William A. Goddard, III, wag@wag.caltech.edu 316 Beckman Institute, x3093

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

2. From lecture 6

3. Bond energies De = EAB(R=∞) - EAB(Re) Get from QM calculations. Re is distance at minimum energy D0 = H0AB(R=∞) - H0AB(Re) H0=Ee + ZPE is enthalpy at T=0K ZPE = S(½Ћw) This is spectroscopic bond energy from ground vibrational state (0K) Including ZPE changes bond distance slightly to R0 Experimental bond enthalpies at 298K and atmospheric pressure D298(A-B) = H298(A) – H298(B) – H298(A-B) D298 – D0 = 0∫298 [Cp(A) +Cp(B) – Cp(A-B)] dT =2.4 kcal/mol if A and B are nonlinear molecules (Cp(A) = 4R). {If A and B are atoms D298 – D0 = 0.9 kcal/mol (Cp(A) = 5R/2)}. (H = E + pV assuming an ideal gas)

4. Snap Bond Energy: Break bond without relaxing the fragments Snap DErelax = 2*7.3 kcal/mol Adiabatic Dsnap De (95.0kcal/mol) Desnap (109.6 kcal/mol)

5. CH2 +CH2  ethene 3B1 Starting with two methylene radicals (CH2) in the ground state (3B1) we can form ethene (H2C=CH2) with both a s bond and a p bond. 3B1 3B1 The HCH angle in CH2 was 132.3º, but Pauli Repulsion with the new s bond, decreases this angle to 117.6º (cf with 120º for CH3)

6. Twisted ethene Consider now the case where the plane of one CH2 is rotated by 90º with respect to the other (about the CC axis) This leads only to a s bond. The nonbonding pl and pr 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 Klr ~ 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 (s,p on same center)

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

8. CC double bond energies The bond energies for ethene are De=180.0, D0 = 169.9, D298K = 172.3 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 CH2 so that Desnap = 180.0 + 4.7 = 184.7 kcal/mol Since the Desnap = 109.6 kcal/mol, for H3C-CH3, The p 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

9. bond energy of F2C=CF2 The snap bond energy for the double bond of ethene of Desnap = 180.0 + 4.7 = 184.7 kcal/mol As an example of how to use this consider the bond energy of F2C=CF2, Here the 3B1 state is 57 kcal/higher than 1A1 so that the fragment relaxation is 2*57 = 114 kcal/mol, suggesting that the F2C=CF2 bond energy is Dsnap~184-114 = 70 kcal/mol. The experimental value is D298 ~ 75 kcal/mol, close to the prediction 3B1 57 kcal/mol 1A1 9

10. CC triple bonds Since the first CCs bond is De=95 kcal/mol and the first CCp 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 2P to 4S-, which costs 17 kcal each, weakening the bond by 34 kcal/mol. Adding this to the 55 would lead to a total 2ndp bond of 89 kcal/mol comparable to the first 2P 4S-

12. Cn What is the structure of C3?

13. Cn

14. Energetics Cn Note extra stability of odd Cn by 33 kcal/mol, this is because odd Cn has an empty px orbital at one terminus and an empty py on the other, allowing stabilization of both p systems

15. Stability of odd Cn

17. Bond energies and thermochemical calculations

18. Bond energies and thermochemical calculations

19. Heats of Formation

20. Heats of Formation

21. Heats of Formation

22. Heats of Formation

23. Bond energies

24. Bond energies

25. Bond energies Both secondary

27. Average bond energies

28. Average bond energies

29. Real bond energies Average bond energies of little use in predicting mechanism

30. Group values

31. Group functions of propane

32. Examples of using group values

33. Group values

34. Strain

35. Strain energy cyclopropane from Group values

36. Strain energy c-C3H6 using real bond energies

37. Stained GVB orbitals of cyclopropane

38. Benson Strain energies

39. Allyl radical

40. Allyl Radical

41. Allyl wavefunctions It is about 12 kcal/mol

42. Resonance in thermochemical Calculations

43. Resonance in thermochemical Calculations

44. Resonance energy butadiene

45. Benzene resonance

46. Benzene resonance

47. Benzene resonance

48. Benzene resonance

49. Benzene resonance

50. Benzene and Resonance referred to as Kekule or VB structures