Intensities in Raman spectra I. A bond polarizability theory

Abstract

Theories of Raman intensities are reviewed, and it is shown that no satisfactory theory exists which enables relative intensities to be predicted. A matrix method for calculating the derived invariants of the molecular polarizability in terms of polarizability functions characteristic of bonds and general coefficients defining the normal mode of vibration is presented. The method is an extension of the well-known matrix techniques for the vibrational problem. The general theory is simplified by making approximations first suggested by Wolkenstein (1941). In this approximation each distinct bond is characterized by three polarizability functions; these may be deduced from measured intensities in much the same way as force constants may be deduced from frequencies. General formulae for setting up the matrices are given, and completely general formulae for intensities in terms of bond polarizabilities, to the Wolkenstein approximation, are quoted in full for molecules of the types MX$_{2}$(C$_{2v}$), MX$_{4}$(T$_{d}$), MX$_{3}$Y(C$_{3v}$) and MX$_{2}$Y$_{2}$(C$_{2v}$).