2. G(r) r – r e  r – r e is the vibrational coordinate rere

3. Vibrational Energy Levels Harmonic Oscillator G(v) = ω (v + ½) cm -1

4. Equidistantly spaced levels G(r) r 

5. This is a quite unrealistic curve G(r) r 

6. G(r) r  H + H

7. G(r) r  H + H Dissociation

8. G(r) r  H + H Dissociation Chemical Bond Energies

9. G(r) r  H + H Dissociation Chemical Bond Energies DeDe

10. G(r) r  H + H Dissociation Chemical Bond Energies D e is called the Equilibrium Dissociation Energy Nuclear Energies DeDe

11. G(r) r  H + H Dissociation Chemical Bond Energies D e is called the Equilibrium Dissociation Energy Nuclear Energies DeDe

12. G(r) r  H + H Dissociation

13. G(r) r  H + H Dissociation

14. G(r) r  H + H Dissociation 0

15. G(r) r  H + H Dissociation 1 0

16. G(r) r  H + H Dissociation 2 1 0

17. G(r) r  H + H Dissociation v=3 2 1 0

18. G(r) r  H + H Dissociation v=3 2 1 0

19. G(r) r  H + H Dissociation v=3 2 1 0

20. G(r) r  H + H Dissociation v=3 2 1 0

21. G(r) r  H + H Dissociation v=3 2 1 0

22. G(r) r  H + H Dissociation v=3 2 1 0

23. G(r) r  H + H Dissociation v=3 2 1 0

24. G(r) r  H + H Dissociation v=3 2 1 0

26. H + H Nuclear Energies Chemical Energies E(r) r  0 Rotational levels

27. H + H Nuclear Energies Chemical Energies E(r) r  0 Morse Potential V(r) = D e (1-e -a(r-re) ) 2 Anharmonicity G(v) = ω(v+ ½) - α ω 2 (v+ ½) 2 α = ¼D e -4

28. G(r) r – r e  rere ½ ω 1½ ω 2½ ω 3½ ω 4½ ω 5½ ω 6½ ω Notice that the energy levels are equidistantly space by ω v = 6 v = 5 v = 4 v = 3 v = 2 v = 1 v = 0

29. Harry Kroto 2004

30. H + H Nuclear Energies Chemical Energies r  E(r) v=3 2 1 0 Harry Kroto 2004

31. G(r) r  H + H Dissociation Chemical Bond Energies D e is called the Equilibrium Dissociation Energy Nuclear Energies DeDe

32. Harry Kroto 2004

35. E(r) r 

36. - gif - www.files.chem.vt.edu/chem-ed/quantum/graphic...

37. Harry Kroto 2004