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Put two carbons in the center and arrange hydrogena toms on the sides. PO4-3 CN- SO3-2 ClO2- N2H2 N2H4 C2H2 C2H4. What is the polar Lewis dot structure of C2H2Br2. Get the free "Lewis structure" widget for your website, blog, Wordpress, Blogger, or iGoogle. The Lewis Structure for Li is Li with one dot to the right of the element. The Lewis Dot Structure is a graphical representation of how electrons are distributed around the atoms which comprise a molecule. 55) and hydrogen (2. [Section 8. The special structural characteristics of NbU-1 such as the planar, mixed-valence copper clusters and Lewis-basic adsorption channels enforce interactions with acetylene molecules that lead to the highest kinetic separation efficiency for C2H2/C2H4. The Lewis Structure of D-Glucose consists of 6 carbon elements, 6 hydrogen elements, and 12 hydrogen elements. The structure is H-C=C-H (where = is a triple bond). Each atom in the bond has a full valence, with carbon having access to eight electrons and each hydrogen having access to two (this is why hydrogen only needs two). 67 estimate) = 1. The Lewis structure for oxygen (O2) shows the bond between two oxygen atoms. Creating a Lewis structure helps make intuiting the formation and structure of molecules easier. Single lines are single bonds, double lines are double bonds, and triple lines are triple bonds. To draw the Lewis structure for C2H4, the total number of valence electrons must be known. Which of the following molecules contains a covalent triple bond? a. The exception, of course, being the. Problem: Draw one Lewis structure for CH3N. Video: Drawing the Lewis Structure for SO 4 2-. I am very confused about how to draw a lewis structure. The electron pair Acceptor is the Lewis Acid (NOTE there is a typo in the book p. Answer the following questions using principles of chemical bonding and molecular structure. Key: M = metals. For the N2H2 Lewis structure, calculate the total number of valence electrons for the N2H2 molecule. Atoms are written using their element symbols. If we consider the ground state electronic configuration. Thus, its Lewis structure must account for 22 valence electrons. Two single bonds around sulfur use up "1 bond" xx "2 electron groups" xx. S Si Cl Xe Ca K Draw the Lewis Structures for the following molecules. Draw the Lewis structure, then ID shape and polarity. Lewis Electron Dot Structures - Simple Procedure for writing Lewis Structures – Lewis Structures for Dinitrogen Dioxide (N2O2), lewis electron dot structure of N2O2, σ bonds in N2O2, π bonds in N2O2, calculate the number of electrons in π bonds, resonance structures in N2O2, octet rule in N2O2, Lewis structures for dinitrogen dioxide N2O2, resonance structures for dinitrogen dioxide, N2O2. NASA Astrophysics Data System (ADS) Dolenc, Boštjan; <NAME>; <NAME>. 70 More Lewis Dot Structures. Acetylene-13C2 | C2H2 | CID 10877042 - structure, chemical names, physical and chemical properties, classification, patents, literature, biological activities, safety. 5 °C SynQuest-139 °C OU Chemical Safety Data (No longer updated) More details-139 °C Jean-Claude Bradley Open Melting Point Dataset 15632-137. You dismissed this ad. Lewis structure example. The exception, of course, being the hydrogen's. The exception, of course, being the hydrogen's. The middle carbon has two hydrogens bonded to it, while the two end carbons have three hydrogens bonded. H-CEC-H H B. A Lewis structure (or electron-dot formula) is a two-dimensional structural formula showing the arrangement of electrons around atoms in covalently bonded molecules—i. They illustrate the lone pairs of electrons in molecules. Bubble in A Then, draw the Lewis symbol for O2 24. There are a total of 18 valence electrons for the Lewis structure for NO2-. Step 1: Find valence e- in all atoms. The simple Lewis structure for the simple molecule and help show all bonding valence electrons pairs as lines and all nonbonding valence electron pairs as dots, please ecplain how. 0 23,658 2 minutes read. The molecular shape is said to be bent and is shown below. For example, the Lewis structure for the. 2016-01-01. Question: Connect CHEMISTRY Am 2 V1 Question 11 Of 29) Which Of These Represents The Best Lewis Structure For Acetylene (C2H2)? A. Name few properties of polyester fibres ? - 17228065. shadowboy220 12,493 views. Since all the atoms are in either period 1 or 2, this molecule will adhere to the octet rule. It is a colorless flammable gas with a faint "sweet and musky" odour when pure. C:2x4=8 H:4x1=4. Covalent Interim Sage M and Sam w. Construct the Lewis structures and predict the polarity of the molecules. The simplest alkene has the formula C 2 H 4 and the following Lewis structure. 1021/ed078p1457. Cl - 7 valence electrons. What is the lewis structure for(HN3). ShadowScizor wrote: You will need variables for smoother movement… Not in my opinion. Lewis structure for HOCl; The properly way to determine the Lewis structure, based on this example, is: Total valence electrons: $7 + 6 + 1 = 14$ Total electrons needed for octets/doublets: $8\cdot2+2\cdot1 = 18$ Total shared/bonding electrons: $18-14 = 4$ (In other words, there are only two single bonds. Find more Chemistry widgets in Wolfram|Alpha. Lewis Dot of Propyne. Qual a massa de gás carbônico,C02(g),obtida na queima photo. Draw the dot structures in between each letter. Total Domains Generic Formula Picture Bonded Atoms Lone Pairs Molecular Shape Electron Geometry. 95 Boiling Pt, Melting Pt, Vapor Pressure Estimations (MPBPWIN v1. Calculate the total number of valence electrons. Thus, its Lewis structure must account for 22 valence electrons. Download this CHEM 110 class note to get exam ready in less time! Class note uploaded on Oct 26, 2015. It is unstable in its pure form and thus is usually handled as a solution. Lewis structure of an element is the representation of the chemical symbol surrounded by dots which represent the valence electrons. Drawing the Lewis structure for C 2 H 4 (named ethene) requires the use of a double bond. Remember that hydrogen atoms always go on the outside of a Lewis structure and that they only need two valence electrons for a full outer shell. Add them together. Alternatively a dot method can be used to draw the lewis structure. Daily Highlight: Triiodide Ion I3 - Lewis Dot Structure Hey guys: Here is the next of my daily highlights Lewis Dot Structure, each day showing you one of my Lewis Dot Structure video guides. NH3 stands for the Ammonia or also known as Nitrogen Trihydride. Bubble in A Then, draw the Lewis symbol for O2 24. Write the Lewis structure for each molecule. It is a hydrocarbon and the simplest alkyne. Trans methyl groups favor chair and both are axial. Use the above information to determine the enthalpy of reaction for the equation given. 3] The partial Lewis structure below is for a hydrocarbon CQ molecule. COM Alqurumresort. Search chemicals by name, molecular formula, structure, and other identifiers. Used in oxy-acetylene torches used for welding. ) Dots are drawn. They are "correct" in that they fill the outer shells of each atom in the structure and use the exact number of valence electrons available for the C6H6 Lewis structure. Nitric oxide, mononitrogen monoxide, is a gas at room temperature. The formal charge on each atom in CO 2 is zero, so a different example will be used. Beverly Hills surgeon reveals at home fix (no creams needed). How many single bonds are there? Quizlet Live. a) carbon tetrachloride. Step 1: Find valence e- in all atoms. For example, the Lewis structure for the. Lewis Structure for C2H4 - University Of Maryland. Since each line represents 2 shared electrons, the carbon atoms share 8 electrons. Ethyne has a triple bond between the two carbon atoms. The feedback you provide will help us show you more relevant content in the. Drawing the Lewis Structure for C 2 H 2 - Ethyne or Acetylene. 05 seconds in between movement. --- A, for some reason, is. It also shows the number of paired and unpaired electrons present in the molecule. Find chemical and physical properties, biological activities, safety and toxicity information, patents, literature citations and more. Answer: Since C2H2 is a linear molecule the C must be sp. The formal charge on each atom in CO 2 is zero, so a different example will be used. To avoid this, cancel and sign in to YouTube on your computer. Note, the Hydrogen atoms (H) should not have lone pair electrons! We'll determine the C2H2. I quickly take you through how to draw the Lewis Structure of CHCH (Acetylene or ethyne). The correct Lewis structure for a molecule of the compound C2H2 contains an alkyne bond. Cach O Ос Oo. Design and construction of stable adsorbents for efficient separation and purification of natural gas and C2H2 is fundamentally important in the chemical industry, and hierarchical cage-based MOFs are attractive in this regard due to their intrinsic structural advantages. The 3D structure will automatically be calculated by CORINA Classic and displayed on the right-hand side in the Jmol app. the bond angles are not drawn to scale. Draw the Lewis structures of C2H6, C2H4, and C2H2. The chemical reaction pathways to soot were investigated by experimenting with detailed kinetic models of soot formation under the conditions used in …. Put oxygen in center and arrange chlorine atoms on the sides. 95 Boiling Pt, Melting Pt, Vapor Pressure Estimations (MPBPWIN v1. Carbon is not a good central atom. A Lewis structure can be drawn for any covalently bonded molecule, as well as coordination compounds. As a result, one 2s 2 pair is moved to the empty 2pz orbital. Draw the Lewis structure of C2H2. Account for the fact that the carbon-oxygen bond length in C03 is greater than the carbon-oxygen. NASA Technical Reports Server (NTRS) Kunze, J. Get an answer for 'How many total of CO^3 2- valence electrons?What is lewis structure?What is molecular shape?What is bond angle?Is CO^3 2-polor or non-polar?' and find homework help for other. If you are new in the field of molecular geometry and Lewis structure, firstly you should understand the meaning of Lewis structure for the better understanding of the molecule's shape. a) water,H2O b)Oxygen gas,O2 c)Ammonia, NH3 d)Ammonium ion,NH4. The Lewis structure of it will appear as O being in the middle of the H and Na atom. 11)Motor oil largely consists of molecules that consist of long chains of carbon atoms with hydrogen atoms attached to them. It contains six carbon and hydrogen atoms each. I believe amine (NH3) is tetrahedral. C:4×2=8 H:1×6=6 O:6. Using the VSEPR theory, predict the molecules structure of each of the molecules. There are four covalent bonds in the skeleton structure for SF 4. sp2 carbon would give a trigonal planar arrangement. The following Lewis structures for (a) HCN, (b)C 2 H 2, (C) Sn0 2, (d) BF 3, (e) HOF, (f) HCOF. The trial structure has the correct number of electrons. from-http://en. Lewis structures and VSEPR theory offer useful. Ionic Bonding - Example3. The electron pair Acceptor is the Lewis Acid (NOTE there is a typo in the book p. Lewis structure of c2h2 how many lone and bond pair - 5224923. It exists as a colorless, odorless gas at room temperature and is the primary chemical used to create ethylene, the most widely used organic compound in the world. (i) What is the valency of carbon in C2H4 and C2H2 ? (ii) What types of bonds and how many of each are present in NH4+ ? 10. Add to cart. Benzene, a constituent of crude oil, is an organic chemical compound. Ammonia gas is known as Azane. Total Domains Generic Formula Picture Bonded Atoms Lone Pairs Molecular Shape Electron Geometry. two double bonds. How many of the following will have Lewis structures with multiple bonds? CO, CO2, CO32 , N2, O2. It is helpful if you: Try to draw the H 2 O Lewis structure before watching the video. then put 3 h's around each c with a line between the c and each h" for ethane (C2H6). Answer to Draw the Lewis structure of O22 –. Key: M = metals. "H-C-N" Step 2. For illustrative purposes only. 9/19) CO2 & C2H2. Used in oxy-acetylene torches used for welding. Step 4: Fill in lone pair electrons on everyone - giving all species an octet (except hydrogen!) Step 5: count up the electrons on your Lewis structure. 55) and hydrogen (2. Lewis Electron Dot Structures - Simple Procedure for writing Lewis Structures – Lewis Structures for Dinitrogen Dioxide (N2O2), lewis electron dot structure of N2O2, σ bonds in N2O2, π bonds in N2O2, calculate the number of electrons in π bonds, resonance structures in N2O2, octet rule in N2O2, Lewis structures for dinitrogen dioxide N2O2, resonance structures for dinitrogen dioxide, N2O2. 