Lecture 17 February 12, 2010 Hydrocarbons

1. Lecture 17 February 12, 2010 Hydrocarbons 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.edu 316 Beckman Institute, x3093 Charles and Mary Ferkel Professor of Chemistry, Materials Science, and Applied Physics, California Institute of Technology Teaching Assistants: Wei-Guang Liu <wgliu@wag.caltech.edu> Ted Yu <tedhyu@wag.caltech.edu>

2. Course schedule All lectures on schedule Friday Feb. 12, 2pm L17 Monday Feb. 15, caltech holiday Wednesday Feb. 17, 2pm L18 Friday Feb. 19, 2pm L19

3. Last time

4. Nature of the phase transitions <111> polarized rhombohedral <110> polarized orthorhombic <100> polarized tetragonal Non-polar cubic Temperature 120oC -90oC 5oC Displacive model Assume that the atoms prefer to distort toward a face or edge or vertex of the octahedron Increasing Temperature Different phases of BaTiO3 face edge vertex center

5. Nature of the phase transitions Displacive model Assume that the atoms prefer to distort toward a face or edge or vertex of the octahedron Increasing Temperature Order-disorder

6. Comparison to experiment Cubic Tetra. Ortho. Rhomb. Displacive  small latent heat This agrees with experiment R  O: T= 183K, DS = 0.17±0.04 J/mol O  T: T= 278K, DS = 0.32±0.06 J/mol T  C: T= 393K, DS = 0.52±0.05 J/mol Diffuse xray scattering Expect some disorder, agrees with experiment

7. Problem displacive model: EXAFS & Raman observations d (001) α (111) 7 • EXAFS of Tetragonal Phase[1] • Ti distorted from the center of oxygen octahedral in tetragonal phase. • The angle between the displacement vector and (111) is α= 11.7°. Raman Spectroscopy of Cubic Phase[2] A strong Raman spectrum in cubic phase is found in experiments. But displacive model  atoms at center of octahedron: no Raman • B. Ravel et al, Ferroelectrics, 206, 407 (1998) • A. M. Quittet et al, Solid State Comm., 12, 1053 (1973)

8. QM calculations The ferroelectric and cubic phases in BaTiO3 ferroelectrics are also antiferroelectric Zhang QS, Cagin T, Goddard WA Proc. Nat. Acad. Sci. USA, 103 (40): 14695-14700 (2006) Even for the cubic phase, it is lower energy for the Ti to distort toward the face of each octahedron. How do we get cubic symmetry? Combine 8 cells together into a 2x2x2 new unit cell, each has displacement toward one of the 8 faces, but they alternate in the x, y, and z directions to get an overall cubic symmetry

9. QM results explain EXAFS & Raman observations d (001) α (111) 9 • EXAFS of Tetragonal Phase[1] • Ti distorted from the center of oxygen octahedral in tetragonal phase. • The angle between the displacement vector and (111) is α= 11.7°. PQEq with FE/AFE model gives α=5.63° Raman Spectroscopy of Cubic Phase[2] A strong Raman spectrum in cubic phase is found in experiments. • B. Ravel et al, Ferroelectrics, 206, 407 (1998) • A. M. Quittet et al, Solid State Comm., 12, 1053 (1973)

10. Ti atom distortions and polarizations determined from QM calculations. Ti distortions are shown in the FE-AFE fundamental unit cells. Yellow and red strips represent individual Ti-O chains with positive and negative polarizations, respectively. Low temperature R phase has FE coupling in all three directions, leading to a polarization along <111> direction. It undergoes a series of FE to AFE transitions with increasing temperature, leading to a total polarization that switches from <111> to <011> to <001> and then vanishes.

11. Phase Transition at 0 GPa Thermodynamic Functions Transition Temperatures and Entropy Change FE-AFE Vibrations important to include

12. Mystery: Origin of Oxygen Vacancy Trees! 0.1μm Oxgen deficient dendrites in LiTaO3 (Bursill et al, Ferroelectrics, 70:191, 1986)

13. Oxygen Vacancy Structure (Vz) Ti Ti O O O O 2.12Å 2.12Å O O 1.93Å 1.84Å Ti O Ti O O O 2.12Å O 4.41Å 1.93Å Ti O O O O Ti 2.12Å O 1.85Å O 1.93Å Ti 2.10Å O O O O Ti P P P O O Ti 1 domain No defect defect leads to domain wall 1.93Å O 2.12Å O O Remove Oz Ti 1.93Å O 2.12Å O O Ti 1.93Å O 2.12Å O O Ti P Leads to Ferroelectric Fatigue

14. O O O Ti O Ti O O O O Ti O Ti O O O Divacancy in the x-y plane • V1 is a fixed Vx oxygen vacancy. • V2 is a neighboring oxygen vancancy of type Vx or Vy. • Interaction energy in eV.. Vacancy Interaction • Short range attraction due to charge redistribution. • Anisotropic: vacancy pair prefers to break two parallel chains (due to coherent local relaxation) O O O Ti Ti O O O y O Ti Ti O z O O z

15. 0.335eV 0.360 eV 0.456 eV 0.636 eV 0.669 eV 0.650 eV 1.878 eV 0.1μm Vacancy Clusters z Vx cluster in y-z plane: y Best 1D Best branch 2D Dendritic Bad • Prefer 1-D structure • If get branch then grow linearly from branch • get dendritic structure • n-type conductivity, leads to breakdown

