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G(r)

G(r). r – r e is the vibrational coordinate. r e. r – r e . Vibrational Energy Levels Harmonic Oscillator G(v) = ω (v + ½) cm -1. G(r). Equidistantly spaced levels. r . G(r). This is a quite unrealistic curve. r . H + H. G(r). r . H + H Dissociation.

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G(r)

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  1. G(r) r – re is the vibrational coordinate re r – re

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

  3. G(r) Equidistantly spaced levels r 

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

  5. H + H G(r) r 

  6. H + H Dissociation G(r) r 

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

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

  9. Nuclear Energies H + H Dissociation Chemical Bond Energies De is called the Equilibrium Dissociation Energy G(r) De r 

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

  11. H + H Dissociation G(r) r 

  12. H + H Dissociation G(r) r 

  13. H + H Dissociation G(r) 0 r 

  14. H + H Dissociation G(r) 1 0 r 

  15. H + H Dissociation G(r) 2 1 0 r 

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

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

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

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

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

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

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

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

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

  25. Nuclear Energies H + H E(r) Chemical Energies Morse Potential V(r) = De(1-e-a(r-re))2 Anharmonicity G(v) = ω(v+ ½) - αω2(v+ ½)2 α = ¼De-4 0 r 

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

  27. Harry Kroto 2004

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

  29. Nuclear Energies H + H Dissociation Chemical Bond Energies De is called the Equilibrium Dissociation Energy G(r) De r 

  30. Harry Kroto 2004

  31. Harry Kroto 2004

  32. Harry Kroto 2004

  33. E(r) r 

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

  35. Harry Kroto 2004

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