2016-01-01. There are 32 valence electrons available for the Lewis structure for SO 4 2-. The number of valence electrons in nitrogen is, 5. The structure is H-C=C-H (where = is a triple bond). You're signed out. The Lewis Structure for Li is Li with one dot to the right of the element. Consider each central atom independently. If you are given C2H6O. ( 4 Pts) Write a Lewis structure for the chlorate ion, Cl03-, that obeys the octet rule, and give the total number ofresonance structures for Cl03-that obey the octet rule. In the formation of C2H2, the carbon atom needs extra electrons to form 4 bonds with hydrogen and other carbon atoms. It also shows the number of paired and unpaired electrons present in the molecule. C2H2(g) + 2H2(g) --> C2H6(g) Information about the substances involved in the reaction represented above is summarized in the following table: C2H2(g) 226. 5 o bond angles. With one sulfur atom, we place it at the center, since it is less electronegative than oxygen. We all know that it is the formula of water and also one of the. In a double bond two pairs of valence electrons are shared (for a total of four valence electrons). C2H2 is kinda a weird one. Draw the skeletal structure showing how the atoms are connected using single bonds. H-CEC-H H B. When writing it is necessary to observe the rules: the hydrogen atom tends to have the configuration of the valence shell of helium in the formation of a chemical bond, the other elements - by an octet of external electrons. This is a triple bond between two C atoms. Calculate the total valence electrons in the molecule. "H-C-N" Step 2. For radicals, the lewis structure usually gives the single electron to the element with the least electronegativity, while trying to make a structure that is as close as possible to maintaining the octet rule. Single lines are single bonds, double lines are double bonds, and triple lines are triple bonds. The y component was large and positive, and the z component was small and negative. one triple bond. They follow the duet rule (2 electrons). It also shows the number of paired and unpaired electrons present in the molecule. Hydrazine Lewis Structure. LEWIS STRUCTURES Ammonia, NH 3, is a weak base. Remember that Hydrogen (H) atoms always go on the outside of a Lewis Structure. Lewis Electron Dot Structures - Simple Procedure for writing Lewis Structures – Lewis Structures for Dinitrogen Dioxide (N2O2), lewis electron dot structure of N2O2, σ bonds in N2O2, π bonds in N2O2, calculate the number of electrons in π bonds, resonance structures in N2O2, octet rule in N2O2, Lewis structures for dinitrogen dioxide N2O2, resonance structures for dinitrogen dioxide, N2O2. SO4 2- Lewis Structure - How to Draw the Lewis Structure for SO4 2- (Sulfate Ion) - Duration. HCCH is also known as C2H2, Ethyne, and Acetylene For the HCCH Lewis structure, calculate the total number of valence electrons for the HCCH molecule. A quick explanation of the molecular geometry of C2H2 including a description of the C2H2 bond angles. Organic Chemistry 9th Edition Test Bank quantity. A molecule with 2 atoms bonded to the central atom generally has which shape? a. This feature is customizable with publication quality graphics output in ChemDoodle 2D. Small amounts are formed naturally by plants in the ocean. --- A, for some reason, is. Make sure to indicate formal charge for all atoms in your structures. They illustrate the lone pairs of electrons in molecules. The two oxygen atom can both achieve a stable structure by sharing two pairs of electrons. Divide by two, and voila - these are the number of bonds. Check out the links below. Lewis structure is a theory that helps in understanding the structure of a given compound, based on the octet rule. How to Identify the Molecules Having Resonance. 9,993 results Science. Lewis Structures & Quantum Mechanics. It is slightly toxic to humans, on account of its tendency to react in the human body and produce reactive species of nitrogen and. Drawing Molecules on Paper. is fully correct? Trans methyl groups favor chair and both are equatorial. There is at least 1 N - H bond. makethebrainhappy. It contains six carbon and hydrogen atoms each. We could also write Mg4O4 or whatever, but it serves no purpose. The Lewis Structure consists of single bonds between the elements, meaning that the when the valence electron level of one element isn't full, it pairs up with another element that either. Gas adsorption measurements on the desolvated framework reveal unusual selective CO2 adsorption over C2H2 and CH4 linked to a framework phase chang. H-CEC-H H B. Which of the following number of atoms can form a tetrahedral molecule?  a. Explain what is wrong with each one and give a correct structure for the molecule. C:4×2=8 H:1×6=6 O:6. In these cases, the entire structure is placed in brackets, and the charge is written as a superscript on the upper right, outside of the bracket. d) PO4 3-e) N2. Single bonds are the weakest because the distance between the atoms in a single bond is greater than that of a double and a triple. *Liquid Structure (Viscosity, Surface Tension, Liquid Crystals, Ionic Liquids) Molecular Shape and Structure Determining Molecular Shape (VSEPR) Hybridization *Molecular Orbital Theory (Bond Order, Diamagnetism, Paramagnetism) Coordination Compounds and their Biological Importance Naming Shape, Structure, Coordination Number, Ligands. Lewis-dot structure : The number of valence electrons are represented in the Lewis-dot structure by the dot. They follow the duet rule (2 electrons). the resonance forms) The important points to remember about resonance forms are:. Consider the structure of trans-1,4-dimethylcyclohexane. The Lewis Dot Structure for CH4 is shown above. Lewis structure of C 2 H 4 O. 3] The partial Lewis structure below is for a hydrocarbon CQ molecule. ; Shaffer, C. chemical bonding and molecular structure - ncert Write the Lewis dot structure of CO molecule. This is the amount of electrons allowed in the Lewis Structure. Calculate the total valence electrons in the molecule. The Lewis Structure for Li is Li with one dot to the right of the element. Draw the Lewis structure of Cl2. Mg2O2 is 2 MgO. sp2 carbon would give a trigonal planar arrangement. On the periodic table, Carbon is in group 4 or 14, so it has 4 valence electrons, but we have 2 of them. Problem 11PP from Chapter 3:. This feature is customizable with publication quality graphics output in ChemDoodle 2D. The Lewis structure for the simplest amino acid, glycine, H 2 NCH 2 CO 2 H, is shown here. As you may know, I have already explained about the molecular shape of CO2, SO2, SO3, SF4, and XeF4. Some of the molecules are beyond the scope of this class, so skip the ones that are too confusing. Viewing Notes: With C 2 H 2 you are going to run out of valence electrons and will have to share more than one pair of electrons between the Carbon atoms. The Lewis dot structure for Magnesium is an Mg with 2 dots which stand for its two valence electrons. is it polar? __no_____ 6. show its Lewis Structure. Lewis Structure for C2H4 - University Of Maryland. It contains six carbon and hydrogen atoms each. Which of the following number of atoms can form a tetrahedral molecule?  a. Get more help from Chegg. hgbr2 ionic compound, Cansimilarly the vsepr structure to see which structure cansimilarly the vsepr. Creating a Lewis structure helps make intuiting the formation and structure of molecules easier. Lewis Structure Perspective Drawing Instructions: Construct a model of acetylene (ethyne), C2H2. A molecular compound is composed of 58. It is the simplest alkene (a hydrocarbon with carbon-carbon double bonds). Title: anavasquezmidterm, Author: <NAME>, Length: 9 pages, Published: 2014-10-06. CH is not a stable unit of structure, it requires something else to become stable. NASA Astrophysics Data System (ADS) Huang, Yongsheng; Huang, Ruoshi. Cl - C = N. Similar images, called "Lewis structures," reflect the electronic structure of the molecule. SO4 2- Lewis Structure - How to Draw the Lewis Structure for SO4 2- (Sulfate Ion) - Duration. Acetylene-13C2 | C2H2 | CID 10877042 - structure, chemical names, physical and chemical properties, classification, patents, literature, biological activities, safety. Page 7 - Lewis Structures and Molecular Geometry Lewis Structures and Molecular Geometry Models of Covalent Bonding Introduction Molecules have shape! The structure and shape of a molecule influences its physical proper- ties and affects its chemical behavior as well. Use the Lewis-dot structure to the right to answer the following questions: (2 points) How many π (pi) bonds are in the structure? __3__ (4 points) The bond between which two atoms would you expect to be the strongest? __C_ and __N__ (6 points) Give the hybridization of each. A Lewis structure is a type of shorthand notation. 3: Chemical Bonding Sections: 10. If you are new in the field of molecular geometry and Lewis structure, firstly you should understand the meaning of Lewis structure for the better understanding of the molecule's shape. Chemistry Lewis Dot Structures shadowboy220; 86 videos; 4,477 views; Last updated on Apr 22, 2014 Acetylene or Ethyne C2H2 Lewis Dot Structure by shadowboy220. C:4x2=8 H=1x6=6. C2H2(g) + 2H2(g) --> C2H6(g) Information about the substances involved in the reaction represented above is summarized in the following table: C2H2(g) 226. It has a linear bond geometry and no lone pairs. You have eight valence electrons in your trial structure, so it has the correct number of electrons. Viewing Notes: With C 6 H 6 there are sevearl possible Lewis structures that can be drawn. This is the amount of electrons allowed in the Lewis Structure. Check out the links below. Alternatively a dot method can be used to draw the C 2 H 5 OH Lewis structure. Structure, properties, spectra, suppliers and links for: Acetylene, 74-86-2. Deprecated: Function create_function() is deprecated in /www/wwwroot/dm. trigonal-planar d. Beverly Hills surgeon reveals at home fix (no creams needed). Terms in this set (28) linear, nonpolar. diethyl ether, C2H5OC2H5 A picture of diethyl ether (the top structure) Tert Butyl Methyl Ether Structure. Cach O Ос Oo. Draw the Lewis Structure of the ammonium ion and deduce its shape and bond angles Tuesday, October 13, 15. 8 °C Jean-Claude Bradley Open Melting Point Dataset 19379-139. draw the structure. We all know that it is the formula of water and also one of the. Justify your reasoning. 6What is the structure of N2O. And in fact, sulfur can do this because it has #3d# orbitals to utilize. Dear student! The acetylene (C 2 H 2) has sp-hybridization and it is explained as the two carbon atoms undergo mixing of one s and one p-orbitals to form two sp-hybridized orbitals and the sp-hybridized orbital of the C-atoms make a C-C sigma bond while the other sp-hybrid orbital of each C-atom overlaps with the s-orbital of one H-atom to form a C-H sigma bond. makethebrainhappy. Terpconnect. This is the only Lewis structure that has a sum of formal charges that add up to zero, the charge on the molecule. Since all the atoms are in either period 1 or 2, this molecule will adhere to the octet rule. Valence bond theory does. Gear Fault Diagnosis Based on BP Neural Network. C2H2 is kinda a weird one. i dont understand the way like c:c. Publishing platform for digital magazines, interactive publications and online catalogs. The given molecule is, Acetylene As we know that carbon has '4' valence electrons and hydrogen has '1' valence electron. 9 Polar SF4. Illustrated Glossary of Organic Chemistry Kekule structure : A Lewis structure in which bonded electron pairs in covalent bonds are shown as lines. Include playlist. Answer to Draw the Lewis structure of O22 –. Put two carbons in the center and arrange hydrogena toms on the sides. Total = 20. Schröder1, A. On rencontre cependant quelques cas, emblématiques, où cette écriture est mis en défaut, et ne peut être. Hey guys: Here is the next of my daily highlights Lewis Dot Structure, each day showing you one of my Lewis Dot Structure video guides. Its Lewis Structure is: There is no single central atom for the molecule, but there are three carbons. A compound can have multiple Lewis Structures that contribute to the shape of the overall compound, so one Lewis structure of a compound may not necessarily be exactly what the compound looks like. We could also write Mg4O4 or whatever, but it serves no purpose. And then Hydrogen, group 1, one valence electron; we have 6, multiply that by 6, for a total of 14 valence electrons to work with. This is a total of 10. Now draw, an H above and below both C. As a result, one 2s 2 pair is moved to the empty 2pz orbital. If we talk in general, you may know that Ammonia is a colorless inorganic compound of Nitrogen and Hydrogen. 