C 2 : More complicated than it sounds
The present work is another contribution to a better understanding of the chemical bond in C2. A density functional approach is employed, and the obtained results (bond distance and bond dissociation energy) agrees very well with the previously [2-4] valence bond results. The obtained results also points to a bond order of four, reinforcing previously obtained data [3]. Furthermore, based on the calculated IR and Raman spectra, is proposed that C2 exhibits, at an electronic level, an asymmetry, and that such molecule has not, in fact, a centre of inversion.
Introduction<!>Metodhology<!>Results and discussion
<p>Although not stable (isolable) species C2 is of great practical importance, being present, for example, in the blue flame resulting from the combustion of hydrocarbons. From a theoretical point of view, C2 is a real challenge given the intriguing and even enigmatic nature of the chemical bond in this molecule. The present work is another contribution to a better understanding of the chemical bond in C2.</p><!><p>C2 molecule was modelled by density functional (DFT) approach ( ωB97X-D/6-31+G* and ωB97X-D/6-311+G** basis sets).</p><!><p>As can be verified form Table 1 data, the DF-ωB97X-D/6-31+G* theoretical approach is the one that provide a bond dissociation energy (kJ mol -1 ) calculated value of 593.40, only 3.2% below the available experimental value [1] of 613.08±0.25. The Mulliken and Löwdin bond orders are respectively, 3.42 and 3.66.</p><p>The obtained bond distance and bond energy are in very good agreement with the values previously obtained by Su et al [2] by the ab initio VB study for the electronic structure of the C2 molecule in the ground state (the calculations involved 78 chemically relevant VB structures).</p><p>The obtained results are also in very good agreement with those obtained by Xu et al [3] by full generalized valence bond (GVB) calculations.</p><p>Despite the minor bond dissociation energy value (584.71 kJmol -1 ) the DF-ωB97X-D/6-311+G** approach provides Mulliken and Löwdin bond orders of 3.55 and 3.97, respectively. Such results are in very good agreement with the ones obtained by Shaik [4] showing that the properties of C2 are reproduced when such specie is modelled as a quadruple bonding one.</p><p>By following a molecular orbital approach, the calculated MO energies (DF-ωB97X-D/6-31+G*).to C2 are shown in Figure 2. If the first four orbitals are ligand orbitals, then, a bond order of 4 can be calculate (considering only the 2s and 2p eletrons).</p><p>Shaik [4] has concluded that "the quadruply bonded structure is made of two strong π bonds, one strong σ bond and a weaker fourth σ-type bond, the bond strength of which is estimated as 17-21 kcalmol -1 ".</p><p>Hence, as can be verified, the DFT approach employed in the present work agrees very well with the VB approach [2,4] previously employed.</p><p>However, some surprisingly results were obtained, as follows:</p><p>The calculated (DF-ωB97X-D/6-31+G*) IR and Raman spectra for C2 are shown in Figure 1. In the Raman spectrum a very intense band at 1906 cm -1 is observed. In the IR spectrum no band is observed. However, checking the calculated IR bands table, a band at 1906 cm -1 is present. Hence, can be concluded that such band is really very little intense, and is because this that is cannot be seen in the "drawn" spectrum. At a first looking, C2 belongs to the D∞h point group. Such point group has an inversion centre as symmetry element. However, as is well known, a molecule that has a vibrational mode active simultaneously in IR and Raman cannot have an inversion centre.</p><p>Hence, in fact, C2 has not an inversion centre, and such asymmetry between the two carbon atoms can only be explained at an electronic level, that is, from a geometrical point of view, C2 has an inversion centre (D∞h point group) but, at an electronic level, there is a asymmetric distribution of electrons. In order words, one of the carbon atoms must be "richer" in electrons than the other one.</p><p>Since in C2 we have two carbon atoms, it is not possible to explain such asymmetric electron distribution based on the electronegativity values.</p><p>As is well known, despite the strong bond in C2, this molecule is very highly reactive and is not isolable. Hence, is valid to suppose that the two carbon atoms in C2 "prefers" to make bonds with another elements (hydrogen, for example) and that the C2 specie is formed only while a "better thermodynamic option" is not available. In a simple image, the two carbon atoms in C2 "try hard" to remain bonded, until they cannot take part in reactions with other elements and, in such "effort" an asymmetric electronic distribution between the two atoms can provide an "extra" thermodynamic stability (by "adding some ionic character to the C-C bond). Such qualitative proposal is also in agreement with the VB modelling previously performed [2,4] in which a set of covalent and lowest energy mono-ionic and di-ionic structures were involved. Furthermore, Xu et al have concluded that "C2 does not possess a set of traditional covalent σ and π bonds. Instead, the full GVB calculations show that the molecule is best, although still incompletely, described as having a traditional covalent σ bond with the electrons in the remaining orbitals on the two centers antiferromagnetically coupled". Such conclusion reinforces, in some sense, the previous proposal of an "electronic asymmetry" in C2 (even a slight one, not enough to be detected, by conventional means, since the asymmetry is not enough to change, in a measurable amount, the dipole moment).</p>