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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 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 Slide 2 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 From lecture 6 2 Slide 3 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 = ) 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) Slide 4 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) Slide 5 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 132.3, but Pauli Repulsion with the new bond, decreases this angle to 117.6 (cf with 120 for CH 3 ) 3B13B1 3B13B1 3B13B1 Slide 6 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 90 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, Hunds rule suggests that T is lower than N (for 90). 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) Slide 7 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 =0 to obtain the highest overlap while the T state prefers =90 to obtain the lowest overlap Slide 8 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 117.6 to 132.x, 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 Slide 9 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 Slide 10 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 24-24- Slide 11 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 11 Slide 12 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 12 Cn What is the structure of C 3 ? Slide 13 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 13 Cn Slide 14 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 Slide 15 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 15 Stability of odd Cn Slide 16 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 16 Slide 17 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 17 Bond energies and thermochemical calculations Slide 18 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 18 Bond energies and thermochemical calculations Slide 19 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 19 Heats of Formation Slide 20 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 20 Heats of Formation Slide 21 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 21 Heats of Formation Slide 22 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 22 Heats of Formation Slide 23 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 23 Bond energies Slide 24 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 24 Bond energies Slide 25 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 25 Bond energies Both secondary Slide 26 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 26 Slide 27 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 27 Average bond energies Slide 28 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 28 Average bond energies Slide 29 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 29 Real bond energies Average bond energies of little use in predicting mechanism Slide 30 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 30 Group values Slide 31 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 31 Group functions of propane Slide 32 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 32 Examples of using group values Slide 33 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 33 Group values Slide 34 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 34 Strain Slide 35 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 35 Strain energy cyclopropane from Group values Slide 36 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 36 Strain energy c-C3H6 using real bond energies Slide 37 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 37 Stained GVB orbitals of cyclopropane Slide 38 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 38 Benson Strain energies Slide 39 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 39 Allyl radical Slide 40 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 40 Allyl Radical Slide 41 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 41 Allyl wavefunctions It is about 12 kcal/mol Slide 42 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 42 Resonance in thermochemical Calculations Slide 43 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 43 Resonance in thermochemical Calculations Slide 44 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 44 Resonance energy butadiene Slide 45 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 45 Benzene resonance Slide 46 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 46 Benzene resonance Slide 47 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 47 Benzene resonance Slide 48 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 48 Benzene resonance Slide 49 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 49 Benzene resonance Slide 50 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 50 Benzene and Resonance referred to as Kekule or VB structures Slide 51 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 51 Resonance Slide 52 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 52 Benzene wavefunction like structure + benzene as is a superposition of the VB structures in (2) Slide 53 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. Slide 54 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 Slide 55 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 Slide 56 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 Slide 57 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 Slide 58 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 58 energetics Slide 59 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 Stopped Feb. 4, 2013 59 Slide 60 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 60 Graphene: generalize benzene in all directions Slide 61 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 Slide 62 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 62 C 60 flat sheet Cut from graphene 6 arm chair pairs @92 5 zig-zag atoms @56 Total cost 832 kcal/mol! Slide 63 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! Slide 64 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: 162163. doi:10.1038/318162a0.doi10.1038/318162a0 Slide 65 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 65 Nature 1985: discovery of C 60 Slide 66 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 66 Evidence for C60, Nature 1985 760 torr He 10 torr He maximize cluster- cluster reactions in integration cup Slide 67 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 67 1985-1990 Many papers on C60, no definitive proof that it had fullerene structure, lots of skepticism Slide 68 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. Krtschmer, Lowell D. Lamb, K. Fostiropoulos & Donald R. Huffman; Solid C60: a new form of carbon In 1990 physicists W. Krtschmer 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. Slide 69 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 69 Nature 1990, Krtschmer, Lamb, Fostiropoulos, Huffman Sears arc welder with flowing He, get soot of C60. grams per hour Slide 70 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 70 Nature 1990, Krtschmer, Lamb, Fostiropoulos, Huffman Sears arc welder with flowing He, get soot of C60. grams per hour Slide 71 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 Slide 72 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 72 Polyyne chain precursors fullerenes, all even Slide 73 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 73 Slide 74 copyright 2011 William A. Goddard III, all rights reservedCh120a-Goddard-L07,08 74 C 540 All fullerens have 12 pentagonal rings