3 C2H2 C6H6 Reactions of Benzene Benzene undergoes substitution reactions readily. Hydrogen has one valance electrons, Carbon has four, and Oxygen has six. The solution is to share three pairs of valence electrons and. This demo will convert a skeletal figure, provided by a drawing in the HTML5 SketcherCanvas component on the left, into a Lewis Dot Structure in the Canvas on the right. Lewis dot structure for c2h2, How to configure tp link router tl wr840n, 70 More Lewis Dot Structures. Calculate the total valence electrons in the molecule. Describe the shape of your molecular model using terms from your textbook or other chemistry reference. Lewis structures can be utilized to make. 6 years ago. <NAME>, <NAME>, <NAME>, <NAME>, <NAME>. Show work By signing up, you'll get thousands of step-by-step. A pure substance is composed of molecules with the same average geometrical structure. The Chime plugin is needed to see the 3-D structure of the molecules in these pages. Each carbon atom has 4 valence electrons, and each hydrogen atom has 2 valence electrons. For each of the following compounds, draw the Lewis structure, determine the bond angles and molecular shapes. Each has a total of 6 valence atoms making a sum total of 12. Pure acetylene is odorless, but commercial grades usually have a marked odor due to impurities. Explain what is wrong with each one and give a correct structure for the molecule. At each end, the chlorine atoms are spaced approximately 120 degrees from each other and from the carbon atom. The exception, of course, being the. Lewis structure of c2h2 how many lone and bond pair - 5224923. Lewis dot structure looks like this:-----. Acetylene is the industrial name for ethyne which belongs to the alkyne family which are unsaturated compounds because they possess triple bond between carbon atoms. Its molecular formula is C6H6. Title: anavasquezmidterm, Author: <NAME>, Length: 9 pages, Published: 2014-10-06. Ethylene Acetylene Acetylene, C2H2, has a triple bond (one σ-bond and two π-bonds). Its common name is acetylene a. Video: Drawing the Lewis Structure for H2O. In constructing Lewis Dot Structure, the author suggests this: Count the number of valence electrons for each element. Answer: Since C2H2 is a linear molecule the C must be sp. Lewis Structure and Molecular Structure Homework # of # of lone Total # of atoms around pairs atoms and Molecule around central lone pairs central on central electronic molecular geometry Lewis Structure atom atom atom geometry CIO4 NO2 NO3 CO2 C2H6 C2H4 C2H2 CO. It contains six carbon and hydrogen atoms each. 2—Drawing Molecules. In the full Lewis structure, each carbon atom satisfies the octet rule, and there are no unshared electron pairs in the molecule. Some of the molecules are beyond the scope of this class, so skip the ones that are too confusing. Drawing Molecules on Paper. Draw the structure of ammonia and state the shape of the molecule and its bond angles. Question: Connect CHEMISTRY Am 2 V1 Question 11 Of 29) Which Of These Represents The Best Lewis Structure For Acetylene (C2H2)? A. lewis structure of H2S , PH3 ,BF3 , BeCl3, NF3 ,CO2 ,C2H2, C2H4, CS2, CCL4 - Science - Carbon and its Compounds. I have a pretty good idea about drawing the Lewis structures for both of these ions, but I don't know how to determine which one has a coordinate covalent bond. Request PDF | Microporous metal–organic framework with dual functionalities for highly efficient removal of acetylene from ethylene/acetylene mixtures | The removal of acetylene from ethylene. Mg2O2 is 2 MgO. Atoms are written using their element symbols. All electrons are shared within bonds in this compound. In 1902 teaching at Harvard, Lewis developed a model of the atom, which was cubic in shape. Lewis-dot structure : The number of valence electrons are represented in the Lewis-dot structure by the dot. H-CEC-H H B. The structure on the right is the Lewis electron structure, or Lewis structure, for H 2 O. C2H2 (ethyne) 11. Lewis structure of c2h2 how many lone and bond pair - 5224923. Distributed bearing faults appear under various circumstances, for example due to electroerosion or the progression of localized faults. Draw the skeletal structure showing how the atoms are connected using single bonds. On the periodic table, Carbon is in group 4 or 14, so it has 4 valence electrons, but we have 2 of them. No new information is provided. Which of the following molecules has a Lewis Structure that contains a multiple bond ? a) Cl2. This is the amount of electrons allowed in the Lewis Structure. The structure is H-C=C-H (where = is a triple bond). Both structures (2 and 3) must be used to represent the molecule's structure. H2O CH4 CH3OH HCl O2 C2H2 NH3 C2H4. In the (CH 3) 2 S molecule, carbon uses all its four valence electrons to form bond thus, the carbon atom has zero nonbonding electron pair and sulfur has two nonbonding electron pairs because only two electrons are used in bond formation and two pairs of electrons remain as non-bonded. At room temperatures, nitrogen dioxide is a reddish-brown gas that has a density of 1. Thus, it is termed ‘hydrocarbon’. 4 how many valence electrons should you use to draw a lewis structure of ammonia nh3 points 1 3 5 8 15. O:6 Cl:7x2=14. Lewis structure of C 2 H 4 O. Terms in this set (28) linear, nonpolar. Learn this topic by watching Formal Charge Concept Videos. Distributed bearing fault diagnosis based on vibration analysis. Use information from step 4 and 5 to draw the lewis structure. Using the VSEPR theory, predict the molecules structure of each of the molecules. Include all hydrogen atoms. Draw the Lewis structure of parahydroxybenzoic acid, (PABA, C7H6O3). Search chemicals by name, molecular formula, structure, and other identifiers. Answer: Since C2H2 is a linear molecule the C must be sp. Lewis structures of acetaldehyde,ethylene oxide and vinyl alcohol. Arguably, one could construct a resonance structure where only the third lone pair on one oxygen forms a #pi# bond, but that is less stable of a resonance structure. The 2s orbital in each carbon hybridizes with one of the 2p orbitals and forms two sp hybrid orbitals. Get more help from Chegg. Same thing as CH4 (with respect to the 3-d view) Except this compound is polar because the two electrons produce a different pull on the Nitrogen than the hydrogens do. At each end, the chlorine atoms are spaced approximately 120 degrees from each other and from the carbon atom. ( c) A Lewis electron-do( diagram of a molecule of ethanoic acid is given below. Draw a skeleton for the molecule which connects all atoms using only single bonds. They are "correct" in that they fill the outer shells of each atom in the structure and use the exact number of valence electrons available for the C6H6 Lewis structure. It also shows the number of paired and unpaired electrons present in the molecule. Lewis structure of PO3-1 – Simple Procedure for Dot structures - #51 A simple procedure for writing Lewis Structures was given in a previous article entitled “Lewis Structures and the Octet Rule”. There is at least 1 N - H bond. For the N2H2 Lewis structure, calculate the total number of valence electrons for the N2H2 molecule. Lewis structures of acetaldehyde,ethylene oxide and vinyl alcohol. The structure is H-C=C-H (where = is a triple bond). then put 3 h's around each c with a line between the c and each h" for ethane (C2H6). C3H8 is a linear molecule because it has no specific central atom. For smooth movement, make the program wait. Download this CHEM 110 class note to get exam ready in less time! Class note uploaded on Oct 26, 2015. They follow the duet rule (2 electrons). ; Neale, <NAME>. Start studying babychem test 2. 9/19) CO2 & C2H2. In this example, we can draw two Lewis structures that are energetically equivalent to each other — that is, they have the same types of bonds, and the same types of formal charges on all of the structures. The most stable resonance structure has two double bonds. This is the only Lewis structure that has a sum of formal charges that add up to zero, the charge on the molecule. If you are new in the field of molecular geometry and Lewis structure, firstly you should understand the meaning of Lewis structure for the better understanding of the molecule's shape. As a result, one 2s 2 pair is moved to the empty 2pz orbital. Usually try to draw the most symmetrical structure with the atom of least electronegativity in the center. In C2H2 there is three bond between two C atom. Drawing the Lewis Structure for C 2 H 2 (Ethyne or Acetylene). Note: Keep in mind the exceptions to the octet rule discussed in the Pre-Lab Questions. The best Lewis structure that can be drawn for carbon dioxide is: 6. Understand Lewis structure. is fully correct? Trans methyl groups favor chair and both are equatorial. 1s 2 2s 2 2p 6. 8 * Copyright © The McGraw-Hill Companies, Inc. If we consider the ground state electronic configuration. (Sometimes pairs of dots are used instead of lines, but this is uncommon. com/39dwn/4pilt. CH is not a stable unit of structure, it requires something else to become stable. The conjugate acid of ammonia is the the ammonium ion, NH 4+. Answers are based on your structure. Which is the correct Lewis dot structure of C2H2 - 11479490. A commonly used sulfate is sodium lauryl ether sulfate found in shampoo, toothpaste, etc. Since all the atoms are in either period 1 or 2, this molecule will adhere to the octet rule. 1 sigma bond, and 2 pi bond. This one looks strange but is the only correct Lewis dot structure. Chemical Bonding. Find and bonds in the following molecules : CH3 CH3 , CH2 = CH2 , CH CH , CH2 = CHCOOH, C2 (CN)4. then put 3 h's around each c with a line between the c and each h" for ethane (C2H6). Sulfur Tetrafluoride, SF 4 Lewis and Three-Dimensional Structures. Quiz: Take This Easiest Chemical Bonding Trivia Questions! Featured Quizzes. Structure and Bonding in Organic Chemistry Electron Configurations Lewis Dot Structures Hybridization Orbital depictions Depictions of 2-Methylbutane Bonding Characteristics of Period 2 Elements “Saturated” with Hydrogen A Model of a Saturated Hydrocarbon sp2 Hybridization 3 Regions of Electron Density Hybridization of 1 s and 2 p Orbitals – sp2 An sp2 Hybridized Atom The p bond Overlap. The molecular formula of D-Glucose is C6H12O6. KIDA : Species C2H2 photo. Check out the links below. Explain what is wrong with each one and give a correct structure for the molecule. Q : Calculate the moles of nahco present in each trial From the volume of NaHCO3 solution used and the initial mass of NaHCO3 used, determine the mass of NaHCO3 present in each trial. Write the Lewis structure for each molecule. Carbon has 4 and hydrogen has 1, making a grand total of 12 e- (4*2 + 4*1). This one looks strange but is the only correct Lewis dot structure. Include playlist. It exists as a colorless, odorless gas at room temperature and is the primary chemical used to create ethylene, the most widely used organic compound in the world. How many double. Draw the Lewis structure of [NH2]- Draw the Lewis structure of [(CH3)3O]+ Label(or unlabel) the sp-hybridized atoms, sp2-hybridized atoms and sp3-hybridized atoms. and (g) NF 3 are incorrect. You dismissed this ad. In other cases choose the element that is the least electronegative (farthest to the left) on the periodic table. 