Normal mode theory of two step relaxation in liquids: Polarizability dynamics in CS2

Abstract

An instantaneous normal mode (INM) theory is given for relaxation in liquids by a fast β process followed by a slow α process. The β process is harmonic dynamics in the wells of the N-body potential, while the α process is structural relaxation coincident with barrier crossing to a neighbor well. The theory introduces a new parameter, the ‘‘harmonic fraction’’ denoted FH, which is the fraction of the mean-square fluctuations of a dynamical variable capable of being relaxed by the harmonic β process. Theory and computer simulation are compared for the polarizability correlation function, PC(t), and the polarizability time derivative correlation function, DPC(t), in a model of CS2 including internal degrees of freedom. Agreement is good, with the INM theory clearly showing the ‘‘signature’’ time dependence of a correlation function undergoing αβ relaxation in a low temperature liquid; there are no adjustable parameters in the theory. The polarizability is calculated in the ‘‘point atomic polarizability approximation’’ (PAPA) which is sensitive to molecular vibrations, so a preliminary classical INM treatment of Raman scattering is obtained. The PAPA overestimates the derivative of the polarizability with respect to the internal coordinates, and in reality the vibrations behave quantum mechanically, so the Raman intensities are inaccurate, but otherwise a plausible description is obtained for several features of the spectrum. It is explained how an improved PAPA will be combined with a quantum INM theory in future Raman calculations.