© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 Ch120a- Goddard- L01 1 Nature of the Chemical Bond with applications.

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 Ch120a- Goddard- L01 1 Nature of the Chemical Bond with applications to catalysis, materials science, nanotechnology, surface science, bioinorganic chemistry, and energy William A. Goddard, III, wag@wag.caltech.eduwag@wag.caltech.edu 316 Beckman Institute, x3093 Charles and Mary Ferkel Professor of Chemistry, Materials Science, and Applied Physics, California Institute of Technology Lecture 11 January 31, 2014 Graphite, graphene, bucky balls, bucky tubes Course number: Ch120a Hours: 2-3pm Monday, Wednesday, Friday Teaching Assistants:Sijia Dong Samantha Johnson sjohnson@wag.caltech.edu

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 3 Bond energies D e = E AB (R=∞) - E AB (R e ) Get from QM calculations. Re is distance at minimum energy D 0 = H 0AB (R=∞) - H 0AB (R e ) H 0 =Ee + ZPE is enthalpy at T=0K ZPE =  ½Ћ  ) This is spectroscopic bond energy from ground vibrational state (0K) Including ZPE changes bond distance slightly to R 0 Experimental bond enthalpies at 298K and atmospheric pressure D 298 (A-B) = H 298 (A) – H 298 (B) – H 298 (A-B) D 298 – D 0 = 0 ∫ 298 [C p (A) +C p (B) – C p (A-B)] dT =2.4 kcal/mol if A and B are nonlinear molecules (C p (A) = 4R). {If A and B are atoms D 298 – D 0 = 0.9 kcal/mol (C p (A) = 5R/2)}. (H = E + pV assuming an ideal gas)

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 4 Snap Bond Energy: Break bond without relaxing the fragments Snap Adiabatic  E relax = 2*7.3 kcal/mol D snap De snap (109.6 kcal/mol) D e (95.0kcal/mol)

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 5 CH2 +CH2  ethene Starting with two methylene radicals (CH 2 ) in the ground state ( 3 B 1 ) we can form ethene (H2C=CH2) with both a  bond and a  bond. The HCH angle in CH2 was 132.3º, but Pauli Repulsion with the new  bond, decreases this angle to 117.6º (cf with 120º for CH 3 ) 3B13B1 3B13B1 3B13B1

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 6 Twisted ethene Consider now the case where the plane of one CH 2 is rotated by 90º with respect to the other (about the CC axis) This leads only to a  bond. The nonbonding  l and  r orbitals can be combined into singlet and triplet states Here the singlet state is referred to as N (for Normal) and the triplet state as T. Since these orbitals are orthogonal, Hund’s rule suggests that T is lower than N (for 90º). The K lr ~ 0.7 kcal/mol so that the splitting should be ~1.4 kcal/mol. Voter, Goodgame, and Goddard [Chem. Phys. 98, 7 (1985)] showed that N is below T by 1.2 kcal/mol, due to Intraatomic Exchange (  on same center)

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 7 Twisting potential surface for ethene The twisting potential surface for ethene is shown below. The N state prefers θ=0º to obtain the highest overlap while the T state prefers θ=90º to obtain the lowest overlap

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 8 CC double bond energies Breaking the double bond of ethene, the HCH bond angle changes from 117.6º to 132.xº, leading to an increase of 2.35 kcal/mol in the energy of each CH 2 so that D esnap = 180.0 + 4.7 = 184.7 kcal/mol Since the D esnap = 109.6 kcal/mol, for H3C-CH3, The  bond adds 75.1 kcal/mol to the bonding. Indeed this is close to the 65kcal/mol rotational barrier. For the twisted ethylene, the CC bond is De = 180-65=115 Desnap = 115 + 5 =120. This increase of 10 kcal/mol compared to ethane might indicate the effect of CH repulsions The bond energies for ethene are D e =180.0, D 0 = 169.9, D 298K = 172.3 kcal/mol

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 9 bond energy of F 2 C=CF 2 The snap bond energy for the double bond of ethene of D esnap = 180.0 + 4.7 = 184.7 kcal/mol 9 1A11A1 3B13B1 57 kcal/mol As an example of how to use this consider the bond energy of F 2 C=CF 2, Here the 3 B 1 state is 57 kcal/higher than 1 A 1 so that the fragment relaxation is 2*57 = 114 kcal/mol, suggesting that the F 2 C=CF 2 bond energy is D snap ~184-114 = 70 kcal/mol. The experimental value is D298 ~ 75 kcal/mol, close to the prediction

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 10 CC triple bonds Since the first CC  bond is D e =95 kcal/mol and the first CC  bond adds 85 to get a total of 180, one might wonder why the CC triple bond is only 236, just 55 stronger. The reason is that forming the triple bond requires promoting the CH from 2  to 4  -, which costs 17 kcal each, weakening the bond by 34 kcal/mol. Adding this to the 55 would lead to a total 2 nd  bond of 89 kcal/mol comparable to the first 24-24-

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 14 Energetics Cn Note extra stability of odd C n by 33 kcal/mol, this is because odd C n has an empty p x orbital at one terminus and an empty p y on the other, allowing stabilization of both  systems

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 53 More on resonance like structure That benzene would have a regular 6-fold symmetry is not obvious. Each VB spin coupling would prefer to have the double bonds at ~1.34A and the single bond at ~1.47 A (as the central bond in butadiene) Thus there is a cost to distorting the structure to have equal bond distances of 1.40A. However for the equal bond distances, there is a resonance stabilization that exceeds the cost of distorting the structure, leading to D 6h symmetry.