1991-01-01. Calculate the total number of valence electrons. Lewis dot structure of OCl 2. Draw Lewis structures for each of the following: a. Write the Lewis structure of nitrogen trifluoride (NF3). Distributed bearing faults appear under various circumstances, for example due to electroerosion or the progression of localized faults. Answer the following questions using principles of chemical bonding and molecular structure. There is at least 1 N - H bond. Gas adsorption measurements on the desolvated framework reveal unusual selective CO2 adsorption over C2H2 and CH4 linked to a framework phase chang. They follow the duet rule (2 electrons). The Lewis Structure for Li is Li with one dot to the right of the element. Lewis structures for polyatomic ions are drawn by the same methods that we have already learned. Draw a Lewis structure for SO(subscript 2) in which all atoms obey the octet rule. The Lewis structure of C2Cl4 includes a double-bonded, two-carbon chain with two chlorine atoms attached to each carbon atom. Now customize the name of a clipboard to store your clips. atom structure, atomic structure, basic atomic structure worksheet, business structure, c2h2 lewis structure, capital structure, cell structure, company structure, critical structure corruption, critical structure corruption windows 10, crystal structure, data structure, dna, dna structure, essay structure, fee structure, hcn lewis structure. Explain what is wrong with each one and give a correct structure for the molecule. Lewis structure for HOCl; The properly way to determine the Lewis structure, based on this example, is: Total valence electrons: $7 + 6 + 1 = 14$ Total electrons needed for octets/doublets: $8\cdot2+2\cdot1 = 18$ Total shared/bonding electrons: $18-14 = 4$ (In other words, there are only two single bonds. Lewis structures were first introduced in 1916 by <NAME> and have been adopted as standard fare in high school and college. Show formal charges. Draw the Lewis structure for N2H2, a neutral molecule. To learn how to represent and resonance structures in Lewis Dot Diagrams. To learn how to draw a Lewis Dot Diagram for a molecule which has a double or triple bond. 5 °C SynQuest 43110, 1300-9-01-220--218 F (-140--138. Viewing Notes: With C 2 H 2 you are going to run out of valence electrons and will have to share more than one pair of electrons between the Carbon atoms. um i dont know how to do this on the computer but ill try. 0 Nonpolar OF2 20 Bent 105 0. Drawing the Lewis Structure for HCCH. 00 M phosphoric acid and 2. 3 More Lewis Structures. Benzene, a constituent of crude oil, is an organic chemical compound. C2H2, to form carbon dioxide and water vapor. Calculate the total valence electrons in the molecule. The Lewis Structure (electron dot diagram) of each ion is used to construct the Lewis Structure (electron dot diagram) for the ionic compound. Carbon has a positive formal charge. 10 C) < CH4 (-161. CO has a double bond but its unstable and is mostly a result of incomplete transformation. 2—Drawing Molecules. Answer the following questions using principles of chemical bonding and molecular structure. NASA Astrophysics Data System (ADS) Harrop, Bryce E. The Lewis Structure for Li is Li with one dot to the right of the element. C:4x2=8 H=1x6=6. Now customize the name of a clipboard to store your clips. HCN (cyanide – a deadly poison) More Compounds: Try drawing these compounds as electron dot configurations (also called Lewis structures) and Kekule structures that satisfy the octet rule and identify them as either covalent or ionic compounds. We all know that it is the formula of water and also one of the. In drawing the Lewis structure for C2H2 (also called ethyne) you'll find that you don't have enough valence electrons available to satisfy the octet for each element (if you use only single bonds). Answer: Since C2H2 is a linear molecule the C must be sp. Janice Powell October 26, 2017. Other interesting subjects, use "search for" Normal Chest X Ray Labeled Tvr Tuscan Speed 12 Body Art Graffiti Markers Lana Del Rey Pat Grant Lady Gaga Do What U Want Ama Beach Sunset Pencil Drawing Gokaiger Luka Millfy Lewis Dot Structure For C2h2 First Mobile Phone 1973 Chevy Vs Ford Nirma Logo Miami Heat Black And White Logo. The conjugate acid of ammonia is the the ammonium ion, NH 4+. The molecular shape of the #C_2Cl_2# molecule is linear. 3] The partial Lewis structure below is for a hydrocarbon CQ molecule. Which of the following has a double bond? a. Draw the Lewis structure of benzene, C6H6. Complete the Lewis dot structure(s) for C2H4 Complete the Lewis dot structure(s) for C2H2 Complete the Lewis dot structure(s) for CH30H (Hint: The three H atoms are connected to the C atom and the last H atom is connected to the O atom) H Complete. Chemical Bonding. Some are easy, some are not. They give you some Lewis Structure practice. The exception, of course, being the hydrogen's. In a double bond two pairs of valence electrons are shared (for a total of four valence electrons). Chattaraj and B. When determining the best Lewis structure (or predominant resonance structure) for a molecule, the structure is chosen such that the formal. Which of the following molecules has a Lewis Structure that contains a multiple bond ? a) Cl2. Using your knowledge of intermolecular forces, why wouldn’t it be better to use a compound like glycerol. All electrons are shared. I need to draw a Lewis Dot Structure for each ion or molecule: PO4-3 CN- SO3-2 ClO2- N2H2 N2H4 C2H2 C2H4. makethebrainhappy. Easy Way – Treat them like Puzzle Pieces Lewis structure of C 2 H 5 OH. The Lewis structure of water, H 2 O, is shown below. show its Lewis Structure. 8 °C Jean-<NAME> Open Melting Point Dataset 19379-139. asked by Shady on March 19, 2013; chem. Use information from step 4 and 5 to draw the C 2 H 5 OH lewis structure. Step 3: Put in single bonds creating a skeleton structure. Since the molecule is linear, it has 180 degree bond angles. Show why this chemical is dangerous, by showing chemical reactions for its formation in the environment and its reactions in the atmosphere. How to draw Lewis Diagrams. Lewis structures of acetaldehyde,ethylene oxide and vinyl alcohol. C2H4 12 Planar A B C E F G Molecules or Polyatomic Ion No. HCCH is also known as C2H2, Ethyne, and Acetylene For the HCCH Lewis structure, calculate the total number of valence. Back: 70 More Lewis Dot Structures. 1-hexene is an alkene that is hexane carrying a double bond at position 1. Some of the molecules are beyond the scope of this class, so skip the ones that are too confusing. two double bonds. Pure acetylene is odorless, but commercial grades usually have a marked odor due to impurities. Each atom in the bond has a full valence shell, with nitrogen having access to eight electrons and each hydrogen having access to two (learn why. ) Dots are drawn. This demo will convert a skeletal figure, provided by a drawing in the HTML5 SketcherCanvas component on the left, into a Lewis Dot Structure in the Canvas on the right. A step-by-step explanation of how to draw the HCCH Lewis Structure (Ethyne). It is slightly toxic to humans, on account of its tendency to react in the human body and produce reactive species of nitrogen and. Remember that hydrogen atoms always go on the outside of a Lewis structure and that they only need two valence electrons for a full outer shell. The two helices move in a highly correlated. 5 o bond angles. Which of the following has a double bond? a. asked by anonymous on April 8, 2013; Chemistry. Cach O Ос Oo. Come back to it later, or ask for help. The Role of Lewis Structures in Teaching Covalent Bonding. The 2s orbital in each carbon hybridizes with one of the 2p orbitals and forms two sp hybrid orbitals. Arrange electrons until both atoms get 8. four   b. HCN (cyanide – a deadly poison) More Compounds: Try drawing these compounds as electron dot configurations (also called Lewis structures) and Kekule structures that satisfy the octet rule and identify them as either covalent or ionic compounds. The molecular formula of D-Glucose is C6H12O6. Benzene, a constituent of crude oil, is an organic chemical compound. A total of 47 expressed Q-type C2H2 zinc finger genes in bread wheat (Triticum aestivum) (designated TaZFP) were identified from the current databases. Consider the molecule H 2 CO 2. Lewis Structures: Lewis structures show the connectivity of the atoms in a molecule. Hey guys: Here is the next of my daily highlights Lewis Dot Structure, each day showing you one of my Lewis Dot Structure video guides. Example $$\PageIndex{5}$$: Predicting Structure in Multicenter Molecules. Draw the Lewis structures of C2H6, C2H4, and C2H2. Feasibility study of full-reactor gas core demonstration test. The Lewis dot structure for Cl2, the chemical formula for chlorine gas, is written with two Cl symbols, each of which is surrounded by three pairs of dots, connected by a single line. Non polar C2H2Br2 (one structure) 2. Distributed bearing fault diagnosis based on vibration analysis. shadowboy220 12,493 views. CCl 2 F 2 d. The Lewis Dot Structure is a graphical representation of how electrons are distributed around the atoms which comprise a molecule. The relationship between alkanes and alkenes can be understood by thinking about the following hypothetical reaction. Fill octets with lone pair electrons. It has a linear bond geometry and no lone pairs. The reason for drawing/creating a Lewis dot structure is that it helps one predict the kinds of bonds, as well as a number of bonds, that can be formed around an atom. Get the free "Lewis structure" widget for your website, blog, Wordpress, Blogger, or iGoogle. The common name for this molecule is acetylene. Most of the bromoform and dibromochloromethane that enters the environment is formed as byproducts when chlorine is added to drinking water to kill bacteria. COCL2 has a double bond with Oxygen as it make two bonds while two single bonds with each Chlorine atom. Lewis Structures, Shapes, and Polarity W 319 Everett Community College Student Support Services Program Draw Lewis structures, name shapes and indicate polar or non-polar for the following molecules: a. The Lewis Structure, or Lewis Dot Diagram, shows the bonding between atoms of a molecule and any electrons that may exist. The THAP-type zinc finger can be found in one or more copies and can be associated with other domains, such as the C2H2-type zinc finger. Several worked examples relevant to this procedure were given in previous posts please see the Sitemap. Draw the skeletal structure showing how the atoms are connected using single bonds. calculate the heat of hydrogenation of C2H2 into C2H4 given that the heat of combustion of C2H2,H2 and C2H4 are -310. H2O , C2H4 , CO2 , NH4+, CO32- , NO3-, SO3 , NO2 , SO2 , BF3, CCl4, SO3 , CHCl3 , Q10: Using VSEPR theory predict the structure of the molecules. NH3 stands for the Ammonia or also known as Nitrogen Trihydride. um i dont know how to do this on the computer but ill try. But before we begin, there are a few things to know. What is the Lewis Dot Structure of CH3COOH (Acetic Acid)? Update Cancel. P= polyatomic ions. Ethane has one of the most simple chemical structures of any organic molecules. This had a central positively charged mass onto which electrons were just stuck in. Since C has 4 valence electrons, and each H atoms contributes 1 valence electron, the total number of electrons will be 2*4 + 6*1 = 14 "e"^(-) This means that the Lewis dot structure for C_2H_6 must account for 14 valence electrons, either through. Draw the Lewis structures of C2H6, C2H4, and C2H2. Complete the Lewis dot structure(s) for C2H4 Complete the Lewis dot structure(s) for C2H2 Complete the Lewis dot structure(s) for CH30H (Hint: The three H atoms are connected to the C atom and the last H atom is connected to the O atom) H Complete. Lewis structures can be utilized to make. 7 kj/mol [the values are the change in enthalpy] a. H-CEC-H H B. When you are finished drawing your 2D structure, click on the Get Lewis Dot Structure button to see the result. There are a total of 10 valence electrons for the HCCH. The overall charge on the compound must equal zero, that is, the number of electrons lost by one atom must equal the number of electrons gained by the other atom. The conjugate acid of ammonia is the the ammonium ion, NH 4+. The structure on the right is the Lewis electron structure, or Lewis structure, for H 2 O. It exists as a colorless, odorless gas at room temperature and is the primary chemical used to create ethylene, the most widely used organic compound in the world. Drawing the Lewis Structure for C 2 H 2 (Ethyne or Acetylene). Start studying babychem test 2. Problem write the started by removal of hydrazine 7. The in a zig-zag fashion. For each of the following compounds, draw the Lewis structure, determine the bond angles and molecular shapes, and tell whether each is. php on line 143 Deprecated: Function create_function() is deprecated in. Mg2O2 is 2 MgO. AlBr3 Physical Properties: Bond Type: Ionic (Metal bonding with a none metal) Lewis Structure: Sigma and Pi bonds: 3 Sigma, 1 Pi. 🤓 Based on our data, we think this question is relevant for Professor Bindell's class at UCF. For the N2H2 Lewis structure, calculate the total number of valence electrons for the N2H2 molecule. Lewis dot structure for c2h2, How to configure tp link router tl wr840n, 70 More Lewis Dot Structures. Remembering that Boron is an exception, draw the Lewis structure for BF3. Cl - C = N. Count the valence electrons you can use "H + C + N =1 + 4 + 5 = 10" Step 3. MgSO 4 is also known as Epsom Salts.
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# Mode-resolved reciprocal space mapping of electron-phonon interaction in the Weyl semimetal candidate Td-WTe2

