Theory for the Raman Scattering Tensor for Combination and Overtones

Abstract

Theoretical expressions have been derived for the scattering tensor of Raman transitions which involve the excitation of one particular vibration by 2 quanta or the simultaneous excitation of two vibrations by one quantum each.

In order to incorporate the latter process it is necessary to expand [1] the electronic wave functions to second order in the nuclear coordinates; for the former process only the first order terms need to be considered. The electric dipole matrix element which appears in the expression for the Raman scattering tensor can be rewritten by introducing the expanded wave functions and selection rules. The symmetry of the scattering tensor and the theoretical relations of the intensity ratio of phonon bands of a solid or vibrational band of liquids and gases follow directly from this theoretical approach. It is found that asymmetry occurs in the scattering tensor for combination bands and the importance of this new phenomena for Raman bands, in particular those in solids, and the effect on the polarization properties shall be pointed out. It is now necessary to introduce in the character tables of the more familiar point groups the transformation properties of the antisymmetric part of the scattering tensor. This can be done in a relatively simple way [2].

The theory suggests also that the degree of antisymmetry increases if the Raman process involves the excitation of increasing numbers of vibrations.