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

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Presentation transcript:

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

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

Equidistantly spaced levels G(r) r 

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

G(r) r  H + H

G(r) r  H + H Dissociation

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

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

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

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

G(r) r  H + H Dissociation

G(r) r  H + H Dissociation

G(r) r  H + H Dissociation 0

G(r) r  H + H Dissociation 1 0

G(r) r  H + H Dissociation 2 1 0

G(r) r  H + H Dissociation v=

G(r) r  H + H Dissociation v=

G(r) r  H + H Dissociation v=

G(r) r  H + H Dissociation v=

G(r) r  H + H Dissociation v=

G(r) r  H + H Dissociation v=

G(r) r  H + H Dissociation v=

G(r) r  H + H Dissociation v=

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

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

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

Harry Kroto 2004

H + H Nuclear Energies Chemical Energies r  E(r) v= Harry Kroto 2004

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

Harry Kroto 2004

E(r) r 

- gif -

Harry Kroto 2004