Raman intensities, depolarization ratios, and polarizability derivatives: Matrix notation, relation to other molecular constants and simple isotopic rules

Abstract

New matrix relations for the Raman intensities Ii, the polarizability derivatives (∂?/∂Qi)2 as well as (∂γ/∂Qi)2, and the depolarization ratios ρi are presented. These matrix formulations have been utilized to relate the Raman data to other molecular constants such as the mean square amplitudes of vibration, Coriolis constants, etc. In order to serve as a check on quantum mechanical calculations the extremal properties of the derivatives of the polarizability components with respect to the symmetry coordinates Si are derived. The Jacobians related to the Raman intensities are presented with a view to study the sensitivity of the force constants to the Raman intensities. Based on the first order perturbation theory a new isotopic rule involving the change in each Ii, (∂?/∂Qi)2, and (∂γ/∂Qi)2 is presented to study the isotopic substitution of heavy atoms in general.