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

Vibrational Energy Levels Harmonic Oscillator G(v) = ω (v + ½) cm -1. Vibrational Energy Levels Harmonic Oscillator G(v) = ω (v + ½) cm -1 Remember the Potential Energy for a SHO is. Vibrational Energy Levels Harmonic Oscillator G(v) = ω (v + ½) cm -1

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

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

  2. Vibrational Energy Levels Harmonic Oscillator G(v) = ω(v + ½) cm-1 Remember the Potential Energy for a SHO is

  3. Vibrational Energy Levels Harmonic Oscillator G(v) = ω(v + ½) cm-1 Remember the Potential Energy for a SHO is V(x) = - k x2

  4. symmetric stretch of a homonuclear diatomic molecule such as H2

  5. symmetric stretch of a homonuclear diatomic molecule such as H2

  6. symmetric stretch of a homonuclear diatomic molecule such as H2 re

  7. symmetric stretch of a homonuclear diatomic molecule such as H2 re

  8. symmetric stretch of a homonuclear diatomic molecule such as H2 r re

  9. symmetric stretch of a homonuclear diatomic molecule such as H2 r re The vibrational coordinate is thus x = r – re

  10. G(r) re

  11. G(r) re is called the equilibrium bond length re

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

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

  14. G(r) re r – re

  15. G(r) G(v) = ω(v + ½) re r – re

  16. G(r) G(v) = ω(v + ½) v = 0 ½ ω re r – re

  17. G(r) v = 1 1½ ω G(v) = ω(v + ½) v = 0 ½ ω re r – re

  18. G(r) v = 2 2½ ω v = 1 1½ ω G(v) = ω(v + ½) v = 0 ½ ω re r – re

  19. G(r) v = 3 3½ ω v = 2 2½ ω v = 1 1½ ω G(v) = ω(v + ½) v = 0 ½ ω re r – re

  20. G(r) v = 4 4½ ω v = 3 3½ ω v = 2 2½ ω v = 1 1½ ω G(v) = ω(v + ½) v = 0 ½ ω re r – re

  21. G(r) 5½ ω v = 5 v = 4 4½ ω v = 3 3½ ω v = 2 2½ ω v = 1 1½ ω G(v) = ω(v + ½) v = 0 ½ ω re r – re

  22. v = 6 6½ ω G(r) 5½ ω v = 5 v = 4 4½ ω v = 3 3½ ω v = 2 2½ ω v = 1 1½ ω G(v) = ω(v + ½) v = 0 ½ ω re r – re

  23. v = 6 6½ ω G(r) 5½ ω v = 5 v = 4 4½ ω v = 3 3½ ω v = 2 2½ ω v = 1 1½ ω G(v) = ω(v + ½) v = 0 ½ ω re r – re

  24. v = 6 6½ ω G(r) 5½ ω v = 5 v = 4 4½ ω v = 3 3½ ω v = 2 2½ ω v = 1 1½ ω G(v) = ω(v + ½) v = 0 ½ ω re r – re

  25. 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

  26. Harry Kroto 2004

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

  28. Harry Kroto 2004

  29. Harry Kroto 2004

  30. Harry Kroto 2004

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

  32. Harry Kroto 2004

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