Lecture 18, March 2, 2015 graphene, bucky balls, bucky tubes

Transcription

1 Lecture 18, March 2, 2015 graphene, bucky balls, bucky tubes Elements of Quantum Chemistry with Applications to Chemical Bonding and Properties of Molecules and Solids Course number: Ch125a; Room 115 BI Hours: 11-11:50am Monday, Wednesday, Friday William A. Goddard, III, 316 Beckman Institute, x3093 Charles and Mary Ferkel Professor of Chemistry, Materials Science, and Applied Physics, California Institute of Technology Special Instructor: Julius Su Teaching Assistants: Hai Xiao Mark Fornace Ch125a- 1 Goddard-

2 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 = [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) 2

3 Snap Bond Energy: Break bond without relaxing the fragments Snap E relax = 2*7.3 kcal/mol Adiabatic D snap De snap (109.6 kcal/mol) D e (95.0kcal/mol) 3

4 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. 3 B 1 3 B 1 3 B 1 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 ) 4

5 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 copyright to Intraatomic 2015 William A. Exchange Goddard III, all ( rights on reserved same center) 5

6 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 6

7 CC double bond energies The bond energies for ethene are D e =180.0, D 0 = 169.9, D 298K = kcal/mol 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 = = kcal/mol Since the D esnap = 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 = =115 Desnap = =120. This increase of 10 kcal/mol compared to ethane might indicate the effect of CH repulsions 7

8 bond energy of F 2 C=CF 2 The snap bond energy for the double bond of ethene of D esnap = = 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 ~ = 70 kcal/mol. The experimental value is D298 ~ 75 kcal/mol, close to the prediction 57 kcal/mol 3 B 1 1 A 1 8

9 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 4-9

10 10

11 Allyl radical 11

12 Allyl Radical 12

13 Allyl wavefunctions It is about 12 kcal/mol 13

14 Benzene resonance 14

15 Benzene and Resonance referred to as Kekule or VB structures 15

16 Resonance 16

17 Pages from Ch120-Chap Pages from Ch120-Chap Benzene wavefunction is a superposition of the VB structures in (2) benzene as + 17

18 More on resonance 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. 18

19 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 A 1.5x 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 19

20 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 This is referred to as graphene 20

21 1x1 Unit cell 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. The filled 1 st band touches the empty 2 nd band at the Fermi energy Get semi metal 2 nd band 1 st band 21

22 Graphite Stack graphene layers as ABABAB Can also get ABCABC Rhombohedral AAAA stacking much higher in energy Distance between layers = A CC bond = 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 = Thus average in-plane bond = (2/3)168.6 = kcal/mol = sp 2 + 1/3 Diamond: average CCs = 85 kcal/mol = 3*27=81 kcal/mol 22

23 energetics 23

24 Graphene: generalize benzene in all directions 24

25 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 = 92 kcal/mol Length = 3*1.4=4.2A 22 kcal/mola Thus both graphene ribbon surfaces (edges) have similar energies 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 25

26 C 60 flat sheet Cut from graphene 6 arm chair 5 zig-zag Total cost 832 kcal/mol! 26

27 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! 27

28 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: doi: /318162a0. 28

29 Nature 1985: discovery of C 60 29

30 10 torr He Evidence for C60, Nature 1985 maximize clustercluster reactions in integration cup 760 torr He 30

31 Many papers on C60, no definitive proof that it had fullerene structure, lots of skepticism 31

32 Many papers on C60, no definitive proof that it had fullerene structure, lots of skepticism 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. Then, Nature 347, (27 September 1990) W. Krätschmer, Lowell D. Lamb, K. Fostiropoulos & Donald R. Huffman; Solid C60: a new form of carbon 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 copyright 2015 of a William few A. per Goddard cent. III, all rights reserved 32

33 Nature 1990, Krätschmer, Lamb, Fostiropoulos, Huffman Sears arc welder with flowing He, get soot of C60. grams per hour 33

34 Nature 1990, Krätschmer, Lamb, Fostiropoulos, Huffman Sears arc welder with flowing He, get soot of C60. grams per hour 34

35 Carbon 13 NMR spectrum of C60 1 peak NMR the key experiment Definitive proof that C60 is fullerene Carbon 13 NMR spectrum of C70 5 peaks, definitive proof of fullerene structure 35

36 bucky ball overheads_page_01 Polyyne chain precursors fullerenes, all even 36

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38 C 540 All fullerens have 12 pentagonal rings 38

39 Fullerene crystal structures fcc structure C 60 hcp structure C 70

40 C 60 supercell with ordered C 60 -C 60 interactions