that no further colors were generated. That is, light of a single color did not change color on refraction. He concluded that white light was made up of all the colors of the rainbow, and that on passing through a prism, these different colors were refracted through slightly different angles, thus separating them into the observed spectrum.
Atomic Line Spectra
The spectrum of hydrogen atoms, which turned out to be crucial in providing the first insight into atomic structure over half a century later, was first observed by Anders Ångström in Uppsala, Sweden, in 1853. His communication was translated into English in 1855. Ångström, the son of a country minister, was a reserved person, not interested in the social life that centered around the court. Consequently, it was many years before his achievements were recognized, at home or abroad (most of his results were published in Swedish).
Most of what is known about atomic (and molecular) structure and mechanics has been deduced from spectroscopy. Figure 1.4.1 shows two different types of spectra. A continuous spectrum can be produced by an incandescent solid or gas at high pressure (e.g., blackbody radiation is a continuum). An emission spectrum can be produced by a gas at low pressure excited by heat or by collisions with electrons. An absorption spectrum results when light from a continuous source passes through a cooler gas, consisting of a series of dark lines characteristic of the composition of the gas.
Fraunhofer Lines
In 1802, William Wollaston in England had discovered that the solar spectrum had tiny gaps - there were many thin dark lines in the rainbow of colors. These were investigated much more systematically by Joseph von Fraunhofer, beginning in 1814. He increased the dispersion by using more than one prism. He found an "almost countless number" of lines. He labeled the strongest dark lines A, B, C, D, etc. Frauenhofer between 1814 and 1823 discovered nearly 600 dark lines in the solar spectrum viewed at high resolution and designated the principal features with the letters A through K, and weaker lines with other letters (Table 1.4.1 ). Modern observations of sunlight can detect many thousands of lines. It is now understood that these lines are caused by absorption by the outer layers of the Sun.
Designation Element Wavelength (nm)
Table 1.4.1 : Major Fraunhofer lines and the elements they are associated with.
y O2 898.765
Z O2 822.696
A O2 759.370
B O2 686.719
C H 656.281
a O2 627.661
D1 Na 589.592
D2 Na 588.995
D3 or d He 587.5618
The Fraunhofer lines are typical spectral absorption lines. These dark lines are produced whenever a cold gas is between a broad spectrum photon source and the detector. In this case, a decrease in the intensity of light in the frequency of the incident photon is seen as the photons are absorbed, then re-emitted in random directions, which are mostly in directions different from the original one. This results in an absorption line, since the narrow frequency band of light initially traveling toward the detector, has been turned into heat or re-emitted in other directions.
By contrast, if the detector sees photons emitted directly from a glowing gas, then the detector often sees photons emitted in a narrow frequency range by quantum emission processes in atoms in the hot gas, resulting in an emission line. In the Sun, Fraunhofer lines are seen from gas in the outer regions of the Sun, which are too cold to directly produce emission lines of the elements they represent.
Gases heated to incandescence were found by Bunsen, Kirkhoff and others to emit light with a series of sharp wavelengths. The emitted light analyzed by a spectrometer (or even a simple prism) appears as a multitude of narrow bands of color. These so called line spectra are characteristic of the atomic composition of the gas. The line spectra of several elements are shown in Figure 1.4.3 .
The Balmer Series of Hydrogen
Obviously, if any pattern could be discerned in the spectral lines for a specific atom (in contract to the mixture that Fraunhofer lines represent), that might be a clue as to the internal structure of the atom. One might be able to build a model. A great deal of effort went into analyzing the spectral data from the 1860's on. The big breakthrough was made by Johann Balmer, a math and Latin teacher at a girls' school in Basel, Switzerland. Balmer had done no physics before and made his great discovery when he was almost sixty.
Balmer decided that the most likely atom to show simple spectral patterns was the lightest atom, hydrogen. Ångström had measured the four visible spectral lines to have wavelengths 656.21, 486.07, 434.01 and 410.12 nm (Figure 1.4.4 ). Balmer concentrated on just these four numbers, and found they were represented by the phenomenological formula:
$\lambda = b \left( \dfrac{n_2^2}{n_2^2 -4} \right) \label{1.4.1}$
where $b$ = 364.56 nm and $n_2 = 3, 4, 5, 6$.
The first four wavelengths of Equation $\ref{1.4.1}$ (with $n_2$ = 3, 4, 5, 6) were in excellent agreement with the experimental lines from Ångström (Table 1.4.2 ). Balmer predicted that other lines exist in the ultraviolet that correspond to $n_2 \ge 7$ and in fact some of them had already been observed, unbeknown to Balmer.
Table 1.4.2 : The Balmer Series of Hydrogen Emission Lines
$n_2$ 3 4 5 6 7 8 9 10
$\lambda$ 656 486 434 410 397 389 383 380
color red teal blue indigo violet not visible not visible not visible
The $n_2$ integer in the Balmer series extends theoretically to infinity and the series represents a monotonically increasing energy (and frequency) of the absorption lines with increasing $n_2$ values. Moreover, the energy difference between successive lines decreased as $n_2$ increases (1.4.4 ). This behavior converges to a highest possible energy as Example 1.4.1 demonstrates. If the lines are plot according to their $\lambda$ on a linear scale, you will get the appearance of the spectrum in Figure 1.4.4 ; these lines are called the Balmer series.
Balmer's general formula (Equation $\ref{1.4.1}$) can be rewritten in terms of the inverse wavelength typically called the wavenumber ($\widetilde{\nu}$).
\begin{align} \widetilde{\nu} &= \dfrac{1}{ \lambda} \[4pt] &=R_H \left( \dfrac{1}{4} -\dfrac{1}{n_2^2}\right) \label{1.4.2} \end{align}
where $n_2 = 3, 4, 5, 6$ and $R_H$ is the Rydberg constant (discussed in the next section) equal to 109,737 cm-1.
He further conjectured that the 4 could be replaced by 9, 16, 25, … and this also turned out to be true - but these lines, further into the infrared, were not detected until the early twentieth century, along with the ultraviolet lines.
The Wavenumber as a Unit of Frequency
The relation between wavelength and frequency for electromagnetic radiation is
$\lambda \nu= c \nonumber$
In the SI system of units the wavelength, ($\lambda$) is measured in meters (m) and since wavelengths are usually very small one often uses the nanometer (nm) which is $10^{-9}\; m$. The frequency ($\nu$) in the SI system is measured in reciprocal seconds 1/s − which is called a Hertz (after the discover of the photoelectron effect) and is represented by Hz.
It is common to use the reciprocal of the wavelength in centimeters as a measure of the frequency of radiation. This unit is called a wavenumber and is represented by ($\widetilde{\nu}$) and is defined by
\begin{align*} \widetilde{\nu} &= \dfrac{1}{ \lambda} \[4pt] &= \dfrac{\nu}{c} \end{align*} \nonumber
Wavenumbers is a convenient unit in spectroscopy because it is directly proportional to energy.
\begin{align*} E &= \dfrac{hc}{\lambda} \nonumber \[4pt] &= hc \times \dfrac{1}{\lambda} \nonumber \[4pt] &= hc\widetilde{\nu} \label{energy} \[4pt] &\propto \widetilde{\nu} \end{align*}
Example 1.4.1 : Balmer Series
Calculate the longest and shortest wavelengths (in nm) emitted in the Balmer series of the hydrogen atom emission spectrum.
Solution
From the behavior of the Balmer equation (Equation $\ref{1.4.1}$ and Table 1.4.2 ), the value of $n_2$ that gives the longest (i.e., greatest) wavelength ($\lambda$) is the smallest value possible of $n_2$, which is ($n_2$=3) for this series. This results in
\begin{align*} \lambda_{longest} &= (364.56 \;nm) \left( \dfrac{9}{9 -4} \right) \[4pt] &= (364.56 \;nm) \left( 1.8 \right) \[4pt] &= 656.2\; nm \end{align*} \nonumber
This is also known as the $H_{\alpha}$ line of atomic hydrogen and is bright red (Figure $\PageIndex{3a}$).
For the shortest wavelength, it should be recognized that the shortest wavelength (greatest energy) is obtained at the limit of greatest ($n_2$):
$\lambda_{shortest} = \lim_{n_2 \rightarrow \infty} (364.56 \;nm) \left( \dfrac{n_2^2}{n_2^2 -4} \right) \nonumber$
This can be solved via L'Hôpital's Rule, or alternatively the limit can be expressed via the equally useful energy expression (Equation \ref{1.4.2}) and simply solved:
\begin{align*} \widetilde{\nu}_{greatest} &= \lim_{n_2 \rightarrow \infty} R_H \left( \dfrac{1}{4} -\dfrac{1}{n_2^2}\right) \[4pt] &= \lim_{n_2 \rightarrow \infty} R_H \left( \dfrac{1}{4}\right) \[4pt] &= 27,434 \;cm^{-1} \end{align*} \nonumber
Since $\dfrac{1}{\widetilde{\nu}}= \lambda$ in units of cm, this converts to 364 nm as the shortest wavelength possible for the Balmer series.
The Balmer series is particularly useful in astronomy because the Balmer lines appear in numerous stellar objects due to the abundance of hydrogen in the universe, and therefore are commonly seen and relatively strong compared to lines from other elements. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/20%3A_d-Block_Metal_Chemistry_-_Coordination_Complexes/20.08%3A_Electronic_Spectra_-_Emission.txt |
The spectra of the aqua ions for some first row transition metal ions are shown below.
For a much more detailed description of the interpretation of the spectra of first row transition metal ion complexes see the notes on the use of Tanabe-Sugano diagrams.
Cr(III) - an example in more detail
For \9d^3\), $d^8$ octahedral and $d^2$, $d^7$ tetrahedral complexes, the above diagrams can be used to interpret the observed electronic absorption spectra.
Figure 2
Take for example the $\ce{Cr^{3+}}$ aquo-ion $\ce{ [Cr(H2O)6]^{3+}}$. From the simplified Orgel diagram in Figure 2, three absorptions transitions are expected. In practice, the spectrum is found to contain three bands which occur at 17,000 cm-1, 24,000 cm-1 and 37,000 cm-1. Of which only two are shown in Figure 1.
$μ_1$ corresponds exactly to Δ (Delta) and since the lowest band is found at 17,000 cm-1 then this enables us to measure Δ directly from the spectrum.
The next band is found at 24,000 cm-1 and this can be equated to:
$μ_2=9/5Δ - x$
where $x$ is the configuration interaction between the T(F) state and the T(P) state of the same symmetry.
Since $Δ$ is 17,000 and μ2 is observed at 24,000 then x must be 6,600 cm-1.
The last band is seen at 37,000 cm-1 and here
$μ_3=6/5Δ + 15B + x \label{eq3}$
where $B$ is one of the RACAH parameters.
Solving Equation \ref{eq3} for $B$ gives a value of $B=667\,cm^{-1}$.
For the free Cr3+ ion, B is ~1030 cm-1 so that in the complex this term is reduced by ~2/3 of the free ion value.
A large reduction in B indicates a strong Nephelauxetic Effect. The Nephelauxetic Series is given by:
$\ce{F^{-} > H2O > urea > NH3 > en \~ C2O42^{-} > NCS^{-} > Cl^{-} ~ CN^{-} > Br^{-} > S2^{-} ~ I^-}$
Ionic ligands such as $\ce{F^{-}}$ give a small reduction in $B$, while covalently bonded ligands such as $\ce{I^{-}}$ give a large reduction of $B$.
Contributors and Attributions
• The Department of Chemistry, University of the West Indies)
20.10A: Magnetic Susceptibility and the Spin-only Formula
Complexes that contain unpaired electrons are paramagnetic and are attracted into magnetic fields. Diamagnetic compounds are those with no unpaired electrons are repelled by a magnetic field. All compounds, including transition metal complexes, posses some diamagnetic component which results from paired electrons moving in such a way that they generate a magnetic field that opposes an applied field. The magnitude of paramagnetism is measured in terms of the magnetic moment, $μ$, where the larger the magnitude of $μ$, greater the paramagnetism of the compound.
Magnetic Susceptibility
The magnetic susceptibility measures the strength of interaction on placing the substance in a magnetic field. For chemical applications the molar magnetic susceptibility ($\chi_{mol}$) is the preferred quantity and is measured in m3·mol−1 (SI) or cm3·mol−1 (CGS) and is defined as
${\displaystyle \chi _{\text{mol}}=M\chi _{v}/\rho }$
where $ρ$ is the density in kg·m−3 (SI) or g·cm−3 (CGS) and M is molar mass in kg·mol−1 (SI) or g·mol−1 (CGS). There are multiple methods for measuring magnetic susceptibilities, including, the Gouy, Evans, and Faraday methods. These all depend on measuring the force exerted upon a sample when it is placed in a magnetic field. The more paramagnetic the sample, the more strongly it will be drawn toward the more intense part of the field.
Origin of Paramagnetism
Electrons in most atoms exist in pairs, with each electron spinning in an opposite direction. Each spinning electron causes a magnetic field to form around it. In most materials, the magnetic field of one electron is cancelled by an opposite magnetic field produced by the other electron in the pair. The atoms in materials materials such as iron, cobalt and nickel have unpaired electrons, so they don't cancel the electrons' magnetic fields. As result, each atom of these elements acts like very small magnets.
There are three origins of paramagnetism in complexes:
1. Nuclear spin ($\mu_n$): Some nuclei, such as a hydrogen atom, have a net spin, which creates a magnetic field.
2. Electron spin ($\mu_s$): An electron has two intrinsic spin states (similar to a top spinning) which we call up ($\alpha$) and down ($\beta$).
3. Electron orbital motion ($\mu_l$): There is a magnetic field due to the electron moving around the nucleus.
Each of these magnetic moments interact with one another and/or with external magnetic fields to generate interesting physics. However, some of these interactions are stronger than others and can be (tentatively) ignored. For example, the nuclear spin magnetic moment (#1 above), which is central to NMR spectroscopy, is appreciably weaker than the other two moments and we can ignore it for this discussion and focus on the electronic moments.
The classical theory of magnetism was well developed before quantum mechanics with (see Lenz Law). From a quantum mechanical picture, for an individual electron in a molecule or atom, we can identify the orbital angular momentum $l$ and spin angular momentum $s$. For multi-electron systems, the total orbital angular momentum ($L$) and total spin angular momentum ($S$) are sum of the constituent electron spins.
$L = l_1 + l_2 + l_3 + \ldots$
and
$S = s_1 + s_2 + s_3 + \ldots \label{spin}$
The total magnetic susceptibility from both orbital and spin angular momenta is
$\mu_{L+S} = \sqrt{4S(S+1)+ L(L+1)} \,\mu_B$
where $\mu_B$ is the Bohr Magneton ($9.274×10^{−24} J/T$).
nuclear magneton vs. Bohr magneton
The associated the nuclear magneton $\mu_N$ attributed to nuclear spin magnetic moments is ~2000 fold smaller than the Bohr magneton. This is why we can ignore the nuclear spin components for this discussion.
That is, the rotation of electrons about the nucleus is restricted which leads to
$L = 0$
and
$\mu_s = \sqrt{4S(S+1)} \,\mu_B$
Equation \ref{spin} can be simplified to
$S = n(1/2) = n/2$
where $n$ is the number of unpaired electrons in the complex. Hence
\begin{align} \mu_s &= \sqrt{4S(S+1)} \,\mu_B \[4pt] &= \sqrt{4(n/2)(n/2+1)} \,\mu_B \[4pt] &= \sqrt{n(n+2)} \,\mu_B \label{SpinOnly} \end{align}
Equation \ref{SpinOnly} is called Spin-Only Formula. For transient metal complexes, the magnetic properties arise primarily from the exposed d-orbitals that are perturbed by ligands. Hence, experimentally measured magnetic moment can provide some important information about the compounds themselves including: (1) number of unpaired electrons present, (2) high-spin vs. low-spin states, (3). spectral behavior, and (4) even structure of the complexes (Table $1$).
Table $1$: Predicted Spin only Magnetic Moment
Ion Number of unpaired electrons $\mu_s$ observed moment /μB
Ti3+ 1 $\sqrt{3} \approx 1.73 \,\mu_B$ 1.73
V4+ 1 $\sqrt{3} \approx 1.73 \,\mu_B$ 1.68–1.78
Cu2+ 1 $\sqrt{3} \approx 1.73 \,\mu_B$ 1.70–2.20
V3+ 2 $\sqrt{8} \approx 2.83 \,\mu_B$ 2.75–2.85
Ni2+ 2 $\sqrt{8} \approx 2.83 \,\mu_B$ 2.8–3.5
V2+ 3 $\sqrt{15} \approx 3.87 \,\mu_B$ 3.80–3.90
Cr3+ 3 $\sqrt{15} \approx 3.87 \,\mu_B$ 3.70–3.90
Co2+ 3 $\sqrt{15} \approx 3.87 \,\mu_B$ 4.3–5.0
Mn4+ 3 $\sqrt{15} \approx 3.87 \,\mu_B$ 3.80–4.0
Cr2+ 4 $\sqrt{24} \approx 4.90 \,\mu_B$ 4.75–4.90
Fe2+ 4 $\sqrt{24} \approx 4.90 \,\mu_B$ 5.1–5.7
Mn2+ 5 $\sqrt{35} \approx 5.92 \mu_B$ 5.65–6.10
Fe3+ 5 $\sqrt{35} \approx 5.92 \mu_B$ 5.7–6.0
The small deviations from the spin-only formula for these octahedral complexes can result from the neglect of orbital angular momentum or of spin-orbit coupling. Tetrahedral d3, d4, d8 and d9 complexes tend to show larger deviations from the spin-only formula than octahedral complexes of the same ion because quenching of the orbital contribution is less effective in the tetrahedral case. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/20%3A_d-Block_Metal_Chemistry_-_Coordination_Complexes/20.09%3A_Evidence_for_Metal-Ligand_Covalent_Bonding/20.9A%3A_The_Nephelauxetic_Effect.txt |
Normal paramagnetic substances obey the Curie Law
$\chi = \dfrac{C}{T}$
where $C$ is the Curie constant. Thus a plot of 1/ χ versus $T$ should give a straight line of slope 1/C passing through the origin (0 K). Whereas many substances do give a straight line it often intercepts just a little above 0 K and these are said to obey the Curie-Weiss Law:
$\chi =\dfrac{C}{T+Φ}$
where $Φ$ is known as the Weiss constant.
Quantum Mechanics Approach
A similar expression (where χ is inversely proportional to Temperature) is obtained but now the constant $C$ is given by the Langevin expression, which relates the susceptibility to the magnetic moment:
$\chi_m =\dfrac{N \mu^2}{3kT}$
where
• $N$ is Avogadro's number
• $k$ is the Boltzmann constant and
• $T$ the absolute temperature
rewriting this gives the magnetic moment as
$μ= 2.828 \sqrt{\chi_mT} B.M.$
There are two main types of magnetic compounds, those that are diamagnetic (compounds that are repelled by a magnetic field) and those that are paramagnetic (compounds that are attracted by a magnetic field). All substances possess the property of diamagnetism due to the presence of closed shells of electrons within the substance. Note that diamagnetism is a weak effect while paramagnetism is a much stronger effect.
Paramagnetism derives from the spin and orbital angular momenta of electrons. This type of magnetism occurs only in compounds containing unpaired electrons, as the spin and orbital angular momenta is canceled out when the electrons exist in pairs. Compounds in which the paramagnetic centers are separated by diamagnetic atoms within the sample are said to be magnetically dilute.
If the diamagnetic atoms are removed from the system then the paramagnetic centers interact with each other. This interaction leads to ferromagnetism (in the case where the neighboring magnetic dipoles are aligned in the same direction) and antiferromagnetism (where the neighboring magnetic dipoles are aligned in alternate directions).
These two forms of paramagnetism show characteristic variations of the magnetic susceptibility with temperature.
In the case of ferromagnetism, above the Curie point the material displays "normal" paramagnetic behavior. Below the Curie point the material displays strong magnetic properties.
• Ferromagnetism is commonly found in compounds containing iron and in alloys.
• For antiferromagnetism, above the Neel point the material displays "normal" paramagnetic behavior. Below the Neel point the material displays weak magnetic properties which at lower and lower temperatures can become essentially diamagnetic. Antiferromagnetism is more common and is found to occur in transition metal halides and oxides, such as TiCl3 and VCl2.
20.10D: Spin Crossover
Octahedral complexes with between 4 and 7 d electrons can be either high-spin or low-spin depending on the size of Δ When the ligand field splitting has an intermediate value such that the two states have similar energies, then the two states can coexist in measurable amounts at equilibrium. Many "crossover" systems of this type have been studied, particularly for iron complexes.
The change in spin state is a transition from a low spin (LS) ground state electron configuration to a high spin (HS) ground state electron configuration of the metal’s d atomic orbitals (AOs), or vice versa. The magnitude of the ligand field splitting along with the pairing energy of the complex determines whether it will have a LS or HS electron configuration. A LS state occurs because the ligand field splitting (Δ) is greater than the pairing energy of the complex (which is an unfavorable process).
Figure \(1\) is a simplified illustration of the metal’s d orbital splitting in the presence of an octahedral ligand field. A large splitting between the t2g and eg AOs requires a substantial amount of energy for the electrons to overcome the energy gap (Δ) to comply with Hund’s Rule. Therefore, electrons will fill the lower energy t2g orbitals completely before populating the higher energy eg orbitals. Conversely, a HS state occurs with weaker ligand fields and smaller orbital splitting. In this case the energy required to populate the higher levels is substantially less than the pairing energy and the electrons fill the orbitals according to Hund’s Rule by populating the higher energy orbitals before pairing with electrons in the lower lying orbitals. An example of a metal ion that can exist in either a LS or HS state is Fe3+ in an octahedral ligand field. Depending on the ligands that are coordinated to this complex the Fe3+ can attain a LS or a HS state, as in Figure \(1\).
In the d6 case of Fe(phen)2(NCS)2, the crossover involves going from S=2 to S=0.
At the higher temperature the ground state is 5T2g while at low temperatures it changes to 1A1g. The changeover is found at about 174 K. In solution studies, it is possible to calculate the heat of conversion from the one isomer to the other. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/20%3A_d-Block_Metal_Chemistry_-_Coordination_Complexes/20.10%3A_Magnetic_Properties/20.10C%3A_The_Effects_of_Temperature_on_Magnetic_Moment.txt |
The general stability sequence of high spin octahedral metal complexes for the replacement of water by other ligands is:
$\ce{Mn(II) < Fe(II) < Co(II) < Ni(II) < Cu(II) > Zn(II)} \nonumber$
This trend is essentially independent of the ligand. In the case of 1,2-diaminoethane (en), the first step-wise stability constants (logK1) for M(II) ions are shown below.
The Irving-Williams sequence is generally quoted ONLY for Mn(II) to Zn(II) since there is little data available for the other first row transition metal ions because their M(II) oxidation states are not very stable. The position of Cu(II) is considered out-of-line with predictions based on Crystal Field Theory and is probably a consequence of the fact that Cu(II) often forms Jahn-Teller distorted octahedral complexes.
One explanation
Crystal Field Theory is based on the idea that a purely electrostatic interaction exists between the central metal ion and the ligands. This suggests that the stability of the complexes should be related to the ionic potential; that is, the charge to radius ratio. In the Irving-Williams series, the trend is based on high-spin M(II) ions, so what needs to be considered is how the ionic radii vary across the d-block.
For free metal ions in the gaseous phase it might be expected that the ionic radius of each ion on progressing across the d-block should show a gradual decrease in size. This would come about due to the incomplete screening of the additional positive charge by the additional electron, as is observed in the Lanthanide Contraction.
For high-spin octahedral complexes it is essential to consider the effect of the removal of the degeneracy of the d-orbitals by the crystal field. Here the d-electrons will initially add to the lower t2g orbitals before filling the eg orbitals since for octahedral complexes, the t2g subset are directed in between the incoming ligands whilst the eg subset are directed towards the incoming ligands and cause maximum repulsion.
For d1-d3 (and d6-d8) the addition of the electrons to the t2g orbitals will mean that the screening of the increasing attractive nuclear charge is not very effective and the radius should be smaller than for the free ion.
The position of d4 and d9 on the plot is difficult to ascertain with certainty since six-coordinate complexes are expected to be distorted due to the Jahn-Teller Theorem. Cr(II) is not very stable so few measurements are available. For Cu(II) however, most complexes are found to have 4 short bonds and 2 long bonds although 2 short and 4 long bonds is feasible. The radii are expected to show an increase over the d3 and d8 situation since electrons are being added to the eg subset. The reported values have been found to lie on both sides of the predicted value.
For d0, d5 and d10 the screening expected is essentially that of a spherical arrangement equivalent to the absence of a crystal field. The plot above shows that these points return to the line drawn showing a gradual decrease of the radius on moving across the d-block.
Once the decrease in radius with Z pattern is understood, it is a small step to move to a pattern for q/r since this only involves taking the reciprocal of the radius and holding the charge constant. The radius essentially decreases with increasing $Z$, therefore 1/r must increase with increasing $Z$.
For the sequence Mn(II) to Zn(II), the crystal field (q/r) trend expected would be
$\ce{Mn(II) < Fe(II) < Co(II) < Ni(II) > Cu(II) > Zn(II)} \nonumber$
Apart from the position of Cu(II), this corresponds to the Irving-Williams series (Eqution 1). The discrepancy is once again accounted for by the fact that copper(II) complexes are often distorted or not octahedral at all. When this is taken into consideration, it is seen that the Irving-Williams series can be explained quite well using Crystal Field Theory.
Contributors and Attributions
• Prof. Robert J. Lancashire (The Department of Chemistry, University of the West Indies) | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/20%3A_d-Block_Metal_Chemistry_-_Coordination_Complexes/20.12%3A_Thermodynamic_Aspects_-_The_Irving-Williams_Series.txt |
Occurrence
Manganese is the 12th most abundant element and 3rd most abundant transition metal (cf. Fe, Ti). A number of forms of manganese occur in nature (~ 300 minerals) giving an overall abundance of 0.106%. 12 of these minerals are economically viable including: pyrolusite (MnO2), manganite (Mn2O3.H2O), hausmannite (Mn3O4) rhodochrosite (MnCO3) and Mn-nodules. The main deposits are found in South Africa and the Ukraine (> 80%) and other important manganese deposits are in China, Australia, Brazil, Gabon, India, and Mexico.
Extraction
The metal is obtained by reduction with Al, or in a Blast furnace. The metal resembles iron in being moderately reactive and at high temperatures reacts vigorously with a range of non-metals. For example it burns in N2 at 1200 °C to form Mn3N2 and roasting in air gives Mn3O4
Uses
85-90% of the Manganese produced goes in to the fabrication of ferromanganese alloys. The 1 and 2 Euro coins contain manganese since there it is more abundant and cheaper than nickel. Manganese dioxide has been used in the cathodes of dry cell batteries and is used in newer alkaline batteries as well. Manganese salts have been used in glass making since the Eygyptian and Roman times and found in paints from as early as 17,000 years ago. Its use in glass is either to add color or to reduce the effect iron impurities have on the color of glass, see below.
Manganese in Biology
Manganese is an essential trace element for all forms of life. It accumulates in mitochondria and is essential for their function. The manganese transport protein, transmanganin, is thought to contain Mn(III). Several metalloenzymes are known: arginase, pyruvate carboxylase and superoxide dismutase. Humans excrete roughly 10 kg of urea per year, this results from the hydrolysis of arginine by the enzyme arginase found on the liver which is the final step of the urea cycle. This reaction allows for the disposal of nitrogenous waste from the breakdown of proteins.
In mammalian arginases I and II, binuclear manganese clusters are present at the active site. In the structure 1rla the Manganese nearest neighbours were identifed as: Asp124, Asp128, Asp232, Asp234, His101, His126.
Contributors and Attributions
• The Department of Chemistry, University of the West Indies)
21.03: Physical Properties - An Overview
Now given in more detail in individual pages covering each Transition Metal
Ti V Cr Mn Fe Co Ni Cu
Halides
Titanium
Titanium(IV) Halides
Formula Color MP BP Structure
TiF4 white - 284 fluoride bridged
TiCl4 Colorless -24 136.5 -
TiBr4 yellow 38 233.5 hcp I- but essentially monomeric cf. SnI4
TiI4 violet-black 155 377 hcp I- but essentially monomeric cf. SnI4
Preparations:
They can all be prepared by direct reaction of Ti with halogen gas (X2). All are readily hydrolysed.
They are all expected to be diamagnetic.
Titanium(III) halides
Formula Color MP BP μ (BM) Structure
TiF3 blue 950d - 1.75 -
TiCl3 violet 450d - - BiI3
TiBr3 violet - - - BiI3
TiI3 violet-black - - - -
Preparations:
They can be prepared by reduction of TiX4 with H2.
Vanadium
Vanadium(V) halides
Formula Color MP BP μ (BM) Structure
VF5 white 19.5 48.3 0 trigonal bipyramid in gas phase
Preparations:
Prepared by reaction of V with F2 in N2 or with BrF3 at 300C.
In the solid state it is an infinite chain polymer with cis-fluoride bridging.
Vanadium(IV) halides
Formula Color MP BP μ (BM) Structure
VF4 lime-green 100 (a) - 1.68 -
VCl4 red-brown -25.7 148 1.61 tetrahedral (monomeric)
VBr4 purple -23d - - -
(a) sublimes with decomposition at 100 C.
Preparations:
VCl4 is prepared by reaction of V with chlorinating agents such as Cl2, SOCl2, COCl2 etc.
Reaction of VCl4 with HF in CCl3F at -78C gives VF4.
Chromium
Chromium(III) halides
Formula Color MP M-X (pm) μ (BM) (b) Structure
CrF3 green 1404 190 - -
CrCl3 red-violet 1152 238 - CrCl3
CrBr3 green-black 1130 257 - BiI3
CrI3 black >500d - - -
(b) all 3.7-4.1 BM.
Preparations:
CrX3 are prepared from Cr with X2, dehydration of CrCl3.6H2O requires SOCl2 at 650C.
Chromium(II) halides
Formula Color MP μ (BM) Structure
CrF2 green 894 4.3 distorted rutile
CrCl2 white 820-824 5.13 distorted rutile
CrBr2 white 844 - -
CrI2 red-brown 868 - -
Preparations:
Reduction of CrX3 with H2/HX gives CrX2.
Manganese
Manganese(II) halides
Formula Color MP BP μ (BM) Structure
MnF2 pale-pink 920 - - rutile
MnCl2 pink 652 1190 5.73 CdCl2
MnBr2 rose 695 - 5.82 -
MnI2 pink 613 - 5.88 CdI2
Preparations:
Prepared from MnCO3 + HX -> MnX2 + CO2 + H2O
Iron
Iron(III) halides
Formula Color MP Structure
FeF3 green 1000 sublimes -
FeCl3 black 306 sublimes BiI3
FeBr3 dark-red-brown - BiI3
Preparations:
Prepared by reaction of Fe + X2 -> FeX3.
Note that FeBr3.aq when boiled gives FeBr2.
Iron(II) halides
Formula Color MP BP Structure
FeF2 white 1000 1100 rutile
FeCl2 pale yellow-grey 670-674 - CdCl2
FeBr2 yellow-green 684 - CdI2
FeI2 grey red heat - CdI2
Preparations:
Fe +HX at red heat -> FeX2 for X=F,Cl and Br
Fe + I2 -> FeI2
Cobalt
Cobalt(II) halides
Formula Color MP μ (BM) Structure
CoF2 pink 1200 - rutile
CoCl2 blue 724 5.47 CdCl2
CoBr2 green 678 - CdI2
CoI2 blue-black 515 - CdI2
Preparations:
Co or CoCO3 + HX -> CoX2.aq -> CoX2
Nickel
Nickel(II) halides
Formula Color MP μ (BM) Structure
NiF2 yellow 1450 2.85 tetragonal rutile
NiCl2 yellow 1001 3.32 CdCl2
NiBr2 yellow 965 3.0 CdCl2
NiI2 Black 780 3.25 CdCl2
Preparations:
Ni + F2 55 C /slow -> NiF2
Ni + Cl2 EtOH/ 20 C -> NiCl2
Ni + Br2 red heat -> NiBr2
NiCl2 + 2NaI -> NiI2 + 2NaCl
Copper
Copper(II) halides
Formula Color MP BP μ (BM) Structure
CuF2 white 950d - 1.5
CuCl2 brown 632 993d 1.75 CdCl2
CuBr2 black 498 - 1.3
Preparations:
Copper(II) halides are moderate oxidising agents due to the Cu(I)/ Cu(II) couple. In water, where the potential is largely that of the aquo-complexes, there is not a great deal of difference between them, but in non-aqueous media, the oxidising (halogenating) power increases in the sequence: CuF2 << CuCl2 << CuBr2.
Cu + F2 -> CuF2
Cu + Cl2 450 C -> CuCl2
Cu + Br2 -> CuBr2
or from CuX2.aq by heating -> CuX2
Copper(I) halides
Formula Color MP BP Structure
CuCl white 430 1359 -
CuBr white 483 1345 -
CuI white 588 1293 Zinc Blende
Preparations:
Reduction of CuX2 -> CuX except for F which has not been obtained pure.
Note that Cu(II)I2 can not be isolated due reduction to CuI.
Oxides and Aquo Species
Titanium
Titanium oxides
Formula Color MP μ (BM) Structure
TiO2 white 1892 diam. rutile - Refractive Index 2.61-2.90 cf. Diamond 2.42
Preparations:
obtained from hydrolysis of TiX4 or Ti(III) salts.
TiO2 reacts with acids and bases.
In Acid:
TiOSO4 formed in H2SO4 (Titanyl sulfate)
In Base:
MTiO3 metatitanates (eg Perovskite, CaTiO3 and ilmenite, FeTiO3)
M2TiO4 orthotitanates.
Peroxides are highly Colored and can be used for Colorimetric analysis.
pH <1 [TiO2(OH)(H2O)x]+
pH 1-2 [(O2)Ti-O-Ti(O2)](OH) x2-x; x=1-6
[Ti(H2O)6]3+ -> [Ti(OH)(H2O)5]2+ + [H+] pK=1.4
TiO2+ + 2H+ + e- -> Ti3+ + H2O E=0.1V
Vanadium
Vanadium oxides
Formula Color Common name Oxidation State MP V-O distance (pm)
V2O5 brick-red pentoxide V5+ 658 158.5-202
V2O4 blue dioxide V4+ 1637 176-205
V2O3 grey-black sesquioxide V3+ 1967 196-206
Preparations:
V2O5 is the final product of the oxidation of V metal, lower oxides etc.
Aqueous Chemistry very complex:
In alkaline solution,
VO43- + H+ -> HVO42-
2HVO42- -> V2O74- + H2O
HVO42- + H+ -> H2VO4-
3H2VO4- -> V3O93- + 3H2O
4H2VO4- -> V3O124- + 4H2O
In acidic solution,
10V3O93- + 15H+ -> 3HV10O285- + 6H2O
H2VO4- + H+ -> H2VO4
HV10O285- + H+ -> H2V10O284-
H3VO4 + H+ -> VO2+ + 2H2O
H2V10O284- + 14H+ -> 10VO2+ + 8H2O
VO(H2O)4SO4
The crystal structure of this salt was first determined in 1965. The V=O bond length was 159.4 pm, the aquo group trans to this had the longest V-O bond length (228.4pm) and the equatorial bond lengths were in the range 200.5-205.6 pm. Note that SO42- was coordinated in an equatorial position.
The IR stretching frequency for the V=O in vanadyl complexes generally occurs at 985 +/- 50 cm-1.
Redox properties of oxovanadium ions:
VO2+ + 2H+ + e- -> VO2+ + H2O E=1.0v
VO2+ + 2H+ + e- -> V3+ + H2O E=0.34V
Chromium
Chromium oxides
Formula Color Oxidation State MP
CrO3 deep red Cr6+ 197d
Cr3O8 - intermediate -
Cr2O5 - - -
Cr5O12 etc - - -
CrO2 brown-black Cr4+ 300d
Cr2O3 green Cr3+ 2437
Dichromate and chromate equilibria is pH dependent:
HCrO4- -> CrO42- + H+ K=10-5.9
H2CrO4 -> HCrO4- + H+ K=10+0.26
Cr2O72- + H2O -> 2HCrO4- K=10-2.2
HCr2O7- -> Cr2O72- + H+ K=10+0.85
CrO3
pH > 8 CrO42- yellow
2-6 HCrO4- & Cr2O72- orange-red
< 1 H2Cr2O7
[Cr(H2O)6]3+ -> [Cr(H2O)5(OH)]2+ -> [(H2O)4Cr Cr(H2O)4]4+ pK=4 etc.
Manganese
Manganese oxides
Formula Color Oxidation State MP
Mn2O7 green oil Mn7+ 5.9
MnO2 black Mn4+ 535d
Mn2O3 black Mn3+ 1080d
Mn3O4 - Haussmanite black Mn2/3+ 1705
MnO grey-green Mn2+ 1650
Preparations:
Mn3O4 is prepared from the other oxides by heating in air. MnO is prepared from the other oxides by heating with H2 at temperatures below 1200 C
Redox properties of KMnO4.
``` strong base
MnO4- + e- → MnO42- E=0.56V (RAPID)
MnO42- + 2H2O + e- → MnO2 + 4OH- E=0.60V (SLOW)
moderate base
MnO4- + 2H2O + 3e- → MnO2 + 4OH- E=0.59V
dil. H2SO4
MnO4- + 8H2O + 5e- → Mn2+ + 4H2O E=1.51V
```
Iron
Iron oxides
Formula Color Oxidation State MP Structure / comments
Fe2O3 red brown Fe3+ 1560d α-form Haematite,
β-form used in cassettes
Fe3O4 black Fe2+/3+ 1538d magnetite/lodestone
FeO black Fe2+ 1380 pyrophoric
Preparations:
α-Fe2O3 is obtained by heating alkaline solutions of Fe(III) and dehydrating the solid formed.
``` FeO,Fe3O4, γ-Fe2O3 ccp
α-Fe2O3 hcp
```
The Fe(III) ion is strongly acidic:
```[Fe(H2O)6]3+ + H2O -> [Fe(H2O)5(OH)]2+ + H3O+ K=10-3.05
[Fe(OH)(H2O)5]2+ + H2O -> [Fe(OH)2(H2O)4]+ + H3O+ K=10-3.26
```
olation
``` 2Fe(H2O)63+ + 2H2O -> [Fe2(OH)2(H2O)8]4++ 2H3O+ K=10-2.91
```
The Fe2+ ion is barely acidic:
``` Fe(H2O)62+ + H2O -> [Fe(OH)(H2O)5]+ + H3O+ K=10-9.5
```
The Redox chemistry of Iron is pH dependent:
``` Fe(H2O)63+ + e- -> Fe(H2O)62+ E=0.771V
E=E-RT/nF Ln[Fe2+]/[Fe3+]
at precipitation
[Fe2+].[OH-]2 ~ 10-14
[Fe3+].[OH-]3 ~ 10-36
or for OH- =1M then [Fe2+]/[Fe3+] = 1022
E =0.771 -0.05916 log10(1022)
=0.771 -1.301
=-0.530v
```
thus in base the value of E is reversed and the susceptibility of Fe2+ to oxidation increased. In base it is a good reducing agent and will reduce Cu(II) to Cu(0) etc. Note the implications for rust treatment.
Cobalt
Cobalt oxides
Formula Color Oxidation State MP Structure / comments
Co2O3 Co3+
Co3O4 black Co2+/3+ 900-950d normal spinel
CoO olive green Co2+ 1795 NaCl -antiferromag. < 289 K
Preparations:
Co2O3 is formed from oxidation of Co(OH)2.
CoO when heated at 600-700 converts to Co3O4
Co3O4 when heated at 900-950 reconverts back to CoO.
no stable [Co(H2O)6]3+ or [Co(OH)3 exist.
[Co(H2O)6]2+ not acidic
Nickel
Nickel oxides
Formula Color Oxidation State MP Structure / comments
NiO green powder Ni2+ 1955 NaCl
thermal decomposition of Ni(OH)2, NiCO3, or NiNO3 gives NiO.
[Ni(H2O)6]2+ not acidic
Copper
Copper oxides
Formula Color Oxidation State MP
CuO black Cu2+ 1026d
Cu2O red Cu+ 1230
[Cu(H2O)6]2+ not acidic
Preparations:
Cu2O is prepared from thermal decomposition of CuCO3, Cu(NO3)2 or Cu(OH)2. The Fehling's test for reducing sugars also gives rise to red Cu2O. It is claimed that 1 mg of dextrose produces sufficient red Color for a positive test.
The Redox chemistry of Copper:
``` Cu2+ + e- → Cu+ E=0.15V
Cu+ + e- → Cu E=0.52V
Cu2+ + 2e- → Cu E=0.34V
```
By consideration of this data, it will be seen that any oxidant strong enough to covert Cu to Cu+ is more than strong enough to convert Cu+ to Cu2+ (0.52 cf 0.14V). It is not expected therefore that any stable Cu+ salts will exist in aqueous solution.
Disproportionation can also occur:
``` 2Cu+ → Cu2+ + Cu E=0.37V or K=106
```
Representative Coordination Complexes
Titanium
TiCl4 is a good Lewis acid and forms adducts on reaction with Lewis bases such as;
``` 2PEt3 → TiCl4(PEt3)2
2MeCN → TiCl4(MeCN)2
bipy → TiCl4(bipy)
```
Solvolysis can occur if ionisable protons are present in the ligand;
``` 2NH3 → TiCl2(NH2)2 + 2HCl
4H2O → TiO2.aq + 4HCl
2EtOH → TiCl2(OEt)2 + 2HCl
```
TiCl3 has less Lewis acid strength but can form adducts also;
``` 3pyr → TiCl3pyr3
```
Vanadium
The Vanadyl ion (eg. from VO(H2O)4SO4 retains the V=O bond when forming complexes.
``` VO2+ + 2acac → VO(acac)2
```
Vanadyl complexes are often 5 coordinate square pyramidal and are therefore coordinately unsaturated. They can take up another ligand to become octahedral, eg;
```
VO(acac)2 + pyr → VO(acac)2pyr
```
The V=O stretching frequency in the IR can be monitored to see the changes occurring during these reactions. It generally is found at 985 cm-1 but will shift to lower wavenumbers when 6-coordinate, since the bond becomes weaker.
Chromium
The Chromium(III) ion forms many stable complexes which being inert are capable of exhibiting various types of isomerism. "CrCl3.6H2O" exists as hydrate isomers, including:
``` trans-[Cr(H2O)4Cl2]Cl.2H2O etc
```
CrCl3 anhydrous reacts with pyridine only in the presence of Zinc powder. This allows a small amount of Cr(II) to be formed, which is very labile.
``` CrCl3 + pyr/Zn → CrCl3pyr3
```
[Cr2(OAc)4].2H2O is an example of a Cr(II) complex which is reasonably stable in air once isolated. Each Cr(II) ion has 4 d electrons but the complex is found to be diamagnetic which is explained by the formation of a quadruple bond between the two metal ions. The Cr-Cr bond distance in a range of these quadruply bonded species has been found to vary between 195-255 pm.
Manganese
Octahedral complexes of Mn(III) are expected to show Jahn-Teller distortions. It was of interest therefore to compare the structures of Cr(acac)3 with Mn(acac)3 since the Cr(III) ion is expected to give a regular octahedral shape. In fact the Mn-O bond distances were all found to be equivalent.
An unusual Mn complex is obtained by the reaction of Mn(OAc)2 with KMnO4 in HOAc. This gives [MnO(OAc)6 3H2O] OAc. It is used as an industrial oxidant for the conversion of toluene to phenol.
Iron
An important Fe complex which is used in Actinometry since it is photosensitive is K3[Fe(C2 O4)3.3H2O.
It can be prepared from:
Fe(C2O4) in K2C2O4 by reacting with H2O2 in H2C2O4 to give green crystals. It is high spin m =5.9 BM at 300K and has been resolved into its two optical isomers, although they racemise in less than 1 hour.
In light the reaction is:
``` K3Fe(C2O4)3.3H2O → 2Fe(C2O4) + 2CO2 + 3K2C2O4
```
Another important complex is used as a redox indicator since the Fe(II) and Fe(III) complexes are both quite stable and have different Colors:
``` Fe(phen)33+ + e- → Fe(phen)32+ E=1.12V
blue red
```
The ligand is 1,10 phenanthroline and the indicator is called ferroin.
Cobalt
The Cobalt(III) ion forms many stable complexes, which being inert, are capable of exhibiting various types of isomerism. The preparation and characterisation of many of these complexes dates back to the pioneering work of Werner and his students.
Coordination theory was developed on the basis of studies of complexes of the type:
Werner Complexes
[Co(NH3)6]Cl3 yellow
[CoCl(NH3)5]Cl2 red
trans-[CoCl2(NH3)4]Cl green
cis-[CoCl2(NH3)4]Cl purple
Another important complex in the history of coordination chemistry is HEXOL. This was the first complex that could be resolved into its optical isomers that did not contain Carbon atoms. Since then, only three or four others have been found.
An interesting complex which takes up O2 from the air reversibly is Cosalen. This has been used as an emergency oxygen carrier in jet aircraft.
Nickel
The Nickel(II) ion forms many stable complexes. Whilst there are no other important oxidation states to consider, the Ni(II) ion can exist in a wide variety of CN's which complicates its coordination chemistry.
For example, for CN=4 both tetrahedral and square planar complexes can be found,
for CN=5 both square pyramid and trigonal bipyramid complexes are formed.
The phrase "anomalous nickel" has been used to describe this behaviour and the fact that equilibria often exist between these forms.
Some examples include:
(a) addition of ligands to square planar complexes to give 5 or 6 coordinate species
(b) monomer/polymer equilibria
(c) square-planar/ tetrahedron equilibria
(d) trigonal-bipyramid/ square pyramid equilibria.
• (a) substituted acacs react with Ni2+ to give green dihydrates (6 Coord) by heating the waters are removed to give tetrahedral species. The unsubstituted acac complex, Ni(acac)2 normally exists as a trimer.
Lifschitz salts containing substituted ethylenediamines can be isolated as either 4 or 6 coordinate species depending on the presence of coordinated solvent.
• (b) Ni(acac)2 is only found to be monomeric at temperatures around 200 C in non-coordinating solvents such as n-decane. 6-coordinate monomeric species are formed at room temperature in solvents such as pyridine but in the solid state Ni(acac)2 is a trimer, where each Ni atom is 6-coordinate. Note that Co(acac)2 actually exists as a tetramer.
• (c) Complexes of the type NiL2X2 where L are phosphines can give rise to either tetrahedral or square planar complexes. It has been found that:
``` L=P(aryl)3 are tetrahedral
L=P(alkyl)3 are square planar
```
L= mixed aryl and alkyl phosphines, both stereochemistries can occur in the same crystalline substance. The energy of activation for conversion of one form to the other has been found to be around 50 kJ mol-1. Similar changes have been observed with variation of the X group:
```
Ni(PPh3)2Cl2 green tetrahedral μ = 2.83 BM
Ni(PPh3)2(SCN)2 red sq. planar μ = 0.
```
Ni2+ reacts with CN- to give Ni(CN)2.nH2O (blue-green) which on heating at 180-200 is dehydrated to yield Ni(CN)2. Reaction with excess KCN gives K2Ni(CN)4.H2O (orange crystals) which can be dehydrated at 100C. Addition of strong concentrations of KCN produces red solutions of [Ni(CN)5]3-.
The crystal structure of the double salt prepared by addition of [Cr(en)3]3+ to [Ni(CN)5]3- showed that two types of Ni stereochemistry were present in the crystals in approximately equal proportions;
50% as square pyramid and 50% as trigonal bipyramid .
Copper
The Copper(II) ion forms many stable complexes which are invariably described as either 4 coordinate or distorted 6 coordinate species.
Cu(OH)2 reacts with NH3 to give a solution which will dissolve cellulose. This is exploited in the industrial preparation of Rayon. The solutions contain tetrammines and pentammines. With pyridine, only tetramines are formed eg Cu(py)4 SO4.
A useful reagent for the analytical determination of Cu2+ is the sodium salt of N,N-diethyldithiocarbamate. In dilute alcohol solutions, the presence of trace levels of Cu2+ is indicated by a yellow Color which can be measured by a spectrometer and the concentration determined from a Beer's Law plot. The complex is Cu(Et2dtc)2 which can be isolated as a brown solid.
Contributors and Attributions
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Transition Metal Oxides
The high oxidation state oxides are good oxidising agents with V2O5< CrO3< Mn2O7 becoming progressively more acidic as well.
Mixed oxidation state species M(II)M(III) 2O4 are formed by a number of elements, many of which adopt the spinel structure. The Normal Spinel structure, named after a mineral form of MgAl2O4 and of generic formula AB2O4 may be approximated as a cubic close packed lattice of oxide ions with one-eighth of the tetrahedral holes occupied by the A(II) ions and one-half of the octahedral holes occupied by the B(III) ions. Closely related is the Inverse Spinel structure where there is a site change between the A(II) ions and half of the B(III) ions. Given the fact that this occurs, it is evident that the energy factors directing the two different ions to the different sites are not overwhelmingly large, and it is not surprising that such structures are highly susceptible to defects in actual crystals. One factor that may influence this site selectivity is the crystal field stabilisation energy of transition metal ions.
Another ternary oxide structural type that is found is perovskite (CaTiO3). Again, the oxygens can be considered as cubic close packed.
All the elements from Ti to Fe give stable M2O3 oxides with corundum-type structures. These oxides are all ionic and predominantly basic. In air the M2O3 is the most stable oxide for Cr, Mn and Fe.
Dioxides-The elements Ti,V,Cr and Mn give MO2 oxides with rutile or distorted rutile structures. Note that CrO2 is ferromagnetic and used in the production of magnetic tapes.
All of the 3d elements from Ti to Cu form a monoxide, either by direct combination of the elements or by reduction of a higher oxide by the metal. Most of these have the NaCl structure and are basic. With the exception of TiO, they all dissolve in mineral acids to give stable salts or complexes of M2+ ions. The Ti 2+ ion liberates hydrogen from aqueous acid and so dissolution of TiO gives Ti3+ and hydrogen.
The monoxides show a variety of physical properties. Thus Ti and V are quasi-metallic, CrO is marginal but Mn to Cu are typical ionic insulators (or more precisely, semiconductors).
Summary of ionic lattice structures
Fraction of holes occupied by cations Sequence of close packed anionic layers Formula CN of M and X
hcp (ABAB..) ccp (ABCABC..)
all octahedral NiAs NaCl MX 6:6
1/2 octahedral - all in alternate layers CdI2 CdCl2 MX2 6:3
1/3 octahedral - 2/3 in alternate layers BiI3 CrCl3 MX3 6:2
1/2 tetrahedral ZnS - wurtzite ZnS - zinc blende MX 4:4
all tetrahedral - CaF2- fluorite MX2 8:4
For further details on the structures of some of these salts see The Virtual Museum of Minerals and Molecules.
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• The Department of Chemistry, University of the West Indies) | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/21%3A_d-Block_Metal_Chemistry_-_The_First_Row_Metals/21.02%3A_Occurrence_Extraction_and_Uses.txt |
The discovery of titanium in 1791 is attributed to William Gregor, a Cornish vicar and amateur chemist. He isolated an impure oxide from ilmenite (FeTiO3) by treatment with HCl and H2SO4. Titanium is the second most abundant transition metal on Earth (6320 ppm) and plays a vital role as a material of construction because of its: Excellent Corrosion Resistance, High Heat Transfer Efficiency, and Superior Strength-To-Weight Ratio. For example, when it's alloyed with 6% aluminum and 4% vanadium, titanium has half the weight of steel and up to four times the strength.
While a biological function in man is not known, it has excellent biocompatibility--that is the ability to be ignored by the human body's immune system--and an extreme resistance to corrosion. Titanium is now the metal of choice for hip and knee replacements.
Properties of titanium
Extraction of Titanium - the Kroll process
Wilhelm J. Kroll (Born November 24, 1889 - Died March 30, 1973) developed the process in Luxemburg around the mid 1930's and then after moving to the USA extended it to enable the extraction of Zirconium as well.
Titanium ores, mainly rutile (TiO2) and ilmentite (FeTiO3), are treated with carbon and chlorine gas to produce titanium tetrachloride.
$\ce{TiO_2 + Cl_2 \rightarrow TiCl_4 + CO_2}$
Fractionation
Titanium tetrachloride is purified by distillation (BP 136.4) to remove iron chloride.
Reduction
Purified titanium tetrachloride is reacted with molten magnesium under argon to produce a porous “titanium sponge”.
$\ce{TiCl4 + 2Mg -> Ti + 2MgCl2}$
Melting
Titanium sponge is melted under argon to produce ingots.
The Kroll process (ISIS Draw .skc file)
Titanium Halides
Titanium(IV) Halides
Formula Color MP BP Structure
TiF4 white - 284 fluoride bridged
TiCl4 Colorless -24 136.4 -
TiBr4 yellow 38 233.5 hcp I- but essentially monomeric cf. SnI4
TiI4 violet-black 155 377 hcp I- but essentially monomeric cf. SnI4
Preparations:
They can all be prepared by direct reaction of Ti with halogen gas (X2). All are readily hydrolysed.
They are all expected to be diamagnetic.
Titanium(III) halides
Formula Color MP BP m (BM) Structure
TiF3 blue 950d - 1.75 -
TiCl3 violet 450d - - BiI3
TiBr3 violet - - - BiI3
TiI3 violet-black - - - -
Preparations:
They can be prepared by reduction of TiX4 with H2.
Titanium Oxides and Aqueous Chemistry
Titanium oxides
Formula Color MP m (BM) Structure
TiO2 white 1892 diam. rutile - Refractive Index 2.61-2.90 cf. Diamond 2.42
Preparations:
obtained from hydrolysis of TiX4 or Ti(III) salts.
TiO2 reacts with acids and bases.
In Acid:
TiOSO4 formed in H2SO4 (Titanyl sulfate)
In Base:
MTiO3 metatitanates (eg Perovskite, CaTiO3 and ilmenite, FeTiO3)
M2TiO4 orthotitanates.
Peroxides are highly Colored and can be used for Colorimetric analysis.
pH <1 [TiO2(OH)(H2O)x]+
pH 1-2 [(O2)Ti-O-Ti(O2)](OH) x2-x; x=1-6
[Ti(H2O)6]3+ -> [Ti(OH)(H2O)5]2+ + [H+] pK=1.4
TiO2+ + 2H+ + e- -> Ti3+ + H2O E=0.1V
Representative complexes
TiCl4 is a good Lewis acid and forms adducts on reaction with Lewis bases such as;
2PEt3 -> TiCl4(PEt3)2
2MeCN -> TiCl4(MeCN)2
bipy -> TiCl4(bipy)
Solvolysis can occur if ionisable protons are present in the ligand;
2NH3 -> TiCl2(NH2)2 + 2HCl
4H2O -> TiO2.aq + 4HCl
2EtOH -> TiCl2(OEt)2 + 2HCl
TiCl3 has less Lewis acid strength but can form adducts also;
3pyr -> TiCl3pyr3
Contributors and Attributions
• The Department of Chemistry, University of the West Indies) | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/21%3A_d-Block_Metal_Chemistry_-_The_First_Row_Metals/21.05%3A_Group_4_-_Titanium/21.5A%3A_Titanium_Metal.txt |
The discovery of vanadium is attributed to Andres Manuel del Rio (a Spanish mineralogist working in Mexico City) who prepared a number of salts from a material contained in "brown lead" around 1801. Unfortunately, the French chemist Collett-Desotils incorrectly declared that del Rio's new element was only impure Chromium. Del Rio thought himself to be mistaken and withdrew his claim. The element was rediscovered in 1830 by the Swedish chemist Nils Gabriel Sefström who named it after the Norse goddess Vanadis, the goddess of beauty and fertility.
Metallic vanadium was not isolated until 1867 when Sir Henry Enfield Roscoe (1833-1915), Professor of Chemistry at Owens College (later the University of Manchester) from 1857 to 1885, reduced vanadium chloride (VCl5) with gaseous hydrogen to give vanadium metal and HCl.
Properties of vanadium
An excellent site for finding the properties of the elements, including vanadium is at
Introduction
Vanadium has been found to play a number of roles in biological systems. It is present in certain vanadium dependent haloperoxidase and nitrogenase enzymes.
A tunicate (Clavelina Puertosecensis) discovered near Discovery Bay, Jamaica
Many sea squirts, such as Ciona Intestinalis accumulate vanadium in very high concentration, although the reason is not known.
The mushroom Amanita muscaria accumulate vanadium in the form of a coordination complex called amavadin, whose function is still unknown.
A number of vanadium complexes have been shown to alleviate many of the symptoms of diabetes in both in vitro and in vivo (in rats and mice) studies. These complexes are being studied as potential alternatives to insulin therapy.
Vanadium Halides
Vanadium(V) halides
Formula Colour MP BP m (BM) Structure
VF5 white 19.5 48.3 0 trigonal bipyramid in gas phase
Preparations:
Prepared by reaction of V with F2 in N2 or with BrF3 at 300C.
In the solid state it is an infinite chain polymer with cis-fluoride bridging.
Vanadium(IV) halides
Formula Colour MP BP m (BM) Structure
VF4 lime-green 100 (a) - 1.68 -
VCl4 red-brown -25.7 148 1.61 tetrahedral (monomeric)
VBr4 purple -23d - - -
(a) sublimes with decomposition at 100 C.
Preparations:
VCl4 is prepared by reaction of V with chlorinating agents such as Cl2, SOCl2, COCl2 etc.
Reaction of VCl4 with HF in CCl3F at -78C gives VF4.
Vanadium Oxides and Aqueous Chemistry
Vanadium oxides
Formula Colour Common name Oxidation State MP V-O distance (pm)
V2O5 brick-red pentoxide V5+ 658 158.5-202
V2O4 blue dioxide V4+ 1637 176-205
V2O3 grey-black sesquioxide V3+ 1967 196-206
Preparations:
V2O5 is the final product of the oxidation of V metal, lower oxides etc.
Aqueous Chemistry very complex:
a VO2+
b VO(OH)3
c V10O26(OH)24-
d V10O27(OH)5-
e V10O286-
f V3O93-
g VO2(OH)2-
h V4O124-
i V2O6(OH)3-
j VO3(OH)2-
k V2O74-
l VO43-
a VO2+
b V10O26(OH)24-
c V10O27(OH)5-
d V10O286-
e V4O124-
f V3O93-
g V2O6(OH)3-
h V2O74-
i VO3(OH)2-
j VO43-
In alkaline solution,
VO43- + H+ → HVO42-
2HVO42- → V2O74- + H2O
HVO42- + H+ → H2VO4-
3H2VO4- → V3O93- + 3H2O
4H2VO4- → V3O124- + 4H2O
In acidic solution,
10V3O93- + 15H+ → 3HV10O285- + 6H2O
H2VO4- + H+ → H2VO4
HV10O285- + H+ → H2V10O284-
H3VO4 + H+ → VO2+ + 2H2O
H2V10O284- + 14H+ → 10VO2+ + 8H2O
VO(H2O)4SO4
The crystal structure of this salt was first determined in 1965. The V=O bond length was 159.4 pm, the aquo group trans to this had the longest V-O bond length (228.4pm) and the equatorial bond lengths were in the range 200.5-205.6 pm. Note that SO42- was coordinated in an equatorial position.
The IR stretching frequency for the V=O in vanadyl complexes generally occurs at 985 +/- 50 cm-1.
Redox properties of oxovanadium ions:
VO2+ + 2H+ + e- → VO2+ + H2O E=1.0 V
VO2+ + 2H+ + e- → V3+ + H2O E=0.34 V
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• The Department of Chemistry, University of the West Indies) | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/21%3A_d-Block_Metal_Chemistry_-_The_First_Row_Metals/21.06%3A_Group_5_-_Vanadium/21.6A%3A_The_Metal.txt |
Discovered in 1797 by the French chemist Louis Nicolas Vauquelin, it was named chromium (Greek chroma, "color") because of the many different colors characteristic of its compounds. Chromium is the earth's 21st most abundant element (about 122 ppm) and the 6th most abundant transition metal. The principal and commercially viable ore is chromite, $\ce{FeCr2O4}$, which is found mainly in southern Africa (with 96% of the worlds reserves), the former U.S.S.R and the Philippines. Less common sources include crocoite, $\ce{PbCrO4}$, and chrome ochre, $\ce{Cr2O3}$, while the gemstones emerald and ruby owe their colors to traces of chromium.
Extraction
Chromite ($\ce{FeCr2O4}$) is the most commercially useful ore, and is extensively used for extraction of chromium. Chromium is produced in two forms:
1. Ferrochrome by the reduction of chromite with coke in an electric arc furnace. A low-carbon ferrochrome can be produced by using ferrosilicon instead of coke as the reductant. This iron/chromium alloy is used directly as an additive to produce chromium-steels which are "stainless" and hard.
2. Chromium metal by the reduction of Cr2O3. This is obtained by aerial oxidation of chromite in molten alkali to give sodium chromate, Na2CrO4, which is leached out with water, precipitated and then reduced to the Cr(III) oxide by carbon. The oxide can be reduced by aluminum (aluminothermic process) or silicon:
$\ce{Cr_2O_3 + 2Al \rightarrow 2Cr + Al_2O_3}$
$\ce{2Cr_2O_3 + 3Si \rightarrow 4Cr + 3SiO_2}$
The main use of the chromium metal so produced is in the production of nonferrous alloys, the use of pure chromium being limited because of its low ductility at ordinary temperatures. Alternatively, the Cr2O3 can be dissolved in sulfuric acid to give the electrolyte used to produce the ubiquitous chromium-plating which is at once both protective and decorative. The sodium chromate produced in the isolation of chromium is itself the basis for the manufacture of all industrially important chromium chemicals. World production of chromite ores approached 12 million tonnes in 1995.
Chromium Compounds
Most compounds of chromium are colored (why is Cr(CO)6 white?); the most important are the chromates and dichromates of sodium and potassium and the potassium and ammonium chrome alums. The dichromates are used as oxidizing agents in quantitative analysis, also in tanning leather. Other compounds are of industrial value; lead chromate is chrome yellow, a valued pigment. Chromium compounds are used in the textile industry as mordants, and by the aircraft and other industries for anodizing aluminium.
Halides
CrX3 are prepared from Cr with X2, dehydration of CrCl3.6H2O requires SOCl2 at 650C.
Table 1: Chromium(III) halides
Formula Color MP M-X (pm) μ(BM) (b) Structure
CrF3 green 1404 190 - -
CrCl3 red-violet 1152 238 - CrCl3
CrBr3 green-black 1130 257 - BiI3
CrI3 black >500decomp - - -
(b) all 3.7-4.1 BM.
Reduction of CrX3 with H2/HX gives CrX2.
Table 2: Chromium(II) halides
Formula Color MP μ (BM) Structure
CrF2 green 894 4.3 distorted rutile
CrCl2 white 820-824 5.13 distorted rutile
CrBr2 white 844 - -
CrI2 red-brown 868 - -
Oxides
Table 3: Chromium oxides
Formula Color Oxidation State MP Magnetic Moment
CrO3 deep red Cr6+ 197decomp -
Cr3O8 - intermediate - -
Cr2O5 - - - -
Cr5O12 etc - - - -
CrO2 brown-black Cr4+ 300decomp -
Cr2O3 green Cr3+ 2437 -antiferromagnetic < 35 C
Dichromate and chromate equilibria is pH dependent:
$\ce{HCrO4- → CrO42- + H+ } \,\, K=10^{-5.9}$
H2CrO4 → HCrO4- + H+ K=10+0.26
Cr2O72- + H2O → 2HCrO4- K=10-2.2
HCr2O7- → Cr2O72- + H+ K=10+0.85
Hence the variation found for solutions of CrO3 are:
• pH > 8 CrO42- yellow
• pH 2-6 HCrO4- and Cr2O72- orange-red
• pH < 1 H2Cr2O7
One of the most obvious characteristics of Cr(III) is that it is acidic i.e it has a tendency to hydrolyse and form polynuclear complexes containing OH- bridges in a process known as OLATION. This is thought to occur by the loss of a proton from coordinated water, followed by coordination of the OH- to a second cation:
[Cr(H2O)6]3+ → [Cr(H2O)5(OH)]2+
H
O
/ \
[(H2O)4Cr Cr(H2O)4]4+ pK=4 etc.
\ /
O
H
The ease with which the proton is removed can be judged by the fact that the hexaaquo ion (pKa ~ 4) is almost as strong as acetic acid. Further deprotonation and polymerization can occur and, as the pH is raised, the final product is hydrated chromium(III) oxide or "chromic hydroxide".
Representative Complexes
The Chromium(III) ion forms many stable complexes and since they are inert are capable of exhibiting various types of isomerism.
anhydrous CrCl3 and hydrated "CrCl3.6H2O",
Hydrated chromium chloride, "CrCl3.6H2O", exists as hydrate isomers, including:
• the violet [Cr(H2O)6]Cl3
• the dark green trans-[CrCl2(H2O)4]Cl.2H2O salt shown above, etc.
• the pale green [CrCl(H2O)5]Cl2.H2O
Anhydrous CrCl3 reacts with pyridine only in the presence of Zinc powder. This allows a small amount of the Cr(II) ion to be formed, which is very labile but unstable with respect to oxidation back to Cr(III).
$CrCl_3 + pyr/Zn \rightarrow CrCl_3pyr_3$
See the laboratory manual for this course for a range of other Cr(III) complexes for which you should know the structure.
[Cr2(OAc)4].2H2O is an example of a Cr(II) complex which is reasonably stable in air once isolated. Each Cr(II) ion has 4 d electrons but the complex is found to be diamagnetic which is explained by the formation of a quadruple bond between the two metal ions. The Cr-Cr bond distance in a range of these quadruply bonded species has been found to vary between 195-255 pm.
Cr(II) acetate complex.
In case you think that quadruple bonds are as far as it goes.... a recent report describes the structure of a Cr complex with a quintuple bond between two Cr(I) ions.
Cr(I) - Cr(I) quintuple bonded structure.
The compound Ar'CrCrAr' (R = isopropyl) was very air and moisture sensitive and crystallised as dark red crystals. X-ray diffraction revealed a Cr-Cr bond length of about 184 pm and a planar, trans-bent core geometry. Published in Science by P Power et. al., UC Davis, 22 September 2005 [DOI: 10.1126/science.1116789].
Another recent innovation is the formation of "zeolite-type" architectures from Metal-Organic-Frameworks (MOF's). The synthesis of MIL-101 consists of the hydrothermal reaction of 1,4-benzene dicarboxylate, H2BDC (166 mg, 1 mmol) with Cr(NO3)3.9H2O (400 mg, 1 mmol), hydrofluoric acid (1 mmol), and 4.8 mL of H2O (265 mmol) for 8 h at 220 °C, producing a pure and highly crystallized green powder of the chromium terephthalate with formula Cr3F(H2O)2O[(O2C)-C6H4-(CO2)]3.nH2O (n=25), based on chemical analysis.
MIL 101 Chromium MOF structure. "First Direct Imaging of Giant Pores of the Metal-Organic Framework MIL-101" Millange and co-workers Chem. Mater. 2005, 17, 6525-6527
Uses
More than half the production of chromium goes into metallic products, and about another third is used in refractories. It is an ingredient in several important catalysts. The chief use of chromium is to form alloys with iron, nickel, or cobalt. The addition of chromium imparts hardness, strength, and corrosion resistance to the alloy. In the stainless steels, chromium makes up 10 percent or more of the final composition. Because of its hardness, an alloy of chromium, cobalt, and tungsten is used for high-speed metal-cutting tools. When deposited electrolytically, chromium provides a hard, corrosion-resistant, lustrous finish. For this reason it is widely used as body trim on automobiles and other vehicles. The extensive use of chromite as a refractory is based on its high melting point, its moderate thermal expansion, and the stability of its crystalline structure.
In chromites and chromic salts, chromium has a valence of +3. Most of these compounds are green, but some are red or blue. Chromic oxide (Cr2O3) is a green solid. In chromates and dichromates, chromium has a valence of +6. Potassium dichromate (K2Cr2O7) is a red, water-soluble solid that, mixed with gelatin, gives a light-sensitive surface useful in photographic processes. The chromates are generally yellow, the best known being lead chromate (PbCrO4), an insoluble solid widely used as a pigment called chrome yellow. Chrome green is a mixture of chrome yellow and Prussian blue.
Chromium is used to harden steel, to manufacture stainless steel, and to form many useful alloys. Much is used in plating to produce a hard, beautiful surface and to prevent corrosion. Chromium gives glass an emerald green color and is widely used as a catalyst. The refractory industry has found chromite useful for forming bricks and shapes, as it has a high melting point, moderate thermal expansion, and stability of crystalline structure.
Health
Chromium is an essential trace element in mammalian metabolism. In addition to insulin, it is responsible for reducing blood glucose levels, and is used to control certain cases of diabetes. It has also been found to reduce blood cholesterol levels by diminishing the concentration of (bad) low density lipoproteins "LDLs" in the blood. It is supplied in a variety of foods such as Brewer's yeast, liver, cheese, whole grain breads and cereals, and broccoli. It is claimed to aid in muscle development, and as such dietary supplements containing chromium picolinate (its most soluble form), is very popular with body builders.
mer- isomer of Cr(III) picolinate complex.
Ammonium Reineckate, NH4(Cr(NH3)2(SCN)4).H 2O, is used to test for the presence of dihydromorphinone and other substances generally found in persons involved in substance abuse.
Contributors and Attributions
• The Department of Chemistry, University of the West Indies) | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/21%3A_d-Block_Metal_Chemistry_-_The_First_Row_Metals/21.07%3A_Group_6_-_Chromium/21.7A%3A_Chromium_Metal.txt |
Oxides
Table $1$: Manganese oxides
Formula Color Oxidation State MP °C
Mn2O7 green oil Mn7+ 5.9
MnO2 black Mn4+ 535d
Mn2O3 black Mn3+ 1080d
Mn3O4 - Haussmanite black Mn2/3+ 1705
MnO grey-green Mn2+ 1650
Preparations
• Mn3O4 is prepared from the other oxides by heating in air at 1000 °C
• MnO is prepared from the other oxides by heating with H2 at temperatures below 1200 °C above that Mn metal is produced.
• MnO2 has been used for many years to decolorise commercial glass. When added to molten glass a small amount of red-brown Mn(III) results that masks the blue-green color from iron impurities. That is, by adding a reagent with the complimentary color of the impurity, the resultant effect is to balance out and give a clear glass.
• MnO2 is used as an oxidant for the conversion of aniline to hydroquinone.
• Mn2O7 is dangerously explosive above 3 °C. It is thought that some accidents have occurred when instead of adding conc HCl to solid KMnO4 to produce Cl2 the wrong bottle is selected and conc H2SO4 was used leading to the formation of a green oil that explodes.
High Oxidation State Oxide Salts
Fusion of MnO2 with an alkali metal hydroxide and an oxidizing agent such as KNO3 produces very dark-green manganate(VI) salts (manganates) which are stable in strongly alkaline solution but which disproportionate readily in neutral or acid solution.
$3MnO_4^{2-} + 4H^+ → 2MnO_4^- + MnO_2+ 2H_2O$
The deep-purple manganate(VII) salts (permanganates) may be prepared in aqueous solution by oxidation of manganese(II) salts with very strong oxidizing agents such as PbO2 or NaBiO3. They are manufactured commercially by alkaline oxidative fusion of $MnO_2$ followed by the electrolytic oxidation of manganate(VI):
$2MnO_2+ 4KOH + O2 → 2K_2MnO_4+ 2H_2O$
$2K_2MnO_4+ 2H_2O → 2KMnO_4+ 2KOH + H_2$
The most important manganate(VII) is KMnO4 and the very intense purple color is due to a charge transfer band and not a d-d transition. It is a well-known oxidizing agent; the usual conditions for its use are 0.02 M KMnO4 and 1.5 M H2SO4.
Redox properties of $KMnO_4$
• strong base
$MnO_4^- + e^- → MnO_4^{2-} \,\,\, \text{ (RAPID)}$
with $E=0.56\,V$
$MnO_4^{2-} + 2H_2O + e^- → MnO_2 + 4OH^-\,\,\, \text{ (SLOW)}$
with $E=0.60\,V$
• moderate base
$MnO_4^- + 2H_2O + 3e^- → MnO_2 + 4OH^-$
with $E=0.59\,V$
• dil. H2SO4
$MnO_4^- + 8H_2O + 5e^- → Mn^{2+} + 4H_2O$
with $E=1.51\,V$
In the industrial production of saccharin and benzoic acid, KMnO4 is the oxidant, medically, it has been used as a disinfectant. It is gaining in use for water purification, since it has an advantage over chlorine that it does not affect the taste, and has the bonus that the MnO2 produced acts as a coagulant for colloidal impurities.
Table $2$: Manganese(II) halides
Formula Color MP °C BP °C m (BM) Structure
MnF2 pale-pink 920 - - rutile
MnCl2 pink 652 1190 5.73 CdCl2
MnBr2 rose 695 - 5.82 -
MnI2 pink 613 - 5.88 CdI2
Preparations:
Prepared from
$MnCO_3 + HX → MnX_2 + CO_2 + H_2O$
Manganese complexes
Octahedral complexes of Mn(III) are expected to show Jahn-Teller distortions. It was of interest therefore to compare the structures of Cr(acac)3 with Mn(acac)3 since the Cr(III) ion is expected to give a regular octahedral shape. In fact the Mn-O bond distances were all found to be equivalent. An unusual Mn complex is obtained by the reaction of Mn(OAc)2 with KMnO4 in HOAc. This gives [Mn3O(OAc)6 3H2O]OAc. It is used as an industrial oxidant for the conversion of toluene to phenol.
Contributors and Attributions
• The Department of Chemistry, University of the West Indies) | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/21%3A_d-Block_Metal_Chemistry_-_The_First_Row_Metals/21.08%3A_Group_7_-_Manganese/21.8A%3A_The_Metal.txt |
Iron is the most abundant transition metal on Earth (62000 ppm).
Extraction of Iron
Iron is generally extracted in a Blast furnace.
Iron Halides
Iron(III) halides
Formula Color MP Structure
FeF3 green 1000 sublimes
FeCl3 black 306 sublimes BiI3
FeBr3 dark-red-brown decomposes above 200°C BiI3
Preparations:
Prepared by reaction of Fe + X2 → FeX3.
Note that FeBr3.aq when boiled gives FeBr2.
An important application of the chloride is as an etching material for copper electrical printed circuits.
Iron(II) halides
Formula Color MP BP Structure
FeF2 white 1000 1100 rutile
FeCl2 pale yellow-grey 670-674 - CdCl2
FeBr2 yellow-green 684 - CdI2
FeI2 grey red heat - CdI2
Preparations:
Fe +HX at red heat → FeX2 for X=F,Cl and Br
Fe + I2 → FeI2
Iron Oxides and Aqueous Chemistry
Iron oxides
Formula Color Oxidation State MP Structure / comments
Fe2O3 red brown Fe3+ 1560d α-form Haematite,
β-form used in cassettes
Fe3O4 black Fe2+/3+ 1538d magnetite/lodestone
FeO black Fe2+ 1380 pyrophoric
Preparations
$α-Fe_2O_3$ is obtained by heating alkaline solutions of Fe(III) and dehydrating the solid formed.
FeO, Fe3O4, γ-Fe2O3 ccp, α-Fe2O3 hcp
The Fe(III) ion is strongly acidic:
$[Fe(H_2O)_6]^{3+} + H_2O \rightarrow [Fe(H_2O)_5(OH)]^{2+} + H_3O^+\;\;\; K=10^{-3.05} \tag{1}$
$[Fe(OH)(H_2O)_5]^{2+} + H_2O \rightarrow [Fe(OH)_2(H_2O)_4]^+ + H_3O^+\;\;\; K=10^{-3.26} \tag{2}$
olation
$2Fe(H_2O)_6^{3+} + 2H_2O \rightarrow [Fe_2(OH)_2(H_2O)_8]^{4+}+ 2H_3O^+ \;\;\; K=10^{-2.91} \tag{3}$
The Fe2+ ion is barely acidic:
$Fe(H_2O)_6^{2+} + H_2O \rightarrow [Fe(OH)(H_2O)_5]^+ + H_3O^+ \;\;\; K=10^{-9.5} \tag{4}$
Rusting of Iron
The economic importance of rusting is such that it has been estimated that the cost of corrosion is over 1% of the world's economy. (25% of the annual steel production in the USA goes towards replacement of material that has corroded.) Rusting of iron consists of the formation of hydrated oxide, Fe(OH)3 or FeO(OH), and is an electrochemical process which requires the presence of water, oxygen and an electrolyte - in the absence of any one of these rusting does not occur to any significant extent. In air, a relative humidity of over 50% provides the necessary amount of water and at 80% corrosion is severe.
The process is complex and will depend in detail on the prevailing conditions, for example, in the presence of a small amount of $O_2$,
• the anodic oxidation will be:
$Fe \rightarrow Fe^{2+} + 2e^- \tag{5}$
• and the cathodic reduction:
$2H_2O + 2e^- \rightarrow H_2 + 2OH^-\tag{6}$
• i.e. overall:
$Fe + 2H_2O \rightarrow H_2 + Fe^{2+} + 2OH^-\tag{7}$
i.e Fe(OH)2 and this precipitates to form a coating that slows further corrosion.
If both water and air are present, then the corrosion can be severe with oxygen now as the oxidant
• the anodic oxidations:
$2Fe \rightarrow 2Fe^{2+} + 4e^-\tag{8}$
• and the cathodic reduction:
$O_2 + 2H_2O + 4e^- \rightarrow 4OH^-\tag{9}$
• i.e. overall:
$2Fe + O_2 + 2H_2O \rightarrow 2Fe(OH)_2\tag{10}$
with limited O2, magnetite is formed (Fe3O4), otherwise the familiar red-brown Fe2O3 H2O “rust” is found.
The presence of an electrolyte is required to provide a pathway for the current and, in urban areas, this is commonly iron(II) sulfate formed as a result of attack by atmospheric $SO_2$ but, in seaside areas, airborne particles of salt are important. The anodic oxidation of the iron is usually localized in surface pits and crevices which allow the formation of adherent rust over the remaining surface area.
The illustration above shows 2 nails immersed in an agar gel containing phenolphthalein and [Fe(CN)6]3-. The nails can be seen to have started to corrode since the Prussian blue formation indicates the formation of Fe(II) (the Anodic sites which correspond to the end of the nails and the bend in the middle). The phenolphthalein (change to pink in presence of base) shows the build up of OH- and shows that essentially the whole length of the nail is acting as the cathode.
Eventually the lateral extension of the anodic area undermines the rust to produce loose flakes. Moreover, once an adherent film of rust has formed, simply painting over gives but poor protection. This is due to the presence of electrolytes such as iron(II) sulfate in the film so that painting merely seals in the ingredients for anodic oxidation. It then only requires the exposure of some other portion of the surface, where cathodic reduction can take place, for rusting beneath the paint to occur.
The protection of iron and steel against rusting takes many forms, including: simple covering with paint; coating with another metal such as zinc (galvanizing) or tin; treating with "inhibitors" such as chromate(VI) or (in the presence of air) phosphate or hydroxide, all of which produce a coherent protective film of Fe2O3. Another method uses sacrificial anodes, most usually Mg or Zn which, being higher than Fe in the electrochemical series, are attacked preferentially. In fact, the Zn coating on galvanized iron is actually a sacrificial anode.
Rust prevention
Galvanised iron is the name given to iron that has been dipped into molten zinc (at about 450°C) to form a thin covering of zinc oxide. One level of rust prevention occurs through a purely mechanical method since it is more difficult for water and oxygen to reach the iron. Even if the layer becomes somewhat worn though another reason corrosion is inhibited is that the anodic processes are affected.
The E° for zinc oxidation (0.76V) is considerably more positive that E° for iron oxidation (0.44V) so the zinc metal is oxidized before the iron. Zn2+ is lost to the solution and the zinc coating is called a sacrificial anode.
Foodstuffs are often distributed in "tin cans" and it has generally been easier to coat the iron with a layer of tin than with zinc. Another benefit is that tin is less reactive then zinc so does not react as readily with the contents. However the electrode oxidation potential for Sn/Sn2+ is 0.14V so once again iron becomes the anode and rust will occur once the coating is worn or punctured.
Another technique is to treat the iron surface with dichromate solution.
$2 Fe + 2 Na_2CrO_4 + 2 H_2O \rightarrow> Fe_2O_3 + Cr_2O_3 + 4 NaOH$
The iron oxide coating formed has been found to be impervious to water and oxygen so no further corrosion can occur.
The Fe(III)/Fe(II) Couples
A selection of standard reduction potentials for some iron couples is given below, from which the importance of the participating ligand can be judged. Thus Fe(III), being more highly charged than Fe(II) is stabilized (relatively) by negatively charged ligands such as the anions of edta and derivatives of 8-hydroxyquinoline, whereas Fe(II) is favoured by neutral ligands which permit some charge delocalization in π-orbitals (e.g. bipy and phen).
Table 1: E° at 25°C for some FeIII/FeII couples in acid solution
FeIII FeII E°/V
[Fe(phen)3]3+ + e- [Fe(phen)3]2+ 1.12
[Fe(bipy)3]3+ + e- [Fe(bipy)3]2+ 0.96
[Fe(H2O)6]3+ + e- [Fe(H2O)6]2+ 0.77
[Fe(CN)6]3- + e- [Fe(CN)6]4- 0.36
[Fe(C2O4)3]3- + e- [Fe(C2O4)2]2- + (C2O4)2- 0.02
[Fe(edta)]- + e- [Fe(edta)]2- -0.12
[Fe(quin)3] + e- [Fe(quin)2] + quin- -0.30
where quin- = 5-methyl-8-hydroxyquinolinate,
The value of E° for the couple involving the simple aquated ions, shows that Fe(II)(aq) is thermodynamically stable with respect to hydrogen; which is to say that Fe(III)(aq) is spontaneously reduced by hydrogen gas. However, under normal circumstances, it is not hydrogen but atmospheric oxygen which is important and, for the process 1/2O2 + 2H+ + 2e- → H2O, E° = 1:229 V, i.e. oxygen gas is sufficiently strong an oxidizing agent to render [Fe(H2O)6]2+ (and, indeed, all other Fe(II) species in the Table) unstable with respect to atmospheric oxidation. In practice the oxidation in acidic solutions is slow and, if the pH is increased, the potential for the Fe(III)/Fe(II) couple remains fairly constant until the solution becomes alkaline and hydrous Fe2O3 (considered here for convenience to be Fe(OH)3) is precipitated. But here the change is dramatic, as explained below.
The Redox chemistry of Iron is pH dependent:
$Fe(H_2O)_6^{3+} + e^- \rightarrow Fe(H_2O)_6^{2+}\;\;\; E°=0.771V \tag{X}$
The actual potential E of the couple is given by the Nernst equation,
where E= E° when all activities are unity. However, once precipitation occurs, the activities of the iron species are far from unity; they are determined by the solubility products of the 2 hydroxides. These are:
[Fe(III)][OH-]2 ~ 10-14 (mol dm-3)3
and
[Fe(III)][OH-]3 ~ 10-36 (mol dm-3)4
Therefore when [OH-] =1 mol dm-3; [Fe(II)]/[Fe(III)] ~ 1022
Hence E ~ 0.771 - 0.05916 log10.(1022) = 0.771 - 1.301 = -0.530 V
Thus by making the solution alkaline the sign of E has been reversed and the susceptibility of Fe(II)(aq) to oxidation (i.e. its reducing power) enormously increased. In base the white, precipitated Fe(OH)2 and FeCO3 is a good reducing agent and samples are rapidly darkened by aerial oxidation and this explains why Fe(II) in alkaline solution will reduce nitrates to ammonia and copper(II) salts to metallic copper.
Representative complexes
An important Fe complex which is used in Actinometry since it is photosensitive is $K_3[Fe(C_2O_4)_3 \cdot 3H_2O$. It can be prepared from $Fe(C_2O_4)$ in $K_2C_2O_4$ by reacting with $H_2O_2$ in $H_2C_2O_4$ to give green crystals. It is high spin μ =5.9 BM at 30 0K and has been resolved into its two optical isomers, although they racemize in less than 1 hour.
In light, the photodissociation reaction is:
$K_3Fe(C_2O_4)_3 \cdot 3H_2O \overset{h\nu}{\longrightarrow} 2Fe(C_2O_4) + 2CO_2 + 3K_2C_2O_4 \tag{10}$
Another important complex is used as a redox indicator since the Fe(II) and Fe(III) complexes are both quite stable and have different colors
$\underset{\text{blue}}{Fe(phen)_3^{3+}} + e^- \rightarrow \underset{\text{red}}{Fe(phen)_3^{2+}} \;\;\; E°=1.12\;V \tag{11}$
The ligand is 1,10 phenanthroline and the indicator is called ferroin. An interesting example of how acetates can bind to metal ions is seen in what has been described as a "molecular ferric wheel". The structure was determined in 1990 and contains [Fe(OMe)2(O2CCH2Cl)]10. see J. Amer. Chem. Soc., 1990, 112, 9629.
Contributors and Attributions
• The Department of Chemistry, University of the West Indies) | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/21%3A_d-Block_Metal_Chemistry_-_The_First_Row_Metals/21.09%3A_Group_8_-_Iron/21.9A%3A_The_Metal.txt |
The origin of the name Cobalt is thought to stem from the German kobold for "evil spirits or goblins", who were superstitiously thought to cause trouble for miners, since the cobalt minerals contained arsenic that injured their health and the cobalt ores did not yield metals when treated using the normal methods. The name could also be derived from the Greek kobalos for "mine". Cobalt was discovered in 1735 by the Swedish chemist Georg Brandt.
Occurrence
The principal ores of Cobalt are cobaltite, [(Co,Fe)AsS], erythrite, [Co3(AsO4)2.8(H2O)], glaucodot, [(Co,Fe)AsS], and skutterudite, [CoAs3]. World production of cobalt has steadily increased in recent years, almost trebling since 1993. The dominance of African copper-cobalt producers has been replaced by a more even spread of output between leading producing countries, with Canada, Norway and more recently Australia, together with exports from Russia, replacing lost production in the Democratic Republic of Congo (Zaire). The strongest growth in production of cobalt has come from Finland, where output grew at over 16% between 1990 and 2002.
Extraction
Not covered in this course.
Uses
• Alloys, such as:
Superalloys, for parts in gas turbine aircraft engines.
Corrosion- and wear-resistant alloys. Estimated as about 20% of production in 2003
• High-speed steels.
• Cemented carbides (also called hard metals) and diamond tools.
• Magnets and magnetic recording media.
• Catalysts for the petroleum and chemical industries.
• electroplating because of its appearance, hardness, and resistance to oxidation.
• Drying agents for paints, varnishes, and inks.
• Ground coats for porcelain enamels.
• Pigments (cobalt blue, known in ancient times, and Cobalt green).