## Abstract

The excitation of coherent phonons provides unique capabilities to control fundamental properties of quantum materials on ultrafast time scales. Recently, it was predicted that a topologically protected Weyl semimetal phase in the transition metal dichalcogenide Td-WTe2 can be controlled and, ultimately, be destroyed upon the coherent excitation of an interlayer shear mode. By monitoring electronic structure changes with femtosecond resolution, we provide here direct experimental evidence that the shear mode acts on the electronic states near the phase-defining Weyl points. Furthermore, we observe a periodic reduction in the spin splitting of bands, a distinct electronic signature of the Weyl phase-stabilizing non-centrosymmetric Td ground state of WTe2. The comparison with higher-frequency coherent phonon modes finally proves the shear mode-selectivity of the observed changes in the electronic structure. Our real-time observations reveal direct experimental insights into electronic processes that are of vital importance for a coherent phonon-induced topological phase transition in Td-WTe2.

## Introduction

With their first experimental observation in 2015, topological Weyl semimetals (WSMs) attracted enormous attention1,2,3,4. In these materials, long-sought-after Weyl fermions are realized as quasi-particle excitations in condensed matter5,6,7. WSMs feature an unusual electronic structure with topologically protected crossing points in the bulk band structure, the so-called Weyl points. In the particular case of type-II WSMs, the Weyl points are located at touching points of electron and hole pockets close to the Fermi level EF8,9,10. The transition metal dichalcogenide Td-WTe2 was the first material proposed to support such a scenario and band structure calculations using low-temperature lattice parameters predicted the existence of four pairs of Weyl points in the ΓXY plane of the Brillouin zone (see Fig. 1a)8. Even though angle-resolved photoemission spectroscopy (ARPES) studies did not succeed in observing Weyl points in this material so far11,12,13,14,15,16,17, the observation of Weyl orbit related quantum oscillations and an anisotropic magnetoresistance18, the detection of Weyl points via scanning tunneling spectroscopy19, and the observation of an anisotropic Adler–Bell–Jackiw anomaly20 give strong experimental evidence that Td-WTe2 is indeed a type-II WSM.

The lack of an inversion center in the crystal structure is the prerequisite for a WSM phase in non-magnetic materials8. Recently, an ultrafast and reversible way of manipulating the structural symmetry of Td-WTe2 was demonstrated in a combined ultrafast electron diffraction (UED) and time-resolved second-harmonic generation (TRSHG) study21. Upon excitation with terahertz pump pulses, a coherent 0.24 THz interlayer shear excitation was observed that, at sufficiently high excitation densities, drives a structural phase transition from the non-centrosymmetric Td ground state of the material (see Fig. 1b) into a meta-stable centrosymmetric $$1T^{\prime}$$(*) phase21. Band structure calculations imply the periodic modulation of the Weyl point intra-pair separation upon excitation of the shear mode. Even more, the complete annihilation of the Weyl points is expected as the material undergoes the transition into the $$1T^{\prime}$$(*) phase. However, experimental data on how the shear mode affects the band structure of Td-WTe2 is still lacking.

Here, we present a time-resolved ARPES (TRARPES) study on the electronic structure response of Td-WTe2 to the excitation of coherent phonons. Upon absorption of 827 nm femtosecond laser pulses, we observe in the TRARPES data clear oscillations in photoemission (PE) intensity, band positions, and bandwidths. The comparison with Raman spectroscopy22,23,24 and optical pump-probe spectroscopy results25,26 allows assigning these oscillations to the excitation of five different A1 optical phonon modes, with one of them being the interlayer shear mode mentioned above. An energy- and momentum-resolved Fourier transformation of the TRARPES data enables us to perform a phonon mode-selective analysis of the electronic structure response. We observe that the excitation of the interlayer shear mode periodically modulates occupied bands that are spin split due to the broken inversion symmetry of the crystal including a hole pocket that is directly involved in the formation of the Weyl points at low temperatures27. Even more, we observe that also the PE signal from the energy-momentum region of the Weyl points shows clear oscillations at the shear mode frequency. Although the presented experiments were performed at room temperature, for which theory excludes the presence of Weyl points11, our results give direct experimental support for a coherent phonon mediated control of the electronic structure relevant for the Weyl physics in Td-WTe2.

