Raman Intensities and Molecular Symmetry

According to the haimonic oscillator selection rule, as briefly discussed in Section 8.1, fundamental transitions are only allowed in Raman spectra. In practice, it means that the fundamental lines will appear with higher intensity than the overtone and combination lines. In this section the relationship between molecular symmetiy and the intensity of the Raman line will be considered. 

25) shows that the intensity of each fundamental transition in the Raman spectrum is governed by integrals of the following type 

in the wdinaiy Raman experiment, d e polarizability toisor has six independmit components, six integrals with such a structure exist 

A vibrational transitioa is allowed if at least one of these integrals differs from zero. The symmetry selection rule states that die integral ( n I c ( I m ) is not zero if the direct product of representations for the i b vibrational mode 

The molecular polarizability tensor a is defined in relation with two vectors die induced dipole p and the electric field vector f [Eq. (8.1)]. Hence, the representation of a can be expressed as a direct product of the representations of the respective vectors [265] 

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