• Battery sector (e.g. electrodes) estimated as about 11% of production in 2003.
• Steel-belted radial tires.
• Cobalt-60 has multiple uses as a gamma ray source:
* It is used in radiotherapy.
* It is used in radiation treatment of foods for sterilization (cold pasteurization).
* It is used in industrial radiography to detect structural flaws in metal parts.
Cobalt compounds
Oxides
Table 1: Cobalt oxides
Formula Color Oxidation State MP Structure / comments
Co2O3 Co3+
Co3O4 black Co2+/3+ 900-950decomp normal spinel
CoO olive green Co2+ 1795 NaCl -antiferromag. < 289 K
Preparations
• Co2O3 is formed from oxidation of Co(OH)2.
• CoO when heated at 600-700°C converts to Co3O4
• Co3O4 when heated at 900-950°C reconverts back to CoO.
\[Co^{3+} + e^- \leftrightharpoons Co^{2+}\;\; 1.81\,V\]
\[Co^{2+} + 2e^- \leftrightharpoons Co \;\; -0.28\;V\]
no stable [Co(H2O)6]3+ or [Co(OH)3 exist since these convert to CoO(OH).
[Co(H2O)6]2+ not acidic and a stable carbonate exists.
Cobalt Blue
One of the earliest uses of cobalt was in the coloring of glass by the addition of cobalt salts.
The cobalt blue pigment is based on the spinel CoAl2O4 and in the laboratory can be readily synthesized by pyrolysis of a mixture of AlCl3 and CoCl2.
Halides
Cobalt(II) halides
Formula Color MP μ(BM) Structure
CoF2 pink 1200 - rutile
CoCl2 blue 724 5.47 CdCl2
CoBr2 green 678 - CdI2
CoI2 blue-black 515 - CdI2
Preparations:
Co or CoCO3 + HX → CoX2.aq → CoX2
Cobalt complexes
The Cobalt(III) ion forms many stable complexes, which being inert, are capable of exhibiting various types of isomerism. The preparation and characterization of many of these complexes dates back to the pioneering work of Werner and his students. Coordination theory was developed on the basis of studies of complexes of the type:
Werner Complexes
[Co(NH3)6]Cl3 yellow
[CoCl(NH3)5]Cl2 red
trans-[CoCl2(NH3)4]Cl green
cis-[CoCl2(NH3)4]Cl purple
Another important complex in the history of coordination chemistry is hexol. This was the first complex that could be resolved into its optical isomers that did not contain carbon atoms. Since then, only three or four others have been found.
Recently a structure that Werner apparently misassigned has been determined to be related to the original hexol although in this case the complex contains 6 Co atoms, i.e. is hexanuclear. The dark green compound is not resolvable into optical isomers.
Werner's hexol and "2nd hexol"
A noticeable difference between chromium(III) and cobalt(III) chemistry is that cobalt complexes are much less susceptible to hydrolysis, though limited hydrolysis, leading to polynuclear cobaltammines with bridging OH- groups, is well known. Other commonly occurring bridging groups are NH2-, NH2- and NO2-, which give rise to complexes such as the bright-blue amide bridged [(NH3)5Co-NH2-Co(NH3) 5]5+.
In the preparation of cobalt(III) hexaammine salts by the oxidation in air of cobalt(II) in aqueous ammonia it is possible to isolate blue [(NH3)5Co-O2-Co(NH3) 5]4+. This is moderately stable in concentrated aqueous ammonia and in the solid state but readily decomposes in acid solutions to Co(II) and O2, while oxidizing agents such as (S2O8)2- convert it to the green, paramagnetic [(NH3)5Co-O2-Co(NH3) 5]5+300 = 1.7 B.M.).
In the brown compound both cobalt atoms are Co(III) and are joined by a peroxo group, O22-, this fits with the observed diamagnetism; in addition the stereochemistry of the central Co-O-O-Co group is similar to that of H2O2. The green compound is less straightforward. Werner thought that it too involved a peroxo group but in this instance bridging between Co(III) and Co(IV) atoms.
This could account for the paramagnetism, but EPR evidence shows that the 2 cobalt atoms are equivalent, and X-ray evidence shows the central Co-O-O-Co group to be planar with an O-O distance of 131 pm, which is very close to the 128 pm of the superoxide, O2-, ion.
A more satisfactory formulation therefore is that of 2 Co(III) atoms joined by a superoxide bridge.
A range of Co(II) dioxygen complexes are known, some of which are able to reversibly bind O2 from the air. During WWII, some US aircraft carriers are reported to have used these complexes as a solid source for oxy-acetylene welding. By slightly warming the solid complex the oxygen was released and when cooled again oxygen would be coordinated again. Unlike an oxygen cylinder, the solid would not explode if hit by a stray bullet!
[CosalenO2]
A laboratory experiment designed to measure the uptake of dioxygen by Cosalen is available online.
Co(acac)3 is a green octahedral complex of Co(III). In the case of Co(II) a comparison can be made to the Ni(II) complexes.
Ni(acac)2 is only found to be monomeric at temperatures around 200C in non-coordinating solvents such as n-decane. 6-coordinate monomeric species are formed at room temperature in solvents such as pyridine, but in the solid state Ni(acac)2 is a trimer, where each Ni atom is 6-coordinate. Note that Co(acac)2 actually exists as a tetramer.
[Ni(acac)2]3 [Co(acac)2]4
Cobalt(II) halide complexes with pyridine show structural isomerism. Addition of pyridine to cobalt(II) chloride in ethanol can produce blue, purple or pink complexes each having the composition "CoCl2pyr2". The structures are 4, 5 and 6 coordinate with either no bridging chlorides or mono- or di- bridged chlorides.
blue-[CoCl2pyr2] CN=4 pink-[CoCl2pyr2] CN=6
See the notes on isomerism for examples of Co(III) compounds that show linkage and structural isomerism.
Health
see the notes at The University of Bristol on Vitamin B12 and other Cobalt species essential for good health.
Contributors and Attributions
• The Department of Chemistry, University of the West Indies)
21.10D: Cobalt(II)
The color of Co(II) complexes has interested chemists for many years and the pale-pink, octahedral to bright-blue, tetrahedral colour change is seen in such devices as weather guides and in the dye in silica gel desiccant used in the laboratory. Assignment of the bands for these spectra can present some problems however where the different stereochemistries are interpreted on each side of an F Orgel diagram.
For a typical tetrahedral complex, [CoCl4]2- and assuming Δt = 4/9 Δo where Δo is around 9000 cm-1 then we can predict that the transition
4T24A2 should be observed below 4000 cm-1. Only 1 band is seen in the visible region at 15,000 cm-1 although a full scan from the IR through to the UV reveals an additional band at 5,800 cm-1. (ε value for the 15,000 band is ~60 m2 mol-1). The lower energy band must therefore correspond to 4T1(F) ← 4A2 and the other to 4T1(P) ← 4A2 (which shows splitting thought to arise from spin-orbit coupling).
The Octahedral aqua ion
For the octahedral aqua ion, a band is observed at around 8000 cm-1 and a broad band centrrd around 20,000 cm-1 (ε for these bands is less than 1 m2 mol-1).
The lowest energy band must correspond to:
4T2g4T1g which leaves the bands at 16,000, 19,400 and 21,600 cm-1 to be assigned.
A tentative assignment puts the 4T1g(P) ← 4T1g transition at 19,400 and hence the 16,000 band is due to 4A2g4T1g.
The band at 21,600 cm-1 is believed to come from spin-orbit effects.
From this Δ ~ 9000 cm-1 and B ~ 900 cm-1.
Low spin Co(II) complexes
The ground term for the low spin case is 2Eg and looking at the right hand side of the TS diagram where Δ is quite large then it can be seen there are numerous doublet excited states. The quartets would now correspond to spin-forbidden states and be the weaker bands in the spectrum.
Contributors and Attributions
• The Department of Chemistry, University of the West Indies) | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/21%3A_d-Block_Metal_Chemistry_-_The_First_Row_Metals/21.10%3A_Group_9_-_Cobalt/21.10A%3A_The_Metal.txt |
Nickel had been in use centuries before its actual discovery and isolation. As far back as 3500 BC Syrian bronzes contained a small amount of the element. In 235 BC, coins in China were minted from nickel. However there was no real documentation of the element until thousands of years later. In the 17thcentury, German miners discovered a red colored ore they believed to contain copper. They discovered upon analysis that there was no copper but that a useless, smelly material was actually present. Thinking the ore was evil they dubbed it "Kupfernickel" or Old Nick's Copper, which meant false or bad copper. Swedish scientist Baron Axel Frederich Cronstedt in 1751 finally isolated nickel from an ore closely resembling kupfernickel. Hence, he named this new element after the traditional mineral.
At the time of its discovery nickel was thought to be useless but over time as its valuable properties came to light the demand for the metal dramatically increased. The usefulness of nickel as a material in alloys was eventually appreciated since it added to the strength, corrosion resistance and hardness of the other metals. In the 1800s, the technique of silver plating was developed with a nickel-copper-zinc alloy being utilised in the process. Today, stainless steel, another nickel containing alloy, is recognised as one of the most valuable materials of the 20th and 21st centuries.
Occurrence
Nickel is the earth's 22nd most abundant element and the 7th most abundant transition metal. It is a silver white crystalline metal that occurs in meteors or combined with other elements in ores. Two important groups of ores are:
1. Laterites: oxide or silicate ores such as garnierite, (Ni,Mg)6 Si4O10(OH)8 which are predominantly found in tropical areas such as New Caledonia, Cuba and Queensland.
2. Sulphides: these are ores such as pentlandite, (Ni,Fe)9S8 which contain about 1.5%, nickel associated with copper, cobalt and other metals. They are predominant in more temperate regions such as Canada, Russia and South Africa.
Canada is the world's leading nickel producer and the Sudbury Basin of Ontario contains one of the largest nickel deposits in the world.
Extraction of Nickel
In 1899 Ludwig Mond developed a process for extracting and purifying nickel. The so-called "Mond Process" involves the conversion of nickel oxides to pure nickel metal. The oxide is obtained from nickel ores by a series of treatments including concentration, roasting and smelting of the minerals.
In the first step of the process, nickel oxide is reacted with water gas, a mixture of H2 and CO, at atmospheric pressure and a temperature of 50 °C. The oxide is thus reduced to impure nickel. Reaction of this impure material with residual carbon monoxide gives the toxic and volatile compound, nickel tetracarbonyl, Ni(CO)4. This compound decomposes on heating to about 230 °C to give pure nickel metal and CO, which can then be recycled.
The actual temperatures and pressures used in this process may very slightly from one processing plant to the next. However the basic process as outlined is common to all.
The process can be summarised as follows:
50°C 230°C
Ni + 4CO → Ni(CO)4 → Ni + 4CO.
(impure) (pure)
Properties
Nickel is a hard silver white metal, which occurs as cubic crystals. It is malleable, ductile and has superior strength and corrosion resistance. The metal is a fair conductor of heat and electricity and exhibits magnetic properties below 345°C. Five isotopes of nickel are known.
In its metallic form nickel is chemically unreactive. It is insoluble in cold and hot water and ammonia and is unaffected by concentrated nitric acid and alkalis. It is however soluble in dilute nitric acid and sparingly soluble in dilute hydrochloric and sulphuric acids.
Nickel Compounds
Nickel is known primarily for its divalent compounds since the most important oxidation state of the element is +2. There do exist however certain compounds in which the oxidation state of the metal is between -1 to +4. Blue and green are the characteristic colors of nickel compounds and they are often hydrated.
Nickel hydroxide usually occurs as green crystals that can be precipitated when aqueous alkali is added to a solution of a nickel (II) salt. It is insoluble in water but dissolves readily in acids and ammonium hydroxide.
Nickel oxide is a powdery green solid that becomes yellow on heating.
It is difficult to prepare this compound by simply heating nickel in oxygen and it is more conveniently obtained by heating nickel hydroxide, carbonate or nitrate. Nickel oxide is readily soluble in acids but insoluble in hot and cold water.
Formula color Oxidation State MP Structure / comments
NiO green powder Ni2+ 1955 NaCl
Thermal decomposition of Ni(OH)2, NiCO3, or NiNO3 gives NiO.
Nickel sulfides consist of NiS2, which has a pyrite structure, and Ni3S4, which has a spinel structure.
All the nickel dihalides are known to exist. These compounds are usually yellow to dark brown in color. Preparation directly from the elements is possible for all except NiF2, which is best prepared from reaction of F2 on NiCl2 at 350°C. Most are soluble in water and crystallisation of the hexahydrate containing the [Ni(H2O)6]2+ ion can be achieved. NiF2 however is only slightly soluble in water from which the trihydrate crystallizes. The only nickel trihalide known to exist is an impure specimen of NiF3.
Nickel(II) halides
Formula color MP μ (BM) Structure
NiF2 yellow 1450 2.85 tetragonal rutile
NiCl2 yellow 1001 3.32 CdCl2
NiBr2 yellow 965 3.0 CdCl2
NiI2 Black 780 3.25 CdCl2
Preparations:
Ni + F2 55°C /slow → NiF2
Ni + Cl2 EtOH/ 20°C → NiCl2
Ni + Br2 red heat → NiBr2
NiCl2 + 2NaI → NiI2 + 2NaCl
Nickel carbonate usually occurs as a light green crystalline solid or a brown powder. It dissolves in ammonia and dilute acids but is insoluble in hot water. It exhibits vigorous reaction with iodine, hydrogen sulphide or a mixture of barium oxide and air. It decomposes on heating before melting occurs.
Nickel carbonyl is a colorless, volatile, liquid. It is soluble in alcohol, benzene, and nitric acid but only slightly soluble in water, and insoluble in dilute acids and alkalis. Upon heating or in contact with acid or acid fumes, nickel carbonyl emits toxic carbon monoxide gas, a property exploited in preparation of nickel metal. When exposed to heat or flame the compound explodes and it can react violently with air, oxygen and bromine.
Identification of nickel compounds can be achieved by employing the use of an organic reagent dimethylglyoxine. This compound forms a red flocculent precipitate on addition to a solution of a nickel compound.
Nickel Complexes
The Nickel (II) ion forms many stable complexes as predicted by the Irving Williams series. Whilst there are no other important oxidation states to consider, the Ni(II) ion can exist in a wide variety of CN's which complicates its coordination chemistry.
For example, for CN=4 both tetrahedral and square planar complexes can be found. For CN=5 both square pyramid and trigonal bipyramid complexes are formed.
The phrase "anomalous nickel" has been used to describe this behavior and the fact that equilibria often exist between these forms. Some examples include:
1. (a) addition of ligands to square planar complexes to give 5 or 6 coordinate species
2. (b) monomer/polymer equilibria
3. (c) square-planar/ tetrahedron equilibria
4. (d) trigonal-bipyramid/ square pyramid equilibria.
(a) substituted acacs react with Ni2+ to give green dihydrates (6 coordinate). On heating, the two coordinated water groups are generally removed to give tetrahedral species. The unsubstituted acac complex, Ni(acac)2 normally exists as a trimer, see below.
Lifschitz salts containing substituted 1,2-diaminoethanes can be isolated as either 4 or 6 coordinate species depending on the presence of coordinated solvent.
(b) Ni(acac)2 is only found to be monomeric at temperatures around 200°C in non-coordinating solvents such as n-decane. 6-coordinate monomeric species are formed at room temperature in solvents such as pyridine, but in the solid state Ni(acac)2 is a trimer, where each Ni atom is 6-coordinate. Note that Co(acac)2 actually exists as a tetramer.
[Ni(acac)2]3 [Co(acac)2]4
(c) Complexes of the type NiL2X2, where L are phosphines, can give rise to either tetrahedral or square planar complexes. It has been found that:
L=P(aryl)3 are tetrahedral
L=P(alkyl)3 are square planar
for L= mixed aryl and alkyl phosphines, both stereochemistries can occur in the same crystalline substance.
The energy of activation for conversion of one form to the other has been found to be around 50kJ mol-1.
Similar changes have been observed with variation of the X group:
Ni(PΦ3)2Cl2 green tetrahedral μ =2.83 BM
Ni(PΦ3)2(SCN)2 red sq. planar μ =0 BM
where Φ is shorthand for C6H5
Ni2+ reacts with CN- to give Ni(CN)2.nH2O (blue-green) which on heating at 180-200°C is dehydrated to yield Ni(CN)2. Reaction with excess KCN gives K2Ni(CN)4.H2O (orange crystals) which can be dehydrated at 100°C. Addition of strong concentrations of KCN produces red solutions of Ni(CN)53-.
The crystal structure of the double salt prepared by addition of Cr(en)33+ to Ni(CN)53- showed that two types of Ni stereochemistry were present in the crystals in approximately equal proportions.
50% as square pyramid and 50% as trigonal bipyramid.
Uses of Nickel and its Compounds
The primary use of nickel is in the preparation of alloys such as stainless steel, which accounts for approximately 67% of all nickel used in manufacture. The greatest application of stainless steel is in the manufacturing of kitchen sinks but it has numerous other uses as well.
Other nickel alloys also have important applications. An alloy of nickel and copper for example is a component of the tubing used in the desalination of sea water. Nickel steel is used in the manufacture of armour plates and burglar proof vaults. Nickel alloys are especially valued for their strength, resistance to corrosion and in the case of stainless steel for example, aesthetic value.
Electroplating is another major use of the metal. Nickel plating is used in protective coating of other metals. In wire form, nickel is used in pins, staples, jewellry and surgical wire. Finely divided nickel catalyses the hydrogenation of vegetable oils. Nickel is also used in the coloring of glass to which it gives a green hue.
Other applications of nickel include:
• Coinage
• Transportation and construction
• Petroleum industry
• Machinery and household appliances
• Chemical industry.
Nickel compounds also have useful applications. Ceramics, paints and dyes, electroplating and preparation of other nickel compounds are all applications of these compounds. Nickel oxide for example is used in porcelain painting and in electrodes for fuel cells. Nickel acetate is used as a mordant in the textiles industry. Nickel carbonate finds use in ceramic colors and glazes.
Nickel and Human Health
The first crystallisation of an enzyme was reported in the 1920's. The enzyme was urease which converts urea to ammonia and bicarbonate. One source of the enzyme is the bacterium Helicobacter Pylori. The release of ammonia is beneficial to the bacterium since it partially neutralizes the very acidic environment of the stomach (whose function in part helps kill bacteria). In the initial study it was claimed that there were no metals in the enzyme. Fifty years later this was corrected when it was discovered that nickel ions were present and an integral part of the system.
The Nobel Prize in Physiology or Medicine for 2005 was awarded to Barry J. Marshall and J. Robin Warren "for their discovery of the bacterium Helicobacter pylori and its role in gastritis and peptic ulcer disease".
The display below shows the crystal structure found for a Helicobacter Pylori urease [published 2001]. The nickel ions can be identified by clicking the approriate button.
Contributors and Attributions
• The Department of Chemistry, University of the West Indies) | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/21%3A_d-Block_Metal_Chemistry_-_The_First_Row_Metals/21.11%3A_Group_10_-_Nickel/21.11A%3A_Chromium_Metal.txt |
Information on the history of Copper is available at the Copper Development Association, Inc where they make the point that: "For nearly 5000 years copper was the only metal known to man. Today it is one of the most used and reused of our modern metals." Humans first used copper about 10,000 years ago. A copper pendant discovered in Northern Iraq is thought to date back to around 8700 BC. Prehistoric man probably used copper for weapon making. Ancient Egyptians too seemed to have appreciated the corrosion resistance of the metal. They used copper bands and nails in ship building and copper pipes were used to convey water. Some of these artifacts survive today in good condition. An estimate of the total Egyptian copper output over 1500 years is 10,000 tons.
Years later, copper alloys appeared. Bronzes (copper-tin alloys) came about first followed much later by brass (copper-zinc alloys). The " Bronze Age" saw the extensive use of copper and bronze for arms, coins, household utensils, furniture and other items. The earliest known example of brass use is a Roman coin minted during the reign of Augustus 27 BC- AD 14. Copper later played an important role in the advent of electricity and today is still among our most valued materials.
Usage of copper compounds also dates back to before 4000 BC. Copper sulphate for example was an especially important compound in early times. Ancient Egyptians used it as a mordant in their dyeing process. The compound was also used to make ointments and other such preparations. Later, medicinal use of copper sulphate came about with its prescription for pulmonary diseases. Copper sulphate is still extensively used today and no harmful side effects of its prescribed use have been reported.
Occurrence
Copper is the earth's 25th most abundant element, but one of the less common first row transition metals. It occurs as a soft reddish metal that can be found native as large boulders weighing several hundred tons or as sulphide ores. The latter are complex copper, iron and sulphur mixtures in combination with other metals such as arsenic, zinc and silver. The copper concentration in such ores is typically between 0.5-2%.
The commonest ore is chalcopyrite, CuFeS2, a brass yellow ore that accounts for approximately 50% of the world's copper deposits. Numerous other copper ores of varying colors and compositions exist. Examples are malachite, Cu2CO3(OH)2, a bright green ore, and the red ore cuprite, Cu2O.
Copper occurs in biological systems as a part of the prosthetic group of certain proteins. For examples of copper containing proteins see the article originally from the University of Leeds, Department of Biochemistry and Molecular Biology at the Scripps Institute. The red pigment in the softbilled T(o)uraco Bird contains a copper porphyrin complex. The pigment is highly water soluble under alkaline conditions and it was reported in 1952 that attempts by zookeepers to wash a bird resulted in the water becoming tinged with red. T(o)uracos are said to be the only birds to possess true red and green color. Generally, the color you perceive when observing birds, is due to reflections produced by the feather structure. The red and green pigments (turacin and turacoverdin) found in the feathers of the T(o)uraco both contain copper.
The Extraction of Copper
Copper is extracted from its ore by two principal methods:
1. Pyrometallurgical method
2. Hydrometallurgical method
Pyrometallurgical Method
This technique is often used in the extraction of sulphide ores. There are four main stages:
• Mining and Milling: The ore is crushed and ground into a powder usually containing less than 1% copper. Minerals are concentrated into a slurry that is about 15% copper. Copper minerals are separated from useless material by flotation using froth forming solutions.
• Smelting: Smelting of the copper concentrate and extraction by heat, flux and addition of oxygen. Sulfur, iron and other undesirable elements are removed and the product is called blister copper.
• Refining: This is the final stage in the process for obtaining high grade copper. Fire and electro-refining methods are the techniques used. The latter produces high purity copper fit for electrical uses.
Hydrometallurgical Method -SX/EW
Solvent Extraction / Electrowinning is the most dominant leaching process used today in the recovery of copper from chemical solutions. As the name suggests the method involves two major stages:
• Solvent Extraction- the process by which copper ions are leached or otherwise extracted from the raw ore using chemical agents.
• Electrowinning- electrolysis of a metal ion containing solution such that Cu ions within it are plated onto the cathode and thereafter removed in elemental form.
The process takes place in the following steps:
• A lixivant (leaching solution) is selected for use in leaching Cu ions from the ore. Common reagents are weak acids e.g. H2SO4, H2SO4 + Fe2(SO4)3, acidic chloride solutions e.g. FeCl2, ammonium chloride and ammonium salt compositions.
• When applied to the ore the chosen lixivant dissolves the copper ions present to give a lixivant product called a "pregnant leach solution".
• An organic extractant is then selected to remove Cu ions from the aqueous solution. Preferred organic extractants consist of hydroxyphenyl oximes having the basic chemical formula:
• C6H3 (R)(OH) CNOHR*, R= C9H19 or C12H25 and R*= H, CH3, or C6H5
Examples of such extractants are 5-nonylsalicylaldoxime and a mixture of this compound and 2-hydroxy-5-nonyl-acetophenone oxime. The commercially available reagents usually contain 5%-10% of the oxime in a 90-95% petroleum dilutant such as kerosene.
Prior to mixing with lixivant product the extractant will contain little or no copper and is at this stage called the "barren organic extractant".
• Copper ions are transferred from the leaching solution to the organic extractant upon mixing of the two reagents. A phase separation takes place to give an aqueous and an organic phase termed the first aqueous and first organic phases respectively. The first aqueous phase, the "raffinate", is the lixivant stripped of its copper ions while the first organic phase is the "loaded organic extractant" i.e. extractant with copper ions present.
• The raffinate is recycled to the leaching pad while the loaded organic extractant is mixed with an electrolyte solution called the "lean electrolyte" (i.e. containing no copper). Typical electrolytes are acidic solutions such as sulphuric acid, H2SO4. The copper ions that were present in the organic extractant thus dissolve in the electrolyte solution to give a copper containing "rich electrolyte." Here again there is a phase separation. The second organic phase is the barren organic extractant while the second aqueous phase is the "rich electrolyte". The barren organic extractant is then recycled for reuse in application to lixivant product.
• The final stage of the process is the electrolysis of the acidic metal ion solution. As a result dissolved copper ions become plated onto the cathode and elemental copper is removed. The recovery process is thus complete.
A Note on Impurities
The presence of suspended contaminants within a SX/EW system can significantly compromise its operating efficiency. Such contaminants may be introduced into the system from the ore or from the surroundings. The system is susceptible to contamination from rain, wind and other environmental forces since the first containment vessel, which stores lixivant product, is typically uncovered and located outdoors. Thus solid waste material in the form of dirt, sand, rock dust, vegetable matter, mineral residue and suspended solids is often introduced into the system in the early stages and persists in the subsequent stages of the process.
The effects of these contaminants are considerable and include:
• increased phase separation time at stages when organic and aqueous solvents are mixed.
• lack of complete phase separation after extraction, this results in loss of expensive organic extractant since much of it remains within the aqueous solution.
• a decrease in the current efficiency and reduction in the purity of the plated copper product in the electrolysis stage.
In most SX/EW systems purification steps have been introduced in order to alleviate this problem. In US patent (number 573341) for example, at least a portion of the second organic phase is filtered to remove solid contaminants before reuse in treating lixivant product. The recycled organic extractant therefore contains little or no impurities dependent on whether a portion or the entire second organic phase was filtered. It has been found that this filtration step considerably improves the operating efficiency, even when only a portion of the extractant is treated.
Uses of copper and its compounds
Copper is second only to iron in its usefulness down the ages. The metal and its compounds are used in every sphere of life from the electrical to medicinal and agricultural industries.
Uses of copper metal
The electrical industry is the beneficiary of most of the world's copper output. The metal is used in the manufacture of electrical apparatus such as cathodes and wires. Other uses include:
• Roofing
• Utensils
• Coins
• Metal work
• Plumbing
• Refrigerator and Air Conditioning coils
• Alloys e.g. bronze, brass
Uses of copper compounds
Copper compounds have their most extensive use in Agriculture. Since the discovery of their toxicity to certain insects, fungi and algae these compounds have been used in insecticides, fungicides and to prevent algal development in potable water reservoirs. They are therefore used in the control of animal and plant diseases. Fertilisers are also often supplemented with copper compounds, e.g. copper sulphate, in order to increase soil fertility and thus boost crop growth. Copper compounds are also used in photography and as colorants for glass and porcelain.
Copper for Good Health
Copper is one of many trace elements required for good health. It is part of the prosthetic groups of many proteins and enzymes and thus is essential to their proper function. Since the body can not synthesize copper it must be taken in the diet. Nuts, seeds, cereals, meat (e.g. liver) and fish are good sources of copper.
Copper has also found medicinal use. It has been used from early times in the treatment of chest wounds and water purification. It has recently been suggested that copper helps to prevent inflammation associated with arthritis and such diseases. Research continues into medicines containing copper for treatment of this and other conditions.
Copper Compounds
Copper exhibits a variety of compounds, many of which are colored. The two principal oxidation states of copper are +1 and +2 although some +3 complexes are known. Copper(I) compounds are expected to be diamagnetic in nature and are usually colorless, except where color results from charge transfer or from the anion. The +1 ion has tetrahedral or square planar geometry. In solid compounds, copper(I) is often the more stable state at moderate temperatures.
The copper(II) ion is usually the more stable state in aqueous solutions. Compounds of this ion, often called cupric compounds, are usually colored. They are affected by Jahn Teller distortions and exhibit a wide range of stereochemistries with four, five, and six coordination compounds predominating. The +2 ion often shows distorted tetrahedral geometry.
Copper Halides
All of the copper(I) halides are known to exist although the fluoride has not yet been obtained in the pure state. The cuprous chlorides, bromides and iodides are colouless, diamagnetic compounds. They crystallize at ordinary temperatures with the zinc blende structure in which Cu atoms are tetrahedrally bonded to four halogens. The copper(I) chloride and bromide salts are produced by boiling an acidic solution of copper(II) ions in an excess of copper. On dilution, the white CuCl or the pale yellow CuBr is produced. Addition of soluble iodide to an aqueous solution of copper(II) ions results in the formation of a copper(I) iodide precipitate, which rapidly decomposes to Cu(I) and iodine.
The copper(I) halides are sparingly soluble in water and much of the copper in aqueous solution is in the Cu(II) state. Even so, the poor solubility of the copper(I) compounds is increased upon addition of halide ions. The table below shows some properties of copper(I) halides.
Copper(II) halides
Formula color MP BP m (BM) Structure
CuF2 white 950decomp - 1.5
CuCl2 brown 632 993decomp 1.75 CdCl2
CuBr2 black 498 - 1.3
All four copper(II) halides are known although cupric iodide rapidly decomposes to cuprous iodide and iodine. The yellow copper(II) chloride and the almost black copper(II) bromide are the common halides. These compounds adopt a structure with infinite parallel bands of square CuX4 units. Cupric chlorides and bromides are readily soluble in water and in donor solvents such as acetone, alcohol and pyridine.
Copper(II) halides are moderate oxidising agents due to the Cu(I)/ Cu(II) couple. In water, where the potential is largely that of the aqua-complexes, there is not a great deal of difference between them, but in non-aqueous media, the oxidising (halogenating) power increases in the sequence;
\[\ce{CuF2 \ll CuCl2 \ll CuBr2}\]
They can be prepared by direct reaction with the respective halogens:
\[\ce{Cu + F2 → CuF2}\]
\[\ce{Cu + Cl2 / 450 C → CuCl2}\]
\[\ce{Cu + Br2 → CuBr2}\]
Alternatively they can be prepared from CuX2.aq by heating -> CuX2
Copper(I) halides
Formula color MP BP Structure
CuCl white 430 1359 -
CuBr white 483 1345 -
CuI white 588 1293 Zinc Blende
Prepared by reduction of CuX2 -> CuX;
except for the F which has not been obtained pure.
Note that CuI2 has not been isolated because of the ease of reduction to CuI.
Copper Oxides
Copper(I) oxides are more stable than the copper(II) oxides at high temperatures. Copper(I) oxide occurs native as the red cuprite. In the laboratory, the reduction of Fehling's solution with a reducing sugar such as glucose produces a red precipitate. The test is sensitive enough for even 1 mg of sugar to produce the characteristic red color of the compound. Cuprous oxide can also be prepared as a yellow powder by controlled reduction of an alkaline copper(II) salt with hydrazine. Thermal decomposition of copper(II) oxide also gives copper(I) oxide since the latter has greater thermal stability. The same method can be used to prepare the compound from the copper(II) nitrate, carbonate and hydroxide.
Copper(II) oxide occurs naturally as tenorite. This black crystalline solid can be obtained by the pyrolysis of the nitrate, hydroxide or carbonate salts. It is also formed when powdered copper is heated in air or oxygen. The table below shows some characteristics of copper oxides.
Copper oxides
Formula color Oxidation State MP
CuO black Cu2+ 1026decomp
Cu2O red Cu+ 1230
Redox Chemistry of Copper
Cu2+ + e- → Cu+ E=0.15V
Cu+ + e- → Cu E=0.52V
Cu2+ + 2e- → Cu E=0.34V
By consideration of this data, it will be seen that any oxidant strong enough to covert Cu to Cu+ is more than strong enough to convert Cu+ to Cu2+ (0.52 cf. 0.14V). It is not expected therefore that any stable Cu+ salts will exist in aqueous solution.
Disproportionation can also occur:
2Cu+ → Cu2+ + Cu E=0.37V or K=106
Coordination complexes
The reaction of EDTA4- with copper(II) gave a complex where the EDTA was found to be pentadentate NOT hexadentate, unlike other M(II) ions.
Cu(EDTA)2-
The structure of the [Cu(ox)2]2- ion can be described as square planar or as a distorted octahedron when the packing in the crystal lattice is considered. In the case of the sodium salt, the individual units are parallel in the cell with the copper linked to the oxygens coordinated to the copper in the units sitting both above and below, whereas in the potassium salt, the units are not parallel and when looking at three units the central one is almost at right angles to the other two. Here the copper is linked to one of the non-coordinated oxygens in the units above and below it.
Na+ and K+ salts of [Cu(ox)2]2-
Cu(OH)2 reacts with NH3 to give a solution which will dissolve cellulose. This is exploited in the industrial preparation of Rayon. The solutions contain tetrammines and pentammines. With pyridine, only tetramines are formed eg Cu(py)4SO4.
The reaction of copper(II) with amino-acids has been extensively studied. In nearly all cases the product contains the groups in a trans configuration, which is expected to be the more stable. In the case of glycine, the first product precipitated is always the cis- isomer which converts to the trans- on heating. See the Laboratory Manual for C31L for more details.
Analytical Determination of Copper(II)
A useful reagent for the analytical determination of the copper(II) ion is the sodium salt of N,N-diethyldithiocarbamate. In dilute alcohol solutions the presence of trace levels of Cu2+ is indicated by a yellow color, which can be measured by a spectrophotometer, and the concentration determined from a Beer's Law plot. The complex is Cu(Et2dtc)2, which can be isolated as a brown solid.
Cu(Et2dtc)2
Contributors and Attributions
• The Department of Chemistry, University of the West Indies)
21.13A: The Metal
Occurrence and extraction of zinc from zinc blende
Zinc occurs only in combined state. The important ores of zinc are zinc blende (Zns), calamine etc. These two are the important ores for the extraction of zinc.
Extraction
Zinc blende is crushed, concentrated and heated in air.
$2ZnS + 3O_2 \rightarrow 2ZnO + 2SO_2$
Zinc oxide formed above is mixed with coke in a fireclay retort. It is fitted with a condenser. The metal distills and condenses in the retort. The metal obtained is purified by electrolysis.
$ZnO (s) + C (s) \rightarrow Zn + CO(g)$ | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/21%3A_d-Block_Metal_Chemistry_-_The_First_Row_Metals/21.12%3A_Group_11_-_Copper/21.12A%3A_Copper_Metal.txt |
Heavy metals are generally defined as metals with relatively high densities, atomic weights, or atomic numbers. The criteria used, and whether metalloids are included, vary depending on the author and context. In metallurgy, for example, a heavy metal may be defined on the basis of density, whereas in physics the distinguishing criterion might be atomic number, while a chemist would likely be more concerned with chemical behavior. More specific definitions have been published, but none of these have been widely accepted.
22: d-Block Metal Chemistry - The Heavier Metals
Group 3 is a group of elements in the periodic table. This group, like other d-block groups, should contain four elements, but it is not agreed what elements belong in the group. Scandium (Sc) and yttrium (Y) are always included, but the other two spaces are usually occupied by lanthanum (La) and actinium (Ac), or by lutetium (Lu) and lawrencium (Lr); less frequently, it is considered the group should be expanded to 32 elements (with all the lanthanides and actinides included) or contracted to contain only scandium and yttrium. When the group is understood to contain all of the lanthanides, its trivial name is the rare-earth metals.
• Wikipedia
22.04: Group 3 - Yttrium
In 1787, Carl Axel Arrhenius found a new mineral near Ytterby in Sweden and named it ytterbite, after the village. Johan Gadolin discovered yttrium's oxide in Arrhenius' sample in 1789, and Anders Gustaf Ekeberg named the new oxide yttria. Elemental yttrium was first isolated in 1828 by Friedrich Wöhler.Yttrium is a chemical element with symbol Y and atomic number 39. It is a silvery-metallic transition metal chemically similar to the lanthanides and has often been classified as a "rare-earth element". Yttrium is almost always found in combination with lanthanide elements in rare-earth minerals, and is never found in nature as a free element. 89Y is the only stable isotope, and the only isotope found in the Earth's crust.
22.4B: Yttrium(III) Ion
As a trivalent transition metal, yttrium forms various inorganic compounds, generally in the oxidation state of +3, by giving up all three of its valence electrons. A good example is yttrium(III) oxide ($\ce{Y2O3}$), also known as yttria, a six-coordinate white solid.
Yttrium forms a water-insoluble fluoride, hydroxide, and oxalate, but its bromide, chloride, iodide, nitrate and sulfate are all soluble in water. The $\ce{Y^{3+}}$ ion is colorless in solution because of the absence of electrons in the d and f electron shells. With halogens, yttrium forms trihalides such as yttrium(III) fluoride ($\ce{YF3}$), yttrium(III) chloride ($\ce{YCl3}$), and yttrium(III) bromide ($\ce{YBr3}$) at temperatures above roughly 200 °C.
$\ce{2 Y(s) + 3F2 \rightarrow YF3(s)}$
Similarly, carbon, phosphorus, selenium, silicon and sulfur all form binary compounds with yttrium at elevated temperatures.
Water readily reacts with yttrium and its compounds to form $\ce{Y2O3}$. Concentrated nitric and hydrofluoric acids do not rapidly attack yttrium, but other strong acids do.
Organoyttrium chemistry is the study of compounds containing carbon-yttrium bonds. They are studied in academic research, but have not received widespread use otherwise. These compounds use $\ce{YCl3}$ as a starting material, which is in turn obtained in a reaction of $\ce{Y2O3}$ with concentrated hydrochloric acid and ammonium chloride.
Hapticity is a term to describe the coordination of a group of contiguous atoms of a ligand bound to the central atom; it is indicated by the Greek character eta, $η$. Yttrium complexes were the first examples of complexes where carboranyl ligands were bound to a d0-metal center through a η7-hapticity. Vaporization of the graphite intercalation compounds graphite–Y or graphite–Y2O3 leads to the formation of endohedral fullerenes such as Y@C82. Electron spin resonance studies indicated the formation of $\ce{Y^{3+}}$ and (C82)3− ion pairs. The carbides Y3C, Y2C, and YC2 can be hydrolyzed to form hydrocarbons.
• Wikipedia
22.5B: Zirconium(IV) and Hafnium(IV)
Group 4 is a group of elements in the periodic table. It contains the elements titanium (Ti), zirconium (Zr), hafnium (Hf) and rutherfordium (Rf). This group lies in the d-block of the periodic table. The group itself has not acquired a trivial name; it belongs to the broader grouping of the transition metals. Like other groups, the members of this family show patterns in its electron configuration, especially the outermost shells resulting in trends in chemical behavior:
• Wikipedia
22.05: Group 4 - Zirconium and Hafnium
As tetravalent transition metals, all three elements form various inorganic compounds, generally in the oxidation state of +4. For the first three metals, it has been shown that they are resistant to concentrated alkalis, but halogens react with them to form tetrahalides. At higher temperatures, all three metals react with oxygen, nitrogen, carbon, boron, sulfur, and silicon. Because of the lanthanide contraction of the elements in the fifth period, zirconium and hafnium have nearly identical ionic radii. The ionic radius of Zr4+ is 79 picometers and that of Hf4+ is 78 pm.
22.10A: The Metals
Ruthenium is a chemical element with symbol Ru and atomic number 44. It is a rare transition metal belonging to the platinum group of the periodic table. Like the other metals of the platinum group, ruthenium is inert to most other chemicals. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/22%3A_d-Block_Metal_Chemistry_-_The_Heavier_Metals/22.04%3A_Group_3_-_Yttrium/22.4A%3A_The_Metal.txt |
Mercury is a heavy, silvery d-block metal that forms weak bonds and is a liquid at room temperature.
LEARNING OBJECTIVE
• Identify mercury based on its physical properties.
KEY POINTS
• Mercury is the only metal that is liquid at standard conditions for temperature and pressure.
• Mercury is a poor conductor of heat, but a fair conductor of electricity.
• Mercury has a unique electron configuration which strongly resists removal of an electron, making it behave similarly to noble gas elements. As a result, mercury forms weak bonds and is a liquid at room temperature.
• Mercury dissolves to form amalgams with gold, zinc, and many other metals.
TERM
• amalgam
An alloy containing mercury.
Properties of Mercury
Mercury is a dense, silvery d-block element. It is the only metal that is liquid at standard conditions for temperature and pressure. The only other element that is liquid under these conditions is bromine, though metals such as caesium, gallium, and rubidium melt just above room temperature. With a freezing point of −38.83 °C and boiling point of 356.73 °C, mercury has one of the narrowest liquid state ranges of any metal. Mercury occurs in deposits throughout the world mostly as cinnabar (mercuric sulfide), an ore that is highly toxic by ingestion or inhalation. Mercury poisoning can also result from exposure to water-soluble forms of mercury (such as mercuric chloride or methylmercury), inhalation of mercury vapor, or ingestion of seafood contaminated with mercury.
Compared to other metals, mercury is a poor conductor of heat, but a fair conductor of electricity. Mercury has a unique electronic configuration which strongly resists removal of an electron, making mercury behave similarly to noble gas elements. The weak bonds formed by these elements become solids which melt easily at relatively low temperatures.
Mercury
Mercury is a silvery metal that is liquid at standard temperature and pressure (STP).
Reactivity and Amalgams
Mercury does not react with most acids, although oxidizing acids such as concentrated sulfuric acid and nitric acid dissolve it to give sulfate, nitrate, and chloride salts. Like silver, mercury reacts with atmospheric hydrogen sulfide. Mercury even reacts with solid sulfur flakes, which are used in mercury spill kits to absorb mercury vapors.
Mercury dissolves to form amalgams with gold, zinc, and many other metals. Iron is an exception, and iron flasks have been traditionally used to trade mercury. Sodium amalgam is a common reducing agent in organic synthesis, and it is also used in high-pressure sodium lamps. Mercury readily combines with aluminium to form a mercury-aluminium amalgam when the two pure metals come into contact. Since the amalgam destroys the aluminium oxide layer which protects metallic aluminium from oxidizing, even small amounts of mercury can seriously corrode aluminium. For this reason, mercury is not allowed aboard an aircraft under most circumstances because of the risk in forming an amalgam with exposed aluminium parts.
Uses of Mercury
Mercury is used in thermometers, barometers, manometers, float valves, mercury switches, and other devices. Concerns about the element's toxicity have led to mercury thermometers being largely phased out in clinical environments in favor of alcohol-filled instruments. Mercury is still used in scientific research and as amalgam material for dental restoration. It is also used in lighting—electricity passed through mercury vapor in a phosphor tube produces short-wave ultraviolet light, causing the phosphor to fluoresce and produce visible light. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/22%3A_d-Block_Metal_Chemistry_-_The_Heavier_Metals/22.13%3A_Group_12_-_Cadmium_and_Mercury/22.13A%3A_The_Metals.txt |
Main Group Organometallic Chemistry
Introduction
Organometallic compounds have been known and studied for over 250 years. Many of these early compounds were prepared directly from the metal by oxidative addition of alkyl halides. All these metals have strong or moderately negative reduction potentials, with lithium and magnesium being the most reactive. Halide reactivity increases in the order: Cl < Br < I.
In 1757 Louis Claude Cadet de Gassicourt prepared what is believed to be the first synthetic organometallic compound and it was isolated from arseneous oxide (As2O3) and potassium acetate. The mixture was named after him "Cadet's fuming liquid" from which came cacodyl oxide.
4 KCH3COO + As2O3 → As2(CH3)4O + 4 K2CO3 + CO2 → → As2(CH3)4
which disproportionates to produce among other things cacodyl, As2(CH3)4. The poisonous garlic-smelling red oily-liquid is unstable undergoing spontaneous combustion in dry air.
Another organoarsenic compound, Salvarsan, was one of the first pharmaceuticals, and earned a Nobel Prize in Medicine for Paul Ehrlich in 1908 (jointly with Ilya Ilyich Mechnikov). Its activity against syphilis was discovered as a result of the first largescale testing of chemicals and had a code name of 606 since it was apparently the 606th chemical that had been tested in Ehrlich's laboratory in his quest for the "magic bullet". The compound was synthesised by reaction of 3-nitro-4- hydroxyphenylarsonic acid with dithionite.
The structure has only recently been characterised as a mixture of polyarsines (AsR)n n= 3-6, and originally it was proposed that it was a dimer with an As=As double bond.
trimer
pentamer
Edward Frankland prepared the first organozinc compound (diethylzinc) in 1848 from zinc metal and ethyl iodide, he went on to improve the synthesis of diethylzinc by using diethyl mercury as starting material.
2R-X + 2Zn → R2Zn + ZnX2
Grignard reagents are formed via the action of an alkyl or aryl halide on magnesium metal.
R-X + Mg → R-Mg-X
Victor Grignard was jointly awarded the 1912 Nobel Prize in Chemistry.
Carl Jacob Lowig (1803-1890) reported the preparation of the first alkyltin and alkyllead compounds in 1852/3. He reacted ethyl iodide and Sn/Na or Pb/Na alloy
Wilhelm Johann Schlenk discovered organolithium compounds around 1917.
R-X + 2Li → R-Li + LiX
He also investigated free radicals and carbanions and discovered (together with his son) that organomagnesium halides are capable of participating in a complex chemical equilibrium, now known as a Schlenk equilibrium.
2RMgX → MgX2 + MgR2
Karl Ziegler
His work with free radicals led him to the organo compounds of the alkali metals. He discovered that ether scission opened a new method of preparing sodium and potassium alkyls; later (1930) he directly synthesized lithium alkyls and aryls from metallic lithium and halogenated hydrocarbons. This important discovery made the lithium compounds as readily available as the familiar Grignard reagents.
Ziegler is perhaps best remembered for his work with Giulio Natta on what are called Ziegler-Natta catalysts. These catalysts are typically based on titanium compounds and organometallic aluminium compounds, such triethylaluminium, (C2H5)3Al and are used to polymerize terminal 1-alkenes.
n CH2=CHR → -[CH2-CHR]n-
Together they won the Nobel Prize in Chemistry in 1963.
Classification of organometallic compounds
Examples will be selected from the circled elements.
The organometallic compounds to be considered in this course are those containing a M-C bond, excluding carbonyls (M-CO), cyanides (M-CN) or carbides (M-C). A useful subdivision is by the type of M-C bond:
• ionic - with most Group 1 elements
• covalent - with many Group 12, 13, 14 and 15 elements
• electron deficient - with Li, Be, Mg, B, Al
Ionic
Ionic organometallic compounds are generally formed from elements such as sodium, potassium etc. where the metals are considered electropositive. If the organic groups are able to delocalise the negative charge over several carbon atoms then less electropositive elements like magnesium can also form ionic compounds, eg Cp2Mg. In this case the charge is considered to be delocalised over each of the five carbon atoms in each ring.
Covalent
The simplest model of the M-C bond is where it consists of essentially a single covalent 2-electron bond. These compounds are often volatile and are comparable to typical organic compounds being soluble in organic solvents.
Electron deficient
Electron deficient organometallic compounds are generally associated with elements that have less than half-filled valence shells and are designated as such because of an insufficient number of valence electrons to allow all the atoms to be linked by traditional two-electron two-centre bonds. The compounds often have bridged or polymeric structures. The methyl derivatives of Li, Be and Al are found to be 3-D polymers, linear chains and dimeric respectively and despite the increase in RMM of the monomeric unit there is actually an increase in volatility.
Compound RMM of monomeric unit Structure Volatility
LiMe 21.96 3D-polymer infusible
BeMe2 39.08 Linear chain sublimes at 473 K
AlMe3 72.08 Dimer Melts at 288 K
There has been some criticism of the term electron deficient since if a MO approach to the bonding is used then the bonding MO's derived from combination of the available atomic orbitals of suitable energy are generally full. Rundle (who determined the structure of BeMe2) is reported to have made the comment that:
There is no such thing as electron deficient compounds, only theory deficient chemists.
Stability of Organometallic compounds
The M-C bond energies for some methyl derivatives are shown in the Table below. Plotting these values against Atomic Number of the metal shows that there is a decrease down a Group. This behaviour is expected since there should be better orbital overlap between similar valence orbitals and this would decrease for the larger more diffuse elements lower down a Group.
Bond dissociation energies and Heats of Formation
Me2M D / kJ mol-1 ΔHf / kJ mol-1 BP /K Me3M D / kJ mol-1 ΔHf / kJ mol-1 BP /K Me4M D / kJ mol-1 ΔHf / kJ mol-1 BP /K
Me2Be 490.2 Me3B 364.0 -122.6 251.2 Me4C 347.3 -167.4 283.2
Me2Mg Me3Al 276.1 -129.7 399.2 Me4Si 292.9 -238.5 300.2
Me2Zn 175.7 54.8 317.2 Me3Ga 246.9 -45 329.2 Me4Ge 246.9 -71 316.2
Me2Cd 138.1 109.6 379.2 Me3In 171.5 409.2 Me4Sn 217.6 -19.2 350.2
Me2Hg 121.3 93.3 366.2 Me3Tl 420.2 Me4Pb 154.8 136.4 383.2
Me3As 230.1 15.5 325.2
Me3Sb 217.6 31.0 352.2
Me3Bi 142.3 192.9 383.2
Thermal Stability
In general terms thermodynamic stability means that the ΔG° is negative i.e. the energy of the products is more stable than that of the starting materials. Since little free energy data is available, it is often assumed that ΔH can be considered as a guide remembering that the entropies of gases are much larger than for liquids, which is again much larger than for solids and this can be taken into account as well.
if we take as an example the thermal decomposition of EtLi:
EtLi → LiH + CH2=CH2
ΔHf EtLi = -58.55 kJ mol-1
ΔHf CH2=CH2 = +52.40 kJ mol-1
ΔHf LiH = -90.45 kJ mol-1
so that the overall enthalpy change is: = (RHS - LHS) = 52.40 - 90.45 + 58.55
= +20.50 kJ mol-1
This therefore suggests that the data favours the stability of EtLi over the products. However, given that at room temperature the Entropy of gaseous ethylene (ethene) is high TΔS = +64.4 kJ mol-1 and the entropies for solids will be much smaller, then using ΔG = ΔH - TΔS it is likely that ΔG will be a sizable NEGATIVE value which would suggest that EtLi should be unstable.
Kinetic Stablity
Calculations of free energy would suggest that many organometallic compounds should be unstable. However, kinetic stability needs to be considered as well since if there is no low activation energy pathway for a reaction to proceed then it may be very slow.
Stability to Oxidation
All organometallic compounds are expected to be thermodynamically unstable with respect to oxidation to give metal oxide, carbon dioxide and water. Some are spectacularly so, being highly pyrophoric. In general organometallic compounds need to be handled under dry nitrogen or some other inert gas to avoid oxidation.
Stability to Hydrolysis
Hydrolysis of organometallic compounds often involves nucleophilic attack by water which is accentuated when there are low-lying empty orbitals on the metal atom. This is seen for Groups I, II and for Zn, Cd, Al, Ga etc and the speed of hydrolysis is dependent on the M-C bond polarity. For "Me3Al" rapid attack occurs whereas Me3B is unaffected at room temperature.
Classification of Synthetic Reactions
1. Elemental Reactions
a) with organic halides - the most important method
eg RX + M → RM + MX
b) with hydrocarbons
i)substitution
where the hydrocarbons are acidic
eg RC≡C-H + K → RC≡C-K + ½H2
eg R + K → RK + ½H2
ii) addition
eg Na + naphthalene → Na+ naphth- (C8H10)-
c) with other organometallics - transmetallation
eg M + M'R → MR + M'
2. Reactions with Element halides or salts
a) with hydrocarbons
eg RH + HgX2 → RHgX + HX
b) with other organometallics
eg MX + M'R → M'X + MR
3. Addition and Elimination Reactions
a) addition
eg -M-X + RHC=CH2 → M-C-C-X
Ph3SnH + PhCH=CH2 → Ph3SnCH2CH2.Ph
b) elimination
eg -M-A-B-C → -M-C + A=B
Hg(-OOC-R)2 + heat → HgR2 + 2CO2
Contributors and Attributions
• The Department of Chemistry, University of the West Indies)
23.01: Introduction
Learning Objectives
In this lecture you will learn the following
• Various synthetic methodologies to make M—C bonds.
• How to choose an appropriate synthetic method.
• Reaction conditions and the role of solvents.
An organometallic compound contains one or more metal-carbon bonds.
Synthesis
General Methods of Preparation
Most organometallic compounds can be synthesized by using one of four M-C bond forming reactions of a metal with an organic halide, metal displacement, metathesis and hydrometallation.
The net reaction of an electropositive metal M and a halogen-substituted hydrocarbon is
If, one metal atom takes the place of another, it is called transmetallation
Transmetallation is favorable when the displacing metal is higher in the electrochemical series than the displaced metal.
1. Reaction with metal and transmetallation
Metathesis
The metathesis of an organometallic compound MR and a binary halide EX is a widely used synthetic route in organometallic chemistry.
Metathesis reaction can frequently be predicted from electronegativity or hard and soft acid-base considerations.
Hydrocarbon groups tends to bond to the more electronegative element; the halogen favors the formation of ionic compounds with the more electropositive metal.
In brief, the alkyl and aryl group tends to migrate from the less to the more electronegative element [χ = electronegativity].
When the electronegativities are similar, the correct outcome may be predicted, with care*, by considering the combination of the softer element with organic group and harder element with fluoride or chloride.
*An insoluble product or reactant may change the outcome, e.g.;
HgPhBr turns out to be insoluble in THF
Metathesis reactions involving the same central element are often referred to as redistribution reactions.
Al is more electropositive than Ge, this reaction occurs as it is thermodynamically favorable.
Hydrometallation
The net outcome of the addition of a metal hydride to an alkene is an alkylmetal compound.
The reaction is driven by the high strength of E-C bond relative to that of most E-H bonds, and occurs with a wide variety of compounds that contain E-H bonds.
Hydroboration
Hydrosilylation
Ionic and electron-deficient compounds of Group 1, 2
Organometallic derivatives of all Group 1 metals are known. Amongst, the alkyllithium compounds are most thoroughly studied and useful reagents.
Many of them are commercially available.
MeLi is generally handled in ether solution, but RLi compounds with longer chains are soluble in hydrocarbons.
Commercial preparation:
The best method would be:
MeLi exists as a tetrahedral cluster in the solid state and in the solution. Many of its higher homologs exist in solution as hexamers or equilibrium mixture of aggregates ranging up to haxamers.
The larger aggregates can be broken down by Lewis bases, such as, TMEDA.
Common organolithium compounds have one Li per organic group.
Several polylithiated organic molecules containing several lithium atoms per molecule are known.
Ionic and electron-deficient compounds of Group 1, 2 (contd..)
The simplest example is Li2CH2, which can be prepared by the pyrolysis of MeLi which crystallizes in a distorted antifulorite* structure. However, the finer details of the orientation of the CH2 groups are yet to be established.
*the antifluorite structure is the inverse of the fluorite structure in which the locations ofcations and anions are reversed. Look into the structures of CaF2 (fluorite structure) and K2O (antifluorite structure). An fcc array of cations and all the tetrahedral holes are filled with anions.
Radical anion salts
Sodium naphthalide is an example of an organometallic salt with a delocalized radical anion, C10H8-.
Such compounds are readily prepared by reacting an aromatic compound with an alkali metal in a polar aprotic solvent.
Naphthalene dissolved in THF reacts with Na metal to produce a dark green solution of sodium naphthalide.
EPR spectra show that the odd electron is delocalized in an antibonding orbital of C10H8.
Formation of radical anion is more favorable when the π of LUMO of the arene is low in energy.
Simple MOT predicts that the energy of LUMO decreases steadily on going from benzene to more extensively conjugated hydrocarbons.
Sodium naphthalide and similar compounds are highly reactive reducing agents.
They are preferred to sodium because unlike sodium, they are readily soluble in ethers.
Radical anion salts (contd..)
The resulting homogeneous reaction is generally faster and easier to control than a heterogeneous reaction between one reagent in solution and pieces of sodium metal, which are often coated with unreactive sodium oxide or with insoluble reaction products.
The additional advantage is that by proper choice of the aromatic group the reduction potential of the reagent can be chosen to match the requirements of a particular synthetic task.
Alternative route to delocalized anion is the reductive cleavage of acidic C—H bonds by an alkali metal or alkylmetallic compound.
Example:
Problems:
1. Classify the following reactions into, (i) hydrometallation, metal displacement, metathesis OR transmetallation reactions; (ii) give an example for each case in the form of a balanced chemical equation.
Solution:
1. M + Mx’R → M’ + MR ….Transmetallation
e.g.: 2Ga + 3CH3-Hg-CH3→ 3Hg + 2Ga(CH3)3
2. MR + EX → ER + MX ….Metathesis
e.g.: Li4(CH3)4 + SiCl4 → 4LiCl + Si(CH3)4 or
Al2(CH3)6 + 2BF3 à 2AlF3 + 2B(CH3)3
3. EH + H2C=CH2 → E—CH2—CH3 ….Hydrometallation
e.g.: Hydroboration
Hydrosilylation
Problems:
1. For each of the following compounds, indicate those that may serve as
(1) a good carbanion nucleophile reagent,
(2) a mild Lewis acid,
(3) a mild Lewis base at the central atom,
(4) a strong reducing agent. (A compound may have more than one of these properties)
(a) Li4(CH3)4, (b) Zn(CH3)2, (c) (CH3)MgBr, (d) B(CH3)3, (e) Al2(CH3)6, (f) Si(CH3)4, (g) As(CH3)3.
Solution:
1. (MeLi)4 - good carbanion nucleophile and strong reducing agent
2. ZnMe2 - reasonable carbanion nucleophile, mild Lewis acid, reducing agent
3. MeMgBr - good carbanion nucleophile
4. BMe3 - mild Lewis acid
5. Al2Me6 - good carbanion nucleophile, strong reducing agent
6. SiMe4 - mild Lewis acid
7. AsMe3 - mild Lewis base
Contributors | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/23%3A_Organometallic_chemistry-_s-Block_and_p-Block_Elements/23.01%3A_Introduction/23.1A%3A_General_Methods_of_preparation.txt |
Learning Objectives
In this lecture you will learn the following
• Solid state structures of nickel-arsenide, alkyl lithium and alkyl aluminium compounds.
Structure and bonding
The slight differences that arise between organometallic compounds and binary hydrogen compounds are mainly due to the tendency of alkyl groups to avoid ionic bonding. The molecular structures of AlMe3and MeLi differ from AlH3and LiH. Even the more ionic MeK crystallizes in the nickel-arsenide structure rather than the rock-salt structure adopted by KCl.
Nickel-arsenide structure is typical of soft-cation, soft-anion combinations.
Electron deficient compounds such as AlMe3contain 3c-2e bonds analogous to the B—H—B bridges in diborane.
The Nickel-Arsenide, NiAs, Structure
MeLi in nonpolar solvents consists of tetrahedron of Li atoms with each face bridged by a methyl group. Similar to Al2Me6, the bonding in MeLi consists of a set of localized molecular orbitals. The symmetric combination of three Li 2s orbitals on each face of the Li4 tetrahedron and one sp3 hybrid orbital from CH3 gives an orbital that can accommodate a pair of electron to form a 4c-2e bond.
The lower energy of the C orbital compared with the Li orbitals indicates that the bonding pair of electrons will be associated primarily with the CH3 group, thus supporting the carbanionic character of the molecule. Some analysis has indicated that about 90% ionic character for the Li-CH3 interaction.
The interaction between an sp3 orbital from a methyl group and the three 2s orbitals of the Li atoms in a triangular face of Li4(CH3)4 to form a totally symmetric 4c,2e bonding orbital. The next higher orbital is non-bonding and the uppermost is antibonding.
Me2Be and Me2Mg exist in a polymeric structure with two 3c,2e-bonding CH3 bridges between each metal atom.
Contributors and Attributions
http://nptel.ac.in/courses/104101006/6
23.1C: Characterization of Organometallic Complexes
Learning Objectives
In this lecture you will learn the following
• The characterization techniques of organometallic compounds.
• The NMR analysis of these compounds.
• The IR analysis of these compounds.
• The X-ray single crystal diffraction studies of these compounds.
The characterization of an organometallic complex involves obtaining a complete understanding of the same right from its identification to the assessment of its purity content, to even elucidation of its stereochemical features. Detailed structural understanding of the organometallic compounds is critical for obtaining an insight on its properties and which is achieved based on the structure-property paradigm.
Synthesis and isolation
Synthesis and isolation are two very important experimental protocols in the overall scheme of things of organometallic chemistry and thus these needs to be performed carefully. The isolation of the organometallic compounds is essential for their characterization and reactivity studies. Fortunately, many of the methods of organic chemistry can be used in organometallic chemistry as the organometallic compounds are mostly nonvolatile crystalline solids at room temperature and atmospheric pressure though a few examples of these compounds are known to exist in the liquid [(CH3C5H4Mn(CO)3] and even in the vapor [Ni(CO)4] states. The organometallic compounds are comparatively more sensitive to aerial oxygen and moisture, and because of which the manipulation of these compounds requires stringent experimental skills to constantly provide them with anaerobic environment for their protection. All of these necessities led to the development of the so-called special Schlenk techniques, requiring special glasswares and which in conjunction with a high vacuum line and a dry box allow the lab bench-top manipulation of these compounds. Successful isolation of organometallic compounds naturally points to the need for various spectroscopic techniques for their characterizations and some of the important ones are discussed below.
1H NMR spectroscopy
The 1H NMR spectroscopy is among the extensively used techniques for the characterization of organometallic compounds. Of particular interest is the application of 1H NMR spectroscopy in the characterization of the metal hydride complexes, for which the metal hydride moiety appear at a distinct chemical shift range between 0 ppm to −40 ppm to the high field of tetramethyl silane (TMS). This upfield shift of the metal hydride moiety is attributed to a shielding by metal d−electrons and the extent of the upfield shift increases with higher the dn configuration. Chemical shifts, peak intensities as well as coupling constants from the through-bond couplings between adjacent nuclei like that of the observation of JP-H, if a phosphorous nucleus is present within the coupling range of a proton nucleus, are often used for the analysis of these compounds. The 1H NMR spectroscopy is often successfully employed in studying more complex issues like fluxionality and diastereotopy in organometallic molecules (Figure 1).
13C NMR spectroscopy
Although the natural abundance of NMR active 13C (I = ½) nuclei is only 1 %, it is possible to obtain a proton decoupled 13C{1H} NMR spectra for most of the organometallic complexes. In addition, the off−resonance 1H decoupled 13C experiments yield 1JC-H coupling constants, which contain vital structural information, and hence are very critical to the 13C NMR spectral analysis. For example, the 1JC-H coupling constants directly correlate with the hybridization of the C−H bonds with sp center exhibiting a 1JC-H coupling constant of ~250 Hz, a sp2 center of 160 Hz and a sp3 center of 125 Hz. Similar to what is seen in 1H NMR, a phosphorous−carbon coupling is also observed in a 13C NMR spectrum with the trans coupling (~100 Hz) being larger than the cis coupling (~10 Hz).
31P NMR spectroscopy
The 31P NMR spectroscopy, which in conjunction with 1H and 13C NMR spectroscopies, is a useful technique in studying the phosphine containing organometallic complexes. The 31P NMR experiments are routinely run under 1H decoupled conditions for simplification of the spectral features that allow convenience in spectral analysis. Thus, for this very reason, many mechanistic studies on catalytic cycle are conveniently undertaken by 31P NMR spectroscopy whenever applicable.
IR spectroscopy
Qualitative to semi-quantitative analysis of organometallic compounds using IR spectroscopy are performed whenever possible. In general the signature stretching vibrations for chemical bonds are more conveniently looked at in these studies. The frequency (ν) of a stretching vibration of a covalent bond is directly proportional to the strength of the bond, usually given by the force constant (k) and inversely proportional to the reduced mass of the system, which relates to the masses of the individual atoms.
The organometallic compounds containing carbonyl groups are regularly studied using IR spectroscopy, and in which the CO peaks appear in the range between 2100−1700 cm-1 as distinctly intense peaks.
Crystallography
The solid state structure elucidation using single crystal diffraction studies are extremely useful techniques for the characterization of the organometallic compounds and for which the X-ray diffraction and neutron diffraction studies are often undertaken. As these methods give a three dimensional structural rendition at a molecular level, they are of significant importance among the various available characterization methods. The X-ray diffraction technique is founded on Bragg’s law that explains the diffraction pattern arising out of a repetitive arrangement of the atoms located at the crystal lattices.
2d sin θ = A major limitation of the X-ray diffraction is that the technique is not sensitive enough to detect the hydrogen atoms, which appear as weak peaks as opposed to intense peaks arising out of the more electron rich metal atoms, and hence are not very useful for metal hydride compounds. Neutron diffraction studies can detect hydrogens more accurately and thus are good for the analysis of the metal hydride complexes.
Summary
Along with the synthesis, the isolation and the characterization protocols are also integral part of the experimental organometallic chemistry. Because of their air and moisture sensitivities, specialized experimental techniques that succeed in performing the synthesis, isolation and storage of these compounds in an air and moisture-free environment are often used. The organometallic compounds are characterized by various spectroscopic techniques including the 1H NMR, 13C NMR and IR spectroscopies and the X-ray and the neutron diffraction studies.
Contributors and Attributions
http://nptel.ac.in/courses/104101006/32 | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/23%3A_Organometallic_chemistry-_s-Block_and_p-Block_Elements/23.01%3A_Introduction/23.1B%3A_Structure_and_bonding.txt |
Learning Objectives
In this lecture you will learn the following
• How to synthesize and handle sodium, lithium compounds.
• Structural features.
Organometallic compounds of alkaline metals
Organic compounds such as terminal alkynes which contain relatively acidic hydrogen atoms form salts with the alkali metals.
NaCp is pyrophoric in air, but air-sensitivity can be lessened by complexing the Na+ with dme.
In the solid state, [Na(dme)][Cp] is polymeric
*Pyrophoric material: is one that burns spontaneously when exposed to air.
Organolithium compounds are of particular importance among the group 1 organometallics.
Many of them are commercially available as solutions in hydrocarbon solvents.
Solvent choices for reactions involving organometallics of the alkali metals are critical. For example, nBuLi is decomposed by Et2O to give nBuH, C2H4 and LiOEt.
Alkali metal organometallics are extremely reactive and must be handled in air- and moisture-free environments; NaMe, for example, burns explosively in air.
Lithium alkyls are polymeric both in solution and in the solid state.
NMR is very useful in understanding the solution structures; 6Li (I = 1), 7Li (I = ½), 13C (I = ½)
The structures of (tBuLi)4 and (MeLi)4 are similar. nBuLi when mixed with TMEDA, gives a polymeric chain. TMEDA link cubane units together through the formation of Li-N bonds.
Alkyllithium compounds are soluble in organic solvents whereas Na and K salts are insoluble, but are solubilized by the chelating ligand TMEDA. Addition of TMEDA may break down the aggregates of lithium alkyls to give lower nuclearity complexes. E.g. [nBuLi.TMEDA]2
However, detailed studies have revealed that the system is far from simple, and it is possible to isolate crystals of either [nBULi.TMEDA]2 or [(nBuLi)4.TMEDA].
In the case of (MeLi)4, the addition of TMEDA does not lead to cluster breakdown, and the X-ray structure confirms the composition (MeLi)4.2TMEDA, the presence of both tetramers and the amine molecules in the crystal lattice.
N. D. R. Barnett et al. J. Am. Chem. Soc., 1993, 115, 1573.
Lithium alkyls and aryls are very useful reagents in organic synthesis and also in making corresponding carbon compounds of main group elements. Lithium alkyls are important catalysts in the synthetic rubber industry for the stereospecific polymerization of alkenes.
Transmetallation:
Organolithium compounds:
Some typical examples include:
MeLi and nBuLi which depending on solvent may exist as tetramers or hexamers.
(cyclohexyl)Li which exists as a hexamer.
t-BuLi exists as a tetramer and can coordinate diethylether to form a dimer or a bulky diamine like tetraethylethylenediamine (TEEDA) to give a monomer.
n-butyllithium
Sodium forms ionic salts with terminal alkynes and cyclopentadiene:
2Na+ + 2 HC≡CEt → 2 Na+[C≡CEt]- + H2
(in THF) Cp + NaH → Na+ Cp- + H2
This salt is pyrophoric but it has been found that when 1,2-dimethoxyethane is added as complexing agent the product is less air-sensitive. Both the Na and K salts have been isolated and their structures determined.
Na(dme)Cp and K(dme)Cp.
The nomenclature used to denote the idea that the 5-carbons of the cp ring are equally attached is by the use of η5. For the case where only 1-carbon is attached then the designation would be η1. Here the Greek letter "eta" is used and the term is generally called "hapticity".
Sodium and potassium form intensely coloured salts with aromatic compounds. The alkali metal is oxidised and transfers one electron to the aromatic system and this becomes a paramagnetic radical anion:
Na + naphthalene → Na+[C8H10]-
In the case of napthalene, the salt is deep blue.
Contributors and Attributions
• The Department of Chemistry, University of the West Indies) | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/23%3A_Organometallic_chemistry-_s-Block_and_p-Block_Elements/23.02%3A_Group_1_-_Alkali_Metal_Organometallics.txt |
Learning Objectives
In this lecture you will learn the following
• Organometallic compounds of beryllium and magnesium.
• Structural features of alkyl lithium and beryllium sandwich compounds.
Synthesis
Organoberyllium compounds are best prepared via transmetallation reactions or by reaction of beryllium halides with other organometallic compounds e.g.,
$\ce{HgMe2 + Be ->[\text{383 K}] Me2Be + Hg}$
$\ce{2PhLi + BeCl2 ->[\text{diethyle ether}] Ph2Be + 2LiCl}$
In the vapor phase $\ce{Me2Be}$ is monomeric with a linear C—Be—C (Be-C = 170 pm), but in the solid state it is polymeric and resembles that of $\ce{BeCl2}$ with a bonding that is considered electron deficient with 3-center-2-electron bonds. With higher alkyls the amount of polymerisation decreases and the tert-butyl derivative is monomeric and linear in both solid and vapour phases.
$\ce{2NaCp + BeCl2 -> Cp2Be + 2NaCl}$
However, 1H NMR spectrum shows that all protons environments are equivalent even at 163 K. Also, the solid state structure shows the Be atom is disordered over two equivalent sites and NMR data can be interpreted in terms of fluxional process in which the Be atom moves between these two sites.
Beryllocene
The reaction of $\ce{NaCp}$ with beryllium chloride leads to beryllocene (Cp2Be)
$\ce{2 K [C5Me5] + BeCl2 ->[\text{388 K}][ether/toluene] (C5Me5)2Be + 2 KCl}$
The solid state structure suggests that the two rings are bound to the Be differently such that 1 is designated η5 and the other η1.
Structure of $\ce{(η^{1}-Cp)(η^{5}-Cp)Be}$ also called Beryllocene
The experimental 1H NMR spectrum adds to the confusion of the bonding since even at 163 K the protons all appear equivalent. This is accounted for by fluxional processes. Some variations of the compound have been prepared to see how general this effect is, for example, 4 protons on each ring replaced by methyl groups and all 5 protons replaced by methyl groups, (meCp)2Be, and even 4 on one ring and 5 on the other replaced with methyl groups. In the first case the fluxional process was observed down to 183K and in the second case the two rings were found to be coparallel and staggered. (Note that the structure of ferrocene is described as eclipsed when prepared at very low temperatures or in the gas phase but when formed at higher temperatures it is disordered and more staggered and since the barrier to rotation of the two rings is quite low, at 298 K in the solid state there is motion).
However, Cp*2Be possesses a sandwich structure with both the rings are coplanar.
Contributors and Attributions
• The Department of Chemistry, University of the West Indies)
23.3B: Magnesium
Grignard Reagents
Alkyl and aryl magnesium halides (Grignard reagents, $\ce{RMgX}$) are extremely well-known on account of their uses in synthetic chemistry. Over the past 100 years, Gringnard reagents had probably been the most widely used organometallic reagents. The general procedure for their preparation was discovered by Victor Grignard in 1900 and involved the direct reaction of magnesium with organohalides.
$\ce{R-X + Mg → R-Mg-X, (X= Cl, Br, I)}$
When the reaction is performed in diethyl ether or THF and in the absence of air and moisture, the compounds are reasonably stable although they need to be used immediately. Grignard reactions often start slowly. As is common for reactions involving solids and solution, initiation follows an induction period during which reactive magnesium becomes exposed to the organic reagents. After this induction period, the reactions can be highly exothermic.
Transmetallation is useful means of preparing pure Grignard reagents
$\ce{Mg + RHgBr -> Hg + RMgBr}$
$\ce{Mg + R2Hg \rightarrow Hg + R2Mg}$
Two-coordination at Mg in $\ce{R2Mg}$ is observed only when the $\ce{R}$ groups are sufficiently bulky, e.g. Mg{C(SiMe3)3}2. $\ce{RMgX}$ are generally solvated and $\ce{Mg}$ center is typically tetrahedral (e.g. EtMgBr.2Et2O; PhMgBr.2Et2O); Cp2Mg has a staggered sandwich structure.
The composition of ether solutions of Grignards was investigated by the Schlenk's who reported what is now called the Schlenk Equilibrium:
$\ce{2 RMgX \rightleftharpoons MgX2 + MgR2} \label{schlenk}$
The notation of $\ce{RMgX}$ for Grigarnd reacgents is therefore an oversimplification of what truly exists in ether solutions. In diethyl ether, a tendency to form monomeric, dimeric and higher oligomeric species was found and was dependent on the halogen and organic substituents. Figure $1$ indicates the percentage of $\ce{RMgX}$ for a range of Grignard Reagents.
Figure $1$: Composition of solutions of Grignard Reagents in diethyl ether solution at equilibrium. In diethyl ether, a tendency to form monomeric, dimeric and higher oligomeric species was found and was dependent on the halogen and organic substituents.
Solutions of Grignard reagent may contain several species, e.g. RMgX, R2Mg, MgX2, RMg(μ-X)2MgR, which are further complicated by solvation. The position of equilibrium between these species is markedly dependent on concentration, temperature and solvent; strongly donating solvents favor monomeric species in which they coordinate to the metal center.
In tetrahydofuran (THF) the structures were found to be closer to monomeric but it was recognized that the solid state structures may be very different to what exists in solution. For example, when "EtMgCl" is isolated from a THF solution a tetramer was found where the Mg have coordination numbers higher than the expected 4.
Figure $3$: EtMgCl isolated from THF.
In the polymeric structures it is generally the halide, rather than the organic group that bridges between the magnesiums.
Reactions of Grignard Reagents
The most common application for the use of Grignard Reagents in Organic Chemistry is for alkylation of aldehydes and ketones, for example:
$\ce{R1R2C=O + R3MgX → R1R2R3C-OMgX → R1R2R3C-OH}$
and more generally:
Figure $4$: Reactions with carbonyls
Other reactions include carbon-carbon coupling which is often affected using a catalyst like transition metal halides.
$\ce{2 ArMgX + MXn → Ar-Ar + MgX2 + MX_{n-2}}$
and for cross-coupling reactions:
$\ce{ArMgX + RCH=CHX ->[\text{5 mol% CoCl}_2] ArCH=CHR + MgBrX}$
using, for example, 5 mol% CoCl2 as catalyst and to determine the difference in reactivity of the halides, a series of competitive reactions were performed:
Figure $5$: Cross-coupling Reactions with Grignard Reagents - 2008 review
Terao and Kambe reported that when they took a mixture of equimolar amounts of n-octyl fluoride, n-nonyl chloride, and n-decyl bromide and added to this CuCl2, 1-phenylpropyne, and a THF solution of n-ButylMgCl, then after the reaction was stirred for 30 min in THF at reflux, GC analysis of the resulting mixture indicated the selective formation of tetradecane in 98% yield along with 2% yield of dodecane. A similar reaction using only alkyl fluorides and chlorides gave dodecane and tridecane in 95% and 5% yields, respectively. These results indicated that the reactivity of alkyl halides was in the order:
$\ce{bromide > fluoride > chloride}$
Table $1$: Transition metal halide catalyzed coupling of phenylmagnesium iodide
metal halide amt, mol amt of C6H5MgI, mol yield of biphenyl, %
FeCl2 0.01 0.03 98
CoBr2 0.01 0.03 98
NiBr2 0.03 0.095 100
RuCl3 0.0036 0.0108 99
RhCl3 0.0036 0.013 97.5
PdCl2 0.00566 0.0163 98
OsCl3 0.00275 0.007 53
IrCl3 0.003 0.01 28
Industrial Use
A Grignard reaction that is a key step in an industrial production is shown below, where the target is Tamoxifen. Tamoxifen is an antagonist of the estrogen receptor in breast tissue and it is the standard endocrine (anti-estrogen) therapy for hormone-positive early breast cancer in post-menopausal women.
Figure $5$: Tamoxifen synthesis using a Grignard Reagent
Problems
Q1
If a typical Grignard reagent exists as an equilibrium mixture of dialkylmagnesium and magnesium halide, give a method of isolating pure dialkyl magnesium. Your answer should be in the form of balanced chemical equations only.
Solution:
Treatment of equilibrium mixture with dioxane results in the precipitation of, say, MgCl2(dioxane) (if, X = Cl), leaving behind pure R2Mg in the solution.
Q2
The compound (Me3Si)2C(MgBr)2.nTHF is monomeric. Suggest a value of ‘n’ and propose a structure for this Grignard reagent.
Solution:
Contributors and Attributions
• The Department of Chemistry, University of the West Indies) | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/23%3A_Organometallic_chemistry-_s-Block_and_p-Block_Elements/23.03%3A_Group_2_Organometallics/23.3A%3A_Beryllium.txt |
Organoboron Compounds
BMe3 is colorless, gaseous ( b.p. -22 °C), and is monomeric. It is pyrophoric but not rapidly hydrolyzed by water.
Alkylboranes can be synthesized by metathesis between BX3 and organometallic compounds of metals with low electronegativity, such as RMgX or AlR3.
Why dibutyl ether as a solvent: Has much lower vapor pressure than BMe3 and as a result the separation by trap-to-trap distillation on a vacuum line is easy.
Also, there is a very weak association between BMe3 and OBu2(Me3B:OBu2).
Although, trialkyl- and triarylboron compounds are mild Lewis acids, strong carbanion reagents lead to anions of the type [BR4]-.
Example, Na[BPh]4: The bulky anion hydrolyses very slowly in neutral or basic water and is useful for the preparation of large positive cations.
K[BPh]4 is insoluble, used for the gravimetric estimation (determination) of potassium, an example of the low solubility of large-cation and large-anion salts in water.
Organohaloboron compounds are more reactive than simple trialkylboron compounds.
Preparation
Reactions: (Protolysis reactions with ROH, R2NH and other reagents)
Boron
Most alkyl and aryl organoboron compounds are reasonably stable in water, although they may still be fairly air sensitive even pyrophoric. They are usually monomeric. For example, triethylborane (TEB) is strongly pyrophoric, igniting spontaneously in air. It burns intensely with a very hot flame. The color of the flame is apple-green, which is characteristic for boron compounds. Its vapours may cause flash fires. This was first noted by Frankland in 1860 when he first prepared Et3B from Et2Zn by transmetallation.
Et3B is soluble in tetrahydrofuran and hexane, and is not pyrophoric when in solution. However the solution can slowly react with atmospheric moisture. If the TEB solutions are exposed to air for prolonged time, unstable organic peroxides may form. It has been found to be toxic to the peripheral nervous system, kidneys and testes and is extremely corrosive.
The Lockheed SR-71 strategic reconnaissance aircraft uses as fuel a mixture of hydrocarbons known as JP-7. The very low volatility and relative unwillingness of JP-7 to be ignited required a pyrophoric material like triethylborane (TEB) to be injected into the engine in order to initiate combustion and allow afterburner operation in flight.
Lockheed SR-71, 'Blackbird'
JP-7 jet fuel was designed to have a relatively high flash point (60 °C) to cope with the heat. In fact, the fuel was used as a coolant and hydraulic fluid in the aircraft before being burned. The fuel also contained fluorocarbons to increase its lubricity, an oxidizing agent to enable it to burn in the engines, and even a caesium compound, A-50, to help disguise the exhaust's radar signature.
JP-7 is very slippery and extremely difficult to light in any conventional way. The slipperiness was a disadvantage on the ground, because inevitably the aircraft leaked small amounts of fuel when not flying, fortunately JP-7 was not a fire hazard. When the engines of the aircraft were started, puffs of triethylborane (TEB), which ignites on contact with air, were injected into the engines to produce temperatures high enough to ignite the JP-7 initially. The TEB produced a characteristic puff of greenish flame that could often be seen as the engines were ignited. TEB was also used to ignite the afterburners. The aircraft had only 600 ml of TEB on board for each engine, enough for at least 16 injections (a counter advised the pilot of the number of TEB injections remaining), but this was considered more than enough for the requirements of any missions it was likely to carry out.
The triarylborane, BPh3, is less reactive and forms the salt Na[BPh4] that is water soluble and is useful as a precipitating agent for large metal ions.
R2BCl and RBCl2 have been prepared by transmetallation and these have been used to generate species like R2B(μ-H)2BR2. One example of this is the reagent (9-BBN) that is used for the regioselective reduction of ketone, aldehydes, alkynes and nitriles. Its highly stereoselective addition on olefins allows the preparation of terminal alcohols by subsequent oxidative cleavage with H2O2 in aq. KOH. The steric demand of 9-BBN greatly suppresses the formation of the 2-substituted isomer compared to the use of borane.
It has been found to be a useful reagent for the Suziki Reaction:
Suzuki Reaction Scheme
Hydroboration
The hydroboration-oxidation reaction is a two-step organic chemical reaction that converts an alkene into a neutral alcohol by the net addition of water across the double bond. The hydrogen and hydroxyl group are added in a syn addition leading to cis stereochemistry. Hydroboration-oxidation is an anti-Markovnikov reaction, with the hydroxyl group attaching to the less-substituted carbon. The reaction was first reported by Herbert C. Brown in the late 1950s and he received the Nobel Prize in Chemistry in 1979. Shown below is the original reaction described in 1957 where hex-1-ene is converted to hexanol.
H. C. Brown reaction of 1957 other hydroboration reactions
Diborene
The first structurally characterized neutral diborene containing a B=B double bond was reported in 2007. It was prepared by the following scheme:
Synthesis of a diborene
According to the authors, the carbene ligands were the key to the ability of boron to form the diborene's B=B bond. The divalent carbon atom of each carbene is able to donate its two free electrons to form a carbon-boron bond, allowing the boron's three valence electrons to form a bond to hydrogen and a σ and a π bond to the other boron. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/23%3A_Organometallic_chemistry-_s-Block_and_p-Block_Elements/23.04%3A_Group_13/23.4A%3A_Boron.txt |
Learning Objectives
In this lecture you will learn the following
• Preparation and reactivity of organoboron and organo aluminium compounds.
• Influence of Lewis acidity on structural features.
Organoaluminium compounds
With less bulky alkyl groups, dimerization occurs and one of the distinguishing features of alkyl bridge is the small Al-C-Al angle, which is ~ 75°.
The 3c,2e bonds are very weak and tend to dissociate in the pure liquid which increases with increase in the bulkiness of the alkyl group.
Perpendicular orientation of pheynl groups in Al2Ph6
Triphenylaluminium exists as a dimer with bridging η1-phenyl groups lying in a plane perpendicular to the line joining the two Al atoms.
This structure is favored partly on steric grounds and partly by supplementation of the Al-C-Al bond by electron donation from the phenyl π-orbitals to the Al atoms.
Tendency for bridging: X > Ph > alkyl
3c,2e bonds formed by a symmetric combination of Al and C orbitals
An additional interaction between the pπ orbital on C and an antisymmetric combination of Al orbitals.
Synthesis
Very useful as alkene polymerization catalysts and chemical intermediates.
Expensive carbanion reagents for the replacement of halogens organic groups by metathesis.
Laboratory scale preparations involves:
Commercial method:
Commercial method for ethylaluminium and higher homologs:
The reaction probably proceeds by the formation of a surface Al—H species that adds across the double bond of the alkene in a hydrometallation reaction.
Reactions:
Alkylaluminum compounds are mild Lewis acids and form complexes with ethers, amines and anions. When heated, often β-hydrogen elimination is responsible for the decomposition of ethyl and higher alkylaluminium compounds. E.g. Al(iC4H9)3
Tendency towards bridging structure is: PR2-> X -> H -> Ph-> R-.
The first organoaluminium compound, an alkylaluminium sesqui-halide, Et3Al2I3 was reported in 1859 and was formed by reaction of elemental Al and EtI. "Me3Al" was obtained by George Buckton from aluminium and dimethylmercury as early as 1865. In hydrocarbon solution and in the solid state there is a tendency for R3Al to dimerise; this is very dependent on the size of the R group, eg a dimer for Me but monomer for tert-butyl. Me(t-Bu)5Al2 is found to be a dimer as well with the methyl group and 1 of the t-Bu groups in the bridging positions. The bridging ability is found to be Me > Et > t-Bu and clearly the case above is not what would be predicted on purely statistical terms since there are 5 times as many t-Bu groups as Me groups and there are twice as many terminal positions as bridging positions so the methyl group might have been expected to fill a terminal position.
Et3Al2I3
Many organoaluminium compounds are commercially available at quite reasonable prices so that is is rarely necessary to have to prepare them in the laboratory. Reaction of Al turnings with organic halides leads to the alkylaluminium sesqui-halides. The reaction is very exothermic. The sesqui-halides do not have sharp melting or boiling points because they are in fact equilibrium mixtures:
R3Al2X3 sesqui halide equilibria
It took almost 100 years before K. Ziegler discovered the synthetic and catalytic potential of organoaluminum compounds. From an industrial viewpoint, the organic compounds of aluminium are probably the most important organometallic compounds.
The reasons for this include:
• inexpensive synthesis from olefin + H2 + Al (pressure).
• R3Al can dimerise olefins
• higher alcohols (→ detergents) are made from R3Al + CH2=CH2.
• In combination with Ti and Zr compounds, R3Al can polymerise ethylene to give polyethylene
• Reactions with R3Al proceed in hydrocarbons or even without solvent (unlike RMgX !).
• Useful commercially for polymer synthesis catalysts
Karl Ziegler, who pioneered basic research in the field of organoaluminium compounds developed a strikingly simple yet versatile process for the synthesis of organoaluminium compounds from inexpensive starting materials. The Ziegler Direct Process allows the synthesis of triethylaluminium from aluminum metal, hydrogen and ethylene. The process involves the following:
2Al + 3H2 + 6RHC=CH2 → Al2(CH2CH2R)6 {R=H for (Et3Al)2}
The Ziegler-Natta polymerisation catalysts were originally formed from Et3Al with TiCl4 and a schematic representation of the reactions at the heterogeneous surface is given below:
Ziegler Natta polymerisation
Polymerisation of ethene to high-molecular mass polyethylene occurred at relatively low pressures and the polymers were stereoregular. What this means is that isotactic polymers are formed where the R groups are all located on the same side of the carbon backbone. The resulting product gives a crystalline material since packing is more regular. The other varieties of linear polymer are called syndiotactic and atactic and in the first the R groups are on alternate sides of the carbon backbone and in the latter they are randomly distributed.
