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In real molecules, highly sensitive vibrational spectroscopy can detect overtones , which are transitions originating from the n = 0 state for which Δn = +2, +3, …. Anharmonicity.

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Presentation Transcript
anharmonicity

In real molecules, highly sensitive vibrational spectroscopy can detect overtones, which are transitions originating from the n = 0 state for which Δn = +2, +3, …

Anharmonicity

Overtones are due to anharmonicity. A good approximation of realistic anharmonicity is given by the Morse potential.

slide2

Put x = r – r0 and Taylor expand:

Comparing to the harmonic oscillator

we see that

So we do

to keep the force constant the same but change the anharmonicity

slide5

Morse model

dissociated above this

are the generalized Laguerre polynomials

slide6

Harmonic oscillator model

are the Hermite polynomials

slide15

Selection rules

For anharmonicity, can replace the H.O. wavefunctions with Morse wavefunctions…

…or can keep more terms in the Taylor expansion of the dipole moment

slide17

Correspondence principle

Where xturn is the maximum value of x