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 54 Cyclobutadiene For cyclobutadiene, we have the same situation, but here the rectangular structure is more stable than the square. That is, the resonance energy does not balance the cost of making the bond distances equal. 1.5x A 1.34 A The reason is that the pi bonds must be orthogonalized, forcing a nodal plane through the adjacent C atoms, causing the energy to increase dramatically as the 1.54 distance is reduced to 1.40A. For benzene only one nodal plane makes the pi bond orthogonal to both other bonds, leading to lower cost

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 55 graphene This is referred to as graphene Graphene: CC=1.4210A Bond order = 4/3 Benzene: CC=1.40 BO=3/2 Ethylene: CC=1.34 BO = 2 CCC=120° Unit cell has 2 carbon atoms 1x1 Unit cell

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 56 Graphene band structure Unit cell has 2 carbon atoms Bands: 2p  orbitals per cell  2 bands of states each with N states where N is the number of unit cells 2  electrons per cell  2N electrons for N unit cells The lowest N MOs are doubly occupied, leaving N empty orbitals. 1x1 Unit cell 1 st band 2 nd band The filled 1 st band touches the empty 2 nd band at the Fermi energy Get semi metal

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 57 Graphite Stack graphene layers as ABABAB Can also get ABCABC Rhombohedral AAAA stacking much higher in energy Distance between layers = 3.3545A CC bond = 1.421 Only weak London dispersion attraction between layers D e = 1.0 kcal/mol C Easy to slide layers, good lubricant Graphite: D 0K =169.6 kcal/mol, in plane bond = 168.6 Thus average in-plane bond = (2/3)168.6 = 112.4 kcal/mol 112.4 = sp 2  + 1/3  Diamond: average CCs = 85 kcal/mol   = 3*27=81 kcal/mol

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 61 Have to terminate graphene: two simple cases Armchair edge For each edge atom break two sp2 sigma bonds but form bent pi bond in plane 111.7 – 20 = 92 kcal/mol Length = 3*1.4=4.2A 22 kcal/molA Zig-zag edge For each edge atom break sp2 sigma bond, maybe not break pi bond? 111.7/2 = 56 kcal/mol per dangling bond Length = 1.4*sqrt(3)= 2.42A 23 kcal/mol/A Thus both graphene ribbon surfaces (edges) have similar energies

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 63 C 60 fullerene No broken bonds Just ~11.3 kcal/mol strain at each atom 678 kcal/mol Compare with 832 kcal/mol for flat sheet Lower in energy than flat sheet by 154 kcal/mol!

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 64 First observation Heath, Smalley, Krotos Laser evaporation of carbon + supersonic nozzle Observe various sized clusters in mass spect Change various conditions found peak at C60! Smalley and Krotos each independently postulated futball (soccer ball structure) ~1986 ^^ H. W. Kroto, J. R. Heath, S. C. O'Brien, R. F. Curl and R. E. Smalley (1985). "C60: Buckminsterfullerene". Nature 318: 162–163. doi:10.1038/318162a0.doi10.1038/318162a0

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 68 1985-1990 Many papers on C60, no definitive proof that it had fullerene structure, lots of skepticism Then, Nature 347, 354 - 358 (27 September 1990) W. Krätschmer, Lowell D. Lamb, K. Fostiropoulos & Donald R. Huffman; Solid C60: a new form of carbon In 1990 physicists W. Krätschmer and D.R. Huffman for the first time produced isolable quantities of C60 by causing an arc between two graphite rods to burn in a helium atmosphere and extracting the carbon condensate so formed using an organic solvent. A new form of pure, solid carbon has been synthesized consisting of a somewhat disordered hexagonal close packing of soccer-ball-shaped C60 molecules. Infrared spectra and X-ray diffraction studies of the molecular packing confirm that the molecules have the anticipated 'fullerene' structure. Mass spectroscopy shows that the C70 molecule is present at levels of a few per cent.

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 69 Nature 1990, Krätschmer, Lamb, Fostiropoulos, Huffman Sears arc welder with flowing He, get soot of C60. grams per hour

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 70 Nature 1990, Krätschmer, Lamb, Fostiropoulos, Huffman Sears arc welder with flowing He, get soot of C60. grams per hour

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 71 NMR the key experiment Carbon 13 NMR spectrum of C70 5 peaks, definitive proof of fullerene structure Carbon 13 NMR spectrum of C60 1 peak Definitive proof that C60 is fullerene

© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 Ch120a- Goddard- L01 1 Nature of the Chemical Bond with applications.

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© copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 Ch120a- Goddard- L01 1 Nature of the Chemical Bond with applications.

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