Isotactic, syndiotactic and atactic linear polymer chains
The importance of his research was soon recognized and he received the 1963 Nobel Prize for Chemistry, together with Giulio Natta who made fundamental contributions to the polymerization field.
Compounds of the type Me2Al(μ-Ph)2AlMe2 and Ph2Al(μ-Ph)2AlPh2 show that the bridging phenyl groups are almost vertical compared to the R2Al-AlR2 plane and the ipso-carbon is a distorted tetrahedral.
A similar case is found with bridging alkynes -C≡C-R where the terminal groups are t-Bu and when the Al is changed to Ga. Although in the latter case the phenyl groups are at right angles to each other.
However a very different arrangement with bridging alkynes has been found where they point towards one of the Al centres. Here the bonding is interpreted as a mixture of σ and π bonds; an Al-C σ bond connects to the first Al but the second Al centre is bound using the C≡C π bond. Examples of this are for Me2Al(PhC≡C)2AlMe2 and for the analogous Gallium compound.
Problems
1. Propose a structure for Al2(Me)4Cl2.
Solution:
Similar to diborane:
2. Solution:
Lower force constant for Si-O-Si bending.
3. Explain how the difference in reactivity between Al-C and Si-C bonds with O-H groups leads to the choice of different strategies for the synthesis of aluminum and silicon alkoxides.
Solution:
Al2Me6 + 6 MeOH → 2Al(OMe)3 + 6 CH4
For reaction of Al2Me6 with alcohols, see the text book by Shriver and Atkins.
Tetramethylsilane does not react with methyl alcohol. Therefore, the appropriate reagent is tetrachlorosilane and the reaction is:
SiCl4 + 4 MeOH → Si(OMe)4 + 4HCl.
Problems: (contd..)
1. Compare formulas of the most stable hydrogen compounds of germanium and arsenic with those of their methyl compounds. Can the differences be explained in terms of the relative electronegativities of C and H?
Solution:
GeH4, GeR4; AsH3, AsR3.
The stability of hydrides and alkyls are very similar for each element. This may due to similar H and C electronegativity.
1. To buy from a chemical company, the price of trimethylaluminum is higher than that of triethylaluminum. Is it due to the methods of synthesis? Rationalize the price difference.
Solution:
Triethylaluminum can be made in larger quantities by direct reaction of aluminum, hydrogen gas and ethane gas which is a cheaper method.
Preparation of trimethyaluminum involves a more expensive route such as MeCl and aluminum to form Al2Me4Cl2 followed by treatment with sodium metal. The sodium metal and MeCl are not cheap as compared to ethane and hydrogen gases. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/23%3A_Organometallic_chemistry-_s-Block_and_p-Block_Elements/23.04%3A_Group_13/23.4B%3A_Aluminium.txt |
Learning Objectives
In this lecture you will learn the following
• Chemistry of gallium and indium.
• How to stabilize M—M multiple bonds.
Organometallic compounds of gallium and indium
Trialkylgallium compounds are mild Lewis acids, so the corresponding metathesis reaction in ether produces the complex (C2H5)2OGa(C2H5)3. Similarly excess use of C2H5Li leads to the salt, Li[Ga(C2H5)4].
Alkylindium and alkylthalium compounds may be prepared similar to gallium analogs. InMe3 is monomeric in the gas phase and in the solid the bond lengths indicate that association is very weak. Partial hydrolysis of TlMe3 yields the linear (MeTiMe]+ion, which is isoelectronic and isostructural with HgMe2.
CpIn and CoTl exist as monomers in the gas phase but are associated in solids {Inert-pair effect is displayed for In and Tl}. CpTl is useful as a synthetic reagent in organometallic chemistry because it is not as highly reducing as NaCp.
Species of the type R4E2(single E-E bond) and [R4E2] - (with E-E bond order of 1.5) can be prepared for Ga and In with bulky R groups (R = (Me3Si)2CH, 2,4,6-iPr3C6H2), and reduction of [(2,4,6-iPr3C6H2)4Ga2] to [(2,4,6-iPr3C6H2)4Ga2] - is accompanied by a shortening of the Ga—Ga bond from 252-234 pm.
Using even bulkier substituents, it is possible to prepare gallium(I) compounds, RGa starting from GaI. No structural data are yet available for these monomers
(We are working on it).
Crystallized as dimer but reverts to monomer when dissolved in cyclohexane.
Interest in organometallic comounds of Ga, In and Tl is mainly because of their potential use as precursors to semiconducting materials such as GaAs and InP. Volatile compounds can be used in the growth of thin films by MOCVD (metal organic chemical vapor deposition) or MOVPE (metal organic vapor phase epitaxy) techniques. Precursors include appropriate Lewis base adducts of metal alkyls, e.g. Me3Ga.NMe3 and Me3In.PEt3. Thermal decomposition of gaseous precursors result in semiconductors (III-V semiconductors) which can be deposited in thin films.
III-V semiconductors: Derive their name from the old groups 13 and 15, and include AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs and InSb. Off these GaAs is of the greatest commercial interest. Although Si is probably the most important commercial semiconductor, a major advandage of GaAs over Si is that the charge carrier mobility is much greater. This makes GaAs suitable for high-speed electronic devices.
Another important difference is that GaAs exhibits a fuly allowed electronic transition between valence and conduction bands (i.e. it is direct band gap semiconductor) whereas Si is an indirect band gap semiconductor. The consequence of difference is that GaAs (also other III-V types) are more suited than Si for use in optoelectronic devices, since light is emitted more efficiently. The III-Vs have important applications in light-emitting diodes (LEDs).
Problems
1. Predict the structure of monomeric, Cp3Ga; polymeric Cp3In and CpIn.
Solution:
See the articles Organometallics 1985, 4, 751.
Inorg. Chem. 1972, 11, 2832.
Organometallics 1988, 7, 105.
2. The reaction of [(R3C)4Ga4] ( R = a bulky substituent) (i) with I2 in boiling hexane results in the formation of [(R3C)GaI]2(ii) and [(R3C)GaI2]2(iii). Draw the structure and state the oxidation state for (i) - (iii).
Solution:
3. The I2 oxidation of [(tBu}4In4] leads to the formation of the InII compound [(tBu}4In4I4] in which each indium atom retains a tetrahedral environment. Draw the correct structure.
Solution:
Contributors and Attributions
http://nptel.ac.in/courses/104101006/9 | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/23%3A_Organometallic_chemistry-_s-Block_and_p-Block_Elements/23.04%3A_Group_13/23.4C%3A_Gallium_Indium_and_Thallium.txt |
Learning Objectives
In this lecture you will learn the following
• Organosilicon and organogermanium compounds.
• Compounds with Si=Si and Ge=Ge bonds.
Organosilicon Compounds
Organosilicon compounds are extensively studied due to the wide range of commercial applications as water repellents, lubricants, and sealants. Many oxo-bridged organosilicon compounds can be synthesized. e.g. (CH3)3Si—O—Si(CH3)3 which is resistant to moisture and air.
The lone pairs on O are partially delocalized into vacant σ*- orbitals of Si, as a result the directionality of the Si-O bond is reduced making the structure more flexible. This flexibility permits silicone elastomers to remain rubber-like down to very low temperature. Delocalization also accounts for low basicity of an O atom attached to silicon as the electrons needed for the O atom to act as a base are partially removed. The planarity of N(SiH3)3 is also explained by the delocalization of the lone pair on N which makes it very weakly basic.
$\ce{nMeCl + Si/Cu ->[ 573 K] Me_{n}SiCl_{4-n}}$
$\ce{SiCl4 + 4RLi \rightarrow R4Si}$
$\ce{SiCl4 + RLi \rightarrow RSiCl3}$
$\ce{SiCl4 + 2RMgCl \rightarrow R2SiCl2 + 2MgCl2}$
$\ce{Me2SiCl2 + ^{t}BuLi \rightarrow ^{t}BuMe2SiCl + LiCl}$
Si—C bonds are relatively strong (bond enthalpy is 318 kJ mol-1) and R4Si derivatives possess high thermal stabilities.
Et4Si on chlorination gives (ClCH2CH2)4Si. The hydrolysis of $\ce{Me2SiCl2}$ produce silicones.
$\ce{Me3SiCl2 + NaCp \rightarrow (\eta^1-Cp)SiHMe3}$
$\ce{(η^1-C5Me5) 2SiBr2}$ on treatment with anthracene/potassium gives Cp*2Si . The solid state structure of Cp*2Si consists of two independent molecules which differ in the relative orientations of the Cp rings. In one molecule, they are parallel and staggered whereas in the other, they are tilted with an angle of 167° at Si.
The reaction between R2SiCl2 and alkali metal or alkali naphthalides give cyclo-(R2Si)n by loss of Cl- and Si—Si bond formation.
Bulky R groups favor small rings [e.g. (2,6-Me2C6H3)6Si3 and tBu6Si3] while smaller R groups encourage the formation of large rings [Me12Si6, Me14Si7 and Me32Si16]
$\ce{Ph2SiCl2 + Li(SiPh2)Li \rightarrow cyclo-Ph12Si6 + 2LiCl}$
Bulky substituents stabilize $\ce{R2Si=SiR2}$ compounds. The sterically demanding 2,4,6-iPr3C6H2 provided first example of compound containing conjugated Si=Si bonds. Has s-cis configuration in both solution and the solid state.
*The spatial arrangement of two conjugated double bonds about the intervening single bond is described as s- cis if synperiplanar and s-trans if antiperiplanar.
Organogermanium compounds
Et4Si on chlorination gives ($\ce{(ClCH2CH2)4Si}$), in contrast to the chlorination of R4Ge or R4Sn which yields RnGeCl4-n or RnSnCl4-n. Similar germanium compounds wiht conjugated Ge=Ge bonds are also known
23.5C: Tin
Learning Objectives
In this lecture you will learn the following
• Organotin and organolead compounds and their preparation.
• Bonding in tin compounds with Sn=Sn double bonds.
• Uses and environmental issues with tin compounds.
• Reactivity of tetraethyl lead.
• Structural features of organolead compounds.
Preparation of Sn(IV) derivatives
Tin(II) organometallics of the type R2Sn, containing Sn-C σ-bonds, are stabilized only if R is sterically demanding.
(monomeric in solution and dimeric in solid state). But the dimer does not possess a planar Sn2R4framework unlike an analogous alkene, and Sn—Sn bond distance (267 pm) is shorter than a normal Sn—Sn single bond (276 pm).
Sn2R4 has a trans bent structure with a weak Sn=Sn double bond
Look into the reactions of R3SnCl with various reagents to form useful tin containing starting materials
The first organotin(II) hydride was reported only in 2000.
Shows dimeric structure in the solid state containing hydride bridges (Sn-Sn = 312 pm).
Commercial uses and environmental problems
Organotin(II) compounds find wide range of applications due to their catalytic and biocidal properties.
nBu3SnOAc is an effective fungicide and bactericide and also a polymerization catalyst.
nBu2Sn(OAc)2 is used as a polymerization catalyst and a stabilizer for PVC.
nBu3SnOSnnBu3 is algicide, fungicide and wood-preserving agent.
nBu3SnCl is a bactericide and fungicide.
Ph3SnOH used as an agricultural fungicide for crops such as potato, sugar beet and peanuts.
The cylic compound (nBu2SnS)3 is used as a stabilizer for PVC.
Tributyltin derivatives have been used as antifouling agents, applied to the underside of ships’ hulls to prevent the build-up of, for example, barnacles.
Global legislation now bans or greatly restricts the use of organotin-based anti-fouling agents on environmental grounds. Environmental risks associated with the uses of organotin compounds as pesticides, fungicides and PVC stabilizers are also a cause for concern.
*A barnacle is a type of arthropod belonging to infraclass Cirripedia in the sub-phylum Crustacea, and is hence related to crabs and lobsters.
Contributors and Attributions
http://nptel.ac.in/courses/104101006/12
23.5D: Lead
Organolead compounds
Tetraethyllead
Laboratory Scale,
Thermolysis leads to radical reactions.
Tetraalkyl and tetraaryl lead compounds are inert with respect to attack by air and water at room temperature. WHY ????
Me3PbCl consists of linear chain
Solid state structure of Cp2Pb shows polymeric nature, but in the gas phase, discrete Cp2Pb molecules are present which possess the bent structure similar to silicon analogue.
R2Pb=PbR2 are similar to analogues tin compounds
Problems
1. Find out the structures of (Me3SiCH2)3SnF and Me2SnF2
Solution: use VSEPR theory
2. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/23%3A_Organometallic_chemistry-_s-Block_and_p-Block_Elements/23.05%3A_Group_14/23.5A%3A_Silicon.txt |
Learning Objectives
In this lecture you will learn the following
• Organoaresnic and organoantimony compounds.
• Preparation and reactivity of pentavlent As and Sb compounds.
Organic chemistry of non-metal phosphorus, metalloids such as arsine and antimony along with metallic element bismuth is termed as organoelement chemistry. The importance given to organoarsenic compounds earlier due to their medicinal values was waded out after antibiotics were discovered and also their carcinogenic and toxic properties were revealed. Also, the synthetically important organometallic compounds of group 13 and 14 masked the growth of group 15 elements. However, the organoelement compounds of phosphorus, arsenic and antimony find usefulness as ligands in transition metal chemistry due to their σ-donor and π-acceptor abilities which can be readily tuned by simply changing the substituents. These donor properties are very useful in tuning them as ligands to make suitable metal complexes for metal mediated homogeneous catalysis. Although organoelement compounds can be formed in both +3 (trivalent and tricoordinated) and +5(pentavalent and tetra or pentacoordinated) oxidation states, trivalent compounds are important in coordination chemistry.
For organoelement compounds of group 15, the energy of E—C bond decreases in the order, E = P > As > Sb > Bi, and in the same sequence E—C bond polarity increases.
Organometallic compounds of As(V) and Sb(V)
Due to the strong oxidizing nature of pentahalides, the direct alkylation or arylation to generate ER5 is not feasible, but can be prepared in two steps.
A few representative methods of preparation are given below:
Structures and properties
Pentaalkyl or pentaaryl derivatives are moderately thermally stable. On heating above 100°C, they form trivalent compounds as shown below:
Reaction with water,
Pentavalent compounds readily form “tetrahedral onium” cations and “octahedral and hexacoordinatged ate” anions.
In solid state, Ph5As adopts trigonal bipyramidal geometry, whereas Ph5Sb prefers square based pyramidal geometry although the energy difference between the two is marginal.
The salts of the type [R4E]+ adopt tetrahedral geometry, whereas hexacoordinated anions [R6E]-assume octahedral geometry.
Mixed organo-halo compounds of the type RnEX5-n adopt often dimeric structures due to the presence of lone pairs of electrons on X which can readily coordinate to the second molecule. The following structural types can be anticipated.
The thermal stability of RnEX5-n decreases with decreasing ‘n’. Thermal reactions are essentially the reverse reactions of addition reactions used in the preparation of R5E.
Organometallic compounds of As(III) and Sb(III)
In this lecture you will learn the following
• Preparation of trivalent compounds.
• Mono and bis derivatives.
• Reaction of organo arsenic and antimony compounds.
• Structural features of organolead compounds.
Organometallic compound of As(III) and Sb(III).
Direct synthesis
Mono- derivatives
Direct synthesis (contd..)
Bis derivatives:
Reactions of trialkyl derivatives, R3E
The transition metal chemistry of R3E, phosphines, arsines or stibines has been extensively studied because of their distinct donor and acceptor properties. Among them, the phosphines or tertiary phosphines (R3P) are the most valuable ligands in metal mediated homogeneous catalysis. Interestingly, the steric and electronic properties can be readily tuned by changing the substituents on phosphorus atoms. Chapter 16 is fully dedicated to the chemistry of phosphines.
Properties
Trialkyl derivatives are highly air-sensitive liquids with low boiling points and some of them are even pyrophyric. Triphenyl derivatives are solids at room temperature and are moderately stable and oxidizing agents such as KMnO4, H2O2 or TMNO are needed for oxidation to form Ph3E=O.
Cyclic and acyclic derivatives containing E—E bonds
E—E single bonds:
The E—E bond energies suggest that they do not have greater stability and the stability decreases down the group.
The simplest molecules include Ph2P—PPh2, Me2As—AsMe2 prepared by coupling reactions:
The weakness of E—E bonds accounts for many interesting reactions and a few of such reactions are listed below:
Cyclic and polycyclic derivatives can be prepared by employing any of the following methods:
Problems
1. Confirm that the octahedral structure of [Ph6Bi]- is consistent with VSEPR theory.
Solution:
Octahedral similar to PF6-
5 (Bi valence electrons) + 6 (each Ph ) + 1 (-ve charge) = 12 electrons
i.e. six pairs, octahedral geometry
2. Comment on the stability of BiMe3 and Al2(iBu)6 with respect to their thermal decomposition and give chemical equations for their decomposition.
Solution:
Similar to other heavy p-block elements, Bi—C bonds are weak and readily undergo homolytic cleavage. The resulting methyl radicals will react with other radicals or form ethane
The Al2(iBu)6 dimer readily dissociates. At elevated temperature dissociation is followed by β-hydrogen elimination. This type of elimination is common for organometallic compounds that have alkyl groups with β-hydrogens, can form stable M—H bonds, and can provide a coordination site on the central metal.
The decomposition reaction is:
Problems: (contd..)
1. Using a suitable Grignard reagent, how would you prepare (i) MeC(Et)(OH)Ph; (ii) AsPh3.
Solution:
1. Add a Grignard reagent to a C=O bond, then acidify.
Several possibilities, e.g.
Me-C(O)-Et + PhMgBr → Me-C(OMgBr)(Et)(Ph) → MeC(Et)(OH)Ph or Me-C(O)-Ph + EtMgBr →etc
2. AsCl3 + 3PhMgBr → AsPh3 + 3MgBrCl.
This Module focuses on Main Group Organometallic Chemistry will look at some "simple" methyl and ethyl compounds; (Me2As)2, Me3As, Me2Hg and Et4Pb.
Organoarsenic Chemistry
"Cadet's fuming liquid"
The French pharmacist-chemist, Louis-Claude Cadet de Gassicourt prepared what became known as "Cadet's fuming liquid" in 1757. The reaction involved heating 2 ounces of arsenious oxide with 2 ounces of potassium acetate.
$As_2O_3 + 4 CH_3COOK \rightarrow As_2(CH_3)_4O + 4 K_2CO_3 + CO_2 \rightarrow \rightarrow As_2(CH_3)_4$
gives cacodyl oxide which disproportionates to produce among other things cacodyl, As2(CH3)4.
cacodyl
He noted that:
"a slightly colored liquid of an extremely penetrating garlic odor distills and then a red-brown liquid which fills the receiver with thick fumes".
All of the early studies of Cadet's fuming liquid were qualitative in nature, made difficult by the liquid's horrible stench and inflammability, and it was not until the investigations of Robert Wilhelm Bunsen during 1837-1843 that more useful information concerning Cadet's fuming liquid became available. The history of studies on this mixture was reviewed in 2001 [Ref 3.]
Bunsen opted for a large-scale preparation, despite the fact that he was aware of the repulsive and dangerous nature of the expected products. Starting out with one kilogram of a 1:1 by weight As2O3/KOOCCH3 mixture in a glass retort, he heated it very slowly to red heat in a sand bath. As Cadet had reported, two liquid layers and a solid phase collected in the receiver. Bunsen reported that he obtained ~150 g of the red-brown liquid.
In 1841, Berzelius suggested to Bunsen that the name for the liquid be called "kakodyl" from the Greek meaning "stinking", the English spelling of this was cacodyl.
"Accidents with cacodyl compounds could have serious consequences. During his study of cacodyl cyanide, (CH3)2AsCN, prepared by reaction of 'cacodyl oxide' with a concentrated aqueous solution of mercuric cyanide, an explosion cost Bunsen the partial sight of his right eye and, as Roscoe reports, 'Bunsen was nearly poisoned, lying for days between life and death.' Bunsen recovered and completed his study of cacodyl cyanide, a most unpleasant compound. After distillation of the 'cacodyl oxide'/Hg(CN)2 reaction mixture, the cacodyl cyanide formed beautiful, prismatic crystals underneath the water layer. These were quite volatile (mp 32.5 °C). They were dried by pressing them between sheets of blotting paper. Bunsen noted that it is absolutely necessary to carry out this operation in the open air while breathing through a long glass tube that extends to fresh air far beyond the volatile crystals. And well might this compound be avoided! Bunsen reported that the vapour from 1 grain (0.0648 g) of cacodyl cyanide in a room produces sudden numbness of the hands and feet, and dizziness and insensibility to the point of unconsciousness. The tongue becomes covered with a black coating. These effects, however, are only temporary, with no lasting problems. (Bunsen, it may be noted, lived to the ripe old age of 88.)" Ref 3.
Seventy years after its discovery, the question of the composition of Cadet's fuming liquid was addressed by Valeur and Gailliot by means of its fractional distillation under an atmosphere of CO2. Valeur, A.; Gailliot, P. C. R. Acad. Sci. 1927, 185, 956.
Composition of Cadet's fuming liquid (1927)
Compound % in Cadet's liquid melting point boiling point density
(CH3)3As 2.6 liquid at -80°C 50°C 1.144
(CH3)2AsOAs(CH3)2
"cacodyl oxide"
40 -57°C 150°C 1.486
(CH3)2As-As(CH3)2
"cacodyl"
55.9 -5°C 163°C 1.447
Me7As3 and
Me5As3 (mixture)
1.3 very viscous at -80°C 115-120°C
/5 mmHg
1.647
(CH3As)5 0.2 10°C 190°C
/5 mmHg
2.15
The use of Cadet's fuming liquid was considered for use in chemical warfare during both WWI and WWII and plants in both Germany and the USA were said to have developed processes for large-scale production. During WWI an organoarsenic compound was used ( Lewisite) but not Cadet's liquid.
The exact composition of Cadet's fuming liquid is still unclear but with todays array of sophisticated spectroscopic instruments it should be possible to find a definitive answer. The problems of toxicity etc. are no longer an insurmountable problem given the handling techniques and glassware that were developed beginning with the experimental work of the early synthetic chemists like Bunsen and Schlenk.
"Gosio gas"
Another "simple" methyl derivative, Me3As, has a long history as well. In 1893 the Italian physician Bartolomeo Gosio published his results on "Gosio gas" that was subsequently shown to contain trimethylarsine. Under wet conditions, the mould Scopulariopsis brevicaulis produces significant amounts of methyl arsines via methylation of arsenic-containing inorganic pigments, especially Paris green/Schweinfurt-green("copper arsenite plus copper acetate") and Scheele's Green ("copper arsenite") which were once used in indoor wallpapers. In other cases the arsenic had been added to the wallpaper paste to discourage rodents and insects. Gosio gas was responsible for a number of deaths, and the air in the buildings in which it was being produced had a characteristic garlic-like odour. Gosio established the source of the problem and isolated some of the moulds capable of metabolizing inorganic arsenicals. Pietro Biginelli aspirated the gas from cultures through acidified (HCl) mercuric chloride solution. On the basis of an analysis of the precipitate so obtained, he incorrectly identified the gas as diethylarsine (Et2AsH). Nonetheless, this was a considerable achievement and established the methodology that Frederick Challenger was to use some 30 years later in his classic studies, beginning with the positive identification of the mould metabolite as trimethylarsine.
Newer studies suggest that trimethylarsine has a lower toxicity than originally thought and may not account for the death and the severe health problems observed in the 19th century which may have arisen due to volatile organics produced from moulds (now linked to what has been called "sick-building syndrome")
Lead arsenate dust from a painted ceiling was the source of the arsenic that caused health problems for Clare Boothe Luce when she was living in Rome as U.S. Ambassador in 1954. No mould action was implicated. One theory was that a washing machine in an upstairs room caused vibrations that dislodged some arsenic containing paint from the stucco decorating her bedroom ceiling!
Me3As
AsMe3 is a pyramidal molecule as predicted by VSEPR theory. The As-C distances average 151.9 nm, and the C-As-C angles are 91.83°
Methylmercury
The usual method of ingestion of a metal into the body is:
1. Orally - the Gastrointestinal Tract
2. via the lungs - the Respiratory Tract
a) Orally - (mouth, stomach, small intestine).
Food digestion begins in the mouth where saliva containing the enzyme amylase beaks down starch to lower sugars. Most digestion occurs in the stomach in the presence of HCl (pH ~1.6 ie. 0.17M HCl). In the case of mercury it is quite readily absorbed through the stomach since reaction of mercury salts with HCl produces HgCl2. This neutral covalent molecule (solubility in H2O 0.5 g/100 mL but 8g/100 mL in ethanol) is absorbed far better than most inorganic ions and this no doubt contributes to its high toxicity.
b) Respiratory tract (nose, lungs).
This is usually unimportant for most metals but in some cases it can be more efficient that via the gastrointestinal tract. For example, lead where 50% of Pb in air can be absorbed but only 5-10% via the gastrointestinal tract. Volatile dimethyl mercury is another case for concern.
dimethylmercury
The mercury cycle
Mercury is 62nd in terms of natural abundance and is found everywhere, usually as the mineral cinnabar, HgS, although 30 minerals containing Hg are known. The oxidation states are Hg(0), Hg(I) and Hg(II), where Hg(I) has been shown to exist as Hg22+.
HgS - cinnabar
The three Hg species are related by the disproportionation:
Hg22+ → Hg0 + Hg2+ E° = -0.131 V
or K= 6 x 10-3
In addition:
Hg22+/Hg E° = 0.789 V
Hg2+/Hg E° = 0.854 V
This means that to oxidise Hg to Hg22+ an oxidising agent with potential > 0.789V is required, but very importantly < 0.854 V, otherwise oxidation to Hg2+ will occur. There are no common oxidants that fit this arrangement so if any reaction occurs the product will be Hg2+. The equilibrium constant of 6 x 10-3 shows that when Hg(I) is formed it is moderately stable, however any agent that reduces the Hg(II) concentration automatically drives the reaction from Left → Right. Given that many Hg(II) derivatives are insoluble then this clearly restricts the range of Hg(I) compounds.
Minamata Disease
There have been several serious outbreaks of mercury poisoning. The most famous was between 1953 and 1965 at Minamata Bay in Japan when 46 people died and 120 suffered severe symptoms. As of March 2001, 2,265 victims had been officially recognised (1,784 of whom had died) and over 10,000 had received financial compensation from Chisso. By 2004, Chisso Corporation had paid \$86 million in compensation, and in the same year was ordered to clean up its contamination. On March 29th, 2010, a settlement was reached to compensate as-yet uncertified victims.
The disease was first noticed in cats (who were seen throwing themselves into the sea) and was quickly traced to mercury poisoning acquired as a result of eating contaminated fish (5-10 ppm Hg). The investigations that followed showed that the fish had acquired the high mercury due to the dumping of inorganic mercury salts and methylmercury from the Chisso Co. plastics factory upstream.
Analysis of fish exhibits from museums, some over 90 years old, has shown that mercury levels for ocean fish are similar but that river fish levels have risen as a result of man-made contamination. The forms of mercury occuring in the environment are Hg2+ and methylmercury, either MeHg+ or Me2Hg. Interconversion can be affected by microorganisms.
Aerobes can solubilise Hg2+ from cinnabar (Ksp ~10-53) which in sediments was considered safe since the solubility product was so small. The conversion of S2- → SO32- → SO42- allows the insoluble sulfide to breakdown and in the process other Hg(II) salts are formed or the mercury may get reduced to Hg(0) enzymatically.
Hg2+ + NADH + H+ → Hg0 + NAD+ + 2 H+, where NADH = reduced form of nicotinamideadeninedinucleotide
This conversion can be considered as a detoxification process since Hg0 is more easily eliminated.
In the environment, sulfate-reducing bacteria take up mercury in its inorganic form and through metabolic processes convert it to methylmercury. Sulfate-reducing bacteria are found in anaerobic conditions, typical of the well-buried muddy sediments of rivers, lakes, and oceans where methylmercury concentrations tend to be highest. Sulfate-reducing bacteria use sulfur rather than oxygen as their cellular energy-driving system. One hypothesis is that the uptake of inorganic mercury by sulfate-reducing bacteria occurs via passive diffusion of the dissolved complex HgS. Once the bacterium has taken up this complex, it utilizes detoxification enzymes to strip the sulfur group from the complex and replaces it with a methyl group:
HgS → CH3Hg(II)X + H2S
Upon methylation, the sulfate-reducing bacteria transport the new mercury complex back to the aquatic environment, where it is taken up by other microorganisms. Bacteria eliminate Hg by methylating it first to MeHg+ and Me2Hg. The detoxification process for them is the reverse for us unfortunately! The conversion probably involves vitamin B12 a methyl-cobalt organometallic compound so this is another example of synthesis involving transmetallation.
The major source of methylmercury exposure in humans is consumption of fish, marine mammals, and crustaceans. Once inside the human body, roughly 95% of the fish-derived methylmercury is absorbed from the gastrointestinal tract and distributed throughout the body. Uptake and accumulation of methylmercury is rapid due to the formation of methylmercury-cysteine complexes. Methylmercury is believed to cause toxicity by binding the sulfhydryl groups at the active centers of critical enzymes and structural proteins. Binding of methylmercury to these moieties constitutively alters the structure of the protein, inactivating or significantly lowering its functional capabilities.
Once the Me2Hg is formed it is volatile and when released into the atmosphere it is readily photolysed by UV light
Me2Hg → Hg0 + 2 CH3° → CH4 or C2H6
Other microorganisms can convert MeHg+ to Hg0 + CH4 that is make the mercury considerably less toxic to humans.
The Mercury Cycle
Summary
Organic mercury tends to increase up the food chain, particularly in lakes. The mud at the bottom of a lake may have 100 or 1000 times the amount of mercury than is in the water. Bacteria, worms and insects in the mud extract and concentrate the organic mercury. Small fish that eat them further concentrate the mercury in their bodies. This concentration process, known as "bioaccumulation", continues as larger fish eat smaller fish until the top predator fish in the lake may have methylmercury levels in their tissues that are up to 1,000,000 times the level in the water in which they live. We then eat the fish....
To consume a human being would be extremely unhealthy for any animal. Humans carry the highest concentration of toxic chemicals of all creatures on the planet. Their livers, hearts, kidneys and brains are so heavily contaminated with hundreds of different synthetic chemicals that if humans were slaughtered as a meat source, they'd never pass USDA food safety standards.
from Hg in Humans
Properties of Me2Hg
Molecular formula C2H6Hg
Molar mass 230.66 g mol-1
Appearance Colourless liquid
Density 2.96 g/mL
Melting point -43 °C
Boiling point 87-97 °C
Solubility in water Insoluble
Laboratory Preparation:
Hg + 2 Na + 2 CH3I → (CH3)2Hg + 2 NaI
1H NMR of dimethylmercury showing 199Hg coupling (J ~100.9 Hz)
199Hg has a nuclear spin of ½ and natural abundance of 16.87%. Can you explain the observed splitting pattern?
Methylmercury
Dimethylmercury
Prof Wetterhahn -mercury
Tetraethyllead
Like mercury, lead is primarily obtained from its sulfide ore, in this case Galena, PbS, yet once again there are quite a number of other minerals containing lead. In terms of natural abundance it exists at about 14 ppm in the Earth's crust (37th compared to O), however it has become well known due to its ease of extraction and the number of uses with technical importance.
galena, PbS
Lead was probably discovered around 6500 BC in Turkey and by 300 BC the Romans had lead smelters in operation. The toxicity of lead was recorded by the Greeks as early as 100BC. A report from 2BC noted that: "the drinking of lead causes oppression to the stomach, belly and intestines with wringing pains; it suppresses the urine, while the body swells and acquires and unsightly leaden hue".
The possible hazards associated with the use of lead piping in water systems was recognised as long ago as the first century BC and it has even been suggested that the "decline of the Roman Empire" might have been ascribed to the use of lead acetate as an additive to sweeten wine. It is somewhat surprising therefore that the first legislation controlling the industrial hazards of lead industries was not introduced until 1864.
Note that Dr. Wilton Turner (born in Clarendon, Jamaica in the early 1800's) wrote on the inappropriate use of lead in sugar and rum production while running a rum distillery in Guyana. One advocate said he had fed lead to dogs and guinea pigs for several weeks and seen no adverse affects in fact the guinea pigs were stolen which he thought was because they looked so fat and healthy!
An examination (in the early 1970's) of the annual snow strata in Northern Greenland and Poland revealled most elegantly that levels in air-borne lead had increased significantly since the Industrial Revolution and very sharply since 1940. Considering that 40-50% can be absorbed by inhalation compared to only 5-10% through ingestion this was cause for concern.
Lead content in North Greenland snow layers (µg per kg)
Leaded gasoline was an economic success from 1926 until 1976, and in fact, its discovery by Thomas Midgley at Charles Kettering's General Motors laboratory was among the most celebrated achievements of automotive engineering. It was often portrayed as the result of genius, luck and a great deal of hard work. It is now considered to be a catastrophic failure and is banned for environmental and public health reasons. {There are still a few countries selling petrol with lead additives.} Even more surprising is that the use of ethanol in fuel was already well established by the time tetraethyllead was introduced as an additive.
Tetraethyllead was supplied for mixing with raw gasoline in the form of "ethyl fluid", which was Et4Pb blended together with the lead scavengers 1,2-dibromoethane and 1,2-dichloroethane. "Ethyl fluid" also contained a reddish dye to distinguish treated from untreated gasoline and discourage the use of leaded gasoline for other purposes such as cleaning.
Ethyl fluid was added to gasoline in the ratio of 1:1260, usually at the refinery. The purpose was to increase the fuel's octane rating. A high enough octane rating is required to prevent premature detonations known as engine knocking ("knock" or "ping"). Antiknock agents allow the use of higher compression ratios for greater efficiency and peak power. The formulation of "ethyl fluid" was:
• Tetraethyllead 61.45%
• 1,2-Dibromoethane 17.85%
• 1,2-Dichloroethane 18.80%
• Inert materials and dye 1.90%
Effect on Health
Humans have been mining and using this heavy metal for thousands of years, poisoning themselves in the process. Although lead poisoning is one of the oldest known work and environmental hazards, the modern understanding of the small amount of lead necessary to cause harm did not come about until the latter half of the 20th century. No safe threshold for lead exposure has been discovered, that is, there is no known amount of lead that is too small to cause the body harm.
Lead pollution from engine exhaust is dispersed into the air and into the vicinity of roads and easily inhaled. Lead is a toxic metal that accumulates and has subtle and insidious neurotoxic effects especially at low exposure levels, such as low IQ and antisocial behavior. It has particularly harmful effects on children. These concerns eventually led to the ban on Et4PB in automobile gasoline in many countries. For the entire U.S. population, during and after the Et4PB phaseout, the mean blood lead level dropped from 13 µg/dL in 1976 to only 3 µg/dL in 1991. The U.S. Centers for Disease Control considered blood lead levels "elevated" when they were above 10 µg/dL. Lead exposure affects the intelligence quotient (IQ) such that a blood lead level of 30 µg/dL is associated with a 6.9-point reduction of IQ, with most reduction (3.9 points) occurring below 10 µg/dL.
Also in the U.S., a statistically significant correlation has been found between the use of Et4PB and violent crime: taking into account a 22-year time lag, the violent crime curve virtually tracks the lead exposure curve. After the ban on Et4PB, blood lead levels in U.S. children dramatically decreased.
Even though leaded gasoline is largely gone in North America, it has left high concentrations of lead in the soil adjacent to all roads that were constructed prior to its phaseout. Children are particularly at risk if they consume this, as in cases of pica.
Note as well the work done in 1995 by ICENS on the problem of the old disused lead mine and tailings that affected school children in Kintyre. Over 40 cases were detected with unacceptable levels. ICENS at that time cleaned the community and sought to educate residents about the dangers. A continuation of the research done in Kintyre was to test 628 children at 17 basic schools across the island. Children at a number of basic schools in Kingston and St Catherine were discovered with blood lead levels as low as 45 µg/dL and as high as 60. In two of the cases, children had lead levels of 130 and 202. At this level, they would likely die from the poisoning if untreated.
Properties of Et4Pb
Molecular formula C8H20Pb
Molar mass 323.44 g mol-1
Appearance Colourless, viscous liquid
Density 1.653 g/mL (20 °C)
Melting point -136 °C
Boiling point 84-85 °C/15 mm Hg
Solubility in water Insoluble
Laboratory Preparation:
The industrial preparation of tetraethyllead was from the reaction below:
~373K in an autoclave
4 NaPb + 4 EtCl → Et4Pb + 3 Pb + 4 NaCl
alloy
or by electrolysis of NaAlEt4 or EtMgCl using a Pb anode.
Laboratory syntheses of R4Pb compounds in general include the use of Grignard reagents or organolithium compounds.
in ether
2 PbCl2 + 4 RLi → R4Pb + 4LiCl + Pb
tetraethyllead
lead timeline
Tetraethyllead
"ethyl" articles | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/23%3A_Organometallic_chemistry-_s-Block_and_p-Block_Elements/23.06%3A_Group_15/23.6B%3A_Arsenic_Antimony_and_Bismuth.txt |
The study of Organometallic chemistry has been important in the growth of chemistry ever since the first compound was synthesized in 1827. Organometallic compounds can be defined as a compound that contains at least one metal-carbon bond, not including cyanide. Organometallic compounds are used in numerous reactions, including but not limited to, the Grignard reaction, and the Simmons-Smith reaction.
24: Organometallic chemistry- d-block elements
Learning Objectives
In this lecture you will learn the following
• Get a general prospective on the historical background of transition metal organometallic compounds with particular emphasis on metal alkyls.
• Know more about stable metal alkyls.
• Get introduced to transition metal agostic alkyls.
• Develop an understanding of reactions of relevance to metal alkyls like the reductive eliminations, oxidative additions and the halide eliminations.
Transition metal σ−bonded organometallic compounds like the metal alkyls, aryls and the hydrides derivatives are by for the most common organometallic species encountered in the world of chemistry. Yet, these compounds remained elusive till as late as the 1960s and the 1970s.
Historical Background
Metal alkyls of the main group elements namely, Li, Mg, Zn, As and Al, have been known for a long time and which over the years have conveniently found applications in organic synthesis whereas development on similar scale and scope in case of the transition metal counterparts were missing till only recently. The origin of the organometallic compounds traces back to 1757, when Cadet prepared a foul smelling compound called cacodyl oxide from As2O3 and CH3COOK, while working in a military pharmacy in Paris. Years later in 1840, R. W. Bunsen gave the formulation of cacodyl oxide as Me2As−O−AsMe2. The next known transition metal organometallic compound happens to be Et2Zn, which was prepared serendipitously in 1848 from the reaction of ethyl iodide (EtI) and Zn with the objective of generating free ethyl radical. Frankland further synthesized alkyl mercury halides like, CH3HgI, from the reaction of methyl iodide (CH3I) and Hg in sunlight. It is important to note that the dialkyl mercury, R2Hg, and the dialkyl zinc, R2Zn, have found applications as alkyl transfer reagents in the synthesis of numerous main group organometallic compounds.
Another notable development of the time was of the preparation of Et4Pb from ethyl iodide (EtI) and Na/Pb alloy by C. J. Lowig and M. E. Schweizer in 1852. They subsequently extended the same method for the preparation of the Et3Sb and Et3Bi compounds. In 1859, aluminumalkyliodides, R2 AlI, were prepared by W. Hallwachs and A Schafarik from alkyl iodide (RI) and Al. The year 1863 saw the preparation of organochlorosilanes, RmSiCl4−m, by C. Friedel and J. M. Crafts while the year 1866 saw the synthesis of halide-free alkyl magnesium compound, Et2Mg, by J. A. Wanklyn from the reaction of Et2Hg and Mg. In 1868, M. P. Schutzenberger reported the first metal−carbonyl complex in the form of [Pt(CO)Cl2]2. In 1890, the first binary metal−carbonyl compound, Ni(CO)4 was reported by L. Mond, who later founded the well−known chemical company called ICI (Imperial Chemical Industries). In 1909, W. J. Pope reported the first σ−organotransition metal compound in the form of (CH3)3PtI. In 1917, the alkyllithium, RLi, compounds were prepared by W. Schlenk by transalkylation reactions. In 1922, T. Midgley and T. A. Boyd reported the utility of Et4Pb as an antiknock agent in gasoline. A. Job and A. Cassal prepared Cr(CO)6 in 1927. In 1930, K. Ziegler showed the utility of organolithium compounds as alkylating agent while in the following year in 1931, W. Heiber prepared Fe(CO)4H2 as the first transition metal−hydride complex. O. Roelen discovered the much renowned hydroformylation reaction in 1938, that went on to become a very successful industrial process worldwide.
The large scale production and the use of silicones were triggered by E. G. Rochow, when he reported the ‘direct synthesis’ from methyl chloride (CH3Cl) and Si using Cu catalyst at 300 °C in 1943. The landmark compound, ferrocene (C5H5)2Fe, known as the first sandwich complex was obtained by P. Pauson and S. A. Miller in 1951. H. Gilman introduced the important utility of organocuprates when he prepared LiCu(CH3)2, in 1952. In the subsequent year 1953, G. Wittig found a new method of synthesizing olefins from phosphonium ylides and carbonyl compounds that fetched him a Nobel prize in 1979. The year 1955 turned out to be a year of path breaking discoveries with E. O. Fischer reporting the rational synthesis of bis(benzene)chromium, (C6H6)2Cr while K. Ziegler and G. Natta announcing the ground breaking polyolefin polymerization process that subsequently gave them the Nobel prizes, E. O. Fischer sharing with G. Wilkinson in 1973 while K. Ziegler and G. Natta shared the same in 1963. In 1956, H. C. Brown reported hydroboration for which he too received the Nobel prize in 1979. In 1963, L. Vaska reported the famous Vaska’s complex, trans−(PPh3)2Ir(CO)Cl, that reversibly binds to molecular oxygen. In 1964, E. O. Fischer reported the first carbene complex, (CO)5WC(OMe)Me. In 1965, G. Wilkinson and R. S. Coffey reported the Wilkinson catalyst, (PPh3)3RhCl, for the hydrogenation of alkenes. In 1973, E. O. Fischer synthesized the first carbyne complex, I(CO)4Cr(CR).
After the early 1970s, there were tremendous outburst in activity, in the area of transition metal organometallic chemistry leading to phenomenal developments having far-reaching consequences in various branches of the main stream and interfacial chemistry. Several Nobel prizes that have been awarded to the area in recent times fully recognized the significance of these efforts with Y. Chauvin, R. R. Schrock, and R. H. Grubbs winning it in 2005 for olefin metathesis and Akira Suzuki, Richard F Heck and E. Negishi receiving the same for the Pd catalyzed C−C cross-coupling reactions in organic synthesis in 2010.
Metal alkyls
In day to day organic synthesis, particularly from the application point of view, the metal alkyls are often perceived as a source of stabilized carbanions for reactions with various electrophiles. The extent of stabilization of alkyl carbanions in metal alkyl complexes depend upon the nature of the metal cations. For example, the alkyls of electropositive metals like that of Group 1 and 2, Al and Zn are regarded as polar organometallics as the alkyl carbanions remain weakly stabilized while retaining strong nucleophilic and basic character of a free anion. These polar alkyls are extremely air and moisture sensitive as in their presence they often get hydrolyzed and oxidized readily. Similar high reactivity was also observed in case of the early transition metal organometallic compounds particularly of Ti and Zr. On the contrary the late transition metal organometallic compounds are much less reactive and stable. For example, the Hg−C bond of (Me−Hg)+ cation is indefinitely stable in aqueous H2SO4 solution in air. Thus, on moving from extremely ionic Na alkyls to highly polar covalent Li and Mg alkyls and to essentially covalent late−transition metal alkyls, a steady decrease in reactivity is observed. This trend can be correlated to the stability of alkyl carbanions that also depended on the nature of hybridization of the carbon center, with sp3 hybridized carbanions being the least stable and hence most reactive, followed by the sp2 carbanions being moderately stable while the sp carbanions being the least reactive and most stable. The trend also correlates well with the respective pKa values observed for CH4 (pKa = ~50), C6H6 (pKa = ~43) and RC≡CH (pKa = ~25).
Stable alkyls
As has been mentioned earlier, that the β−elimination is a crucial destabilizing influence on the transition metal organometallic complexes. Hence, inhibition of this decomposition pathway leads to increased stabilities of organometallic compounds. Thus, many stable alkyl transition metal complexes do not possesses β−hydrogens like, W(Me)6 and Ti(CH2Ph)4. In some cases despite the presence of the β−hydrogens the organometallic complexes are stable as the β−hydrogens are deposed away from the metal center like in, Cr(CHMe2)4, and Cr(CMe3)4. In this category of stable transition metal organometallic compounds also falls the ones that contain β−hydrogens but cannot β−eliminate owing to the formation of a olefinic bond at a bridgehead, which is unfavorable, like in Ti(6−norbornyl)4 and Cr(1−adamantyl)4. Lastly, some 18 VE metal complexes are stable, again despite having β−hydrogens, for reasons of being electronically as well as coordinatively saturated at the metal center owing to attaining the stable 18 electron configuration.
Agostic alkyls
Agostic alkyls are extremely rare but very interesting species that represents a frozen point in a β−elimination pathway that have fallen short of the completion of the decomposition reaction. Thus, these agostic alkyl complexes can be viewed as snap shots of a β−elimination trajectory thereby providing valuable mechanistic understanding of the decomposition reaction. The agostic interaction has characteristic signatures in various spectroscopic techniques as observed from the decreasing JC−Hcoupling constant values in the 1H NMR and the 13C NMR spectra and the lowering of the νCHstretching frequencies in the IR spectroscopy. The agostic alkyl complexes can be definitively proven by X−ray diffraction or neutron diffraction studies. The agostic alkyls thus have activated C−H bonds which are of interest for their utility in chemical catalysis. Quite interestingly, many d0 Ti agostic alkyl complexes do not β−eliminate primarily for the metal center being too electron deficient to donate electron to the σ* C−H orbital as required for the subsequent β−elimination process.
Reductive elimination
Reductive elimination represents a major decomposition pathway of the metal alkyls. Opposite of oxidative addition, the reductive elimination is accompanied by the decrease in the oxidation state and the valence electron count of the metal by two units. The metal alkyl complexes may thus reductively eliminate with an adjacent hydrogen atom to yield an alkane, (R−H) or undergo the same with an adjacent alkyl group to give an even larger alkane (R−R) as shown below.
The reductive elimination is often facilitated by an electron deficient metal center and by sterically demanding ligand systems. Often d8 metals like Ni(II), Pd(II), and Au(III) and d6 metals in high oxidation state like, Pt(IV), Pd(IV), Ir(III), and Rh(III) exhibit reductive elimination.
Oxidative addition
Unlike the reductive elimination that represents a decomposition pathway of metal alkyls, the oxidative addition reaction represents a useful method for the formation of the metal alkyl complexes. The oxidative addition thus leads to increase in valence electron count and the oxidation state of the metal center by two units. The oxidative addition reactions are often facilitated by low valent electron rich metal centers and by less sterically demanding ligands.
Halide elimination
β−halide elimination is observed for the early transition metals and the f−block elements resulting in the formation of stable alkyl halides. The phenomenon is mostly seen in case of the metal fluorides and arise owing to the very high alkyl−fluoride bond strengths that favor the halide elimination.
Summary
A broader outlook on metal alkyls is obtained from the study of its historical background thus dispelling many myths about these compounds like them being inherently unstable. It also establishes newer founding principles like these compounds indeed being thermodynamically stable under certain experimental conditions and thus facilitating further attempts to take up the synthesis of these compounds. Another important class of transition metal organometallic compounds are the agostic alkyls, which can be viewed as the ones that have proceeded along but have fallen short of the final sequence of the β−elimination step. While oxidative addition reaction remains a key method for synthesizing metal alkyls, the complementary reaction, i.e, the reductive elimination, represents a decomposition reaction of these compounds. β−halide elimination reactions are observed for early transition metal elements and f−block elements.
Problems
1. Who elucidated the structure of cacodyl oxide?
Ans: R. W. Bunsen in 1840
2. Give the example of the first olefin bound transition metal complex?
Ans: Zeise's salt, Na[PtCl3(C2H4)]
3. Who discovered olefin polymerization? Ans: K. Ziegler and G. Natta 4. What kind of metal center promotes oxidative addition reactions? Ans: Electron rich 5. The 18 VE complex would favor/disfavor oxidative addition reactions? Ans: Disfavor
Self Assessment test
1. O. Roelen discovered which famous reaction?
Ans: Hydroformylation
2. What is the first binary metal−carbonyl complex?
Ans: Ni(CO)4
3. Who discovered the hydroboration reaction? Ans: H. C. Brown 4. Reductive elimination reaction is favored by what kind of ligands? Ans: Sterically demanding 5. β−halide elimination is mainly observed for what type of metal halide complexes? Ans: Metal fluorides
Contributors and Attributions
http://nptel.ac.in/courses/104101006/20 | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/24%3A_Organometallic_chemistry-_d-block_elements/24.01%3A_Introduction.txt |
Learning Objectives
In this lecture you will learn the following
• Understand the role lead by ligands in stabilizing organometallic transition metal complexes.
• Know about various synthetic methods available for preparing the organometallic transition metal complexes.
• Understand the various factors like β-elimination and other bimolecular decomposition pathways that contribute to the observed instability of the organometallic transition metal complexes.
• Obtain insight about making stable organometallic transition metal complexes by suppression of the destabilizing factors mentioned.
Ligands play a vital role in stabilizing transition metal complexes. The stability as well as the reactivity of a metal in its complex form thus depend upon the number and the type of ligands it is bound to. In this regard, the organometallic carbon based ligands come in diverse varieties displaying a wide range of binding modes to a metal. In general, the binding modes of the carbon-derived ligands depend upon the hybridization state of the metal bound carbon atom. These ligands can thus bind to a metal in many different ways as depicted below. Lastly, these ligands can either be of (a) purely σ−donor type, or depending upon the capability of the ligand to form the multiple bonds may also be of (b) a σ−donor/π−acceptor type, in which the σ−interaction is supplemented by a varying degree of π−interaction.
Preparation of transition metal-alkyl and transition metal-aryl complexes
The transition metal−alkyl and transition−metal aryl complexes are usually prepared by the following routes discussed below,
Metathesis
This involves the reactions of metal halides with organolithium, organomagnesium, organoaluminium, organotin and organozinc reagents.
Of the different organoalkyl compounds listed above, the organolithium and organomagnesium compounds are strongly carbanionic while the remaining main group organometallics like the organoalkyl, organozinc and organotin reagents are relatively less carbanionic in nature. Thus, the main group organometallic reagents have attenuated alkylating power, that can be productively used in partial exchange of halide ligands.
Alkene insertion or Hydrometallation
As the name implies, this category of reaction involves an insertion reaction between metal hydride and alkene as shown below. These type reactions are relevant to certain homogeneous catalytic processes in which insertion of an olefin to M−H bond is often observed.
Carbene insertion
This category represents the reaction of metal hydrides with carbenes.
Metallate alkylation reaction
This category represents the reaction of carbonylate anions with alkyl halides as shown below.
Preparation of transition metal-alkyl and transition metal-aryl complexes (contd..)
Metallate acylation reaction
This category involves the reaction of carbonylate anions with acyl halides.
Oxidative addition reaction
Many unsaturated 16 VE transition metal complexes having d8 or d10 configuration undergo oxidative addition reactions with alkyl halides. The oxidative addition reactions proceed with the oxidation state as well as coordination number of the metal increasing by +2.
Addition reaction
This category involves the reaction of an activated metal bound olefin complex with a nucleophile as shown below.
Thermodynamic Stability and Kinetic Lability
The transition metal organometallic compounds are often difficult to synthesize under ordinary laboratory conditions and require stringent experimental protocols involving the exclusion of air and moisture for doing so. As a consequence, many homoleptic binary transition metal−alkyl and transition metal−aryl compounds like, Et2Fe or Me2Ni cannot be made under normal laboratory conditions. More interestingly, most of the examples of transition metal−aryl and transition metal−alkyl compounds, known in the literature, invariably contain additional ligands like η5-C5H5, CO, PR3 or halides.
For example,
Transition metal−carbon (TM−C) bond energy values are important for understanding the instability of transition metal organometallic compounds. In general, the TM−C bonds are weaker than the transition metal−main group element (TM−MGE) bonds (MGE = F, O, Cl, and N) and more interestingly so, unlike the TM−MGE bond energies, the TM−C bond energy values increase with increasing atomic number. The steric effects of the ligands also play a crucial role in influencing the TM−C bond energies and thus have to be given due consideration.
Contrary to the popular belief, the difficulty in obtaining transition metal−aryl and transition metal−alkyl complexes does primarily arise from the thermodynamic reasons but rather the kinetic ones. β−elimination is by far the most general decomposition mechanism that contribute to the instability of transition metal organometallic compounds. β−elimination results in the formation of metal hydrides and olefin as shown below.
β−elimination can also be reversible as shown below.
The instability of transition metal organometallic compounds can arise out of kinetic lability like in the case of the β−elimination reactions that trigger decomposition of these complexes. Thus, the suppression of the decomposition reactions provides a viable option for the stabilization of the transition metal organometallic complexes. The β−elimination reactions in transition metal organometallic complexes may be suppressed under any of the following three conditions.
1. Formation of the leaving olefin becomes sterically or energetically unfavorable
In the course of β−elimination, this situation arises when the olefinic bond is formed at a bridgehead carbon atom or when a double bond is formed with the elements of higher periods. For instance, the norbornyl group is less prone to decomposition by β−elimination because that would require the formation of olefinic double bond at a bridgehead carbon atom in the subsequent olefin, i.e. norbornene, and which is energetically unfavorable.
1. Absence of β−hydrogen atom in organic ligands
Transition metal bound ligands that do not possess β−hydrogen cannot decompose by β−elimination pathway and hence such complexes are generally more stable than the ones containing β−hydrogen atoms. For example, the neopentyl complex, Ti[CH2C(CH3)3]4 (m.p 90 °C), and the benzyl complex, Zr(CH2Ph)4 (m.p. 132 °C), exhibit higher thermal stability as both of the neopentyl and benzyl ligands lack β−hydrogens.
2. Central metal atom is coordinatively saturated
Transition metal organometallic complexes in which the central metal atom is coordinatively saturated tend to be more stable due to the lack of coordination space available around the metal center to facilitate β−elimination reaction or other decomposition reactions. Thus, the absence of free coordination sites at the metal is crucial towards enhancing the stability of the transition metal organometallic complexes. For example, Ti(Me)4, which is coordinatively unsaturated can undergo a bimolecular decomposition reaction via a binuclear intermediate (A), is unstable and exhibits a decomposition temperature of –40 °C. On the contrary, Pb(Me)4, that cannot undergo decomposition by such bimolecular pathway, is more stable and distills at 110 °C at 1 bar atmospheric pressure.
The Ti(Me)4 decomposes by dimerization involving the formation of Ti−C (3c−2e) bonds. For Pb(Me)4, such bimolecular decomposition pathway is not feasible, as being a main group element it has higher outer d orbital for extending the coordination number. If the free coordination site of Ti(Me)4 is blocked by another ligand, as in [(bipy)Ti(Me)4], then the thermal stability of the complex, [(bipy)Ti(Me)4], increased significantly. Other bidentate chelating ligands like bis(dimethylphosphano)ethane (dmpe) also serve the same purpose.
Coordinative saturation thus brings in kinetic stabilization in complexes. For example, Ti(Me)4is extremely reactive as it is coordinatively unsaturated, while W(Me)4 is relatively inert for reasons of being sterically shielded and hence, coordinatively saturated. Thus, if all of the above discussed criteria for the suppression of β-elimination are taken care of, then extremely stable organometallic complexes can be obtained like the one shown below.
Problems
1. Arrange the following compounds in the order of their stability.
(a). Ti(Et)4 (b). Ti(Me)4 and (c). Ti(6-norbornyl)4
Ans: Ti(Et)4 < Ti(Me)4 < Ti(6-norbornyl)4 2. Predict the product of the reaction given below.
Ans: Equi molar amounts of (Bu3P)CuD and CH2=CDC2H5 3. Will the compound β-eliminate,
(a). readily, (b). slowly and (c). not at all.
Explain your answer with proper reasoning.
Ans: Not at all as the ß-hydrogens are pointing away from the metal and cannot participate in ß-elimination recation.
Self Assessment test
1. Write the product(s) of the reactions.
Ans:
Summary
Ligands assume a pivotal role in the stabilization of the organometallic transition metal complexes. There are several methods available for the preparation of the organometallic transition metal complexes. The observed instability of the organometallic transition metal complexes can be attributed to two main phenomena namely β-elimination and bimolecular decomposition reaction that severely undermine the instability of these complexes. The suppression of these decomposition pathway thus pave way for obtaining highly stable organometallic transition metal complexes.
24.02: Common Types of Ligand - Bonding and Spectroscopy
Learning Objectives
In this lecture you will learn the following
• The metal−allyl complexes.
• The metal−diene complexes.
• The metal−cyclobutadiene complexes.
• The respective metal−ligand interactions.
The allyl ligand is often referred to as an “actor” ligand rather than a “spectator” ligand. It binds to metals in two ways i.e. in a η1 (monohapto) form and a η3 (trihapto) form (Figure 1). (i). In its monohapto (η1) form, it behaves as an anionic 1e−donor X type of a ligand analogous to that of a methyl moiety while (ii) in a trihapto (η3) form, it acts as an anionic 3e−donor LX type of a ligand.
Metal−allyl interaction
Of particular interest are the molecular orbitals namely Ψ1, Ψ2 and Ψ3 of the allyl ligand that interact with the metal in a metal allyl complex. The energy of these molecular orbitals increase with the increase in the number of nodes. Of the three, the Ψ1 and Ψ2 orbitals usually engage in ligand to metal σ−donation, with Ψ1 involving in a dative L−type bonding and Ψ2 participating in a covalent X−type bonding with the metal d orbitals (Figure 2).
Synthesis of the metal allyl complexes
The metal allyl complexes are synthesized by the following methods.
1. From an alkene complex as shown below.
2. By a nucleophilic attack of an allyl compound as shown below.
3. By an electrophilic attack of an allyl compound as shown below.
4. From a diene complex as shown below.
Reactions of metal allyl complexes
The reactivities of the metal allyl complexes toward various species are illustrated below.
1. Reaction with nucleophiles
2. Reaction with electrophiles
3. Insertion reaction
4. Reductive elimination
Diene complexes
1,3−Butadiene is a 4e−donor ligand that binds to a metal in a cisoid conformation. The Dewar−Chatt model, when applied to 1,3−butadiene, predicts that the ligand may bind to metal either as a L22) donor type, similar to that of an alkene, or as an LX22π) donor type, similar to that of a metalacyclopropane form. The L2 binding of 1,3−butadiene is rare, e.g. asin (butadiene)Fe(CO)3, while the LX2 type binding is more common, e.g. as in Hf(PMe3)2Cl2. An implication of the LX2 type binding is in the observed shortening of the C2−C3 (1.40 Å) distance alongside the lengthening of the C1−C2(1.46 Å) and C3−C4 (1.46 Å) distances (Figure 3).
The molecular orbitals of the 1,3−butadiene ligand comprises of two filled Ψ1 (HOMO−1) and Ψ2(HOMO) orbitals and two empty Ψ3 (LUMO) and Ψ4 (LUMO+1) orbitals. In a metal−butadiene interaction the ligand to metal σ−donation occurs from the filled Ψ2 orbital of the 1,3−butadiene ligand while the metal to ligand π−back donation occurs on to the empty Ψ3 orbital of the 1,3−butadiene ligand (Figure 4).
Though cisoid binding is often observed in metal butadiene complexes, a few instances of transoidbinding is seen in dinuclear, e.g. as in Os3(CO)10(C4H6), and in mononuclear complexes e.g. as in Cp2Zr(C4H6) (Figure 5).
Synthesis of metal butadiene complex
Metal butadiene complexes are usually prepared by the same methods used for synthesizing metal alkene complexes. Two noteworthy synthetic routes are shown below.
Metal cyclobutadiene complexes
Cyclobutadiene is an interesting ligand because of the fact that its neutral form, being anti−aromatic (−electrons), is unstable as a free molecule (Figure 6), but its dianionic form is stable because of being aromatic (−electrons). Consequently, the cyclobutadiene ligand is stabilized by significant metal to ligand π−back donation to the vacant ligand orbitals.
A synthetic route to metal cyclobutadiene complex is shown below.
Problems
1. The hapticities displayed by an allyl moiety in binding to metals are? Ans: 1 and 3. 2. Identify which molecular orbitals of an allyl moiety engage in σ−interaction with a suitable d orbital of a metal in a η3−metal allyl complex? Ans: Ψ1 and Ψ2.
3. Predict the product of the reaction.
Ans:
4. Identify which molecular orbitals of a butadiene moiety engage in σ−interaction with a suitable dorbital of a metal in a η4−metal butadiene complex? Ans: Ψ2.
Self Assessment test
1. Predict the product of the reaction.
Ans:
2. Identify which molecular orbitals of a butadiene moiety engage in π−interaction with a suitable dorbital of a metal in a η4−metal allyl complex? Ans: Ψ3. 3. Mention the type of orientations displayed by butadiene ligands for binding to metal. Ans: Cisoid (common) and transoid (rare). 4. Comment on the number of π−electrons present in the cyclobutadiene moiety of a metal cyclobutadiene complex. Ans: 6 π−electrons.
Summary
Allyl, 1,3−butadiene and cyclobutadiene together constitute an important class of σ−donor/π−acceptor ligands that occupy a special place in organometallic chemistry. The complexes of these ligands with metals are important intermediates in many catalytic cycles and hence an understanding of their interaction with metal is of significant importance. In this context, the synthesis, characterization and the reactivities of the organometallic complexes of these ligands are described alongside the respective metal−ligand interactions. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/24%3A_Organometallic_chemistry-_d-block_elements/24.02%3A_Common_Types_of_Ligand_-_Bonding_and_Spectroscopy/24.2.01%3A_Metal_allyl_and_diene_complexes.txt |
σ−complexes
σ−complexes are rare compounds, in which the σ bonding electrons of a X−H bond further participate in bonding with a metal center (X = H, Si, Sn, B, and P). The σ complexes thus exhibit an askewed binding to a metal center with the hydrogen atom, containing no lone pair, being more close to the metal center and thereby resulting in a side−on structure. Many times if the metal center is electron rich, then further back donation to the σ* orbital of the metal bound X−H moiety may occur resulting in a complete cleavage of the X−H bond.
24.2B: Carbonyl Ligands
Learning Objectives
In this lecture you will learn the following
• The historical background of metal carbonyl complexes.
• The CO ligand and its binding ability to metal.
• Synergism between the ligand to metal forward σ–donation and the metal to ligand backward π–donation observed in a metal-CO interaction.
• The synthesis, characterization and their reactivity of the metal carbonyl compounds.
Metal carbonyls are important class of organometallic compounds that have been studied for a long time. Way back in 1884, Ludwig Mond, upon observing that the nickel valves were being eating away by CO gas in a nickel refining industry, heated nickel powder in a stream of CO gas to synthesize the first known metal carbonyl compound in the form Ni(CO)4. The famous Mond refining process was thus born, grounded on the premise that the volatile Ni(CO)4 compound can be decomposed to pure metal at elevated temperature. Mond subsequently founded the Mond Nickel Company Limited for purifying nickel from its ore using this method.
The carbonyl ligand (CO) distinguishes itself from other ligands in many respects. For example, unlike the alkyl ligands, the carbonyl (CO) ligand is unsaturated thus allowing not only the ligand to σ−donate but also to accept electrons in its π* orbital from dπ metal orbitals and thereby making the CO ligand π−acidic. The other difference lies in the fact that CO is a soft ligand compared to the other common σ−and π−basic ligands like H2O or the alkoxides (RO−), which are considered as hard ligands.
Being π−acidic in nature, CO is a strong field ligand that achieves greater d−orbital splitting through the metal to ligand π−back donation. A metal−CO bonding interaction thus comprises of a CO to metal σ−donation and a metal to CO π−back donation (Figure 1). Interestingly enough, both the spectroscopic measurements and the theoretical studies suggest that the extent of the metal to CO π−back donation is almost equal to or even greater than the extent of the CO to metal σ−donation in metal carbonyl complexes. This observation is in agreement with the fact that low valent−transition metal centers tend to form metal carbonyl complexes.
In the metal carbonyl complexes, the direct bearing of the π−back donation is observed on the M−C bond distance that becomes shorter as compared to that of a normal M−C single bond distance. For example, the CpMo(CO)3CH3 complex, exhibits two kind of M−C bond distances that comprise of a longer Mo−CH3 distance (2.38 Å) and a much shorter Mo−CO distance (1.99 Å) arising out of a metal to ligand π−back donation. It becomes thus apparent that the metal−CO interaction can be easily characterized using X−ray crystallography. The infrared spectroscopy can also be equally successfully employed in studying the metal−CO interaction. Since the metal to CO π−back bonding involves a π−donation from the metal dπ orbital to a π* orbital of a C−O bond, significant shift of the ν(CO) stretching frequency towards the lower energy is observed in metal carbonyl complexes with respect to that of free CO (2143 cm−1).
Preparation of metal carbonyl complexes
The common methods of the preparation of the metal carbonyl compounds are,
1. Directly using CO
The main requirement of this method is that the metal center must be in a reduced low oxidation state in order to facilitate CO binding to the metal center through metal to ligand π−back donation.
2. Using CO and a reducing agent
This method is commonly called reductive carbonylation and is mainly used for the compounds having higher oxidation state metal centers. The reducing agent first reduces the metal center to a lower oxidation state prior to the binding of CO to form the metal carbonyl compounds.
3. From carbonyl compounds
This method involves abstraction of CO from organic compounds like the alcohols, aldehydes and CO2.
Reactivities of metal carbonyls
1. Nucleophilic attack on carbon
The reaction usually gives rise to carbene moiety.
2. Electrophilic attack at oxygen
3. Migratory insertion reaction
The metal carbonyl displays two kinds of bindings in the form of the terminal and the bridging modes. The infrared spectroscopy can easily distinguish between these two binding modes of the metal carbonyl moiety as the terminal ones show ν(CO) stretching band at ca. 2100-2000 cm−1 while the bridging ones appear in the range 1720−1850 cm−1. The carbonyl moiety can bridge between more than two metal centers (Figure 2).
Problems
1. How many lone pairs are there in the CO molecule? Ans: Three (one from carbon and two from oxygen). 2. Despite O being more electronegative than C, the dipole moment of CO is almost zero. Explain. Ans: Because of the electron donation from oxygen to carbon. 3. What type of metal centers form metal carbonyl complexes? Ans: Low−valent metal centers. 4. What are the two main modes of binding exhibited by CO ligand? Ans: Terminal and bridging modes of binding.
Self Assessment test
1. Predict the product of the reaction?
Ans: Three (one from carbon and two from oxygen).
2. Upon binding to a metal center the C−O stretching frequency increases/decreases with regard to that of the free CO?
Ans: Decreases. 3. Explain why do low−valent metal centers stabilize CO binding in metal carbonyl complexes? Ans: Because metal to ligand π−back donation. 4. Give an example of a good σ−donor and π−donor ligand? Ans: Alkoxides (RO-).
Summary
CO is a hallmark ligand of organometallic chemistry. The metal carbonyl complexes have been studied for a long time. The CO ligands bind tightly to metal center using a synergistic mechanism that involves σ−donation of the ligand lone pair to metal and followed by the π−back donation from a filled metal d orbital to a vacant σ* orbital of C−O bond of the CO ligand. The metal carbonyl complexes are prepared by several methods. The metal carbonyl complexes are usually stabilized by metal centers in low oxidation states. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/24%3A_Organometallic_chemistry-_d-block_elements/24.02%3A_Common_Types_of_Ligand_-_Bonding_and_Spectroscopy/24.2A%3A_%28sigma%29-bonded_Alkyl_Aryl_and_Related_Lig.txt |
Learning Objectives
In this lecture you will learn the following
• Know about metal hydrides, their synthesis, characterization and their reactivity.
Metal hydrides occupy an important place in transition metal organometallic chemistry as the M−H bonds can undergo insertion reactions with a variety of unsaturated organic substrates yielding numerous organometallic compounds with M−C bonds. Not only the metal hydrides are needed as synthetic reagents for preparing the transition metal organometallic compounds but they also are required for important hydride insertion steps in many catalytic processes. The first transition metal hydride compound was reported by W. Heiber in 1931 when he synthesized Fe(CO)4H2. Though he claimed that the Fe(CO)4H2 contained Fe−H bond, it was not accepted until 1950s, when the concept of normal covalent M−H bond was widely recognized.
The metal hydride moieties are easily detectable in 1H NMR as they appear high field of TMS in the region between 0 to 60 ppm, where no other resonances appear. The hydride moieties usually couple with metal centers possessing nuclear spins. Similarly, the hydride moieties also couple with the adjacent metal bound phosphine ligands, if at all present in the complex, exhibiting characteristic cis (J = 15 − 30 Hz) and trans (J = 90 − 150 Hz) coupling constants. In the IR spectroscopy, the M−H frequencies appear between (1500 − 2200) cm−1 but their intensities are mostly weak. Crystallographic detection of metal hydride moiety is difficult as hydrogen atoms in general are poor scatterer of X−rays. Located adjacent to a metal atom in a M−H bond, the detection of hydrogen atom thus becomes challenging and as a consequence the X−ray crystallographic method systematically underestimates the M−H internuclear distance by ~ 0.1 Å. However, better data could be obtained by performing the X−ray diffraction studies at a low temperature in which the thermal motion of the atoms are significantly reduced. In light of these facts, the neutron diffraction becomes a powerful method for detection of the metal hydride moieties as hydrogen scatters neutrons more effectively and hence the M−H bond distances can be measured more accurately. A limitation of neutron diffraction method is that large sized crystals are required for the study.
Synthesis
Following reactions are employed for synthesizing metal hydrides.
1. Protonation reactions
For this reaction to occur the metal center has to be basic and electron rich.
2. From hydride donors
Generally for this method, a main group hydride is reacted with metal halide.
3. Using dihydrogen (H2) addition
This method involves oxidative addition of H2 and thus requires metal centers that are capable of undergoing the oxidative addition step.
4. From a ligand
This method takes into account the β−elimination that occur in a variety of metal bound ligand moieties, thereby yielding a M−H bond.
Reactions of metal hydrides
Metal hydrides are reactive species kinetically and thus participate in a variety of transformations like the ones discussed below.
1. Deprotonation reactions
The deprotonation reaction can be achieved by a hydride moiety resulting in the formation of H2gas as shown below.
2. Hydride transfer and insertion
In this reaction a hydride transfer from a metal center to formaldehyde resulting in the formation of a metal bound methoxy moiety is observed as shown below.
3. Hydrogen atom transfer reaction
An example of hydrogen atom transfer reaction is given below.
It is interesting to note that the nature of hydrogen atom in a M−H bond can vary from being protic in nature, when bound to electron deficient metal centers as in metal carbonyl compounds, to that of being hydridic in nature, when bound to more electropositive early transition metals. In the latter case, the hydride moieties tend to be basic and exhibit hydride transfer reactions with electrophiles like aldehydes or ketones. Furthermore, the protonation of these basic metal hydrides leads to the elimination of dihydrogen (H2) gas along with the generation of a vacant coordination site at the metal center.
Bridging hydrides
The metal hydrides usually show two modes of binding, namely terminal and bridging. In case of the bridging hydrides, the hydrogen atom can bridge between two or even more metal centers and thus, the bridging hydrides often display bent geometries.
Problems
1. Predict the product of the reaction.
Ans:
2. Give the oxidation state and total valence electron count of the metal center.
Ans: Oxidation state 0 and 18 VE 3. What kind of metal centers would stabilize metal dihydrogen complexes? Ans: Electron deficient and less π basic ligands 4. Specify whether the nature of hydrogen moiety in the complex, HCo(CO)4 is acidic or basic? Ans: Acidic 5. Where do the M−H stretching bands appear in the IR spectrum of metal hydride complexes?
Ans: 1500 to 2200 cm-1
Self Assessment test
1. Predict the product of the reaction.
Ans:
2. Give the oxidation state and total valence electron count of the metal center.
Ans: Oxidation state +2 and 18 VE 3. What kind of metal centers would stabilize classical dihydride complexes? Ans: Electron rich and more p basic ligands 4. Specify whether the nature of hydrogen moiety in the complex, IrH5(PCy3)2 is acidic or basic? Ans: Basic
5. Between X−ray diffraction and neutron diffraction, which is a better method for the characterization of the M−H moiety?
Ans: Neutron diffraction
Summary
Metal hydrides are important compounds in the overall scheme of organometallic chemistry as they are involved in many crucial steps of numerous catalytic reactions. Apart from metal hydrides another important class of compounds are transition metal σ−complexes whose simplest variant are the metal dihydrogen complexes. These σ−complexes and the metal dihydrogen complexes are important for the heterolytic activations of the respective metal bound H−heteroatom and the H−H bonds. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/24%3A_Organometallic_chemistry-_d-block_elements/24.02%3A_Common_Types_of_Ligand_-_Bonding_and_Spectroscopy/24.2C%3A_Hydride_Ligands.txt |
Learning Objectives
In this lecture you will learn the following
• Classification of ligands
• Nature of bonding in phosphines
• Steric and electronic properties of phosphines
• Bonding in phosphines and CO
• Cone angle and its application in catalysis
Classification of Ligands by donor atoms
Ligand is a molecule or an ion that has at least one electron pair that can be donated. Ligands may also be called Lewis bases; in terms of organic chemistry, they are ‘nucleophiles’. Metal ions or molecules such as BF3 (with incomplete valence electron shells (electron deficient) are called Lewis acids or electrophiles).
• Why do molecules like H2O or NH3 give complexes with ions of both main group and transition metals. E.g [Al(OH2)6]3+ or [Co(NH3)6]3+
• Why other molecules such as PF3 or CO give complexes only with transition metals.
• Although PF3 or CO give neutral molecules such as Ni(PF3)4 or Ni(CO)4 or Cr(CO)6.
• Why do, NH3, amines, oxygen donors, and so on, not give complexes such as Ni(NH3)4.
Classical or simple donor ligands
Act as electron pair donors to acceptor ions or molecules, and form complexes of all types of Lewis acids, metal ions or molecules. Non-classical ligands, π-bonding or π-acid ligands: Form largely with transition metal atoms. In this case special interaction occurs between the metals and ligands. These ligands act as both σ-donors and π-acceptors due to the availability of empty orbitals of suitable symmetry, and energies comparable with those of metal t2g (non-bonding) orbitals. e.g. Consider PR3 and NH3: Both can act as bases toward H+, but P atom differs from N in that PR3 has σ* orbitals of low energy, whereas in N the lowest energy d orbitals or σ* orbitals are far too high on energy to use.
Consider CO that do not have measurable basicity to proton, yet readily reacts with metals like Ni that have high heats of atomization to give compounds like Ni(CO)4.
Ligands may also be classified electronically depending upon how many electrons that they contribute to a central atom. Atoms or groups that can form a single covalent bond are one electron donors. e.g., F, SH, CH3 etc.,
Compounds with an electron pair are two-electron donors. E.g., NH3, H2O, PR3 etc.,
Bonding in Metal –Carbonyl and Metal-Phosphines
Steric factors in phosphines (Tolman’s cone angle)
Cone angle is very useful in assessing the steric properties of phosphines and their coordination behavior.
The electronic effect of phosphines can be assessed by IR and NMR spectroscopic data especially when carbonyls are co-ligands. In a metal complex containing both phosphines and carbonyl, the ν(CO) frequencies would reveal the σ-donor or π–acceptor abilities of phosphines. If the phosphines employed are strong σ-donors, then more electron density would move from M (t2g orbitals)- π*(CO) and as a result, a lowering in the ν(CO) is observed. In contrast, if a given phosphine is a poor σ-donor but strong π -acceptor, then phosphine(σ*-orbitals) also compete with CO for back bonding which results in less lowering in ν(CO) frequency.
Another important aspect is the steric size of PR3 ligands, unlike in the case of carbonyls, which can be readily tuned by changing R group. This is of great advantage in transition metal chemistry, especially in metal mediated catalysis, where stabilizing the metals in low coordination states is very important besides low oxidation states. This condition can promote oxidative addition at the metal centre which is an important step in homogeneous catalysis. The steric effects of phosphines can be quantified with Tolman’s cone angle.
Cone angle can be defined as a solid angle at metal at a M—P distance of 228 pm which encloses the van der Waal’s surfaces of all ligand atoms or substituents over all rotational orientations. The cone angles for most commonly used phosphines are listed in the following table.
Phosphine Cone Angle (°)
PH3 87
PF3 104
P(OMe)3 107
PMe3 118
PMe2Ph 122
PEt3 132
PPh3 145
PCy3 170
P(But)3 182
P(mesityl)3 212
Phosphines with different cone angles versus coordination number for group 8 metals:
ML4
ML3
ML2
(Me3P)4Ni
(Me3P)4Pd
(Me3P)4Pt
(Ph3P)3Pt
(tert-Bu3P)2Pt
Tolman Angle and Catalysis
Sterically demanding phosphine ligands can be used to create an empty coordination site (16 VE complexes) which is an important trick to fine tune the catalytic activity of phosphine complexes.
Contributors and Attributions
http://nptel.ac.in/courses/104101006/15
In this lecture you will learn the following
• Know about metal phosphine complexes.
• Have an understanding of the steric and electronic properties of the phosphine ligands.
• Obtain a deeper insight about the metal phosphine interactions.
• Be introduced to other π−basic ligands.
Phosphines are one of the few ligands that have been extensively studied over the last few decades to an extent that the systematic fine tuning of the sterics and electronics can now be achieved with certain degree of predictability. Phosphines are better spectator ligands than actor ligands. Tolman carried out pioneering infrared spectroscopy experiments on the PR3Ni(CO)3 complexes looking at the ν(CO)stretching frequencies for obtaining an insight on the donor properties of the PR3 ligands. Thus, a stronger σ−donor phosphine ligand would increase the electron density at the metal center leading to an enhanced metal to ligand π−back bonding and thereby lowering of the ν(CO) stretching frequencies in these complexes. Another important aspect of the phosphine ligand is its size that has significant steric impact on its metal complexes. Thus, unlike CO ligand, which is small and hence many may simultaneously be able to bind to a metal center, the same is not true for the phosphine ligands as only a few can bind to a metal center. The number of phosphine ligands that can bind to a metal center also depends on the size of its R substituents. For example, up to two can bind to a metal center in case of the PCy3 or P(i−Pr)3 ligands, three or four for PPh3, four for Me2PH, and five or six for PMe3. The steric effect of phosphine was quantified by Tolmann and is given by a parameter called Cone Angle that measures the angle at the metal formed by the PR3 ligand binding to a metal (Figure 1).
The Cone Angle criteria has been successfully invoked in rationalizing the properties of a wide range of metal phosphine complexes. One unique feature of the phosphine ligand is that it allows convenient change of electronic effect without undergoing much change in its steric effects. For example, PBu3 and P(OiPr)3 have similar steric effects but vary in their electronic effects. The converse is also true as the steric effect can be easily changed without undergoing much change in the electronic effect. For example, PMe3 and P(o−tolyl)3 have similar electronic effect but differ in their steric effects. Thus, the ability to conveniently modulate the steric and the electronic effects make the phosphine ligands a versatile system for carrying out many organometallic catalysis.
Structure and Bonding
Phosphines are two electron donors that engage a lone pair for binding to metals. These are thus considered as good σ−donors and poor π−acceptors and they belong to the same class with the aryl, dialkylamino and alkoxo ligands. In fact they are more π−acidic than pure σ−donor ligands like NH3and, more interestingly so, their π−acidity can be varied significantly by systematic incorporation of substituents on the P atom. For example, PF3 is more π−acidic than CO. Analogous to what is observed in case of the benchmark π−acidic CO ligand, in which the metal dπ orbital donates electron to a π* orbital of a C−O bond, in the case of the phosphines ligands, such π−back donation occurs from the metal dπ orbital occurs on to a σ* orbital of a P−R bond (Figure 2). In phosphine ligands, with the increase of the electronegativity of R both of the σ and the σ* orbitals of the P−R bond gets stabilized. Consequently, the contribution of the atomic orbital of the P atom to the σ*−orbital of the P−R bond increases, which eventually increases the size of the σ* orbital of the P−R bond. This in turn facilitates better overlap of the σ* orbital of the P−R bond with the metal dπ orbital during the metal to ligand π−back donation in these metal phosphine complexes.
Starting from CO, which is a strong π−acceptor ligand, to moving to the phosphines, which are good σ−donors and poor π−acceptor ligands, to even going further to other extreme to the ligands, which are both good σ−donors as well as π−donors, a rich variety of phosphine ligands thus are available for stabilizing different types of organometallic complexes. In this context the following ligands are discussed below.
π-basic ligands
Alkoxides (RO) and halides like F, Cl and Br belong to a category of π−basic ligands as they engage a second lone pair for π−donation to the metal over and above the first lone pair partaking σ−donation to the metal. Opposite to what is observed in the case of π−acidic ligands, in which the π* ligand orbital stabilizes the dπ metal orbital and thereby affecting a larger ligand field splitting, as consistent with the strong field nature of these ligands (Figure 3), in the case of the π−basic ligands, the second lone pair destabilizes the dπ metal orbitals leading to a smaller ligand field splitting, which is in agreement with the weak field nature of these ligands. The orbitals containing the lone pair of the ligands are usually located on the more electronegative heteroatoms and so they are invariably lower in energy than the metal dπ orbitals. Hence, the destabilization of the metal dπ orbitals occurs due to the repulsion of the filled ligand lone pair orbital with the filled metal dπ orbitals. In case of the situations in which the metal dπ orbitals are vacant, like in d0 systems of Ti4+ ions, the possibility of the destabilization of the metal dπ orbitals do not arise but instead stabilization occurs through the donation of the filled ligand lone pair orbital electrons to the empty metal dπ orbitals as seen in the case of TiF6 and W(OMe)6. Thus, this scenario in π−basic ligands is opposite to that observed in case of the π−acidic ligands, for which the empty π* ligand orbitals are higher in energy than the filled metal dπ orbitals. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/24%3A_Organometallic_chemistry-_d-block_elements/24.02%3A_Common_Types_of_Ligand_-_Bonding_and_Spectroscopy/24.2D%3A_Phosphine_and_Related_Ligands.txt |
Learning Objectives
In this lecture you will learn the following
• The metal alkene complexes.
• The metal−olefin bonding interactions.
• The synthesis and reactivities of the metal−olefin complexes.
• The umpolung reactivities of olefins in the metal alkene complexes.
Though the first metal olefin complex dates back a long time to the beginning of 19th century, its formulation was established only a century later in the 1950s. While reacting K2PtCl4 with EtOH in 1827, the Danish chemist Zeise synthesized the famous Zeise’s salt K[PtCl3(C2H4)]•H2O containing a Pt bound ethylene moiety and which incidentally represented the first metal−olefin complex (Figure 1).
The metal−olefin bonding interaction is best explained by the Dewar−Chatt model, that takes into account two mutually opposing electron donation involving σ−donation of the olefinic C=C π−electrons to an empty dπ metal orbital followed by π−back donation from a filled metal dπ orbital into the unoccupied C=C π* orbital. Quite understandably so, for the d0 systems, the formations of metal−olefin complexes are not observed. The extent of the C=C forward π-donation to the metal and the subsequent π−back donation from the filled dπ orbital to the olefinic C=C π* orbital have a direct bearing on the C=C bond of the metal bound olefinic moiety in form of bringing about a change in hybridization as well as in the C−C bond distance (Figure 2).
If the metal to ligand π−back donation component is smaller than the ligand to metal σ−donation, then the lengthening of the C−C bond in the metal bound olefin moiety is observed. This happens primarily because of the fact that the alkene to metal σ−donation removes the C=C π−electrons away from the C−C bond of the olefin moiety and towards the metal center, thus, decreasing its bond order and increasing the C−C bond length. Additionally, as the metal to ligand π−back donation increases, the electron donation of the filled metal dπ orbital on to the π* orbital of the metal bound olefin moiety is enhanced. This results in an increase in the C−C bond length. The lengthening of the C−C bond in metal bound olefin complex can be correlated to the π−basicity of the metal. For example, for a weak π−basic metal, the C−C bond lengthening is anticipated to be small while for a strong π−basic metal, the C−C lengthening would be significant.
Another implication of ligand−metal π−back donation is in the observed change of hybridization at the olefinic C atoms from pure sp2, in complexes with no metal to ligand π−back donation, to sp3, in complexes with significant metal to ligand π−back donation, is observed. The change in hybridization from sp2 to sp3 centers of the olefinic carbon is accompanied by the substituents being slightly bent away from the metal center in the final metalacyclopropane form (Figure 3). This change in hybridization can be conveniently detected by 1H and 13C NMR spectroscopy. For example, in case of the metalacyclopropane systems, which have strong metal to ligand π−back donation, the vinyl protons appear 5 ppm (in the 1H NMR) and 100 ppm (in the 13C NMR) high field with respect to the respective position of the free ligands.
An interesting fallout of the metal to ligand π−back bonding is the tighter binding of the strained olefins to the metal center as observed in the case of cyclopropene and norbornene. The strong binding of these cyclopropene and norbornene moieties to the metal center arise out of the relief of ring strain upon binding to the metal. Lastly, in the metal−olefin complexes having very little π−back bonding component, the chemical reactivities of the metal bound olefin appear opposite to that of a free olefin. For example, a free olefin is considered electron rich by virtue of the presence of π−electrons in its outermost valence orbital and hence it undergoes an electrophilic attack. However, the metal bound olefin complexes having predominantly σ−donation of the olefinic π−electrons and negligible metal to ligand π−back donation, the olefinic C becomes positively charged and hence undergoes a nuclophilic attack. This nature of reversal of olefin reactivity is called umpolung character.
Synthesis
Metal alkene complexes are synthesized by the following methods.
1. Substitution in low valent metals $\ce{AgOSO2CF3 + C2H4 \rightarrow (C2H4)AgOSO2CF3}$
2. Reduction of high valent metal in presence of an alkene $\ce{ (cod)PtCl2 + C2H4 \rightarrow [PtCl3(C2H4)]^{+} + Cl^{-}}$
3. From alkyls and related species $\ce{Cp2TaCl3 + n-BuMgX \rightarrow \{Cp2TaBu3\}}$
Reaction of alkenes
The metal alkene complexes show the following reactivities.
