High-frequency vibrational energy relaxation in liquids: The foundations of instantaneous-pair theory and some generalizations

Abstract

When the relevant frequencies get high enough, vibrational energy relaxation in liquids should, in principle, be governed by instantaneous-pair theory. The basic idea is that in any significantly contributing liquid configuration there is a single critical solvent molecule and that solute relaxation rates are determined by the time evolution of that molecule’s distance from the solute. The theory posits, moreover, that dynamics can always be modeled as a simple one-dimensional, two-body, scattering process with the liquid playing a role only in determining the initial conditions for the scattering. In this article we reformulate this theory so that it can address both polyatomic solutes and molecular solvents and we show that fundamental assumptions and basic approach remain valid even with multiple solute and solvent sites and with long-ranged intermolecular forces. We further show that while the corrections are often not large, it is possible to make systematic improvements by allowing for the multidimensionality of the solute–solvent scattering. We then turn to the instantaneous-normal-mode (INM) interpretation and implementation of the theory. At the lowest level, INM analysis enables us to define the “high frequencies” relevant to the theory as being outside the INM band of the liquid’s intermolecular vibrations and to think of the liquid as generating these frequencies from the overtones of a single INM mode. This kind of analysis predicts a temperature dependence to high-frequency vibrational relaxation remarkably similar to that of solid-state multiphonon models. However, by systematically improving this INM formulation we find that we can also explore the steps a liquid has to take to handle the relaxation of frequencies within its natural band. As the frequency decreases, a liquid evidently needs to invoke more and more of its band to drive the important solvent dynamics. Nonetheless, we continue to find that none of this important dynamics ever seems to involve anything more than the solute’s first solvation shell.