Advances in calculating Raman excitation profiles by means of the transform theory

Abstract

Powerful transform methods for calculating Raman excitation profiles from the resonant absorption spectrum have recently been introduced. In the present work, previous results are extended to include both Condon and non-Condon sources of scattering and individual transform laws are presented for a number of commonly encountered symmetry conditions. In contrast to time correlator based methods, here the Kramers–Heisenberg polarizability expression, itself, serves as the starting point. Furthermore, the adiabatic approximation is limited to only one dimension, that of the scattered vibration. The remaining space of the resonant molecular eigenstates is formally free of many of the encumbering effects which find expression within the usual application of the adiabatic approximation in 3N-6 dimensions. This leads to a set of approximations which formally differ from those previously identified with the transform method. Their nature is less restrictive and encourages the view that the transform method is quite fundamental and deserves wide, though not uncritical, application. After deriving the basic set of transform laws, and discussing the underlying approximations, an illustration of the interference between Condon and non-Condon sources of scattering is presented. Then the transform law, at the Condon level, is shown to predict a strong discrimination against the scattering of low frequency modes. Finally, the problems involved in applying the transform theory to an ensemble of molecules are examined. Theoretical models as well as results from cytochrome-c are used as examples.