1. Insertion reaction
These reactions are commonly displayed by alkenes as they insert into metal−X bonds yielding metal alkyls. The reaction occurs readily at room temperature for X = H, whereas for other elements (X = other atoms), such insertions become rare. Also, the strained alkenes and alkynes undergo such insertion readily.
2. Umpolung reactions
Umpolung reactions are observed only for those metal−alkene complexes for which the metal center is a poor π−base and as a result of which the olefin undergoes a nuclophilic attack.
3. Oxidative addition
Alkenes containing allylic hydrogens undergo oxidative addition to give a allyl hydride complex.
Problems
1. Predict the product of the reaction.
Ans: A = {(CF2=CF2)AuMe(PPh3)} and B = Au(CF2-CF2Me)(PPh3) 2. Specify whether the lengthening/shortening of the C−C bond distance in the metal bound olefin moiety is observed as a result of metal to ligand π−back donation? Ans: Lengthening. 3. Draw the structure of Zeise’s salt. Ans:
4. The change in hybridization at the olefinic C from sp2 to sp3 primarily arise due to? Ans: Metal-ligand π-back donation.
Self Assessment test
1. Predict the product of the reaction.
Ans: [PtCl3(C2H4)]- and Cl- 2. Specify whether the lengthening/shortening of the C−C bond distance in the metal bound olefin moiety is observed as a result of ligand to metal σ− donation? Ans: Lengthening. 3. Metalacyclopropane intermediate in a metal bound olefin complex is primarily formed due to which kind of interaction? Ans: Metal−ligand π−back donation 4. The oxidation state of Pt in Zeise’s salt is? Ans: PtII
Summary
Alkenes are an important class of unsaturated ligands that bind to a metal by σ−donating its C=C π−electrons and also accepts electrons from the metal in its π* orbital of C=C bond. These symbiotic σ−donation and π−back donation in metal bound olefin complexes have a significant impact on their structure and reactivity properties. Quite importantly, the structural manifestations arising out of these forward σ−donation and π−back donation can be characterized by using 1H, 13C NMR and IR spectroscopic methods.
Pi-ligands are those that bond to a metal via donating electron density to the metal from their σ-orbitals and their π-orbitals and by the metal center’s donation of electron density into the π* orbitals of the ligands. The degree of π* back-donation from the metal depends upon the energy level of the ligand’s π* orbitals, the lower the energy, the easier it is for the metal to donate electron density. According to molecular orbital theory, it is the metal’s d-electrons that share common symmetry with ligands’ p-orbitals that lead to direct bonding with the metal while those that lie in between the axes of the ligands, including dxz and dyz can donate electron density into the empty π* orbitals[1]. The metal orbitals that the ligand participates in backbonding with will help determine the orientation of the ligands in space around the molecule, for example, ethylene blinded to iron will lie in the equatorial plane of the Oh (Octahedral) complex due to the π* orbital being closer in energy to the dx2-y2 metal orbital than the dxz orbital[2]. The energy of these orbitals and thus the degree of backbonding that occurs can be changed by altering the substituents of the pi-lignads. substituents. The more electronegative the substituents on an alkene ligand, the lower in energy the π* orbitals and the greater the degree of backbonding. $\pi$ bonding is not limited to a metal's d-orbitals, but can also occur between f-orbitals and pi-electron density as in more exotic organometallic compounds including uranocene, where δ-bonds play an important role[4]. In addition to alkenes, alkynes can also act as pi-ligands and are more stable than alkenes and thus are better π* acceptors in-part because they have 2 additional π and π* orbitals that can participate in bonding.
Bonding and Pi-Backbonding in a generic metal-ethylene system. Image adapted from Pfenning, Brian W., Principles of Inorganic Chemistry (2015) p. 642. Image used with perimssion (CC BY-SA 4.0; Macbaband).
These type of ligand are anionic and thus act to increase the oxidation state of the metal center. When determining the likely stability of a metal complex using an ionic method of electron counting, each “double-bond” that participates in bonding donates two electrons to the metal center. In an olefin ligand, especially conjugated arenes, not all of the carbons participate directly in bonding[5]. The number of carbon atoms that participate in bonding in an arene ring is referred to as the hapticity symbolized ηn where n is the number of carbon atoms that are directly bonded to the metal center. This allows ligands of this type to play unique roles in organic mechanisms such as what's referred to as "ring slippage" where, in a ligand substitution, the hapticity of a ligand is reduced followed by the addition of a new ligand to the metal center which is then followed by an increase in the hapticity and the rejection of a different ligand.
Hapticity of greater than 1 in a pi-ligand is not limited to cyclic alkenes or aromatic alkenes corresponding to double bonds but whenever the electron density is spread out over multiple carbons. For example, CH2=CH-CH2- (Allyl Anion) can act as a ligand with η3 because its delocalized pi-MO's can share symmetry with the metal center's d-orbitals.
Examples of pi-ligands are cylclopentadiene (as in the famous ferrocene sandwich compound), ethylene, benzene and many other alkenes and alkynes.
Contributors and Attributions
• Advanced Inorganic Chemistry (Wikibooks)
24.2H: Dihydrogen
Metal dihydrogen complexes
The simplest variant of a σ−complex contains a dihydrogen ligand. The first dihydrogen complex was isolated by Kubas, after which many new ones were reported.
Quite expectedly, the dihydrogen moiety bound to a metal in a σ−complex is found to be more acidic (pKa = 0 − 20) when compared to the free dihydrogen molecule (pKa = 35). It is interesting to note that the pKa change associated with the binding of dihydrogen to a metal in a σ−complex relative to that of the free H2 molecule is significantly larger than the change associated with binding of H2O to metal. Owing to this inherent acidity, the deprotonation of the metal bound dihydrogen moiety by a base can thus be appropriately employed for heterolytic activation of the dihydrogen moiety as illustrated below.
The dihydrogen complexes of metals are often referred to as nonclassical hydrides. The electron rich π basic metals are anticipated to split the metal bound dihydrogen moieties resulting in classical dihydride complexes. Along the same line of thinking, the electron deficient and less π basic metal would tend to stabilize a dihydrogen complex. The dihydrogen complexes can also be characterized by the X ray diffraction as well as neutron diffraction methods. In IR spectrum, the metal bound H−H stretch appear in the range (2300 − 2900) cm−1 while in the 1H NMR spectrum the same appear between 0 to −10 ppm as a broad peak. The dihydrogen complexes are often characterized by isotopic labeling studies of metal bound H−D moiety that shows a coupling constant of 20 – 34 Hz as supposed to 43 Hz observed in case of the free H−D molecule. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/24%3A_Organometallic_chemistry-_d-block_elements/24.02%3A_Common_Types_of_Ligand_-_Bonding_and_Spectroscopy/24.2E%3A_%28pi%29-bonded_Organic_Ligands.txt |
Learning Objectives
In this lecture you will learn the following
• Have an insight about the stability of the transition metal complexes with respect to their total valence electron count.
• Be aware of the transition metal complexes that obey or do not obey the 18 Valence Electron Rule.
• Have an appreciation of the valence electron count in the transition metal organometallic complexes that arise out of the metal-ligand orbital interactions.
The transition metal organometallic compounds exhibit diverse structural variations that manifest in different chemical properties. Many of these transition metal organometallic compounds are primarily of interest from the prospectives of chemical catalysis. Unlike the main group organometallic compounds, which use mainly ns and np orbitals in chemical bonding, the transition metal compounds regularly use the (n−1)d, ns and np orbitals for chemical bonding (Figure 1). Partial filling of these orbitals thus render these metal centers both electron donor and electron acceptor abilities, thus allowing them to participate in σ-donor/π-acceptor synergic interactions with donor-acceptor ligands like carbonyls, carbenes, arenes, isonitriles and etc,.
The 18 Valence Electron (18 VE) Rule or The Inert Gas Rule or The Effective Atomic Number (EAN) Rule: The 18-valence electron (VE) rule states that thermodynamically stable transition metal compounds contain 18 valence electrons comprising of the metal d electrons plus the electrons supplied by the metal bound ligands. The counting of the 18 valence electrons in transition metal complexes may be obtained by following either of the two methods of electron counting, (i). the ionic method and (ii). the neutral method. Please note that a metal-metal bond contributes one electron to the total electron count of the metal atom. A bridging ligand donates one electron towards bridging metal atom.
Example 1: Ferrocene Fe(C5H5)2
Example 2. Mn2(CO)10
Transition metal organometallic compounds mainly belong to any of the three categories.
1. Class I complexes for which the number of valence electrons do not obey the 18 VE rule.
2. Class II complexes for which the number of valence electrons do not exceed 18.
3. Class III complexes for which the valence electrons exactly obey the 18 VE rule.
The guiding principle which governs the classification of transition metal organometallic compounds is based on the premise that the antibonding orbitals should not be occupied; the nonbonding orbitals may be occupied while the bonding orbitals should be occupied.
Class I:
In class I complexes, the Δo splitting is small and often applies to 3d metals and σ ligands at lower end of the spectrochemical series. In this case the t2g orbital is nonbonding in nature and may be occupied by 0−6 electrons (Figure 2). The eg* orbital is weakly antibonding and may be occupied by 0−4 electrons. As a consequence, 12−22 valence electron count may be obtained for this class of compounds. Owing to small Δtetr splitting energy, the tetrahedral transition metal complexes also belongs to this class.
Class II:
In class II complexes, the Δo splitting is relatively large and is applicable to 4d and 5d transition metals having high oxidation state and for σ ligands in the intermediate and upper range of the spectrochemical series. In this case, the t2g orbital is essentially nonbonding in nature and can be filled by 0−6 electrons (Figure 3). The eg* orbital is strongly antibonding and is not occupied at all. Consequently, the valence shell electron count of these type of complexes would thus be 18 electrons or less.
Class III:
In class III complexes, the Δo splitting is the largest and is applicable to good σ donor and π acceptor ligands like CO, PF3, olefins and arenes located at the upper end of the spectrochemical series. The t2gorbital becomes bonding owing to interactions with ligand orbitals and should be occupied by 6 electrons. The eg* orbital is strongly antibonding and therefore remains unoccupied.
Problems
State the oxidation state of the metal and the total valence electron count of the following species.
1. V(C2O4)33−
Ans: +3 and 14 2. Mn(acac)3 Ans: +3 and 16 3. W(CN)83− Ans: +5 and 17 4. CpMn(CO)3 Ans: 0 and 18 5. Fe2(CO)9 Ans: 0 and 18 Self Assessment test
State the oxidation state of the metal and the total valence electron count of the following species.
1. TiF62-
Ans: +4 and 12 2. Ni(en)32+ Ans: +2 and 20 3. Cu(NH3)62+ Ans: +2 and 21 4. W(CN)84- Ans: +4 and 18 5. CH3Co(CO)4 Ans: 0 and 18
Summary
The transition metal complexes may be classified into the following three types. (i). The ones that do not obey the 18 valence electron rule are of class I type (ii). the ones that do not exceed the 18 valence electron rule are of class II and (iii). the ones that strictly follow the 18 valence electron rule. Depending upon the interaction of the metal orbitals with the ligand orbitals and also upon the nature of the ligand position in spectrochemical series, the transition metal organometallic compounds can form into any of the three categories.
The 18-electron rule is used primarily for predicting and rationalizing formulae for stable metal complexes, especially organometallic compounds. The rule is based on the fact that the valence shells of transition metals consist of nine valence orbitals (one s orbital, three p orbitals and five d orbitals), which collectively can accommodate 18 electrons as either bonding or nonbonding electron pairs. This means that, the combination of these nine atomic orbitals with ligand orbitals creates nine molecular orbitals that are either metal-ligand bonding or non-bonding. When a metal complex has 18 valence electrons, it has achieved the same electron configuration as the noble gas in the period. The rule and its exceptions are similar to the application of the octet rule to main group elements.
This rule applies primarily to organometallic compounds, and the 18 electrons come from the 9 available orbitals in d orbital elements (1 s orbital, 3 p orbitals, and 5 d orbitals). The rule is not helpful for complexes of metals that are not transition metals, and interesting or useful transition metal complexes will violate the rule because of the consequences deviating from the rule bears on reactivity. If the molecular transition metal complex has an 18 electron count, it is called saturated. This means that additional ligands cannot bind to the transition metal because there are no empty low-energy orbitals for incoming ligands to coordinate. If the molecule has less than 18 electrons, then it is called unsaturated and can bind additional ligands.
Electron counting
Two methods are commonly employed for electron counting:
1. Neutral atom method: Metal is taken as in zero oxidation state for counting purpose
2. Oxidation state method: We first arrive at the oxidation state of the metal by considering the number of anionic ligands present and overall charge of the complex
To count electrons in a transition metal compound:
1. Determine the oxidation state of the transition metal and the resulting d-electron count.
• Identify if there are any overall charges on the molecular complex.
• Identify the charge of each ligand.
2. Determine the number of electrons from each ligand that are donated to the metal center.
3. Add up the electron counts for the metal and for each ligand.
Typically for most compounds, the electron count should add up to 18 electrons. However, there are many exceptions to the 18 electron rule, just like there are exceptions to the octet rule.
Reactivity
The 18 electron rule allows one to predict the reactivity of a certain compound. The associative mechanism means that there is an addition of a ligand while a dissociative mechanism means that there is a loss of a ligand. When the electron count is less than 18, a molecule will most likely undergo an associative reaction. For example: (C2H4)PdCl2
• 16 electron count
• Would it more likely lose a C2H4 or gain a CO? Losing a C2H4 results in a 14 electron complex while gaining a CO gives an 18 electron complex. From the 18 electron rule, we will expect that the compound will more likely undergo an associative addition of CO.
Example \(1\):
1. There is no overall charge on the molecule and there is one anionic ligand (CH3-)
• The Re metal must have a positive charge that balances out the anionic ligand charge to equal the 0 overall molecular charge. Since there is a -1 charge contribution from the methyl ligand, the Re metal has a +1 charge.
• Because the Re metal is in the +1 oxidation state, it is a d6 electron count. It would have been its regular d7 electron count if it had a neutral (0) oxidation state.
2. The CH3- ligand contributes 2 electrons. Each CO ligand contributes 2 electrons. Each PR3 ligand contributes 2 electrons. The H2C=CH2 ligand contributes 2 electrons.
3. Adding up the electrons:
• Re(1): 6 electrons
• CH3-: 2 electrons
• 2 x CO: 2 x 2 electrons = 4 electrons
• 2 x PR3: 2 x 2 electrons = 4 electrons
• H2C=CH2: 2 electrons
• Total: 18 electrons
In this example, the molecular compound has an 18 electron count, which means that all of its orbitals are filled and the compound is stable.
Example \(2\): [M(CO)7]+
The 18 electron rule can also be used to help identify an unknown transition metal in a compound. Take for example [M(CO)7]+. To find what the unknown transition metal M is, simply work backwards:
1. 18 electrons
2. Each (CO) ligand contributes 2 electrons
• 7 x 2 electrons = 14 electrons
3. 18 - 14 = 4 electrons
4. d4
5. M(I) oxidation state
6. The unknown metal M must be V, Vanadium
Example \(3\): [Co(CO)5]z
Similarly to Example 2, the 18 electron rule can also be applied to determine the overall expected charge of an molecule. Take for example [Co(CO)5]z. To find the unknown charge z:
1. 18 electrons
2. Each CO ligand contributes 2 electrons
1. 5 x 2 electrons = 10 electrons
3. Co is typically d9
4. 9 + 10 = 19 electrons
5. To satisfy the 18 electron rule, the [Co(CO)5]z compound must have a charge of z = +1.
Ligand Contributions
Below is a list of common organometallic ligands and their respective electron contributions.
Neutral 2e donors Anionic 2e donors Anionic 4e donors Anionic 6e donors
PR3 (phosphines) X- (halide) C3H5- (allyl) Cp- (cyclopentadienyl)
CO (carbonyl) CH3- (methyl) O2- (oxide) O2- (oxide)
alkenes CR3- (alkyl) S2- (sulfide)
alkynes Ph- (phenyl) NR2- (imide)
nitriles H- (hydride) CR22- (alkylidene)
RnE- (silyl, germyl, alkoxo, amido etc.) OR- (alkoxide, bridging ligand)
SR- (thiolate, bridging ligand)
NR2- (inorganic amide, bridging ligand)
PR2- (phosphide, bridging ligand)
Exceptions
Generally, the early transition metals (group 3 to 5) could have an electron count of 16 or less. Middle transition metals (group 6 to group 8) commonly have 18 electron count while late transition metals (group 9 to group 11) generally have 16 or lower electron count. When a structure has less than an 18 electron count, it is considered electron-deficient or coordinately unsaturated. This means that the compound has empty valence orbitals, making it electrophilic and extremely reactive. If a structure has "too many electrons," that means that not all of the bonds are covalent bonds, and thus some has to be ionic bonds. These bonds are weaker compared to covalent bonds. However, these organometallic compounds that have an electron count greater than 18 are fairly rare.
Summary
The 18-electron rule is similar to the octet rule for main group elements, something you might be more familiar with, and thus it may be useful to bear that in mind. So in a sense, there's not much more to it than "electron bookkeeping".
References
1. Pfenning, Brian (2015). Principles of Inorganic Chemistry. Hoboken, New Jersey: John Wiley & Sons, Inc. pp. 629–631. ISBN 9781118973868. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/24%3A_Organometallic_chemistry-_d-block_elements/24.03%3A_The_18-electron_Rule.txt |
Ken Wade developed a method for the prediction of shapes of borane clusters; however, it may be used for a wide range of substituted boranes (such as carboranes) as well as other classes of cluster compounds. Wade’s rules are used to rationalize the shape of borane clusters by calculating the total number of skeletal electron pairs (SEP) available for cluster bonding. In using Wade’s rules it is key to understand structural relationship of various boranes.
Structural relationship between closo, nido, and arachno boranes (and hetero-substituted boranes). The diagonal lines connect species that have the same number of skeletal electron pairs (SEP). Hydrogen atoms except those of the B-H framework are omitted. The red atom is omitted first, the green atom removed second. Adapted from R. W. Rudolph, Acc. Chem. Res., 1976, 9, 446.
Wade’s rules:
The general methodology to be followed when applying Wade’s rules is as follows:
1. Determine the total number of valence electrons from the chemical formula, i.e., 3 electrons per B, and 1 electron per H.
2. Subtract 2 electrons for each B-H unit (or C-H in a carborane).
3. Divide the number of remaining electrons by 2 to get the number of skeletal electron pairs (SEP).
4. A cluster with n vertices (i.e., n boron atoms) and n+1 SEP for bonding has a closo structure.
5. A cluster with n-1 vertices (i.e., n-1 boron atoms) and n+1 SEP for bonding has a nido structure.
6. A cluster with n-2 vertices (i.e., n-2 boron atoms) and n+1 SEP for bonding has an arachno structure.
7. A cluster with n-3 vertices (i.e., n-3 boron atoms) and n+1 SEP for bonding has an hypho structure.
8. If the number of boron atoms (i.e., n) is larger than n+1 SEP then the extra boron occupies a capping position on a triangular phase.
Example \(1\): B5H11
What is the structure of B5H11?
Solution
1. Total number of valence electrons = (5 x B) + (11 x H) = (5 x 3) + (11 x 1) = 26
2. Number of electrons for each B-H unit = (5 x 2) = 10
3. Number of skeletal electrons = 26 – 10 = 16
4. Number SEP = 16/2 = 8
5. If n+1 = 8 and n-2 = 5 boron atoms, then n = 7
6. Structure of n = 7 is pentagonal bipyramid, therefore B5H11 is an arachno based upon a pentagonal bipyramid with two apexes missing.
Ball and stick representation of the structure of B5H11.
Example \(2\): B5H9?
What is the structure of B5H9?
Solution
1. Total number of valence electrons = (5 x B) + (9 x H) = (5 x 3) + (9 x 1) = 24
2. Number of electrons for each B-H unit = (5 x 2) = 10
3. Number of skeletal electrons = 24 – 10 = 14
4. Number SEP = 14/2 = 7
5. If n+1 = 7 and n-1 = 5 boron atoms, then n = 6
6. Structure of n = 6 is octahedral, therefore B5H9 is a nido structure based upon an octahedral structure with one apex missing.
Ball and stick representation of the structure of B5H9.
Example \(3\): B6H62-
What is the structure of B6H62-?
1. Total number of valence electrons = (6 x B) + (3 x H) = (6 x 3) + (6 x 1) + 2 = 26
2. Number of electrons for each B-H unit = (6 x 2) = 12
3. Number of skeletal electrons = 26 – 12 = 14
4. Number SEP = 14/2 = 7
5. If n+1 = 7 and n boron atoms, then n = 6
6. Structure of n = 6 is octahedral, therefore B6H62- is a closo structure based upon an octahedral structure.
Ball and stick representation of the structure of B6H62-.
Table \(1\) provides a summary of borane cluster with the general formula BnHnx- and their structures as defined by Wade’s rules.
Table \(1\): Wade’s rules for boranes.
Type Basic formula Example # of verticies # of vacancies # of e- in B + charge # of bonding MOs
Closo BnHn2- B6H62- n 0 3n + 2 n + 1
Nido BnHn4- B5H9 n + 1 1 3n + 4 n + 2
Arachno BnHn6- B4H10 n + 2 2 3n + 6 n + 3
Hypho BnHn8- B5H112- n + 3 3 3n + 8 n + 4
Bibliography
• R. W. Rudolph, Acc. Chem. Res., 1976, 9, 446.
• K. Wade, Adv. Inorg. Chem. Radiochem., 1976, 18, 1. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/24%3A_Organometallic_chemistry-_d-block_elements/24.05%3A_The_Isolobal_Principle_and_Application_of_Wade%27s_Rules.txt |
Organometallic reactions can usually be classified as one of the following classes:
• ligand dissociation/ligand association
• reductive elimination/oxidative addition
• σ bond metathesis/4-centered reaction
• insertion/de-insertion
• Lewis acid activation of electrophile
24.07: Types of Organometallic Reactions
Learning Objectives
In this lecture you will learn the following
• The oxidative addition reactions.
• The reductive elimination reactions.
• Various mechanistic pathways prevalent for these reactions.
Oxidative addition (OA) is a process that adds two anionic ligands e. g. A and B, that originally are a part of a A-B molecule, like in H2 or Me−I, on to a metal center and is of significant importance from the perspective of both synthesis and catalysis. The exact reverse of the same process, in which the two ligands, A and B, are eliminated from the metal center forming back the A−B molecule, is called the reductive elimination (RA). As A and B are anionic X type ligands, the oxidative addition is accompanied by an increase in the coordination number, valence electron count as well as in the formal oxidation state of the metal center by two units. The oxidative addition step may proceed by a variety of pathways. It requires the metal center to be both coordinatively unsaturated and electron deficient.
Oxidative addition transfers a single mononuclear metal center having 16 VE to a 18 VE species upon oxidative addition. Another frequently observed pathway is that a 18 VE complex looses a ligand to become a 16 VE species which then undergoes an oxidative addition. Apart from above two types, another possible pathway for oxidative addition proceeds as a binuclear oxidative addition in which each of the two metal centers undergo change in oxidation state, electron count and coordination number by one unit instead of two. This type of a binuclear oxidative addition is observed for a 17 VE metal complex or for a binuclear 18 VE metal complex having a metal−metal bond and, for which the metal has a stable oxidation state at a higher positive oxidation state by one unit.
It is interesting to note that in the oxidative addition the breakage of A−B σ−bond occurs as a result of a net transfer of electrons from the metal center to a σ*−orbital of the A−B bond, thus resulting in the formation of the two new M−A and M−B bonds. The oxidative addition is facilitated by electron rich metal centers having low oxidation state whereas the reductive elimination is facilitated by metal centers in higher oxidation state. Table 1. Common types of oxidative addition reactions.
Abbreviations: Lin. = linear, Tet. = tetrahedral, Oct. = octahedral, Sq. Pl. = square planar, TBP = trigonal bipyramidal, Sq. Pyr. = square pyramidal: 7-c, 8-c = 7- and 8-coordinate.
In principle, the oxidative addition is the reverse of reductive elimination, but in practice one may dominate over the other. Thus, the favorability of one over the other is depends on the position of equilibrium, which is further dependent on the stability of the two oxidation states of the metal and on the difference of bond strengths of A−B versus that of the M−A and M−B bonds. For example, metal hydride complexes frequently undergo reductive elimination to give alkanes but rarely an alkane undergoes oxidative addition to give an alkyl hydride complex. Along the same line, alkyl halides frequently undergo oxidative addition to a metal giving metal−alkyl halide complexes but these complexes rarely reductively eliminate to give back alkyl halides. Usually the oxidative addition is more common for 3rd row transition metals because they tend to possess stronger metal ligand bond strengths. The oxidative addition is also favored by strong donor ligands, as they stabilize the higher oxidation state of the metal. The oxidative addition reaction can expand beyond transition metals as observed in the case of the Grignard reagents as well as for some main group elements.
Oxidative addition may proceed by several pathways as discussed below.
Concerted oxidative addition pathway
Oxidative addition may proceed by a concerted 3−centered associative mechanism involving the incoming ligand with the metal center. Specifically, the addition proceeds by the formation of a σ−complex upon binding of an incoming ligand say, H2, followed by the cleavage of the H−H bond as a result of the back donation of electrons from the metal to the σ*−orbital of the H−H bond. Such type of addition is common for the H−H, C−H and Si−H bonds. As expected these proceed by two steps (i) the formation of a σ−complex and (ii) the oxidation step. For example, the oxidative addition of H2 to Vaska’s complex (PMe3)2Ir(CO)Cl proceeds by this pathways.
SN2 pathway
This pathway of oxidative addition is operational for the polarized AB type of ligand substrates like the alkyl, acyl, allyl and benzyl halides. In this mechanism, the LnM fragment directly donates electrons to the σ*−orbital of the A−B bond by attacking the least electronegative atom, say A, of the AB molecule and concurrently initiating the elimination of the most electronegative atom of the AB molecule in its anionic form, B. These reactions proceed via a polar transition state that is accompanied by an inversion of the stereochemistry at the atom of attack by the metal center and are usually accelerated in polar solvents.
Radical pathway
This type of oxidative addition proceeds via a by radical pathway that generally are vulnerable to the presence of impurities. The radical processes can be of non−chain and chain types. In a non−chain type of mechanism, the metal (M) transfer one electron to the σ*−orbital of the RX bond resulting in the formation of a radical cation M+• and a radical anion RX−•. The generation of the two radical fragments occurs by the way of the elimination of the anion X from the radical anion RX−• leaving behind the radical R while the subsequent reaction of X anion with the radical cation M+• generates the other radical MX in the course of the reaction. Such type of non−chain type of oxidative addition is observed for the addition of the alkyl halide to Pt(PPh3)3 complexes.
The other type in this category is the chain radical type reaction that is usually observed for the oxidative addition of EtBr and PhCH2Br to the (PMe3)2Ir(CO)Cl complex. For this process a radical initiator is required and the reaction proceeds along a series of known steps common to a radical process.
Ionic pathway
This is kind of pathway for the oxidative addition reaction is common to the addition of hydrogen halides (HX) in its dissociated H+ and Xforms. The ionic pathways are usually of the following two types (i) the ones in which the starting metal complex adds to H+ prior to the addition of the halide Xand (ii) the other type, in which the halide anion Xadds to the starting metal complex first, and then the addition of proton H+ occurs on the metal complex.
Reductive Elimination
The reductive eliminations are reverse of the oxidative addition reactions and are accompanied by the reduction of the formal oxidation state of the metal and the coordination numbers by two units. The reductive eliminations are commonly observed for d8 systems, like the Ni(II), Pd(II) and Au(III) ions and the d6 systems, like the Pt(IV), Pd(IV), Ir(III) and Rh(III) ions. The reaction may proceed by the elimination of several groups.
Binuclear Reductive Elimination
Similar to what has been observed in the case of binuclear oxidative addition, the binuclear reductive elimination is also observed in some instances. As expected, the oxidation state and the coordination number decrease by one unit in the binuclear reductive elimination pathway.
Problems
1. What kind of metal centers favor oxidative addition? Ans: Electron rich low valent metal centers. 2. Complete the sentence correctly.
(a) Reductive elimination is frequently observed in coordinatively saturated/unsaturated metal complexes.
(b) Reductive elimination is accompanied by increase/decrease in the oxidation state of the metal.
(c) Oxidative addition is accompanied by increase/decrease in the coordination number of the metal.
Ans:
(a) Saturated.
(b) Decrease in the oxidation state by two units.
(c) Increase in the coordination number by two units. 3. State the various mechanistic pathways involved in oxidative addition reactions. Ans: Concerted oxidative addition, SN2 mechanism, radical and ionic mechanism. 4. Complete the reaction.
Ans:
Self Assessment test
1. What kind of metal centers favor reductive elimination? Ans: Electron deficient high valent metal centers.
2. Complete the sentence correctly.
(a) Oxidative addition is frequently observed in coordinatively saturated/unsaturated metal complexes.
(b) Oxidative addition is accompanied by increase/decrease in the oxidation state of the metal.
(c) Reductive elimination is accompanied by increase/decrease in the coordination number of the metal.
Ans:
(a) Unsaturated.
(b) Increase in the oxidation state by two units.
(c) Decrease in the coordination numbers by two units. 3. How does the geometry of the square planar complexes change upon oxidative addition reactions? Ans: Square planar to octahedral. 4. Complete the reaction.
Ans:
Summary
The oxidative addition and the reductive elimination reactions are like the observe and reverse of the same coin. The oxidative addition is generally observed for metal centers with low oxidation state and is usually accompanied by the increase in the oxidation state, the valence electron count and the coordination number of the metal by two units. Being opposite, the reductive elimination is seen in the case of the metal centers with higher oxidation state and is accompanied by the decrease in the oxidation state, the valence electron count and the coordination number of the metal by two units. The oxidative addition may proceed by a variety of pathways that involve concerted, ionic and the radical based mechanisms. More interestingly, the oxidative addition and reductive elimination reactions are not solely restricted to the mononuclear metal complexes but can also be observed for the binuclear complexes.
http://nptel.ac.in/courses/104101006/27 | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/24%3A_Organometallic_chemistry-_d-block_elements/24.07%3A_Types_of_Organometallic_Reactions/24.7B%3A_Oxidative_Addition.txt |
In organic chemistry class, one learns that elimination reactions involve the cleavage of a σ bond and formation of a π bond. A nucleophilic pair of electrons (either from another bond or a lone pair) heads into a new π bond as a leaving group departs. This process is called β-elimination because the bond β to the nucleophilic pair of electrons breaks. Transition metal complexes can participate in their own version of β-elimination, and metal alkyl complexes famously do so. Almost by definition, metal alkyls contain a nucleophilic bond—the M–C bond! This bond can be so polarized toward carbon, in fact, that it can promote the elimination of some of the world’s worst leaving groups, like –H and –CH3. Unlike the organic case, however, the leaving group is not lost completely in organometallic β-eliminations. As the metal donates electrons, it receives electrons from the departing leaving group. When the reaction is complete, the metal has picked up a new π-bound ligand and exchanged one X-type ligand for another.
Comparing organic and organometallic β-eliminations. A nucleophilic bond or lone pair promotes loss or migration of a leaving group.
In this post, we’ll flesh out the mechanism of β-elimination reactions by looking at the conditions required for their occurrence and their reactivity trends. Many of the trends associated with β-eliminations are the opposite of analogous trends in 1,2-insertion reactions. A future post will address other types of elimination reactions.
β-Hydride Elimination
The most famous and ubiquitous type of β-elimination is β-hydride elimination, which involves the formation of a π bond and an M–H bond. Metal alkyls that contain β-hydrogens experience rapid elimination of these hydrogens, provided a few other conditions are met.
The complex must have an open coordination site and an accessible, empty orbital on the metal center. The leaving group (–H) needs a place to land. Notice that after β-elimination, the metal has picked up one more ligand—it needs an empty spot for that ligand for elimination to occur. We can envision hydride “attacking” the empty orbital on the metal center as an important orbital interaction in this process.
The M–Cα and Cβ–H bonds must have the ability to align in a syn coplanar arrangement. By “syn coplanar” we mean that all four atoms are in a plane and that the M–Cα and Cβ–H bonds are on the same side of the Cα–Cβ bond (a dihedral angle of 0°). You can see that conformation in the figure above. In the syn coplanar arrangement, the C–H bond departing from the ligand is optimally lined up with the empty orbital on the metal center. Hindered or cyclic complexes that cannot achieve this conformation do not undergo β-hydride elimination. The need for a syn coplanar conformation has important implications for eliminations that may establish diastereomeric olefins: β-elimination is stereospecific. One diastereomer leads to the (E)-olefin, and the other leads to the (Z)-olefin.
β-elimination is stereospecific. One diastereomer of reactant leads to the (Z)-olefin and the other to the (E)-olefin.
The complex must possess 16 or fewer total electrons. Examine the first figure one more time—notice that the total electron count of the complex increases by 2 during β-hydride elimination. Complexes with 18 total electrons don’t undergo β-elimination because the product would end up with 20 total electrons. Of course, dissociation of a loose ligand can produce a 16-electron complex pretty easily, so watch out for ligand dissociation when considering the possibility of β-elimination in a complex. Ligand dissociation may be reversible, but β-Hydride elimination is almost always irreversible.
The metal must bear at least 2 d electrons. Now this seems a bit strange, as the metal has served as nothing but an empty bin for electrons in our discussion so far. Why would the metal center need electrons for β-hydride elimination to occur? The answer lies in an old friend: backbonding. The σ C–H → M orbital interaction mentioned above is not enough to promote elimination on its own; an M → σ* C–H interaction is also required! I’ve said it before, and I’ll say it again: backbonding is everywhere in organometallic chemistry. If you can understand and articulate it, you’ll blow your instructor’s mind.
Other β-Elimination Reactions
The leaving group does not need to be hydrogen, of course, and a number of more electronegative groups come to mind as better candidates for leaving groups. β-Alkoxy and β-amino eliminations are usually thermodynamically favored thanks to the formation of strong M–O and M–N bonds, respectively. These reactions are so favored in β-alkoxyalkyl “complexes” of alkali and alkaline earth metals (R–Li, R–MgBr, etc.) that using these as σ-nucleophiles at carbon is untenable. Such compounds eliminate immediately upon their formation. I had an organic synthesis professor in undergrad who was obsessed with this—using a β-alkoxyalkyl lithium or β-alkoxyalkyl Grignard reagent in a synthesis was a recipe for red ink. β-Haloalkyls were naturally off limits too.
Watch out…these are not stable compounds!
The atom bound to the metal doesn’t have to be carbon. β-Elimination of alkoxy ligands affords ketones or aldehydes bound at oxygen or through the C=O π bond (this step is important in many transfer hydrogenations, and an analogous process occurs in the Oppenauer oxidation). Amido ligands can undergo β-elimination to afford complexes of imines; however, this process tends to be slower than β-alkoxy elimination.
β-Elimination helps transfer the elements of dihydrogen from one organic compound to another.
Incidentally, I haven’t seen any examples in which the β atom is not carbon, but would be interested if anyone knows of an example!
Applications of β-Eliminations
As with many concepts in organometallic chemistry, there are two ways to think about applications of β-elimination. One can take either the “inorganic” perspective, which focuses on the metal center, or the “organic” perspective, which focuses on the ligands.
With the metal center in focus, we can recognize that β-hydride elimination has the wonderful side effect of establishing an M–H bond—a feat generally difficult to achieve in a selective manner via oxidative addition of X–H. If the ligand from which the hydrogen came displaced something more electronegative, the whole process represents reduction at the metal center. For example, imagine rhodium(III) chloride is mixed with sodium isopropoxide, NaOCH(CH3)2. The isopropoxide easily displaces chloride, and subsequent β-hydride elimination affords a rhodium hydride, formally reduced with respect to the chloride starting material. See p. 236 of this review for more.
With the ligand in focus, we see that the organic ligand is oxidized in the course of β-hydride elimination. Notice that the metal is reduced and the ligand oxidized! A π bond replaces a σ bond in the ligand, and if the conditions are right, this represents a bona fide oxidation (as opposed to a mere elimination). For example, oxidative addition into a C–H bond followed by β-hydride elimination at a C–H bond next door sets up an alkene where two adjacent C–H bonds existed before, an oxidation process. These dehydrogenation reactions are incredibly appealing in a theoretical sense, but still at an early stage when it comes to scope and practicality.
Summary
We already encountered β-hydride elimination in an earlier series of posts on metal alkyl complexes, where we noted that it’s a very common decomposition pathway for metal alkyls. β-Hydride elimination isn’t all bad, however, as it can be an important step in catalytic reactions that result in the oxidation of organic substrates (dehydrogenations and transfer hydrogenations) and in reactions that reduce metal halides to metal hydrides. The general idea of β-elimination involves the transfer of a leaving group from a ligand to the metal center with simultaneous formation of a π bond in the ligand. β-Elimination requires an open coordination site and at least two d electrons on the metal center, and eliminations of chiral complexes are stereospecific. The leaving group is commonly hydrogen, but need not be—the more electronegative the leaving group, the more favorable the elimination. Stronger π bonds in the product also encourage β-elimination, so eliminations that form carbonyl compounds or imines are common.
In the next post, we’ll explore other types of organometallic elimination reactions, which establish π bonds at different positions in metal alkyl or other complexes. α-Eliminations, for example, establish metal-carbon, -oxygen, or -nitrogen multiple bonds, which are generally difficult to forge through other means | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/24%3A_Organometallic_chemistry-_d-block_elements/24.07%3A_Types_of_Organometallic_Reactions/24.7D%3A_%28beta%29-Hydrogen_Elimination.txt |
http://nptel.ac.in/courses/104101006...mod13/lec2.pdf
http://nptel.ac.in/courses/104101006/
http://mcindoe.pbworks.com/w/page/20...67/Alkylidynes
http://mcindoe.pbworks.com/w/page/20651670/FrontPage
http://www.massey.ac.nz/~gjrowlan/adv/lct6.pdf
http://www.f.u-tokyo.ac.jp/~kanai/se.../Hartwig13.pdf
Learning Objectives
In this lecture you will learn the following
• The metal−ligand multiple bonding and their relevance in.
• The Fischer type carbene complexes.
• The Schrock type carbene complexes.
The organometallic compounds containing metal−ligand multiple bonds of the types, M=X and M≡X (X = C, N, O) are of current interest as they are valuable intermediates in many important catalytic cycles. In this regard, considerable attention has been paid towards developing an understanding of the metal−ligand multiply bonded systems like that of the metal carbene LnM=CR2 type complexes and of the metal carbyne LnM≡CR type complexes. A detailed account of the metal−carbene complexes is presented in this chapter.
Metal-carbene Complexes
Carbenes are highly reactive hexavalent species that exist in two spin states, i.e. (i) in a singlet form (), in which two electrons are paired up and (ii) in a triplet form (), in which the two electrons remain unpaired. Of the two, the singlet form is the more reactive one. The instability of carbene accounts for its unique reactivity like that of the insertion reaction, which has aroused significant interest in recent years. The singlet carbene and the triplet carbene bind differently to metals, with the singlet one yielding Fischer type carbene complexes while the triplet one yielding Schrock type carbene complexes (Figure 1).
The LnM=CR2 type Fischer carbene complexes comprise of two dative covalent interactions that include (i) a LnM←CR2 type ligand to metal σ−donation and (ii) a LnM→CR2 type metal to ligand π−back donation. The Fischer type carbene complexes are usually formed with metal centers at a low oxidation state. These are also commonly observed for the more electron rich late−transition metals that participate in the LnM→CR2 type metal to ligand π−back donation. Another characteristic of the Fischer type carbene complex is the presence of the heteroatom substituents like R = OMe or NMe2 on the carbene CR2 moiety which makes the carbene carbon significantly cationic (δ+) to facilitate the LnM→CR2 type metal to ligand π−back donation.
Similarly, the LnM=CR2 type Schrock carbene complexes comprise of two covalent interactions that involve one electron donation towards the σ−bond from each of the metal LnM and the carbene CR2 fragments. Schrock carbene complexes are thus formed with the metal centers having high oxidation state and are usually observed for electron deficient early−transition metals (Figure 2).
Carbene complexes can be prepared by the following methods.
1. by the reaction with electrophiles
2. by H/H+ abstraction reactions as shown below
3. from low−valent metal complexes
Because of the electronically different metal−ligand interaction that exist between the LnM and the carbene CR2 moiety, the reactivity of Fischer and Schrock carbene complexes are completely different. For example, the Fischer type carbene complexes undergo attack by nucleophiles at its carbene−C center.
The Schrock type carbene complexes on the other hand undergo attack by electrophiles at its carbene−C center.
Summary
The metal−ligand multiple bonding is of significant interest as many of the compounds containing such bonds are important intermediates in various catalytic cycles. The metal−ligand doubly bonded carbene systems can exist in two varieties like the Fischer type and the Schrock type carbene complexes. Due to their different electronic structures, the reactivities of these Fischer type and the Schrock type carbene complexes differ significantly, with the former undergoing nucleophilic attack while the later undergo electrophilic attack at their respective carbene−C centers.
Metal-carbyne complexes
The metal−ligand multiply bonded systems even extended beyond the doubly bonded Fischer and the Schrock carbenes to the triply bonded LnM≡CR type Fischer carbyne and the Schrock carbyne complexes. Similar to carbene that exists in a singlet and a triplet spin state, the carbyne also exists in two other spin states i.e in a doublet and a quartet form.
Upon binding to the metal in its doublet spin state as in the Fischer carbene system, the carbyne moiety donates two electrons via its sp hybridized lone pair containing orbital to an empty metal d orbital to yield a LnM←CR type ligand to metal dative bond. It also makes a covalent π−bond through one of its singly occupied pz orbital with one of the metal d orbitals. The carbyne−metal interaction consist of two ligand to metal interactions namely a dative one and a covalent one that together makes the carbyne moiety a LX type of a ligand. In addition to these two types of ligand to metal bonding interactions, there remains an empty py orbital on the carbyne−C atom that can accommodate electron donation from a filled metal d orbital to give a metal to ligand π−back bonding interaction (Figure 1).
Analogously, in the quartet carbyne spin state in the Schrock carbyne systems three covalent bonds occur between the singly occupied sp, pyand pz orbitals of carbyne−C moiety with the respective singly occupied metal d orbitals (Figure 1).
Similar to what has been observed earlier in the case of the Fischer carbenes and Schrock carbenes, the Fischer carbyne complexes are formed with metal centers in lower oxidation states for e.g. as in Br(CO)4W≡CMe, while the Schrock carbyne complexes are formed with metals in higher oxidation state, e.g. as in (t−BuO)3W≡Ct−Bu.
Carbyne complexes can be prepared by the following methods.
1. The Fischer carbyne complexes can be prepared by the electrophilic abstraction of a methoxy group from a methoxy methyl substituted Fischer carbene complex.
2. Schrock carbynes can be prepared by the deprotonation of a α−CH bond of a metal−carbene complex.
3. by an α−elimination reaction on a metal−carbene complex
4. by metathesis reaction
The reactivities of Fischer and the Schrock carbynes mirror that of the Fischer and Schrock carbenes. For example, the Fischer carbyne undergo nucleophilic attack at the carbyne−C atom while the Schrock carbyne undergo electrophilic attack at the carbyne−C atom.
Summary
The theme of metal−ligand multiple bonding extends beyond the doubly bonded Fischer and the Schrock carbene systems to even triply bonded Fischer and the Schrock carbyne systems. The carbyne moieties in these Fischer and the Schrock carbyne systems respectively exist in a doublet and a quartet spin state. The carbyne complexes are generally prepared from the respective carbene analogues by the abstraction of alkoxy (OR), proton (H+), hydride (H) moieties, the α−elimination reactions and the metathesis reactions. The reactivity of the Fischer and the Schrock carbyne complexes parallel the corresponding Fischer and the Schrock carbene counterparts with regard to their reactivities toward electrophiles and nucleophiles.
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Learning Objectives
In this lecture you will learn the following
• The cyclopentadienyl ligands.
• The synthesis and reactivity of metal−cyclopentadienyl complexes.
• The metal−cyclopentadienyl interaction.
Cyclopentadienyl moiety acts as an important “spectator” ligand and is quite ubiquitous in organometallic chemistry. It remains inert to most nucleophiles and electrophiles and solely engages in stabilizing organometallic complexes. The cyclopentadienyl ligands form a wide array of organometallic compounds exhibiting different formulations that begin with the so-called “piano stool” CpMLn (n = 2,3 or 4) type ones and extends to the most commonly observed “metallocene” Cp2M type ones to even go beyond further to the “bent metallocene” Cp2MXn (n = 1,2 or 3) type ones. In the “piano stool” CpMLn structure, the cyclopentadienyl (Cp) ligand is regarded as the “seat” of the piano stool while the remaining L ligands are referred to as the “legs” of the piano stool. Though the cyclopentadienyl ligand often binds to metal in a η5 (pentahapto) fashion, e. g. as in ferrocene, the other form of binding to metal at lower hapticities, like that of the η3 (trihapto) binding e. g. as in (η5−Cp)(η3−Cp)W(CO)2 and that of the η1 (monohapto) binding e. g. as in (η5−Cp)(η1−Cp)Fe(CO)2, are also seen on certain rare occasions.
The binding modes of the cyclopentadienyl ligand in metal complexes can be ascertained to a certain degree by 1H NMR in the diamagnetic metal complexes, in which the Cp−protons appear as a singlet between 5.5−3.5 ppm while the β and γ hydrogens come at 7−5 ppm.
Cyclopentadienyl−metal interaction
The frontier molecular orbital of the cyclopentadienyl ligand contains 5 orbitals (Ψ1−Ψ5) residing in three energy levels (Figure 1). The lowest energy orbital Ψ1 does not contain any node and is represented by an a1 state, followed by a doubly degenerate e1 states that comprise of the Ψ2 and Ψ3orbitals, which precede another doubly degenerate e2 states consisting of Ψ4 and Ψ5 orbitals.
Figure 1.Molecular orbital diagram of cyclopentadienyl ligand.
The above frontier molecular orbital diagram becomes more intriguing on moving over to the metallocenes that contain two such cyclopentadienyl ligands. Specifically, in the Cp2M system, (e. g. ferrocene) each of these above five molecular orbital of the two cyclopentadienyl ligands combines to give ten ligand molecular orbitals in three energy levels (Figure 2). Of these, the orbitals that subsequently interact with the metal orbitals to generate the overall molecular orbital correlation diagram for the Cp2M type of complexes are shown below (Figure 3).
Generic metallocene Cp2M type complexes are formed for many from across the 1st row transition metal series along Sc to Zn. The number of unpaired electrons thus correlates with the number unpaired electrons present in the valence orbital of the metal (Figure 4). Of the complexes of the 1st row transition metal series, the manganocene exists in two distinct forms, one in a high-spin form with five unpaired electrons, e.g. as in Cp2Mn and the other in a low-spin form with one unpaired electron, e.g. as in Cp*2Mn owing to the higher ligand field strength of the Cp* ligand. Cobaltocene, Cp2Co, has 19 valence electrons (VE) and thus gets easily oxidized to the diamagnetic 18 VE valence electron species, Cp2Co+. Of these metallocenes, the much-renowned ferrocene, Cp2Fe is a diamagnetic 18 VE complex, whose molecular orbital diagram is shown above (Figure 3).
Bent metallocenes
Bent metallocenes are Cp2MXn type complexes formed of group 4 and the heavier elements of groups 5−7. In these complexes the frontier doubly degenerate e2g orbitals of Cp2M fragment interacts with the filled lone pair orbitals of the ligand (Figure 5).
Synthesis of cyclopentadienyl-metal complexes
The metal−cyclopentadienyl complexes are synthesized by the following methods.
1. from Cp−
2. from Cp+
3. from hydrocarbon
Reactivity of cyclopentadienyl-metal complexes
The reactivity of cyclopentadienyl−metal complexes of the type Cp2M is shown for a representative nickellocene complex.
1. reaction with NO
2. reaction with PR3
1. reaction with CO
2. reaction with H+
Summary
Cyclopentadienyl moiety is almost synonymous with the transition metal organometallic complexes as the ligand played a pivotal role at the early developmental stages of the field of organometallic chemistry in the 1960s and 1970s. An important quality of the cyclopentadienyl ligand is that it behaves as an extremely good “spectator” ligand being inert to nucleophiles and electrophiles and displays uncanny ability towards stabilizing metal complexes of elements from across the different parts of the periodic table. Cyclopentadienyl moiety thus forms several types of complexes of different formulations like that of the “piano stool” CpMLn (n = 2,3 or 4) types, the metallocene Cp2M types and the bent metallocene Cp2MXn (n = 1,2 or 3) types. Cyclopentadienyl metal complexes make valuable catalysts for many chemical transformations of interest to academia and industries alike. The cyclopentadienyl moiety participates in a complex interaction with the metal involving ligand frontier molecular orbitals and the metal valence orbitals. Cyclopentadienyl metal complexes can be accessed by many methods.
Problems
1. Comment on the p−acceptor property of the cyclopentadienyl ligand. Ans: The ligand being anionic shows very little π-acceptor properties. 2. Give the total valence electron count at the metal in a nickellocene complex. Ans: 20 electrons. 3. Explain why the metal center in cobalticene gets easily oxidized. Ans: 19 electrons cobalticene gets easily oxidized to 18 electron Cp2Co+. 4. Specify the number unpaired electrons present in chromocene. Ans: 2
Self Assessment test
1. Specify the number of unpaired electron present in vanadocene. Ans: The ligand being anionic shows very little π-acceptor properties. 2. What different hapticities are exhibited by cyclopentadienyl ligand? Ans: 1, 3, and 5. 3. Specify the hapticities of the cyclopentadienyl ligands in Cp2W(CO)2. Ans: 5 and 3. 4. Specify the hapticity of the cyclopentadienyl ligands in CpRh(CO)2(PMe3). Ans: 3.
Contributors and Attributions
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Tetraethyllead
Like mercury, lead is primarily obtained from its sulfide ore, in this case Galena, PbS, yet once again there are quite a number of other minerals containing lead. In terms of natural abundance it exists at about 14 ppm in the Earth's crust (37th compared to O), however it has become well known due to its ease of extraction and the number of uses with technical importance.
galena, PbS
Lead was probably discovered around 6500 BC in Turkey and by 300 BC the Romans had lead smelters in operation. The toxicity of lead was recorded by the Greeks as early as 100BC. A report from 2BC noted that:
"the drinking of lead causes oppression to the stomach, belly and intestines with wringing pains; it suppresses the urine, while the body swells and acquires and unsightly leaden hue".
The possible hazards associated with the use of lead piping in water systems was recognized as long ago as the first century BC and it has even been suggested that the "decline of the Roman Empire" might have been ascribed to the use of lead acetate as an additive to sweeten wine. It is somewhat surprising therefore that the first legislation controlling the industrial hazards of lead industries was not introduced until 1864.
Note that Dr. Wilton Turner (born in Clarendon, Jamaica in the early 1800's) wrote on the inappropriate use of lead in sugar and rum production while running a rum distillery in Guyana. One advocate said he had fed lead to dogs and guinea pigs for several weeks and seen no adverse affects in fact the guinea pigs were stolen which he thought was because they looked so fat and healthy!
An examination (in the early 1970's) of the annual snow strata in Northern Greenland and Poland revealed most elegantly that levels in air-borne lead had increased significantly since the Industrial Revolution and very sharply since 1940. Considering that 40-50% can be absorbed by inhalation compared to only 5-10% through ingestion this was cause for concern.
Lead content in North Greenland snow layers (µg per kg)
Leaded gasoline was an economic success from 1926 until 1976, and in fact, its discovery by Thomas Midgley at Charles Kettering's General Motors laboratory was among the most celebrated achievements of automotive engineering. It was often portrayed as the result of genius, luck and a great deal of hard work. It is now considered to be a catastrophic failure and is banned for environmental and public health reasons. {There are still a few countries selling petrol with lead additives.} Even more surprising is that the use of ethanol in fuel was already well established by the time tetraethyllead was introduced as an additive.
Tetraethyllead was supplied for mixing with raw gasoline in the form of "ethyl fluid", which was Et4Pb blended together with the lead scavengers 1,2-dibromoethane and 1,2-dichloroethane. "Ethyl fluid" also contained a reddish dye to distinguish treated from untreated gasoline and discourage the use of leaded gasoline for other purposes such as cleaning.
Ethyl fluid was added to gasoline in the ratio of 1:1260, usually at the refinery. The purpose was to increase the fuel's octane rating. A high enough octane rating is required to prevent premature detonations known as engine knocking ("knock" or "ping"). Antiknock agents allow the use of higher compression ratios for greater efficiency and peak power. The formulation of "ethyl fluid" was:
• Tetraethyllead 61.45%
• 1,2-Dibromoethane 17.85%
• 1,2-Dichloroethane 18.80%
• Inert materials and dye 1.90%
Effect on Health
Humans have been mining and using this heavy metal for thousands of years, poisoning themselves in the process. Although lead poisoning is one of the oldest known work and environmental hazards, the modern understanding of the small amount of lead necessary to cause harm did not come about until the latter half of the 20th century. No safe threshold for lead exposure has been discovered, that is, there is no known amount of lead that is too small to cause the body harm.
Lead pollution from engine exhaust is dispersed into the air and into the vicinity of roads and easily inhaled. Lead is a toxic metal that accumulates and has subtle and insidious neurotoxic effects especially at low exposure levels, such as low IQ and antisocial behavior. It has particularly harmful effects on children. These concerns eventually led to the ban on Et4PB in automobile gasoline in many countries. For the entire U.S. population, during and after the Et4PB phaseout, the mean blood lead level dropped from 13 µg/dL in 1976 to only 3 µg/dL in 1991. The U.S. Centers for Disease Control considered blood lead levels "elevated" when they were above 10 µg/dL. Lead exposure affects the intelligence quotient (IQ) such that a blood lead level of 30 µg/dL is associated with a 6.9-point reduction of IQ, with most reduction (3.9 points) occurring below 10 µg/dL.
Also in the U.S., a statistically significant correlation has been found between the use of Et4PB and violent crime: taking into account a 22-year time lag, the violent crime curve virtually tracks the lead exposure curve. After the ban on Et4PB, blood lead levels in U.S. children dramatically decreased.
Even though leaded gasoline is largely gone in North America, it has left high concentrations of lead in the soil adjacent to all roads that were constructed prior to its phaseout. Children are particularly at risk if they consume this, as in cases of pica.
Note as well the work done in 1995 by ICENS on the problem of the old disused lead mine and tailings that affected school children in Kintyre. Over 40 cases were detected with unacceptable levels. ICENS at that time cleaned the community and sought to educate residents about the dangers. A continuation of the research done in Kintyre was to test 628 children at 17 basic schools across the island. Children at a number of basic schools in Kingston and St Catherine were discovered with blood lead levels as low as 45 µg/dL and as high as 60. In two of the cases, children had lead levels of 130 and 202. At this level, they would likely die from the poisoning if untreated.
Properties of Et4Pb
Molecular formula C8H20Pb
Molar mass 323.44 g mol-1
Appearance Colourless, viscous liquid
Density 1.653 g/mL (20 °C)
Melting point -136 °C
Boiling point 84-85 °C/15 mm Hg
Solubility in water Insoluble
Laboratory Preparation:
The industrial preparation of tetraethyllead was from the reaction below:
~373K in an autoclave
\[\ce{4 NaPb + 4 EtCl → Et4Pb + 3 Pb + 4 NaCl}\]
alloy or by electrolysis of NaAlEt4 or EtMgCl using a Pb anode. Laboratory syntheses of R4Pb compounds in general include the use of Grignard reagents or organolithium compounds.
\[\ce{2 PbCl2 + 4 RLi → R4Pb + 4LiCl + Pb}\]
in ether
tetraethyllead
lead timeline
Tetraethyllead
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Learning Objectives
In this lecture you will learn the following
• Dialkymercury preparation.
• Mercury toxicity.
• Mercury poisoning.
Organometallic compounds of mercury:
$2 \mathrm{RMgX}+\mathrm{HgX}_2 \longrightarrow \mathrm{HgR}_2+\mathrm{MgX}_2$
Reaction proceeds due to both electronegativity and hardness considerations.
Dialkylmercury compounds are very versatile starting materials for the synthesis of many organometallic compounds of more elctropositive metals by transmetallation. However, owing to high toxicity of alkylmercury compounds, other synthons are preferred. In striking contrast to the high sensitivity of dimethylzinc to oxygen, dimethylmercury survives exposure to air.
Mercury Toxicity
The toxicity of mercury arises from the very high affinity of the soft Hg atom for sulfhydryl (—SH) groups in enzymes. Simple mercury-sulfur compounds have been studied as potential analogs of natural systems. The Hg atoms are most commonly four-coordinated, as in [Hg2(SMe)6]2-.
Mercury poisoning was a serious concern even from early days. Issac Newton, Alfred Stock worked in the early 20th century. Later in 60s awareness came following the incidence of brain damage and death it caused among the inhabitants in Minamata, Japan. Mercury from a plastic company was allowed to escape into a bay where it found its way into fish that were later eaten. Research has shown that bacteria found in sediments are capable of methylating mercury, and that species such HgMe2 and [HgCH3]+ enter the food chain because they readily penetrate cell walls. The bacteria appear to produce HgMe2 as a means of eliminating toxic mercury ions through their cell walls and into the environment.
Methylmercury
The usual method of ingestion of a metal into the body is:
a) Orally - the Gastrointestinal Tract
b) via the lungs - the Respiratory Tract
a) Orally - (mouth, stomach, small intestine): Food digestion begins in the mouth where saliva containing the enzyme amylase beaks down starch to lower sugars. Most digestion occurs in the stomach in the presence of HCl (pH ~1.6 ie. 0.17M HCl). In the case of mercury it is quite readily absorbed through the stomach since reaction of mercury salts with HCl produces HgCl2. This neutral covalent molecule (solubility in H2O 0.5 g/100 mL but 8g/100 mL in ethanol) is absorbed far better than most inorganic ions and this no doubt contributes to its high toxicity.
b) Respiratory tract (nose, lungs): This is usually unimportant for most metals but in some cases it can be more efficient that via the gastrointestinal tract. For example, lead where 50% of Pb in air can be absorbed but only 5-10% via the gastrointestinal tract. Volatile dimethyl mercury is another case for concern.
dimethylmercury
The Mercury Cycle
Mercury is 62nd in terms of natural abundance and is found everywhere, usually as the mineral cinnabar, HgS, although 30 minerals containing Hg are known. The oxidation states are Hg(0), Hg(I) and Hg(II), where Hg(I) has been shown to exist as Hg22+.
HgS - cinnabar
The three Hg species are related by the disproportionation:
Hg22+ → Hg0 + Hg2+ E° = -0.131 V or K= 6 x 10-3
In addition:
Hg22+/Hg E° = 0.789 V
Hg2+/Hg E° = 0.854 V
This means that to oxidise Hg to Hg22+ an oxidising agent with potential > 0.789V is required, but very importantly < 0.854 V, otherwise oxidation to Hg2+ will occur. There are no common oxidants that fit this arrangement so if any reaction occurs the product will be Hg2+. The equilibrium constant of 6 x 10-3 shows that when Hg(I) is formed it is moderately stable, however any agent that reduces the Hg(II) concentration automatically drives the reaction from Left → Right. Given that many Hg(II) derivatives are insoluble then this clearly restricts the range of Hg(I) compounds.
Minamata Disease
There have been several serious outbreaks of mercury poisoning. The most famous was between 1953 and 1965 at Minamata Bay in Japan when 46 people died and 120 suffered severe symptoms. As of March 2001, 2,265 victims had been officially recognised (1,784 of whom had died) and over 10,000 had received financial compensation from Chisso. By 2004, Chisso Corporation had paid \$86 million in compensation, and in the same year was ordered to clean up its contamination. On March 29th, 2010, a settlement was reached to compensate as-yet uncertified victims.
The disease was first noticed in cats (who were seen throwing themselves into the sea) and was quickly traced to mercury poisoning acquired as a result of eating contaminated fish (5-10 ppm Hg). The investigations that followed showed that the fish had acquired the high mercury due to the dumping of inorganic mercury salts and methylmercury from the Chisso Co. plastics factory upstream.
Analysis of fish exhibits from museums, some over 90 years old, has shown that mercury levels for ocean fish are similar but that river fish levels have risen as a result of man-made contamination. The forms of mercury occuring in the environment are Hg2+ and methylmercury, either MeHg+ or Me2Hg. Interconversion can be affected by microorganisms.
Aerobes can solubilize Hg2+ from cinnabar (Ksp ~10-53) which in sediments was considered safe since the solubility product was so small. The conversion of S2- → SO32- → SO42- allows the insoluble sulfide to breakdown and in the process other Hg(II) salts are formed or the mercury may get reduced to Hg(0) enzymatically.
$\ce{Hg^{2+} + NADH + H^{+} → Hg^{0} + NAD^{+} + 2 H^{+}}$
where NADH = reduced form of nicotinamideadeninedinucleotide. This conversion can be considered as a detoxification process since Hg0 is more easily eliminated.
In the environment, sulfate-reducing bacteria take up mercury in its inorganic form and through metabolic processes convert it to methylmercury. Sulfate-reducing bacteria are found in anaerobic conditions, typical of the well-buried muddy sediments of rivers, lakes, and oceans where methylmercury concentrations tend to be highest. Sulfate-reducing bacteria use sulfur rather than oxygen as their cellular energy-driving system. One hypothesis is that the uptake of inorganic mercury by sulfate-reducing bacteria occurs via passive diffusion of the dissolved complex HgS. Once the bacterium has taken up this complex, it utilizes detoxification enzymes to strip the sulfur group from the complex and replaces it with a methyl group:
$\ce{HgS → CH3Hg(II)X + H2S }$
Upon methylation, the sulfate-reducing bacteria transport the new mercury complex back to the aquatic environment, where it is taken up by other microorganisms. Bacteria eliminate Hg by methylating it first to MeHg+ and Me2Hg. The detoxification process for them is the reverse for us unfortunately! The conversion probably involves vitamin B12 a methyl-cobalt organometallic compound so this is another example of synthesis involving transmetallation.
The major source of methylmercury exposure in humans is consumption of fish, marine mammals, and crustaceans. Once inside the human body, roughly 95% of the fish-derived methylmercury is absorbed from the gastrointestinal tract and distributed throughout the body. Uptake and accumulation of methylmercury is rapid due to the formation of methylmercury-cysteine complexes. Methylmercury is believed to cause toxicity by binding the sulfhydryl groups at the active centers of critical enzymes and structural proteins. Binding of methylmercury to these moieties constitutively alters the structure of the protein, inactivating or significantly lowering its functional capabilities.
Once the Me2Hg is formed it is volatile and when released into the atmosphere it is readily photolysed by UV light
$\ce{Me2Hg → Hg^{0} + 2 CH3^{\cdot} → CH4 \,text{ or } C2H6}$
Other microorganisms can convert MeHg+ to Hg0 + CH4 that is make the mercury considerably less toxic to humans.
Summary
Organic mercury tends to increase up the food chain, particularly in lakes. The mud at the bottom of a lake may have 100 or 1000 times the amount of mercury than is in the water. Bacteria, worms and insects in the mud extract and concentrate the organic mercury. Small fish that eat them further concentrate the mercury in their bodies. This concentration process, known as "bioaccumulation", continues as larger fish eat smaller fish until the top predator fish in the lake may have methylmercury levels in their tissues that are up to 1,000,000 times the level in the water in which they live. We then eat the fish....
To consume a human being would be extremely unhealthy for any animal. Humans carry the highest concentration of toxic chemicals of all creatures on the planet. Their livers, hearts, kidneys and brains are so heavily contaminated with hundreds of different synthetic chemicals that if humans were slaughtered as a meat source, they'd never pass USDA food safety standards.
Table $1$: Properties of Me2Hg
Molecular formula C2H6Hg
Molar mass 230.66 g mol-1
Appearance Colourless liquid
Density 2.96 g/mL
Melting point -43 °C
Boiling point 87-97 °C
Solubility in water Insoluble
Laboratory Preparation:
Hg + 2 Na + 2 CH3I → (CH3)2Hg + 2 NaI
1H NMR of dimethylmercury showing 199Hg coupling (J ~100.9 Hz)
199Hg has a nuclear spin of ½ and natural abundance of 16.87%. Can you explain the observed splitting pattern?
Methylmercury
Dimethylmercury
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Learning Objectives
In this lecture you will learn the following
• Organometallic compounds of zinc and cadmium.
• Structural features of organozinc compounds.
Organometallic compounds of zinc and cadmium
Dialkyl compounds of Zn, Cd and Hg do not associate through alkyl bridges. Dialkylzinc compounds are only weak Lewis acids, organocadmium compounds are even weaker, and organomercury compounds do not act as Lewis acids except under special circumstances.
The Group 12 metals form linear molecular compounds, such as ZnMe2, CdMe2 and HgMe2, that are not associated in solid, liquid or gaseous state or in hydrocarbon solution.
They form 2c, 2e bonds. Unlike Be and Mg analogs, they do not complete their valence shells by association through alkyl bridges. The bonding in these molecules are similar to d10 metals such as CuI, AgI and AuI with linear geometry ([N≡C-M-C≡N]-, M = Ag or Au). This tendency is sometimes rationalized by invoking pd hybridization in the M+ ion, which leads to orbitals that favor linear attachment of ligands (similar to spd hybridization).
The preference for the linear coordination may be due to the similarity in energy of the outer ns, np and (n-1)d orbitals, which permits the formation of collinear spd hybrids.
The hybridization of s, pz and dz2 with the choice of phases shown here produces a pair of collinear orbitals that can be used to form strong σ-bonds.
Organozinc and organocadmium compounds
Convenient route is metathesis with alkylaluminium or alkyllithium compounds.
With alkyllithium compounds it is the electronegativity which is decisive, whereas between Al and Zn it is hardness considerations correctly predict the formation of softer ZnCH3 and harder AlCl pairs.
Alkylzinc compounds are pyrophoric and readily hydrolyzed, whereas alkylcadmium compounds react more slowly with air. Due to mild Lewis acidity, dialkylzinc and dialkylcadimum compounds form stable complexes with amines, especially with chelating amines.
The Zn—C has greater carbanionic character than the Cd—C bond.
For example, addition of alkylzinc compounds across the carbonyl group of a ketone:
This reaction do not proceed with the less polar alkylcadmium or alkylmercury compounds, but organolithium, organomagnesium and organoaluminium compounds can promote this reaction readily since all of which contain metals with lower electronegativity than zinc.
Interestingly, the cyclodipentadienyl compounds are structurally unusual. CpZnMe is monomeric in the gas phase with a pentahapto Cp group.
In the solid state it is associated in a zig-zag chain, each Cp group being pentahapto with respect to two Zn atoms.
Problems:
1. Do you think that the following reaction proceeds? If so, why and how?
Solution:
Al2Me6 being an electron deficient molecule readily exchanges two methyl groups with zinc for two chloride ions. Since chloride ions have sufficient electron in their valence shell act as four electron donor through bridging coordination mode. Al2Cl2Me4 is no longer an electron deficient molecule.
Diethyzinc is the cheapest available organozinc compound and accounts for 60% of all references to diorganozinc reagents. The remainder coming from dimethyl (21%), dibutyl (4%), diisopropyl (4%), diphenyl (5%) and others (6%).
The different methods for preparing diorganozinc compounds can be grouped into four general approaches:
(a) the oxidative addition between zinc metal and an alkyl halide followed by Schlenk equilibration,
\[\ce{ 2 RX + 2 Zn → R2Zn + ZnX2}\]
(b) the transmetallation of a zinc halide with an organometallic reagent,
\[\ce{ 2 RM + 2 ZnX2 → R2Zn + 2 MX}\]
(c) the transmetallation of a diorganozinc starting material with an organometallic reagent, and
\[\ce{ 2 RM + R'2Zn → R2Zn + 2 R'M}\]
(d) the zinc-halogen exchange between an alkyl halide and a diorganozinc
\[\ce{2 RX + R'2Zn → R2Zn + 2 R'X}\]
Frankland prepared Et2Zn from EtI and Zn metal via EtZnI by distilling the more volatile Et2Zn which shifted the Schlenk equilibrium towards further product. No reaction occurred until 150 °C, but at 200 °C the Zn/EtI reaction proceeded with "tolerable rapidity", giving white crystals and leaving a colourless, mobile liquid. The sealed tube containing this reaction mixture remained sealed for some months because the only eudiometer required for the combustion of the product gases for their analysis was destroyed. In October 1848, Frankland returned to the University of Marburg to the laboratory of Robert Bunsen in order to obtain his Ph.D. under Bunsen's guidance. He took along with him the sealed tube from his EtI/Zn experiment at Queenwood College, Hampshire, England. He prepared the methyl derivative at about the same time and the apparatus shown in the paper reporting their preparation shows just how imaginative Frankland had become to cope with the air and moisture sensitivity of the products.
Apparatus for the preparation of diorganozinc compounds. Section A was where MeI was heated, B is the receiver containing the sample tubes d and e, C was a CaCl2 drying tube to prevent moisture and D was for generation of gaseous H2 to flush out and rid the system of air.
Frankland described these procedures in such detail to illustrate the painstaking, time-consuming care required in those days when working with extremely air and moisture-sensitive liquids. In 1877 Frankland noted in a 1000 page English translation of his papers that when
"I cut off the upper part of the tube in order to try the action of water upon the solid residue. On pouring a few drops of water upon the residue, a green-blue flame, several feet long, shot out of the tube, causing great excitement among those present. Professor Bunsen, who had suffered from arsenical poisoning during his research on cacodyl, suggested that the spontaneously inflammable body, which diffused an abominable odour through the laboratory, was that terrible compound, which might have been formed by arsenic present as an impurity in the zinc used in the reaction, and that I might be already irrecoverably poisoned. These forebodings were, however, quelled in a few minutes by an examination of the black stain [which was zinc] left upon porcelain by the flame; nevertheless, I did afterward experience some symptoms of zinc poisoning."
Dimethyl- and diethylzinc were the first available sources of nucleophilic alkyl groups, useful for the alkylation of inorganic and organometallic halides and of organic C=O and C=N-containing electrophiles. Early examples of the alkylation of metal-halogen functions were described by Frankland and others, and the dialkylzincs have been useful in this application ever since. Since they are less reactive than the comparable Grignard and organolithium reagents, they are particularly useful in the partial alkylation of element polyhalides, e.g., \(\ce{PCl3 → RPCl2}\).
The first use of a dialkylzinc in organic synthesis appears to have been reported by Freund of the University of Lemberg in 1861. In his search for a synthesis of ketones, he added acetyl chloride to diethylzinc. He had a difficult time obtaining a pure product but finally identified it as CH3C(O)Et.
\[\ce{2 CH3C(O)Cl + Et2Zn → 2 CH3C(O)Et + ZnCl2}\]
In 1867 Butlerow, in Russia, prepared tertbutyl alcohol by reaction of 2 equiv of dimethylzinc with acetyl chloride on a large scale, using 250 g of dimethylzinc. In this paper, Butlerow disputes Frankland's report of the toxic effects of dimethylzinc, saying that he and co-workers had worked with this compound for 5 years without taking any special precautions and never had a problem. He noted that smoking in the presence of dimethylzinc vapors (or, more correctly, vapors of the oxidation and hydrolysis products of dimethylzinc) changes the taste of the tobacco; it becomes unpleasantly sweetish!!
Following the discovery of the usefulness of Grignards in organic synthesis there was a decrease in the studies on Zn compounds until about 1984 when it was noted that enantioselective reactions could be performed using diorganoZn compounds.
Addition reaction of organozinc compounds to carbonyl compounds
The Barbier reaction (1899) is an organic reaction between an alkyl halide and a carbonyl group as an electrophilic substrate in the presence of magnesium, aluminium, zinc, indium, tin or its salts. The reaction product is a primary, secondary or tertiary alcohol. The reaction is similar to the Grignard reaction but the crucial difference is that the Barbier reaction is a one-pot synthesis whereas a Grignard reagent is prepared separately before addition of the carbonyl compound. Barbier reactions are nucleophilic addition reactions that usually take place with relatively inexpensive and water insensitive metals or metal compounds in contrast to Grignard reagents or organolithium reagents. For this reason it is possible in many cases to run the reaction in water which makes the procedure part of green chemistry. On the downside organozincs are much less nucleophilic than Grignards. The Barbier reaction is named after Victor Grignard's teacher Philippe Barbier.
An example of the Barbier reaction is the reaction of allyl bromide with benzaldehyde and zinc powder in water:
Barbier Reaction: The observed diastereoselectivity for this reaction is erythro : threo = 83 : 17
The catalytic enantioselective alkylation of aldehydes to afford enantioenriched secondary alcohols has been extensively studied since the 1980s. Diorganozinc reagents were the most widely used nucleophiles in this reaction, due to their low propensity to add to carbonyl derivatives without the presence of a suitable catalyst. A wide range of catalysts were investigated to optimise the conditions and conversion and to obtain the secondary alcohols in high enantiomeric excess. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/24%3A_Organometallic_chemistry-_d-block_elements/24.16%3A_Transition_Metal_Complexes/24.16.03%3A_Organozinc_Chemistry.txt |
Thumbanil: Wilkinson's Catalyst.
25: Catalysis and some industrial processes
Learning Objectives
In this lecture you will learn the following
• The application of organometallic complexes in homogeneous catalysis.
• Alkene isomerization.
• Alkene and the arene hydrogenations.
• Transfer hydrogenation.
One of the most important exploits of the organometallic chemistry is its application in the area of homogeneous catalysis. The field has now expanded its territory to accommodate in equal measures many large-scale industrial processes as well as numerous small scale reactions of the day-to-day organic synthesis. A few representative examples of organometallic catalysis are outlined below.
Alkene Isomerization
Alkene isomerization is a transformation that involve a shift of a double bond to an adjacent position followed by 1,3−migration of a H atom. The isomerization reaction is transition metal catalyzed.
The alkene isomerization reaction may proceed by two pathways, (i) one through a η1−alkyl intermediate and (ii) the other through η3−allyl intermediate. In the η1−alkyl pathway, an alkene first binds to a metal at a vacant site next to M−H bond and then subsequently undergoing an insertion into the M−H bond thus creating back the vacant site. The resultant species then undergoes a H atom transfer from the alkyl moiety to give the isomerized olefin along with the regeneration of the M−H species.
The η3−allyl mechanism requires the presence of two vacant sites. This mechanism goes through a η3−allyl intermediate formed by a C−H activation at the allylic position of the olefin formed after binding to the metal and alongside leads to the formation of a M−H bond. Subsequent H transfer from the metal back to the η3−allyl moiety leads to the alkene isomerized product.
Alkene Hydrogenation
The transition metal catalyzed alkene hydrogenation reactions are of significant industrial and academic interest. These reactions involve the H2 addition on a C=C bond of olefins to give alkenes. The alkene hydrogenation may proceed by three different pathways namely the (i) oxidative addition (ii) heterolytic activation and (iii) the homolytic activation of the H2 molecule.
The oxidative addition pathway is commonly observed for the Wilkinson’s catalyst (PPh3)3RhCl and is the most studied among all of the three pathways that exist. The catalytic cycle initiates with the oxidative addition of H2 followed by alkene coordination. The resultant species subsequently get converted to the hydrogenated product.
The second pathway proceeds by the heterolytic activation of the H2 molecule and requires the presence of a base like NEt3, which facilitates the heterolytic cleavage by abstracting a proton from the H2 molecule and leaving behind a hydride H ion that participates in the hydrogenation reaction. This type of mechanism is usually followed by the (PPh3)3RuCl2 type of complexes.
Homolytic cleavage of H2 is the third pathway for the alkene hydrogenation. It is the rarest of all the three methods and proceeds mainly in a binuclear pathway. Paramagnetic cobalt based Co(CN)53− type catalysts carries out alkene hydrogenation by this pathway via the formation of the HCo(CN)53−species.
Arene hydrogenations
Examples of homogeneous catalysts for arene hydrogenation are rare though it is routinely achieved using catalysts like Rh/C under the heterogeneous conditions. A representative example of a homogeneous catalyst of this class is (η3−allyl)Co[P(OMe)3]3 that carry out the deuteration of benzene to give the all-cis-C6H6D6 compound.
Transfer hydrogenation
This is a new kind of a hydrogenation reaction in which the source of the hydrogen is not the H2molecule but an easily oxidizable substrate like isopropyl alcohol. The method is particularly useful for the reduction of ketones and imines but not very effective for the olefins.
Summary
The applications of organometallic compounds in homogeneous catalysis have transcend the boundaries of industry to meet the day-to-day synthesis in laboratory scale reactions. The alkene isomerization is one such application of homogeneous catalysis by the transition metal organometallic complexes. The hydrogenation reactions of alkene, arene, ketone and imine substrates are achieved by several types of the transition metal organometallic catalysts. They also proceed by different mechanisms involving oxidative addition, heterolytic and homolytic cleavages of the H−H bond. The transfer hydrogenation reaction uses easily oxidizable substrates like i−PrOH instead of H2 as the hydrogenation source.
Contributors and Attributions
http://nptel.ac.in/courses/104101006/30 | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/25%3A_Catalysis_and_some_industrial_processes/25.03%3A_Homogeneous_Catalysis_-_Alkene_%28Olefin%29_and_Alkyne_Metathesis.txt |
Learning Objectives
In this lecture you will learn the following
• The hydroformylation reaction and its mechanism.
• The C−C cross-coupling reactions and their mechanisms.
It is truly an exciting time for the field of organometallic chemistry as its potentials in homogeneous catalysis are being realized in an unprecedented manner. The growth in the field organometallic chemistry has been rightly acknowledged by the award of three Nobel prizes in over a decade in the areas of asymmetric hydrogenation (Nyori and Knowles in 2001), olefin metathesis (Grubbs, Schrock and Chauvin in 2006) and palladium mediated C−C cross coupling reactions (Suzuki, Negishi and Heck, 2010). A few representative examples of such landmark discoveries of homogeneous catalysis by organometallic compounds are discussed below.
Hydroformylation reaction
Hydroformylation, popularly known as the "oxo" process, is a Co or Rh catalyzed reaction of olefins with CO and H2 to produce the value-added aldehydes.
The reaction, discovered by Otto Roelen in 1938, soon assumed an enormous proportion both in terms of the scope and scale of its application in the global production of aldehydes. The metal hydride complexes namely, the rhodium based HRh(CO)(PPh3)3 and the cobalt based HCo(CO)4 complexes, catalyzed the hydroformylation reaction as shown below.
Hydroformylation, also known as oxo synthesis or oxo process, is an important homogeneously catalyzed industrial process for the production of aldehydes from alkenes.[1] This chemical reaction entails the addition of a formyl group (CHO) and a hydrogen atom to a carbon-carbon double bond. This process has undergone continuous growth since its invention in 1938: Production capacity reached 6.6×106 tons in 1995. It is important because the resulting aldehydes are easily converted into many secondary products. For example, the resulting aldehydes are hydrogenated to alcohols that are converted to plasticizers or detergents. Hydroformylation is also used in specialty chemicals, relevant to the organic synthesis of fragrances and natural products. The development of hydroformylation, which originated within the German coal-based industry, is considered one of the premier achievements of 20th-century industrial chemistry.
25.5E: Alkene Oligomerization
Learning Objectives
In this lecture you will learn the following
• The alkene metathesis reactions and their different variants.
• The application of metal carbenes in alkene metathesis reactions.
• The functional group tolerance, air and moisture sensitivity and high efficiency as important catalyst attributes for the alkene metathesis reactions.
The application of organometallic chemistry in homogenous catalysis is progressively increasing with the fast pace of discovery of new catalysts in the area. The benefits of organometallic catalysis have now percolated to all facets of the chemical world that span from the confines of the industry to the day-to-day small scale use in organic synthesis in academic laboratories. Quite a few of these applications of organometallic complexes in homogeneous catalysis have made a permanent imprint on the ever going developmental process that is constantly transforming our day-to-day life. An example of such a success story is of alkene metathesis, which is described in this chapter.
Alkene metathesis
Alkene metathesis reactions are gaining wide popularity in synthesizing unsaturated olefinic compounds as well as the unsaturated polymeric counterparts. Central to this catalysis is a metal carbene intermediate that reacts with olefins to give different olefinic compounds or even the unsaturated olefinic polymers depending upon the reaction conditions of the metathesis reaction. Metathesis is an unusual transformation in which a C=C is broken and also formed during catalysis to generate new unsaturated olefins.
Though a large variety of metal−carbene catalysts have been developed for the metathesis reaction, only a few have been found to be functional group tolerant. Thus a critical step in broadening the utility of metathesis reaction has been in developing catalysts that are functional group tolerant. In this regard, the early-transition metal based carbene catalysts like that of the Ti based ones are highly oxophilic and hence are intolerant to the functional groups. On the other hand, the more electron-rich Mo and W based catalysts are of intermediate character. Finally, the late-transition metal based Ru catalysts are found to be exceptionally tolerant toward functional groups but all the while exhibiting high reactivity toward olefinic bonds. In this context notable are the Grubb’s Ru catalyst, which is easy to handle, and the Schrock’s Mo catalyst, which display high activity.
The metathesis reaction as such stands for a family of related reactions all of which involve a “cutting and stitching” of olefinic bonds leading to different unsaturated products. When two different olefin substrates are used, the reaction is called the “cross metathesis” owing to the fact that the olefinic ends are exchanged.
The metathesis reactions can even extend further to the conjugated dienes that can undergo Ring Closing Metathesis (RCM) in systems where the ring strain is not too high in the final product. The reverse of Ring Closing Metathesis (RCM) is called the Ring Opening Metathesis (ROM), and which is usually favored in the presence of large excess of C2H4.
The variants of metathesis often used in producing polymers are, (i) the Acyclic Diene Metathesis (ADMET) and (ii) the Ring Opening Metathesis Polymerization (ROMP), in which the relief of ring-strain of cycloalkenes drives the polymerization reaction forward. Both of these reactions, produce long chain polymers in a living fashion and as a result of which these reactions are useful for producing block copolymers −(AAABBBB) n−.
Though several possibilities have been debated for the mechanism of the metathesis reaction, the one proceeding via a metalacyclobutane intermediate has gained credence.
Several important industrial applications have emerged out of the metathesis reaction like that of the commercial synthesis of the housefly pheromone.
Similarly, the polycyclopentadiene polymer, which is formed from the Ring Opening Metathesis Polymerization (ROMP) of dicyclopentadiene substrate, is used for bullet proof related applications because of its exceptional strength owing to its cross-linked nature.
Summary
Alkene metathesis represents a distinct class of related chemical reactions that involve the “cutting and stitching” of olefinic bonds to give unsaturated organic products. Depending upon the nature of the product formed, different type of alkene metathesis reactions exist like the alkene metathesis, cross-metathesis, Ring Closing Metathesis (RCM), Ring Opening Metathesis (ROM), Acyclic Diene Metathesis (ADMET), and the Ring Opening Metathesis Polymerization (ROMP). A commonality that runs through all of these different varieties of the metathesis reaction is its mechanism that involves a catalytically active metal−carbene species. The mechanism is said to be proceed via a 4−membered metalacyclobutane intermediate. The alkene metathesis has found important applications in organic synthesis as well as in the chemical industry.
Contributors and Attributions
http://nptel.ac.in/courses/104101006/35
25.5F: CC cross-coupling reactions
Learning Objectives
In this lecture you will learn the following
• The C−C cross-coupling reactions and their mechanisms.
The palladium catalyzed cross-coupling reactions are a class of highly successful reactions with applications in the organic synthesis to have emerged recently. The reactions carry out a coupling of the aryl, vinyl or alkyl halide substrates with different organometallic nucleophiles and as such encompasses a family of C−C cross-coupling reactions that are dependent on the nature of nucleophiles like that of the B based ones in the Suzuki-Miyuara coupling, the Sn based ones in the Stille coupling, the Si based ones in the Hiyama coupling, the Zn based ones in the Negishi coupling and the Mg based ones in the Kumada coupling reactions (Figure 1).
An unique feature of these reactions is the exclusive formation of the cross-coupled product without the accompaniment of any homo-coupled product. Another interesting feature of these coupling reactions is that they proceed via a common mechanism involving three steps that include the oxidative addition, the transmetallation and the reductive elimination reactions (Figures 2 and 3).
Summary
Organometallic complexes play a pivotal role in several successful homogeneous catalysis reactions like that of the hydroformylation and the C−C cross-coupling reactions. These reactions are important because of the fact that both of the hydroformylation and the C−C cross-coupling reactions give more value added products compared to the starting reactants. The palladium catalyzed C−C cross-coupling reactions are a class of highly successful reactions that have permanently impacted the area of organic synthesis in a profound way to an extent that the 2010 Nobel prize has been conferred on one of these reactions thereby recognizing the importance of the C−C cross-coupling recations. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/25%3A_Catalysis_and_some_industrial_processes/25.05%3A_Homogeneous_Catalysis_-_Industrial_Applications/25.5D%3A_Hydroformylation_%28Oxo-process%29.txt |
Learning Objectives
In this lecture you will learn the following
• Olefin polymerization.
• Mechanism involved in polymerization process.
Ziegler Natta Polymerization Catalysts
Insertion of aluminum alkyls into olefins was studied by Ziegler. During the systematic investigation of olefin polymerization, Ziegler realized that the most effective catalyst is the combination of TiCl4/AlEt3which can polymerize ethylene at pressure as low as 1 bar. The application of Ziegler method to the polymerization of propylene and its establishment and the investigation of bulk properties was carried out by Natta and hence the methodology is called Ziegler-Natta process.
Important discovery: R3Al + Lewis acids.
In the absence of reaction mechanism with solid proof, it is presumed that the reaction is due to the heterogeneous catalysis in which fibrous TiCl3, alkylated on its surface is considered to be the active catalyst species.
Contributors and Attributions
http://nptel.ac.in/courses/104101006/10
26: d-Block Metal Complexes- Reaction Mechanisms
Mechanisms of ligand substitution and electron-transfer reactions in coordination complexes. While, a proposed mechanism must be consistent with all experimental facts. it cannot be proven, since another mechanism may also be consistent with the experimental data.
28.4B: High-temperature Superconductors
Learning Objectives
• To become familiar with the properties of superconductors.
Contributors
• Anonymous
Video from Wisconsin MRSEC @ YouTube
28.5A: White Pigments (Opacifiers)
An opacifier is a substance added to a material in order to make the ensuing system opaque. An example of a chemical opacifier is titanium dioxide (\(TiO_2\)), which is used to opacify ceramic glazes and milk glass. Opacifiers must have a refractive index substantially different from the system. Conversely, clarity may be achieved in a system by choosing components with very similar refractive indices.