## Results

### Coherent phonon excitation

Figure 1c shows TRARPES data of Td-WTe2 recorded before the optical excitation (Δt = −1 ps) in comparison with data recorded at a pump-probe delay of Δt = 120 fs. Overall, the spectra are consistent with ARPES and TRARPES data recorded at a similar probe photon energy of hν ≈ 6 eV11,15,28. In agreement with previous TRARPES studies, we observe the transient population of an electron pocket above EF in response to the near-infrared (NIR) excitation28,29,30. A difference intensity map of the two ARPES spectra (see Fig. 2a) emphasizes the presence of spectral changes also below EF. Part of the observed transient reduction of spectral weight (blue areas) results from the depopulation of the occupied bands due to the absorption process. However, the observation of an increase in spectral weight in some regions below EF (red areas) hints also to the presence of transient band renormalization processes.

Figure 2b shows transient difference energy distribution curves (EDCs) around the $$\overline{\Gamma }$$ point as a function of Δt. Above EF, the data clearly reveals the presence of an excited carrier population that decays on a timescale of several picoseconds. Furthermore, part of the transient spectral changes are periodically modulated indicative for the excitation of at least two coherent phonon modes exhibiting oscillation periods in the few hundred femtoseconds and few picoseconds range, respectively. Significant long-lived spectral changes survive the damping of the coherent phonon modes and show barely any changes even at delays of 400 ps (Supplementary Note 1). Our observations qualitatively resemble the findings of previous time-resolved studies of Td-WTe2: electronic excitation and relaxation processes were studied in detail using TRARPES28,29,30 and time-resolved reflectivity (TRR) measurements25. The excitation of coherent phonons was observed in TRR25,26 and TRSHG experiments21 as well as via UED21, but, notably, in none of the past TRARPES studies28,29,30. Also the observed long-lived spectral changes are compatible with the findings of different other studies21,25. In the following, we will exclusively focus on the analysis of the coherent phonon oscillations and their impact on the electronic structure of Td-WTe2.

Figure 2c, d shows PE intensity transients around $$\overline{\Gamma }$$ and E − EF = −0.25 eV. The data were taken with different sampling rates (60 and 15 THz) and cover different delay ranges (3 and 20 ps) to separately illustrate both the high- and low-frequency contributions to the PE intensity modulations (Supplementary Note 2). Raw data (red lines) were fitted with an exponential model function (Supplementary Note 3) to account for the carrier population dynamics (black lines) and to extract the pure oscillatory part of the signals (blue lines). The beating of the 3 ps range data clearly reveals the presence of more than one high-frequency mode. Additionally, a well-separated low-frequency modulation can be identified in the 20 ps range data. Figure 2e shows a Fourier amplitude spectrum of the 20 ps range intensity transient. Overall, we find main peaks at 0.23, 2.41, 3.57, 4.00, and 6.35 THz indicative for the excitation of at least five different coherent phonon modes. A comparison with the results of Raman studies of WTe2 and MoTe2 allows assigning all frequencies to A1 optical phonon modes22,23,24,31 that belong to the group of m-modes with the atoms vibrating in the bc-mirror plane of the unit cell31. Of particular relevance is the assignment of the 0.23 THz mode, which is responsible for the distinct long-periodic spectral modulations visible in Fig. 2b, d: In agreement with UED, TRSHG, and TRR results21,25,26, and predictions from Raman studies22,23,24,31, we assign this frequency to the low-energy optical phonon interlayer shear mode along the b axis (see below). The excitation of this mode periodically drives WTe2 from its non-centrosymmetric Td structure towards a centrosymmetric $$1T^{\prime}$$(*) structure. It is therefore expected to periodically modulate the spin splitting of bands27 as well as the Weyl point intra-pair separation in this material21.

### Mode-resolved electronic structure response

Figure 3a shows the results of an energy- and momentum-resolved Fourier analysis of the TRARPES data (Supplementary Note 4) illustrating the phonon mode-selectivity of the electronic structure response. The figure separately displays energy-momentum maps of the Fourier amplitudes of the 0.23, 2.41, and 3.57 THz coherent phonon excitations in comparison to the ARPES intensity map at Δt = 120 fs. The data clearly illustrates the band-selectivity of the phonon excitations, as seen for instance for the band marked by the red arrow. A more detailed analysis shows, furthermore, that even in the case that the same band is affected by several modes, its response can be quite different. This is illustrated by band energy (Eband) and bandwidth (ΔE) transients (Fig. 3b) and their Fourier amplitude spectra (Fig. 3c) for the feature in the TRARPES map centered at $$\overline{\Gamma }$$ at an energy E − EF ≈ −0.3 eV marked by the black arrow. The excitation of the four high-frequency modes results in small but clearly detectable shifts in Eband, which becomes particularly evident in the Fourier amplitude spectrum of the band energy transient. For the excitation of the 0.23 THz interlayer shear mode, such a band shift, if present at all, stays below the detection limit. In contrast, a finite and—also in comparison to the other modes—now significant contribution of the shear mode to the broadening of the band is evident from the ΔE transient as well as from the 0.23 THz peak in the corresponding Fourier amplitude spectrum. It is finally noteworthy that the Fourier analysis of the TRARPES data not only shows a finite signal amplitude below EF but also at energies above EF up to E − EF ≈ 0.3 eV (see blue arrow). This sensitivity partly results from the laser excitation, which transiently heats up the electron gas so that states above EF are substantially populated even on timescales of several tens of picoseconds.

In comparison to the ARPES intensity maps, the Fourier maps exhibit additional fine structures showing spectral details even below the 40 meV energy resolution of the experiment. The fine structure is particularly striking in the 2.41 THz Fourier map. A comparison with experimental data of a low temperature, high-resolution ARPES study11 shows that the fine structure resembles in large part the band structure of Td-WTe2. We account non-linearities in the dynamical signal response to the coherent phonon excitation being responsible for this resolution enhancement. More details are given in Supplementary Note 5.

Apart from the mode-selective amplitude analysis, we also performed a mode-selective phase analysis of the transient peak energies (Supplementary Note 6). The four high-frequency oscillations all show a cosinusoidal behavior with respect to time zero of the experiment implying a displacive excitation of the coherent phonons32. For the 0.23 THz mode, we observe, in contrast, a sinusoidal modulation of the peak energies, in agreement with UED and TRSHG results using THz and NIR excitation pulses, respectively21. Typically, such a response is associated with an impulsive Raman stimulated excitation mechanism33. It should be added that for the excitation of the interlayer shear mode in Td-WTe2 using THz pulses a field-driven photo-doping process was alternatively suggested to explain the observed sinusoidal response21.

### Shear mode excitation and electronic structure

In further discussion, we will focus on the excitation of the 0.23 THz interlayer shear mode periodically modulating the WTe2 crystalline Td structure towards a centrosymmetric $$1T^{\prime}$$(*) structure21. Based on values given in ref. 21 and under consideration of a TRR study at 800 nm excitation26, we estimate the shear displacement amplitude at the excitation fluence applied in our experiment to be in the order of 1 pm (Supplementary Note 7).

Figure 4a shows close-ups of the ARPES intensity map at Δt = 120 fs and the 0.23 THz Fourier map of Fig. 3a. The data is overlaid with the bulk band structure of Td-WTe2 along the $$\overline{\Gamma }$$$$\overline{{\rm{X}}}$$ direction experimentally determined in a high-resolution ARPES study at hν = 6.01 eV11. The color coding was chosen to discriminate between an electron pocket (blue), two hole pockets (green), and further bulk bands (gray). Calculated band structure data along Γ–X is shown for comparison in Fig. 4c. Due to thermal broadening and the limited energy resolution of our experiment in combination with strong variations in the spectral weight among the different bands11, it is difficult to discern the individual bands in the ARPES intensity map. However, even though broadened, the dispersing amplitude maxima in the Fourier map match part of the experimental band structure data strikingly well. The main amplitude maximum at k ≈ 0.2 Å−1 shows a branching (see also Fig. 3a) that follows the dispersion of the lower hole pocket and the two gray-colored lower bulk bands, respectively. The data also reproduces the dispersion of the upper hole pocket up to energies close to EF with a distinct amplitude maximum in the plateau region at k ≈ 0.3 Å−1. Above EF, we observe two weak but distinct local amplitude maxima at k ≈ 0.22 Å−1 and k ≈ 0.34 Å−1 with the former one being approximately located at the surface projection of the Weyl points marked by the blue cross in Fig. 4a8,19.

Within the energy-momentum region probed in our experiments, different ARPES studies reported also on the observation of surface states11,12,13,15. Owing to the limited energy resolution and the fact that our experiments were performed at room temperature, no distinct signatures of these surface states could be observed in our ARPES intensity maps. A comparison with the experimental surface state data of ref. 11 showed, furthermore, that also the 0.23 THz Fourier map yields no clear indication for a response of the surface states to the excitation of the shear mode. In Fig. 4a, we therefore omitted the inclusion of the surface bands for the sake of clarity. A comparison including surface bands is, however, provided in Supplementary Note 8.

For further analysis, we selected four regions of interest (ROI) in the Fourier maps at positions indicated by the crosses in Fig. 4a. ROI A, B, and C are located at Fourier amplitude maxima. ROI B and C are furthermore intersected by the lower and upper hole pocket, respectively, whereas ROI A is positioned in between the two lowest bulk bands. ROI D is centered on the surface projection of the Weyl points above EF. For reference, we selected an additional ROI E (see Fig. 3a) at a local intensity maximum in the ARPES intensity maps that, however, shows a negligible amplitude in the 0.23 THz Fourier map. Where possible, we evaluated for the different ROI the transient evolution of the PE intensity, peak energy, and peak width in response to the excitation of the interlayer shear mode. For all ROI, we chose a signal integration area of 50 meV × 0.025 Å−1.

Results of the PE intensity analysis are summarized in Fig. 4d. For ROI A, B, and C, we observe clear periodic modulations at the frequency of the shear mode. Relative amplitude and phase of the PE intensity transients of the ROI match each other extremely well (see top graph of Fig. 4d) and can be described by a damped π-shifted sinusoidal function with a relative amplitude in the order of 1% (see full black line). Also the PE intensity of ROI D, which probes the Weyl point region, shows clear oscillations at 0.23 THz in spite of some signal distortions at Δt ≈ 7.5 ps resulting from limitations of the signal background subtraction (Supplementary Note 3). Notably, the oscillatory response of ROI D shows a π-phase shift with respect to ROI A, B, and C as indicated by the black dashed line and also with respect to the second amplitude maximum above EF at k ≈ 0.34 Å−1 (Supplementary Note 9). Contrary to ROI A–D, the transient PE intensity signal of ROI E exhibits no evidence for a response to the shear mode as expected from the vanishing signal in the Fourier map.

