A theoretical investigation of isotropic raman polarizability correlation functions in dense molecular fluids

Abstract

This paper is concerned with the derivation of a kinetic equation for the description of the relaxation of the isotropic (rotational invariant) part of the Raman polarizability correlation function, with a goal to aid interpretations of experimental results. The isotropic polarizability correlation function is closely associated with the Raman spectral line-shape of a totally symmetric mode of an ensemble of molecules in a liquid. The kinetic equation was derived for an interaction potential consisting of two parts: one associated with a hard-core potential which is assumed to be unaffected by the intramolecular vibrations, and another associated with a potential which is modulated by molecular vibrations. The interaction potential chosen for this work is applicable to the intermolecular dipole-dipole interaction, hydrogen bonding interaction and other types of interactions. While we have included in the derivation the mechanism of the vibrational energy dissipation to nonvibrational degrees of freedom and of the resonant energy transfer to other oscillators, the theory gives a natural emphasis on the latter mechanism. It is shown that the resonant energy transfer mechanism has a greater effectiveness in causing the decay of the isotropic part of the polarizability correlation function than the other mechanisms. Also included is the effect of the pair correlation on the Raman polarizability correlation function. The dynamic pair-correlation function is shown to have an effect on the Raman spectral band shape, contrary to the assumption generally used in the spectral analysis. The kinetic equation derived is an integral-differential equation involving a memory function, which is expressed in terms of the correlation functions of fluctuating lattice variables. For the assumed potential, the equation is exact to second order in the interaction potential and, moreover, is capable of explaining the spectral line-narrowing phenomena observed in the isotropic part of the polarized Raman spectrum of a totally symmetric mode in a molecular liquid. As an application of the general theoretical expression, we have calculated the memory function for the dipole-dipole interaction potential. Assuming that the translational and rotational motions which modulate the dipole-dipole interaction obey diffusion equations, we have calculated the memory function analytically. The result shows clearly the importance of the resonant energy transfer mechanism over the vibrational dissipation mechanisms. The line-narrowing effect is also demonstrated in this model.

Additional information

Notes on contributors

C.H. Wang

Alfred P. Sloan Foundation Fellow (1973-1977).