• Wikipedia
29.3B: Hemocyanin
Hemocyanin is used for oxygen transport in many arthropods (spiders, crabs, lobsters, and centipedes) and in mollusks (shellfish, octopi, and squid); it is responsible for the bluish-green color of their blood. The protein is a polymer of subunits that each contain two copper atoms (rather than iron), with an aggregate molecular mass of greater than 1,000,000 amu. Deoxyhemocyanin contains two Cu+ ions per subunit and is colorless, whereas oxyhemocyanin contains two Cu2+ ions and is bright blue. As with hemerythrin, the binding and release of O2 correspond to a two-electron reaction:
$\ce{2Cu^{+} + O2 <=> Cu^{2+}–O2^{2−}–Cu^{2+}} \label{23.18}$
Although hemocyanin and hemerythrin perform the same basic function as hemoglobin, these proteins are not interchangeable. In fact, hemocyanin is so foreign to humans that it is one of the major factors responsible for the common allergies to shellfish.
29.3C: Hemerythrin
Hemerythrin is used to transport O2 in a variety of marine invertebrates. It is an octamer (eight subunits), with each subunit containing two iron atoms and binding one molecule of O2. Deoxyhemerythrin contains two Fe2+ ions per subunit and is colorless, whereas oxyhemerythrin contains two Fe3+ ions and is bright reddish violet. These invertebrates also contain a monomeric form of hemerythrin that is located in the tissues, analogous to myoglobin. The binding of oxygen to hemerythrin and its release can be described by the following reaction, where the HO2 ligand is the hydroperoxide anion derived by the deprotonation of hydrogen peroxide (H2O2):
$\ce{2Fe^{2+} + O2 + H^{+} <=> 2Fe^{3+}–O2H} \label{23.17}$
Thus O2 binding is accompanied by the transfer of two electrons (one from each Fe2+) and a proton to O2. | textbooks/chem/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/25%3A_Catalysis_and_some_industrial_processes/25.08%3A_Heterogeneous_Catalysis_-_Commercial_Applications/25.8A%3A_Alkene_Polymerization_-_Ziegler-Natta_Catalysis_.txt |
Let’s face it: organometallic chemistry is a somewhat esoteric subject. Unfortunately, this fact makes it difficult to find cheap, current textbooks on the subject, but there are a few used gems for sale on the Internet. Crabtree’s Organometallic Chemistry of the Transition Metals is a short but solid book that’s a good jumping-off point for deeper studies. Spessard and Miessler’s Organometallic Chemistry is a longer but still informative classic. Hartwig’s “biblical” Organotransition Metal Chemistry is a nice reference work, but I wouldn’t start off with this back-breaking tome. If you do, skip around and avoid the vast sections of text describing “what’s known” with little explanation.
What resources are available for the interested organometallics student?
For the penny-pinching student or layman, there are several good resources for organometallic chemistry on the Web. Nothing as exhaustive as Reusch’s Virtual Textbook of Organic Chemistry exists for organometallic chemistry, but the base of resources available on the Web is growing. Rob Toreki’s Organometallic HyperTextBook could use a CSS refresh, but contains some nice introductions to different organometallic concepts and reactions. Try the electron-counting quiz!
VIPER is a collection of electronic resources for teaching and learning inorganic chemistry, and includes a nice section on organometallic chemistry featuring laboratory assignments, lecture notes, and classroom activities. Awesome public lecture notes are available from Budzelaar at the University of Manitoba and Shaughnessy at Alabama (Roll Tide?). For practice problems, check out Fu’s OpenCourseWare material from MIT and Shaughnessy’s problem sets.
1.02: What is Organometallic Chemistry
Let’s begin with a few simple questions: what is organometallic chemistry? What, after studying organometallic chemistry, will we know about the world that we didn’t know before? Why is the subject worth studying? And what kinds of problems is the subject meant to address? The purpose of this post is to give the best answers I currently know of to these questions. The goal of this otherwise content-free post is twofold: (1) to help motivate us as we move forward (that is, to constantly remind us that there is a point to all this!); and (2) to illustrate the kinds of problems we’ll be able to address using concepts from the field. You might be surprised by the spine-chilling power you feel after learning about the behavior of organometallic compounds and reactions!
Put most bluntly, organometallic (OM) chemistry is the study of compounds containing, and reactions involving, metal-carbon bonds. The metal-carbon bond may be transient or temporary, but if one exists during a reaction or in a compound of interest, we’re squarely in the domain of organometallic chemistry. Despite the denotational importance of the M-C bond, bonds between metals and the other common elements of organic chemistry also appear in OM chemistry: metal-nitrogen, metal-oxygen, metal-halogen, and even metal-hydrogen bonds all play a role. Metals cover a vast swath of the periodic table and include the alkali metals (group 1), alkali earth metals (group 2), transition metals (groups 3-12), the main group metals (groups 13-15, “under the stairs”), and the lanthanides and actinides. We will focus most prominently on the behavior of the transition metals, so called because they cover the transition between the electropositive group 2 elements and the more electron-rich main group elements.
Why is the subject worth studying? Well, for me, it mostly comes down to synthetic flexibility. There’s a reason the “organo” comes first in “organometallic chemistry”—our goal is usually the creation of new bonds in organic compounds. The metals tend to just be along for the ride (although their influence, obviously, is essential). And the fact is that you can do things with organometallic chemistry that you cannot do using straight-up organic chemistry. Case in point:
The venerable Suzuki reaction...unthinkable without palladium!
The establishment of the bond between the phenyl rings through a means other than dumb luck seems unthinkable to the organic chemist, but it’s natural for the palladium-equipped metal-organicker. Bromobenzene looks like a potential electrophile at the bromine-bearing carbon, and if you’re familiar with hydroboration you might see phenylboronic acid as a potential nucleophile at the boron-bearing carbon. Catalytic palladium makes it all happen! Organometallic chemistry is full of these mind-bending transformations, and can expand the synthetic toolbox of the organic chemist considerably.
To throw another motive into the mix for the non-specialist (or the synthesis-spurning chemist), organometallic chemistry is full of intriguing stories of scientific inquiry and discovery. Exploring how researchers take a new organometallic reaction from “ooh pretty” to strong predictive power is instructive for anyone interested in “how science works,” in a practical sense. We’ll examine a number of classical experiments in organometallic chemistry, both for their value to the field and their contributions to the general nature of scientific inquiry.
What kinds of problems should we be able to address as we move forward? Here’s a bulleted list of the most commonly encountered types of problems in an organometallic chemistry course:
• Describe the structure of an organometallic complex…
• Predict the product of the given reaction conditions…
• Draw a reasonable mechanism based on evidence…
• Devise a synthetic route to synthesize a target organometallic compound…
• Explain the observation(s)…
• Predict the results of a series of experiments…
The first four are pretty standard organic-esque problems, but it’s the last two, more general classes that really make organometallic chemistry compelling. Just imagine putting yourself in the shoes of the pioneers and making the same predictions they did!
There you have it, a short introduction to organometallic chemistry and why it’s worth studying. Of course, we’ll use the remainder of space in the blog to fully describe what organometallic chemistry really is…but it’s helpful to keep these motives in mind as you study. Keep a thirst for predictive power, and it’s hard to go wrong with organometallic chemistry! | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/01%3A_Introduction_to_Organometallic_Chemistry/1.01%3A_Resources_for_Organometallic_Chemistry.txt |
• 2.1: Carbenes
Fischer carbenes, Shrock carbenes, and vinylidenes are usually actor ligands, but they may be either nucleophilic or electrophilic, depending on the nature of the R groups and metal. In addition, these ligands present some interesting synthetic problems: because free carbenes are quite unstable, ligand substitution does not cut the mustard for metal carbene synthesis.
• 2.2: Carbon Monoxide
• 2.3: σ Complexes
Ligands can, shockingly enough, bind through their σ electrons in an L-type fashion. This binding mode depends as much on the metal center as it does on the ligand itself.
• 2.4: Dative Ligands of N, O, and S
L-type ligands of nitrogen, oxygen, and sulfur are important for at least two reasons: (1) coordination to a metal can modify the reactivity of the bound functional group, and (2) dative coordination is a critical element of organometallic reactions that depend on intramolecular directing group effects. “Long-term” ligands containing two-connected nitrogens, such as pyridines and oxazolines, are now among the most commonly used for organometallic reactions.
• 2.5: Metal Alkyls
Metal alkyls feature a metal-carbon σ bond and are usually actor ligands, although some alkyl ligands behave as spectators. Our aim will be to understand the general dependence of the behavior of alkyl ligands on the metal center and the ligand’s substituents. Using this knowledge, we can make meaningful comparisons between related metal alkyl complexes and educated predictions about their likely behavior.
• 2.6: Metal Hydrides
Metal-hydrogen bonds are ubiquitous X-type ligands in organometallic chemistry. There is much more than meets the eye to most M-H bonds: although they’re simple to draw, they vary enormously in polarization and pKa. They may be acidic or hydridic or both, depending on the nature of the metal center and the reaction conditions. In this post, we’ll develop some heuristics for predicting the behavior of M-H bonds and discuss their major modes of reactivity.
• 2.7: N-heterocyclic Carbenes
N-heterocyclic carbenes (NHCs) exhibit their unique structure, properties, and steric tunability. Unlike most metal carbenes, NHCs are typically unreactive when coordinated to a metal (with some exceptions). Like phosphines, they are commonly used to modulate the steric and electronic properties of metal complexes. In fact, the similarities between NHCs and phosphines are notable. Overall, few ligands are as effective as NHCs at ramping up the electron density on a metal center while remaining i
• 2.8: Odd-numbered π Systems
Odd-numbered π systems—most notably, the allyl and cyclopentadienyl ligands—are formally LnX-type ligands bound covalently through one atom (the “odd man out”) and datively through the others. This formal description is incomplete, however, as resonance structures reveal that multiple atoms within three- and five-atom π systems can be considered as covalently bound to the metal.
• 2.9: Phosphines
Phosphines ligands are most notable for their remarkable electronic and steric tunability and their “innocence”—they tend to avoid participating directly in organometallic reactions, but have the ability to profoundly modulate the electronic properties of the metal center to which they’re bound
• 2.10: π Systems
In contrast to the spectator L-type ligands we’ve seen so far, π systems most often play an important role in the reactivity of the OM complexes of which they are a part (since they act in reactions, they’re called “actors”). π Systems do useful chemistry, not just with the metal center, but also with other ligands and external reagents.
02: Organometallic Ligands
In a previous post, we were introduced to the N-heterocyclic carbenes, a special class of carbene best envisioned as an L-type ligand. In this post, we’ll investigate other classes of carbenes, which are all characterized by a metal-carbon double bond. Fischer carbenes, Shrock carbenes, and vinylidenes are usually actor ligands, but they may be either nucleophilic or electrophilic, depending on the nature of the R groups and metal. In addition, these ligands present some interesting synthetic problems: because free carbenes are quite unstable, ligand substitution does not cut the mustard for metal carbene synthesis.
General Properties
Metal carbenes all possess a metal-carbon double bond. That’s kind of a given. What’s interesting for us about this double bond is that there are multiple ways to deconstruct it to determine the metal’s oxidation state and number of d electrons. We could give one pair of electrons to the metal center and one to the ligand, as we did for the NHCs. This procedure nicely illustrates why compounds containing M=C bonds are called “metal carbenoids”—the deconstructed ligand is an L-type carbenoid. Alternatively, we could give both pairs of electrons to the ligand and think of it as an X2-type ligand. The appropriate procedure depends on the ligand’s substituents and the electronic nature of the metal. The figure below summarizes the two deconstruction procedures.
The proper method of deconstruction depends on the electronic nature of the ligand and metal.
When the metal possesses π-acidic ligands and the R groups are π-basic, the complex is best described as an L-type Fischer carbene and the oxidation state of the metal is unaffected by the carbene ligand. When the ligands are “neutral” (R = H, alkyl) and the metal is a good backbonder—that is, in the absence of π-acidic ligands and electronegative late metals—the complex is best described as an X2-type Schrock carbene. Notice that the oxidation state of the metal depends on our deconstruction method! Thus, we see that even the oxidation state formalism isn’t perfect.
Deconstruction reveals the typical behavior of the methylene carbon in each class of complex. The methylene carbon of Schrock carbenes, on which electron density is piled through backbonding, is nucleophilic (the 2– charge screams nucleophilic!). On the other hand, the methylene carbon of Fischer carbons is electrophilic, because backbonding is weak and does not compensate for σ-donation from the ligand to the metal. To spot a Fischer carbene, be on the lookout for reasonable zwitterionic resonance structures like the one at right below.
Thanks to the pi-accepting CO ligands, the metal handles the negative charge well. This is a Fischer carbene.
The clever reader may notice that we haven’t mentioned π-acidic R groups, such as carbonyls. Complexes of this type are best described as Fischer carbenes as well, as the ligand is still electrophilic. However, complexes of this type are difficult to handle and crazy reactive (see below) without a π-basic substituent to hold them in check.
Vinylidenes are the organometallic analogues of allenes, and are best described as intermediate in behavior between Fischer and Schrock carbenes. They are electrophilic at the α carbon and nucleophilic at the β carbon—in fact, a nice analogy can be made between vinylidenes and carbon monoxide. Tautomerization to form alkyne π-complexes is common, as the vinylidene and alkyne complexes are often comparable in stability.
Vinylidene tautomerization, and an analogy between vinylidenes and CO.
Take care when diagnosing the behavior of metal carbenes. In these complexes, there is often a subtle interplay between the R groups on the carbene and other ligands on the metal. In practice, many carbenes are intermediate between the Fischer and Schrock ideals.
Synthesis
Metal carbenes present a fascinating synthetic problem. A cursory look at the deconstruction procedures above reveals that these complexes cannot be made using ligand substitution reactions, because the free ligands are far too unstable. Although the synthetic methods introduced here will be new for us, the attuned organic chemist will find them familiar. The conceptual foundations of metal carbene synthesis are similar to methods for the synthesis of alkenes in organic chemistry.
In the post on NHCs, we saw that the free carbene is both nucleophilic (via the lone pair in its σ system) and electrophilic (via its empty 2pz orbital). Organic precursors to metal carbenes and alkenes also possess this property—they can act both as nucleophiles and electrophiles. Fundamentally, this “ambi-electronic” behavior is useful for the creation of double bonds. One bond comes from “forward flow,” and the other from “reverse flow.” Naturally, the other reacting partner also needs to be ambi-electronic for this method to work.
A fundamental paradigm for double bond synthesis: ambi-electronic compounds doing what they do.
What sets carbene precursors apart from free carbenes? What other kinds of molecules may act as both nucleophiles and electrophiles at the same atom? Watch what happens when we tack a third group onto the free carbene…the figure below shows the result in general and a few specific examples in gray.
A "dative ligand" R' is the difference between a carbene and an ylide. Both are ambi-electronic.
An ylide, which contains adjacent positive and negative charges, results from this purely hypothetical process. Ylides (diazo compounds, specifically) are the most common precursors to metal carbene complexes. Like free carbenes, ylides are ambi-electronic. The electrophilic frontier orbital of an ylide is just the σ* orbital of the bond connecting the charged atoms, which makes sense if we consider the positively charged fragment as a good leaving group (it always is). The lone pair is still nucleophilic. The figure above depicts some of the most famous ylides of organic chemistry, including those used for alkene synthesis (Corey-Chaykovsky and Wittig) and cycloaddition reactions (the carbonyl ylide).
Although diazo compounds are most commonly drawn with charges on the two nitrogen atoms, the diazo carbon is a good nucleophile and can attack electrophilic metal centers to initiate metal carbene formation. A slick 15N kinetic isotope effect study showed that C–N bond cleavage is the rate-limiting step of the reaction below. Visualize the carbanionic resonance structure to kick off the mechanism! Don’t think too hard about the structure of rhodium(II) acetate here. Rhodium, copper, ruthenium, and iridium all form carbene complexes with diazo compounds in a similar way.
After association of the nucleophilic carbon to Rh, elimination with loss of nitrogen gas is the slow step of this reaction.
Diazo compounds work well for metal carbene formation when they possess an electron-withdrawing group, which stabilizes the ylide through conjugation. What about Fischer carbenes, which possess electron-donating groups on the carbene carbon? An interesting method that still involves a “push-and-pull” of electron flow (but not ylides) employs metal-CO complexes. Upon addition of a strong nucleophile (“forward flow”) to the carbonyl carbon, a metalloenolate of sorts is produced. Treatment with an electrophile RX that prefers oxygen over the metal (“reverse flow”) results in an OR-substituted Fischer carbene. Reactions reminiscent of transesterification trade out the OR group for an –SR group (using a thiol) or an –NR2 group (using a secondary amine).
Fischer's classical route to L-type carbenes.
As counterintuitive as it may seem, it’s possible to use metal dianions for the synthesis of Fischer carbenes via a method pioneered by Hegedus and Semmelhack. Potassium intercalated in graphite—the mysterious “KC8“—reduces group 6 metal carbonyl complexes to the corresponding dianions, which subsequently unleash a deluge of electrons on a poor, unsuspecting amide to afford NR2-substituted Fischer carbenes after treatment with trimethylsilyl chloride.
One-directional electron flow for Fischer carbene synthesis: the Hegedus-Semmelhack approach.
For other methods for the synthesis of Fischer carbenes, check out this nice review from the Baran group.
Reactions
In many ways, the reactivity of metal carbenes parallels that of ylides. Olefin metathesis catapulted metal carbenes to international stardom, but in many ways, metathesis is conceptually similar to the Wittig reaction, which employs phosphorus ylides. During both mechanisms, an ylide/carbene hooks up with another doubly bound molecule to form a four-membered ring. This step is followed by what we might call “orthogonal breakdown” to yield two new double bonds.
Wittig, Grubbs, and Schrock: Lords of the Chemical Dance. Ambi-electronic molecules are the dancers!
In my opinion, bond insertion reactions are the most interesting processes in which carbenes regularly engage. Bond insertions may be subdivided into cyclopropanation (π-bond insertion) and σ-bond insertion. Evidence suggests that most cyclopropanations take place by a mechanism that overlaps with metathesis—instead of orthogonal breakdown, reductive elimination occurs to release the three carbon atoms as a cyclopropane.
The metallacyclobutane mechanism of cyclopropanation.
σ-Bond insertion involves electron-rich C–H bonds most prominently, suggesting that electrophilic Fischer carbenes should be best for this chemistry. Fischer carbenes incorporating electron-withdrawing groups love to dimerize to form olefins and/or cyclopropanate olefins—how might we put the brakes on this behavior? If we simply tack a π-basic substituent onto the carbene carbon, the reactivity of these complexes is “just right” for C–H insertion. Notably, no covalent organometallic intermediates are involved; the electrophilic carbene carbon snuggles in between C and H in a single step. The transition state of this step resembles the transfer of a hydride from the organic substrate to the carbene, with “rebound” of electron density toward the partial positive charge.
Donor-acceptor carbenoids are the "Goldilocks complexes" of C–H insertion.
Let’s end with a nod to the similarity between Fischer carbenes and carboxylic acid derivatives (esters and amides). Transesterification-type reactions allow the chemist to swap out heteroatomic substituents on the carbene carbon at will (see above). Alkyl substitutents can even be deprotonated at the α carbon, just like esters! When we see the electronic similarities between the M=C bond of a Fischer carbene and the O=C bond of carboxylic acid derivatives, the similar behavior is only natural. | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/02%3A_Organometallic_Ligands/2.01%3A_Carbenes.txt |
As a young, growing field, organometallic chemistry may be taught in many ways. Some professors (e.g., Shaugnessy) spend a significant chunk of time discussing ligands, while others forego ligand surveys (e.g., White) to dive right in to reactions and mechanisms. I like the ligand survey approach because it lays out many of the general concerns associated with certain ligand sets before organometallic intermediates pop up. With the general concerns in hand, it becomes easier to generate explanations for certain observed effects on reactions that depend on ligands. Instead of generalizing from complex, specific examples in the context of reaction mechanisms, we’ll look at general trends first and apply these to reaction intermediates and mechanisms later. This post kicks off our epic ligand survey with carbon monoxide, a simple but fascinating ligand.
General Properties
CO is a dative, L-type ligand that does not affect the oxidation state of the metal center upon binding, but does increase the total electron count by two units. We’ve recently seen that there are really two bonding interactions at play in the carbonyl ligand: a ligand-to-metal ndσ interaction and a metal-to-ligand dππ* interaction. The latter interaction is called backbonding, because the metal donates electron density back to the ligand. To remind myself of the existence of backbonding, I like to use the right-hand resonance structure whenever possible; however, it’s important to remember to treat CO as an L-type ligand no matter what resonance form is drawn.
CO is a fair σ-donor (or σ-base) and a good π-acceptor (or π-acid). The properties of ligated CO depend profoundly upon the identity of the metal center. More specifically, the electronic properties of the metal center dictate the importance of backbonding in metal carbonyl complexes. Most bluntly, more electron-rich metal centers are better at backbonding to CO. Why is it important to ascertain the strength of backbonding? I’ll leave that question hanging for the moment, but we’ll have an answer very soon. Read on!
Infrared spectroscopy has famously been used to empirically support the idea of backbonding. The table below arranges some metal carbonyl complexes in “periodic” order and provides the frequency corresponding to the C=O stretching mode. Notice that without exception, every complexed CO has a stretching frequency lower than that of free CO. Backbonding is to blame! The C–O bond order in complexed carbon monoxide is (almost always) lower than that of free CO.
The figure above depicts a clear increase in frequency (an increase in C–O bond order) as we move left to right across the periodic table. This finding may seem odd if we consider that the number of d electrons in the neutral metal increases as we move left to right. Shouldn’t metal centers with more d electrons be better at backbonding (and more “electron rich”)? What’s going on here? Recall the periodic trend in orbital energy. As we move left to right, the d orbital energies decrease and the energies of the dπ and π* orbitals separate. As a result, the backbonding orbital interaction becomes worse (remember that strong orbital interactions require well-matched orbital energies) as we move toward the more electronegative late transition metals! We can draw an analogy to enamines and enols from organic chemistry. The more electronegative oxygen atom in the enol is a worse electron donor than the enamine’s nitrogen atom.
Of course, the contribution of other ligands on the metal center to backbonding cannot be forgotten, either. Logically, electron-donating ligands will tend to make the backbond stronger (they make the metal a better electron donor), while electron-withdrawing ligands will worsen backbonding. Adding electron-rich phosphine ligands to a metal center, for instance, decreases the CO stretching frequency due to improved backbonding.
Carbonyl ligands are famously able to bridge multiple metal centers. Bonding in bridged carbonyl complexes may be either “traditional” or delocalized, depending on the structure of the complex and the bridging mode. The variety of bridging modes stems from the different electron donors and acceptors present on the CO ligand (and the possibility of delocalized bonding). Known bridging modes are shown in the figure below.
Synthesis
Metal carbonyl complexes containing only CO ligands abound, but most cannot be synthesized by the method we all wish worked, bathing the elemental metal in an atmosphere of carbon monoxide (entropy is a problem, as we already discussed for W(CO)6). This method does work for nickel(0) and iron(0) carbonyls, however.
M + n CO → M(CO)n [M = Fe, n = 5; M = Ni, n = 4]
Other metal carbonyl complexes can be prepared by reductive carbonylation, the treatment of a high-oxidation-state complex with CO. These methods usually require significant heat and pressure. One example:
WCl6 + CO + heat, pressure → W(CO)6
Still other methods employ deinsertion from organic carbonyl compounds like dimethylformamide. These methods are particularly useful for preparing mixed carbonyl complexes in the presence of reducing ligands like phosphines.
IrCl3(H2O)3 + 3 PPh3 + HCONMe2 + PhNH2 → IrCl(CO)(PPh3)2 + (Me2NH2)Cl + OPPh3 + (PhNH3)Cl + 2 H2O
The key thing to notice about the reaction above is that the CO ligand is derived from dimethylformamide (DMF).
Reactions
The dissociation of carbonyl ligands is common in reactions that require an open coordination site at the metal. Naturally, the favorability of dissociation is governed by electron density at the metal—weaker backbonding metals lose CO more easily. This is one reason understanding trends in backbonding strength is important!
Like the carbonyl carbon in organic compounds, the carbon of ligated CO is often an exquisite electrophile—particularly when the metal is a poor π-base, leaving the carbonyl carbon starved of electrons. CO ligands are susceptible to nucleophilic attack at the carbonyl carbon in the presence of strong nucleophiles. Treating the adduct with an electrophile yields a Fischer carbene complex. If we imagine M=C=O as an analogue of ketene, this reactivity just corresponds to classic nucleophilic addition across the C=O bond.
Perhaps the most important elementary step in which the CO ligand participates is migratory insertion, a step typical of oxidized organic ligands (CO, alkenes, alkynes, etc.). The net result of the process is the insertion of the carbonyl carbon into an M–X bond (X is most commonly C or H, but can be any X-type ligand). An empty coordination site—the strange-looking box in the figure below—is left behind after migration. The hydroformylation reaction involves the insertion of CO into an M–C bond as a key step. We’ll talk about this fascinating processes in more detail in a later post.
For CO, it’s useful to think about migratory insertion as a sort of intramolecular nucleophilic attack by the X-type ligand on coordinated CO. In this respect its similar to the intermolecular nucleophilic addition process leading to carbenes described above. Just view the carbonyl carbon as an electrophile (as if you don’t already!) and it becomes easy to keep these ideas in mind. We’ll see migratory insertion in more detail in a future post as well. | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/02%3A_Organometallic_Ligands/2.02%3A_Carbon_Monoxide.txt |
Ligands can, shockingly enough, bind through their σ electrons in an L-type fashion. This binding mode depends as much on the metal center as it does on the ligand itself—to see why, we need only recognize that σ complexes look like intermediates in concerted oxidative additions. With a slight reorganization of electrons and geometry, an L-type σ ligand can become two X-type ligands. Why, then, are σ complexes stable? How can we control the ratio of σ complex to X2 complex in a given situation? How does complexation of a σ bond change the ligand’s properties? We’ll address these questions and more in this post.
General Properties
The first thing to realize about σ complexes is that they are highly sensitive to steric bulk. Any old σ bond won’t do; hydrogen at one end of the binding bond or the other (or both) is necessary. The best studied σ complexes involve dihydrogen (H2), so let’s start there.
Mildly backbonding metals may bind dihydrogen “side on.” Like side-on binding in π complexes, there are two important orbital interactions at play here: σH–H→dσ and dπ→σ*H–H. Dihydrogen complexes can “tautomerize” to (H)2 isomers through oxidative addition of the H–H bond to the metal.
Orbital interactions and L-X2 equilibrium in σ complexes.
H2 binding in an L-type fashion massively acidifies the ligand—changes in pKa of over thirty units are known! Analogous acidifications of X–H bonds, which we touched on in a previous post, rarely exhibit ΔpKa > 5. What gives? What’s causing the different behavior of X–H and H–H ligands? The key is to consider the conjugate base of the ligand—in particular, how much it’s stabilized by a metal center relative to the corresponding free anion. The principle here is analogous to the famous dictum of organic chemistry: consider charged species when making acid/base comparisons. Stabilization of the unhindered anion H– by a metal is much greater than stabilization of larger, more electronegative anions like HO– and NH2– by a metal. As a result, it’s more favorable to remove a proton from metal-complexed H2 than from larger, more electronegative X–H ligands.
Remarkably large stabilization by an acidic metal fragment, without any counterbalancing from steric factors, explains the extreme acidification of dihydrogen upon metal binding.
The electronic nature of the metal center has two important effects on σ complexes. The first concerns the acidity of H2 upon metal binding. The principle here is consistent with what we’ve hammered into the ground so far. In the same way cationic organic acids are stronger than their neutral counterparts, σ complexes of electron-poor metals—including (and especially) cations—are stronger acids than related complexes of electron-rich metals. The second concerns the ratio of L-type to X2-type binding. We should expect more electron-rich metal centers to favor the X2 isomer, since these should donate more strongly into the σ*H–H orbital. This idea was masterfully demonstrated in a study by Morris, in which he showed that H2 complexes of π-basic metal centers show all the signs of X2 complexes, rather than L complexes. More generally, metal centers in σ complexes need a good balance of π basicity and σ acidity (I like to call this the “Goldilocks effect”). Because of the need for balance, σ complexes are most common for centrally located metals (groups 6-9).
Oxidative addition of H2 is important for electron-rich, π-basic metal centers. Groups 6-9 hit the "Goldilocks" spot.
The M–H bond in hydride complexes is a good base—anyone who’s ever quenched lithium aluminum hydride can attest to this! Intriguingly, because it’s a good base, the M–H bond can participate in hydrogen bonding with an acidic X–H bond, where X is a heteroatom. This kind of bonding, called dihydrogen bonding (since two hydrogen atoms are involved), is best described as a sort of σM–H→σ*X–H orbital interaction. Think of it as analogous to a traditional hydrogen bond, but using a σ bond instead of a lone pair. Crazy, right?!
Dihydrogen bonding in metal hydrides: a sort of "interrupted protonation" of M–H.
Other kinds of σ complexes are known, but these are rarer than H–H complexes. One class that we’ve seen before involve agostic interactions of C–H bonds in alkyl ligands. σ Complexes of inorganic ligands like silanes and stannanes may involve complex bonding patterns, but we won’t concern ourselves with those here.
Synthesis
If a metal center with an open coordination site has the “Goldilocks combination” of electronic factors, simply treating it with dihydrogen gas is enough to form the σ complex. Metals that bear labile L- or X-type ligands can also yield σ complexes upon treatment with H2.
Methods for the synthesis of σ complexes from dihydrogen gas. Displacement of a labile ligand or occupation of a vacant site represent the essence of these methods.
An alternative synthetic method involves the protonation of a basic M–H bond…taking dihydrogen bonding to the extreme! This method is especially nice if a cationic complex is the goal; of course, the metal needs to be π basic to make protonation favorable.
Protonation of an M–H bond for the synthesis of dihydrogen σ complexes.
Reactions
Deprotonation of an L-type X–H ligand is probably the simplest reaction of this class of ligands. This process is just the reverse of the synthetic method described above. We can refer to it as heterolytic cleavage, since the X atom that stays bound to the metal holds on to the electrons of the X–H bond. The charge of the product complex is one less than that of the starting material. A variation on this theme involves intramolecular proton transfer.
Deprotonation of dihydrogen complexes produces metal hydrides.
Homolytic cleavage of X–H is also possible, and it can happen in two ways. Intramolecular oxidative addition is the first, and we’ve seen it already. Since this process is intramolecular and little geometric reorganization is necessary, kinetic barriers tend to be low and the process may be reversible (unless the electronic circumstances of the metal are extreme). This sort of oxidative addition is important for many hydrogenation reactions, such as those employing Wilkinson’s catalyst.
Oxidative addition of dihydrogen via a sigma complex. In some cases, this process is a finely balanced equilibrium.
And the second way? In theory at least, intermolecular homolytic cleavage is possible. This process corresponds to one-electron oxidation of two distinct metal centers. Contrast this pattern of electron exchange with intramolecular oxidative addition, which involves two-electron oxidation of a single metal center. This kind of reactivity is rare in practice.
Ligand substitutions with other L-type ligands— including CO, N2, phosphines, and unsaturated organics—are also known. In fact, this process has been implicated in catalytic cycles for some hydrogenation reactions.
Ligand substitution reactions of sigma complexes. Can you justify the favorability of these reactions? | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/02%3A_Organometallic_Ligands/2.03%3A__Complexes.txt |
In this post, we’ll take a quick look at L-type ligands of nitrogen, oxygen, and sulfur. Ligands of this type are important for at least two reasons: (1) coordination to a metal can modify the reactivity of the bound functional group, and (2) dative coordination is a critical element of organometallic reactions that depend on intramolecular directing group effects. “Long-term” ligands containing two-connected nitrogens, such as pyridines and oxazolines, are now among the most commonly used for organometallic reactions. The behavior of coordinated dinitrogen is also a hot research area right now. Although they look boring on the surface, dative ligands of N, O, and S are rich in chemistry!
General Properties
This might be the first class of ligand for which we can reliably say that backbonding is rarely important. Dative coordination of amines and alcohols involves a straightforward n → dσ orbital interaction. Intuitively, we should expect the acidity of amines, alcohols, and thiols to increase upon coordination, because removal of electron density from nitrogen and oxygen through coordination makes these atoms more electrophilic. Consider the charged model of dative bonding at left in the figure below.
Coordination increases acidity.
Transfer of the lost proton to an organic substrate is an important aspect of hydrogenation reactions employing amine ligands (see below).
Food for thought: why aren’t (cheaper) amines found in place of phosphines in organometallic catalysts? History has ruled against tertiary amines, but are there any good reasons why? Yes—for one thing, amine nitrogens are more sterically hindered than analogous phosphorus atoms, because N–C bonds are shorter than P–C bonds. Plus, the cone angles of amines are generally wider than those of phosphines. Getting amines to play nice with hindered metal centers can thus be very difficult.
Although dinitrogen (N2) is isoelectronic with carbon monoxide, it’s been a tough nut for organometallic chemists to crack. An electron-rich metal center lacking π-acidic ligands is an absolute must for dinitrogen-containing complexes, as the π*NN orbital does not easily participate in backbonding. What sets nitrogen apart from CO is its ability to participate in side-on bonding and bridging through its π system—for this application, dinitrogen’s higher-energy orbitals are a perk over CO. While migratory insertion and nucleophilic addition reactions of N2 bound “end-on” (through a non-bonding lone pair) are virtually unknown, functionalization of “side-on” nitrogen ligands is a growing field. Dinitrogen has been known to bridge multiple metals in “end-end,” “side-end,” and “side-side” modes.
Activation of dinitrogen by molybdenum—a complex containing an "end-end," linear bridging dinitrogen (not shown) is proposed as an intermediate in this mechanism.
Imines are another important class of ligands that fit into this post; unlike carbonyl compounds, imines more commonly bind through the nitrogen atom rather than the π system. These are very common directing groups but are also important for hydrogenation and hydroamination reactions.
DMSO is an interesting, archetypal sulfur-containing ligand that may bind through either S or O. As sulfur is softer and more polarizeable than oxygen, sulfur binds to softer (low-valent) metals and oxygen to harder metal centers.
The soft Ru(II) center with hydrocarbyl ligands contains S-bound DMSO, while the harder Ru(II) with chloride ligands includes one O-bound DMSO.
Most ligands binding through dative sulfur require chelation, as M–S bond strengths tend to be low.
Synthesis
Ligand substitution reactions are most commonly used to load dative ligands of N, O, and S onto metal centers. In some cases, when the heteroatom bears a hydrogen atom, deprotonation can produce a covalent, X-type ligand. Usually, however, these types of ligands are incorporated into organic substrates and used as directing groups—coordination brings the metal center into close contact with a target functional group, such as an alkene, C–H bond, or C–X bond. They may also be part of chelating ligands containing a second, more robust electron donor, like a phosphine.
P,N ligands for organometallic chemistry.
Reactions
I’ll showcase only one reaction in this section: the Noyori hydrogenation employing amine ligands as proton donors. The reaction is a nice illustration of the influence of metal coordination on the reactivity of amines.
"External" hydrogenation without substrate binding. The metal is a hydride source, and the ligand a proton source.
Easy, breezy, beautiful, right? Dative ligands of N, O, and S are usually employed as spectators, not actors, so reactions like this are somewhat hard to come by. I’ll pass on discussing the reactivity of dinitrogen complexes in detail, but for an interesting recent example of metal-dinitrogen chemistry, check this out. | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/02%3A_Organometallic_Ligands/2.04%3A_Dative_Ligands_of_N_O_and_S.txt |
Part 1:
With this post we finally reach the defining ligands of organometallic chemistry, alkyls. Metal alkyls feature a metal-carbon σ bond and are usually actor ligands, although some alkyl ligands behave as spectators. Our aim will be to understand the general dependence of the behavior of alkyl ligands on the metal center and the ligand’s substituents. Using this knowledge, we can make meaningful comparisons between related metal alkyl complexes and educated predictions about their likely behavior. Because alkyl ligands are central to organometallic chemistry, I’ve decided to spread this discussion across multiple posts. We’ll deal first with the general properties of metal alkyls.
In the Simplifying the Organometallic Complex series, we decomposed the M–C bond into a positively charged metal and negatively charged carbon. This deconstruction procedure is consistent with the relative electronegativities of carbon and the transition metals. It can be very useful for us to imagine metal alkyls essentially as stabilized carbanions—but it’s also important to understand that M–C bonds run the gamut from extremely ionic and salt-like (NaCH3) to essentially covalent ([HgCH3]+). The reactivity of the alkyl ligand is inversely related to the electronegativity of the metal center.
The hybridization of the carbon atom is also important, and the trend here follows the trend in nucleophilicity as a function of hybridization in organic chemistry. sp-Hybridized ligands are the least nucleophilic, followed by sp2 and sp3 ligands respectively.
The history of transition metal alkyls is an intriguing example of an incorrect scientific paradigm. After several unsuccessful attempts to isolate stable metal alkyls, organometallic chemists in the 1920s got the idea that metal-carbon bonds were weak in general. However, later studies showed that it was kinetic instability, not thermodynamic, that was to blame for our inability to isolate metal alkyls. In other words, most metal alkyls are susceptible to decomposition pathways with low activation barriers—the instability of the M–C bond per se is not to blame. Crabtree cites typical values of 30-65 kcal/mol for M–C bond strengths.
What are the major decomposition pathways of metal alkyl complexes? β-hydride elimination is the most common. Thermodynamically, the ubiquity of β-hydride elimination makes sense—M–C bonds run 30-65 kcal/mol, while M–H bonds tend to be stronger. The figure below summarizes the accepted mechanism and requirements of β-hydride elimination. We’ll revisit this fundamental reaction of organometallic complexes in a future post.
Kinetically stable metal alkyl complexes violate one of the requirements for β-hydride elimination. Methyl and neopentyl complexes lack β-hydrogens, violating requirement 1. Tightly binding, chelating ligands may be used to prevent the formation of an empty coordination site, violating requirements 3a and 3b. Titanium complexes are known that violate requirement 4 and eliminate only very slowly—back-donation from the metal to the σ*C–H is required for rapid elimination (see below).
Reductive elimination is a second common decomposition pathway. The alkyl ligand hooks up with a second X-type ligand on the metal, and the metal is reduced by two units with a decrease in the total electron count by two units. I’ve omitted curved arrows here because different mechanisms of reductive elimination are known. We’ll discuss the requirements of reductive elimination in detail in a future post; for now, it’s important to note that the thermodynamic stability of C–X versus that of (M–X + M–C) is a critical driving force for the reaction.
When X = H, reductive elimination is nearly always thermodynamically favorable; thus, isolable alkyl hydride complexes are rare. This behavior is a feature, not a bug, when we consider that hydrogenation chemistry depends on it! On the other hand, when X = halogen reductive elimination is usually disfavored. Reductive elimination of C–C (X = C) can be favored thermodynamically, but is usually slower than the corresponding C–H elimination.
Complexes that cannot undergo β-hydride elimination are sometimes susceptible to α-elimination, a mechanistically similar process that forms a metal carbene. This process is particularly facile when the α-position is activated by an adjacent electron donor (Fischer carbenes are the result).
In some metal alkyl complexes, C–H bonds at the α, β, or even farther positions can serve as electron donors to the metal center. This idea is supported by crystallographic evidence and NMR chemical shifts (the donating hydrogens shift to high field). Such interactions are called agostic interactions, and they resemble an “interrupted” transition state for hydride elimination. Alkyl complexes that cannot undergo β-hydride elimination for electronic reasons (high oxidation state, d0 metals) and vinyl complexes commonly exhibit this phenomenon. The fact that β-hydride elimination is slow for d0 metals—agostic interactions are seen instead—suggests that back-donation from a filled metal orbital to the σ*C–H is important for β-hydride elimination. Here’s an interesting, recent-ish review of agostic interactions.
In the next post in this series, we’ll explore the synthesis of metal alkyl complexes in more detail, particularly clarifying the question: how can we conquer β-hydride elimination?
Part 2:
In this post, we’ll explore the most common synthetic methods for the synthesis of alkyl complexes. In addition to enumerating the reactions that produce alkyl complexes, this post will also describe strategies for getting around β-hydride elimination when isolable alkyl complexes are the goal. Here we go!
Properties of Stable Alkyl Complexes
Stable alkyl complexes must be resistant to β-hydride elimination. In the last post we identified four key conditions necessary for elimination to occur:
1. The β-carbon must bear a hydrogen.
2. The M–C and C–H bonds must be able to achieve a syn coplanar orientation (pointing in the same direction in parallel planes).
3. The metal must bear 16 total electrons or fewer and possess an open coordination site.
4. The metal must be at least d2.
Stable alkyl complexes must violate at least one of these conditions. For example, titanium(IV) complexes lacking d electrons β-eliminate very slowly. The complex below likely also benefits from chelation (see below).
Complexes have been devised that are unable to achieve the syn coplanar orientation required for elimination, or that lack β-hydrogens outright. A few examples are provided below—one has to admire the cleverness of the researchers who devised these complexes. The metallacyclobutane is particularly striking!
Using tightly binding, chelating ligands or a directing group on the substrate, the formation of 16-electron complexes susceptible to β-hydride elimination can be discouraged. Notice how the hyrdrogen-bonding L2 ligands in the central complex below hold the metal center in a death grip.
Finally, it’s worth noting that complexes with an open coordination site—such as 16-electron, square-planar complexes of Ni, Pd, and Pt important for cross-coupling—are susceptible to reactions with solvent or other species at the open site. Bulky alkyl ligands help prevent these side reactions. In the example below, the methyl groups of the o-tolyl ligands extend into the space above and below the square plane, discouraging the approach of solvent molecules perpendicular to the plane.
Many transition metal complexes catalyze (E)/(Z) isomerization and the isomerization of terminal alkenes (α-olefins) to internal isomers via β-hydride elimination. This is a testament to the importance of this process for alkyl complexes. Of course, transient alkyl complexes may appear to be susceptible to β-hydride elimination, but if other processes are faster, elimination will not occur. Thus, the optimization of many reactions involving alkyl complexes as intermediates has involved speeding up other processes at the expense of β-hydride elimination—hydrocyanation is a good example.
Synthesis of Alkyl Complexes
The dominant synthetic methods for alkyl complexes are based on nucleophilic attack, electrophilic attack, oxidative addition, and migratory insertion. The first two methods should be intuitive to the organic chemist; the second two are based on more esoteric (but no less important) reactions of organometallic complexes.
Metals bearing good leaving groups are analogous to organic electrophiles, and are susceptible to nucleophilic attack by organolithiums, Grignard reagents, and other polarized organometallics. These reactions can be viewed as a kind of transmetalation, as the alkyl ligand moves from one metal to another. Electron-withdrawing X-type ligands like –Cl and –Br should jump out as good leaving groups. On the other hand, clean substitution of L-type ligands by anionic nucleophiles is much more rare (anionic complexes would result).
Many anionic metal complexes are nucleophilic enough to attack electrophilic sources of carbon such as alkyl and acyl halides in an electrophilic attack mode. An available lone pair on the metal and open coordination site are prerequisites for this chemistry. The charge on the complex increases by one unit (in effect, negative charge is transferred to the electrophile’s leaving group). We can classify these as oxidative ligation reactions—notice that the oxidation state of the metal increases by two units.
Oxidative addition results in the cleavage of a W–Z bond and placement of two new X-type ligands (–W and –Z) on the metal center, with an increase in the oxidation state of the metal and the total electron count by two units. Organic halides are extremely common substrates for this reaction, the first step in the mechanism of cross-coupling reactions. The oxidized metal complex containing new alkyl and halide ligands is the final product. Notice that two open coordination sites are required (not necessarily simultaneously), the metal center must be amenable to two-electron oxidation, and the number of total electrons of the complex increases by two. In essence, the electrons of the W–Z bond join the complex’s party. Take note that there are many known mechanisms for oxidative addition! We’ll explore these different mechanisms in detail in a future post.
Finally, migratory insertion of unsaturated organic compounds is an important method for the synthesis of certain alkyl complexes, and an important step of organometallic reactions that result in addition across π bonds. Migratory insertion is the microscopic reverse of β-hydride elimination. The clever among you may notice that the use of migratory insertion to synthesize alkyl complexes seems inconsistent with our observation that its reverse is ubiquitous for metal alkyls—shouldn’t equilibrium favor the olefin hydride complex? In many cases this is the case; however, there are some notable exceptions. For example, perfluoroalkyl complexes are exceptionally stable (why?), so the insertion of fluoroalkenes is often favored over elimination.
As we noted above, we can still invoke kinetically stable alkyl complexes as intermediates in reactions provided subsequent steps are faster. In the next post, we’ll examine the general classes of reactions in which alkyl complexes find themselves the major players, focusing on the specific mechanistic steps that involve the alkyl complex (reductive elimination, transmetalation, migratory insertion, and [naturally] β-hydride elimination).
Part 3:
In this last post on alkyl ligands, we’ll explore the major modes of reactivity of metal alkyls. We’ve discussed β-hydride elimination in detail, but other fates of metal alkyls include reductive elimination, transmetallation, and migratory insertion into the M–C bond. In a similar manner to our studies of other ligands, we’d like to relate the steric and electronic properties of the metal alkyl complex to its propensity to undergo these reactions. This kind of thinking is particularly important when we’re interested in controlling the relative rates and/or extents of two different, competing reaction pathways.
Reactions of Metal Alkyl Complexes
Recall that β-hydride elimination is an extremely common—and sometimes problematic—transformation of metal alkyls. Then again, there are reactions for which β-hydride elimination is desirable, such as the Heck reaction. Structural modifications that strengthen the M–H bond relative to the M–C bond encourage β-hydride elimination; the step can also be driven by trapping of the metal hydride product with a base (the Heck reaction uses this idea).
On the flip side, stabilization of the M–C bond discourages elimination and encourages its reverse: migratory insertion of olefins into M–H. Previously we saw the example of perfluoroalkyl ligands, which possess exceptionally stable M–C bonds. The fundamental idea here—that electron-withdrawing groups on the alkyl ligand stabilize the M–C bond—is quite general. Hartwig describes an increase in the “ionic character” of the M–C bond upon the addition of electron-withdrawing groups to the alkyl ligand (thereby strengthening the M–C bond, since ionic bonds are stronger than covalent bonds). Bond energies from organic chemistry bear out this idea to an extent; for instance, see the relative BDEs of Me–Me, Me–Ph, and Me–CCH in this reference. I still find this explanation a little “hand-wavy,” but it serves our purpose, I suppose.
Metal alkyls are subject to reductive elimination, the microscopic reverse of oxidative addition. The metal loses two covalent ligands, its formal oxidation state decreases by two units, total electron count decreases by two units, and an R–X bond forms. Reductive elimination is favorable when the R–X bond in the organic product is more stable than the M–R and M–X bonds in the starting complex (a thermodynamic issue). It should be noted, however, that the kinetics of reductive elimination depend substantially on the steric bulk of the eliminating ligands. Concerted reductive elimination of R–H usually possesses a lower activation energy than R–R elimination.
Transmetalation involves the transfer of an alkyl ligand from one metal to the other. An interesting problem concerns the relative reactivity of metal alkyls toward transmetalation. Assuming similar, uncomplicated ligand sets, which of two metal centers is more likely to hold on to an alkyl ligand? Consider the two situations below.
$\ce{MR + M’ <=> M + M’R} \nonumber$
$\ce{MR + M’R’ <=> MR’ + M’R} \nonumber$
The first is a bona fide transmetalation; the second is really a double replacement reaction. The distinction is rarely drawn in practice, but it’s important! The difference is that in the first case, a single-electron transfer of sorts must take place, while in the second case, no redox chemistry is necessary. Favorability in the first case is governed by the relative reduction potentials of M and M’ (the reaction goes forward when M’ is more easily oxidized than M); in the second case, the relative electropositivities of the metals is key, and other factors like lattice energies may be important. The distinction between transmetalation per se and double replacement explains the paradoxical synthetic sequence in the figure below. In practice, both are called “transmetalation.” See these slides (page 6) for a summarizing reference.
This brings our extended look at metal alkyl complexes to a temporary close. Of course, metal alkyls are everywhere in organometallic chemistry…so seeing them again is pretty much inevitable! The next installment in the Epic Ligand Survey series concerns allyl, cyclopentadienyl, and other odd-membered pi systems. These LnX-type ligands can, like arenes, pile as many as six electrons on the metal center at once. | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/02%3A_Organometallic_Ligands/2.05%3A_Metal_Alkyls.txt |
Metal-hydrogen bonds, also known (misleadingly) as metal hydrides, are ubiquitous X-type ligands in organometallic chemistry. There is much more than meets the eye to most M-H bonds: although they’re simple to draw, they vary enormously in polarization and pKa. They may be acidic or hydridic or both, depending on the nature of the metal center and the reaction conditions. In this post, we’ll develop some heuristics for predicting the behavior of M-H bonds and discuss their major modes of reactivity (acidity, radical reactions, migratory insertion, etc.). We’ll also touch on the most widely used synthetic methods to form metal hydrides.
General Properties
Metal hydrides run the gamut from nucleophilic/basic to electrophilic/acidic. Then again, the same can be said of X–H bonds in organic chemistry, which may vary from mildly nucleophilic (consider Hantzsch esters and NADH) to extremely electrophilic (consider triflic acid). As hydrogen is what it is in both cases, it’s clear that the nature of the X fragment—more specifically, the stability of the charged fragments X+ and X–—dictate the character of the X–H bond. Compare the four equilibria outlined below—the stabilities of the ions dictate the position of each equilibrium. By now we shouldn’t find it surprising that the highly π-acidic W(CO)5 fragment is good at stabilizing negative charge; for a similar reason, the ZrCp2Cl fragment can stabilize positive charge.*
Metal-hydrogen bonds may be either hydridic (nucleophilic) or acidic (electrophilic). The nature of other ligands and the reaction conditions are keys to making predictions.
Let’s turn our attention now to homolytic M–H bond strength. A convenient thermodynamic cycle allows us to use the acidity of M–H and the oxidation potential of its conjugate base in order to determine bond strength. This clever method, employed by Tilset and inspired by the inimitable Bordwell, uses the cycle in the figure below. BDE values for some complexes are provided as well. From the examples provided, we can see that bond strength increases down a group in the periodic table. This trend, and the idea that bridging hydrides have larger BDEs than terminal M–H bonds, are just about the only observable trends in M–H BDE.
A clever cycle for determining BDEs from other known quantities, with select BDE values. I've left out solvation terms from the thermodynamic cycle. For more details, see the Tilset link above.
Why is knowing M-H BDEs useful? For one thing, the relative BDEs of M-C and M-H bonds determine the thermodynamics of β-hydride elimination, which results in the replacement of a covalent M-C bond with an M-H bond. Secondly, complexes containing weak M-H bonds are often good hydrogen transfer agents and may react with organic radicals and double bonds, channeling stannane and silane reductants from organic chemistry.
Hydricity refers to the tendency of a hydride ligand to depart as H–. A similar thermodynamic cycle relates the energetics of losing H– to the oxidation potentials of the conjugate base and the oxidized conjugate base; however, this method is complicated by the fact that hydride loss establishes an open coordination site. I’ve provided an abridged version of the cycle below. Hydricities are somewhat predictable from the electronic and steric properties of the metal center: inclusion of electron-donating ligands tends to increase hydricity, while electron-withdrawing or acidic ligands tend to decrease it. For five-coordinate hydrides that form 16-electron, square planar complexes upon loss of hydride, the bite angle of chelating phosphines plays an interesting role. As bite angle increases, hydricity does as well.
A thermodynamic cycle for hydricity, with some examples. Hydricity and bite angle are well correlated in five-coordinate palladium hydrides.
Bridging hydrides are an intriguing class of ligands. A question to ponder: how can a ligand associated with only two electrons possibly bridge two metal centers? How can two electrons hold three atoms together? Enter the magic of three-center, two-electron bonding. We can envision the M–H sigma bond as an electron donor itself! With this in mind, we can imagine that hydrides are able to bind end-on to one metal (like a standard X-type ligand) and side-on to another (like an L-type π system ligand, but using sigma electrons instead). Slick, no? We’ll see more side-on bonding of sigma electrons in a future post on sigma complexes.
Resonance forms of bridging hydrides, with an example. Sigma complexes like these show up in other contexts, too!
Consistent with the idea that bridging is the result of “end-on + side-on” bonding, bond angles of bridging hydrides are never 180°.
Synthesis
Here we’ll discuss four ways to make hydrides: metal protonation, oxidative addition of H2, addition of nucleophilic main-group hydrides (borohydrides, aluminum hydrides, and silanes), and β-hydride elimination.
Just as in organic chemistry, the basicity of an organometallic complex is inversely related to the acidity of its conjugate base. Furthermore, charges have a predictable effect on the basicity of organometallic complexes: negatively charged complexes lacking π-acidic ligands are highly basic. Even neutral complexes containing strong donor ligands, like the tungsten complex below, can be protonated effectively. Notice that protonation is actually a kind of oxidative addition—the oxidation state of Fe in the first reaction below goes from -2 to 0 to +2! All coordination events of isolated electrophiles can also be viewed in this light. Reactions of this type are sometimes called oxidative ligations to distinguish them from oxidative addition reactions, which involve the addition of two ligands to the metal center with oxidation.
Metal protonation reactions involve the metal center as a base.
Contrast oxidative ligation with the oxidative addition of dihydrogen (H2), a second method for the synthesis of hydride complexes. A key requirement here is that the starting metal center is at least d2—two electrons are formally lost from the metal center, and metals can’t possess a negative number of d electrons. An open coordination site on the starting material must also be present (or possible through ligand dissociation). The reaction below is a standard example of the addition of H2 to Vaska’s complex, but there are some funky variations on this theme. These riffs include third-order homolytic cleavage of H2 by two metal radicals, and oxidative addition followed by deprotonation by the starting complex (apparent heterolytic cleavage).
Oxidative addition of dihydrogen for the synthesis of metal hydrides.
Main-group hydrides like borohydrides and aluminum hydrides are great sources of H– for organometallic complexes. These reactions seem more natural than metal protonations, since we often think of metals as electropositive or electrophilic species. Indeed, the combination of main-group sources of nucleophilic hydride with complexes containing metal–leaving group bonds is a very general method for the synthesis of metal hydride complexes. Check out the reaction below—what’s the most likely mechanism? Is associative or dissocative substitution more likely? Hint: count electrons!
Nucleophilic substitution with a hydride source. What's the most likely mechanism?
β-hydride elimination forms metal hydride complexes and double bonds within organic ligands. Alkoxide ligands are commonly used for this purpose—elimination to form the hydride complex and aldehyde is more favorable than the reverse, migratory insertion of C=O into the M–H bond. Since the unsaturated byproduct is thrown away, it’s desirable to make it something small, cheap, and gaseous. Hydroxycarbonyl, formate, and tert-butyl ligands have been applied successfully with this goal in mind…what are the byproducts?
Beta-hydride elimination for the synthesis of metal hydrides.
Reactions
Metal hydrides are characterized by nucleophilic, electrophilic, and radical behavior. The exact behavior of a given metal hydride complex depends on its electronic properties, its M–H bond dissociation energy, and the nature of the reacting partner. Basic metal hydrides react with acids to free up a coordination site on the metal center (file this reaction alongside photolytic M–CO cleavage and M–CO cleavage with amine oxides).
"Protonolysis" generates two open coordination sites with loss of hydrogen gas.
Migratory insertion reactions involving M–H bonds are extremely important in a practical sense (see hydrogenation and hydroformylation), and are conceptually related to nucleophilic hydride transfers from the metal center. We can think of insertions of π bonds into M–H as internal nucleophilic attack by the hydride ligand at one end of the π bond, with coordination of the metal center to the other. The figure below depicts the transition state for migratory insertion of an olefin into M–H and an example reaction. Notice the coplanarity of M, H, and the C=C bond in the transition state for insertion, which determines the cis configuration of the product. The same is required for the microscopic reverse (β-hydride elimination) but this essential geometry is easily overlooked for β-hydride elimination.
Migratory insertion of an olefin into M–H. Note the relative configuration of M–C and C–H!
It is important to note that insertions of CO into M–H bonds are rare, because such insertions are usually unfavorable thermodynamically.
Finally, the radical behavior of certain metal hydrides in the presence of olefins deserves a nod. The behavior of the cobalt hydride complex in the reaction below is typical of these types of reactions.
Hydrogen atom transfer to olefins. Radical reduction of carbon tetrachloride is a related process.
And there you have it: the properties, synthesis, and reactivity of metal hydrides in a nutshell. Like other ligands we’ve seen so far, the behavior of hydrides is controlled by the nature of the metal center and its accompanying ligands. However, it’s interesting to note that the observed behavior of hydrides often depends on the nature of the reaction conditions, as well. Some complexes display “schizophrenic” behavior, so to speak, putting on their nucleophile hat in the presence of an electrophile and their electrophile hat in the presence of a nucleophile. | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/02%3A_Organometallic_Ligands/2.06%3A_Metal_Hydrides.txt |
Odd-numbered π systems—most notably, the allyl and cyclopentadienyl ligands—are formally LnX-type ligands bound covalently through one atom (the “odd man out”) and datively through the others. This formal description is incomplete, however, as resonance structures reveal that multiple atoms within three- and five-atom π systems can be considered as covalently bound to the metal. To illustrate the plurality of equally important resonance structures for this class of ligands, we often just draw a curved line from one end of the π system to the other. Yet, even this form is not perfect, as it obscures the possibility that the datively bound atoms may dissociate from the metal center, forming σ-allyl or ring-slipped ligands. What do the odd-numbered π systems really look like, and how do they really behave?
General Properties
Allyls are often actor ligands, most famously in allylic substitution reactions. The allyl ligand is an interesting beast because it may bind to metals in two ways. When its double bond does not become involved in binding to the metal, allyl is a simple X-type ligand bound covalently through one carbon—basically, a monodentate alkyl! Alternatively, allyl can act as a bidentate LX-type ligand, bound to the metal through all three conjugated atoms. The LX or “trihapto” form can be represented using one of two resonance forms, or (more common) the “toilet-bowl” form seen in the general figure above. I don’t like the toilet-bowl form despite its ubiquity, as it tends to obscure the important dynamic possibilities of the allyl ligand.
Can we use FMO theory to explain the wonky geometry of the allyl ligand?
The lower half of the figure above illustrates the slightly weird character of the geometry of allyl ligands. In a previous post on even-numbered π systems, we investigated the orientation of the ligand with respect to the metal and came to some logical conclusions by invoking FMO theory and backbonding. A similar treatment of the allyl ligand leads us to similar conclusions: the plane of the allyl ligand should be parallel to the xy-plane of the metal center and normal to the z-axis. In reality, the allyl plane is slightly canted to optimize orbital overlap—but we can see at the right of the figure above that π2–dxy orbital overlap is key. Also note the rotation of the anti hydrogens (anti to the central C–H, that is) toward the metal center to improve orbital overlap.
Exchange of the syn and anti substituents can occur through σ,π-isomerization followed by bond rotation and formation of the isomerized trihapto form. Notice that the configuration of the stereocenter bearing the methyl group is unaffected by the isomerization! It should be noted that 1,3-disubstituted allyl complexes almost exclusively adopt a syn,syn configuration without danger of isomerization.
The methylene and central C–H simply change places!
Upon deconstruction, the cyclopentadienyl (Cp) ligand yields the aromatic cyclopentadienyl anion, an L2X-type ligand. Cp is normally an η5-ligand, but η3 (LX) and η1 (X) forms are known in cases where the other ligands on the metal center are tightly bound. η1-Cyclopentadienyl ligands can sometimes be fluxional—the metal has the ability to “jump” from atom to atom. Variations on the Cp theme include Cp* (C5Me5) and the monomethyl version (C5H4Me). Cp may be found as a loner alongside other ligands (in “half-sandwich” or “piano-stool” complexes), or paired up with a second Cp ligand in metallocenes. The piano-stool and bent metallocene complexes are most interesting for us, since these have potential for open coordination sites—plain vanilla metallocenes tend to be relatively stable and boring.
Binding modes of Cp and general classes of Cp complexes.
Research for this post has made me appreciate the remarkable electron-donating ability of the cyclopentadienyl (Cp) ligand, which renders its associated metal center electron rich. The LUMO of Cp is high in energy, so the ligand is a weak π-acid and is, first and foremost, a σ-donor. This effect is apparent in the strong backbonding displayed by Cp carbonyl complexes. Despite its strong donating ability, Cp is rarely an actor ligand unless another ligand shakes things up—check out the nucleophilic reactivity of doubly jazzed-up ferrocene for a nice example.
It’s critical to recognize that η5-Cp is a six-electron ligand (!). Because Cp piles on electrons, the numbers of ligands bound to the metal in Cp complexes tend to be lower than we might be used to, especially in bent metallocenes containing two Cp’s. Still, the number of ligands we’d expect on the metal center in these complexes is perfectly predictable. We just need to keep in mind that the resulting complexes are likely to contain 16 or 18 total electrons.
By considering the MCp2 fragment, we can predict the nature of ancillary ligands in bent metallocenes.
Synthesis
Crabtree cleanly divides methods for the synthesis of Cp complexes into those employing Cp+ equivalents, Cp– equivalents, and the neutral diene. Naturally, the first class of reagents are appropriate for electron-rich, nucleophilic complexes, while the second class are best used in conjunction with electron-poor, electrophilic complexes. The figure below provides a few examples.
Methods for the synthesis of Cp complexes. The possibilities are exhausted by anionic, cationic, and neutral Cp equivalents!
Methods for synthesizing allyl complexes can also be classified according to whether the allyl donor is a cationic, anionic, or neutral allyl equivalent. In metal-catalyzed allylic substitution reactions, the allyl donor is usually a good electrophile bearing a leaving group displaced by the metal (an allyl cation equivalent). However, similar complexes may be obtained through oxidative addition of an allylic C–H bond to the metal, as in the synthesis of methallyl palladium chloride dimer below. Transmetalation of nucleophilic allyls from one metal to another, which we can imagine as nucleophilic attacks of an anionic allyl group, are useful when the metal is electron-poor.
Nucleophilic, electrophilic, and neutral allyl donors.
Complexes containing conjugated dienes are also viable precursors to allyl complexes. Migratory insertion of a diene into the M–H bond is a nice route to methyl-substituted allyl complexes, for example. Interestingly, analogous insertions of fulvenes do not appear to lead to Cp complexes, but some funky reductive couplings that yield ansa-metallocenes are known. External electrophilic attack (e.g., protonation) and nucleophilic attack on coordinated dienes also result in allyl complexes. In essence, one double bond of the diene becomes a part of the allyl ligand in the product; the other is used as a “handle” to establish the key covalent bond to the allyl ligand.
Dienes: brave crusaders in the quest for allyl complexes.
Reactions
Since the Cp ligand is typically a spectator, we’ll focus in this section on the reactivity of allyl ligands. As usual, the behavior of the allyl ligand depends profoundly on the nature of its coordinated metal center, which depends in turn on the metal’s ancillary ligands. Avoid “tunnel vision” as you study the examples below—depending on the issue at hand, the ancillary ligands may be as important as (or more important than) the actor ligand.
Nucleophilic allyl complexes react with electrophiles like H+, MeI, X+, and acylium ions to yield cationic alkene complexes.
Attack of electrophiles on nucleophilic allyl complexes. Notice the donating Cp ligand!
In a conceptually related process, nucleophiles can attack allyl ligands bound to electrophilic metals. This process is key in allylic substitution reactions. In some cases, the nucleophile is known to bind to the metal first, then transfer to the allyl ligand through reductive elimination. Alternatively, direct attack on the allyl ligand may occur on the face opposite the metal. The figure below illustrates both possibilities.
External and internal attack of nucleophiles on coordinated allyl ligands.
Migratory insertion of allyl ligands is known, and is analogous to insertions involving alkyl ligands (see the figure below). Movement of the allyl ligand toward the coordination site of the dative ligand is assumed. Of course if oxidative addition to form allyl complexes is possible, reductive elimination of allyl ligands with other X-type ligands is also possible. We’ll hit on these process in more detail in their dedicated posts.
Like alkyl ligands, allyls can migrate onto dative ligands like CO and π bonds.
One final post on σ-complexes will bring this series to a temporary close. In the next post, we’ll look at ligands that, rather surprisingly, bind through their σ-electrons. These “non-classical” ligands behave like other dative ligands we’ve seen before, but are important for many reactions that involve main-group single bonds, such as oxidative addition. Before their discovery, the relevance of σ-ligands for reaction mechanisms went unappreciated by organometallic chemists. | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/02%3A_Organometallic_Ligands/2.08%3A_Odd-numbered__Systems.txt |
The epic ligand survey continues with tertiary phosphines, PR3. Phosphines are most notable for their remarkable electronic and steric tunability and their “innocence”—they tend to avoid participating directly in organometallic reactions, but have the ability to profoundly modulate the electronic properties of the metal center to which they’re bound. Furthermore, because the energy barrier to umbrella flipping of phosphines is quite high, “chiral-at-phosphorus” ligands can be isolated in enantioenriched form and introduced to metal centers, bringing asymmetry just about as close to the metal as it can get in chiral complexes. Phosphorus NMR is a technique that Just Works (thanks, nature). Soft phosphines match up very well with the soft low-valent transition metals. Electron-poor phosphines are even good π-acids!
General Properties
Like CO, phosphines are dative, L-type ligands that formally contribute two electrons to the metal center. Unlike CO, most phosphines are not small enough to form more than four bonds to a single metal center (and for large R, the number is even smaller). Steric hindrance becomes a problem when five or more PR3 ligands try to make their way into the space around the metal. An interesting consequence of this fact is that many phosphine-containing complexes do not possess 18 valence electrons. Examples include Pt(PCy3)2, Pd[P(t-Bu)3]2, and [Rh(PPh3)3]+. Doesn’t that just drive you crazy? It drives the complexes crazy as well—and most of these coordinatively unsaturated compounds are wonderful catalysts.
Bridging by phosphines is extremely rare, but ligands containing multiple phosphine donors that bind in an Ln (n > 1) fashion to a single metal center are all over the place. These ligands are called chelating or polydentate to indicate that they latch on to metal centers through multiple binding sites. For entropic reasons, chelating ligands bind to a single metal center at multiple points if possible, instead of attaching to two different metal centers (the aptly named chelate effect). An important characteristic of chelating phosphines is bite angle, defined as the predominant P–M–P angle in known complexes of the ligand. We’ll get into the interesting effects of bite angle later, but for now, we might imagine how “unhappy” a ligand with a preferred bite angle of 120° would be in the square planar geometry. It would much rather prefer to be part of a trigonal bipyramidal complex, for instance.
The predominant orbital interaction contributing to phosphine binding is the one we expect, a lone pair on phosphorus interacting with an empty metallic d orbital. The electronic nature of the R groups influences the electron-donating ability of the phosphorus atom. For instance, alkylphosphines, which possess P–Csp3 bonds, tend to be better electron donors than arylphosphines, which possess P–Csp2 bonds. The rationale here is the greater electronegativity of the sp2 hybrid orbital versus the sp3 hybrid, which causes the phosphorus atom to hold more tightly to its lone pair when bound to an sp2 carbon. The same idea applies when electron-withdrawing and -donating groups are incorporated into R: the electron density on P is low when R contains electron-withdrawing groups and high when R contains electron-donating groups. Ligands (and associated metals) in the former class are called electron poor, while those in the latter class are electron rich.
As we add electronegative R groups, the phosphorus atom (and the metal to which it's bound) become more electron poor.
Like CO, phosphines participate in backbonding to a certain degree; however, the phenomenon here is of a fundamentally different nature than CO backbonding. For one thing, phosphines lack a π* orbital. In the days of yore, chemists attributed backbonding in phosphine complexes to an interaction between a metallic dπ orbital and an empty 3d orbital on phosphorus. However, this idea has elegantly been proven bogus, and a much more organicker-friendly explanation has taken its place (no d orbitals on P required!). In an illuminating series of experiments, M–P and P–R bond lengths were measured via crystallography for several redox pairs of complexes. I’ve chosen two illustrative examples, although the linked reference is chock full of other pairs. The question is: how do we explain the changes in bond length upon oxidation?
Upon oxidation, M–P bond lengths increase and and P–R bond lengths decrease. Why?
Oxidation decreases the ability of the metal to backbond, because it removes electron density from the metal. This explains the increases in M–P bond length—just imagine a decrease the M–P bond order due to worse backbonding. And the decrease in P–R bond length? It’s important to see that invoking only the phosphorus 3d orbitals would not explain changes in the P–R bond lengths, as the 3d atomic orbitals are most definitely localized on phosphorus. Instead, we must invoke the participation of σ*P–R orbitals in phosphine backbonding to account for the P–R length decreases. When all is said and done, the LUMO of the free phosphine has mostly P–R antibonding character, with some 3d thrown into the mix. The figure below depicts one of the interactions involved in M–P backbonding, a dπ → σ* interaction (an orthogonal dπ → σ* interaction also plays a role). As with CO, a resonance structure depicting an M=P double bond is a useful heuristic! Naturally, R groups that are better able to stabilize negative charge—that is, electron-withdrawing groups—facilitate backbonding in phosphines. Electron-rich metals help too.
Backbonding in phosphines, a sigma-bond-breaking affair.
The steric and electronic properties of phosphines vary enormously. Tolman devised some intriguing parameters that characterize the steric and electronic properties of this class of ligands. To address sterics, he developed the idea of cone angle—the apex angle of a cone formed by a point 2.28 Å from the phosphorus atom (an idealized M–P bond length), and the outermost edges of atoms in the R groups, when the R groups are folded back as much as possible. Wider cone angles, Tolman reasoned, indicate greater steric congestion around the phosphorus atom. To address electronics, Tolman used a not-so-old friend of ours—the CO stretching frequency (νCO) of mixed phosphine-carbonyl complexes. Specifically, he used Ni(CO)3L complexes, where L is a tertiary phosphine, as his standard. Can you anticipate Tolman’s logic? How should νCO change as the electron-donating ability of the phosphine ligands increases?
Tolman’s logic went as follows: more strongly electron-donating phosphines are associated with more electron-rich metals, which are better at CO backbonding (due fundamentally to higher orbital energies). Better CO backbonding corresponds to a lower νCO due to decreased C–O bond order. Thus, better donor ligands should be associated with lower νCO values (and vice versa for electron-withdrawing ligands). Was he correct? Exhibit A…
Tolman's map of the steric and electronic properties of phosphine ligands.
Notice the poor ligand trifluorophosphine stuck in the “very small, very withdrawing” corner, and its utter opposite, the gargantuan tri(tert-butyl)phosphine in the “extremely bulky, very donating” corner. Intriguing! One can learn a great deal just by studying this chart.
Synthesis
Phosphine complexes are most commonly made through ligand substitution processes—the exchange of one ligand for another on a metal center. One interesting method utilizes tertiary N-oxides to essentially “oxidize off” a CO ligand, leaving behind an open coordination site that may be filled by a phosphine. Notice that the carbon of CO is behaving as an electrophile in this process. Shi and Basolo masterfully demonstrate that an intermediate amine complex cannot be involved in this mechanism. Irradiation by ultraviolet light is an alternative method to coax the CO ligand off of metal carbonyl complexes.
Ligand substitution with the help of trimethylamine oxide.
Methods for synthesizing the phosphine ligands themselves are somewhat beyond our scope, but electrophilic phosphorus chemistry is common, particularly when arylphosphines are the target.
Reactions
Phosphines are most often spectator ligands, meaning that they don’t participate in reactions, but hang on for the ride. There are, however, some important exceptions to this rule. First of all, dissociation of a phosphine ligand is often required to generate a site of coordinative unsaturation before catalytic reactions can begin. Good examples are cross-couplings employing the saturated Pd(PPh3)4. This complex is actually just a precatalyst that must lose phosphine ligands to enter the catalytic cycle of cross-coupling. Phosphine association is also an important step of many catalytic reactions.
What decomposition pathways are available to phosphine ligands? P–C bond cleavage is a surprisingly common process. In general, the idea is that the metal center can insert into the P–C bond via concerted oxidative addition, then reductively eliminate to establish a new P–C bond. Reductive elimination can even occur after some intermediate steps, as in the example below.
P–C bond cleavage: also known as the "R group shuffle."
Phosphonium salt formation from arylphosphine complexes is a related process. Here, the complex essentially just falls apart after P–C reductive elimination.
Reductive elimination to form phosphonium salts.
Phosphine ligands are everywhere, and we’ll definitely see more of this fascinating class of ligands in the future. They are particularly powerful as the bearers of asymmetry in chiral metal complexes, which are used to prepare enantioenriched organic products. | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/02%3A_Organometallic_Ligands/2.09%3A_Phosphines.txt |
With this post, we finally reach our first class of dative actor ligands, π systems. In contrast to the spectator L-type ligands we’ve seen so far, π systems most often play an important role in the reactivity of the OM complexes of which they are a part (since they act in reactions, they’re called “actors”). π Systems do useful chemistry, not just with the metal center, but also with other ligands and external reagents. Thus, in addition to thinking about how π systems affect the steric and electronic properties of the metal center, we need to start considering the metal’s effect on the ligand and how we might expect the ligand to behave as an active participant in reactions. To the extent that structure determines reactivity—a commonly repeated, and extremely powerful maxim in organic chemistry—we can think about possibilities for chemical change without knowing the elementary steps of organometallic chemistry in detail yet.
General Properties
The π bonding orbitals of alkenes, alkynes, carbonyls, and other unsaturated compounds may overlap with dσ orbitals on metal centers. This is the classic ligand HOMO → metal LUMO interaction that we’ve beaten into the ground over the last few posts. Because of this electron donation from the π system to the metal center, coordinated π systems often act electrophilic, even if the starting alkene was nucleophilic (the Wacker oxidation is a classic example; water attacks a palladium-coordinated alkene). The π → dσ orbital interaction is central to the structure and reactivity of π-system complexes.
Then again, a theme of the last three posts has been the importance of orbital interactions with the opposite sense: metal HOMO → ligand LUMO. Like CO, phosphines, and NHCs, π systems are often subject to important backbonding interactions. We’ll focus on alkenes here, but these same ideas apply to carbonyls, alkynes, and other unsaturated ligands bound through their π clouds. For alkene ligands, the relative importance of “normal” bonding and backbonding is nicely captured by the relative importance of the two resonance structures in the figure below.
Resonance forms of alkene ligands.
Complexes of weakly backbonding metals, such as the electronegative late metals, are best represented by the traditional dative resonance structure 1. But complexes of strong backbonders, such as electropositive Ti(II), are often best drawn in the metallacyclopropane form 2. Organic hardliners may have a tough time believing that 1 and 2 are truly resonance forms, but several studies—e.g. of the Kulinkovich cyclopropanation—have shown that independent synthetic routes to metallacyclopropanes and alkene complexes containing the same atoms result in the same compound. Furthermore, bond lengths and angles in the alkene change substantially upon coordination to a strongly backbonding metal. We see an elongation of the C=C bond (consistent with decreased bond order) and some pyramidalization of the alkene carbons (consistent with a change in hybridization from sp2 to sp3). A complete orbital picture of “normal” bonding and backbonding in alkenes is shown in the figure below.
Normal bonding and backbonding in alkene complexes.
Here’s an interesting question with stereochemical implications: what is the orientation of the alkene relative to the other ligands? From what we’ve discussed so far, we can surmise that one face of the alkene must point toward the metal center. Put differently, the bonding axis must be normal to the plane of the alkene. However, this restriction says nothing about rotation about the bonding axis, which spins the alkene ligand like a pinwheel. Is a particular orientation preferred, or can we think about the alkene as a circular smudge over time? The figure below depicts two possible orientations of the alkene ligand in a trigonal planar complex. Other orientations make less sense because they would involve inefficient orbital overlap with the metal’s orthogonal d orbitals. Which one is favored?
Two limiting cases for alkene orientation in a trigonal planar complex.
First of all, we need to notice that these two complexes are diastereomeric. They have different energies as a result, so one must be favored over the other. Naive steric considerations suggest that complex 4 ought to be more stable (in most complexes, steric factors dictate alkene orientation). To dig a little deeper, let’s consider any electronic factors that may influence the preferred geometry. We’ve already seen that electronic factors can overcome steric considerations when it comes to complex geometry! To begin, we need to consider the crystal field orbitals of the complex as a whole. Verify on your own that in this d10, Pt(0) complex, the crystal-field HOMOs are the dxy and dx2–y2 orbitals. Where are these orbitals located in space? In the xy-plane! Only the alkene in 3 can engage in efficient backbonding with the metal center. In cases when the metal is electron rich and/or the alkene is electron poor, complexes like 3 can sometimes be favored in spite of sterics. The thought process here is very similar to the one developed in an earlier post on geometry. However, please note that this situation is fairly rare—steric considerations often either match or dominate electronics where alkenes are concerned.
Synthesis
Alkene and alkyne complexes are most often made via ligand substitution reactions, which simply exchange one ligand for another. A nice example of a stable alkene complex synthesized via ligand substitution is [Ir(COD)Cl]2, made from IrCl3 and cyclooctadiene. Similarly, the inimitable Pd2(dba)3 may be prepared from PdCl42– and dibenzylideneacetone (dba). In truth, only a few stable alkene and alkyne complexes find use as organometallic precatalysts and/or catalysts. Substitutions of alkenes for phosphine ligands can be rendered easy, so phosphine precatalysts may be used in reactions that involve intermediate alkene complexes. In addition, unsaturated complexes containing an open coordination site often associate with alkenes and alkynes. Gold(I) chemistry is riddled with examples of this strategy, for example. The unsaturated complexes may be derived from precursors themselves, and the resulting π complexes may be short lived, but that’s often the point! Some transformation of the π system is often desired.
I have to mention the metallacyclopropane route to alkene complexes from the Kulinkovich reaction, which is a surprising but awesome transformation. After displacement of two alkoxide ligands on titanium by ethylmagnesium bromide, a process described as either (1) β-hydride elimination followed by reductive elimination, or (2) concerted σ-bond metathesis leads to the liberation of ethane and formation of the alkene complex. The proof that the product is an alkene complex? Other olefins can displace ethylene, and ethylene can come right back in to re-form the product! Ti(II)’s strong backbonding ability almost certainly figures in to the driving force for the ethane-releasing step(s).
Kulinkovich synthesis of alkene complexes. A remarkable loss of ethane!
Reactions
The reactivity patterns of alkene and alkyne ligands are remarkably similar to those of carbon monoxide: nucleophilic attack and migratory insertion dominate their chemistry. The important issues of site selectivity and stereoselectivity come into play when considering alkenes and alkynes, however—the fundamental questions are…
• Which atom gets the nucleophile/migrating group?
• Which atom gets the metal?
• What is the relative orientation of the nucleophile/migrating group and the metal (cis or trans)?
The wide variety of what we might generally call “atom-metallation” processes (carbopalladation, carboauration, aminopalladation, oxypalladation, etc.) may involve external nucleophilic addition to the π system, with attachment of the metal to the carbon that was not attacked. The net result is the addition of atom and metal across the π bond, in a trans or anti orientation. The anti orientation results because the nucleophile attacks the face opposite the metal center. A cis orientation of nucleophile and metal is indicative of a migratory insertion pathway (see below). In the example in the following figure, the metal alkyl was converted into a chlorohydrin using copper(II) chloride and LiCl (with stereospecific inversion). Subsequent epoxide formation with NaOH afforded only the cis diastereomer, supporting the trans configuration of the metal alkyl.
Nucleophilic attack on a coordinated alkene or alkyne is always trans, or anti.
Migratory insertion of alkenes and alkynes, like insertions of CO, can be thought of as an internal attack by a nucleophile already coordinated to the metal center. Migratory insertion is the C–C bond-forming step of olefin polymerization, and some fascinating studies of this reaction have shown that the alkyl group (the growing polymer chain) migrates to the location of the olefin (not the other way around). Migratory insertion is also important for the Heck reaction—in this case, the olefin inserts into a Pd–Csp2 bond. Finally, a large number of metal-catalyzed addition reactions rely on migratory insertion as the key C–X bond-forming step. cis-Aminopalladation is one example.
cis-Aminopalladation via migratory insertion. Two new bonds are established with stereospecificity!
Importantly, migratory insertion of alkenes and alkynes into M–X bonds takes place in a syn or cis fashion—the metal and the migrating group (X) end up on the same face of the π system. The site selectivity of migratory insertion may be controlled by either steric factors or the π system’s electronics, although the former is more common, I’d say. Electronics are at play in Wacker oxidations of 1-alkenes, for example, which exclusively yield methyl ketones.
Finally, electrophilic attack on π systems coordinated to electron-rich metals can also happen, although it’s much rarer than nucleophilic attack. Usually these reactions involve coordination of the electrophile to the metal, followed by migratory insertion. We’ll hear more about this in a future post on electrophilic attack on coordinated ligands. Coming up next: cyclic π systems!
Arene or aromatic ligands are the subject of this post, the second in our series on π-system ligands. Arenes are dative, L-type ligands that may serve either as actors or spectators. Arenes commonly bind to metals through more than two atoms, although η2-arene ligands are known. Structurally, most η6-arenes tend to remain planar after binding to metals. Both “normal” bonding and backbonding are possible for arene ligands; however, arenes are stronger electron donors than CO and backbonding is less important for these ligands. The reactivity of arenes changes dramatically upon metal binding, along lines that we would expect for strongly electron-donating ligands. After coordinating to a transition metal, the arene usually becomes a better electrophile (particularly when the metal is electron poor). Thus, metal coordination can enable otherwise difficult nucleophilic aromatic substitution reactions.
General Properties
The coordination of an aromatic compound to a metal center through its aromatic π MOs removes electron density from the ring. I’m going to forego an in-depth orbital analysis in this post, because it’s honestly not very useful (and overly complex) for arene ligands. π → dσ (normal bonding) and dπ → π* (backbonding) orbital interactions are possible for arene ligands, with the former being much more important, typically. To simplify drawings, you often see chemists draw “toilet-bowl” arenes involving a circle and single central line to represent the π → dσ orbital interaction. Despite the single line, it is often useful to think about arenes as L3-type ligands. For instance, we think of η6-arenes as six-electron donors.
Multiple coordination modes are possible for arene ligands. When all six atoms of a benzene ring are bound to the metal (η6-mode), the ring is flat and C–C bond lengths are slightly longer than those in the free arene. The ring is bent and non-aromatic in η4-mode, so that the four atoms bound to the metal are coplanar while the other π bond is out of the plane. η4-Arene ligands show up in both stable complexes (see the figure below) and reactive intermediates that possess an open coordination site. To generate the latter, the corresponding η6-arene ligand undergoes ring slippage—one of the π bonds “slips” off of the metal to create an open coordination site. We’ll see ring slippage again in discussions of the aromatic cyclopentadienyl and indenyl ligands.
Arene ligands exhibit multiple coordination modes.
Even η2-arene ligands bound through one double bond are known. Coordination of one π bond results in dearomatization and makes η2-benzene behave more like butadiene, and furan act more like a vinyl ether. With naphthalene as ligand, there are multiple η2 isomers that could form; the isomer observed is the one that retains aromaticity in the free portion of the ligand. In fact, this result is general for polycyclic aromatic hydrocarbons: binding maximizes aromaticity in the free portion of the ligand. In the linked reference, the authors even observed the coordination of two different rhodium centers to naphthalene—a bridging arene ligand! Other bridging modes include σ, π-binding (the arene is an LX-type ligand, and one C–M bond is covalent, not dative) and L2-type bridging through two distinct π systems (as in biphenyl).
Arene ligands are usually hydrocarbons, not heterocycles. Why? Aromatic heterocycles, such as pyridine, more commonly bind using their basic lone pairs. That said, a few heterocycles form important π complexes. Thiophene is perhaps the most heavily studied, as the desulfurization of thiophene from fossil fuels is an industrially useful process.
Synthesis
There are two common methods for the stoichiometric synthesis of arene “sandwich” complexes, in which a metal is squished between two arenes. Starting from a metal halide, treatment with a Lewis acid and mild reductant rips off the halogen atoms and replaces them with arene ligands. The scope of this method is fairly broad metal-wise.
The Fischer-Hafner synthesis. Reduction of metal halides in the presence of arene.
A second method, “co-condensation,” involves the simultaneous condensation of metal atom and arene vapor onto a cold (-196 °C) surface.
Syntheses of metal arene carbonyl complexes take advantage of the fact that arenes are strongly binding, “chelating” ligands. Infrared spectroscopic studies have shown that a single benzene ligand is a stronger electron donor than three CO ligands—C–O stretching frequencies are lower in metal arene carbonyls than homoleptic metal carbonyls. Since the process is entropically driven, a little heat can get the job done.
Entropically driven synthesis of arene complexes: three molecules for the price of one!
Reactions
It’s important here to distinguish aromatic X-type ligands from the topic of this post, Ln-type arenes bound only through their π systems. The figure below nicely summarizes the typical behavior of arene ligands coordinated through their π clouds. Although the figure is for chromium carbonyls specifically, other metals apply as well. Note the reactivity of the benzylic position: both cations and anions are stabilized by the metal.
The magic of metal coordination: increased acidity and electrophilicity and steric hindrance.
Since the coordination of arenes to metals depletes electron density on the arene, it makes sense that metal-arene complexes should be susceptible to nucleophilic aromatic substitution (NAS). In fact, NAS on metal-coordinated arene ligands has been extensively developed for several different metals. However, all of these NAS methods are stoichiometric because the product ligands are as good as (or better than) the starting ligands at coordinating metal. A stoichiometric amount of another reagent—typically an oxidant—is used to free up the arene. Why are oxidants effective at freeing arene ligands from metal centers? Oxidation worsens the metal’s ability to backbond and consequently decreases the enthalpic advantage of arene binding. Entropy is thus able to take over and release the ligand.
Steric hindrance on the side of the arene bound to the metal is a second important factor to consider. Nucleophilic addition takes place on the face opposite the coordinated metal. If rearomatization through the loss of a leaving group isn’t fast, an electrophile can be introduced after nucleophilic addition, resulting in the cis addition of nucleophile and electrophile across an aromatic π bond. Take that, aromaticity!
Aromaticity takes a beating, thanks to chromium!
We already touched a little on the interesting behavior of η2-arene complexes, which behave more like their analogues possessing one less double bond. Here’s a nifty example from Harman of a Diels-Alder reaction in which a substituted styrene is the diene. Strike two for aromaticity!
Harman's Os(II) arene chemistry. Styrene is uniquely acting like a diene!
If you’re interested in learning more about this fascinating chemistry, check out Harman’s review (linked above). The behavior of furan is particularly intriguing.
This brings us to the end of our short series on L-type π-system ligands. However, we’ll encounter ligands that bear great similarity to alkenes and arenes in the near future. π Systems that contain an odd number of atoms, unlike π systems we’ve seen so far, are LnX-type ligands with one covalent M–X bond and n dative bonds. We’ll return to this interesting class of ligands after finishing off the dative ligands with metal carbenes and introducing a few simple X-type ligands (hydrides, alkyls, alkoxides, etc.). | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/02%3A_Organometallic_Ligands/2.10%3A__Systems.txt |
In this post, we’ll begin to explore the molecular orbital theory of organometallic complexes. Some background in molecular orbital theory will be beneficial; an understanding of organic frontier molecular orbital theory is particularly helpful. Check out Fukui’s Nobel Prize lecture for an introduction to FMO theory. The theories described here try to address how the approach of ligands to a transition metal center modifies the electronics of the metal and ligands. The last post on geometry touched on these ideas a little, but we’ll dig a little deeper here. Notably, we need to address the often forgotten influence of the metal on the ligands—how might a metal modify the reactivity of organic ligands?
