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Of bonds and bands How to understand MO theory for extended solids?

Of bonds and bands How to understand MO theory for extended solids?. What does this mean?. Linear chain of hydrogen atoms. Polyene. Energy. The strongest attraction is found for the configuration with the smallest number of nodes.

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Of bonds and bands How to understand MO theory for extended solids?

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  1. Of bonds and bandsHow to understand MO theory for extended solids?

  2. What does this mean?

  3. Linear chain of hydrogen atoms Polyene

  4. Energy The strongest attraction is found for the configuration with the smallest number of nodes. The distances between the nodes is the reciprocal of their number. If there are no nodes, the distance is infinite. If there is a node between every atom the distance is a.

  5. E Nodes between all atoms, k=P/a k=P/2a No nodes, k=0

  6. Linear chain of hydrogen atoms c0 c1 c2 c3 c4 c5 c6 c7 c8 a Y= Sn exp(ikna) cn - What is this?

  7. Yk= Sn exp(ikna) cn - what is this? cn are basis functions, orbitals for H k is an index related to the number of nodes, or rather P times the reciprocal of the distance between the nodes. If there are no nodes k=0. If there are nodes between all atoms, k=P/a

  8. No nodes, k=0 Yk= Sn exp(ikna) cn Y0= Sn cn = c0 + c1 + c2 + c2 +… Strongly bonding

  9. Nodes between all atoms, k=P/a YP/a= Sn exp(i P/a na) cn = Sn exp(iPn) cn (alternating signs) YP/a= c0 - c1 + c2 - c2 +… Strongly anti-bonding

  10. E E(k) 0 P/2a P/a k

  11. E Band width If the hydrogen atoms are at large distances, they do not interact: a=5Å 0 P/2a P/a k

  12. E a=0.5Å k 0 P/2a P/a

  13. A stack of square planar platinum PtL4

  14. Monomer E p s d z x2-y2 z2 yz xz xy 4L Pt PtL4 L4

  15. Monomer E p s d z x2-y2 z2 yz xz xy 4L Pt PtL4 L4

  16. Monomer E p s d z x2-y2 z2 yz xz xy 4L Pt PtL4 L4

  17. Monomer E p s d z x2-y2 z2 yz xz xy 4L Pt PtL4 L4

  18. Monomer E p s d z x2-y2 z2 yz xz xy 4L Pt PtL4 L4

  19. Monomer E p s d z x2-y2 z2 yz xz xy 4L Pt PtL4 L4

  20. Monomer E p s d z x2-y2 z2 yz xz xy 4L Pt PtL4 L4

  21. Monomer E p s d z x2-y2 z2 yz xz xy 4L Pt PtL4 L4

  22. Dispersion – z2 Strongly bonding –stronglyantibonding

  23. Dispersion – z Strong bonding –antibonding

  24. Dispersion – z Strong bonding – antibonding

  25. Dispersion – xz, yz Intermediate bonding – antibonding

  26. Dispersion – x2-y2 Weak bonding – antibonding

  27. Polymer E s z d x2-y2 s p z2 yz xz xy d

  28. Polymer E s z d x2-y2 s p z2 yz xz xy d

  29. Polymer E s z d x2-y2 s p z2 yz xz xy d

  30. s Polymer E d Pt is d8 EF s p d k

  31. In oxidised systems, the Pt-Pt distance shortens. Why? EF

  32. BS DOS COOP

  33. Linear chain of hydrogen atoms E a

  34. Linear chain of hydrogen atoms E Dispersion a k

  35. Peierls distortion - H2 E a+d a-d k P/2a P/a

  36. Peierls distrotion E k P/2a

  37. The Brillouin zone The Brillioun zone is the primitive cell of the reciprocal lattice. Special points in the Brillioun zone have particular properties and are therefore given special symbolms

  38. Special points of the Brillouin zone

  39. Two dimensions - Graphene Face center Body centre Edge centre Face centre

  40. All Pz orbitals in-phase, G, Strongly p-bonding

  41. All Pz orbitals out-of-phase, G, Strongly anti p-bonding

  42. Two dimensions - Graphene Face center Body centre Edge centre Face centre

  43. K M

  44. Pz, p, K: non-bonding

  45. Pz, p*, K: non-bonding

  46. Pz, p, M: bonding

  47. Pz, p, M*: anti-bonding

  48. p bands –no gap at K, gap at M

  49. Px, s, G: strongly bonding, weakly anti-bonding

  50. Px, s*, G: strongly anti-bonding, weakly bonding

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