Selection Rules in Vibrational Transitions

The leading term is /io t vibl vib which vanishes by orthogonality. Group theoretically, the terms dfifdQi)QQi, d /t/dQtdQj)Q Q.Qj, etc., all transform as vector components in effect, the transformation properties of QiQjQ. .. in the expansion (6.98) are cancelled by those of dQidQjdQj. in the corresponding derivative. Consequently, we obtain the symmetry selection rule that T (iAvib) (m) must contain the totally symmetric IR—regardless of 

The selection rules on Av can be extracted by applying the second quantization formalism to Eq. 6.98. In particular, the first-order terms proportional to Qi permit transitions with Avi = 1, the second-order terms in QiQj are responsible for the overtone and combination bands with A Vi + Vj) = 0 or +2, and so on. The symmetry selection rule must simultaneously be satisfied. It is well known to students in organic chemistry that overtone and combination bands are frequently prominent in infrared spectra, and so the second- and higher order terms in Eq. 6.98 are not negligible. 

As in diatomics, vibrational transitions in polyatomic molecules are inevitably accompanied by rotational fine structure. In linear molecules, the vibrational and rotational selection rules in vibration-rotation spectra are closely analogous to the electronic and rotational selection rules, respectively, in diatomic electronic band spectra. When applied to a molecule, the general symmetry arguments of the previous Section lead to the El selection rules 

In symmetric top molecules, the rotational selection rules depend on the relative orientations of the figure axis (Chapter 5) and the vibrational transition 

Analysis of the rotational fine structure in vibration-rotation spectra thus offers potential for deducing the direction of the transition moment (and thus the vibrational symmetry species) of a vibrational band. If the transition moment has components parallel and normal to the figure axis, then both AK = 0 and AK = 1 transitions will be observed. 

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