3.02: Open Coordination Site
The concept of coordinative unsaturation can be confusing for the student of organometallic chemistry, but recognizing open coordination sites in OM complexes is a critical skill.
Introduction
Let’s begin with a famous example of coordinative unsaturation from organic chemistry.
An analogy from organic chemistry. The reactivity of the carbene flows from its open coordination site.
Carbenes are both nucleophilic and electrophilic, but the essence of their electrophilicity comes from the fact that they don’t have their fair share of electrons (8). They have not been saturated with electrons—carbenes want more! To achieve saturation, carbenes may inherit a pair of electrons from a σ bond (σ-bond insertion), π bond (cyclopropanation), or lone pair (ylide formation). Notice that, simply by spotting coordinative unsaturation, we’ve been able to fully describe the carbene’s reactivity! We can do the same with organometallic complexes—open coordination sites suggest specific reactivity patterns. That’s why understanding coordinative unsaturation and recognizing its telltale sign (the open coordination site) are essential skills for the organometallic chemist.
Coordinative unsaturation is not just the possession of a coordination number less than 6, or an apparent space in which a ligand might be able to approach. Sixteen or fewer total electrons on the metal center are a second necessity—just as, in the organic case, 6 or fewer electrons on the unsaturated atom are essential. Sixteen or fewer total electrons and coordination number less than 6 add up to a more fundamental synonym for an open coordination site: an empty metal-centered orbital!
(<= 16 total electrons on M) + (< 6 coordination number on M) = empty d orbital on M
The lesson here is that we can’t just look to the geometry of a complex to determine whether it bears an open coordination site—electron counting is essential too.
Like carbenes and carbocations, metal complexes containing open coordination sites don’t just hang around. They react rapidly with all kinds of electron sources. Furthermore, you won’t see them in stable starting materials or products. Thus, recognizing when a complex has the potential for an open site is important. What are some structural signs that point to the possibility of an open coordination site?
1. Weakly coordinating ligands
Ligand dissociation from an 18-electron complex produces an open coordination site. Solvent ligands and side-on σ ligands—both of which bind relatively weakly to metals—often engage in this process. Try counting electrons in the two pairs of cationic iridium complexes below.
Dissociation of weakly bound ligands reveals open coordination sites.
Dissociation of a π-system ligand may also reveal an open coordination site.
2. Reaction conditions encouraging dissociation
In this category, we might file away photochemical and amine-oxide-mediated dissociations of CO. Conditions like these encourage the loss of a ligand and subsequent replacement with something else, àla SN1 substitution.
3. Potential for reductive elimination
Reductive elimination is the open coordination site’s dream come true: two (sites) for the price of one (step)! Factors affecting the favorability of reductive elimination are beyond the scope of this post, but we can mention a couple here: steric crowding and an electron-poor metal.
Finally, it’s important to note that open coordination sites often show up in fragments of OM complexes examined for one reason or another. We can relate these fragments to organic or main-group intermediates using isolobal analogies, powerful conceptual tools that we’ll explore in detail in another post. For example, the fragment (CO)5Cr is isolobal with the organic carbocation—the two sets of frontier MOs are analogous, and both structures have an open coordination site.
All three of these analogous fragments bear an open coordination site. | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/03%3A_Structural_Fundamentals/3.01%3A_Ligand_Field_Theory_and_Frontier_Molecular_Orbital_Theory.txt |
Periodic trends play a huge role in organic chemistry. Regular changes in electronegativity, atomic size, ionization energy, and other variables across the periodic table allow us to make systematic predictions about the behavior of similar compounds. Of course, the same is true for organometallic complexes! With a firm grip on the periodic trends of the transition metals, we can begin to make comparisons between complexes we’re familiar with and those we’ve never seen before. Periodic trends essentially provide an exponential increase in predictive power. In this post, we’ll hit on the major periodic trends of the transition metals and discuss a few examples for which these trends can be handy.
Before beginning, a couple of caveats are in order. First of all, many of the trends across the transition series are not perfectly regular. Hartwig wisely advises that one should consider the transition series in blocks instead of as a whole when considering periodic trends. For instance, general increases in a quantity may be punctuated by sudden decreases; in such a case, we may say that the quantity increases generally, but definite conclusions are only possible when the metals under comparison are close to one another in the periodic table (and we need to be careful about unexpected jumps). Secondly, periodic trends are significantly affected by the identity of ligands and the oxidation state of the metal center, so comparisons need to be appropriately controlled. Using periodic trends to compare a Pd(II) complex and a Ru(III) complex is largely an exercise in futility, but comparing Pt(II) and Pd(II) complexes with similar ligand sets is reasonable. Keep these ideas in mind to avoid spinning your wheels unnecessarily! Alright, let’s dive in…
3.04: Predicting the Geometry of Organometallic Complexes
An important issue that we’ve glossed over until now concerns what organometallic complexes actually look like: what are their typical geometries? Can we use any of the “bookkeeping metrics” we’ve explored so far to reliably predict geometry? The answer to the latter questions is a refreshing but qualified “yes.” In this post, we’ll explore the possibilities for complex geometry and develop some general guidelines for predicting geometry. In the process we’ll enlist the aid of a powerful theoretical ally, crystal field theory (CFT), which provides some intuitive explanations for geometry the geometry of organometallic complexes.
3.05: Simplifying the Organometallic Complex (Part 1)
Organometallic complexes, which consist of centrally located metals and peripheral organic compounds called ligands, are the workhorses of organometallic chemistry. Just like organic intermediates, understanding something about the structure of these molecules tells us a great deal about their expected reactivity. Some we would expect to be stable, and others definitely not! A big part of our early explorations will involve describing, systematically, the principles that govern the stability of organometallic complexes. From the outset, I will say that these principles are not set in stone and are best applied to well controlled comparisons. Nonetheless the principles are definitely worth talking about, because they form the foundation of everything else we’ll discuss. Let’s begin by exploring the general characteristics of organometallic complexes and identifying three key classes of organic ligands.
When we think of metals we usually think of electropositive atoms or even positively charged ions, and many of the metals of OM chemistry fit this mold. In general, it is useful to imagine organic ligands as electron donors and metals as electron acceptors. When looking at a pair of electrons shared between a transition metal and main-group atom (or hydrogen), I imagine the cationic metal center and anionic main-group atom racing toward one another from oblivion like star-crossed lovers. In the opposite direction (with an important caveat that we’ll address soon), we can imagine ripping apart metal–R covalent bonds and giving both electrons of the bond to the organic atom. This heterolytic bond cleavage method reproduces the starting charges on the metal and ligand. Unsurprisingly, the metal is positive and the ligand negative.
FYI, you might see the blue bipyridine referred to as an L2 ligand elsewhere; this just means that a single bipyridine molecule possesses two L-type binding points. Ligands with multiple binding points are also known as chelating or polydentate ligands. Chelating ligands may feature mixed binding modes; for instance, the allyl ligand is of the LX-type. Chelating ligands can also bind to two different metal centers; when they act in this way, they’re called bridging ligands. But don’t let all this jargon throw you! Deconstruct complexes one binding point at a time, and you cannot go wrong.
Next, we’ll take a closer look at the metal center and expand on the purpose of the deconstruction process described here. | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/03%3A_Structural_Fundamentals/3.03%3A_Periodic_Trends_of_the_Transition_Metals.txt |
Now it’s time to turn our attention to the metal center, and focus on what the deconstruction process can tell us about the nature of the metal in organometallic complexes. We’ll hold off on a description of periodic trends of the transition series, but now is a good time to introduce the general characteristics of the transition metals. Check out groups 3-12 in the table below.
The transition metals are colored dark blue in this table.
The transition metals occupy the d-block of the periodic table, meaning that, as we move from left to right across the transition series, electrons are added to the d atomic orbitals. Just like organic elements, the transition metals form bonds using only their valence electrons. But when working with the transition metals, we need to concern ourselves only with the d atomic orbitals, as none of the other valence subshells contain any electrons. Although the periodic table may lead you to believe that the transition metals possess filled s subshells, we imagine metals in organometallic complexes as possessing valence electrons in d orbitals only! The reason for this is somewhat complicated, but has to do with the partial positive charge of complexed metals. Neutral transition metal atoms do, in fact, possess filled s subshells. Why, then, is it important to remember that the valence electrons of complexed metal centers are all d electrons? We will see that the number of d electrons possessed by a complexed metal is in many ways a useful concept. If you find that your counts are off by two, this common mistake is probably the culprit!
Let’s turn our attention now to a new complex. I’ve gone ahead and deconstructed it for us.
Say hello to rhodium (Rh)! Don't fret; it's just a group 9 element.
The complex possesses one X-type and three L-type ligands, so the rhodium atom ends up with a formal charge of +1. The formal charge on the metal center after deconstruction has a very special name that you will definitely want to commit to memory: it’s called the oxidation state. It’s usually indicated with a roman numeral next to the atomic symbol of the metal (the “+” is implied). In the complex shown above, rhodium is in the Rh(I) or +1 oxidation state. Oxidation state is most useful because changes in oxidation state indicate changes in electron density at the metal center, and this can be a favorable or unfavorable occurrence depending on the other ligands around. We will see this principle in action many, many times! Get used to changes in oxidation state as everyday events in organometallic reaction mechanisms. Unlike carbon (with the exception of carbene…what’s its oxidation state?!) and other second-row elements, the transition metals commonly exhibit multiple different oxidation states. More on that later, though. For now, training yourself to rapidly identify the oxidation state of a complexed metal is most important. Please note that when a complex possesses an overall charge, the oxidation state is affected by this charge!
oxidation state = number of X-type ligands bound to metal + overall charge of complex
What of this number of d electrons concept? A very useful way to think about “number of d electrons” is as the “number of non-bonding electrons on the metal center,” and you’re probably familiar with identifying non-bonding electrons from organic chemistry. The numbers of valence electrons of each organic element are set in stone: carbon has four, nitrogen has five, et cetera. Furthermore, using this knowledge, it’s straightforward to determine the number of lone pair electrons associated with an atom by subtracting its number of covalent bonds from its total number of valence electrons. E.g., for a neutral nitrogen atom in an amine NR3, 5 – 3 = 2 lone pair electrons, typically. The extension to organometallic chemistry is natural! We can analyze complexed metal centers in the same way, but they tend to have a lot more non-bonding electrons than organic atoms, and the number depends on the metal’s oxidation state. For instance, the deconstructed rhodium atom in the figure above has 8 d electrons: 9 valence electrons minus 1 used for bonding to Cl. Dative bonds don’t affect d electron count since both electrons in the bond come from the ligand.
number of non-bonding electrons = number of d electrons = metal’s group number – oxidation state
Drawing all the non-bonding d electrons out as lone pairs would clutter things up, so they are never drawn…but we must remember that they’re around! Why? Because the number of d electrons profoundly affects a complex’s geometry. We will return to this soon, but the key idea is that the ligands muck up the energies of the d orbitals as they approach the metal (recall the “star-crossed lovers” idea), and the most favorable way to do so depends on the number of non-bonding electrons on the metal center.
Oxidation state and d electron count: two tools the OM chemist can't live without!
This post introduced us to two important bookkeeping tools, oxidation state and number of d electrons. In the final installment of the “Simplifying the Organometallic Complex” series, we’ll bring everything together and discuss total electron count. We’ll see that total electron count may be used to draw a variety of insightful conclusions about organometallic complexes. | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/03%3A_Structural_Fundamentals/3.06%3A_Simplifying_the_Organometallic_Complex_%28Part_2%29.txt |
So far, we’ve seen how deconstruction can reveal useful “bookkeeping” properties of organometallic complexes: number of electrons donated by ligands, coordination number, oxidation state, and d electron count (to name a few). Now, let’s bring everything together and discuss total electron count, the sum of non-bonding and bonding electrons associated with the metal center. Like oxidation state, total electron count can reveal the likely reactivity of OM complexes—in fact, it is often more powerful than oxidation state for making predictions. We’ll see that there is a definite norm for total electron count, and when a complex deviates from that norm, reactions are likely to happen.
Let’s begin with yet another new complex. This molecule features the common and important cyclopentadienyl and carbon monoxide ligands, along with an X-type ethyl ligand.
What is the total electron count of this Fe(II) complex?
The Cp or cyclopentadienyl ligand is a polydentate, six-electron L2X ligand. The two pi bonds of the free anion are dative, L-type ligands, which we’ll see again in a future post on ligands bound through pi bonds. Think of the electrons of the pi bond as the source of a dative bond to the metal. Since both electrons come from the ligand, the pi bonds are L-type binders. The anionic carbon in Cp is a fairly standard, anionic X-type binder. The carbon monoxide ligands are interesting examples of two-electron L-type ligands—notice that the free ligands are neutral, so these are considered L-type! Carbon monoxide is an intriguing ligand that can teach us a great deal about metal-ligand bonding in OM complexes…but more on that later.
After deconstruction, we see that the Fe(II) center possesses 6 non-bonding d electrons. The total electron count is just the d electron count plus the number of electrons donated by the ligands. Since the d electron count already takes overall charge into account, we need not worry about it as long as we’ve followed the deconstruction procedure correctly.
total electron count = number of d electrons + electrons donated by ligands
For the Fe(II) complex above, the total electron count is thus 6 + (6 + 2 + 2 + 2) = 18. Let’s work through another example: the complex below features an overall charge of +1. Water is a dative ligand—that “2″ is very important!
Note that the overall charge is lumped into the oxidation state and d electron count of Mo.
The oxidation state of molybdenum is +2 here…remember that the overall charge factors in to that. When everything is said and done, the total electron count is 4 + (6 + 2 + 2 + 2 + 2) = 18.
What’s up with 18?! As it turns out, 18 electrons is a very common number for stable organometallic complexes. So common that the number got its own rule—the 18-electron rule—which states that stable transition-metal complexes possess 18 or fewer electrons. The rule is analogous to organic chemistry’s octet rule. The typical explanation for the 18-electron rule points out that there are 9 valence orbitals (1 s, 3 p, 5 d) available to metals, and using all of these for bonding seems to produce the most stable complexes. Of course, as soon as the rule left the lips of some order-craving chemist, researchers set out to find counterexamples to it, and a number of counterexamples are known. Hartwig describes the rule as an “empirical guideline” with little theoretical support. In fact, theoretical studies have shown that the participation of p orbitals in complex MOs is unlikely. I know that’s not what you want to hear—but hang with me! The 18-electron rule is still a very useful guideline. It’s most interesting, in fact, when it is not satisfied.
One last example…how would you expect the complex below to react?
Cobaltocene: jonesing for chemical change.
If we assume that the 18-electron rule is true, then cobaltocene has a real problem. It possesses 7 + (6 + 6) = 19 total valence electrons! Yet, we can also reason that this complex will probably react to relieve the strain of not having 18 electrons by giving up an electron. Guess what? In practice, cobaltocene is a great one-electron reducing agent, and can be used to prepare anionic complexes through electron transfer.
\[CoCp_2 + ML_n → [CoCp_2]+[ML_n]^–\]
This post described how to calculate total electron count and introduced the power of the 18-electron rule for predicting whether a complex will donate or accept electrons. We will definitely see these ideas again! But what happens when the electron counts of two complexes we’re interested in comparing are the same? We’ll need more information. In the next post, we’ll explore the periodic trends of the transition series. Our goal will be to make meaningful comparisons between complexes of different metals. | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/03%3A_Structural_Fundamentals/3.07%3A_Simplifying_the_Organometallic_Complex_%28Part_3%29.txt |
• 4.1: β-Elimination Reactions
In organic chemistry class, one learns that elimination reactions involve the cleavage of a σ bond and formation of a π bond. A nucleophilic pair of electrons (either from another bond or a lone pair) heads into a new π bond as a leaving group departs. This process is called β-elimination because the bond β to the nucleophilic pair of electrons breaks. Transition metal complexes can participate in their own version of β-elimination, and metal alkyl complexes famously do so.
• 4.2: Associative Ligand Substitution
Ligand substitution in complexes of this class typically occurs via an associative mechanism, involving approach of the incoming ligand to the complex before departure of the leaving group.
• 4.3: Dissociative Ligand Substitution Reactions
• 4.4: Ligand substitution
ligand substitution involves the exchange of one ligand for another, with no change in oxidation state at the metal center. The incoming and outgoing ligands may be L- or X-type, but the charge of the complex changes if the ligand type changes. Keep charge conservation in mind when writing out ligand substitutions.
• 4.5: Migratory Insertion- 1,2-Insertions
Insertions of π systems into M-X bonds establish two new σ bonds in one step, in a stereocontrolled manner. As we saw in the last post, however, we should take care to distinguish these fully intramolecular migratory insertions from intermolecular attack of a nucleophile or electrophile on a coordinated π-system ligand. The reverse reaction of migratory insertion, β-elimination, is not the same as the reverse of nucleophilic or electrophilic attack on a coordinated π system.
• 4.6: Migratory Insertion- Introduction and CO Insertions
• 4.7: Oxidative Addition- General Ideas
• 4.8: Oxidative Addition of Non-polar Reagents
Page notifications Off Save as PDF Share Table of contents How important are oxidative additions of non-polar reagents? Very. The addition of dihydrogen (H2) is an important step in catalytic hydrogenation reactions. Organometallic C–H activations depend on oxidative additions of C–H bonds. In a fundamental sense, oxidative additions of non-polar organic compounds are commonly used to establish critical metal-carbon bonds.
• 4.9: Oxidative Addition of Polar Reagents
• 4.10: Quirky Ligand Substitutions
Over the years, a variety of “quirky” substitution methods have been developed. All of these have the common goal of facilitating substitution in complexes that would otherwise be inert. It’s an age-old challenge: how can we turn a stable complex into something unstable enough to react? Photochemical excitation, oxidation/reduction, and radical chains all do the job, and have all been well studied.
• 4.11: Reductive Elimination- General Ideas
• 4.12: The trans/cis Effects and Influences
The trans effect proper, which is often called the kinetic trans effect, refers to the observation that certain ligands increase the rate of ligand substitution when positioned trans to the departing ligand. The key word in that last sentence is “rate”—the trans effect proper is a kinetic effect. The trans influence refers to the impact of a ligand on the length of the bond trans to it in the ground state of a complex.
04: Fundamentals of Organometallic Chemistry
In organic chemistry class, one learns that elimination reactions involve the cleavage of a σ bond and formation of a π bond. A nucleophilic pair of electrons (either from another bond or a lone pair) heads into a new π bond as a leaving group departs. This process is called β-elimination because the bond β to the nucleophilic pair of electrons breaks. Transition metal complexes can participate in their own version of β-elimination, and metal alkyl complexes famously do so. Almost by definition, metal alkyls contain a nucleophilic bond—the M–C bond! This bond can be so polarized toward carbon, in fact, that it can promote the elimination of some of the world’s worst leaving groups, like –H and –CH3. Unlike the organic case, however, the leaving group is not lost completely in organometallic β-eliminations. As the metal donates electrons, it receives electrons from the departing leaving group. When the reaction is complete, the metal has picked up a new π-bound ligand and exchanged one X-type ligand for another.
Comparing organic and organometallic β-eliminations. A nucleophilic bond or lone pair promotes loss or migration of a leaving group.
In this post, we’ll flesh out the mechanism of β-elimination reactions by looking at the conditions required for their occurrence and their reactivity trends. Many of the trends associated with β-eliminations are the opposite of analogous trends in 1,2-insertion reactions. A future post will address other types of elimination reactions.
β-Hydride Elimination
The most famous and ubiquitous type of β-elimination is β-hydride elimination, which involves the formation of a π bond and an M–H bond. Metal alkyls that contain β-hydrogens experience rapid elimination of these hydrogens, provided a few other conditions are met.
The complex must have an open coordination site and an accessible, empty orbital on the metal center. The leaving group (–H) needs a place to land. Notice that after β-elimination, the metal has picked up one more ligand—it needs an empty spot for that ligand for elimination to occur. We can envision hydride “attacking” the empty orbital on the metal center as an important orbital interaction in this process.
The M–Cα and Cβ–H bonds must have the ability to align in a syn coplanar arrangement. By “syn coplanar” we mean that all four atoms are in a plane and that the M–Cα and Cβ–H bonds are on the same side of the Cα–Cβ bond (a dihedral angle of 0°). You can see that conformation in the figure above. In the syn coplanar arrangement, the C–H bond departing from the ligand is optimally lined up with the empty orbital on the metal center. Hindered or cyclic complexes that cannot achieve this conformation do not undergo β-hydride elimination. The need for a syn coplanar conformation has important implications for eliminations that may establish diastereomeric olefins: β-elimination is stereospecific. One diastereomer leads to the (E)-olefin, and the other leads to the (Z)-olefin.
β-elimination is stereospecific. One diastereomer of reactant leads to the (Z)-olefin and the other to the (E)-olefin.
The complex must possess 16 or fewer total electrons. Examine the first figure one more time—notice that the total electron count of the complex increases by 2 during β-hydride elimination. Complexes with 18 total electrons don’t undergo β-elimination because the product would end up with 20 total electrons. Of course, dissociation of a loose ligand can produce a 16-electron complex pretty easily, so watch out for ligand dissociation when considering the possibility of β-elimination in a complex. Ligand dissociation may be reversible, but β-Hydride elimination is almost always irreversible.
The metal must bear at least 2 d electrons. Now this seems a bit strange, as the metal has served as nothing but an empty bin for electrons in our discussion so far. Why would the metal center need electrons for β-hydride elimination to occur? The answer lies in an old friend: backbonding. The σ C–H → M orbital interaction mentioned above is not enough to promote elimination on its own; an M → σ* C–H interaction is also required! I’ve said it before, and I’ll say it again: backbonding is everywhere in organometallic chemistry. If you can understand and articulate it, you’ll blow your instructor’s mind.
Other β-Elimination Reactions
The leaving group does not need to be hydrogen, of course, and a number of more electronegative groups come to mind as better candidates for leaving groups. β-Alkoxy and β-amino eliminations are usually thermodynamically favored thanks to the formation of strong M–O and M–N bonds, respectively. These reactions are so favored in β-alkoxyalkyl “complexes” of alkali and alkaline earth metals (R–Li, R–MgBr, etc.) that using these as σ-nucleophiles at carbon is untenable. Such compounds eliminate immediately upon their formation. I had an organic synthesis professor in undergrad who was obsessed with this—using a β-alkoxyalkyl lithium or β-alkoxyalkyl Grignard reagent in a synthesis was a recipe for red ink. β-Haloalkyls were naturally off limits too.
Watch out…these are not stable compounds!
The atom bound to the metal doesn’t have to be carbon. β-Elimination of alkoxy ligands affords ketones or aldehydes bound at oxygen or through the C=O π bond (this step is important in many transfer hydrogenations, and an analogous process occurs in the Oppenauer oxidation). Amido ligands can undergo β-elimination to afford complexes of imines; however, this process tends to be slower than β-alkoxy elimination.
β-Elimination helps transfer the elements of dihydrogen from one organic compound to another.
Incidentally, I haven’t seen any examples in which the β atom is not carbon, but would be interested if anyone knows of an example!
Applications of β-Eliminations
As with many concepts in organometallic chemistry, there are two ways to think about applications of β-elimination. One can take either the “inorganic” perspective, which focuses on the metal center, or the “organic” perspective, which focuses on the ligands.
With the metal center in focus, we can recognize that β-hydride elimination has the wonderful side effect of establishing an M–H bond—a feat generally difficult to achieve in a selective manner via oxidative addition of X–H. If the ligand from which the hydrogen came displaced something more electronegative, the whole process represents reduction at the metal center. For example, imagine rhodium(III) chloride is mixed with sodium isopropoxide, NaOCH(CH3)2. The isopropoxide easily displaces chloride, and subsequent β-hydride elimination affords a rhodium hydride, formally reduced with respect to the chloride starting material. See p. 236 of this review for more.
With the ligand in focus, we see that the organic ligand is oxidized in the course of β-hydride elimination. Notice that the metal is reduced and the ligand oxidized! A π bond replaces a σ bond in the ligand, and if the conditions are right, this represents a bona fide oxidation (as opposed to a mere elimination). For example, oxidative addition into a C–H bond followed by β-hydride elimination at a C–H bond next door sets up an alkene where two adjacent C–H bonds existed before, an oxidation process. These dehydrogenation reactions are incredibly appealing in a theoretical sense, but still at an early stage when it comes to scope and practicality.
Summary
We already encountered β-hydride elimination in an earlier series of posts on metal alkyl complexes, where we noted that it’s a very common decomposition pathway for metal alkyls. β-Hydride elimination isn’t all bad, however, as it can be an important step in catalytic reactions that result in the oxidation of organic substrates (dehydrogenations and transfer hydrogenations) and in reactions that reduce metal halides to metal hydrides. The general idea of β-elimination involves the transfer of a leaving group from a ligand to the metal center with simultaneous formation of a π bond in the ligand. β-Elimination requires an open coordination site and at least two d electrons on the metal center, and eliminations of chiral complexes are stereospecific. The leaving group is commonly hydrogen, but need not be—the more electronegative the leaving group, the more favorable the elimination. Stronger π bonds in the product also encourage β-elimination, so eliminations that form carbonyl compounds or imines are common.
In the next post, we’ll explore other types of organometallic elimination reactions, which establish π bonds at different positions in metal alkyl or other complexes. α-Eliminations, for example, establish metal-carbon, -oxygen, or -nitrogen multiple bonds, which are generally difficult to forge through other means | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/04%3A_Fundamentals_of_Organometallic_Chemistry/4.01%3A_-Elimination_Reactions.txt |
Despite the sanctity of the 18-electron rule to many students of organometallic chemistry, a wide variety of stable complexes possess fewer than 18 total electrons at the metal center. Perhaps the most famous examples of these complexes are 14- and 16-electron complexes of group 10 metals involved in cross-coupling reactions.
Ligand substitution in complexes of this class typically occurs via an associative mechanism, involving approach of the incoming ligand to the complex before departure of the leaving group. If we keep this principle in mind, it seems easy enough to predict when ligand substitution is likely to be associative. But how can we spot an associative mechanism in experimental data, and what are some of the consequences of this mechanism?
The prototypical mechanism of associative ligand substitution. The first step is rate-determining. A typical mechanism for associative ligand substitution is shown above. It should be noted that square pyramidal geometry is also possible for the intermediate, but is less common. Let’s begin with the kinetics of the reaction.
Reaction Kinetics
Reaction kinetics are commonly used to elucidate organometallic reaction mechanisms, and ligand substitution is no exception. Different mechanisms of substitution may follow different rate laws, so plotting the dependence of reaction rate on concentration often allows us to distinguish mechanisms. Associative substitution’s rate law is analogous to that of the SN2 reaction—rate depends on the concentrations of both starting materials.
\[ L_nM–L^d + L_i → L_nM–L_i + L^d \]
\[ \dfrac{d[L_nM–L^i]}{dt} = rate = k_1[L_nM–L^d][L^i] \]
The easiest way to determine this rate law is to use pseudo-first-order conditions. Although the rate law is second order overall, if we could somehow render the concentration of the incoming ligand unchanging, the reaction would appear first order. The observed rate constant under these conditions reflects the constancy of the incoming ligand’s concentration (\(k_{obs} = k_1[L^i]\), where both \(k_1\) and \([Li]\) are constants). How can we make the concentration of the incoming ligand invariant, you ask? We can drown the reaction in ligand to achieve this. The teensy weensy bit actually used up in the reaction has a negligible effect on the concentration of the “sea” of starting ligand we began with. The observed rate is equal to \(k_{obs}[L_nM–L^d]\), as shown by the purple trace below. By determining \(k_{obs}\) at a variety of \([L^i]\) values, we can finally isolate \(k_1\), the rate constant for the slow step. The red trace below at right shows the idea.
Associative substitution under pseudo-first-order conditions. The reaction is “swamped out” with incoming ligand.
In many cases, the red trace ends up with a non-zero y-intercept…curious, if we limit ourselves to the simple mechanism shown in the first figure of this post. A non-zero intercept suggests a more complex mechanism. We need to add a new term (called \(k_s\) for reasons to become clear shortly) to our first set of equations:
\[rate = (k_1[L_i] + k_s)[L_nM–L^d]\]
\[k_{obs} = k_1[L_i] + k_s\]
The full rate law suggests that some other step (with rate ks[LnM–Ld]) independent of incoming ligand is involved in the mechanism. To explain this observation, we can invoke the solvent as a reactant. Solvent can associate with the complex first in a slow step, then incoming ligand can displace the solvent in a fast step. Solvent concentration doesn’t enter the rate law because, well, it’s drowning the reactants and its concentration undergoes negligible change! An example of this mechanism in the context of Pt(II) chemistry is shown below.
Associative substitution with solvent participation—a head-scratching mechanism for many an organometallic grad student!
As an aside, it’s worth mentioning that the entropy of activation of associative substitution is typically negative. Entropy decreases as the incoming ligand and complex come together in the rate-determining step. Dissociative substitution shows the opposite behavior: loss of the departing ligand in the RDS increases entropy, resulting in positive entropy of activation.
Stereochemistry of Substitution
As we saw in discussions of the trans effect, the entering and departing ligands both occupy equatorial positions in the trigonal bipyramidal intermediate. Microscopic reversibility is to blame: the mechanism of the forward substitution (displacement of the leaving by the incoming ligand) must be the same as the mechanism of the reverse reaction (displacement of the incoming by the leaving ligand). This can be a confusing point, so let’s examine an alternative mechanism that violates microscopic reversibility.
A mechanism involving approach to an axial position and departure from an equatorial position violates microscopic reversibility. Forward and reverse reactions a and b differ!
The figure above shows why a mechanism involving axial approach and equatorial departure (or vice versa) is not possible. The forward and reverse reactions differ, in fact, in both steps. In forward mechanism a, the incoming ligand enters an axial site. But in the reverse reaction, the incoming ligand (viz., the departing ligand in mechanism a) sits on an equatorial site. The second steps of each mechanism differ too—a involves loss of an equatorial ligand, while b involves loss of an axial ligand. Long story short, this mechanism violates microscopic reversibility. And what about a mechanism involving axial approach and axial departure? Such a mechanism is unlikely on electronic grounds. The equatorial sites are more electron rich than the axial sites, and σ bonding to the axial \(d_{z^2}\) orbital is expected to be strong. Intuitively, then, loss of ligand from an axial site is less favorable than loss from an equatorial site.
I know what you’re thinking: what the heck does all of this have to do with stereochemistry? Notice that, in the equatorial-equatorial mechanism (first figure of this post), the axial ligands don’t move at all. The configuration of the starting complex is thus retained in the product. Although retention is “normal,” complications often arise because five-coordinate TBP complexes—like other odd-coordinate organometallic complexes—are often fluxional. Axial and equatorial ligands can rapidly exchange through a process called Berry pseudorotation, which resembles the axial ligands “cutting through” a pair of equatorial ligands like scissors (animation!). Fluxionality means that all stereochemical bets are off, since any ligand can feasibly occupy an equatorial site. In the example below, the departing ligand starts out cis to L, but the incoming ligand ends up trans to L.
Berry pseudorotation in the midst of associative ligand substitution.
Associative Substitution in 18-electron Complexes?
Associative substitution can occur in 18-electron complexes if it’s preceded by the dissociation of a ligand. For example, changes in the hapticity of cyclopentadienyl or indenyl ligands may open up a coordination site, which can be occupied by a new ligand to kick off associative substitution. An allyl ligand may convert from its π to σ form, leaving an open coordination site where the π bond left. A particularly interesting case is the nitrosyl ligand—conversion from its linear to bent form opens up a site for coordination of an external ligand.
Summary
Associative ligand substitution is common for complexes with 16 total electrons or fewer. The reaction is characterized by a second-order rate law, the possibility of solvent participation, and a trigonal bipyramidal intermediate that is often fluxional. An open coordination site is essential for associative substitution, but such sites are often hidden in the dynamism of 18-electron complexes with labile ligands. | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/04%3A_Fundamentals_of_Organometallic_Chemistry/4.02%3A_Associative_Ligand_Substitution.txt |
Associative substitution is unlikely for saturated, 18-electron complexes—coordination of another ligand would produce a 20-electron intermediate. For 18-electron complexes, dissociative substitution mechanisms involving 16-electron intermediates are more likely. In a slow step with positive entropy of activation, the departing ligand leaves, generating a coordinatively unsaturated intermediate. The incoming ligand then enters the coordination sphere of the metal to generate the product. For the remainder of this post, we’ll focus on the kinetics of the reaction and the nature of the unsaturated intermediate (which influences the stereochemistry of the reaction). The reverse of the first step, re-coordination of the departing ligand (rate constant k–1), is often competitive with dissociation.
A general scheme for dissociative ligand substitution. There’s more to the intermediate than meets the eye!
Reaction Kinetics
Let’s begin with the general situation in which $k_1$ and $k_{–1}$ are similar in magnitude. Since $k_1$ is rate limiting, $k_2$ is assumed to be much larger than $k_1$ and $k_{–1}$. Most importantly, we need to assume that variation in the concentration of the unsaturated intermediate is essentially zero. This is called the steady state approximation, and it allows us to set up an equation that relates reaction rate to observable concentrations Hold onto that for a second; first, we can use step 2 to establish a preliminary rate expression.
$\text{rate} = k_2[L_nM–◊][Li] \tag{1}$
Of course, the unsaturated complex is present in very small concentration and is unmeasurable, so this equation doesn’t help us much. We need to remove the concentration of the unmeasurable intermediate from (1), and the steady state approximation helps us do this. We can express variation in the concentration of the unsaturated intermediate as (processes that make it) minus (processes that destroy it), multiplying by an arbitrary time length to make the units work out. All of that equals zero, according to the SS approximation. The painful math is almost over! Since Δt must not be zero, the other factor, the collection of terms, must equal zero.
$Δ[LnM–◊] = 0 = (k1[LnM–L^d] – k–1[LnM–◊][L^d] – k_2[LnM–◊][Li])Δt \tag{2}$
$0 = k_1[LnM–Ld] – k_{-1}[LnM–◊][Ld] – k_2[LnM–◊][Li] \tag{3}$
Rearranging to solve for [LnM–◊], we arrive at the following.
$[LnM–◊] = k_1 \dfrac{[LnM–L_d]}{(k_{-1}[L_d] + k_2[Li]} \tag{4}$
Finally, substituting into equation (1) we reach a verifiable rate equation.
$\text{rate} = k_2k_1 \dfrac{[LnM–Ld][Li]}{(k_{-1}[L_d] + k_2[Li]} \tag{5}$
When $k_{–1}$ is negligibly small, (5) reduces to the familiar equation (6), typical of dissociative reactions like SN1.
$\text{rate} = k_1[LnM–L_d] \tag{6}$
Unlike the associative rate law, this rate does not depend on the concentration of incoming ligand. For reactions that are better described by (5), we can drown the reaction in incoming ligand to make $k_2[Li]$ far greater than $k_{-1}[Ld]$, essentially forcing the reaction to fit equation (6).
The Unsaturated Intermediate & Stereochemistry
Dissociation of a ligand from an octahedral complex generates an usaturated ML5 intermediate. When all five of the remaining ligands are L-type, as in Cr(CO)5, the metal has 6 d electrons for a total electron count of 16. The trigonal bipyramidal geometry presents electronic problems (unpaired electrons) for 6 d electrons, as the figure below shows. The orbital energy levels come from crystal field theory. Distortion to a square pyramid or a distorted TBP geometry removes the electronic issue, and so five-coordinate d6 complexes typically have square pyramidal or distorted TBP geometries. This is just the geometry prediction process in action!
TBP geometry is electronically disfavored for d6 metals. Distorted TBP and SP geometries are favored.
When the intermediate adopts square pyramidal geometry (favored for good π-acceptors and σ-donors…why?), the incoming ligand can simply approach where the departing ligand left, resulting in retention of stereochemistry. Inversion is more likely when the intermediate is a distorted trigonal bipyramid (favored for good π-donors). As we’ve already seen for associative substitution, fluxionality in the five-coordinate intermediate can complicate the stereochemistry of the reaction.
Encouraging Dissocative Substitution
In general, introducing structural features that either stabilize the unsaturated intermediate or destabilize the starting complex can encourage dissociative substitution. Both of these strategies lower the activation barrier for the reaction. Other, quirky ways to encourage dissociation include photochemical methods, oxidation/reduction, and ligand abstraction.
Let’s begin with features that stabilize the unsaturated intermediate. Electronically, the intermediate loves it when its d electron count is nicely matched to its crystal field orbitals. As you study organometallic chemistry, you’ll learn that there are certain “natural” d electron counts for particular geometries that fit well with the metal-centered orbitals predicted by crystal field theory. Octahedral geometry is great for six d electrons, for example, and square planar geometry loves eight d electrons. Complexes with “natural” d electron counts—but bearing one extra ligand—are ripe for dissociative substitution. The classic examples are d8 TBP complexes, which become d8 square planar complexes (think Pt(II) and Pd(II)) upon dissociation. Similar factors actually stabilize starting 18-electron complexes, making them less reactive in dissociative substitution reactions. d6 octahedral complexes are particularly happy, and react most slowly in dissociative substitutions. The three most common types of 18-electron complexes, from fastest to slowest at dissociative substitution, are:
d8 TBP > d10 tetrahedral > d6 octahedral
Destabilization of the starting complex is commonly accomplished by adding steric bulk to its ligands. Naturally, dissociation relieves steric congestion in the starting complex. Chelation has the opposite effect, and tends to steel the starting complex against dissociation.
As steric bulk on the ligand increases, dissociation becomes more favorable.
I plan to cover the “quirky” methods in a post of their own, but these include strategies like N-oxides for CO removal, photochemical cleavage of the metal–departing ligand bond, and the use of silver cation to abstract halide ligands. Oxidation and reduction can also be used to encourage substitution: 17- and 19-electron complexes are much more reactive toward substitution than their 18-electron analogues.
4.04: Ligand substitution
Ligand substitution is the first reaction one typically encounters in an organometallic chemistry course. In general, ligand substitution involves the exchange of one ligand for another, with no change in oxidation state at the metal center. The incoming and outgoing ligands may be L- or X-type, but the charge of the complex changes if the ligand type changes. Keep charge conservation in mind when writing out ligand substitutions.
How do we know when a ligand substitution reaction is favorable? The thermodynamics of the reaction depend on the relative strength of the two metal-ligand bonds, and the stability of the departing and incoming ligands (or salt sof the ligand, if they’re X type). It’s often useful to think of X-for-X substitutions like acid-base reactions, with the metal and spectator ligands serving as a “glorified proton.” Like acid-base equilibria in organic chemistry, we look to the relative stability of the two charged species (the free ligands) to draw conclusions. Of course, we don’t necessarily need to rely just on primal thermodynamics to drive ligand substitution reactions. Photochemistry, neighboring-group participation, and other tools can facilitate otherwise difficult substitutions.
Ligand substitution is characterized by a continuum of mechanisms bound by associative (A) and dissociative (D) extremes. At the associative extreme, the incoming ligand first forms a bond to the metal, then the departing ligand takes its lone pair and leaves. At the dissociative extreme, the order of events is opposite—the departing ligand leaves, then the incoming ligand comes in. Associative substitution is common for 16-electron complexes (like d8 complexes of Ni, Pd, and Pt), while dissociative substitution is the norm for 18-electron complexes. Then again, reality is often more complicated than these extremes. In some cases, evidence is available for simultaneous dissociation and association, and this mechanism has been given the name interchange (IA or ID).
Over the next few posts, we’ll explore ligand substitution reactions and mechanisms in detail. We’d like to be able to (a) predict whether a mechanism is likely to be associative or dissociative; (b) propose a reasonable mechanism from given experimental data; and (c) describe the results we’d expect given a particular mechanism. Keep these goals in mind as you learn the theoretical and experimental nuts and bolts of substitution reactions. | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/04%3A_Fundamentals_of_Organometallic_Chemistry/4.03%3A_Dissociative_Ligand_Substitution_Reactions.txt |
Insertions of π systems into M-X bonds are appealing in the sense that they establish two new σ bonds in one step, in a stereocontrolled manner. As we saw in the last post, however, we should take care to distinguish these fully intramolecular migratory insertions from intermolecular attack of a nucleophile or electrophile on a coordinated π-system ligand. The reverse reaction of migratory insertion, β-elimination, is not the same as the reverse of nucleophilic or electrophilic attack on a coordinated π system.
1,2-Insertion is distinct from nucleophilic/electrophilic attack on coordinated ligands.
Like 1,1-insertions, 1,2-insertions generate a vacant site on the metal, which is usually filled by external ligand. For unsymmetrical alkenes, it’s important to think about site selectivity: which atom of the alkene will end up bound to metal, and which to the other ligand? To make predictions about site selectivity we can appeal to the classic picture of the M–X bond as M+X–. Asymmetric, polarized π ligands contain one atom with excess partial charge; this atom hooks up with the complementary atom in the M–R bond during insertion. Resonance is our best friend here!
The site selectivity of 1,2-insertion can be predicted using resonance forms and partial charges.
A nice study by Yu and Spencer illustrates these effects in homogeneous palladium- and rhodium-catalyzed hydrogenation reactions. Unactivated alkenes generally exhibit lower site selectivity than activated ones, although steric differences between the two ends of the double bond can promote selectivity.
Reactivity Trends in 1,2-Insertions
The thermodynamics of 1,2-insertions of alkenes depend strongly on the alkene, but we can gain great insight by examining the structure of the product alkyl. Coordinated alkenes that give strong metal-alkyl bonds after migratory insertion tend to undergo the process. Hence, electron-withdrawing groups, such as carbonyls and fluorine atoms, tend to encourage migratory insertion—remember that alkyl complexes bearing these groups tend to have stable M–C bonds.
Insertions of alkenes into both M–H and M–R (R = alkyl) are favored thermodynamically, but the kinetics of M–R insertion are much slower. This observation reflects a pervasive trend in organometallic chemistry: M–H bonds react more rapidly than M–R bonds. The same is true of the reverse, β-elimination. Even in cases when both hydride and alkyl elimination are thermodynamically favored, β-hydride elimination is much faster. Although insertion into M–R is relatively slow, this elementary step is critical for olefin polymerizations that form polyalkenes (Ziegler-Natta polymerization). This reaction deserves a post all its own!
As the strength of the M–X bond increases, the likelihood that an L-type π ligand will insert into the bond goes down. Hence, while insertions into M–H and M–C are relatively common, insertions into M–N and M–O bonds are more rare. Lanthanides and palladium are known to promote insertion into M–N in some cases, but products with identical connectivity can come from external attack of nitrogen on a coordinated π ligand. The diastereoselectivity of these reactions provides mechanistic insight—since migratory insertion is syn (see below), a syn relationship between Pd and N is to be expected in the products of migratory insertion. An anti relationship indicates external attack by nitrogen or oxygen.
The diastereoselectivity of formal insertions provides insight about their mechanisms.
Stereochemistry of 1,2-Insertions
1,2-Insertion may establish two stereocenters at once, so the stereochemistry of the process is critical! Furthermore, 1,2-insertions and β-eliminations are bound by important stereoelectronic requirements. An analogy can be made to the E2 elimination of organic chemistry, which also has strict stereoelectronic demands. For migratory insertion to proceed, the alkene and X-type ligand must be syncoplanar during insertion; as a consequence of this alignment, X and MLn end up on the same face of the alkene after insertion. In other words, insertions into alkenes take place in a syn fashion. Complexes that have difficulty achieving a coplanar arrangement of C=C and M–X undergo insertion very slowly, if at all.
1,2-Insertions take place in a syn fashion. The metal and X end up bound to the same face of the alkene.
This observation has important implications for β-elimination, too—the eliminating X and the metal must have the ability to align syn.
Insertions of Other π Systems
To close this post, let’s examine insertions into π ligands other than alkenes briefly. Insertions of alkynes into metal-hydride bonds are known, and are sometimes involved in reactions that I refer to collectively as “hydrostuffylation”: hydrosilylation, hydroesterification, hydrogenation, and other net H–X additions across the π bond. Strangely, some insertions of alkynes yield trans products, even though cis products are to be expected from syn addition of M–X. The mechanisms of these processes involve initial syn addition followed by isomerization to the trans complex via an interesting resonance form. The cis complex is the kinetic product, but it isomerizes over time to the more thermodynamically stable trans complex.
Migratory insertions of alkynes into M–H produce alkenyl complexes, which have been known to isomerize.
The strongly donating Cp* ligand supports the legitimacy of the zwitterionic resonance form—and suggests that the C=C bond may be weaker than it first appears!
Polyenes can participate in migratory insertion, and insertions of polyenes are usually quite favored because stabilized π-allyl complexes result. In one mind-bending case, a coordinated arene inserts into an M–Me bond in a syn fashion!
Have you ever stopped to consider that the addition of methyllithium to an aldehyde is a formal insertion of the carbonyl group into the Li–Me bond? It’s true! We can think of these as (very) early-metal “insertion” reactions. Despite this precedent, migratory insertion reactions of carbonyls and imines into late-metal hydride and alkyl bonds are surprisingly hard to come by. Rhodium is the most famous metal that can make this happen—rhodium has been used in complexes for arylation and vinylation, for example. Insertion of X=C into the M–R bond is usually followed by β-hydride elimination, which has the nifty effect of replacing H in aldehydes and aldimines with an aryl or vinyl group. | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/04%3A_Fundamentals_of_Organometallic_Chemistry/4.05%3A_Migratory_Insertion-_12-Insertions.txt |
Introduction
We’ve seen that the metal-ligand bond is generally polarized toward the ligand, making it nucleophilic. When a nucleophilic, X-type ligand is positioned cis to an unsaturated ligand in an organometallic complex, an interesting process that looks a bit like nucleophilic addition can occur.
On the whole, the unsaturated ligand appears to insert itself into the M–X bond; hence, the process is called migratory insertion. An open coordination site shows up in the complex, and is typically filled by an added ligand. The open site may appear where the unsaturated ligand was or where the X-type ligand was, depending on which group actually moved (see below). There is no change in oxidation state at the metal (unless the ligand is an alkylidene/alkylidyne), but the total electron count of the complex decreases by two during the actual insertion event—notice in the above example that the complex goes from 18 to 16 total electrons after insertion. A dative ligand comes in to fill that empty coordination site, but stay flexible here: L could be a totally different ligand or a Lewis base in the X-type ligand. L can even be the carbonyl oxygen itself!
We can distinguish between two types of insertions, which differ in the number of atoms in the unsaturated ligand involved in the step. Insertions of CO, carbenes, and other η1 unsaturated ligands are called 1,1-insertions because the X-type ligand moves from its current location on the metal to one spot over, on the atom bound to the metal. η2 ligands like alkenes and alkynes can also participate in migratory insertion; these reactions are called 1,2-insertions because the X-type ligand slides two atoms over, from the metal to the distal atom of the unsaturated ligand.
This is really starting to look like the addition of M and X across a π bond! However, we should take care to distinguish this completely intramolecular process from the attack of a nucleophile or electrophile on a coordinated π system, which is a different beast altogether. Confusingly, chemists often jumble up all of these processes using words like “hydrometalation,” “carbometalation,” “aminometalation,” etc. Another case of big words being used to obscure ignorance! We’ll look at nucleophilic and electrophilic attack on coordinated ligands in separate posts.
Reactivity Trends in CO Insertions
Certain conditions must be met for migratory insertion to occur: the two ligands undergoing the process must be cis, and the complex must be stable with two fewer total electrons. Thermodynamically, the formed Y–X and covalent M–Y bonds must be more stable than the broken M–X and dative M–Y bonds for insertion to be favored. When the opposite is true, the microscopic reverse (elimination or deinsertion) will occur spontaneously.
Migratory aptitudes for insertion into CO have been studied extensively, and the general conclusion here is “it’s complicated.” A few ligands characterized by remarkably stable metal-ligand bonds don’t undergo insertion for thermodynamic reasons—the M–X bond is just too darn strong. Perfluoroalkyl complexes and metal hydrides are two notable examples. Electron-withdrawing groups on the X-type ligand, which strengthen the M–X bond, slow down insertion (likely for thermodynamic reasons though…Hammond’s postulate in action).
What factors affect the relative speed (kinetics) of favorable insertions? Sterics is one important variable. Both 1,1- and 1,2-insertions can relieve steric strain at the metal center by spreading out the ligands involved in the step. In 1,2-insertions, the X-type ligand removes itself completely from the metal! Unsurprisingly, then, bulky ligands undergo insertions more rapidly than smaller ligands. Complexes of the first-row metals tend to react more rapidly than analogous second-row metal complexes, and second-row metal complexes react faster than third-row metal complexes. This trend fits in nicely with the typical trend in M–C bond strengths: first row < second row < third row. Lewis acids help accelerate insertions into CO by coordinating to CO and making the carbonyl carbon more electrophilic. For a similar reason, CO ligands bound to electron-poor metal centers undergo insertion more rapidly than CO’s bound to electron-rich metals. Finally, for reasons that are still unclear, one-electron oxidation often increases the rate of CO insertion substantially.
Although the thermodynamics of alkene 1,2-insertion are more favorable for metal-carbon than metal-hydrogen bonds, M–H bonds react much more rapidly than M–C bonds in 1,2-insertions. This fact has been exploited for olefin hydrogenation, which would be much less useful if it had to complete with olefin polymerization (the result of repeated insertion of C=C into M–C) in the same reaction flask! More on that in the next post.
Stereochemistry in CO Insertions
Migratory insertion steps are full of stereochemistry! Configuration at the migrating alkyl group is retainedduring insertion—a nice piece of evidence supporting a concerted, intramolecular mechanism of migration.
What about stereochemistry at the metal center? Migratory insertion may create a stereogenic center at the metal—see the iron example above. Whether the X-type ligand moves onto the unsaturated ligand or vice versa will impact the configuration of the product complex. Calderazzo’s study of this issue is one of my favorite experiments in all of organometallic chemistry! He took the simple labeled substrate in the figure below and treated it with dative ligand, encouraging insertion. Four products of insertion are possible, corresponding to reaction of the four CO ligands cis to the methyl ligand. Try drawing a few curved arrows to wrap your mind around the four possibilities, and consider both CO migration and Me migration as possible at this point.
Note that product D is impossible if we only allow the Me group to migrate—the spot trans to the labeled CO is another CO ligand, so that spot can only pick up L if CO migrates (not if Me migrates). On the other hand, product C must have come from the migration of Me, since the Me group has moved from a cis to a transposition relative to the labeled CO in product C. Calderazzo observed products AB, and C, but not D, supporting a mechanism involving Me migration. Other experiments since support the idea that most of the time, the alkyl group migrates onto CO. Slick, huh?
I won’t address insertions into alkylidenes, alkylidynes, and other one-atom unsaturated ligands in this post, as insertions into CO are by far the most popular 1,1 insertions in organometallic chemistry. In the next post, we’ll dig more deeply into 1,2-insertions of alkenes and alkynes. Thanks for reading! | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/04%3A_Fundamentals_of_Organometallic_Chemistry/4.06%3A_Migratory_Insertion-_Introduction_and_CO_Insertions.txt |
A critical difference between the transition metals and the organic elements is the ability of the former to exist in multiple oxidation states. In fact, the redox flexibility of the transition metals and the redox obstinacy of the organic elements work wonderfully together. Why? Imagine the transition metal as a kind of matchmaker for the organic elements. Transition metals can take on additional covalent bonds (oxidation), switch out ligands (substitution), then release new covalent bonds (reduction). The resulting organic products remain unfazed by the metal’s redox insanity. Talk about a match made in heaven!
The following series of posts will deal with the first step of this process, oxidation. More specifically, we’ll discuss the oxidation of transition metals via formal insertion into covalent bonds, also known as oxidative addition (OA). Although we often think of oxidative addition as an elementary reaction of organometallic chemistry, it is not an elementary mechanistic step. In fact, oxidative addition can proceed through a variety of mechanisms. Furthermore, any old change in oxidation state does not an oxidative addition make (that almost rhymes…). Formally, the attachment of an electrophile to a metal center (e.g., protonation) represents oxidation, but we shouldn’t call this oxidative addition, since two ligands aren’t entering the fray. Instead, we call this oxidative ligation (OL).
Protonation is (formally) a kind of oxidation. Who knew?! SN2 reactions with the metal as nucleophile are also oxidative ligations. Of course, if the leaving group comes back and forms a new bond to the metal, we’re back to oxidative addition. Both reactions lead to an increase in the oxidation state of the metal by two units and a decrease in the d electron count of the metal by two electrons. However, note how the total electron count changes in each case. The total electron count does not change during an oxidative ligation. Think of it this way: the new ligand brings no electrons with it to the complex. On the other hand, the total electron count of the complex actually increases by two electrons during oxidative addition. As a result, eighteen-electron complexes do not undergo oxidative addition. Carve that sucker on a stone tablet. Seventeen-electron complexes can undergo oxidative addition via bimolecular OA reactions, which leave X on one metal center and Y on another.
What are the mechanisms of oxidative addition, anyway? Let’s begin with the “concerted” mechanism, which can be thought of as σ-complex formation followed by insertion. The metal first sidles up to the X–Y bond and a σ complex forms (ligand dissociation may be required first). As we’ve seen, σ complexes M(X2) are tautomeric with their M(X)2 forms. When back donation from the metal is strong enough, the σ complex disappears and M(X)2 is all that remains. The metal has been formally oxidized: oxidative addition!
There are several variations on this theme. When X and Y are different, the σ complex is skewed and approach to the metal “asynchronous.” When the metal isn’t a great nucleophile, the reaction may stop at the σ-complex stage.
Other mechanisms of oxidative addition require multiple steps and the formation of polar or radical intermediates. An important two-step, polar mechanism involves SN2 attack of a nucleophilic metal on an electrophile, followed by coordination of the leaving group to the metal center. What we might call SN1-type mechanisms, involving dissociation of the electrophile before nucleophilic attack by the metal, also occur (HCl and other strong acids operate like this). Finally, both non-chain and chain radical mechanisms are possible in reactions of metal complexes with alkyl halides. We’ll dive into these mechanisms in more detail in upcoming posts.
Hopefully from this general discussion, you’ve gleaned a few trends. The metal must have a stable oxidation state two units higher than its current OS for oxidative addition to occur. For the reaction to work well, the metal typically needs to be electron rich (and in a relatively low oxidation state) and the organic compound needs to be electron poor. To see why, consider that during oxidative addition, the metal formally loses two delectrons. Furthermore, the main-group atoms X and Y gain electron density, since the new M–X and M–Y bonds are likely polarized toward X and Y. The metal needs to bear two open coordination sites (not necessarily at the same time) for oxidative addition to occur, because two new ligands enter the metal’s coordination sphere. Since the new ligands need space, steric hindrance tends to discourage oxidative addition. Oftentimes ligand dissociation is required before oxidative addition can occur; in many of these cases, the rate of dissociation influences the overall rate of the reaction. | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/04%3A_Fundamentals_of_Organometallic_Chemistry/4.07%3A_Oxidative_Addition-_General_Ideas.txt |
How important are oxidative additions of non-polar reagents? Very. The addition of dihydrogen (H2) is an important step in catalytic hydrogenation reactions. Organometallic C–H activations depend on oxidative additions of C–H bonds. In a fundamental sense, oxidative additions of non-polar organic compounds are commonly used to establish critical metal-carbon bonds. Non-polar oxidative additions get the ball rolling in all kinds of catalytic organometallic reactions. In this post, we’ll examine the mechanisms and important trends associated with non-polar oxidative additions.
Oxidative Additions of H2
Electron-rich metal centers with open coordination sites (or the ability to form them) undergo oxidative additions with dihydrogen gas. The actual addition step is concerted, as we might expect from the dull H2molecule! However, before the addition step, some interesting gymnastics are going on. The status of the σ complex that forms prior to H–H insertion is an open question—for some reactions it is a transition state, others a discrete intermediate. In either case, the two new hydride ligands end up cis to one another. Subsequent isomerization may occur to give a trans dihydride.
There’s more to this little reaction than meets the eye. For starters, either pair of trans ligands in the starting complex (L/L or Cl/CO) may “fold back” to form the final octahedral complex. As in associative ligand substitution, the transition state for folding back is basically trigonal bipyramidal. As we saw before, π-acidic ligands love the equatorial sites of the TBP geometry, which are rich in electrons capable of π bonding. As a consequence, π-acidic ligands get folded back preferentially, and tend to end up cis to their trans partners in the starting complex.
Termolecular oxidative additions of H2, in which the two H atoms find their way to two different metal centers, are also known, but these suffer from entropic issues, since H2 is jammed between two metal complexes in the transition state of the (concerted) mechanism.
Oxidative Additions of Silanes (H–Si)
Silanes bearing Si–H bonds may react with organometallic complexes in oxidative addition reactions. Spectroscopic experiments support the intermediacy of a silyl σ complex before insertion. Since the mechanism is concerted, oxidative addition occurs with retention of configuration at Si. The usual pair of forward bonding (σSi–Hdσ) and backbonding (dπ→σ*Si–H) orbital interactions are at play here. File this reaction away as a great method for the synthesis of silyl complexes.
Oxidative Additions of C–H Bonds
Needless to say, oxidative addition reactions of C–H bonds are highly prized among organometallic chemists. As simple as it is to make silyl complexes through oxidative addition, analogous reactions of C–H bonds that yield alkyl hydride complexes are harder to come by.
The thermodynamics of C–H oxidative addition tell us whether it’s favorable, and depend heavily on the nature of the organometallic complex. The sum of the bond energies of the new M–C and M–H bonds must exceed the sum of the energies of the C–H bond and any M–L bonds broken during the reaction (plus, OA is entropically disfavored). For many complexes, the balance is not in favor of oxidative addition. For example, the square planar Vaska’s complex (L2(CO)IrCl; L = PPh3) seems like a great candidate for oxidative addition of methane—at least to the extent that the product will be six-coordinate and octahedral. However, thermodynamics is a problem:
104 (C–H) – [60 (Ir–H) + 35 (Ir–Me)] + 9 kcal/mol (entropy) = 18 kcal/mol
18 kcal/mol is prohibitively high in energy, and playing with the temperature to adjust the entropy factor can’t “save” the reaction.
More electron-rich complexes exhibit favorable thermodynamics for insertions of C–H bonds. The example below is so favorable (104 – [75 + 55] + 9 = –17 kcal/mol) that the product is a rock!
Arenes undergo C–H oxidative addition faster (and more favorably) than alkanes for several reasons. It seems likely that an intermediate arene π complex and/or C–H σ complex precede insertion, and these complexes ought to be more stable than alkyl σ complexes. In addition, metal-aryl bonds tend to be stronger than metal-alkyl bonds.
Your average organic compound is covered in C–H bonds. Thus, for C–H oxidative addition to be synthetically useful, we need to understand how to control the selectivity of the reaction. In most early studies, selectivity for insertion into primary C–H bonds was observed. It became apparent that primary alkyl complexes (viz., the observed products) are generally much more stable than secondary alkyl complexes, even though the corresponding primary and secondary σ complexes are comparable in energy. Steric factors are a likely culprit!
Naturally, other strategies for controlling selectivity in C–H “activations” have appeared; however, be aware that these may not involve oxidative addition. Lewis basic directing groups have been used with success to direct oxidative addition to a nearby C–H bond—but these reactions are aided by base and do not involve oxidation. Metal carbenoid insertions into C–H bonds also do not involve oxidation at the metal center. The lesson of these reactions: be careful, and don’t assume that all alkyl complexes are the result of C–H oxidative addition! | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/04%3A_Fundamentals_of_Organometallic_Chemistry/4.08%3A_Oxidative_Addition_of_Non-polar_Reagents.txt |
Organometallic chemistry has vastly expanded the practicing organic chemist’s notion of what makes a good nucleophile or electrophile. Pre-cross-coupling, for example, using unactivated aryl halides as electrophiles was largely a pipe dream (or possible only under certain specific circumstances). Enter the oxidative addition of polarized bonds: all of a sudden, compounds like bromobenzene started looking a lot more attractive as starting materials. Cross-coupling reactions involving sp2– and sp-hybridized C–X bonds beautifully complement the “classical” substitution reactions at sp3 electrophilic carbons. Oxidative addition of the C–X bond is the step that kicks off the magic of these methods. In this post, we’ll explore the mechanisms and favorability trends of oxidative additions of polar reagents. The landscape of mechanistic possibilities for polarized bonds is much more rich than in the non-polar case—concerted, ionic, and radical mechanisms have all been observed.
Concerted Mechanisms
Oxidative additions of aryl and alkenyl Csp2–X bonds, where X is a halogen or sulfonate, proceed through concerted mechanisms analogous to oxidative additions of dihydrogen. Reactions of N–H and O–H bonds in amines, alcohols, and water also appear to be concerted. A π complex involving η2-coordination is an intermediate in the mechanism of insertion into aryl halides at least, and probably vinyl halides too. As two open coordination sites are necessary for concerted oxidative addition, loss of a ligand from a saturated metal complex commonly precedes the actual oxidative addition event.
Trends in the reactivity of alkyl and aryl (pseudo)halides toward oxidative addition are some of the most famous in organometallic chemistry. Aryl iodides are most reactive, followed by bromides, tosylates, and chlorides. To counter the lower electrophilicity of aryl chlorides, electron-rich alkyl phosphine ligands may be used to accelerate reactions of aryl chlorides. These “hot” ligands increase electron density at the metal center, facilitating oxidative addition. Because they tend to be bulkier than aryl phosphines, though, complexes of alkyl phosphines sometimes operate through slightly different mechanisms than aryl phosphine complexes. Although the exact species undergoing oxidative addition may differ (see below), all of the actual oxidative addition events are thought to be concerted.
Here, as we’ve seen before, electron-rich organohalides react more slowly than electron-poor compounds. Oxidative addition depletes electron density from the metal center and increases electron density in the organic ligands, so this trend makes sense!
SN2 and Ionic Mechanisms
Very electrophilic halides often react through ionic mechanisms in which oxidative addition per setakes place over multiple steps. As strange as it may be to imagine a metal center as a nucleophile, this exact reactivity is central to the SN2 and ionic mechanisms of oxidative addition. In a slow step, the metal center attacks the electrophilic atom, displacing halide. Rapid recombination of the positively charged metal complex and negative halide ion yields the product of oxidative addition. In essence, this mechanism involves oxidative ligation followed by association of oppositely charged ions. Loss of a dative ligand is sometimes necessary as an intermediate step, if the metal complex is saturated after the SN2 step.
An extremely solid analogy can be drawn between these reactions and classical SN2 reactions from “sophomore organic” chemistry. Primary halides react most quickly, followed by secondary and tertiary halides. Inversion at carbon is observable in these reactions, and entropy of activation is negative (suggesting an associated transition state). Negatively charged metal complexes kick butt in these reactions, and as electron-withdrawing ligands are added to the metal center, reactivity decreases. Added halide anions can actually accelerate SN2 oxidative additions—the anion coordinates to the metal center, making it negative and increasing its electron-donating power.
A nice analogy can also be drawn between SN2-type oxidative additions and oxidative additions of strong acids, which occur basically through the same mechanism (with replacement of hydrogen for carbon). During these so-called “ionic mechanisms,” protonation of the metal center usually occurs first, followed by ligand substitution or simple coordination of the conjugate base. In rarer circumstances and for less nucleophilic metal complexes, coordination of the conjugate base can actually occur first, followed by protonation!
Radical Mechanisms
Radicals are sometimes thought of as the bucking broncos of the chemistry world, and as such, radical mechanisms for oxidative additions are more difficult to control and less appealing. For example, one must be careful to use solvents that don’t react with the intermediate radicals. Still, a considerable amount of effort has been directed at “taming the wild beast.” In some ways, radical reactions offer complementary selectivity to ionic and concerted mechanisms.
Non-chain radical mechanisms involve single-electron transfer from the metal complex to the organohalide, followed by recomination of the resulting radicals. The metallic and organic radicals, when stable, can even be isolated from the reaction as products.
PtL2 + RX → PtL2X· + R· +
PtL2X· + R· → PtL2XR
Reactivity trends here depend on the stability of the intermediate radical species. Tertiary halides react most rapidly, followed by secondary and primary halides. More electron-rich metal centers react more rapidly (are you sick of this trend yet?), since they can more easily donate an electron to the organohalide.
Chain radical mechanisms involve reactions between radical intermediates and even-electron starting materials, resulting in the continuous regeneration of radicals as products form. I like to imagine the radical intermediates as Tom Hanks in Cast Away, floating in an ocean of even-electron starting material. A nice example of this reactivity was explored by Hill and Puddephatt in the mid-1980s.
Excitation of the Pt(II) complex yields a charge-transfer complex that can abstract iodine from isopropyl iodide. A second abstraction event completes the initiation phase. During propagation, isopropyl radical couples with the (unexcited) Pt(II) complex, and the resulting organometallic radical abstracts iodine from the starting organohalide. Free radical scavengers kill the reaction, but interestingly, only the isopropyl radical reacts with radical traps.
Lastly, I’ll just mention briefly that binuclear oxidative additions, which involve two metal centers “tugging” on the organohalide in concert, often involve radicals and/or one-electron transfers. Here’s one example involving chromium, and here’s a somewhat more famous example involving cobalt (by Budzelaar!).
Summing up, oxidative additions of polar reagents are critical steps in many organometallic reactions. We’ve only just barely scratched the surface of this important class of reactions, but a few powerful trends have emerged. In general, more electron-rich OM complexes and more electron-poor polar organics react more rapidly in oxidative additions. Steric hindrance in the metal complex can also play an interesting role, either by changing the actual species that undergoes oxidative addition or by discouraging oxidative addition altogether. Next up, we’ll take a brief look at the microscopic reverse of oxidative addition, reductive elimination. Most of the trends and mechanisms associated with reductive elimination are simply the opposite of those for oxidative addition, so our discussions of reductive elimination will be fairly short. | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/04%3A_Fundamentals_of_Organometallic_Chemistry/4.09%3A_Oxidative_Addition_of_Polar_Reagents.txt |
Over the years, a variety of “quirky” substitution methods have been developed. All of these have the common goal of facilitating substitution in complexes that would otherwise be inert. It’s an age-old challenge: how can we turn a stable complex into something unstable enough to react? Photochemical excitation, oxidation/reduction, and radical chains all do the job, and have all been well studied. We’ll look at a few examples in this post—remember these methods when simple associative or dissociative substitution won’t get the job done.
Photochemical Substitution
Substitution reactions of dative ligands—most famously, CO—may be facilitated by photochemical excitation. Two examples are shown below. The first reaction yields only monosubstituted product without ultraviolet light, even in the presence of a strongly donating phosphine.
Dissociative photochemical substitutions of CO and dinitrogen.
All signs point to dissociative mechanisms for these reactions (the starting complexes have 18 total electrons each). Excitation, then, must increase the M–L antibonding character of the complex’s electrons; exactly how this increase in antibonding character happens has been a matter of some debate. Originally, the prevailing explanation was that the LUMO bears M–L antibonding character, and excitation kicks an electron up from the HOMO to the LUMO, encouraging cleavage of the M–L bond. A more recent, more subtle explanation backed by calculations supports the involvement of a metal-to-ligand charge-transfer state along with the “classical” ligand-field excited state.
Oxidation/Reduction
Imagine a screaming baby without her pacifier—that’s a nice analogy for an odd-electron organometallic complex. Complexes bearing 17 and 19 total electrons are much more reactive toward substitution than their even-electron counterparts. Single-electron oxidation and reduction (“popping out the pacifier,” if you will) can thus be used to efficiently turn on substitution. As you might expect, oxidation and reduction work best on electron-rich and electron-poor complexes, respectively. The Mn complex in the oxidative example below, for instance, includes a strongly donating MeCp group (not shown).
Oxidation accelerates substitution in electron-rich complexes through a chain process.
Reduction works well for electron-poor metal carbonyl complexes, which are happy to accept an additional electron.
There is a two-electron oxidation method that’s also worth knowing: the oxidation of CO with amine oxides. This nifty little method releases carbon dioxide, amine, and an unsaturated complex that may be quenched by a ligand hanging around. The trick is addition to the CO ligand followed by elimination of the unsaturated complex. As the oxidized CO2 and reduced amine float away, the metal complex finds another ligand.
Oxidation of CO with amine oxides. A fun method for dissociative substitution of metal carbonyls!
Radical Chain Processes
Atom abstraction from 18-electron complexes produces neutral 17-electron intermediates, which are susceptible to ligand substitution via radical chain mechanisms. The fact that the intermediates are neutral distinguishes these methods from oxidation-based methods. First-row metal hydrides are great for these reactions, owing to their relatively weak M–H bonds. One example is shown below.
Radical-chain substitution involving atom abstraction.
After abstraction of the hydrogen atom by initiator, substitution is rapid and may occur multiple times. Propagation begins anew when the substituted radical abstracts hydrogen from the starting material to regenerate the propagating radical and form the product. These quirky methods are nice to have in your back pocket when you’re backed into a synthetic corner—sometimes, conventional associative and dissociative substitution just won’t do the job. In the next post, we’ll press on to oxidative addition.
Template:Evans | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/04%3A_Fundamentals_of_Organometallic_Chemistry/4.10%3A_Quirky_Ligand_Substitutions.txt |
Reductive elimination is the microscopic reverse of oxidative addition. It is literally oxidative addition run in reverse—oxidative addition backwards in time! My favorite analogy for microscopic reversibility is the video game Braid, in which “resurrection is the microscopic reverse of death.” The player can reverse time to “undo” death; viewed from the forward direction, “undoing death” is better called “resurrection.” Chemically, reductive elimination and oxidative addition share the same reaction coordinate. The only difference between their reaction coordinate diagrams relates to what we call “reactants” and “products.” Thus, their mechanisms depend on one another, and trends in the speed and extent of oxidative additions correspond to opposite trends in reductive eliminations. In this post, we’ll address reductive elimination in a general sense, as we did for oxidative addition.
A general reductive elimination. The oxidation state of the metal decreases by two units, and open coordination sites become available.
During reductive elimination, the electrons in the M–X bond head toward ligand Y, and the electrons in M–Y head to the metal. The eliminating ligands are always X-type! On the whole, the oxidation state of the metal decreases by two units, two new open coordination sites become available, and an X–Y bond forms. What does the change in oxidation state suggest about changes in electron density at the metal? As suggested by the name “reductive,” the metal gains electrons. The ligands lose electrons as the new X–Y bond cannot possibly be polarized to both X and Y, as the original M–X and M–Y bonds were. Using these ideas, you may already be thinking about reactivity trends in reductive elimination…hold that thought.
It’s been observed in a number of cases that a ligand dissociates from octahedral complexes before concerted reductive elimination occurs. Presumably, dissociation to form a distorted TBP geometry brings the eliminating groups closer to one another to facilitate elimination.
Reductive elimination is faster from five-coordinate than six-coordinate complexes.
Square planar complexes may either take on an additional fifth ligand or lose a ligand to form an odd-coordinate complex before reductive elimination. Direct reductive elimination without dissociation or association is possible, too.
Reactivity trends in reductive elimination are opposite those of oxidative addition. More electron-rich ligands bearing electron-donating groups react more rapidly, since the ligands lose electron density as the reaction proceeds. More electron-poor metal centers—bearing π-acidic ligands and/or ligands with electron-withdrawing groups—react more rapidly, since the metal center gains electrons. Sterically bulky ancillary ligands promote reductive elimination since the release of X and Y can “ease” steric strain in the starting complex. Steric hindrance helps explain, for example, why coordination of a fifth ligand to a square planar complex promotes reductive elimination even though coordination increases electron density at the metal center. A second example: trends in rates of reductive eliminations of alkanes parallel the steric demands of the eliminating ligands: C–C > C–H > H–H.
Reactivity trends for reductive eliminations.
Mechanistic trends for reductive elimination actually parallel trends in mechanisms of oxidative addition, since these two reactions are the microscopic reverse of one another. Non-polar and moderately polar ligands react by concerted or radical mechanisms; highly polarized ligands and/or very electrophilic metal complexes react by ionic (SN2) mechanisms. The thermodynamics of reductive elimination must be favorable in order for it to occur! Most carbon–halogen reductive eliminations, for example, are thermodynamically unfavorable (this has turned out to be a good thing, especially for cross-coupling reactions).
Reductive elimination is an important step in many catalytic cycles—it usually comes near the “end” of catalytic mechanisms, just before product formation. For some catalytic cycles it’s the turnover-limiting step, making it very important to consider! Hydrocyanation is a classic example; in the mechanism of this reaction, reductive elimination of C–CN is the slow step. Electron-poor alkyl ligands, derived from electron-poor olefins like unsaturated ketones, are bad enough at reductive elimination to prevent turnover altogether! Of course, the electronegative CN ligand is not helping things either…how would you design the ancillary ligands L to speed up this step?
Reductive elimination is the turnover-limiting step of hydrocyanation. How would you design L to speed it up? | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/04%3A_Fundamentals_of_Organometallic_Chemistry/4.11%3A_Reductive_Elimination-_General_Ideas.txt |
The trans effect is an ancient but venerable observation. First noted by Chernyaev in 1926, the trans effect and its conceptual siblings (the trans influence, cis influence, and cis effect) are easy enough to comprehend. That is, it’s simple enough to know what they are. To understand why they are, on the other hand, is much more difficult.
Definitions & Examples
Let’s begin with definitions: what is the trans effect? There’s some confusion on this point, so we need to be careful. The trans effect proper, which is often called the kinetic trans effect, refers to the observation that certain ligands increase the rate of ligand substitution when positioned trans to the departing ligand. The key word in that last sentence is “rate”—the trans effect proper is a kinetic effect. The trans influence refers to the impact of a ligand on the length of the bond trans to it in the ground state of a complex. The key phrase there is “ground state”—this is a thermodynamic effect, so it’s sometimes called the thermodynamic trans effect. Adding to the insanity, cis effects and cis influences have also been observed. Evidently, ligands may also influence the kinetics or thermodynamics of their cis neighbors. All of these phenomena are independent of the metal center, but do depend profoundly on the geometry of the metal (more on that shortly).
Kinetic trans and cis effects are shown in the figure below. In both cases, we see that X1 exhibits a stronger effect than X2. The geometries shown are those for which each effect is most commonly observed. The metals and oxidation states shown are prototypical.
On to the influences, which are simpler to illustrate since they’re concerned with ground states, not reactions. The lengthened bonds below are exaggerated.
And there we have it folks, the thermodynamic and kinetic cis/trans effects. It’s worth keeping in mind that the kinetic trans effect is most common for d8 square planar complexes, and the kinetic cis effect is most common for d6 octahedral complexes (particularly when the departing L is CO). But a lingering question remains: what makes for a strong trans effect ligand?
Origins of Effects & Influences
The trans effect and its cousins are all electronic, not steric effects. So, the electronic properties of the ligand dictate the strength of its trans effect. Let’s finally dig into the trans effect series:
(weak) F, HO, H2O <NH3 < py < Cl < Br– < I–, SCN, NO2, SC(NH2)2, Ph < SO32 < PR3 < AsR3, SR2, H3C < H, NO, CO, NC, C2H4 (strong)
What’s the electronic progression here? It’s clear that electronegativity decreases across the series: F < Cl < Br < I < H3C. From a bonding perspective, we can say that ligands with strong trans effects are strong σ-donors (or σ-bases). Yet σ-donation doesn’t tell the whole story. What about ethylene and carbon monoxide, which both appear at the top of the heap? Neither of these ligands are strong σ-donors, but their π systems do interact with the metal center through backbonding. Consider the following sub-series: S=C=N– < PR3 < CO. Backbonding increases across this series, along with the strength of the trans effect. Strong backbonders—better known as π-acceptors or π-acids—exhibit strong trans effects.
Strong trans effect = strong σ-donor + strong π-acceptor
Wonderful! Using these ideas we can identify ligands with strong trans effects. But we can dive deeper down the rabbit hole: why does this particular combination of electronic factors lead to a strong trans effect? To understand this, we need to know the mechanism of the ligand substitution reaction that’s sped up by strong trans effect ligands. For 16-electron Pt(II) complexes, associative substitution is par for the course. The incoming ligand binds to the metal first, forming an 18-electron complex (yay!), which jettisons a ligand to yield a new 16-electron product. The mechanism in all its glory is shown in the figure below.
Some very important points about this mechanism:
• The incoming ligand always sits at an equatorial site in the trigonal bipyramidal intermediate. More on this another day, but I think of this result as governed by the principle of least motion. Consider the molecular gymnastics that would have to happen to place the incoming ligand in an axial position.
• Two ligands in the square plane are “pushed down” and become the other two equatorial ligands.
• Owing to microscopic reversibility, the leaving group must be one of the equatorial ligands.
The third point reveals that once L’ has “pushed down” XTE and Ltrans, Ltrans has no choice but to leave (assuming XTE stays put). Thus, the trans effect has nothing to do with the second step of the mechanism, which is not rate determining anyway. The key is the first step—in particular, the “pushing down” event. Apparently, ligands with strong trans effects like to be pushed down. They like to occupy the equatorial plane of the TBP intermediate. Now here’s the kicker: the equatorial sites of the TBP geometry are more π basic than the axial sites. The equatorial plane is just the xy-plane of the metal center, and the d orbitals in that plane (when occupied) are great electron sources for π-acidic ligands. Thus, π-acidic ligands want to occupy those equatorial sites, to receive the benefits of strong backbonding! Boom; strong π-acids encourage loss of the ligand trans to themselves.
What about those pesky σ donors? Well, we can imagine that in a square planar complex, a ligand and its trans partner are competing for donation into the same d orbital. Strong σ donation from a ligand should thus weaken the bond trans to it. Although this is the thermodynamic trans effect (trans influence) in action, the resulting destabilization of the ground state relative to the transition state is a kinetic effect. On the whole, the barrier to substitution of the trans ligand goes down as σ-donating strength goes up.
This idea of “competition for the metal center” is a nice heuristic to use when thinking about the trans and cis influences. The type of metallic orbital involved in M–L bonding determines the strength of L’s trans and cis influences on neighboring ligands that also need that metallic orbital for bonding. For example: both influences are large if the metal’s s orbital is a significant contributor to M–L bonding, since it’s non-directional; the trans influence is much greater than the cis influence when metallic p orbitals are primarily involved in M–L. For a deeper explanation of these ideas, see this paper.
Summing up
Perhaps the most valuable lesson from a study of the trans effect is that many concepts from organometallic chemistry involve more than meets the eye. Geometric effects and influences are real icebergs, in the sense that the observations and trends are easy to grasp, but difficult to explain. We had to dig all the way into the mechanism of associative ligand substitution before a satisfactory explanation emerged! | textbooks/chem/Inorganic_Chemistry/Organometallic_Chemistry_(Evans)/04%3A_Fundamentals_of_Organometallic_Chemistry/4.12%3A_The_trans_cis_Effects_and_Influences.txt |
Consider the symmetry properties of an object (e.g. atoms of a molecule, set of orbitals, vibrations). The collection of objects is commonly referred to as a basis set
• classify objects of the basis set into symmetry operations
• symmetry operations form a group
• group mathematically defined and manipulated by group theory
Definition: Symmetry Operation
A symmetry operation moves an object into an indistinguishable orientation
Definition: Symmetry Element
A symmetry element is a point, line or plane about which a symmetry operation is performed
There are five symmetry elements in 3D space, which will be defined relative to point with coordinate (x1, y1, z1) :
1. identity, E
$E\left(x_{1}, y_{1}, z_{1}\right)=\left(x_{1}, y_{1}, z_{1}\right)$
2. plane of reflection, σ
3. inversion, i
$\mathrm{i}\left(\mathrm{x}_{1}, \mathrm{y}_{1}, \mathrm{z}_{1}\right)=\left(-\mathrm{x}_{1},-\mathrm{y}_{1},-\mathrm{z}_{1}\right)$
4. proper rotation axis, Cn $\text { (where }\left.\theta=\frac{2 \pi}{n}\right)$
convention is a clockwise rotation of the point
$\mathrm{C}_{2}(\mathrm{z})\left(\mathrm{x}_{1}, \mathrm{y}_{1}, \mathrm{z}_{1}\right)=\left(-\mathrm{x}_{1},-\mathrm{y}_{1}, \mathrm{z}_{1}\right)$
5. improper rotation axis, Sn
two step operation: Cn followed by σ through plane ⊥ to Cn
$\mathrm{S}_{4}(\mathrm{z})\left(\mathrm{x}_{1}, \mathrm{y}_{1}, \mathrm{z}_{1}\right)=\sigma(\mathrm{xy}) \mathrm{C}_{4}(\mathrm{z})\left(\mathrm{x}_{1}, \mathrm{y}_{1}, \mathrm{z}_{1}\right)=\sigma(\mathrm{xy})\left(\mathrm{y}_{1},-\mathrm{x}_{1}, \mathrm{z}_{1}\right)=\left(\mathrm{y}_{1},-\mathrm{x}_{1}-\mathrm{z}_{1}\right)$
Note: rotation of pt is clockwise; Corollary is that axes rotate counterclockwise relative to fixed point
In the example above, we took the direct product of two operators:
$\sigma_{\mathrm{h}} \cdot \mathrm{C}_{\mathrm{n}}=\mathrm{S}_{\mathrm{n}}$
Horizontal mirror plane (normal to Cn)
$\text { for } n \text { even }: S_{n}^{n}=C_{n}^{n} \cdot \sigma_{h}^{n}=E \cdot E=E$
\begin{aligned} \text { for } n \text { odd: } & S_{n}^{n}=C_{n}^{n} \cdot \sigma_{h}^{n}=E \cdot \sigma_{h}=\sigma_{h} \ & S_{n}^{2 n}=C_{n}^{2 n} \cdot \sigma_{h}^{2 n}=E \cdot E=\sigma_{h} \end{aligned}
$\text { for } \mathrm{m} \text { even: } \mathrm{S}_{\mathrm{n}}^{\mathrm{m}}=\mathrm{C}_{\mathrm{n}}^{\mathrm{m}} \cdot \sigma_{\mathrm{h}}^{\mathrm{m}}=\mathrm{C}_{\mathrm{n}}^{\mathrm{m}}$
$\text { for } m \text { odd: } \quad S_{n}^{m}=C_{n}^{m} \cdot \sigma_{h}^{m}=C_{n}^{m} \cdot \sigma_{h}=S_{n}^{m}$
Symmetry operations may be represented as matrices. Consider the vector $\overline{\mathbf{v}}$
1. identity: $E\begin{bmatrix} x_1 \ y_1 \ z_1 \end{bmatrix} = \begin{bmatrix} & & \ & ? & \ & & \end{bmatrix} \begin{bmatrix} x_1 \ y_1 \ z_1 \end{bmatrix} = \begin{bmatrix} x_1 \ y_1 \ z_1 \end{bmatrix}$
matrix satisfying this condition is:
$\left[\begin{array}{lll} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array}\right]$
$\therefore \mathrm{E}=\left[\begin{array}{lll} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array}\right]$... E is always the unit matrix
2. reflection: $\sigma(\mathrm{xy})\left[\begin{array}{l} \mathrm{x}_{1} \ \mathrm{y}_{1} \ \mathrm{z}_{1} \end{array}\right]=\left[\begin{array}{r} \mathrm{x}_{1} \ \mathrm{y}_{1} \ -\mathrm{z}_{1} \end{array}\right] \quad \therefore \sigma(\mathrm{xy})=\left[\begin{array}{rrr} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & -1 \end{array}\right]$
similarly $\text { similarly } \sigma(\mathrm{xz})=\left[\begin{array}{rrr} 1 & 0 & 0 \ 0 & -1 & 0 \ 0 & 0 & 1 \end{array}\right] \text { and } \sigma(\mathrm{yz})=\left[\begin{array}{rrr} -1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array}\right]$
3. inversion: $\mathrm{i}\left[\begin{array}{l} \mathrm{x}_{1} \ \mathrm{y}_{1} \ \mathrm{z}_{1} \end{array}\right]=\left[\begin{array}{l} -\mathrm{x}_{1} \ -\mathrm{y}_{1} \ -\mathrm{z}_{1} \end{array}\right] \quad \therefore \quad \mathrm{i}=\left[\begin{array}{rrr} -1 & 0 & 0 \ 0 & -1 & 0 \ 0 & 0 & -1 \end{array}\right]$
4. proper rotation axis:
because of convention, φ, and hence zi, is not transformed under Cn(θ) ∴ projection into xy plane need only be considered… i.e., rotation of vector v(xi,yi) through θ
$x_{1}=\bar{v} \cos \alpha$
$y_{1}=\vec{v} \sin \alpha$
${C}_{n}(\theta)$
$\mathrm{x}_{2}=\overline{\mathrm{v}} \cos [-(\theta-\alpha)]=\overline{\mathrm{v}} \cos (\theta-\alpha)$
$y_{2}=\vec{v} \sin [-(\theta-\alpha)]=-\bar{v} \sin (\theta-\alpha)$
using identity relations:
$x_{2}=\vec{v} \cos (\theta-\alpha)=\vec{v} \cos \theta \cos \alpha+\vec{v} \sin \theta \sin \alpha=x_{1} \cos \theta+y_{1} \sin \theta$
$y_{2}=-\bar{v} \sin (\theta-\alpha)=-[\bar{v} \sin \theta \cos \alpha-\bar{v} \cos \theta \sin \alpha]=-x_{1} \sin \theta+y_{1} \cos \theta$
Reformulating in terms of matrix representation:
$\mathrm{C}_{\mathrm{n}}(\theta)\left[\begin{array}{l} \mathrm{x}_{1} \ \mathrm{y}_{1} \ \mathrm{z}_{1} \end{array}\right]=\left[\begin{array}{r} \mathrm{x}_{1} \cos \theta+\mathrm{y}_{1} \sin \theta \ -\mathrm{x}_{1} \sin \theta+\mathrm{y}_{1} \cos \theta \ \mathrm {z}_{1} \end{array}\right]$
$\therefore \mathrm{C}_{\mathrm{n}}(\theta)=\left[\begin{array}{rrr} \cos \theta & \sin \theta & 0 \ -\sin \theta & \cos \theta & 0 \ 0 & 0 & 1 \end{array}\right] \quad \text { where } \theta=\frac{2 \pi}{\mathrm{n}}$
Note… the rotation above is clockwise, as discussed by HB (pg 39). Cotton on pg. 73 solves for the counterclockwise rotation… and presents the clockwise result derived above. To be consistent with HB (and math classes) we will rotate clockwise as the convention.