A peak shift analysis is only possible for ROI that are located at signal maxima in the ARPES intensity maps. This only applies to ROI C and E. To account for potential spectral shifts affecting ROI A, we selected a nearby PE intensity maximum (ROI A′) separated by  ≈40 meV and intersected by the center bulk band. Distinct PE intensity maxima that could be associated with ROI B and D could not be identified. Results of the peak shift analysis are shown in Fig. 4e. A distinct shift in the peak energy at the shear mode frequency is only observed for ROI A′. The oscillation follows a damped sinusoidal function with an amplitude of approximately 1 meV. The data reveals no detectable peak shift at the shear mode frequency for ROI C and E. The analysis of the peak widths for ROI A′, C, and E did not yield any resolvable changes at the shear mode frequency. However, a detailed Fourier analysis of ROI C shows indirect evidence for subtle changes in the peak width as will be discussed below.

## Discussion

Reference 27 reports on the evolution of the band structure of WTe2 as the crystalline structure undergoes a complete transition from the Td phase to the centrosymmetric $$1T^{\prime}$$ phase upon external charge doping. The calculations show that the changes in the band structure predominantly result from changes in the interlayer interaction that is in an analog manner periodically modulated upon excitation of the 0.23 THz interlayer shear mode following the photoexcitation with ultrashort NIR pulses. More specifically, such a transition is expected to reduce and finally annihilate the spin splitting of the different bands near EF as the inversion symmetry of the crystalline structure is recovered. These findings imply that the oscillatory part of the PE intensity transients from the two hole pockets (ROI B and C) results from a periodic modulation of the spin splitting due to the shear mode excitation. Notably, for the upper hole pocket the Fourier amplitude is indeed maximum in the region at which the experimental band structure data implies the largest spin splitting and also for the lower hole pocket, band structure calculations predict a considerable spin splitting (see Fig. 4c).

A more detailed inspection of the Fourier amplitude signal near ROI C further confirms that the shear mode excitation modulates the spin splitting. Figure 5a shows the 0.23 THz Fourier map near ROI C. In comparison to Figs. 3a and 4a, the original ARPES data were in this case binned over smaller energy-momentum regions for further data processing so that some more details become visible at the cost of signal statistics. The pronounced maximum in the Fourier map at ROI C appears now split by a weak but distinct amplitude minimum that follows the experimental band structure data from ref. 11 strikingly well. A constant momentum cut across the Fourier amplitude maximum (Fig. 5b) confirms this splitting and yields a separation of the resulting two Fourier amplitude maxima of  ≈35 meV. To gain insight into the origin of this Fourier amplitude modulation, we performed simulations mimicking the following three potential scenarios: (i) a rigid shift of the spin-split bands accompanying an overall PE intensity oscillation, (ii) a modulation of the spin splitting that is in phase with a PE intensity oscillation, i.e., a decrease (increase) of the spin splitting is accompanied by a decrease (increase) of the PE intensity, and (iii) a modulation of the spin splitting that is out of phase with a PE intensity oscillation. Details on the simulations, including the choice of parameters, are described in Supplementary Note 10.

Figure 5c–e shows the resulting Fourier amplitudes and phases as a function of energy for the three scenarios. Whereas the amplitude modulation calculated for scenario (iii) clearly deviates from the experimental results, a reasonable match is observed for scenario (i) and scenario (ii). However, inspection of the phase behavior shows that only scenario (ii) can consistently reproduce the experimental data: Fig. 5f depicts a color-coded plot of experimental EDCs along the evaluated energy-momentum cut near ROI C as a function of Δt. The data reveal an in-phase response of the PE signal independent of binding energy across the two Fourier amplitude maxima (see dashed lines), in agreement with the constant phase expected for scenario (ii) and contrary to the π-phase shift right at the Fourier amplitude minimum expected for scenario (i). Notably, the simulation reproduces the experimental amplitude modulation as well as the separation of the two amplitude maxima also quantitatively strikingly well and implies that in our experiment the spin splitting is periodically modulated by the excitation of the shear mode at an amplitude in the order of 1 meV (see Supplemental Note 10). It is finally interesting to also consider the initial phase of the oscillation in the spin splitting. The excitation of the shear mode results in an initial reduction of the PE intensity in ROI C (see Fig. 4d). For the case of scenario (ii), this implies an initial reduction of the spin splitting, i.e., an initial shear motion towards the centrosymmetric $$1T^{\prime}$$(*) structure, in perfect agreement with the observations reported in ref. 21.

Changes in the spin splitting should also affect the response in the Weyl point area (ROI D). However, in this case, the situation is more complex as the area covers at the same time the signal from the close-lying and spin-split electron pocket and upper hole pocket (see Fig. 4c), which at low temperatures give rise to the formation of the Weyl points. A reduction (increase) in the spin splitting upon excitation of the shear mode will at the same time increase (reduce) the separation between electron pocket and hole pocket27. The anti-phase behavior of the latter process with respect to the spin splitting may explain why the PE signal from the Weyl point area is π-shifted in comparison to all other ROI.

Reference 27 finally provides also information on how the highest of the three bulk bands will be affected by a shear motion along the b axis. Due to the much smaller spin splitting of this band in comparison with the electron and hole pockets, the calculation predicts only very subtle changes even for a full phase transition. In the Fourier map, this band is indeed the only band which lacks a clear signal along its band dispersion. The two other bulk bands are in contrast not considered in the calculations in ref. 27. However, band structure calculations imply that these two bands show a distinct dispersion along the Γ–Z direction (Supplementary Note 11), i.e., in c-direction (see Fig. 1). It is therefore not surprising that particularly these bands become affected by a shear displacement among neighboring WTe2 layers giving rise to rather large amplitudes in the Fourier map.

The excitation of coherent phonons provides unique opportunities for the study and coherent control of structural, electronic, and magnetic properties of solids34,35,36. Time- and angle-resolved photoemission spectroscopy is in this context the most direct instrument to map the electronic structure response at the required energy- and momentum sensitivity37,38,39. The phonon mode-resolved Fourier maps introduced in the present work allow in a very direct and intuitive manner for an electron-band selective view onto electron–phonon interaction processes including even electronic states above EF. The striking differences observed among the Fourier maps of Td-WTe2 emphasize the band-selectivity of coherent phonon excitation processes. Remarkably, in the Fourier map representation, the nonlinear signal response to the excitation of coherent phonons can substantially enhance the spectral resolution uncovering spectral details not visible in the ARPES spectra.

Our results reveal, furthermore, that the excitation of a low-frequency interlayer shear mode periodically modulates the spin splitting of bands, a spectral signature that is closely linked to the broken inversion symmetry of the crystalline lattice. In addition, the data prove that the excitation of the shear mode affects the electronic structure in the energy-momentum area comprising the Weyl points in Td-WTe2 at low temperatures. Overall, the presented experimental results strongly support the relevance of the shear mode excitation for the control of the specific Weyl physics in this material as recently predicted in ref. 21.

## Methods

### Sample synthesis

High-quality Td-WTe2 crystals were grown using a chemical vapor transport technique. Stoichiometric tungsten powder (99.9%) and tellurium powder (99.99%) were ground together and loaded into a quartz tube with a small amount of the transport agent TeBr4. All weighing and mixing was carried out in a glove box. The tube was sealed under vacuum and placed in a two-zone furnace. The hot zone and the cold zone were maintained for 1 week at a constant temperature of 800 and 700 °C, respectively.

### TRARPES experiments

For the TRARPES experiments, we used two non-collinear optical parametric amplifiers (NOPAs) which are pumped by the second harmonic of a chirped pulse amplifier. One of the NOPAs delivers 1.5 eV (827 nm), 30 fs, p-polarized pump pulses with an incident fluence of 110 μJ cm−2 on the sample. The 840 nm output of the second NOPA system is used to generate 5.9 eV (210 nm), 95 fs, s-polarized probe pulses by sequential frequency doubling. Cross-correlation measurements at the sample position yielded  ≈100 fs FWHM (Supplementary Note 2). Right before the pump-probe experiments, the Td-WTe2 crystals were cleaved under ultra-high vacuum conditions. The samples were aligned by low-energy electron diffraction in a direction crossing $$\overline{\Gamma }$$ and the projection $$\overline{{\rm{W}}}$$ of the predicted position of two neighboring Weyl points onto the (001) surface (see Fig. 1a). ARPES spectra were recorded using a hemispherical analyzer at a total energy resolution of 40 meV. All experiments were performed at room temperature at a pressure of 2 × 10−10 mbar.

### Band structure calculations

The electronic bulk band structure was calculated by ab-initio calculation based on density functional theory with projector augmented-wave method40 as implemented in the Vienna Ab-initio Simulation Package (VASP)41. The exchange and correlation energies were considered on the level of the generalized gradient approximation with a Perdew–Burke–Ernzerhof functional42. The energy cutoff was set to be 350 eV for the plane wave basis. We included the van der Waals corrections via a pair-wise force field of the Grimme method43. The experimental lattice constants from ref. 44 were used in all the calculations.

## Data availability

All data that support the findings of this study are available from the corresponding author upon reasonable request.

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## Acknowledgements

This work was supported by the German Research Foundation (DFG) through projects INST 257/419-1 and INST 257/442-1 and by the National Natural Science Foundation of China (Grant No. 11774190).

## Author information

Authors

### Contributions

P.H., S.J., and M.B. conceived the experiments. P.H., S.J., and H.E. carried out TRARPES measurements. P.H. performed the data analysis. Y.Q. synthesized and characterized the WTe2 single crystals. Y.S. performed ab-initio calculations. P.H. and M.B. co-wrote the paper. All the authors contributed to scientific planning and discussions.

### Corresponding author

Correspondence to <NAME>.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Rights and permissions

Reprints and Permissions

<NAME>., <NAME>., <NAME>. et al. Mode-resolved reciprocal space mapping of electron-phonon interaction in the Weyl semimetal candidate Td-WTe2. Nat Commun 11, 2613 (2020). https://doi.org/10.1038/s41467-020-16076-0

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text:
Here are the main points that will be addressed in the videos. Please read these and think about them as you watch.