16. Woodward-Hoffmann rulesorbital symmetry rulesFrontier Orbital rules Roald Hoffmann Certain cycloadditions occur but not others 2s+2s 2s+4s 4s+4s

17. Woodward-Hoffmann rulesorbital symmetry rulesFrontier Orbital rules Certain cyclizations occur but not others conrotatory disrotatory disrotatory conrotatory

18. 2+2 cycloaddition – Orbital correlation diagram GS Allowed Forbidden ES

19. WH rules – 2 + 4Ground State A A S A S S Allowed

20. WH rules – 2 + 4Excited State A A S Forbidden A S S

21. Summary WH rules cycloaddition 2n + 2m n+m odd: Thermal allowed Photochemical forbidden n+m even: Thermal forbidden Photochemical allowed n=1, m=1: ethene + ethene n=1, m=2: ethene + butadience (Diels-Alder)

22. S WH rules – cyclization-GS A A A S A A S Forbidden Allowed A S S A S A S S Rotation, C2 Reflection, s

23. Summary WH rules cyclization 2n n odd: thermal disrotatory Photochemical conrotatory n even: Thermal conrotatory Photochemical disrotatory n=2  butadiene n=3  hexatriene

24. GVB view reactions Reactant HD+T H D T During reaction, bonding orbital on D stays on D, Bonding orbital on H keeps its overlap with the orbital on D but delocalizes over H and T in the TS and localizes on T in the product. Thus highly overlapping bond for whole reaction Nonbonding Orbital on free T of reactant becomes partially antibonding in TS and localizes on free H of product, but it changes sign Product H+DT

25. GVB view reactions Reactant HD+T H D T Bond pair keeps high overlap while flipping from reactant to product Transition state nonbond orbital keeps orthogonal, hence changes sign Product H+DT H D T

26. GVB analysis of cyclization (4 e case) Move AB bond; Ignore D; C changes phase as it moves from 3 to 1 4 VB orbitals: A,B,C,D reactant φB φA φB φA φB φC 2 3 4 1 φD φC φA φD φC 2 3 φD 4 1 φB φA 2 3 Now ask how the CH2 groups 1 and 4 must rotate so that C and D retain positive overlap. Clearly 4n is conrotatory φC φD 1 4

27. Apply GVB model to 2 + 2 4 VB orbitals:A,B,C,D reactant Transition state: ignore C φB φA φA φB φC φD φD φB φD Nodal plane 4 VB orbitals product φA φC \ φC

28. Transition state for 2 + 2 2 1 3 4 2 1 3 4 Transition state: ignore C Orbitals A on 1 and B on 2 keep high overlap as the bond moves from 12 to 23 with B staying on 2 and A moving from 1 to 3 φB 2 1 φA Orbital D must move from 3 to 1 but must remain orthogonal to the AB bond. Thus it gets a nodal plane The overlap of D and C goes from positive in reactant to negative in product, hence going through 0. thus break CD bond. 3 4 φD Nodal plane φC Reaction Forbidden

29. GVB model fast analysis 2 + 2 φB φD φA \ φC 4 VB orbitals:A,B,C,D reactant Move A from 1 to 3 keeping overlap with B Simultaneously D moves from 3 to 1 but must change sign since must remain orthogonal to A and B 2 1 φA φB φC φD 3 4 C and D start with positive overlap and end with negative overlap. Thus break bond  forbidden

30. Next examine 2+4

31. GVB 2+4 φC φB φD φA 2 3 1 4 6 5 φE φF φA φB φD φC 2 3 1 4 6 5 φE φF 1. Move AB bond; Ignore D; C changes phase as it moves from 3 to 1

32. GVB 2+4 2. Move EF bond; C changes phase again as it moves from 1 to 5 φA φB φD φC 2 3 1 4 φA φB φD 2 3 6 5 1 4 φE φF φE φC 3. Now examine overlap of D with C. It is positive. Thus can retain bond CD as AB and EF migrate 6 5 φF Reaction Allowed

33. GVB 2+4 2. Move EF bond; C changes phase again as it moves from 1 to 5 φC φB φD φA 2 3 1 4 6 5 φE φF φA φB φD φC 2 3 1 4 φA φB φD 2 3 6 5 1 4 φE φF 3. Examine final overlap of D with C. It is positive. Thus can retain bond CD as AB and EF migrate φE 1. Move AB bond; Ignore D; C changes phase as it moves from 3 to 1 φC 6 5 φF Reaction Allowed

34. New material

35. Benzene and Resonance

36. Resonance

37. Benzene wavefunction

38. Allyl Radical

39. Allyl wavefunctions It is about 12 kcal/mol

40. Graphene

41. 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 Bands: 2pp orbitals per cell 2 bands 1x1 Unit cell This is referred to as graphene

42. Graphene band structure Unit cell has 2 carbon atoms Bands: 2pp orbitals per cell 2 bands of states each with N states where N is the number of unit cells 2 p electrons per cell  2N electrons for N unit cells The lowest N MOs are doubly occupied, leaving N empty orbitals. 1x1 Unit cell The filled 1st band touches the empty 2nd band at the Fermi energy 2nd band Get semi metal 1st band

43. 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 De = 1.0 kcal/mol C Easy to slide layers, good lubricant

44. energetics

45. Cn What is the structure of C3?

46. Cn

47. 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

48. Stability of odd Cn

50. Bond energies and thermochemical calculations