Non-fundamental transitions

Once the fundamental Av = 1 selection rule is breached, the IR and Raman activities of an overtone or combination are governed by the same symmetry selection rules that apply to fundamentals, and these depend on the symmetry of the transition. We can determine this by multiplying the characters of the representations corresponding to each vibration that is excited. For example, if an a2 and a b2 vibration of a Cav molecule are both singly excited, we calculate the representation of the final state. 

The result corresponds to bi symmetry, and so the combination of az and bz vibrations generates a bi transition. Note that in point groups with one or more axes of order three or more, the direct products obtained in this way might have to be reduced in order to discover the symmetry species of the components of the overtone or combination. 

For purely harmonic vibrations, overtone or combination frequencies would be exact sums of the constituent fundamental frequencies, but the effect of anharmonicity is to change (usually to reduce) the frequency of an overtone or combination (Section 8.2.2). Difference bands (v,- — v ) behave exactly like the corresponding combination bands (v, + v ) so far as symmetry selection rules, band contours and polarization are concerned, but the energy levels involved are the same as those involved in fundamental transitions, so the difference frequency is precisely equal to the difference between the frequencies of the corresponding fundamentals. For hot bands, one of the effects of anharmonicity is that they do not have exactly the same frequency as the parent transition. 

Raman spectrum of solid COz, showing the effect of Fermi resonance. Courtesy of Mr Steve Hunter, University of Edinburgh. 

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