• The mean value theorem is a statement about when the instantaneous rate of change of a function at a point is equal to the average rate of change of that function on an interval.
• The conditions for the mean value theorem to apply are:
• $f$ is defined on the closed interval $[a,b]$,
• $f$ is continuous over the closed interval $[a,b]$, and
• $f$ is differentiable over the open interval $(a,b)$
• The mean value theorem says that when the conditions above are satisfied, then there is a number $c$ in $(a,b)$ where


text:
# Existense of semi-stable vector bundles on smooth curves in positive characteristic

Let $k$ be an algebraically closed field of positive characteristic and $X$ be a smooth projective curve over $k$ of genus $g \ge 2$. Fix a polarization $L$ on $X$. Does there exist a semi-stable vector bundle on $X$ of rank $r$ and degree $d$ with gcd$(r,d)=1$?

I know that this result is true in characteristic zero. I have heard this to be true in positive characteristic but have not been able to find a good reference for this fact or a counterexample.

Any reference/hint would be very helpful.

EDIT Assume further that $k$ is countable.

• Is your field uncountable? If so, I believe you can just choose a first-order deformation to which a maximal destabilizing bundle does not extend. – <NAME> Oct 6 '15 at 10:29
• @JasonStarr Sorry, but the field I have in mind in $\overline{\mathbb{F}_p}$, which is countable. I will edit the question. – Ron Oct 6 '15 at 15:42

It seems relatively easy to construct such a bundle by induction. Namely:

Step 0 If $r=1$, there are clearly line bundles of given degree $d$ on $X$, since $k$ is assumed to be algebraically closed.

Step 1 Choose $(r',d')$ such that $0<r'<r$, $d'/r'>d/r$, and there are no integral points within (or on the edges) of the triangle with vertices $(0,0)$, $(r',d')$, and $(r,d)$. For instance, can take $(r',d')$ satisfying the first two inequalities whose distance from the line through $(0,0)$ and $(r,d)$ is minimal.

Step 2 The condition that there are no integral points on the boundary of the triangle implies that $gcd(r',d')=gcd(r-r',d-d')=1$. Let $E_1$ and $E_2$ be stable bundles such that $rk(E_1)=r'$, $deg(E_1)=d'$, $rk(E_2)=r-r'$, $deg(E_2)=d-d'$, which exist by the induction hypothesis. Choose a non-trivial extension $$0\to E_2\to E\to E_1\to 0,$$ which exists by the Riemann-Roch Theorem (here we need that the genus of $X$ is at least one).

Step 3 It is easy to see that $E$ is stable. Indeed, assume it is not, and $F\subset E$ is destabilizing. Then the slope of $F$ is at most $d'/r'$, and dually the slope of $E/F$ is at least $(d-d')/(r-r')$. From the condition that there are no integral points in the triangle, we see that $rk(F)=r'$ and $deg(F)=d'$. Because of stability of $E_1$ and $E_2$, this implies that the map $F\to E\to E_1$ is an isomorphism, which would split the exact sequence for $E$. Contradiction.

Remark The only place where we need the field to be algebraically closed is Step 0. So as long as you know that line bundles of every degree exist on $X$, the statement holds. For instance, it works if $X$ has a $k$-point, or if the base field is finite (see this question), but fails if the field is $\mathbb{R}$.

• I do not understand why the slope of $F$ is at most $d'/r'$ as mentioned in step $3$. Could you please suggest some reference or give a hint. – Ron Oct 7 '15 at 14:02
• Consider the filtration on $F$ induced by the filtration on $E$; that is, consider the exact sequence $0\to(F\cap E_2)\to F\to F/(F\cap E_2)\to 0$. The left (resp. the right) term of the sequence is isomorphic to a subsheaf of $E_2$ (resp. $E_1$), and therefore its slope cannot exceed $(d-d')/(r-r')$ (resp. $d'/r'$). This gives the desired bound on the slope of $F$. This also shows that the slope of $F$ is equal to $d'/r'$ if and only if it projects isomorphically onto $E_1$. – t3suji Oct 7 '15 at 14:36
• Thank you for the hint. I understand the proof now. Although you say that this is an easy solution, I think it is a very interesting solution. I have also not seen this solution anywhere. Since I will reproduce the solution in an upcoming article, I would either like to mention a reference for the solution or acknowledge you for this. In case there is no known reference, you should tell me your identity. – Ron Oct 8 '15 at 11:46
• Well, I don't know a reference... The name is <NAME> (math.wisc.edu/people/faculty-directory) – t3suji Oct 8 '15 at 21:17


text:
# Harmonic Mean Iteratively Reweighted Least Squares for Low-Rank Matrix Recovery

### Abstract

We propose a new Iteratively Reweighted Least Squares (IRLS) algorithm for the problem of recovering a matrix $X \in \mathbb{C}^{d_1 \times d_2}$ from incomplete linear observations, solving a sequence of quadratic problems. The easily implementable algorithm, which we call Harmonic Mean Iteratively Reweighted Least Squares ($\texttt{HM-IRLS}$), is superior compared to state-of-the-art algorithms for the low-rank recovery problem in several performance aspects. More specifically, the strategy $\texttt{HM-IRLS}$ uses to optimize a non-convex Schatten-p penalization to promote low-rankness carries three major strengths, in particular for the matrix completion setting. First, we show empirically that, starting from a trivial initialization, it converges globally to a low-rank minimizer of the non-convex Schatten-p objective function for a large number of interesting cases, for which other (non-)convex optimization approaches fail to recover a low-rank matrix. Secondly, as a main theoretical result, we prove that $\texttt{HM-IRLS}$, unlike other IRLS variants, exhibits a locally superlinear rate of convergence if the linear observations fulfill a suitable null space property. This rate is of order $2-p$, depending on the non-convexity parameter $p$, and thus arbitrarily close to quadratic for $p \ll 1$, which is accurately confirmed by our numerical experiments. Thirdly, our experiments show that $\texttt{HM-IRLS}$ exhibits an empirical recovery probability close to $1$ even for very close to optimal sample complexities, i.e., already for significantly fewer linear observations than any other tractable approach in the literature.

Type
Publication
In 12th International Conference on Sampling Theory and Applications (SampTA), Tallinn, Estonia, pp. 489-493
This work was extended to a paper that has been published in the JMLR.


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# CAPM: Testing for alphas jointly equal to zero

For my project, I need to assess if a certain factor X leads to a CAPM-Anomaly. First, I sorted the monthly stock return (sample size: 500+ observations) according to the X factor in 10 decile portfolios ("DP"). Afterwards, I performed for each decile portfolio a linear regression to evaluate if each alpha is significantly different from zero. The linear Regression for the i-th decile portfolio is: $$R_{i,t}-R^f_t = \alpha_i + \beta_i(R^m_t-R^f_t)+ \epsilon_{i,t}$$

Since I'm dealing with a time serie, I will adjust for heteroskedasticity and autocorrelation with the Newey-West (1987) correlation corrector with 6 lags.

Results: The decile portfolios DP1, DP2 have significant negative alphas and DP8, DP9, DP10 a significant positive alpha. However, I would primarily be interested if/not all alphas are jointly equal to zero. I already saw posts that discussed the GRS-Test proposed by Gibbons, Ross, and Shanken (1989) but this test has the major drawback that it assumes normally distributed uncorrelated homoskedastic error terms. Somebody mentioned a test with the Chi-Squared-Distribution but didn't elaborate what the assumptions were let alone how to perform it in R.

I would be so grateful if somebody would know a less restrictive test for evaluating if all alphas are jointly equal to zero. Specifically, I would be interested in the underlying assumptions of the test (preferably with a source) as well as the concrete code in R (if it doesn't causes too much inconvenience) :D

Here is the code which I have so far (for the first decile portfolio DP1)

library(sandwich)
library(lmtest)

#Performing Linear Regression
L1 <- lm(DP1 ~ MktRf, data = DATA)

#Building NeweyWest Covariance Corrector
NW_VCOV_L1 <- NeweyWest(L1, lag = 6, prewhite = F, adjust = T)

#Performing Covariance Test
coeftest(L1, vcov = NW_VCOV_L1)

which yields following Output

t test of coefficients:

Estimate  Std. Error t value  Pr(>|t|)
(Intercept) -0.00327902  0.00068035 -4.8196 1.799e-06 ***
MktRf        0.92165566  0.02334994 39.4714 < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

• Have you seen the excellent answers by @Matthew Gunn, here and here? Apr 18 at 12:12


text:
# CAT Quantitative Aptitude Questions | CAT Ratios, Mixtures, Alligations and Averages Questions

###### CAT Questions | Alligations and Averages | Alligation

The question is from CAT Ratio, Mixtures and Averages. When a sum of amount is lend at two different percentages, what is the amount lend at one particular rate? CAT exam is known to test on basics rather than high funda ideas. A range of CAT questions can be asked from Ratios and Proportions, Mixtures, Alligations and Averages. Make sure you master the topics. 2IIMs CAT questions bank provides you with CAT questions that can help you gear for CAT Exam CAT 2019.

Question 29: Ram borrows Rs 4000 on simple interest from Shyam for a period of 4 years. He borrows a portion of amount at 2% interest and the remaining at 5%. If the interest Shyam earns is Rs 480, How much money did Ram borrow at 2% interest rate?

1. $$frac{8000}{3}\\$ 2. $\frac{4000}{3}\\$ 3. 3000 4. 2000 ## Try 2IIM Online CAT Coaching #### Signup to sample the Best CAT Online Coaching ## Best CAT Coaching in Chennai #### Starts Sat, Mar 30, 2019 ### Explanatory Answer ##### Method of solving this CAT Question from Ratio, Mixtures and Averages: When we mix two mixtures in a particular ratio, we get a third mixture. Given the third mixture how does one find the ratio in which they were mixed. Interest earned per year = Rs.$\frac{480}{4}\\$ = Rs 120 Therefore, % earned per year = $\frac{120}{4000}\\$ = 3% So, amount invested in 2% = $\frac{2}{3}\\$ * 4000 = $\frac{8000}{3}\\$ The question is "How much money did Ram borrow t 2% interest rate?" ##### Hence, the answer is "$\frac{8000}{3}\\$". Choice A is the correct answer. ###### Online CAT CoachingTry it free! Register in 2 easy steps and start learning in 30 seconds! ###### Already have an Account? ###### CAT Coaching in Chennai Next Weekend Batch Starts Sat, Mar 30th, 2019 ###### Best CAT Coaching in Chennai Sign up for a Free Demo of our CAT Coaching in Chennai ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 10-C, Kalinga Colony, <NAME> Salai K.K.Nagar, Chennai. India. Pin - 600 078 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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