Quantum Theory of Vibrational Relaxation in Liquids

We present a theory of vibrational relaxation of polyatomic molecules in polyatomic solvents, which is also applicable to solid solutions, with Fermi's Golden Rule as the point of departure. We avoid rotating wave or random phase approximations, and treat both the internal degrees of freedom of the relaxing molecule and the bath degrees of freedom in a fully quantum mechanical manner. The results allow one to go beyond earlier analyses which treated only cascade processes and to consider all participating bosons. We construct the theory in a manner which facilitates the use of recent developments in the analysis of instantaneous normal modes of liquids. We address the problem of the inverted temperature dependence of the relaxation rate observed recently by Tokmakoff, Sauter and Fayer (J. Chem. Phys. 100, 9035 (1994)) and provide three different possible explanations of the phenomenon. The first is based on the temperature dependence of the density of states of the instantaneous normal modes as suggested by the authors of the experimental paper. The second stems from an energy mismatch mechanism which gives rise to dressing effects. The third arises naturally from the representation of the dynamics of the liquid in terms of anharmonic oscillators.