The above matrix representation is completely general for any rotation θ…
Example: $C_{3}, \theta=\frac{2 \pi}{n}$
$C_{3}=\left[\begin{array}{ccc} \cos \frac{2 \pi}{3} & \sin \frac{2 \pi}{3} & 0 \ -\sin \frac{2 \pi}{3} & \cos \frac{2 \pi}{3} & 0 \ 0 & 0 & 1 \end{array}\right]=\left[\begin{array}{ccc} -\frac{1}{2} & \frac{\sqrt{3}}{2} & 0 \ -\frac{\sqrt{3}}{2} & -\frac{1}{2} & 0 \ 0 & 0 & 1 \end{array}\right]$
5. improper rotation axis :
σ h ⋅ Cn(θ) = Sn(θ)
$\left[\begin{array}{rrr} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & -1 \end{array}\right] \cdot\left[\begin{array}{rrr} \cos \theta & \sin \theta & 0 \ -\sin \theta & \cos \theta & 0 \ 0 & 0 & 1 \end{array}\right]=\left[\begin{array}{rrr} \cos \theta & \sin \theta & 0 \ -\sin \theta & \cos \theta & 0 \ 0 & 0 & -1 \end{array}\right]$
Like operators themselves, matrix operations may be manipulated with simple matrix algebra…above direct product yields matrix representation for Sn.
Another example:
$\left[\begin{array}{rrr} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & -1 \end{array}\right] \cdot\left[\begin{array}{rrr} -1 & 0 & 0 \ 0 & -1 & 0 \ 0 & 0 & 1 \end{array}\right]=\left[\begin{array}{rrr} -1 & 0 & 0 \ 0 & -1 & 0 \ 0 & 0 & -1 \end{array}\right]$
σxy (≡ σh ) ⋅ C2 (z) = i | textbooks/chem/Inorganic_Chemistry/Principles_of_Inorganic_Chemistry_II_(Nocera)/01%3A_Chapters/1.01%3A_Untitled_Chapter_2.txt |
The inverse of A (defined as (A)–1) is B if A ⋅ B = E
For each of the five symmetry operations:
$( E )^{-1}= E \Longrightarrow( E )^{-1} \cdot E = E \cdot E = E$
$(\sigma)^{-1}=\sigma \Longrightarrow(\sigma)^{-1} \cdot \sigma=\sigma \cdot \sigma= E$
$(i)^{-1}=i \Longrightarrow(i)^{-1} \cdot i=i \cdot i=E$
$\left(C_{n}^{m}\right)^{-1}=C_{n}^{n-m} \Longrightarrow\left(C_{n}^{m}\right)^{-1} \cdot C_{n}^{m}=C_{n}^{n-m} \cdot C_{n}^{m}=C_{n}^{n}=E$
e.g. $\left(C_{5}^{2}\right)^{-1}=C_{5}^{3}$ since $C_{5}^{2} \cdot C_{5}^{3}=E$
$\left(S_{n}^{m}\right)^{-1}=S_{n}^{n-m}(n \text { even }) \Longrightarrow\left(S_{n}^{m}\right)^{-1} \cdot S_{n}^{m}=S_{n}^{n-m} \cdot S_{n}^{m}=S_{n}^{n}=C_{n}^{n} \cdot \sigma_{h}^{n}=E$
$\left(S_{n}^{m}\right)^{-1}=S_{n}^{2 n-m}(n \text { odd }) \Longrightarrow\left(S_{n}^{m}\right)^{-1} \cdot S_{n}^{m}=S_{n}^{2 n-m} \cdot S_{n}^{m}=S_{n}^{2 n}=C_{n}^{2 n} \cdot \sigma_{h}^{2 n}=E$
Two operators commute when A ⋅ B = B ⋅ A
Example: Do C4(z) and σ(xz) commute?
… or analyzing with matrix representations,
$\left[\begin{array}{rrr}0 & 1 & 0 \ -1 & 0 & 0 \ 0 & 0 & 1\end{array}\right] \cdot\left[\begin{array}{rrr}1 & 0 & 0 \ 0 & -1 & 0 \ 0 & 0 & 1\end{array}\right]=\left[\begin{array}{rrr}0 & -1 & 0 \ -1 & 0 & 0 \ 0 & 0 & 1\end{array}\right]$
C4(z) ⋅ σxz = σd´
Now applying the operations in the inverse order,
… or analyzing with matrix representations,
$\left[\begin{array}{rrr}1 & 0 & 0 \ 0 & -1 & 0 \ 0 & 0 & 1\end{array}\right] \cdot\left[\begin{array}{rrr}0 & 1 & 0 \ -1 & 0 & 0 \ 0 & 0 & 1\end{array}\right]=\left[\begin{array}{lll}0 & 1 & 0 \ 1 & 0 & 0 \ 0 & 0 & 1\end{array}\right]$
σxz ⋅ C4(z) = σd
\therefore \quad C_{4}(z) \sigma(x z)=\sigma_{d}^{\prime} \neq \sigma(x z) C_{4}(z)=\sigma_{d} \Rightarrow \text { so } C_{4}(z) \text { does not commute with } \sigma(x z)
A collection of operations are a mathematical group when the following conditions are met:
• closure: all binary products must be members of the group
• identity: a group must contain the identity operator
• inverse: every operator must have an inverse
• associativity: associative law of multiplication must hold $(A ⋅ B) ⋅ C = A ⋅ (B ⋅ C$
(note: commutation not required… groups in which all operators do commute are called Abelian)
Consider the operators C3 and σv. These do not constitute a group because identity criterion is not satisfied. Do E, C3, σv form a group? To address this question, a stereographic projection (featuring critical operators) will be used:
So how about closure?
C3 ⋅ C3 = C3 2 (so C3 2 needs to be included as part of the group)
Thus E, C3 and σv are not closed and consequently these operators do not form a group. Is the addition of C3 2 and σv´ sufficient to define a group? In other terms, are there any other operators that are generated by C3 and σv?
… the proper rotation axis, C3:
$C_{3}$
$C _{3} \cdot C _{3}= C _{3}^{2}$
$C _{3} \cdot C _{3} \cdot C _{3}= C _{3}^{2} \cdot C _{3}= C _{3} \cdot C _{3}^{2}= E$
$C _{3} \cdot C _{3} \cdot C _{3} \cdot C _{3}= E \cdot C _{3}= C _{3}$
etc.
$\therefore C _{3}$ is the generator of $E , C _{3}$ and $C _{3}^{2}$, note: these three operators form a group
… for the plane of reflection, σv
$\sigma_{v}$
$\sigma_{v} \cdot \sigma_{v}=E$
$\sigma_{v} \cdot \sigma_{v} \cdot \sigma_{v}=E \cdot \sigma_{v}=\sigma_{v}$
etc.
So we obtain no new information here. But there is more information to be gained upon considering C3 and σv. Have already seen that C3 ⋅ σv = σv’ … how about σv ⋅ C3
Will discover that no new operators may be generated. Moreover one finds
$\begin{array}{ccccccc} & E ^{-1} & C _{3}^{-1} & \left( C _{3}^{2}\right)^{-1} & \sigma_{ v }^{-1} & \left(\sigma_{ v }^{\prime}\right)^{-1} & \left(\sigma_{ v }^{\prime \prime}\right)^{-1} \ \text {inverses } & \downarrow & \downarrow & \downarrow & \downarrow & \downarrow & \downarrow \ & E & C _{3}^{2} & C _{3} & \sigma_{ v } & \sigma_{ v }^{\prime} & \sigma_{ v }^{\prime \prime}\end{array}$
The above group is closed, i.e. it contains the identity operator and meets inverse and associativity conditions. Thus the above set of operators constitutes a mathematical group (note that the group is not Abelian).
Some definitions:
Operators C3 and σv are called generators for the group since every element of the group can be expressed as a product of these operators (and their inverses).
The order of the group, designated h, is the number of elements. In the above example, h = 6.
Groups defined by a single generator are called cyclic groups.
Example: C3 → E, C3, C3 2
As mentioned above, E, C3, and C32 meet the conditions of a group; they form a cyclic group. Moreover these three operators are a subgroup of E, C3, C3 2, σv, σv’,σv”. The order of a subgroup must be a divisor of the order of its parent group. (Example hsubgroup = 3, hgroup = 6 … a divisor of 2.)
A similarity transformation is defined as: v -1 ⋅ A ⋅ ν = B where B is designated the similarity transform of A by x and A and B are conjugates of each other. A complete set of operators that are conjugates to one another is called a class of the group.
Let’s determine the classes of the group defined by E, C3, C3 2 , σv, σv’,σv”… the analysis is facilitated by the construction of a multiplication table
$\begin{array}{l|llllll} & E & C _{3} & C _{3}^{2} & \sigma_{ v } & \sigma_{ v }^{\prime} & \sigma_{ v }^{\prime \prime} \ \hline E & E & C _{3} & C _{3}^{2} & \sigma_{ v } & \sigma_{ v }^{\prime} & \sigma_{ v }^{\prime \prime} \ C _{3} & C _{3} & C _{3}^{2} & E & \sigma_{ v }^{\prime} & \sigma_{ v }^{\prime \prime} & \sigma_{ v } \ C _{3}^{2} & C _{3}^{2} & E & C _{3} & \sigma_{ v }^{\prime \prime} & \sigma_{ v } & \sigma_{ v }^{\prime} \ \sigma_{ v } & \sigma_{ v } & \sigma_{ v }^{\prime \prime} & \sigma_{ v }^{\prime} & E & C _{3}^{2} & C _{3} \ \sigma_{ v }^{\prime} & \sigma_{ v }^{\prime} & \sigma_{ v } & \sigma_{ v }^{\prime \prime} & C _{3} & E & C _{3}^{2} \ \sigma_{ v }^{\prime \prime} & \sigma_{ v }^{\prime \prime} & \sigma_{ v }^{\prime} & \sigma_{ v } & C _{3}^{2} & C _{3} & E \end{array}$
may construct easily using stereographic projections
$E ^{-1} \cdot C _{3} \cdot E = E \cdot C _{3} \cdot E = C _{3}$
$C _{3}^{-1} \cdot C _{3} \cdot C _{3}= C _{3}^{2} \cdot C _{3} \cdot C _{3}= E \cdot C _{3}= C _{3}$
$\left( C _{3}^{2}\right)^{-1} \cdot C _{3} \cdot C _{3}^{2}= C _{3} \cdot C _{3} \cdot C _{3}^{2}= C _{3} \cdot E = C _{3}$
$\sigma _{ v }^{-1} \cdot C _{3} \cdot \sigma_{ v }=\sigma_{ v } \cdot C _{3} \cdot \sigma_{ v }=\sigma_{ v } \cdot \sigma_{ v }^{\prime}= C _{3}^{2}$
$\left(\sigma_{ v }^{\prime}\right)^{-1} \cdot C _{3} \cdot \sigma_{ v }^{\prime}=\sigma_{ v }^{\prime} \cdot C _{3} \cdot \sigma_{ v }^{\prime}=\sigma_{ v }^{\prime} \cdot \sigma_{ v }^{\prime \prime}= C _{3}^{2}$
$\left(\sigma_{ v }^{\prime \prime}\right)^{-1} \cdot C _{3} \cdot \sigma_{ v }^{\prime \prime}=\sigma_{ v }^{\prime \prime} \cdot C _{3} \cdot \sigma_{ v }^{\prime \prime}=\sigma_{ v }^{\prime \prime} \cdot \sigma_{ v }= C _{3}^{2}$
∴ C3 and C3 2 from a class
Performing a similar analysis on σv will reveal that σv, σv’ and σv’’ form a class and E is in a class by itself. Thus there are three classes:
$E ,\left( C _{3}, C _{3}^{2}\right),\left(\sigma_{ v }, \sigma_{ v }^{\prime}, \sigma_{ v }^{\prime \prime}\right)$
Additional properties of transforms and classes are:
• no operator occurs in more than one class
• order of all classes must be integral factors of the group’s order
• in an Abelian group, each operator is in a class by itself. | textbooks/chem/Inorganic_Chemistry/Principles_of_Inorganic_Chemistry_II_(Nocera)/01%3A_Chapters/1.02%3A_Untitled_Chapter_3.txt |
Similarity transformations yield irreducible representations, Γi, which lead to the useful tool in group theory – the character table. The general strategy for determining Γi is as follows: A, B and C are matrix representations of symmetry operations of an arbitrary basis set (i.e., elements on which symmetry operations are performed). There is some similarity transform operator such that
$\begin{array}{l} \pmb A ^{\prime}=v^{-1} \cdot \pmb A \cdot v \ \pmb B ^{\prime}=v^{-1} \cdot \pmb B \cdot v \ \pmb C ^{\prime}=v^{-1} \cdot \pmb C \cdot v \end{array}$
where v uniquely produces block-diagonalized matrices, which are matrices possessing square arrays along the diagonal and zeros outside the blocks
\mathbf{A}^{\prime}=\left[\begin{array}{rrr}
\mathrm{A}_{1} & & \
& \mathrm{~A}_{2} & \
& & \mathrm{~A}_{3}
\end{array}\right] \quad \mathbf{B}^{\prime}=\left[\begin{array}{llll}
\mathrm{B}_{1} & & \
& \mathrm{~B}_{2} & \
& & \mathrm{~B}_{3}
\end{array}\right] \quad \mathbf{C}^{\prime}=\left[\begin{array}{lll}
\mathrm{C}_{1} & & \
& \mathrm{C}_{2} & \
& & \mathrm{C}_{3}
\end{array}\right]
Matrices A, B, and C are reducible. Sub-matrices Ai, Bi and Ci obey the same multiplication properties as A, B and C. If application of the similarity transform does not further block-diagonalize A’, B’ and C’, then the blocks are irreducible representations. The character is the sum of the diagonal elements of Γi.
As an example, let’s continue with our exemplary group: E, C3, C3 2 , σv, σv’, σv” by defining an arbitrary basis … a triangle
The basis set is described by the triangles vertices, points A, B and C. The transformation properties of these points under the symmetry operations of the group are:
$E\left[\begin{array}{l} A \ B \ C \end{array}\right]=\left[\begin{array}{l} A \ B \ C \end{array}\right]=\left[\begin{array}{lll} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array}\right]\left[\begin{array}{l} A \ B \ C \end{array}\right] \quad \sigma_{V}\left[\begin{array}{l} A \ B \ C \end{array}\right]=\left[\begin{array}{l} A \ C \ B \end{array}\right]=\left[\begin{array}{lll} 1 & 0 & 0 \ 0 & 0 & 1 \ 0 & 1 & 0 \end{array}\right]\left[\begin{array}{l} A \ B \ C \end{array}\right]$
$C _{3}\left[\begin{array}{l} A \ B \ C \end{array}\right]=\left[\begin{array}{l} B \ C \ A \end{array}\right]=\left[\begin{array}{lll} 0 & 1 & 0 \ 0 & 0 & 1 \ 1 & 0 & 0 \end{array}\right]\left[\begin{array}{l} A \ B \ C \end{array}\right] \quad \sigma_{ V }^{\prime}\left[\begin{array}{l} A \ B \ C \end{array}\right]=\left[\begin{array}{l} B \ A \ C \end{array}\right]=\left[\begin{array}{lll} 0 & 1 & 0 \ 1 & 0 & 0 \ 0 & 0 & 1 \end{array}\right]\left[\begin{array}{l} A \ B \ C \end{array}\right]$
$C _{3}^{2}\left[\begin{array}{l} A \ B \ C \end{array}\right]=\left[\begin{array}{l} C \ A \ B \end{array}\right]=\left[\begin{array}{lll} 0 & 0 & 1 \ 1 & 0 & 0 \ 0 & 1 & 0 \end{array}\right]\left[\begin{array}{l} A \ B \ C \end{array}\right] \quad \sigma_{ V }^{\prime \prime}\left[\begin{array}{l} A \ B \ C \end{array}\right]=\left[\begin{array}{l} C \ B \ A \end{array}\right]=\left[\begin{array}{lll} 0 & 0 & 1 \ 0 & 1 & 0 \ 1 & 0 & 0 \end{array}\right]\left[\begin{array}{l} A \ B \ C \end{array}\right]$
These matrices are not block-diagonalized, however a suitable similarity transformation will accomplish the task,
$v=\left[\begin{array}{ccc} \frac{1}{\sqrt{3}} & \frac{2}{\sqrt{6}} & 0 \ \frac{1}{\sqrt{3}} & -\frac{1}{\sqrt{6}} & \frac{1}{\sqrt{2}} \ \frac{1}{\sqrt{3}} & -\frac{1}{\sqrt{6}} & -\frac{1}{\sqrt{2}} \end{array}\right] \quad ; \quad v^{-1}=\left[\begin{array}{ccc} \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \ \frac{2}{\sqrt{6}} & -\frac{1}{\sqrt{6}} & -\frac{1}{\sqrt{6}} \ 0 & \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \end{array}\right]$
Applying the similarity transformation with C3 as the example,
$v^{-1} \cdot \pmb C _{3} \cdot v=\left[\begin{array}{ccc} \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \ \frac{2}{\sqrt{6}} & -\frac{1}{\sqrt{6}} & -\frac{1}{\sqrt{6}} \ 0 & \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \end{array}\right] \cdot\left[\begin{array}{ccc} 0 & 1 & 0 \ 0 & 0 & 1 \ 1 & 0 & 0 \end{array}\right] \cdot\left[\begin{array}{ccc} \frac{1}{\sqrt{3}} & \frac{2}{\sqrt{6}} & 0 \ \frac{1}{\sqrt{3}} & -\frac{1}{\sqrt{6}} & \frac{1}{\sqrt{2}} \ \frac{1}{\sqrt{3}} & -\frac{1}{\sqrt{6}} & -\frac{1}{\sqrt{2}} \end{array}\right]$
$\left[\begin{array}{ccc} \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \ \frac{2}{\sqrt{6}} & -\frac{1}{\sqrt{6}} & -\frac{1}{\sqrt{6}} \ 0 & \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \end{array}\right] \cdot\left[\begin{array}{ccc} \frac{1}{\sqrt{3}} & -\frac{1}{\sqrt{6}} & \frac{1}{\sqrt{2}} \ \frac{1}{\sqrt{3}} & -\frac{1}{\sqrt{6}} & -\frac{1}{\sqrt{2}} \ \frac{1}{\sqrt{3}} & \frac{2}{\sqrt{6}} & 0 \end{array}\right]=\left[\begin{array}{ccc} 1 & 0 & 0 \ 0 & -\frac{1}{2} & \frac{\sqrt{3}}{2} \ 0 & -\frac{\sqrt{3}}{2} & -\frac{1}{2} \end{array}\right]= \pmb C _{3}^{*}$
if v -1 C3*v is applied again, the matrix is not block diagonalized any further. The same diagonal sum is obtained *though off-diagonal elements may change). In this case, C3* is an irreducible representation, Γi.
The similarity transformation applied to other reducible representations yields:
Thus a 3 × 3 reducible representation, Γred, has been decomposed under a similarity transformation into a 1 (1 × 1) and 1 (2 × 2) block-diagonalized irreducible representations, Γi. The traces (i.e. sum of diagonal matrix elements) of the Γi’s under each operation yield the characters (indicated by χ) of the representation. Taking the traces of each of the blocks:
This collection of characters for a given irreducible representation, under the operations of a group is called a character table. As this example shows, from a completely arbitrary basis and a similarity transform, a character table is born.
The triangular basis set does not uncover all Γirr of the group defined by {E, C3, C3 2 , σv, σv’, σv’’}. A triangle represents Cartesian coordinate space (x,y,z) for which the Γis were determined. May choose other basis functions in an attempt to uncover other Γis. For instance, consider a rotation about the z-axis,
The transformation properties of this basis function, Rz, under the operations of the group (will choose only 1 operation from each class, since characters of operators in a class are identical):
E: $R_{z} \rightarrow R_{z}\ \quad C _{3}: R _{2} \rightarrow R _{2} \quad \sigma_{ v }( xy ): R _{2} \rightarrow \overline{ R }_{2}$
Note, these transformation properties give rise to a Γi that is not contained in a triangular basis. A new (1 x 1) basis is obtained, Γ3, which describes the transform properties for Rz. A summary of the Γi for the group defined by E, C3, C3 2 , σv, σv’, σv” is:
Is this character table complete? Irreducible representations and their characters obey certain algebraic relationships. From these 5 rules, we can ascertain whether this is a complete character table for these 6 symmetry operations.
Five important rules govern irreducible representations and their characters:
Rule 1
The sum of the squares of the dimensions, $\ell$, of irreducible representation Γi is equal to the order, h, of the group,
Since the character under the identity operation is equal to the dimension of Γi (since E is always the unit matrix), the rule can be reformulated as,
Rule 2
The sum of squares of the characters of irreducible representation Γi equals h
Rule 3
Vectors whose components are characters of two different irreducible representations are orthogonal
$\sum_{R}\left[x_{i}(R)\right]\left[x_{j}(R)\right]=0 \quad$ for $\quad i \neq j$
Rule 4
For a given representation, characters of all matrices belonging to operations in the same class are identical
Rule 5
The number of Γis of a group is equal to the number of classes in a group.
With these rules one can algebraically construct a character table. Returning to our example, let’s construct the character table in the absence of an arbitrary basis:
Rule 5: E (C3, C3 2 ) (σv, σv’, σv”) … 3 classes ∴ 3 Γis
Rule 1: $\ell_{1}^{2}+\ell_{2}^{2}+\ell_{3}^{2}=6 \quad \therefore \ell_{1}=\ell_{2}=1, \ell_{2}=2$
Rule 2: All character tables have a totally symmetric representation. Thus one of the irreducible representations, Γi, possesses the character set χ1(E) = 1, χ1(C3, C3 2 ) = 1, χ1v, σv’, σv”) = 1. Applying Rule 2, we find for the other irreducible representation of dimension 1,
$1 \cdot 1 \cdot x_{2}( E )+2 \cdot 1 \cdot x_{2}\left( C _{3}\right)+3 \cdot 1 \cdot x_{2}\left(\sigma_{ v }\right)=0$
Since χ2(E) = 1,
$1+2 \cdot x_{2}\left( C _{3}\right)+3 \cdot x_{2}\left(\sigma_{ v }\right)=0 \quad \therefore \quad \chi_{2}\left( C _{3}\right)=1, \chi_{2}\left(\sigma_{ v }\right)=-1$
For the case of Γ3 ( $\ell$3 = 2) there is not a unique solution to Rule 2
$2+2 \cdot \chi_{3} \left(C_{3}\right) +3 \cdot \chi_{3} \left(\sigma_{v}\right)=0$
However, application of Rule 2 to Γ3 gives us one equation for two unknowns. Have several options to obtain a second independent equation:
Rule 1: $1 \cdot 2^{2}+2\left[\chi_{3}\left(C_{3}\right)\right]^{2}+3\left[\chi_{3}\left(\sigma_{v}\right)\right]^{2}=6$
Rule 3: $1 \cdot 1 \cdot 2+2 \cdot 1 \cdot x_{3}\left(C_{3}\right)+3 \cdot 1 \cdot x_{3}\left(\sigma_{v}\right)=0$
or
$1 \cdot 1 \cdot 2+2 \cdot 1 \cdot x_{3}\left(C_{3}\right)+3 \cdot(-1) \cdot x_{3}\left(\sigma_{v}\right)=0$
Solving simultaneously yields $\chi_{3}\left(C_{3}\right)=-1, \chi_{3}\left(\sigma_{x}\right)=0$
Thus the same result shown on pg 4 is obtained:
\begin{array}{c|ccc}
& \mathrm{E} & 2 \mathrm{C}_{3} & 3 \sigma_{\mathrm{v}} \
\hline \Gamma_{1} & 1 & 1 & 1 \
\Gamma_{2} & 2 & -1 & 0 \
\Gamma_{3} & 1 & 1 & -1
\end{array}
Note, the derivation of the character table in this section is based solely on the properties of characters; the table was derived algebraically. The derivation on pg 4 was accomplished from first principles.
The complete character table is:
• Γis of:
$\ell=1 \Longrightarrow A$ or $B$
$\ell=2 \Longrightarrow E$
$\ell=3 \Longrightarrow T$
A is symmetric (+1) with respect to Cn
B is antisymmetric (–1) with respect to Cn
• subscripts 1 and 2 designate Γis that are symmetric and antisymmetric, respectively to ⊥C2s; if ⊥C2s do not exist, then with respect to σv
• primes ( ’ ) and double primes ( ” ) attached to Γis that are symmetric and antisymmetric, respectively, to σh
• for groups containing i, g subscript attached to Γis that are symmetric to i whereas u subscript designates Γis that are antisymmetic to i | textbooks/chem/Inorganic_Chemistry/Principles_of_Inorganic_Chemistry_II_(Nocera)/01%3A_Chapters/1.03%3A_Untitled_Chapter_4.txt |
The symmetry properties of molecules (i.e. the atoms of a molecule form a basis set) are described by point groups, since all the symmetry elements in a molecule will intersect at a common point, which is not shifted by any of the symmetry operations. There are also symmetry groups, called space groups, which contain operators involving translational motion.
The point groups are listed below along with their distinguishing symmetry elements
C1 : E (h = 1) $\Longrightarrow$ no symmetry
Cs : σ (h = 2) $\Longrightarrow$ only a mirror plane
Ci : i (h = 2) $\Longrightarrow$ only an inversion center (rare point group)
isomer of dichloro(difluoro)ethane
Cn : Cn and all powers up to Cn n = E (h = 2) $\Longrightarrow$ a cyclic point group
Cnv : Cn and nσv (h = 2n) … by convention a σv contains Cn (as opposed to σh which is normal to Cn). For n even, there are $\frac{n}{2} \sigma_{v}$ and $\frac{n}{2} \sigma_{v_{v}}$ ' with the σv containing the most atoms and the σvs containing the least atoms
Consider a second example:
Cnh : Cn and σh (normal to Cn) are generators of Sn operations as well (h = 2n)
S2n : S2n and all powers up to S2n 2n = E (h = 2n).
The F’s do not lie in the plane of the cyclopentane rings. If they did, then other symmetry operations arise; these are easiest to see by looking down the line indicated below:
Note Sn, where n is odd, is redundant with Cnh because Sn n = σh for n odd. As an example consider a S3 point group. S3 is the generator for S3, S3 2 (= C3 2 ) S3 3 (= σh), S3 4 (= C3), S3 5 , S3 6 (= E). The C3’s and σh are the distinguishing elements of the C3h point group.
1.05: New Page
The D point groups are distiguished from C point groups by the presence of rotation axes that are perpindicular to the principal axis of rotation.
Dn : Cn and n⊥C2 (h = 2n)
Example: Co(en)3 3+ is in the D3 point group,
In identifying molecules belonging to this point group, if a Cn is present and one ⊥C2 axis is identified, then there must necessarily be (n–1)⊥C2s generated by rotation about Cn.
Dnd : Cn, n⊥C2, nσd (dihedral mirror planes bisect the ⊥C2s)
Example: allene is in the D2d point group,
Two C2s bisect σds. The example on the bottom on pg 3 of the Lecture 4 notes was a harbinger of this point group. As indicated there, it is often easier to see these perpendicular C2s by reorienting the molecule along the principal axis of rotation.
Note: Dnd point groups will contain i, when n is odd
Dnh : Cn, n⊥C2, nσv, σh (h = 4n)
C∞v : C and ∞σv (h = ∞)
linear molecules without an inversion center
D∞h : C, ∞⊥C2, ∞σv, σh, i (h = ∞)
linear molecules with an inversion center
when working with this point group, it is often convenient to drop to D2h and then correlate up to D∞h
Td : E, 8C3, 3C2, 6S4, 6σd (h = 24)
Oh : E, 8C3, 6C2, 6C4, 3C2 (=C4 2 ), i, 6S4, 8S6, 3σh, 6σd (h = 48)
O : E, 8C3, 6C2, 6C4, 3C2 (=C4 2 )
A pure rotational subgroup of Oh, contains only the Cn’s of Oh point group
T : E, 8C3, 3C2
A pure rotational subgroup of Td, contains only the Cn’s of Td point group
Ih : generators are C3, C5, i (h = 120) \(\Longrightarrow\) the icosahedral point group
Kh : generators are Cφ, Cφ’, i (h = ∞) \(\Longrightarrow\) the spherical point group
Flow chart for assigning molecular point groups: | textbooks/chem/Inorganic_Chemistry/Principles_of_Inorganic_Chemistry_II_(Nocera)/01%3A_Chapters/1.04%3A_Untitled_Chapter_5.txt |
A common approximation employed in the construction of molecular orbitals (MOs) is the linear combination of atomic orbitals (LCAOs). In the LCAO method, the kth molecular orbital, $ψ_k$, is expanded in an atomic orbital basis,
$| \psi_{ k } \rangle = c_{ a } \phi_{ a } + c_{ b } \phi_{ b }+\ldots c_{ i } \phi_{ i } \label{eq1}$
where the $\phi_{i}$s are normalized atomic wavefunctions and . Solving Schrödinger’s equation and substituting for $\psi_{k}$ yields,
\begin{align*} H \psi_{ k } &= E \psi_{ k } \[4pt] | H - E | \psi_{ k } \rangle &=0 \end{align*}
Substitute Equation \ref{eq1}
$\left.| H - E | c _{ a } \phi_{ a }+ c _{ b } \phi_{ b }+\ldots+ c _{ i } \phi\right\rangle=0$
Left-multiplying by each $\phi_{i}$ yields a set of i linear homogeneous equations,
\begin{align*} \mathrm{c}_{\mathrm{a}}\left\langle\phi_{\mathrm{a}}|\mathrm{H}-\mathrm{E}| \phi_{\mathrm{a}}\right\rangle+\mathrm{c}_{\mathrm{b}}\left\langle\phi_{\mathrm{a}}|\mathrm{H}-\mathrm{E}| \phi_{\mathrm{b}}\right\rangle+\ldots+\mathrm{c}_{i}\left\langle\phi_{\mathrm{a}}|\mathrm{H}-\mathrm{E}| \phi_{i}\right\rangle &=0\[4pt] c_{a}\left\langle\phi_{b}|H-E| \phi_{a}\right\rangle+c_{b}\left\langle\phi_{b}|H-E| \phi_{b}\right\rangle+\ldots+c_{i}\left\langle\phi_{b}|H-E| \phi_{i}\right\rangle &=0\[4pt] \vdots\[4pt] c_{a}\left\langle\phi_{i}|H-E| \phi_{a}\right\rangle+c_{b}\left\langle\phi_{i}|H-E| \phi_{b}\right\rangle+\ldots+c_{i}\langle\phi_i|H-E| \phi_i\rangle&=0 \end{align*}
Solving the secular determinant,
$\begin{array}{ccccc} \mathrm{H}_{\mathrm{aa}}-\mathrm{ES}_{\text {aa }} & \mathrm{H}_{\mathrm{ab}}-\mathrm{ES}_{\text {ab }} & \cdots & \cdots & \mathrm{H}_{\mathrm{ai}}-\mathrm{ES}_{\mathrm{ai}} \ \mathrm{H}_{\mathrm{ba}}-\mathrm{ES}_{\text {ba }} & \mathrm{H}_{\mathrm{bb}}-\mathrm{ES}_{\mathrm{bb}} & \cdots & \cdots & \mathrm{H}_{\mathrm{bi}}-\mathrm{ES}_{\mathrm{bi}} \ \vdots & & \ddots & & \vdots \ \vdots & & & \ddots & \vdots \ \mathrm{H}_{\mathrm{ia}}-\mathrm{ES}_{\mathrm{ia}} & \mathrm{H}_{\mathrm{ib}}-\mathrm{ES}_{\mathrm{ib}} & \cdots & \cdots & \mathrm{H}_{\mathrm{ii}}-\mathrm{ES}_{\mathrm{ii}} \end{array} \mid=0 \nonumber$
where $H _{ ij }=\int \phi H \phi d \tau ; \quad S _{ ii }=\int \phi \phi d \tau=1 ; \quad H _{ ij }=\int \phi H \phi_{ j } d \tau ; \quad S _{ ij }=\int \phi \phi_{ j } d \tau$
In the Hückel approximation,
• $H _{ iv }=\alpha$
• $H _{ ij }=0$ for $\phi_{ i }$ not adjacent to $\phi_{ j }$
• $H _{ ij }=\beta$ for $\phi_{ i }$ not adjacent to $\phi_{ j }$
• $S _{i j}=1$
• $S _{ ij }=0$
The foregoing approximation is the simplest. Different computational methods treat these integrals differently. Extended Hückel Theory (EHT) includes all valence orbitals in the basis (as opposed to the highest energy atomic orbitals), all Sijs are calculated, the Hiis are estimated from spectroscopic data (as opposed to a constant, α) and Hijs are estimated from a simple function of $S_{ii}$, $H_{ii}$ and $H_{ij}$ (zero differential overlap approximation).
The EHT (and other Hückel methods) are termed semi–empirical because they rely on experimental data for quantification of parameters. Other semi-empirical methods include CNDO, MINDO, INDO, etc. in which more care is taken in evaluating Hij (these methods are based on self-consistent field procedures). Still higher level computational methods calculate the pertinent energies from first principles – ab initio and DFT. Here core potentials must be included and high order basis sets are used for the valence orbitals.
Benzene
As an example of the Hückel method, we will examine the frontier orbitals (i.e. determine eigenfunctions) and their associated orbital energies (i.e. eigenvalues) of benzene. The highest energy atomic orbitals of benzene are the C pπ orbitals. Hence, it is reasonable to begin the analysis by assuming that the frontier MO’s will be composed of LCAO of the C 2pπ orbitals:
The matrix representations for this orbital basis in D6h is,
$E \cdot\left[\begin{array}{l}\phi_{1} \ \phi_{2} \ \phi_{3} \ \phi_{4} \ \phi_{5} \ \phi_{6}\end{array}\right]=\left[\begin{array}{llllll}1 & 0 & 0 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 & 0 & 0 \ 0 & 0 & 1 & 0 & 0 & 0 \ 0 & 0 & 0 & 1 & 0 & 0 \ 0 & 0 & 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 0 & 0 & 1\end{array}\right]\left[\begin{array}{l}\phi_{1} \ \phi_{2} \ \phi_{3} \ \phi_{4} \ \phi_{5} \ \phi_{6}\end{array}\right]=\left[\begin{array}{l}\phi_{1} \ \phi_{2} \ \phi_{3} \ \phi_{4} \ \phi_{5} \ \phi_{6}\end{array}\right] \quad x_{\text {trace }}=6$
$C _{6} \cdot\left[\begin{array}{l}\phi_{1} \ \phi_{2} \ \phi_{3} \ \phi_{4} \ \phi_{5} \ \phi_{6}\end{array}\right]=\left[\begin{array}{llllll}0 & 1 & 0 & 0 & 0 & 0 \ 0 & 0 & 1 & 0 & 0 & 0 \ 0 & 0 & 0 & 1 & 0 & 0 \ 0 & 0 & 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 0 & 0 & 1 \ 1 & 0 & 0 & 0 & 0 & 0\end{array}\right]\left[\begin{array}{l}\phi_{1} \ \phi_{2} \ \phi_{3} \ \phi_{4} \ \phi_{5} \ \phi_{6}\end{array}\right]=\left[\begin{array}{c}\phi_{2} \ \phi_{3} \ \phi_{4} \ \phi_{5} \ \phi_{6} \ \phi_{1}\end{array}\right] \quad x_{\text {trace }}=0$
$C _{2}^{\prime} \cdot\left[\begin{array}{c}\phi_{1} \ \phi_{2} \ \phi_{3} \ \phi_{4} \ \phi_{5} \ \phi_{6}\end{array}\right]=\left[\begin{array}{rrrrrr}-1 & 0 & 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 & 0 & -1 \ 0 & 0 & 0 & 0 & -1 & 0 \ 0 & 0 & 0 & -1 & 0 & 0 \ 0 & 0 & -1 & 0 & 0 & 0 \ 0 & -1 & 0 & 0 & 0 & 0\end{array}\right]\left[\begin{array}{c}\phi_{1} \ \phi_{2} \ \phi_{3} \ \phi_{4} \ \phi_{5} \ \phi_{6}\end{array}\right]=\left[\begin{array}{c}\bar{\phi}_{1} \ \bar{\phi}_{6} \ \bar{\phi}_{5} \ \bar{\phi}_{4} \ \bar{\phi}_{3} \ \bar{\phi}_{2}\end{array}\right] \quad x _{\text {trace }}=-2$
The only orbitals that contribute to the trace are those that transform into +1 or –1 themselves (i.e. in phase or with opposite phase, respectively). Thus the trace of the remaining characters of the pπ basis may be determined by inspection:
\begin{array}{c|cccccccccccc}
\mathrm{D}_{6 \mathrm{~h}} & \mathrm{E} & 2 \mathrm{C}_{6} & 2 \mathrm{C}_{3} & \mathrm{C}_{2} & 3 \mathrm{C}_{2}^{\prime} & 3 \mathrm{C}_{2}^{\prime \prime} & \mathrm{i} & 2 \mathrm{~S}_{3} & 2 \mathrm{~S}_{6} & \sigma_{\mathrm{h}} & 3 \sigma_{\mathrm{v}} & 3 \sigma_{\mathrm{d}} \
\hline \Gamma_{\mathrm{p} \pi} & 6 & 0 & 0 & 0 & -2 & 0 & 0 & 0 & 0 & -6 & 2 & 0
\end{array}
The Γ representation is a reducible basis that must be decomposed into irreducible representations.
Decomposition of reducible representations may be accomplished with the following relation:
Returning to the above example,
$a_{A_{19}}=\frac{1}{24}[6 \cdot 1 \cdot 1+0 \cdot 0 \cdot 0+(-2)(1)(3)+0+0+0+0+(-6)(1)(1)+2 \cdot 1 \cdot 3+0]=0 \nonumber$
thus A1g does not contribute to Γ
How about $a_{A_{2 u}}$?
$a_{A_{2 u}}=\frac{1}{24}[6 \cdot 1 \cdot 1+0 \cdot 0 \cdot 0+(-2)(-1)(3)+0+0+0+0+(-6)(1)(-1)+2 \cdot 1 \cdot 3+0]=1 \nonumber$
Continuing the procedure, one finds,
$\Gamma_{ p \pi}= A _{2 u }+ B _{29}+ E _{19}+ E _{2 u }$
these are the symmetries of the MO’s formed by the LCAO of pπ orbitals in benzene.
With symmetries established, LCAOs may be constructed by “projecting out” the appropriate linear combination. A projection operator, P(i) , allows the linear combination of the ith irreducible representation to be determined,
A drawback of projecting out of the D6h point group is the large number of operators. The problem can be simplified by dropping to the pure rotational subgroup, C6. In this point group, the full extent of mixing among $\phi_{1}$ through $\phi_{6}$ is maintained; however the inversion center, and hence u and g symmetry labels are lost. Thus in the final analysis, the Γis in C6 will have to be correlated to those in D6h. Reformulating in C6,
The projection of the SALC that from $\phi_{1}$ transforms as A is,
Continuing,
• $P ^{( B )} \phi_{1}=\phi_{1}-\phi_{2}+\phi_{3}-\phi_{4}+\phi_{5}-\phi_{6}$
• $P ^{\left( E _{1 a}\right)} \phi_{1}=\phi_{1}+\varepsilon \phi_{2}-\varepsilon^{*} \phi_{3}-\phi_{4}-\varepsilon \phi_{5}+\varepsilon^{*} \phi_{6}$
• $P ^{\left( E _{16}\right)} \phi_{1}=\phi_{1}+\varepsilon^{*} \phi_{2}-\varepsilon \phi_{3}-\phi_{4}-\varepsilon^{*} \phi_{5}+\varepsilon \phi_{6}$
• $P ^{\left( E _{22}\right)} \phi_{1}=\phi_{1}-\varepsilon^{*} \phi_{2}-\varepsilon \phi_{3}+\phi_{4}-\varepsilon^{*} \phi_{5}-\varepsilon \phi_{6}$
• $P ^{\left( E _{26}\right)} \phi_{1}=\phi_{1}-\varepsilon \phi_{2}-\varepsilon^{*} \phi_{3}+\phi_{4}-\varepsilon \phi_{5}-\varepsilon^{*} \phi_{6}$
The projections contain imaginary components; the real component of the linear combination may be realized by taking ± linear combinations:
For $\psi\left( E _{1 a }\right)$ SALC’s:
$\psi_{3}^{\prime}\left(E_{1 a}\right)+\psi_{4}^{\prime}\left(E_{1 b}\right)=2 \phi_{1}+\left(\varepsilon+\varepsilon^{*}\right) \phi_{2}-\left(\varepsilon+\varepsilon^{*}\right) \phi_{3}-2 \phi_{4}-\left(\varepsilon+\varepsilon^{*}\right) \phi_{5}+\left(\varepsilon+\varepsilon^{*}\right) \phi_{6}$
$\psi_{3}^{\prime}\left(E_{1 a}\right)-\psi_{4}^{\prime}\left(E_{1 b}\right)=\left(\varepsilon-\varepsilon^{*}\right) \phi_{2}+\left(\varepsilon-\varepsilon^{*}\right) \phi_{3}+\left(\varepsilon^{*}-\varepsilon\right) \phi_{5}+\left(\varepsilon^{*}-\varepsilon\right) \phi_{6}$
where in the C6 point group,
$\varepsilon=\exp \left(\frac{2 \pi}{6}\right) i =\cos \frac{2 \pi}{6}- i \sin \frac{2 \pi}{6}$
$\therefore \varepsilon+\varepsilon^{*}=\cos \frac{2 \pi}{6}- i \sin \frac{2 \pi}{6}+\cos \frac{2 \pi}{6}+ i \sin \frac{2 \pi}{6}=2 \cos \frac{2 \pi}{6}=1$
$\varepsilon^{*}-\varepsilon=-\cos \frac{2 \pi}{6}+ i \sin \frac{2 \pi}{6}-\cos \frac{2 \pi}{6}+ i \sin \frac{2 \pi}{6}=2 i \sin \frac{2 \pi}{6}= i \sqrt{3}$
$\varepsilon-\varepsilon^{*}=\cos \frac{2 \pi}{6}- i \sin \frac{2 \pi}{6}-\left(\cos \frac{2 \pi}{6}+ i \sin \frac{2 \pi}{6}\right)=-2 i \sin \frac{2 \pi}{6}=- i \sqrt{3}$
∴ the E1a LCAO’s reduce to (again ignoring the constant prefactor),
$\psi_{3}\left( E _{1}\right)=\psi_{3}^{\prime}\left( E _{1 a }\right)+\psi_{4}^{\prime}\left( E _{1 b }\right)=2 \phi_{1}+\phi_{2}-\phi_{3}-2 \phi_{4}-\phi_{5}+\phi_{6}$
$\psi_{4}\left( E _{1}\right)=\psi_{3}^{\prime}\left( E _{1 a }\right)-\psi_{4}^{\prime}\left( E _{1 b }\right)=\phi_{2}+\phi_{3}-\phi_{5}-\phi_{6}$
Similarly for the ψ5(E2) and ψ6(E2) LCAO’s… normalizing the SALC’s
$\begin{array}{ll}\psi_{1}( A )=\frac{1}{\sqrt{6}}\left(\phi_{1}+\phi_{2}+\phi_{3}+\phi_{4}+\phi_{5}+\phi_{6}\right) & \psi_{2}( B )=\frac{1}{\sqrt{6}}\left(\phi_{1}-\phi_{2}+\phi_{3}-\phi_{4}+\phi_{5}+\phi_{6}\right) \ \psi_{3}\left( E _{1}\right)=\frac{1}{\sqrt{12}}\left(2 \phi_{1}+\phi_{2}-\phi_{3}-2 \phi_{4}-\phi_{5}+\phi_{6}\right) & \psi_{4}\left( E _{1}\right)=\frac{1}{2}\left(\phi_{2}+\phi_{3}-\phi_{5}-\phi_{6}\right) \ \psi_{5}\left( E _{2}\right)=\frac{1}{\sqrt{12}}\left(2 \phi_{1}-\phi_{2}-\phi_{3}+2 \phi_{4}-\phi_{5}-\phi_{6}\right) & \psi_{6}\left( E _{2}\right)=\frac{1}{2}\left(\phi_{2}-\phi_{3}+\phi_{5}-\phi_{6}\right)\end{array}$
The pictorial representation of the SALC’s are, | textbooks/chem/Inorganic_Chemistry/Principles_of_Inorganic_Chemistry_II_(Nocera)/01%3A_Chapters/1.06%3A_New_Page.txt |
The energies (eigenvalues) may be determined by using the Hückel approximation.
$E \left( \psi_{B_{2g}} \right) = \dfrac{1}{6}(6)( \alpha - 2\beta ) = \alpha - 2\beta$
The energies of the remaining LCAO’s are:
$E \left( \psi_{E_{1g}}^a \right) = \left( \psi_{E_{1g}}^b \right) = \alpha + \beta$
$E \left( \psi_{E_{2u}}^a \right) = \left( \psi_{E_{2u}}^b \right) = \alpha - \beta$
Note the energies of the E orbitals are degenerate. Constructing the energy level diagram, we set α = 0 and β as the energy parameter (a negative quantity, so an MO whose energy is positive in units of β has an absolute energy that is negative),
The energy of benzene based on the Hückel approximation is
$E_{total} = 2(2\beta) + 4(\beta) = 8\beta$
What is the delocalization energy (i.e. π resonance energy)?
To determine this, we consider cyclohexatriene, which is a six-membered cyclic ring with 3 localized π bonds; in other terms, cyclohexatriene is the product of three condensed ethylene molecules. For ethylene,
Following the procedures outlined above, we find,
\begin{aligned}
&\mathrm{E}\left(\psi_{1}\right)=\left\langle\frac{1}{\sqrt{2}}\left(\phi_{1}+\phi_{2}\right)|\mathrm{H}| \frac{1}{\sqrt{2}}\left(\phi_{1}+\phi_{2}\right)\right\rangle=\frac{1}{2}(2 \alpha+2 \beta)=\beta \
&\mathrm{E}\left(\psi_{2}\right)=\left\langle\frac{1}{\sqrt{2}}\left(\phi_{1}-\phi_{2}\right)|\mathrm{H}| \frac{1}{\sqrt{2}}\left(\phi_{1}-\phi_{2}\right)\right\rangle=\frac{1}{2}(2 \alpha-2 \beta)=-\beta
\end{aligned}
The above was determined in the C2 point group. Correlating to D2h point group gives A in C2 → B1u in D2h and B in C2 → B2g in D2h:
The Hückel energy of ethylene is,
$E_{total} = 2(\beta) = 2\beta$
Therefore, the energy of cyclohexatriene is 3(2β) = 6β. The resonance energy is therefore,
The bond order is given by,
Consider the B.O. between the C1 and C2 carbons of benzene
$[ \psi_{1}(A_{2u})] = 2( \dfrac{1}{ \sqrt{6}} )( \dfrac{1}{ \sqrt{6}}) = \dfrac{1}{3}$
$[ \psi_{3}(E_{1g}^a)] = 2( \dfrac{1}{ \sqrt{12}} )( \dfrac{1}{ \sqrt{12}}) = \dfrac{1}{3}$
$[ \psi_{4}(E_{1g}^b)] = \dfrac{1}{2}(0)( \dfrac{1}{2} ) = \dfrac{0}{ \dfrac{2}{3} }$
1.08: New Page
This lecture will provide a derivation of the LCAO eigenfunctions and eigenvalues of N total number of orbitals in a cyclic arrangement. The problem is illustrated below:
There are two derivations to this problem.
Polynomial Derivation
The Hückel determinant is given by,
$D_{N}(x)=\left|\begin{array}{ccccccccc} x & 1 & & & & & & & \ 1 & x & 1 & & & & & & \ & 1 & x & \ddots & & & & & \ & & 1 & \ddots & \ddots & & & & \ & & & \ddots & \ddots & \ddots & & & \ & & & & \ddots & \ddots & \ddots & & \ & & & & & \ddots & \ddots & 1 & \ & & & & & & \ddots & x & 1 \ & & & & & & 1 & x \end{array}\right|=0$
where
$x=\frac{\alpha-E}{\beta}$
From a Laplace expansion one finds,
DN(x) = xDn-1(x) - DN-2(x)
Where
With these parameters defined, the polynomial form of DN(x) for any value of N can be obtained,
D3(x) = xD2(x) – D1(x) = x(x2–1) – x = x(x2–2)
D4(x) = xD3(x) – D2(x) = x2(x2–2) – (x2–1)
$\vdots \nonumber$
and so on
The expansion of DN(x) has as its solution,
$x={-2}\cos \dfrac{2\pi}{N}j (j= 0, 1, 2, 3...N-1) \nonumber$
and substituting for x,
$E = \alpha + 2\beta\cos \dfrac{2\pi}{N}j (j= 0, 1, 2, 3...N-1) \nonumber$
Standing Wave Derivation
An alternative approach to solving this problem is to express the wavefunction directly in an angular coordinate, θ
For a standing wave of λ about the perimeter of a circle of circumference c,
$\psi_j = \sin \dfrac{c}{\lambda} \theta \nonumber$
The solution to the wave function must be single valued ∴ a single solution must be obtained for ψ at every 2nπ or in analytical terms,
Thus the amplitude of $ψ_j$ at atom m is, (where c/λ = j and θ = (2π/N)m)
$\psi_{j}(m) = \sin{2m\pi}{N}j (j= 0, 1, 2, 3...N-1) \nonumber$
Within the context of the LCAO method, ψj may be rewritten as a linear combination in φm with coefficients cjm. Thus the amplitude of ψj at m is equivalent to the coefficient of φm in the LCAO expansion,
$\psi_{j} = \displaystyle \sum_{k=1}^N C_{jm\phi m}$
Where
$C_{jm} = \sin{2\pi m}{N}j (j= 0, 1, 2, 3...N-1) \nonumber$
The energy of each MO, ψj, may be determined from a solution of Schrödinger’s equation,
The energy of the φm orbital is obtained by left–multiplying by φm,
but the Hückel condition is imposed; the only terms that are retained are those involving φm, φm+1, and φm-1. Expanding,
Evaluating the integrals,
Substituting for cjm,
$\alpha \sin \dfrac{2\pi m}{N}j + \beta \left( \sin \dfrac{2\pi (m+1)}{N}j + \sin \dfrac{2\pi (m-1)}{N}j \right) = E_{j} \sin \dfrac{2\pi m}{N}j \nonumber$
$\alpha + \dfrac{ \beta \left( \sin \dfrac{2\pi (m+1)}{N}j + \sin \dfrac{2\pi (m-1)}{N}j \right)}{ \sin \dfrac{2\pi m}{N}j} = E_{j} \nonumber$
$E_{j} = \alpha + 2\beta \cos k \nonumber$
$E_{j} = \alpha + 2\beta \cos \dfrac{2\pi}{N}j (j= 0, 1, 2, 3...N-1) \nonumber$
Let’s look at the simplest cyclic system, N = 3
Continuing with our approach (LCAO) and using Ej to solve for the eigenfunction, we find…
Using the general expression for ψj, the eigenfunctions are:
$\psi_{0} = e^{i(0)0} \phi_{1} + e^{i(0) \dfrac{2\pi}{3}} \phi_{2} + e^{i(0) \dfrac{4\pi}{3}} \phi_{3} \nonumber$
$\psi_{1} = e^{i(1)0} \phi_{1} + e^{i(1) \dfrac{2\pi}{3}} \phi_{2} + e^{i(1) \dfrac{4\pi}{3}} \phi_{3} \nonumber$
$\psi_{-1} = e^{i(-1)0} \phi_{1} + e^{i(-1) \dfrac{2\pi}{3}} \phi_{2} + e^{i(-1) \dfrac{4\pi}{3}} \phi_{3} \nonumber$
Obtaining real components of the wavefunctions and normalizing,
\begin{array}{ll}
\psi_{0}=\phi_{1}+\phi_{2}+\phi_{3} \rightarrow & \psi_{0}=\frac{1}{\sqrt{3}}\left(\phi_{1}+\phi_{2}+\phi_{3}\right) \
\psi_{+1}+\psi_{-1}=2 \phi_{1}-\phi_{2}-\phi_{3} \rightarrow & \psi_{1}=\frac{1}{\sqrt{6}}\left(2 \phi_{1}-\phi_{2}-\phi_{3}\right) \
\psi_{+1}-\psi_{-1}=\phi_{2}-\phi_{3} \rightarrow & \psi_{2}=\frac{1}{\sqrt{2}}\left(\phi_{2}-\phi_{3}\right)
\end{array}
\]
Summarizing on a MO diagram where α is set equal to 0, | textbooks/chem/Inorganic_Chemistry/Principles_of_Inorganic_Chemistry_II_(Nocera)/01%3A_Chapters/1.07%3A_New_Page.txt |
The LCAO method for cyclic systems provides a convenient starting point for the development of the electronic structure of solids.
At very large N, as the circumference of the circle approaches ∞, the cyclic problem converges to a linear one,
Qualitatively, from a MO energy level perspective,
More quantitatively, in moving from cyclic to linear systems, instead of describing orbital (atom) positions angularly, the position of an atom is described by ma, where m is the number of the atom in the array and a is the distance between atoms. Thus, the θ of the N-cyclic derivation becomes ma,
A few words about $k$. It is:
• a measure of the number of nodes
• an index of wavefunction and accordingly symmetry of wavefunction
• a “quantum number” for a given ψk
• a measure of length, related to wavelength λ–1
• from DeBroglie’s relation, λ = (h/p) , therefore k is also a wave vector that measures momentum
Returning to the foregoing discussion, note that k parametrically depends on a. Since a is a lattice parameter of the unit cell, there are as many k’s as there are unit cells in the crystal. In the linear case, the unit cell is the distance between adjacent atoms: there are n atoms ∴ n unit cells or in other terms – there are as many k’s as atoms in the 1-D chain.
Let’s determine the energy values of limits, k = 0 and k = (π/a) :
The energies for these band structures at the limits of k are:
$E_{0} = \alpha + 2\beta \cos(0)a = \alpha + 2\beta$
$E_{ \dfrac{ \pi }{a}} = \alpha + 2\beta \cos( \dfrac{ \pi }{a} )a = \alpha - 2\beta$
Note that k is quantized; so there are a finite number of values between α+2β and α–2β but for a very large number (~1023 atoms) between the limits of k. Thus, the energy is a continuous and smoothly varying function between these limits.
The range - π/a ≤ k ≤ π/a or |k| ≤ π/a is unique because the function repeats itself a a a outside these limits. This unique range of k values is called the Brillouin zone. The first Brillouin zone is plotted above from 0 to π/a (symmetric reflection from − π/a to 0).
With a given number of e s in the solid, the levels will be filled to a certain energy called the Fermi level, which corresponds to a certain value of k (= kF). In the k above example, there are more electrons than there are orbitals, so kF > k/2a. If each atomic orbital contributed 1e to the system, then EF would occur for kF = π/2a.
The symmetry of the individual atomic orbitals determines much about band structure. Consider p-orbitals overlapping in a linear array (vs the 1s orbitals of the above treatment). Analyzing limiting forms:
The energy band is opposite of that for the sσ orbital LCAO because the (+) LCAO for a pσ orbital is antibonding.
Thus, molecules are easily related to solids via Hückel theory. Not surprisingly, there is a language of chemistry describing the electronic structure of molecules that is related to the language of physics describing the electronic structure of solids. Below are some of the terms that chemists and physicists use to describe similar phenomena in molecules and solids:
Band Width or Dispersion
What determines the width or dispersion of a band? As for the HOMO-LUMO gap in a molecule, the overlap of neighboring orbitals determines the energy dispersion of a band – the greater the overlap, the greater the dispersion. Note how the band dispersion of a linear chain of H atoms varies as the 1s orbitals of the H atoms are spaced 1, 2, 3 Å apart (E of an isolated H atom is –13.6 eV):
Density of States
or in other words, it is the area under the curve to kF. Another useful quantity is the number of orbitals between E(k) + dE(k), called the density of states (DOS). For a 1-D system,
A plot of the above equations is,
In the above DOS diagram, no energy gap separates the filled and empty bands, i.e. there is a continuous density of states – this property is characteristic of a metal. If an energy gap between filled and empty orbitals is present and it can be thermally surmounted, then it is semiconductor; an energy gap that cannot be surmounted is an insulator.
A 1-D Example
Arguably the best known 1-D system in inorganic chemistry is K2Pt(CN)4 and its partially oxidized compound (e.g. K2Pt(CN)4Br0.3).
Normal platinocyanide, K2Pt(CN)4:
Partially oxidized platinocyanide, K2Pt(CN)4Br0.3•3H2O:
Note: d(Pt-Pt) = 2.78 Å in Pt metal
To explain these disparate properties of the 1-D compounds, consider the molecular subunit Pt(CN)42-:
The dispersion of the bands is due to the different overlaps of the dσ, dπ and dδ orbitals.
Band structure (or first Brillouin zones) derived from the frontier MO’s is:
For partially oxidized system, the σ bond derived from dz2 should be partially filled and thus metallic, but it is not, partially oxidized K2Pt(CN)4Brx is a semiconductor. To explain this anomaly, consider how the band structure is perturbed upon partial oxidation:
Isolating on the dz2 band in K2Pt(CN)4, the Pt atoms are evenly spaced with lattice dimension a (I). Upon oxidation, the Pt chain can distort to give a lattice dimension 2a (II). In the case of the K2Pt(CN)4Br0.3•3H2O the distortion is a rotation of Pt subunits and formation of dimers within chain, thus the unit cell dimension is pinned to every other Pt atom.
1.10: General electronic considerations of metal-ligand complexes
Metal complexes are Lewis acid-base adducts formed between metal ions (the acid) and ligands (the base).
The interaction of the frontier atomic (for single atom ligands) or molecular (for many atom ligands) orbitals of the ligand and metal lead to bond formation,
More quantitatively, the interaction energy of stabilization and destabilization, εσ and εσ*, respectively, is defined on the following energy level diagram,
Treating this problem within the LCAO framework comprising metal and ligand orbitals yields,
ψ = cMφM + cLφL
and solving for the Hamiltonian,
\begin{aligned} &\mathrm{H} \psi=\mathrm{E} \psi \ &\left.|\mathrm{H}-\mathrm{E}| \psi\rangle=\left|\mathrm{H}-\mathrm{E}_{\mathrm{j}}\right| \mathrm{c}_{\mathrm{M}} \phi_{\mathrm{M}}+\mathrm{c}_{\mathrm{L}} \phi\right\rangle=0 \end{aligned} \] Left-multiplying by φM and φL yields the set of linear homogeneous equations,
\begin{aligned}
&c_{M}\left\langle\phi_{M}|H-E| \phi_{M}\right\rangle+c_{L}\left\langle\phi_{M}|H-E| \phi\right\rangle=0 \
&c_{M}\left\langle\phi_{L}|H-E| \phi_{M}\right\rangle+c_{L}\langle\phi|H-E| \phi\rangle=0
\end{aligned}
\]
which furnishes the secular determinant,
$\left|\begin{array}{cc} \mathrm{H}_{M M}-\mathrm{E} & \mathrm{H}_{M L}-\mathrm{ES}_{M L} \ \mathrm{H}_{M L}-\mathrm{ES}_{M L} & \mathrm{H}_{L L}-\mathrm{E} \end{array}\right|=\left|\begin{array}{cc} \mathrm{E}_{M}-\mathrm{E} & \mathrm{H}_{M L}-\mathrm{ES}_{M L} \ \mathrm{H}_{M L}-\mathrm{ES}_{M L} & \mathrm{E}_{L}-\mathrm{E} \end{array}\right|=0 \] The Wolfsberg-Hemholz approximation provides a value for HML, defined as HML = SML (EL + EM) Substituting HML in the above expressions for E+ and E yields,$
\varepsilon_{\sigma}=\frac{E_{M}{ }^{2} S_{M L}{ }^{2}}{\Delta E_{M L}} \quad \varepsilon_{\sigma *}=\frac{E_{L}{ }^{2} S_{M L}{ }^{2}}{\Delta E_{M L}}
\]
The derivation highlights the following general rules for the construction of MO diagrams,
(1) M—L atomic orbital mixing is proportional to the overlap of the metal and ligand orbital, i.e., SML
corollary A: only orbitals of correct symmetry can mix and ∴ give a nonzero interaction energy (i.e. SML ≠ 0)
corollary B: σ interactions typically give rise to larger interaction energies than those resulting from π interactions and π interactions are greater than δ interactions owing to more directional bonding along the series SML(σ) > SML(π) > SML(δ)
(2) M–L atomic orbital mixing is inversely proportional to energy difference of mixing orbitals (i.e. ΔEML).
Another issue of interest for the construction of MOs is,
(3) The order of the EL and EM energy levels almost always is:
This energy ordering comes directly from Valence Orbital Ionization Energies (VOIE) of metal and main group atoms and PES spectra of molecular ligands.
PES energies of ligands are in eVs (note: a VOIE is simply the opposite of the ionization energy)
General observations:
(1) The s orbitals are generally too low in energy to participate in bonding (ΔEML(σ) is very large)
(2) Filled p orbitals are the frontier orbitals, and they have VOIEs that place them below the metal orbitals
(3) For molecular ligands, since the frontier orbitals comprise s and p orbitals, here too filled ligand orbitals have energies that are stabilized relative to the metal orbitals | textbooks/chem/Inorganic_Chemistry/Principles_of_Inorganic_Chemistry_II_(Nocera)/01%3A_Chapters/1.09%3A_New_Page.txt |
Before tackling the business of the complex, the nature of the ligand frontier orbitals must be considered. There are three general classes of ligands, as defined by their frontier orbitals: σ-donor ligands, π-donor ligands and π-acceptor ligands.
σ-donor ligands
These ligands donate two e– s from an orbital of σ-symmetry:
H(1s2 ), NH3 (2a1 lp), PR3 (2a1 lp), CH3- (2a1 lp), OH2 (b1 lp)
Note, some of these ligands are atomic, while others are LCAO-MOs. The frontier orbitals for bonding to the metal are thus are either atomic or molecular orbitals, depending on the nature of the ligand.
As an example of a molecular ligand, consider the ammonia ligand. Ammonia is formed from the LCAO between the valence orbitals of a central nitrogen and the three 1s orbitals of three hydrogens,
To begin this problem, the symmetry-adapted linear combinations of the three 1s orbitals must be determined. Hence, the basis will be derived from the H orbitals. Because the H(1s) orbitals can only form σ bonds, the choice of 3 σ N–H bonds is an appropriate basis set,
The transformation properties of the σ bonds (in C3v symmetry) are as follows:
$E \begin{bmatrix} σ_{1} \ σ_{2} \ σ_{3} \end{bmatrix} \rightarrow \begin{bmatrix} σ_{1} \ σ_{2} \ σ_{3} \end{bmatrix} \rightarrow \begin{bmatrix} 0 & 1 & 0 \ 0 & 0 & 1 \ 1 & 0 & 0 \end{bmatrix}$
$C_{3} \begin{bmatrix} σ_{1} \ σ_{2} \ σ_{3} \end{bmatrix} \rightarrow \begin{bmatrix} σ_{1} \ σ_{2} \ σ_{3} \end{bmatrix} \rightarrow \begin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{bmatrix}$
$σ_{v} \begin{bmatrix} σ_{1} \ σ_{2} \ σ_{3} \end{bmatrix} \rightarrow \begin{bmatrix} σ_{1} \ σ_{2} \ σ_{3} \end{bmatrix} \rightarrow \begin{bmatrix} 1 & 0 & 0 \ 0 & 0 & 1 \ 0 & 1 & 0 \end{bmatrix}$
These representation of this basis may be quickly ascertained by realizing that only bonds (or H(1s) orbitals) that do not move will contribute to the trace of the matrix representation,
$\begin{array}{c|ccc} \mathrm{C}_{3 \mathrm{v}} & \mathrm{E} & 2 \mathrm{C}_{3} & 3 \sigma_{\mathrm{v}} \ \hline \Gamma_{\sigma} & 3 & 0 & 1 \end{array}\rightarrow a_{1} + e$
Projecting out the a1 and e SALCs of the 3H orbitals, we realize that the transformation properties of the H orbitals are preserved in the C3 rotational subgroup,
Application of the projection operator in the cyclic C3 point group is an easy task – can simply read out the projections,
\begin{aligned}
&\mathrm{P}^{\mathrm{a}_{1}}\left(\sigma_{1}\right) \rightarrow 1 \cdot \mathrm{E} \sigma_{1}+1 \cdot \mathrm{C}_{3} \sigma_{1}+1 \cdot \mathrm{C}_{3}^{2} \sigma_{1}=\sigma_{1}+\sigma_{2}+\sigma_{3} \
&\mathrm{P}^{\mathrm{e}(1)}\left(\sigma_{1}\right) \rightarrow 1 \cdot \mathrm{E} \sigma_{1}+\left(\varepsilon^{*}\right) \mathrm{C}_{3} \sigma_{1}+\varepsilon \mathrm{C}_{3}^{2} \sigma_{1}=\sigma_{1}+\varepsilon^{*} \sigma_{2}+\varepsilon \sigma_{3} \
&\mathrm{P}^{\mathrm{e}(2)}\left(\sigma_{1}\right) \rightarrow 1 \cdot \mathrm{E} \sigma_{1}+\varepsilon \mathrm{C}_{3} \sigma_{1}+\left(\varepsilon^{*}\right) \mathrm{C}_{3}^{2} \sigma_{1}=\sigma_{1}+\varepsilon \sigma_{2}+\varepsilon^{*} \sigma_{3}
\end{aligned}
Taking appropriate linear combinations and normalizing,
Only orbitals of the same symmetry can form a LCAO; thus the a1 SALC of the 3H(1s) orbitals can only combine with the a1 orbitals of the central N (i.e., the 2s and 2pz valence orbitals),
he 2py orbital combines with e(+) , it is orthogonal to e(–), whereas the opposite is true for 2px orbital,
The MO is constructed by overlapping orbitals of the same symmetry. The greater the overlap, the greater the splitting between the orbitals. Note that the a1 SALC participates in two types of σ interactions, one with the 2s orbital and one with the 2pz orbital of nitrogen. The highest energy orbital, the ligand HOMO orbital, is used for bonding to the metal. This orbital too is composed of two types of interactions: (i) it is Lσ(a1)–N(2s) antibonding and (ii) Lσ(a1)–N(2pz) bonding in character. The energy of the atomic orbitals are shown in parenthesis.
Simple hybridization arguments predict two different of bond energies for NH3: (1) the lone pair and (2) the σ N–H bond. The MO diagram on the other hand predicts three different energies. The photoelectron spectrum of NH3 exhibits three ionization energies, thus verifying the MO bonding model.
A second molecular ligand is water. The ligand has two lone pairs, but only one is used in bonding to the metal. The reason for this electronic asymmetry and why only one lone pair is only available for bonding becomes evident from the electronic structure of the water molecule.
The basis set for water is the 2H(1s) orbitals and the O(2s, 2pz, 2px, 2py) atomic orbitals. The proper symmetry adapted linear combination for the 2H(1s) orbitals may be ascertained using the above σ bonds.
\begin{aligned}
&\begin{array}{c|cccc}
\mathbf{C}_{\mathbf{2 v}} & \mathrm{E} & \mathrm{C}_{2} & \sigma_{\mathrm{v}}(\mathrm{xz}) & \sigma_{\mathrm{v}}(\mathrm{yz}) \
\hline \Gamma_{\sigma} & 2 & 0 & 2 & 0 & \rightarrow a_{1} + b_{1} \
\hline \sigma_{1} \rightarrow & \sigma_{1} & \sigma_{2} & \sigma_{1} & \sigma_{2}
\end{array}\
\end{aligned}
Applying the projection operator,
\begin{aligned}
&\mathrm{P}^{\mathrm{a}_{1}}\left(\sigma_{1}\right) \rightarrow 1 \cdot \overbrace{ {\mathrm{E} \sigma_{1}}}^{ \sigma_{1}}+1 \cdot \overbrace{ {\mathrm{C}_{2} \sigma_{1}} }^{\sigma_{2}}+1 \cdot \overbrace{ {\sigma(\mathrm{xz}) \cdot \sigma_{1}} }^{\sigma_{1}}+1 \cdot \overbrace{ {\sigma(\mathrm{yz}) \cdot \sigma_{1}} }^{\sigma_{2}} \rightarrow \psi_{\mathrm{a}_{1}}=\frac{1}{\sqrt{2}}\left(\sigma_{1}+\sigma_{2}\right)\
&\mathrm{P}^{\mathrm{b}_{1}}\left(\sigma_{1}\right) \rightarrow 1 \cdot \mathrm{E} \sigma_{1}+(-1) \cdot \mathrm{C}_{2} \sigma_{1}+1 \cdot \sigma(\mathrm{xz}) \cdot \sigma_{1}+(-1) \cdot \sigma(\mathrm{yz}) \cdot \sigma_{1} \rightarrow \psi_{\mathrm{b}}=\frac{1}{\sqrt{2}}\left(\sigma_{1}-\sigma_{2}\right)
\end{aligned}
The s and pz orbitals on O have a1 symmetry and thus will mix with the Lσ(a1), the px has b1 symmetry and will mix with Lσ(b1) and the py orbital is rigorously nonbonding, i.e., does not have a symmetry counterpart of the O atom, and hence no LCAO is formed using this orbital.
Again, the simple hybridization picture of bonding is shown to be incorrect, and the MO bonding model is corroborated.
π-donors
π-donors In addition to donating electron density to a metal via a σ-bond, es may be provided to the metal via a π-symmetry interaction. π-donor ligands include X(halide), amide (NR2 ), sulfide (S2–), oxide (O2–), alkoxide (RO ).
The amide MO may be constructed by beginning with the MO of “planar” NH3, followed by its perturbation upon removal of H+,
π-acceptors
This class of ligands donate es from a σ orbital and they accept es from the metal into an empty π* orbital. CO is the archetype of this ligand class. Other π-acceptors are NO+, CN, CNR. Consider the MO diagram of CO below; the HOMO is filled and of σ-symmetry, the LUMO is empty and of π* symmetry. | textbooks/chem/Inorganic_Chemistry/Principles_of_Inorganic_Chemistry_II_(Nocera)/01%3A_Chapters/1.11%3A_Frontier_molecular_orbitals_of_-donor_-donor_and_-acceptor_ligands.txt |
An octahedral complex comprises a central metal ion and six terminal ligands. If the ligands are exclusively σ-donors, then the basis set for the ligands is defined as follows,
Ligands that move upon the application of an operation, R, cannot contribute to the diagonal matrix element of the representation. Since the σ bond is along the internuclear axis that connects the ligand and metal, the transformation properties of the ligand are correspondent with that of the M–L σ bond. Moreover, a σ bond has no phase change within the internuclear axis, hence the bond can only transform into itself (+1) or into another ligand (0).
\begin{array}{c|cccccccccc}
\mathrm{O}_{\mathrm{h}} & \mathrm{E} & \mathrm{8C}_{3} & 6 \mathrm{C}_{2} & 6 \mathrm{C}_{4} & 3 \mathrm{C}_{2}\left(=\mathrm{C}_{4}{ }^{2}\right) & \mathrm{i} & 6 \mathrm{~S}_{4} & 8 \mathrm{~S}_{6} & 3 \sigma_{\mathrm{h}} & 6 \sigma_{\mathrm{d}} \
\hline \Gamma_{\mathrm{L} \sigma} & 6 & 0 & 0 & 2 & 2 & 0 & 0 & 0 & 4 & 2
\end{array}
$\Gamma_{\mathrm{L} \sigma}=\mathrm{a}_{1 \mathrm{~g}}+\mathrm{t}_{1 \mathrm{u}}+\mathrm{e}_{\mathrm{g}}$
Need now to determine the SALCs of the Lσ basis set. Three different methods will deliver the SALCs.
Method 1
As we have done previously, the SALCs of Lσ may be determined using the projection operator. Note that the ligand mixing in Oh is retained in the pure rotational subgroup, O. Can thus drop from Oh → O, thereby saving 24 operations.
The A1 irreducible representation is totally symmetric. Hence the projection is simply the sum of the above ligand transformations.
PA1(L1) ~ 4(L1 + L2 + L3 + L4 + L5 + L6)
and normalizing yields,
$\psi_{a_{19}}=\frac{1}{\sqrt{6}}\left(\mathrm{~L}_{1}+\mathrm{L}_{2}+\mathrm{L}_{3}+\mathrm{L}_{4}+\mathrm{L}_{5}+\mathrm{L}_{6}\right)$
The application of the projection operator for the E irreducible representation furnishes the Eg SALCs.
\begin{aligned} P^{E}\left(L_{1}\right) & \rightarrow\left(2 L_{1}-L_{3}-L_{4}-L_{4}-L_{5}-L_{6}-L_{5}-L_{6}-L_{3}+2 L_{1}+2 L_{2}+2 L_{2}\right) \ & \rightarrow\left(4 L_{1}+4 L_{2}-2 L_{3}-2 L_{4}-2 L_{5}-2 L_{6}\right) \end{aligned}
But Eg is a doubly degenerate representation, and therefore there is a another SALC. As is obvious from above, the projection operator only yields one of the two SALCs. How do we obtain the other?
Method 2
The Schmidt orthogonalization procedure can extract SALCs from a nonorthogonal linear combination of an appropriate basis. Suppose we have a SALC, v1, then there exists a v2 that meets the following condition,
v2 = av1 + u
where u is the non-orthogonal linear combination. Multiplying the above equation by v1 gives,
What is the nature of u? Consider using the projection operator on L3 instead of L1,
$\mathrm{P}^{\mathrm{e}_{9}}\left(\mathrm{~L}_{3}\right)=\frac{1}{\sqrt{12}}\left(2 \mathrm{~L}_{3}+2 \mathrm{~L}_{5}-\mathrm{L}_{1}-\mathrm{L}_{2}-\mathrm{L}_{4}-\mathrm{L}_{6}\right)$
Note, this does not yield any new information, i.e., the atomic orbitals on one axis are twice that and out-of-phase from the atomic orbitals in the equatorial plane. However, this new wavefunction is not ψeg(2) because it is not orthogonal to ψeg(1).
Thus the projection must yield a wavefunction that is a linear combination of ψeg(1) and ψeg(2) , i.e., the wavefunction obtained from the projection is a viable u. Applying the Schmidt orthogonalization procedure,
\begin{aligned} a &=-\mathbf{u v}_{1}=-\left\langle\frac{1}{\sqrt{12}}\left(2 L_{3}+2 L_{5}-L_{1}-L_{2}-L_{4}-L_{6}\right) \mid \frac{1}{\sqrt{12}}\left(2 L_{1}+2 L_{2}-L_{3}-L_{4}-L_{5}-L_{6}\right)\right\rangle \ &=-\frac{1}{12}[-6]=+\frac{1}{2} \end{aligned}
so,
\begin{aligned} \mathbf{v}_{2} &=\frac{1}{2} \frac{1}{\sqrt{12}}\left(2 L_{1}+2 L_{2}-L_{3}-L_{4}-L_{5}-L_{6}\right)+\frac{1}{\sqrt{12}}\left(2 L_{3}+2 L_{5}-L_{1}-L_{2}-L_{4}-L_{6}\right) \ &=\frac{1}{\sqrt{12}}\left[\left(\frac{3}{2} L_{3}+\frac{3}{2} L_{5}\right)-\left(\frac{3}{2} L_{4}+\frac{3}{2} L_{6}\right)\right] \approx\left(L_{3}+L_{5}\right)-\left(L_{4}+L_{6}\right) \end{aligned}
ψeg(2) is orthogonal to ψeg(1), thus it is the other SALC.
The T1g SALCs must now be determined. The projection operator yields,
PT1(L1) → (3L1 – L2 – L2 – L6 – L5 – L4 – L3 + L1 + L1 + L5 + L3 + L4 + L6 – L1– L1 – L2)
PT1(L1) ~ 3(L1 – L2)
and normalizing yields,
Applying the Schmidt orthogonalization method,
$\mathrm{P}^{\mathrm{T}_{1}}\left(\mathrm{~L}_{3}\right) \sim 3\left(\mathrm{~L}_{3}-\mathrm{L}_{5}\right) \rightarrow \psi_{\mathrm{t}_{\mathrm{lu}}}=\frac{1}{\sqrt{2}}\left(\mathrm{~L}_{3}-\mathrm{L}_{5}\right) \] This wavefunction is orthogonal to ψt1u(1) , hence it is likely a SALC. Can prove this by t1u applying the Schmidt orthogonalization process and setting this to be u. Solving for a,$
\begin{aligned}
a &=-\mathbf{u} \mathbf{v}_{1}=-\left\langle\frac{1}{\sqrt{2}}\left(\mathrm{~L}_{1}-\mathrm{L}_{2}\right) \mid \frac{1}{\sqrt{2}}\left(\mathrm{~L}_{3}-\mathrm{L}_{5}\right)\right\rangle \
&=-\frac{1}{2}(0)=0
\end{aligned}
\]
and
$v_{2}=a v_{1}+u=0 \cdot \frac{1}{\sqrt{2}}\left(L_{1}-L_{2}\right)+\frac{1}{\sqrt{2}}\left(L_{3}-L_{5}\right) \] so, as suspected, this is a SALC. And the third SALC of T1u symmetry is the (L4,L6) pair. Method 3 For those SALCs with symmetries that are the same as s, p or d orbitals, may adapt the symmetry of the ligand set to the symmetry of the metal orbitals. Consider the dz2 orbital, which is more accurately defined as 2z2 – x2 – y2 . Thus the coefficient of the z axis is twice that of x and y and out of phase with x and y. The ligands on the z-axis, L1 and L2, should therefore be twice that and of opposite sign to the equatorial ligands, L3,L4,L5,L6. This leads naturally to,$
\begin{aligned}
&\psi_{\mathrm{e}_{9}}^{(1)} \approx 2 \mathrm{~L}_{1}+2 \mathrm{~L}_{2}-\mathrm{L}_{3}-\mathrm{L}_{4}-\mathrm{L}_{5}-\mathrm{L}_{6} \
&\psi_{\mathrm{e}_{9}}^{(1)}=\frac{1}{\sqrt{12}}\left(2 \mathrm{~L}_{1}+2 \mathrm{~L}_{2}-\mathrm{L}_{3}-\mathrm{L}_{4}-\mathrm{L}_{5}-\mathrm{L}_{6}\right)
\end{aligned}
\]
The other SALC of this degenerate set is given by dx2–y2, which has no coefficient on z, and x and y coefficients that are equal but of opposite sign. By symmetry matching to the orbital,
\begin{aligned}
&\psi_{\mathrm{e}_{9}}^{(2)} \approx \mathrm{L}_{3}-\mathrm{L}_{4}+\mathrm{L}_{5}-\mathrm{L}_{6} \
&\psi_{\mathrm{e}_{9}}^{(2)}=\frac{1}{2}\left(\mathrm{~L}_{3}-\mathrm{L}_{4}+\mathrm{L}_{5}-\mathrm{L}_{6}\right)
\end{aligned}
\]
The other SALCs follow suit.
The t2g d-orbital set (i.e. dxy, dxz, dyz) is of incorrect symmetry to interact with the Lσ ligand set and thus is non-bonding. This can be seen from the orbital picture. The Lσ orbitals are directed between the lobes of the t2g d-orbitals,
Only metal orbitals and SALCs of the same symmetry can overlap. In the case of the octahedral ML6 σ-complex,
With above considerations of ΔEML and SML in mind, the MO diagram for M(Lσ)6 is constructed with Co(NH3)6 3+ as the exemplar,
Interaction energies εσ and εσ* (i.e., the off-diagonal matrix elements, HML) are smaller than the difference in energies of the metal and ligand atomic orbitals (i.e., the diagonal matrix elements, HMM and HLL), so molecular orbitals stay within their energy “zones”.
1.13: Octahedral ML complexes
The basis set needs to be expanded for metal complexes with ligands containing π orbitals. An appropriate basis for ligands with two orthogonal π orbitals, e.g. CO, CN , O2–, X, to the σ bond is shown below,
The arrow is indicative of the directional phase of the pπ orbitals. Owing to their ungerade symmetry, in constructing the pπ representation
• a p orbital, i.e. arrow, that transforms into itself contributes +1
• a p orbital that transforms into minus itself contributes –1
• a p orbital that moves, contributes 0
$\begin{array}{c|cccccccccc} \mathrm{O}_{\mathrm{h}} & \mathrm{E} & 8 \mathrm{C}_{3} & 6 \mathrm{C}_{2} & 6 \mathrm{C}_{4} & 3 \mathrm{C}_{2} & \mathrm{i} & 6 \mathrm{~S}_{4} & 8 \mathrm{~S}_{6} & 3 \sigma_{\mathrm{h}} & 6 \sigma_{\mathrm{d}} \ \hline \Gamma_{\sigma} & 6 & 0 & 0 & 2 & 2 & 0 & 0 & 0 & 4 & 2 & \rightarrow \mathrm{a}_{19}+\mathrm{t}_{1 \mathrm{u}}+\mathrm{e}_{\mathrm{g}} \ \Gamma_{\pi} & 12 & 0 & 0 & 0 & -4 & 0 & 0 & 0 & 0 & 0 & \rightarrow \mathrm{t}_{1 \mathrm{~g}}+\mathrm{t}_{1 \mathrm{u}}+\mathrm{t}_{2 \mathrm{~g}}+\mathrm{t}_{2 \mathrm{u}} \end{array} \] There is a second method to derive the pπ basis. The Cartesian coordinate systems on each ligand contains the σ and π basis sets. Thus the Γx,y,z irreducible representation (which is the sum of Γx + Γy + Γz or Γz + Γx,y for irreducible representations for which x,y,z are not triply degenerate) defines the 1σ and 2pπ bonds of each ligand. Since the bond is coincident with the ligand, an unmoved atom is approximated by Γσ. On the basis of geometrical considerations, the following is true,$
\begin{aligned}
&\underset{\text { atomoved }}{\Gamma_{\text {atoms }}}=\Gamma_{\sigma} \
&\Gamma_{\sigma+\pi}=\Gamma_{\mathrm{x}, y, z} \cdot \Gamma_{\sigma} \
&\Gamma_{\pi}=\Gamma_{\sigma+\pi}-\Gamma_{\sigma}
\end{aligned}
\]
The σ SALCs have already been derived in Lecture 12. Methods 1-3 of Lecture 12 can be employed to determine the pπ SALCs. For the orbitals that transform as t1u and t2g, Method 3 (mirror the metal atomic orbital symmetry) is convenient. For the t1u SALC,
The t2g SALCs have the mirrored symmetry of the (dxy,dxz,dyz) orbital set,
Non-bonding SALCs must be ascertained from projection operators and Schmidt orthogonalization methods.
For a π donor complex such as CoF6 3–,
For a π-accepting ligand set, orbitals have the same form (or symmetry) as π donors,
The only difference between the π-donor and π-acceptor MO diagrams is the relative placement of the π* orbitals relative to the metal atomic orbitals; for Co(CN)6 3–, | textbooks/chem/Inorganic_Chemistry/Principles_of_Inorganic_Chemistry_II_(Nocera)/01%3A_Chapters/1.12%3A_Octahedral_ML_Sigma_Complexes.txt |
The Wolfsberg-Hemholtz approximation (Lecture 10) provided the LCAO-MO energy between metal and ligand to be,
$\varepsilon_{\sigma}=\frac{\mathrm{E}_{\mathrm{M}}^{2} \mathrm{~S}_{\mathrm{ML}}^{2}}{\Delta \mathrm{E}_{\mathrm{ML}}} \quad \varepsilon_{\sigma^{*}}=\frac{\mathrm{E}_{\mathrm{L}}^{2} \mathrm{~S}_{\mathrm{ML}}^{2}}{\Delta \mathrm{E}_{\mathrm{ML}}} \] Note that EM, EL and ΔEML in the above expressions are constants. Hence, the MO within the Wolfsberg-Hemholtz framework scales directly with the overlap integral, SML$
\varepsilon_{\sigma}=\frac{\mathrm{E}_{\mathrm{M}}{ }^{2} \mathrm{~S}_{\mathrm{ML}}^{2}}{\Delta \mathrm{E}_{\mathrm{ML}}}=\beta^{\prime} \mathrm{S}_{\mathrm{ML}}^{2} \quad \varepsilon_{\sigma^{*}}=\frac{\mathrm{E}_{\mathrm{L}}^{2} \mathrm{~S}_{\mathrm{ML}}^{2}}{\Delta \mathrm{E}_{\mathrm{ML}}}=\beta \mathrm{S}_{\mathrm{ML}}{ }^{2}
\]
where β and β´are constants. Thus by determining the overlap integral, SML, the energies of the MOs may be ascertained relative to the metal and ligand atomic orbitals.
The Angular Overlap Method (AOM), provides a measure of SML and hence MO energy levels. In AOM, the overlap integral is also factored into a radial and angular product,
SML=S(r)F(θ,Φ)
Analyzing S(r) as a function of the M–L internuclear distance,
Under the condition of a fixed M-L distance, S(r) is invariant, and therefore the overlap integral, SML, will depend only on the angular dependence, i.e., on F(θ,φ).
Because the σ orbital is symmetric, the angular dependence, F(θ,φ), of the overlap integral mirrors the angular dependence of the central orbital.
p-orbital
…is defined angularly by a cos θ function. Hence, the angular dependence of a σ orbital as it angularly rotates about a p-orbital reflects the cos θ angular dependence of the p-orbital.
Similarly, the other orbitals take on the angular dependence of the central metal orbital. Hence, for a
ML Diatomic Complexes
To begin, let’s determine the energy of the d-orbitals for a M-L diatomic defined by the following coordinate system,
There are three types of overlap interactions based on σ, π and δ ligand orbital symmetries. For a σ orbital, the interaction is defined as,
\mathrm{E}\left(\mathrm{d}_{z^{2}}\right)=\mathrm{S}_{\mathrm{ML}}^{2}(\sigma)=\beta \cdot \mathrm{F}_{\sigma}{ }^{2}(\theta, \phi)=\beta \cdot 1=\mathrm{e} \sigma \] The energy for maximum overlap, at θ = 0 (see above) is set equal to 1. This energy is defined as eσ. The metal orbital bears the antibonding interaction, hence dz2 is destablized by eσ (the corresponding L orbital is stabilized by (β’)2 • 1 = eσ’). For orbitals of π and δ symmetry, the same holds…maximum overlap is set equal to 1, and the energies are eπ and eδ, respectively. E(dyz)=E(dxz)=SML2(π)=eπ E(dxy)=E(dx2-y2)=SML2(δ)=eδ As with the σ interaction, the (M-Lπ)* interaction for the d-orbitals is de-stabilizing and the metal-based orbital is destablized by eπ, whereas the Lπ ligands are stabilized by eπ. The same case occurs for a ligand possessing a δ orbital, with the only difference being an energy of stabilization of eδ for the Lδ orbital and the energy of de-stabilization of eδ for the δ metal-based orbitals. SML(δ) is small compared to SML(π) or SML(σ). Moreover, there are few ligands with δ orbital symmetry (if they exist, the δ symmetry arises from the pπ-systems of organic ligands). For these reasons, the SML(δ) overlap integral and associated energy is not included in most AOM treatments. Returning to the problem at hand, the overall energy level diagrams for a M-L diatomic molecule for the three ligand classes are: ML6 Octahedral Complexes Of course, there is more than 1 ligand in a typical coordination compound. The power of AOM is that the eσ and eπ (and eδ), energies are additive. Thus, the MO energy levels of coordination compounds are determined by simply summing eσ and eπ for each M(d)-L interaction. Consider a ligand positioned arbitrarily about the metal, We can imagine placing the ligand on the metal z axis (with x and y axes of M and L also aligned) and then rotate it on the surface of a sphere (thus maintaining M-L distance) to its final coordinate position. Within the reference frame of the ligand, Note, the coordinate transformation lines up the ligand of interest on the z axis so that the normalized energies, eσ and eπ (and eδ) may be normalized to 1. The transformation matrix for the coordinate transformation is:
\begin{array}{c|cccc}
& \mathbf{z}_{2}{ }^{2} & \mathrm{y}_{2} \mathbf{z}_{2} & \mathrm{x}_{2} z_{2} & \mathrm{x}_{2} \mathrm{y}_{2} & \mathrm{x}_{2}{ }^{2}-\mathrm{y}_{2}{ }^{2} \
\hline \mathbf{z}^{\mathbf{2}} & \frac{1}{4}(1+3 \cos 2 \theta) & 0 & -\frac{\sqrt{3}}{2} \sin 2 \theta & 0 & \frac{\sqrt{3}}{4}(1-\cos 2 \theta) \
\mathbf{y z} & \frac{\sqrt{3}}{2} \sin \phi \sin 2 \theta & \cos \phi \cos \theta & \sin \phi \cos 2 \theta & -\cos \phi \sin \theta & -\frac{1}{2} \sin \phi \sin 2 \theta \
\mathbf{x z} & \frac{\sqrt{3}}{2} \cos \phi \sin 2 \theta & -\sin \phi \cos \theta & \cos \phi \cos 2 \theta & \sin \phi \sin \theta & -\frac{1}{2} \cos \phi \sin 2 \theta \
\mathbf{x y} & \frac{\sqrt{3}}{4} \sin 2 \phi(1-\cos 2 \theta) & \cos 2 \phi \sin \theta & \frac{1}{2} \sin 2 \phi \sin 2 \theta & \cos 2 \phi \cos \theta & \frac{1}{4} \sin 2 \phi(3+\cos 2 \theta) \
\mathbf{x}^{2}-\mathbf{y}^{2} & \frac{\sqrt{3}}{4} \cos 2 \phi(1-\cos 2 \theta) & -\sin 2 \phi \sin \theta & \frac{1}{2} \cos 2 \phi \sin 2 \theta & -\sin 2 \phi \cos \theta & \frac{1}{4} \cos 2 \phi(3+\cos 2 \theta)
\end{array}
$\begin{array}{c|cccccc} \text { Ligand } & 1 & 2 & 3 & 4 & 5 & 6 \ \hline \theta & 0 & 90 & 90 & 90 & 90 & 180^{\circ} \ \phi & 0 & 0 & 90 & 180 & 270 & 0 \end{array}$ Consider the overlap of Ligand 2 in the transformed coordinate space; the contribution of the overlap of Ligand 2 with each metal orbital must be considered. This orbital interaction is given by the transformation matrix above. By substituting the θ = 90 and φ = 0 for Ligand 2 into the above transformation matrix, one finds, for dz2 for L2 \begin{aligned} \mathrm{d}_{z^{2}} &=\frac{1}{4}(1+3 \cos 2 \theta) d_{z_{2}{ }^{2}}+0 d_{y_{2} z_{2}}-\frac{\sqrt{3}}{2} \sin 2 \theta d_{x_{2} z_{2}}+0 d_{x_{2} y_{2}}+\frac{\sqrt{3}}{4}(1-\cos 2 \theta) d_{x_{2}^{2}-y_{2}^{2}} \ &=-\frac{1}{2} d_{z_{2}^{2}}+0 d_{y_{2} z_{2}}+0 d_{x_{2} z_{2}}+0 d_{x_{2} y_{2}}+\frac{\sqrt{3}}{2} d_{x_{2}^{2}-y_{2}^{2}} \end{aligned} Thus the dz2 orbital in the transformed coordinate, dz22, has a contribution from dz2 and dx2–y2. Recall that energy of the orbital is defined by the square of the overlap integral. Thus the above coefficients are squared to give the energy of the dz2 orbital as a result of its interaction with Ligand 2 to be, $\mathrm{E}\left(\mathrm{d}_{z^{2}}\right)^{\mathrm{L} 2}=\mathrm{S}_{\mathrm{ML}}{ }^{2}(\sigma)=\beta \cdot \mathrm{F}_{\sigma}^{2}(\theta, \phi)=\frac{1}{4} \mathrm{~d}_{\mathrm{z}_{2}{ }^{2}}+\frac{3}{4} \mathrm{~d}_{\mathrm{x}_{2}{ }^{2}-\mathrm{y}_{2}{ }^{2}}=\frac{1}{4} \mathrm{e} \sigma+\frac{3}{4} \mathrm{e} \delta$ Visually, this result is logical. In the coordinate transformation, a σ ligand residing on the z-axis (of energy eσ) is overlapping with dz2. This is the energy for L1. The normalized energy for L2 is its overlap with the coordinate transformed dz2 2: Note, the dz2 orbital is actually 2z2 –x2 –y2 , which is a linear combination of z2 –x2 and z2 –y2 . Thus in the coordinate transformed system, L2, as compared to L1, is looking at the x2 contribution of the wavefunction to σ bonding. Since it is ½ the electron density of that on the z-axis, it is ¼ the energy (i.e., the square of the coefficient) on the σ-axis, hence ¼ eσ. The δ component of the transformation comes from the 2z2 –(x2 +y2 ) orbital functional form. Thus if L2 has an orbital of δ symmetry, then it will have an energy of ¾ eδ. The transformation properties of the other d-orbitals, as they pertain to L2 orbital overlap, may be ascertained by completing the transformation matrix for θ = 90 and φ = 0,
\left[\begin{array}{c}
\mathrm{d}_{\mathrm{z}^{2}} \
\mathrm{~d}_{\mathrm{yz}} \
\mathrm{d}_{\mathrm{xz}} \
\mathrm{d}_{\mathrm{xy}} \
\mathrm{d}_{\mathrm{x}^{2}-y^{2}}
\end{array}\right]=\left[\begin{array}{rrrrr}
-\frac{1}{2} & 0 & 0 & 0 & \frac{\sqrt{3}}{2} \
0 & 0 & 0 & -1 & 0 \
0 & 0 & -1 & 0 & 0 \
0 & 1 & 0 & 0 & 0 \
\frac{\sqrt{3}}{2} & 0 & 0 & 0 & \frac{1}{2}
\end{array}\right]\left[\begin{array}{c}
\mathrm{d}_{z_{2}{ }^{2}} \
\mathrm{~d}_{\mathrm{y}_{2} z_{2}} \
\mathrm{~d}_{\mathrm{x}_{2} \mathrm{z}_{2}} \
\mathrm{~d}_{\mathrm{x}_{2} y_{2}} \
\mathrm{~d}_{\mathrm{x}_{2}^{2}-\mathrm{y}_{2}{ }^{2}}
\end{array}\right]
\]
The energy contribution from L2 to the d-orbital levels as defined by AOM is,
$\mathrm{E}\left(\mathrm{d}_{\mathrm{yz}}\right)=\mathrm{e} \delta ; \quad \mathrm{E}\left(\mathrm{d}_{\mathrm{xz}}\right)=\mathrm{e} \pi ; \quad \mathrm{E}\left(\mathrm{d}_{\mathrm{xy}}\right)=\mathrm{e} \pi ; \quad \mathrm{E}\left(\mathrm{d}_{x^{2}-y^{2}}\right)=\frac{3}{4} \mathrm{e} \sigma+\frac{1}{4} \mathrm{e} \delta$
Until this point, only the L2 ligand has been treated. The overlap of the d-orbitals with the other five ligands also needs to be determined. The elements of the transformation matrices for these ligands are,
$L_{1}:\left[\begin{array}{lllll} 1 & 0 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 & 0 \ 0 & 0 & 1 & 0 & 0 \ 0 & 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 0 & 1 \end{array}\right] \quad L_{3}:\left[\begin{array}{rrrrr} -\frac{1}{2} & 0 & 0 & 0 & \frac{\sqrt{3}}{2} \ 0 & 0 & -1 & 0 & 0 \ 0 & 0 & 0 & 1 & 0 \ 0 & -1 & 0 & 0 & 0 \ -\frac{\sqrt{3}}{2} & 0 & 0 & 0 & -\frac{1}{2} \end{array}\right] \quad L_{4}:\left[\begin{array}{ccccc} -\frac{1}{2} & 0 & 0 & 0 & \frac{\sqrt{3}}{2} \ 0 & 0 & 0 & 1 & 0 \ 0 & 0 & 1 & 0 & 0 \ 0 & 1 & 0 & 0 & 0 \ \frac{\sqrt{3}}{2} & 0 & 0 & 0 & \frac{1}{2} \end{array}\right]$
$\mathrm{L}_{5}:\left[\begin{array}{rrrrr} -\frac{1}{2} & 0 & 0 & 0 & \frac{\sqrt{3}}{2} \ 0 & 0 & 1 & 0 & 0 \ 0 & 0 & 0 & -1 & 0 \ 0 & -1 & 0 & 0 & 0 \ -\frac{\sqrt{3}}{2} & 0 & 0 & 0 & -\frac{1}{2} \end{array}\right] \quad L_{6}:\left[\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \ 0 & -1 & 0 & 0 & 0 \ 0 & 0 & 1 & 0 & 0 \ 0 & 0 & 0 & -1 & 0 \ 0 & 0 & 0 & 0 & 1 \end{array}\right]$
Squaring the coefficients for each of the ligands and then summing the total energy of each d-orbital,
\begin{array}{lccccccc}
\hline & \text { L1 } & \text { L2 } & \text { L3 } & \text { L4 } & \text { L5 } & \text { L6 } & \text { E_TOTAL } \
\hline \mathbf{E}\left(\mathbf{d}_{\mathbf{z}^{2}}\right) & \text { eo } & \frac{1}{4} \mathrm{e} \sigma+\frac{3}{4} \mathrm{e} \delta & \frac{1}{4} \mathrm{e} \sigma+\frac{3}{4} \mathrm{e} \delta & \frac{1}{4} \mathrm{e} \sigma+\frac{3}{4} \mathrm{e} \delta & \frac{1}{4} \mathrm{e} \sigma+\frac{3}{4} \mathrm{e} \delta & \mathrm{e} \sigma & =3 \mathrm{e} \sigma+3 \mathrm{e} \delta \
\mathbf{E}\left(\mathbf{d}_{\mathrm{yz}}\right) & \mathrm{e} \pi & \mathrm{e} \delta & \mathrm{e} \pi & \mathrm{e} \delta & \mathrm{e} \pi & \mathrm{e} \pi & =4 \mathrm{e} \pi+2 \mathrm{e} \delta \
\mathbf{E}\left(\mathbf{d}_{\mathrm{xz}}\right) & \mathrm{e} \pi & \mathrm{e} \pi & \mathrm{e} \delta & \mathrm{e} \pi & \mathrm{e} \delta & \mathrm{e} \pi & =4 \mathrm{e} \pi+2 \mathrm{e} \delta \
\mathbf{E}\left(\mathbf{d}_{\mathrm{xy}}\right) & \mathrm{e} \delta & \mathrm{e} \pi & \mathrm{e} \pi & \mathrm{e} \pi & \mathrm{e} \pi & \mathrm{e} \delta & =4 \mathrm{e} \pi+2 \mathrm{e} \delta \
\mathbf{E}\left(\mathbf{d}_{\mathbf{x}^{2}-\mathbf{y}^{2}}\right) & \mathrm{e} \delta & \frac{3}{4} \mathrm{e} \sigma+\frac{1}{4} \mathrm{e} \delta & \frac{3}{4} \mathrm{e} \sigma+\frac{1}{4} \mathrm{e} \delta & \frac{3}{4} \mathrm{e} \sigma+\frac{1}{4} \mathrm{e} \delta & \frac{3}{4} \mathrm{e} \sigma+\frac{1}{4} \mathrm{e} \delta & \mathrm{e} \delta & =3 \mathrm{e} \sigma+3 \mathrm{e} \delta \
\hline
\end{array}
\]
As mentioned above, eδ << eσ or eπ… thus eδ may be ignored. The Oh energy level diagram is:
Note the d-orbital splitting is the same result obtained from the crystal field theory (CFT) model taught in freshman chemistry. In fact the energy parametrization scales directly between CFT and AOM
10 Dq = Δ0 = 3eσ – 4eπ | textbooks/chem/Inorganic_Chemistry/Principles_of_Inorganic_Chemistry_II_(Nocera)/01%3A_Chapters/1.14%3A_Angular_Overlap_Method_and_M-L_Diatomics.txt |
1. Determine the general matrix rep for a σv at angle from the xz plane on a point (x1,y1,z1) at angle from the xz plane. Provide matrix reps for the 3σv in C3v.
2. Consider the generators C5 and h.
1. What group is generated from these two operations?
2. Construct a multiplication table.
3. Determine the classes in the group.
4. Do C5 and σh commute? Show both by matrix algebra and by operating on a vector (x1,y1,z1).
3. Do the following problems in Cotton (3rd edition): A3.2, A3.4, 4.4 and 4.7.
4. Consider the trigonal planar molecule, BF3. Use the three fluorine atoms as an arbitrary basis set to describe the matrix representation for each of the operations in the point group (relying on the methods employed above, solve the appropriate eigenvalue problem).
1. Construct the matrix representations for the operations in the D3h point group.
2. Find the three eigenvalues λi and normalize the eigenvectors for the C3 matrix representation (Hint: The eigenvectors are orthogonal to each other. For complex eigenvectors, remember that the normalization is defined as A*A where A* is the complex conjugate).
3. Construct the similarity transformation matrix θ from the eigenvectors and determine θ-1 . For the case where the eigenvectors are complex, take linear combinations to yield eigenvectors in real space. θ-1 is the adjoint of θ divided by the determinant. See pg 424 in Cotton for the definition of an adjoint.
4. Using θ and θ–1 block-diagonalize the matrices in Part (a) and calculate the characters of the irreducible representations for the given basis.
5. To what irreducible representations do the F atom basis functions belong?
6. Complete the D3h character table using the algebraic rules governing irreducible representations. Show work.
5. Assign point groups to the following molecules. Sketch the molecule and the symmetry elements present in each.
1. ethane (staggered)
2. ethane (eclipsed)
3. cyclohexane (chair)
4. cyclohexane (boat)
5. adamantane
6. ferrocene (staggered)
7. ferrocene (eclipsed)
8. P4
9. S8
6. Draw a molecule (not found in the texts or lecture notes) that exemplifies each of the following point groups. Please use molecules that actually exist.
1. C2h
2. D8h
3. D2d
4. CS
5. C6v
2.02: New Page
1. Do Problem 7.1, p. 201 in Cotton (3rd ed).
2. Do Problem 6.1, p. 129 in Cotton (3rd ed), and then solve the appropriate secular determinant to find the energies of the 10 MOs spanned by the SALCs you have derived.
3. Construct the MO diagram for the molecule shown below and assign the photoelectron spectrum.
4. A Hückel analysis may also be used to describe σ-bonding. Consider the three center bond of the Al2(µ-CH3)2 unit in “trimethyl aluminum” which exists as the dimer [Al(CH3)3]2 in the gas phase and nonpolar solvents.
a. Using the 6 σ orbitals shown below, determine the basis for the four Al σ-bonds.
b. Construct the SALC’s using the projection operator method.
c. Follow the same procedure for the carbon σ-bonds.
d. Determine the energy levels of the molecular orbital diagram.
e. Give the explicit expressions for the six molecular orbitals of the Al2(µ-CH3)2 unit.
5. Consider 1,3,5-hexatriene and benzene.
a. For the former construct the MO diagram; calculate the delocalization energy; and construct the molecular orbital eigenfunctions.
b. 1,3,5-hexatriene and benzene are limiting cases for a more general molecular orbital system in which the interaction energy for the terminal orbitals, β1,6, is finite and not equal to the interaction energy between adjacent orbitals.
c. Determine the molecular orbital energies of the general C6 system (i.e. β1,6 ≠ βi,j (i,j ≠ 1,6) and show that in the limiting regimes of this general case, the MO diagrams. For 1,3,5- hexatriene and benzene are obtained.
d. Draw a correlation diagram.
2.03: New Page
1. The octahedral molecular orbital (MO) diagram provides the starting point for the construction of the electronic structure of several metal complexes. But not all complexes are conveniently referenced to octahedral geometry. Other important geometries include tetrahedral, square planar, trigonal bipyramidal and pyramidal. Construct MO diagrams for each in the σ-only ligand framework. For the tetrahedral complex, also show the MO diagram for π- and π*-bonding ligands.
2. Derive the MO diagram for trigonal prismatic WH6. The ReH92 complex has hydride ligands capping the trigonal prismatic faces. Construct the MO diagram for The ReH92.
a. Make a LCAO of two H3 molecules interacting face-to-face.
b. Place W between the two H3 faces and then perturb the orbitals.
c. Mix another set of H3 orbitals into the MO diagram you made in (b) to arrive at the MO diagram for.
3. Consider a one-dimensional chain of orbitals, for example polyacetylene.
(a) Use Hückel theory to generate the energy bands for a geometry in which all C–C distances are equal.
(b) Now generate the energy bands a geometry with alternating long and short C–C bonds. Use β for the Hij across short bonds and β/2 across long bonds.
(c) Will polyacetylene in either one or both geometries be a metal or an insulator? | textbooks/chem/Inorganic_Chemistry/Principles_of_Inorganic_Chemistry_II_(Nocera)/02%3A_Assignments/2.01%3A_New_Page.txt |
1. The raising and lowering operators are:
(a) For the p 2 configuration, we found that Ψ(L = 1, ML = 1, S = 1, MS = 1) for the 3P state was defined by a unique configuration (1+, 0+). Similarily, Ψ(L = 1, ML = 0, S = 1, MS = 1) of the 3P state is defined by the unique configuration, (1+, -1+). Using the angular momentum operator on Ψ(L = 1, ML = 1, S = 1, MS = 1) = (1+, 0+), show that you obtain the result, Ψ(L = 1, ML = 0, S = 1, MS = 1) = (1+, -1+).
(b) The states encompassed by Ψ(L, ML = 0, S, MS = 0) are defined by three configurations, (0+, 0+), (1+, -1-), (1-, -1+). . Beginning with your result for Ψ(L = 1, ML = 0, S = 1, MS = 1) of the 3P state, determine the linear combination that defines Ψ(L = 1, ML = 0, S = 1, MS = 0).
2. LIESST (Light Induced Electronic Spin State Trapping) is a method of changing the electronic spin state of a compound by means of irradiation with light. The overall effect is represented schematically with regard to configurations as follows,
The low spin state is slightly more stable than the high spin state by only a few cm–1. Thus, the complex will exhibit low spin behavior only at very low temperatures (< 10 K). Excitation produces excited states corresponding to the low spin complex. From these low spin excited states, intersystem crossing (isc) occurs to produce the high spin complex. At low temperatures the high spin complex is trapped indefinitely owing to an Arrenhius barrier of ~800 cm–1. Upon warming the barrier is surmounted and the complex converts back to the low spin state. This overall process has been called the Light-Induced Excited Spin State Trapping (LIESST).
A compound displaying LIESST is [Fe(ptz)6](BF4)2. Shown below are the absorption spectra responsible for the effect.
(a) The solid line is the low temperature spectrum of the low spin complex. The energies of the transitions are 18,400 and 26,650 cm–1 , respectively. Using the appropriate TS diagram (from ant standard text), assign the two transitions.
(b) Upon irradiation, the dashed spectrum is produced. This is the absorption spectrum for the high spin complex, which features only a single band at 12,250 cm–1 . Assign this transition. Using the B value obtained from part a, determine Dq for the high spin system.
(c) On the basis of the Tanabe-Sugano diagram, explain the LIESST effect.
3. The spectroscopy and photochemistry of Cr(III) has spanned four decades of spectroscopic and photochemical research. The spectroscopy of Cr(III) in the solid state is the underpinning for the invention in the 1960’s of the first solid state laser, the ruby laser. The photochemistry of these complexes continues to be pursued by a number of research programs around the world. Consider the following.
(a) Ruby is a gemstone composed of Cr(III) embedded in the octahedral oxide environment of Al2O3. The electronic spectrum of the octahedral Cr(III) exhibits three spin-allowed (strong = s) transitions and a number of so called ‘ruby’ lines, spin-forbidden (quartet-doublet) transitions (weak = w), which are extremely narrow and 10–3 times weaker than d-d transitions.
(i) The absorption bands in the electronic spectrum of Cr3+ /Al2O3 system are 14430(w), 18000(s), 21000(w), 24600(s) and 39000(s) cm–1 . Use a d3 Tanabe-Sugano diagram to assign the transitions and calculate Dq.
(ii) The absorption and emission spectra of the lowest energy transitions of Cr(III) are given below. On the basis of your above work, assign the emission and absorption bands to the appropriate transitions. Why is the one transition broad and the other sharp? Why are the absorption and emission maxima of the sharp transition nearly overlapped whereas the absorption and emission maxima of the broad transition so far removed from each other?
(b) Trans-Cr(NH3)4(DMF)Cl2+ cation is a high spin chromium(III) complex. The spectroscopy of this complex is intriguing because it is one of the few systems in which three different simultaneous photoreactions have been fully characterized. A complete scheme of the photoreactions is given below:
Because Cr(III) is in a C4v environment, the octahedral Tanabe-Sugano diagram is invalid. In this case, spectroscopic assignments are achieved by using a descent in symmetry method, where the splitting of the t2g and eg manifolds are analyzed in the desired symmetry field as follows:
(i) The wavelengths (nm) and the extinction coefficients (M–1 cm–1) of the complex are 555 (20), 468 (18) and 384 (42). Assign the quartet transitions and give the state symmetries of the excited states by qualitatively considering the splitting of the d-orbital manifold. For determining the states of the (e)2 electronic configuration, you will need the equations given in the lecture notes and reproduced here:
\begin{aligned}
&\chi^{+}=1 / 2\left\{[\chi(\mathrm{R})]^{2}+\chi\left(\mathrm{R}^{2}\right)\right\} \
&\chi^{-}=1 / 2\left\{[\chi(\mathrm{R})]^{2}-\chi\left(\mathrm{R}^{2}\right)\right\}
\end{aligned}
(ii) The photochemistry originates from specific ligand field states (i.e. the products come from different excited states). By using the MO diagram and the assignments you have made, explain the observed photochemistry.
(iii) Why is DMF substituted more easily than chlorine? | textbooks/chem/Inorganic_Chemistry/Principles_of_Inorganic_Chemistry_II_(Nocera)/02%3A_Assignments/2.04%3A_New_Page.txt |
1. (20 pts) Below are vibrations and orbitals of molecules that transform according to irreducible representations of their given point groups. Note: no derivations are needed to answer this problem.
a. (10 pts) Five bending modes of XeF42- are shown below. Assign the modes to their appropriate irreducible representations.
b. (10 pts) Olefins can bind to metal centers. Consider the simplets homoleptic complex, the bis(ethylene) complex. Ethylene binds to a metal through its pπ-orbitals. The four orbital symmetries appropriate for ligand binding to the metal are: A1, B2 and E. Below are shown the p-orbital contours for four orbitals. Color the p-orbitals to give the proper orbital symmetries. Label each of the completed diagrams with its irreducible representation
2. (20 pts) Show that the point groups C3h and S3 are equivalent. You may use a stereographic projection to answer this problem.
3. (20 pts) Short answers. Point values are assigned in parenthesis on each line.
a. (9 pts) Identify the point group and list the generators for the letter S
b. (5 pts) To which irreducible representation does the fxz2 orbital belong in the D2h point group?
c. (6 pts) A molecule cannot be optically active if it has any Sn axes. Identify the optically active molecules below.
4. (40 pts) H3+ was discovered only 12 years ago by Professor Takeshi Oka of the University of Chicago. The discovery has been profound as this molecule has been observed now at the galactic core. As professor Oka discussed yesterday at MIT, the presence of this molecule in the universe provides an important mechanism for star formation. Construct an energy level diagram for the two molecules using the Hückel approximation to determine the energies. Draw a correlation diagram that relates the Hückel energy levels of the two fragments.
To shorten the time of this problem, consider using the D2h point group for the linear isomer of H3. Also, we provide one SALC for linear H3+ and two SALCs for cyclic H3+. You need only show work for the missing SALCs.
3.02: New Page
1. (30 pts) A Rydberg transition promotes an electron to an orbital of a principal quantum number greater than that of any occupied orbital of the ground state. Consider the nd(n+1)s Rydberg excited state of a d2 ion. Construct the correlation diagram for the excited state in a D4h crystal field. For determining the ligand field states from the free ion states, you may use the equations given in the lecture notes and reproduced here (but it is not necessarily the only way to deduce the ligand field states):
\begin{gathered}
\chi(\alpha)=2 l+1 \quad \text { for } \alpha=0 \
\chi(\alpha)=\frac{\sin (l+1 / 2) \alpha}{\sin \frac{\alpha}{2}} \quad \text { for } \alpha \neq 0
\end{gathered}
2. (30 pts) Short answers.
a. (5 pts) Which ligand will be stronger field, HC≡C- or OH-? Justify your choice.
b. (6 pts) Is the ground state of [CrCl6]3- subject to Jahn-Teller distortion? Explain why the 4T2g state (of (t2g)2 (eg)1 configuration) is subject to a Jahn-Teller distortion.
c. (4 pts) Under pressure, 10Dq of [CrCl6] 3- increases. Why?
d. (5 pts) In the lowest energy d-d excited state, [Ni(CN)4]2- undergoes a D4h → D2d distortion. Explain.
e. (10 pts) List the four states that arise from two electrons residing in two dxy orbitals in a D4h ligand field. The MO diagram with molecular orbital symmetries is given below.
3. (40 pts) The Co(sep)33+ is called a sephulcrate, first synthesized by Alan Sargeson at the Australian National University.
Two absorption bands arising from spin-allowed ligand field transitions are observed for this complex. Assign these transitions by using the d6(Oh) Tanabe-Sugano diagram. Predict the energies of the corresponding spin-forbidden triplet transitions.
3.03: New Page
1. (29 pts) The simplest stable phosphorous sulfide, tetraphosphourous trisulfide, P4S3 is shown below. The bands observed in the IR and Raman spectra of P4S3 in gas phase, melt and solution are listed.
Infrared Data:
ν / cm-1
Gas (550 °C)
Raman Data: Δ / cm-1
Melt (250 °C) CS2 (25 °C)
142
184
187
218 221 218 223
286 292 287 291
339 347 339 343
414 420 420 423
438 446 440 444
a. (20 pts) Determine the normal modes of vibration for P4S3 and how they transform.
b. (9 pts) Which are Raman and IR active?
2. (41 pts) A molecular orbital analysis of transition metal dihydrogen complexes provides critical insight into the bonding interactions between metals and hydrogen and established an elegant framework in which the reactivity between H2 and transition metal complexes can be interpreted.
a. (10 pts) Construct the molecular orbital diagram of a side-on bonded Cr(CO)5(H2) from group fragment orbitals.
b. (6 pts) Pictorially illustrate the σ and π interactions that stabilize the formation of the dihydrogen complex.
c. (15 pts) These interactions can effectively be used to rationalize several aspects of TM dihydrogen chemistry. In this regard, explain the following observations:
i. (5 pts) d6 metals appear to form the most stable TM dihydrogen complexes
ii. (5 pts) many TM dihydrogen complexes synthesized to date have ancillary π-accepting ligands
iii. (5 pts) first row transition metals stabilize dihydrogen compounds while third row metals tend to promote dihydride compounds
d. (10 pts) Construct the MO diagram for an end-on bonded H2 complex; and explain why (using the end- and side-on MO diagrams) end-on complexes are not favored energetically relative to side-on complexes.
3. (30 pts) The nitrogen chemistry of early transition metals was established with the preparation of the Ti complexes from the Bercaw group at Caltech during the mid-1970s. One of the compounds is shown below. Construct the qualitative molecular orbital diagram for the dinuclear titanium complex from the frontier orbitals of the bent Cp2Ti fragment (in C2v symmetry) and the appropriate frontier molecular orbitals of nitrogen. Label the MO with appropriate symmetry labels, identify the nature of the bond (i.e., σ, σ*, π, π*) and fill up the MO with the appropriate number of electrons. | textbooks/chem/Inorganic_Chemistry/Principles_of_Inorganic_Chemistry_II_(Nocera)/03%3A_Exams/3.01%3A_New_Page.txt |
Symmetry elements of the molecule are geometric entities: an imaginary point, axis or plane in space, which symmetry operations: rotation, reflection or inversion, are performed. Their recognition leads to the application of symmetry to molecular properties and can also be used to predict or explain many of a molecule’s chemical properties. Symmetry elements and symmetry operations are two fundamental concepts in group theory, which is the mathematical description of symmetry properties that describe the structure, bonding, and spectroscopy of molecules.
Point Symmetry Operations
Point symmetry of a molecule results when there exists at least one point in space that remains indistinguishable from the original molecule after any symmetry operation is applied. In other words, a rotation, reflection or inversion operations are called symmetry operations if, and only if, the newly arranged molecule is indistinguishable from the original arrangement. There are five kinds of point of symmetry elements that a molecule can possess, thus, there are also five kinds of point symmetry operations. All symmetry elements in a molecule must share at least one point in common and this point occurs at the center of the molecule.
Identity (E)
Identity operation comes from the German ‘Einheit’ meaning unity. This symmetry element means no change. All molecules have this element.
Proper Rotation (Cₙ)
Proper rotation operates with respect to an axis called a symmetry axis (also known as n-fold rotational axis). An axis around which a rotation by 360°/n (or 2π/n) results in an identical molecule before and after the rotation. The axis with the highest $n$ is called the principal axis.
In general, a molecule contains $n$ $C_n$ operations such that {Cn1, Cn2, Cn3,…, Cnn-1, Cnn} where $C_n^n = E$. For example, if there exists C5 axis then there exists 5C5 (2C51, 2C52, C55) operations:
• C51 = C54 since the operation results indistinguishable molecule in clockwise and counter-clockwise, respectively.
• C52 = C53 since the operation results indistinguishable molecule in clockwise and counter-clockwise, respectively.
• C55 = E
Reflection (σ)
Reflection operates with respect to a plane called a plane of symmetry (also known as a mirror plane). There exist three types of mirror planes:
• $σ_h$ – a horizontal mirror plane of a molecule is perpendicular to the primary axis of a molecule.
• $σ_v$ – a vertical mirror plane of a molecule includes the primary axis of a molecule and passes through the bonds (atoms).
• $σ_d$ – a dihedral (also known as a diagonal mirror plane) of a molecule includes the primary axis of a molecule while bisecting the angle between two C2 axes that are perpendicular to it. Therefore, ơd does not pass through the bonds (atoms).
Note
$σ_d$ is a special case of a $σ_v$.
Inversion (i)
Inversion operates with respect to a point called a center of symmetry (also known as an inversion center). It gives the same result to rotating a molecule around C2 axis then reflecting it with respect to a mirror plane that is perpendicular to C2. For example, SF6 in Figure $2$ has an inversion point at the center S.
Improper Rotation (Sₙ)
Improper rotation operates with respect to an axis called rotation-reflection axis. In other words, it is a combination operation of a rotation about an axis by 360°/n (or $2π/n$) followed by reflection in a plane perpendicular to the rotation axis.
Point Groups
The complete collection of symmetry elements of a molecule forms the basis of a mathematical group, and the collection of symmetry operations that are interrelated to each other via certain kind of rules is known as a point group:
• Closure – if any two symmetry operations are in the same group then their product, resulting in another operation, will also be in the same group:
If $A∈G$ and $B∈G$, then $(A∩B)∈G$
• Associativity – the law of associativity applies to all symmetry operations:
$(AB)C=A(BC) \nonumber$
• Identity – there exists an operation that commutes with other operations (identity, E) and leaves them unchanged:
If $A∈G$ and $E∈G$, then $AE=EA=A$
• Inverses – for every symmetry operation in the group, there exists an inverse operation that their product results identity:
If $A∈G$, then there exists $A^{-1}∈G$ such that $AA^{-1}=A^{-1}A=E$ | textbooks/chem/Inorganic_Chemistry/Supplemental_Modules_and_Websites_(Inorganic_Chemistry)/Advanced_Inorganic_Chemistry_(Wikibook)/1.01%3A_Symmetry_Elements.txt |
Introduction
A Point Group describes all the symmetry operations that can be performed on a molecule that result in a conformation indistinguishable from the original. Point groups are used in Group Theory, the mathematical analysis of groups, to determine properties such as a molecule's molecular orbitals.
Assigning Point Groups
While a point group contains all of the symmetry operations that can be performed on a given molecule, it is not necessary to identify all of these operations to determine the molecule's overall point group. Instead, a molecule's point group can be determined by following a set of steps which analyze the presence (or absence) of particular symmetry elements.
1. Determine if the molecule is of high or low symmetry.
2. If not, find the highest order rotation axis, Cn.
3. Determine if the molecule has any C2 axes perpendicular to the principal Cn axis. If so, then there are n such C2 axes, and the molecule is in the D set of point groups. If not, it is in either the C or S set of point groups.
4. Determine if the molecule has a horizontal mirror plane (σh) perpendicular to the principal Cn axis. If so, the molecule is either in the Cnh or Dnh set of point groups.
5. Determine if the molecule has a vertical mirror plane (σv) containing the principal Cn axis. If so, the molecule is either in the Cnv or Dnd set of point groups. If not, and if the molecule has n perpendicular C2 axes, then it is part of the Dn set of point groups.
6. Determine if there is an improper rotation axis, S2n, collinear with the principal Cn axis. If so, the molecule is in the S2n point group. If not, the molecule is in the Cn point group.
Example \(1\)
Find the point group of benzene (C6H6).
Solution
1. Highest order rotation axis: C6
2. Benzene is neither high or low symmetry
3. There are 6 C2 axes perpendicular to the principal axis
4. There is a horizontal mirror plane (σh)
Benzene is in the D6h point group.
Low Symmetry Point Groups
Low symmetry point groups include the C1, Cs, and Ci groups
Group Description Example
C1 only the identity operation (E) CHFClBr
Cs only the identity operation (E) and one mirror plane C2H2ClBr
Ci only the identity operation (E) and a center of inversion (i) C2H2Cl2Br
High Symmetry Point Groups
High symmetry point groups include the Td, Oh, Ih, C∞v, and D∞h groups. The table below describes their characteristic symmetry operations. The full set of symmetry operations included in the point group is described in the corresponding character table.
Group Description Example
C∞v linear molecule with an infinite number of rotation axes and vertical mirror planes (σv) HBr
D∞h linear molecule with an infinite number of rotation axes, vertical mirror planes (σv), perpendicular C2 axes, a horizontal mirror plane (σh), and an inversion center (i) CO2
Td typically have tetrahedral geometry, with 4 C4 axes, 3 C2 axes, 3 S4 axes, and 6 dihedral mirror planes (σd) CH4
Oh typically have octahedral geometry, with 3 C4 axes, 4 C3 axes, and an inversion center (i) as characteristic symmetry operations SF6
Ih typically have an icosahedral structure, with 6 C5 axes as characteristic symmetry operations B12H122-
D Groups
The D set of point groups is classified as Dnh, Dnd, or Dn, where n refers to the principal axis of rotation. Overall, the D groups are characterized by the presence of n C2 axes perpendicular to the principal Cn axis. Further classification of a molecule in the D groups depends on the presence of horizontal or vertical/dihedral mirror planes.
Group Description Example
Dnh n perpendicular C2 axes, and a horizontal mirror plane (σh) benzene, C6H6 is D6h
Dnd n perpendicular C2 axes, and a vertical mirror plane (σv) propadiene, C3H4 is D2d
Dn n perpendicular C2 axes, no mirror planes [Co(en)3]3+ is D3
C Groups
The C set of point groups is classified as Cnh, Cnv, or Cn, where n refers to the principal axis of rotation. The C set of groups is characterized by the absence of n C2 axes perpendicular to the principal Cn axis. Further classification of a molecule in the C groups depends on the presence of horizontal or vertical/dihedral mirror planes.
Group Description Example
Cnh horizontal mirror plane (σh) perpendicular to the principal Cn axis boric acid, H3BO3, is C3h
Cnv vertical mirror plane (σv) containing the principal Cn axis ammonia, NH3, is C3v
Cn no mirror planes P(C6H5)3 is C3
S Groups
The S set of point groups is classified as S2n, where n refers to the principal axis of rotation. The S set of groups is characterized by the absence of n C2 axes perpendicular to the principal Cn axis, as well as the absence of horizontal and vertical/dihedral mirror planes. However, there is an improper rotation (or a rotation-reflection) axis collinear with the principal Cn axis.
Group Description Example
S2n improper rotation (or a rotation-reflection) axis collinear with the principal Cn axis 12-crown-4 is S4
Symmetry Gallery | textbooks/chem/Inorganic_Chemistry/Supplemental_Modules_and_Websites_(Inorganic_Chemistry)/Advanced_Inorganic_Chemistry_(Wikibook)/1.02%3A_Molecular_Point_Groups.txt |
A matrix is a rectangular array of quantities or expressions in rows (m) and columns (n) that is treated as a single entity and manipulated according to particular rules.[1] The dimension of a matrix is denoted by m × n. In inorganic chemistry, molecular symmetry can be modeled by mathematics by using group theory. The internal coordinate system of a molecule may be used to generate a set of matrices, known as a representation, that corresponds to particular symmetry operations.[2] Matrix modeling thus allows for symmetry operations performed on the molecule to be represented in an identical fashion mathematically.
Matrix Operations
Addition
The sum of two matrices, A and B, is carried out by adding or subtracting the element of one matrix with the corresponding element of another matrix. These operations may only be performed on matrices of identical dimension.
$A+B=\displaystyle \sum_{i=1}^{m}\left(\sum_{i=1}^{n} A_{i j}+B_{i j}\right)$ ${\displaystyle \sum _{i=1}^{m}(\sum _{j=1}^{n}A_{ij}+B_{ij})}$ where i refers to a particular row and j to a particular column.
Example:
$\left(\begin{array}{lll}{a_{11}} & {a_{12}} & {a_{13}} \{a_{21}} & {a_{22}} & {a_{23}}\end{array}\right)+\left(\begin{array}{lll}{b_{11}} & {b_{12}} & {b_{13}} \{b_{21}} & {b_{22}} & {b_{23}}\end{array}\right)=\left(\begin{array}{lll}{a_{11}+b_{11}} & {a_{12}+b_{12}} & {a_{13}+b_{13}} \{a_{21}+b_{21}} & {a_{22}+b_{22}} & {a_{23}+b_{23}} \end{array}\right) \nonumber$
Scalar Multiplication
Multiplication of a matrix by a scalar, c, multiplies every element within the matrix by the scalar.
$c A=C \cdot A_{i j} \nonumber$
Example:
$c \cdot\left(\begin{array}{ll}{a_{11}} & {a_{12}} \{a_{21}} & {a_{22}}\end{array}\right)=\left(\begin{array}{ll} {c \cdot a_{11}} & {c \cdot a_{12}} \{c \cdot a_{21}} & {c \cdot a_{22}}\end{array}\right) \nonumber$
Matrix Multiplication
Matrix multiplication entails computing the dot product of the row of one matrix, A, with the column of another matrix, B. Matrix multiplication is only defined if the number if columns of A, denoted by n, is equal to the number of rows of B, denoted by m. Their product is then the m × n matrix, C. Matrix multiplication entails some mathematical properties. First, it is associative; in other words, (A × B) × C = A × (B × C). Furthermore, matrix multiplication is not commutative; in other words, A × B =/= B × A
$\mathrm{C}_{\mathrm{m}\times\mathrm{n}}=\mathrm{A}_{\mathrm{m}\times\mathrm{c}}\cdot \mathrm{B}_{\mathrm{c}\times \mathrm{n}}=\sum_{k=1}^{c} A_{i, k} B_{k, j}\nonumber$
Example:
$\left(\begin{array}{lll}{a_{11}}&{a_{12}}&{a_{13}}\{a_{21}}&{a_{22}}&{a_{23}}\end{array}\right)\times\left(\begin{array}{l}{b_{11}}\{b_{21}}\{b_{31}}\end{array}\right)=\left(\begin{array}{l}{a_{11}b_{11}+a_{12}b_{21}+a_{13}b_{31}}\{a_{21}b_{11}+a_{22}b_{21}+a_{23} b_{31}}\end{array}\right)\nonumber$
Row Operations
There are three kinds of elementary row operations that are used to transform a matrix:
Type Definition Operation
Row Switching The swapping of one row with that of another row ${\displaystyle \mathrm {R} _{i}\leftrightarrow \mathrm {R} _{j}}$$\mathrm{R}_{i} \leftrightarrow \mathrm{R}_{j}$
Row Addition The addition of a multiple of one row to another row
$\mathrm{R}_{i}+k \mathrm{R}_{j} \rightarrow \mathrm{R}_{i}$
Row Multiplication Multiplication of a row by a scalar, c, with c ≠ 0 $c \mathrm{R}_{i}\rightarrow \mathrm{R}_{i}$${\displaystyle \mathrm {R} _{i}\rightarrow \mathrm {R} _{i}}$
Square Matrices
Square matrices are matrices where the number of rows and number of columns are equal, resulting in an n × n matrix.
Identity Matrix
The identity matrix, In, is a diagonal matrix which has all elements along the main diagonal equal to 1 and all other elements equal to 0. Multiplication of another matrix by the identity matrix leaves the first unchanged. Moreover, multiplication with the identity matrix is commutative; in other words, A × I = I × A.
Example:
$A \cdot I_{3}=\left(\begin{array}{lll}{a} & {b} & {c} \{d} & {e} & {f}\end{array}\right) \cdot\left(\begin{array}{lll}{1} & {0} & {0} \{0} & {1} & {0} \{0} & {0} & {1}\end{array}\right)=\left(\begin{array}{lll}{a} & {b} & {c} \{d} & {e} & {f}\end{array}\right)\nonumber$
Trace
Only applicable to square matrices, the trace or character, ${\displaystyle \chi }$, of a matrix is the sum of its diagonal entries along the main diagonal.
Determinant
The determinant of a matrix, denoted det(A), is a real number computed from a square matrix. A non-zero determinant implies matrix invertibility, which further implies that the set of linear equations comprising the matrix has exactly one solution.
For a 2 × 2 matrix, the determinant is computed as follows:
$\operatorname{det}(\mathbf{A})=\left|\begin{array}{ll}{a} & {b} \{c} & {d}\end{array}\right|=a d-b c\nonumber$
For a 3 × 3 matrix, the determinant is computed as follows:
$\operatorname{det}(\mathbf{A})=\left|\begin{array}{ccc}{a} & {b} & {c} \{d} & {e} & {f} \{g} & {h} & {i}\end{array}\right|=a\left|\begin{array}{cc}{e} & {f} \{h} & {i}\end{array}\right|-b\left|\begin{array}{cc}{d} & {f} \{g} & {i}\end{array}\right|+c\left|\begin{array}{cc}{d} & {e} \{g} & {h} \end{array}\right|\nonumber$
Higher order determinants may be calculated by using Cramer's Rule. | textbooks/chem/Inorganic_Chemistry/Supplemental_Modules_and_Websites_(Inorganic_Chemistry)/Advanced_Inorganic_Chemistry_(Wikibook)/1.03%3A_Matrix.txt |
A representation is a set of matrices, each of which corresponds to a symmetry operation and combine in the same way that the symmetry operators in the group combine.1 Symmetry operators can be presented in matrices, this allows us to understand the relationship between symmetry operators through calculation from matrices. In order to understand representations, knowing matrix notions for symmetry operations is essential.
Here is some examples of symmetry operations in matrix form:
\begin{align*} \text { a point in space } &=\left[\begin{array}{l}{x} \{y} \{z}\end{array}\right] \[4pt] E &=\left[\begin{array}{lll} {1} & {0} & {0} \ {0} & {1} & {0} \ {0} & {0} & {1} \end{array}\right] \[4pt] i &=\left[\begin{array}{ccc} {-1} & {0} & {0} \ {0} & {-1} & {0} \ {0} & {0} & {-1} \end{array}\right] \[4pt] \sigma_{x y}&=\left[\begin{array}{lll} {1} & {0} & {0} \ {0} & {1} & {0} \ {0} & {0} & {1} \end{array}\right] \[4pt] \mathrm{C}_{\mathrm{n}}&=\left[\begin{array}{ccc} {\cos \theta} & {-\sin \theta} & {0} \ {\sin \theta} & {\cos \theta} & {0} \ {0} & {0} & {1} \end{array}\right] \[4pt] S_{n}&=\left[\begin{array}{ccc} {\cos \theta} & {-\sin \theta} & {0} \ {\sin \theta} & {\cos \theta} & {0} \ {0} & {0} & {-1} \end{array}\right] \end{align*}
Both $C_n$ and $S_n$ have $z$ set as the principal axis.
For Cn operation, θ depends on n with the relationship of $\theta=\frac{360}{n}$. If the symmetry is C2, then θ would be 180° because the molecule is rotated 180°. For C3, θ would be 120°, C4 θ would be 90°, etc.
To apply a symmetry operation on an atom of a molecule, matrices can be combined to produce another operation in the group. For a C2v symmetry compound such as water shown in Figure $1$, the operations (E, C2, σv1, σv2) can be applied on the vector (x, y, z) to find the representation. To simplify the math, a 1x1 matrix can be done by block diagonalizing for individual vector.
Example $1$
E(y) = [1] [y] = y
C2(y) = [-1] [y] = -y
σv1(y) = σxz = [-1] [y] = -y
σv2(y) = σyz = [1] [y] = y
In this example, if you apply identity (E) on vector y shown in Figure $2$, you would obtain y. If you apply C2 rotation along the principal axis on y, then you would obtain -y, etc. These obtained results show the position of the vector after the symmetry operation. The coefficient of each vector after symmetry operation can be represented as Γy in character table $1$. This set of matrices each of which corresponds to the character of a matrix a representation[1]. The same symmetry operation can be applied on x and z to obtain a representation for Γx and Γz.
Table $1$: xyz representations in C2v.
C2v E C2 σv1 σv2
Γz [1] [1] [1] [1]
Γy [1] [-1] [-1] [1]
Γx [1] [-1] [1] [-1]
A representation can combine in the same way that the symmetry operators in the group combine, thus, the multiplication table for the matrices that represent each symmetry operation must also multiply together in the same way that the symmetry operators themselves multiply.1 Refer to the following tables.
Table $1$: Multiplication tables for the C2v point group, showing how the 1 × 1 matrix representations multiply together in the same way that the symmetry operations do.
C2v E C2 σv1 σv2
E E C2 σv1 σv2
C2 C2 E σv2 σv1
σv1 σv1 σv2 E C2
σv2 σv2 σv1 C2 E
Γz [1] [1] [1] [1]
[1] [1] [1] [1] [1]
[1] [1] [1] [1] [1]
[1] [1] [1] [1] [1]
[1] [1] [1] [1] [1]
Γy [1] [-1] [-1] [1]
[1] [1] [-1] [-1] [1]
[-1] [-1] [1] [1] [-1]
[-1] [-1] [1] [1] [-1]
[1] [1] [-1] [-1] [1]
Γx [1] [-1] [1] [-1]
[1] [1] [-1] [1] [-1]
[-1] [-1] [1] [-1] [1]
[1] [1] [-1] [1] [-1]
[-1] [-1] [1] [-1] [1]
Irreducible Representation and Reducible Representations
A representation can be categorized as irreducible representation and reducible representations. A character table is given with irreducible representations, which are the blue shaded part in Figure 5. There are 5 rules to irreducible representations, shown in the following box.
5 Rules to Irreducible Representations
1. The sum of the squares of the dimensions of the irreducible representations of a group is equal to the order of the group. $h = \sum_i l_i^2 \nonumber$
2. The sum of the squares of the characters in any irreducible representation equals $h$. $h = \sum_i [\chi_i (R)^2] \nonumber$
3. The vectors whose components are the characters of two different irreducible representations are orthogonal. $\sum_R [\chi_iR \times \chi_jR] = 0 \nonumber$ if $i \neq j$.
4. In a given representation (reducible or irreducible), the characters of all matrices belonging to symmetry operations in the same class are identical.
5. The number of irreducible representations of a group is equal to the number of classes in the group.
The classes correspond directly to the sets of equivalent operations. Two operations belong to the same class when one may be replaced by the other in a new coordinate system that is accessible by a symmetry operation. For example, a C7 point group would have C71, C72, C73, C74, C75, C76, C77. Since cos(θ) = cos(θ), the characters associated with these matrices are the same. In this case, C71=C76, C72 = C75, C73 = C74, and C77 = E because they belong to the same class. We can simplify the C7 point group’s symmetry into 2 C71, 2C72, 2C73, and E because there are two operations belonging to the same class.
The green shaded part in Figure $3$ is a the reducible representation that is found based on number of unmoved molecule after a symmetry operation. For example, if we are looking at Γσ of C2v symmetry molecule such as water from Figure $3$, we would focus on the number of unmoved σ bonds after the symmetry operation. In a water molecule, there are two s bonds which are the two O-H bonds. If we apply E, both of the bonds don’t move, so the reducible representation would be 2 because each unmoved σ bonds contribute to 1 reducible representation. If we apply C2 operation on it, both bonds would move, where the O-H bonds would switch places. This means that there are zero unmoved σ bonds, so the reducible representation would be zero as shown in Figure $\PageIndex{3b}$.
The yellow shaded part in Figure $3$ is the reduction of reducible representations into irreducible representations. This can be done by using the formula,
$\mathrm{n}_{\mathrm{i}}=\frac{1}{h} \sum_{\mathrm{N}} \chi_{\mathrm{R}} \chi_{\mathrm{L}} \nonumber$
where
• $n_i$ is the number of times the irreducible representation occurs in the reducible representation,
• $N$ is the coefficient in front of each symmetry element symbol (shown on the top row of the character table),
• $h$ is the order of the group (sum of the coefficients N),
• $\chi_R$ and $\chi_I$ are the characters of the reducible and irreducible representations.
Reference
1. Pfennig, Brian (2015). Principles of Inorganic Chemistry. Hoboken, New Jersey: John Wiley & Sons, Inc.. pp. 195–202. ISBN 978-1-118-85910-0. | textbooks/chem/Inorganic_Chemistry/Supplemental_Modules_and_Websites_(Inorganic_Chemistry)/Advanced_Inorganic_Chemistry_(Wikibook)/1.04%3A_Representations.txt |
Definition of a Character Table
A character table is a 2 dimensional chart associated with a point group that contains the irreducible representations of each point group along with their corresponding matrix characters. It also contains the Mulliken symbols used to describe the dimensions of the irreducible representations, and the functions for symmetry symbols for the Cartesian coordinates as well as rotations about the Cartesian coordinates.
Components of a Character Table
A character table can be separated into 6 different parts, namely:
1. The Point Group
2. The Symmetry Operation
3. The Mulliken Symbols
4. The Characters for the Irreducible Representations
5. The Functions for Symmetry Symbols for Cartesian Coordinates and Rotations
6. The Function for Symmetry Symbols for Square and Binary Products
1. The Point Group
The symbol for the point group is found on the uppermost left corner of the character table. It denotes a collection of symmetry operations that are present in a molecule. It is called a point group because all the symmetry elements will intersect at one point[1].
2. The Symmetry Operations/Elements
A symmetry operation is “a geometrical operation that moves an object about some symmetry element in a way that brings the object into an arrangement that is indistinguishable from the original”(Pfennig, 199)[2]. The symmetry operations are at the first row at the top of the table. They are organized into classes, with each class having an order number in front of it. For example, 2S4 represents the operation S4 with order number 2. Operations can belong to the same class when one operation may be replaced by another in a new coordinate system that is accessible by a similar symmetry operation.
Common symmetry operations that are present in character tables are:
E Cn Cn
σd σv σd
I Sn Cn
3. The Mulliken Symbols
These are symbols that occur under the first column of the character table. They are named after Robert S. Mulliken, who suggested using the symbols to describe the irreducible representations. The meanings of the symbols are as follows:
• The dimensions/degeneracy of characters are denoted by the letters A,B,E,T,G and H with each letter representing degeneracy 1,1,2,3,4 and 5 respectively i.e.
Mulliken Symbol Number of Dimensions
A,B 1
E 2
T 3
G 4
H 5
For example, the Mulliken symbol A is singly degenerate and symmetric with respect to the rotation about the principal axis whereas the symbol B is anti-symmetric with respect to rotation about the principal axis even though it is also singly degenerate[3].
• The subscripts featured with each Mulliken symbol also represent different aspects of symmetry i.e.
4. The Characters for Irreducible Representations[4]
These are the rows of numbers at the center of the character table. They represent the irreducible representations of each Mulliken symbol under the point group. A representation is “a set of matrices, each corresponding to a single operation in the group, which can be combined amongst themselves similarly to how the group elements (symmetry operations) combine” .
These characters correspond to the characters of individual symmetry operations that can be described matrices, themselves. Each character can adopt a +1 or -1 or multiple of this numerical value depending on the symmetric or anti-symmetric behavior of the object undergoing a specific symmetry operation. If the object is symmetric with respect to itself after undergoing the operation, then the character is +1. If the object is anti-symmetric, then the character is -1[5].
5. The Functions for Symmetry Symbols for Cartesian Coordinates and Rotations
These are the symbols that correspond to the symmetry of the Cartesian coordinates (x, y, z) and the symmetry of the rotations about the Cartesian coordinates (Rx, Ry, Rz). They form basis representations for the group and are related to the transformation properties of the group.
For example, for the C3v point group, it can be said that z forms a basis for the A1 representation, x forms a basis for the E representation, and Rz forms a basis for the A2 representation.
6. The Functions for Symmetry Symbols for Square and Binary Products
These are the symbols for the functions that correspond to the square (x2+y2, z2, x2-y2) and binary products (xy, xy, yz) of the Cartesian Coordinates with respect to their transformation properties.
For example, for the C3v point group, it can be said that z2 forms a basis for the A1 representation, (xz,yz) forms a basis for the E representation, and there is no function for the A2 representation.
Mathematics of Character Tables
Each character table follows some main set of mathematical operations that allow for the calculation of important characteristics of the table. These operations are as follows:
1. The order of the group (h) can be calculated by taking the sum of the order of individual symmetry operations in a character table. For example, the order of the C3v point group is 6.
2. The sum of the squares of the dimensions of the irreducible representations of a group is equal to the order of the group.
3. The sum of the squares of the characters in any irreducible representation equals h.
4. The vectors whose components are the characters of two different irreducible representations are orthogonal.
5. In a given representation (reducible or irreducible) the characters of all matrices belonging to symmetry operations in the same class are identical.
6. The number of irreducible representations of a group is equal to the number of classes in the group.
Examples of Character Tables
The Character Table for the C2 Point Group
C2 E C2 Linear Functions, Rotations Quadratic Functions Cubic Functions
A +1 +1 z, Rz x2, y2, z2, xy z3, xyz, y2z, x2z
B +1 -1 x, y, Rx, Ry yz, xz xz2, yz2, x2y, xy2, x3, y3
The Character Table for the Td Point Group
Td E 8C3 3C2 6S4 d Linear Functions, Rotations Quadratic Functions Cubic Functions
A1 +1 +1 +1 +1 +1 - x2+y2+z2 xyz
A2 +1 +1 +1 -1 -1 - - -
E +2 -1 +2 0 0 - (2z2-x2-y2, x2-y2) -
T1 +3 0 -1 +1 -1 (Rx, Ry, Rz) - [x(z2-y2), y(z2-x2), z(x2-y2)]
T2 +3 0 -1 -1 +1 x, y, z xy, xz, yz (x3, y3, z3), [x(z2+y2), y(z2+x2), z(x2+y2)]
The Character Table for the D2d Point Group
D2d E 2S4 C2(z) 2C'2 d Linear Functions, Rotations Quadratic Functions Cubic Functions
A1 +1 +1 +1 +1 +1 - x2+y2, z2 xyz
A2 +1 +1 +1 -1 -1 Rz - z(x2-y2)
B1 +1 -1 +1 +1 -1 - x2-y2 -
B2 +1 -1 +1 -1 +1 z xy z3, z(x2+y2)
E +2 0 -2 0 0 (x, y),(Rx, Ry) (xz, yz) (xz2, yz2),(xy2, x2y),(x3, y3) | textbooks/chem/Inorganic_Chemistry/Supplemental_Modules_and_Websites_(Inorganic_Chemistry)/Advanced_Inorganic_Chemistry_(Wikibook)/1.05%3A_Character_Tables.txt |
SALCs refers to Symmetry Adapted Linear Combinations, which are generated via use of the projection operator technique. This technique is a mathematical method which outputs a function called a SALC that models the orbitals of the atoms of interest.[1] These SALCs are mathematical representations and therefore bare no physical meaning. They are commonly used in the generation of molecular orbitals.
Projection Operator Technique
The Projection Operator Technique utilizes the extended character table which includes each symmetry operation separately. The technique involves multiple steps, listed below in the form of the $\ce{BF_3}$ example.
Step 1. We begin by determining the reducible representations of the orbitals in question. For BF3, which has the D3h point group, the D3h character table is used. For our example, we will consider the sigma and pi bonds of the fluorine atoms and determine their reducible representations. Using the character table, we identify the reducible representations. They are listed below.
\begin{align*} Γ_σ &= Α1^\prime + Ε^\prime \[4pt] Γ_{πx} &= Α2^\prime + Ε^\prime \[4pt] Γ_{πy} &= Α2^{\prime\prime} + Ε^{\prime\prime} \[4pt] Γ_{πz} &= Α1^{\prime} + Ε^{\prime} \end{align*}
It is noted here that the $π_z$ orbitals transform as $σ$ orbitals.
Table $1$. This is the character table for the $D_{3h}$ point group which can be used to determine the irreducible representations of the orbitals.
D3h E C3 C2 σh S3 σv
A1' 1 1 1 1 1 1
A2' 1 1 -1 1 1 -1
E' 2 -1 0 2 -1 0
A1" 1 1 1 -1 -1 -1
A2" 1 1 -1 -1 -1 1
E" 2 -1 0 -2 1 0
Step 2. We now use the extended character table for the D3h Character table to generate the SALCs of the stated orbitals. To do this, we apply each symmetry operation to the given orbital and note which orbital it transforms into. We then add up each projector operator function in accordance to each irreducible representation.
Table $2$. This is the extended character table for the D3h point group which is used to deduce the functions for the SALCs using the projector operator technique.
D3h E C3 C32 C2 C2' C2" σh S3
Γσ σ1 σ2 σ3 σ1 σ2 σ3 σ1 σ2
Γπz $\pi_{1}$ $\pi_{2}$ $\pi_{3}$ $\pi_{1}$ $\pi_{2}$ $\pi_{3}$ $\pi_{1}$ $\pi_{2}$
Γπx $\pi_{1}$ $\pi_{2}$ $\pi_{3}$ $-\pi_{1}$ $-\pi_{2}$ $-\pi_{3}$ $\pi_{1}$ $\pi_{2}$
Γπy $\pi_{1}$ $\pi_{2}$ $\pi_{3}$ $-\pi_{1}$ $-\pi_{2}$ $-\pi_{3}$ $-\pi_{1}$ $-\pi_{2}$
Step 3. Common techniques for dealing with the double degeneracy of the E' and E" representations[2]:
1. If the principal axis is a C3 axis, we subtract the functions corresponding to the σ2 and σ3 orbitals.
2. If the principal axis is a C4 axis, we apply the projection operator technique to the σ2 and use the function that is derived.
3. We must ensure that the representations are orthogonal to one another in order for them to be correct.
Step 4. We can now apply the coefficients within the matrix to determine the coefficients of the function found via the projection operator technique.
We determine the SALCs for the example orbitals to be the following:
\begin{align*} \text{SALC}_σ(A_1') &= 3σ_1 + 3σ_2 + 3σ_3 = σ_1 + σ_2 + σ_3 \[4pt] \text{SALC}_σ(E') &= 4σ_1 - 2σ_2 - 2σ_3 = 2σ_1 - σ_2 - σ_3 \[4pt] \text{SALC}_σ(E') &= 2σ_2 - 2σ_3 = σ_2 - σ_3 \end{align*}
\begin{align*} \text{SALC}_{πz}(A_1') &= 3π_1 + 3π_2 + 3π_3 = π_1 + π_2 + π_3 \[4pt] \text{SALC}_{πz}(E') &= 4π_1 - 2π_2 - 2π_3 = 2π_1 - π_2 - π_3 \[4pt] \text{SALC}_{πz}(E') &= 2π_2 - 2π_3 = π_2 - π_3 \end{align*}
\begin{align*} \text{SALC}_{πx}(A_2') &= 3π_1 + 3π_2 + 3π_3 = π_1 + π_2 + π_3 \[4pt] \text{SALC}_{πx}(E') &= 4π_1 - 2π_2 - 2π_3 = 2π_1 - π_2 - π-3 \[4pt] \text{SALC}_{πx}(E') &= 2π_2 - 2π_3 = π_2 - π_3 \end{align*}
\begin{align*} \text{SALC}_{πy}(A_2'') &= 3π_1 + 3π_2 + 3π_3 = π_1 + π_2 + π_3 \[4pt] \text{SALC}_{πy}(E'') &= 4π_1 - 2π_2 - 2π_3 = 2π_1 - π_2 - π_3 \[4pt] \text{SALC}_{πy}(E'') &= 2π_2 - 2π_3 = π_2 - π_3 \end{align*}
Uses of SALCs
SALCs help us to understand which orbitals will be bonding, antibonding, and nonbonding. For example, by comparing the symmetry of the SALCs to that of the orbitals of the central atom, it is possible to generate the corresponding molecular orbitals. Although SALCs are mathematical representations that have no physical meaning, they are useful in providing a tool for deriving molecular orbitals. | textbooks/chem/Inorganic_Chemistry/Supplemental_Modules_and_Websites_(Inorganic_Chemistry)/Advanced_Inorganic_Chemistry_(Wikibook)/1.06%3A_SALCs_and_the_projection_operator_technique.txt |
The simplicity of diatomic molecular orbitals allows for their inspection using the theory of linear combinations of atomic orbitals (LCAO). As two atoms approach each other, their atomic orbitals overlap. In order to form bonding molecular orbitals, sufficient overlap should occur between atomic orbitals and they must have similar energies and matching symmetries. Anti-bonding molecular orbitals occur when two atomic orbitals cancel each other out. This gives rise to a node or area with zero electron density in between the two atoms.
Molecular Orbitals
Just like the atomic orbitals, molecular orbitals(MO) are used to describe the bonding in molecules by applying the group theory. The basic thought of what is molecular orbitals can be the organized combinations of the atomic orbitals according to the symmetry of the molecules and the characteristics of atoms. By applying the MO diagram, the properties such as magnetism and chirality of the molecules can be predicted.
Just like atomic orbitals can be solved as wavefunctions by applying Hermitian Operator to Schrödinger equations, molecule orbitals can be approximated by the linear combinations of atomic orbitals(LCAO):
$\Psi=\sum_{n=0}^{\mathrm{N}} c_{i} \psi_{i} \nonumber$
is the molecular wave function, ${\displaystyle \psi }$ is the atomic wave functions for atoms, ${\displaystyle c_{i}}$ is the adjustable coefficients. This means that when the atoms get closer to each other, their atomic orbitals can overlap and the probability of the occurring of the electrons from the atoms becomes significantly in the overlap regions, which is the formation of the molecular orbitals.
Bonding, Anti-bonding and Non-bonding Molecular Orbitals
Before it goes further, some acknowledge about bonding and anti-bonding should be emphasized. When two atomic orbitals overlap, they can form new orbitals in two ways: one is the bonding orbital and another one is the anti-bonding orbital. In a molecular orbital diagram, if atomic orbitals form a bonding orbital, they must form an anti-bonding orbital. The bonding orbitals and anti-bonding orbitals always have the same number and relate with each other. For example, if there is a 1σ bonding orbital, then there must be a 1σ*, which is the relevant anti-bonding orbital of 1σ, where * is used to represent anti-bonding. This bonding and anti-bonding orbitals caused by the different ways of overlapping of the atomic orbitals.
Besides the bonding and anti-bonding molecular orbitals, there can also be some non-bonding orbitals. These orbitals only exist when some atomic orbitals of an atom cannot find any atomic orbital from another atom that has the same symmetry properties, then these atomic orbitals will remain at the same energy and form no bond. That’s why they are called “non-bonding” molecular orbitals.
Diatomic Molecular Orbitals
Normally, in diatomic molecular orbitals, the atomic orbitals with the closest energy level can overlap with each other and form molecular orbitals. Therefore, the atomic orbitals generally tend to overlap one by one from the lowest potential energy to the highest potential energy. For example, in a homonuclear diatomic molecule, which means that both atoms are the same element, the same orbitals will overlap together and form molecular orbitals.
Eg. in the oxygen O2, the 1s orbital will overlap with 1s orbital to form a σ orbital and a σ* orbital and the 2s orbital will overlap with 2s orbital to form a σ orbital and a σ* orbital. The 1s orbital cannot overlap with 2s orbital in this case.
For another example, in a heteronuclear diatomic molecule, which means that the atoms in the molecule are different elements, the orbitals with the closest energy can overlap with each other and form molecular orbitals.
Eg. in the hydrogen fluoride HF, hydrogen's 1s orbital will overlap with one of the fluorine's 2p orbitals to form a σ orbital and a σ* orbital since the orbital potential energy of H1s orbital is -13.61eV and of F2p is -18.65eV. Comparing with F2s orbital which has -40.17eV as its orbital potential energy, they are really close to each other. That's why H1s will form molecular orbitals with F2p instead of F2s.[1]
Also notice that only two atomic orbitals with similar symmetry properties can combine together. For example, s orbital can’t overlap with px orbital if the overlap equally with both the same and opposite signs, this will cancel the bonding and anti-bonding effect which will result in no molecular orbital forms.
Besides that, we normally only consider the valence atomic orbitals. That's why the F1s orbital does not be considered here since it's full-filled.
MO from s Orbitals
The overlap of two s orbitals will form a σ orbital and a σ* orbital.
MO from p Orbitals
The overlap of two p orbitals will form either a σ and a σ* orbitals or a π and a π*orbitals. Generally, we choose to assign the z axis of two atoms point to each other which allows the pz orbitals overlap “head” to “head” and form σ and σ* orbitals. This also allows the px orbitals overlap “side” to “side” and form π and π*orbitals. This also applies for the py orbitals.
Sometimes, when p orbitals can’t find another orbital has a similar symmetry with it, these p orbitals will remain as non-bonding orbitals.
MO from d Orbitals
Start from the third row, all the elements after sodium (Na) have d orbitals. There are totally 5 d orbitals, which are named as dz2,dxy,dxz,dyz and dx2-y2. Elements with d orbitals, especially the transition metals, can also form bonds by using d orbitals. As shown in Figure $4$, the different overlap of the d orbitals will result in different electron density, which results in different types of bonds. Just like what happens to the p-orbital-overlapping molecular orbitals, d atomic orbitals can also overlap with other orbitals in different orbital potential energy levels such as p orbitals and s orbitals. This is also the reason for the formation of a metal complex. However, d orbitals normally are not applied to form molecular orbitals in a diatomic molecule.
Nonbonding Orbitals
As mentioned before, if an atomic orbital cannot find any other orbital with similar symmetry, then it will remain as non-bonding molecular orbital. The non-bonding molecular orbitals normally have the same energies as the atomic orbitals that form them, although there are some special cases can happen (not in diatomic MO, but in some metal complex). For example, in the ion FHF-, by solving the irreducible representation, it can be found that the base of FHF- has ag, b2u, b3u, b2g, b3g and b1u. However, since the H atom has only a 1s orbital, it can only form molecular orbitals with ag. Therefore, b2u, b3u, b2g, b3g and b1u will remain as non-bonding molecular orbitals. Also, notice that b1u has a higher level in energy state. This can be caused by the extreme unsymmetrical structure of this molecular orbital. Another guess of the increase in the b1u energy level can be the slightly mixing with the 2s orbital from two fluorines.
Orbital Mixing
This is the most tricky part for the diatomic molecular orbitals. In general, we only consider the interactions between atomic orbitals have the same energies unless there is no atomic orbital satisfy the request. However, the interaction between two atomic orbitals with relatively close energies that have the same symmetry can also happen. This will result in the raising of the energies of the molecular orbitals.
Considering Figure $2$ above, this is an example without interaction between two atomic orbitals with close energies that have the same symmetry. The ${\displaystyle \pi _{u}}$ molecular orbitals have higher energy than the ${\displaystyle \sigma _{g}}$ molecular orbital. However, since the ${\displaystyle \sigma _{g}(2s)}$ and ${\displaystyle \sigma _{g}(2p)}$ orbitals both have ${\displaystyle \sigma _{g}}$ symmetry,these orbitals can interat to lower the energy of the ${\displaystyle \sigma _{g}(2s)}$ and to increase the energy of the ${\displaystyle \sigma _{g}(2p)}$. This will result the energy of ${\displaystyle \sigma _{g}(2p)}$ orbital has higher energy than ${\displaystyle \pi _{u}(2p)}$ orbitals, as shown in Figure $7$. This phenomenon is called mixing.
For example, this s-p mixing will happen for B2 and C2.
Heteronuclear Diatomic Molecule
Unlike the homonuclear diatomic molecule, many heteronuclear diatomic molecules are polar molecules. This means that the electron density does not evenly distribute over each atom. The electron density always favors the atom that is more electronegative. MO theory can also be applied in this situation.
As mentioned before, since here we deal with different two elements in molecules, the orbital potential energies will be considered. This will result in uneven contributions of molecular orbitals from the overlap of the atomic orbitals. Fortunately, farther the two atomic potential energies (APE) are, less the magnitude of the interaction between them. This means that only two atomic orbitals with similar energies can overlap enough to form molecular orbitals. Use the example of HF (Figure $3$). According to Table $1$, 1s orbital of the hydrogen atom has APE as -13.61eV, 2s orbital of fluorine has APE as -40.17eV and 2p orbitals of fluorine have APE as -18.65eV. It is obvious that ${\displaystyle H1s}$ orbital has a much closer potential energy to the ${\displaystyle F2p}$ instead of ${\displaystyle F2s}$. Therefore, ${\displaystyle H1s}$ orbital overlaps much more with ${\displaystyle F2p}$ and form molecular orbitals. ${\displaystyle F2s}$ will remain as a non-bonding orbital.
Table $1$. Orbital Potential Energy. Notice that only the valence atomic orbitals are counted.
Atomic Number Elemment 1s 2s 2p 3s 3p 4s
1 H -13.61
2 He -24.59
3 Li -5.39
4 Be -9.32
5 B -14.05 -8.3
6 C -19.43 -10.66
7 N -25.56 -13.18
8 O -32.38 -15.85
9 F -40.17 -18.65
10 Ne -48.47 -21.59
11 Na -5.14
12 Mg -7.65
13 Al -11.32 -5.98
14 Si -15.89 -7.78
15 P -18.84 -9.65
16 S -22.71 -11.62
17 Cl -25.23 -13.67
18 Ar -29.24 -15.82
19 K -4.34
20 Ca -6.11
Drawing Diatomic MO Diagram
Here are some common steps to help you draw the diatomic MO diagram.
1. Recognize the diatomic molecule is a homonuclear molecule or heteronuclear molecule;
2. Recognize the orbital potential energies of their valence atomic orbitals, find the closest pair;
3. Recognize the symmetry of these atomic orbitals to Figure out if the interaction can actually happen. Then determine the {\displaystyle \sigma } and {\displaystyle \pi } bonding and anti-bonding, and even non-bonding orbitals;
4. Recognize the mixing effect to see if there are any energy shift for the molecular orbitals;
5. Draw the electrons from the lowest molecular orbital. Follow the rules like the Pauli exclusion principle to draw the ground state MO diagram.
Reference
1. Miessler, Gary. “Chapter 5. Molecular Orbital Theory.” Inorganic Chemistry, by Gary L. Miessler et al., Pearson, 2014, pp. 117–138.
2. ↑ Greeves, Nick. “ChemTube3D.” ChemTube3D. [1] | textbooks/chem/Inorganic_Chemistry/Supplemental_Modules_and_Websites_(Inorganic_Chemistry)/Advanced_Inorganic_Chemistry_(Wikibook)/1.07%3A_Diatomic_Molecular_Orbitals.txt |
Point Group of NH3
The symmetry elements of NH3 are E, 2C3, and 3 sigma-v. To elaborate, the molecule is of C3v symmetry with a C3 principal axis of rotation and 3 vertical planes of symmetry. The image of the ammonia molecule (NH3) is depicted in Figure \(1\) and the following character table is displayed below.[1]
C3v E 2C3v 3 σv
A1 1 1 1 z x2+y2, z2
A2 1 1 -1 Rz
E 2 -1 0 (x,y)(Rx,Ry) (x2-y2,xy)(xz,yz)
The Construction of Molecular Orbitals of NH3
The Molecular Orbital Theory (MO) is used to predict the electronic structure of a molecule. Molecular orbitals are formed from the interaction of 2 or more atomic orbitals, and the interactions between atomic orbitals can be bonding, anti-bonding, or non-bonding. A bonding orbital is the interaction of two atomic/group orbitals in phase while an anti-bonding orbital is formed by out-of-phase combinations.
In general, the energy level of molecular orbitals increases from bonding, to non-bonding, and anti-bonding molecular orbitals. Pi-bonding molecular orbitals generally have greater energies than sigma-bonding molecular orbitals because the pi interactions are less effective than sigma interactions. The energy of molecular orbitals increases when the number of nodes also increases, and vice versa.[6] Within bonding molecular orbitals of the same symmetry, the lowest energy are from completely symmetrical sigma bonding molecular orbitals.
Projection Operator Methode:
The Projection Operator Methode can be used to determine MO of NH3, the next steps can be used:
1) Determine the point group of melecular;
2) Lable S orbital of H;
3) Generate a reducible representation (ᒥ) for H;
4) Reduce reducible representation to irreducible representation;
5) Generate the symmetry adapted linear combinations (SALCs) of orbitals that arise from these irreducible representations;
6) Drawing group orbital combinations and determine the atomic orbitals of the centeral atom;
7) MO
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1.09: Td Molecular Orbitals
Td Point Group
The Td symmetry group is a one of the point groups considered to have higher symmetry. Molecules in the Td group, such as methane (CH4) have four C3 rotational axes.
The character table for the Td point group is shown below:
Td E 8C3 3C2 6S4 6σd
A1 1 1 1 1 1 x2+y2+z2
A2 1 1 1 −1 −1
E 2 −1 2 0 0 (2z2x2y2, x2y2)
T1 3 0 −1 1 −1 (Rx, Ry, Rz)
T2 3 0 −1 −1 1 (x, y, z) (xy, xz, yz)
Constructing Molecular Orbitals
Determining Reducible Representations
The first step to constructing the molecular orbitals (MOs) is to determine the reducible representations for the σ and π bond vectors, denoted ${\displaystyle \Gamma _{\sigma }}$ and ${\displaystyle \Gamma _{\pi }}$, respectively. The character corresponding to each symmetry operation can be determined by tracking how the bond vectors transform. Each vector that is left unmoved will contribute +1, each vector that is shifted to a new position will contribute 0, and each vector that undergoes a sign reversal will contribute −1. The reducible representations ${\displaystyle \Gamma _{\sigma }}$ and ${\displaystyle \Gamma _{\pi }}$ are listed below:
Td E 8C3 3C2 6S4 6σd
${\displaystyle \Gamma _{\sigma }}$ 4 1 0 0 2
${\displaystyle \Gamma _{\pi }}$ 8 −1 0 0 0
Reducing the Reducible Representations
The reducible representations obtained from the previous section can be written as linear combinations of the irreducible representations shown in the character table. The contribution of each irreducible representation to the reducible representation is given by the formula:
$n_{i}=\frac{1}{h} \sum N \chi_{R} \chi_{I}\nonumber$
where ${\displaystyle n_{i}}$ is the coefficient of the ith reducible representation, ${\displaystyle h}$ is the order of the point group, ${\displaystyle N}$ is the number of symmetry operations in the class, ${\displaystyle \chi _{R}}$ is the character of the reducible representation corresponding to the class, ${\displaystyle \chi _{I}}$ is the character of the irreducible representation corresponding to the class, and the summation is taken over all classes of symmetry operations. Applying this method to the ${\displaystyle \Gamma _{\sigma }}$ and ${\displaystyle \Gamma _{\pi }}$ representations gives:
$\Gamma_{\sigma}=A_{1}+T_{2}\nonumber$
$\Gamma_{\pi}=E+T_{1}+T_{2}\nonumber$
Determining SALCs of Pendant Ligands
The Symmetry Adapted Linear Combinations (SALCs) can be found using the projection operator technique. For example, suppose we using the following labeling scheme for the ligand groups in Figure 1: (1) top-left-front, (2) top-right-back, (3) bottom-right-front, (4) bottom-left-back. Then the normalized SALCs for the s orbitals of the ligand groups are:
$S A L C\left(A_{1}\right)=\frac{1}{2}\left(s_{1}+s_{2}+s_{3}+s_{4}\right)\nonumber$
$S A L C\left(T_{2}\right)=\frac{1}{2}\left(s_{1}-s_{2}-s_{3}+s_{4}\right)\nonumber$
$S A L C\left(T_{2}\right)=\frac{1}{2}\left(s_{1}-s_{2}+s_{3}-s_{4}\right)\nonumber$
$S A L C\left(T_{2}\right)=\frac{1}{2}\left(s_{1}+s_{2}-s_{3}-s_{4}\right)\nonumber$
The purpose of using the projection operator method is to be able to draw the SALCs.
Drawing the Molecular Orbital Diagram
Consider CH4 as a specific example of a molecule within the Td symmetry group. Before drawing the MO diagram, the valence atomic orbitals on the central atom and their symmetries must be noted. The symmetry of the orbitals can be determined by determining how they transform under the symmetry operations or by simply looking at the right most columns on the character table. The valence orbitals of the carbon atom include 2s (A1 symmetry) and 2px, 2py, 2pz (T2 symmetry).
In CH4, the only potentially bonding orbitals of the ligand groups are the 1s orbitals in the hydrogen atom. The irreducible representations contributing to the symmetry of the ligand group SALCs determines the AOs of the central atom with which they can interact. As found previously, the SALCs of the hydrogen atoms have A1 + T2 symmetry, so they can interact with all of the valence orbitals on the carbon atom to form bonding and antibonding MOs. Bonding MOs are positive linear combinations of the central atom AOs and ligand group SALCs, while antibonding MOs are negative linear combinations. The number of bonding and antibonding MOs created must be equal to the number of AOs and ligand group orbitals used to create them.
Although in CH4, all AOs and SALCs formed of bonding and antibonding MOs, this is not always the case. For example, if a central atom AO has symmetry that is absent from the ligand group SALCs, it will be unable to participate in the formation of bonding and antibonding MOs. In such cases, non-bonding MOs are formed.
The relative energy of the MOs are influenced by a few trends. For MOs formed with similar AOs, the following tend to be true:
• Bonding MOs have lower energy than antibonding MOs. Non-bonding MOs tend to have energy intermediate between bonding and antibonding MOs.
• π bonding MOs have higher energy than σ bonding MOs.
• The energy of MOs increases with the number of nodes.
• The totally symmetric σ bonding MO has the lowest energy among σ bonding MOs.
Illustrations of CH4 MOs can be found in Pfennig's text, Principles of Inorganic Chemistry, pp. 300. | textbooks/chem/Inorganic_Chemistry/Supplemental_Modules_and_Websites_(Inorganic_Chemistry)/Advanced_Inorganic_Chemistry_(Wikibook)/1.08%3A_NH3_Molecular_Orbitals.txt |
The D4h point group are one of the most common molecular symmetry found in nature. For example, the XeF4 molecule belongs to the D4h point group. the XeF4 contains one C4 rotation axis, one C2 rotation axis, and four C2 perpendicular rotation axis, 2σv planes, 2σd planes and 1σh plane, those composed the character table of the D4h Point group.
E 2C4 C2 2C'2 2C"2 i 2S4 σh v d Linear's Rotation Quadractic
A1g 1 1 1 1 1 1 1 1 1 1 x2+y2, z2
A2g 1 1 1 -1 -1 1 1 1 -1 -1 Rz x2-y2
B1g 1 -1 1 1 -1 1 -1 1 1 -1 xy
B2g 1 -1 1 -1 1 1 -1 1 -1 1 (xz, yz)
Eg 2 0 -2 0 0 2 0 -2 0 0 (Rx, Ry)
A1u 1 1 1 1 1 -1 -1 -1 -1 -1
A2u 1 1 1 -1 -1 -1 -1 -1 1 1 z
B1u 1 -1 1 1 -1 -1 1 -1 -1 1
B2u 1 -1 1 -1 1 -1 1 -1 1 -1
Eu 2 0 -2 0 0 -2 0 2 0 0 (x, y)
σ 4 0 0 2 0 0 0 4 2 0
$\pi$ 8 0 0 -4 0 0 0 0 0 0
To compose a Molecular Diagram of a molecule with D4h symmetry group, we should first find the irreducible representation of the ligands and of the center molecule. and then find the SALCS for each of the irreducible representation and finally, compose the molecular diagram. To take an easy example, the Square Planar Complexes.. starting with the sigma orbital of the ligands, the reducible representation of the sigma orbital is the total number of atoms that do not move under each operation. For the Pi orbital, we have to degenerate the pi orbital has two degrees of freedom, thus, the reducible representation of the pi orbital can also be found by using the similar method. and then, by using the projection operation method, we can find the irreducible representations of the ligand's sigma and pi orbital. In this case, the sigma orbital has A1g, B1g, Eu three irreducible representations and the pi orbital has A2g, A2u, B2g, B2u, Eg and Eu.
E 2C4 C2 2C’2 2C’’2 i 2S4 σh 2σv 2σd
sigma 4 0 0 2 0 0 0 4 2 0
Pi 8 0 0 -4 0 0 0 0 0 0
Move on the central atom, we can find irreducible representation of the valence orbitals on the central atoms by using the character table. The results are as follow:
Representation Orbital
A1g s, dz2
B1g dx2- y2
B2g dxy
Eg dxz, dyz
A2u Pz
Eu Px, py
1.11: Pi Donor and Acceptor Ligands
The nature of ligands coordinated to the center metal is an important feature of a complex compound along with other properties such as metal identify and its oxidation state. More specifically, it is the identity and consequently the ability of the ligand to donate or accept electrons to the center atom that will determine the molecular orbitals.
The spectrochemical series shows the trend of compounds as weak field to strong field ligands. Furthermore, ligands can be characterized by their π-bonding interactions. This interaction reveals the amount of split between eg and t2g energy levels of the molecular orbitals that ultimately dictates the strength of field of the ligands.
Examples of Weak Field Ligands X-, OH-, H2O ; Examples of Strong Field Ligands H-, NH3, CO, PR3
Electron configuration of high and low spin.
In a π-donor ligand, the SALCs of the ligands are occupied, hence it donates the electrons to the molecular σ σ* and π π* orbitals. The orbitals associated to eg are not involved in π interactions therefore it stays in the same energy level (Figure \(1\)). On the other hand, the occupied ligand SALC t2g orbitals that would form molecular orbitals with the metal t2g orbitals (ie. dxy, dxz, dyz) are lower in energy than its metal counterparts. The resulting MO has π* orbitals that are energetically lower than the σ* orbitals that are formed from the non bonding orbitals (eg). The difference between the t2g π* and eg σ orbitals is denoted as Δ, split. In the π-donor case, the Δ is small due to the low π* level.
Conversely, the t2g SALCs of a pi accepting orbitals are higher in energy than the metal t2g orbitals because they are unoccupied. The resulting t2g π* orbitals are higher than the σ* orbitals. This creates a larger Δ between the eg and t2g π orbitals, making these π-accepting orbitals high split ligands.
Finally, the magnitude of Δ as influenced by the identify of the ligand will dictate how electrons are distributed in the metal d orbitals (Figure \(2\)). Weak field ligands produce a small Δ hence a high spin configuration. Strong field ligands produce a large Δ hence a low spin configuration on the d electrons.
1.12: Normal Modes of Vibration
Molecular vibrations
Molecular vibrations are one of three kinds of motion, occurs when atoms in a molecule are in periodic motion. Molecular vibrations include constant translational and rotational motion. Translational motion occurs when the whole molecule goes in the same direction while the rotational motion occurs when the molecule spins like a top. Molecule vibrations fall into two main categories of stretching and bending. Stretching changes in interatomic distance along bong axis, while bending changes in angle between two bonds in a molecule.
There are two types of stretching, symmetric stretching and asymmetric stretching as the following Figure shows:
There are four types of bend, rocking, scissoring, wagging, and twisting.
Normal modes of vibration
Each atom in a molecule has three degree of freedom. A molecule with n atoms has 3n degree of freedom. 3n degree of freedom composes of translation, rotations and vibrations. All 3n degrees of freedom have symmetry relationships consistent with the irreducible representations of the molecule's point groups. Non-vibration modes (NVM) include translations and rotations. The vibrational motions of the atoms in a molecule can always be resolved into fundamental vibrational modes for the entire molecule.
Atomic displacement coordinates
The number of normal modes of vibration:
• 3n-6 for non-linear molecules
• 3n-5 for linear molecules
To indicate the the number of normal modes of vibration:
• Locate a set of three vectors along the Cartesian coordinates at each atom, representing the 3n degrees of freedom
• Find the reducible representation
• Reduce it to irreducible representations, subtract rotations and translations
• The rest of irreducible representations will give the symmetry of the NMVs
Samples
vibrations for SO2
C2v E C2 σv(xz) σ’v(yz)
A1 1 1 1 1 z x2, y2, z2
A2 1 1 -1 -1 Rz xy
B1 1 -1 1 -1 x, Ry xz
B2 1 -1 -1 1 y, Rx yz
Γ3n 9 -1 1 3
Ni 3 1 1 3
Xi 3 -1 1 1
Reduce
Γ3n=3A1+A2+2B1+3B2
Γtrans=A1+B1+B2
Γrotations=A2+B1+B2
ΓNMV3n-6=2A1+B2
NMVs are also identified by frequency numbers: v1, v2, v3,... The numbering is often assigned systematically in descending order of the symmetry species and among modes of the same symmetry in descending order of the vibrational frequency. Stretching modes have higher frequency than bending modes. | textbooks/chem/Inorganic_Chemistry/Supplemental_Modules_and_Websites_(Inorganic_Chemistry)/Advanced_Inorganic_Chemistry_(Wikibook)/1.10%3A_D4h_Molecular_Orbitals.txt |
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