The short-time intramolecular dynamics of solutes in liquids. II. Vibrational population relaxation

Abstract

Events such as the vibrational relaxation of a solute are often well described by writing an effective equation of motion—a generalized Langevin equation—which expresses the surrounding medium’s influence on the intramolecular dynamics in terms of a friction and a fluctuating force acting on the solute. These quantities, though, can be obtained from the instantaneous normal modes (INMs) of the system when the relaxation takes place in a fluid, suggesting that we should be able to analyze in some detail the solvent motions driving the relaxation, at least for short times. In this paper we show that this promise can indeed be realized for the specific case of a vibrating diatomic molecule dissolved in an atomic solvent. Despite the relatively long times typical of vibrational population relaxation, it turns out that understanding the behavior of the vibrational friction at the short times appropriate to INMs (a few hundred femtoseconds) often suffices to predict T1 times. We use this observation to probe the dependence of these relaxation rates on thermodynamic conditions and to look at the molecular mechanisms underlying the process. We find that raising the temperature at any given density or raising the density at any given temperature will invariably increase the rate of energy relaxation. However, since these two trends may be in conflict in a typical constant-pressure laboratory experiment, we also find that it is possible to make sense of the “anomalous” inverted temperature dependence recently seen experimentally. We find, as well, that the INM theory—which has no explicit collisions built into it—predicts exactly the same density dependence as the venerable independent-binary-collision (IBC) theory (an intriguing result in view of recent claims that experimental observations of this kind of dependence provide support for the IBC theory). The actual mechanisms behind vibrational population relaxation are revealed by looking in detail at the vibrational friction “influence spectrum”—the spectrum of INMs weighted by how efficiently each mode acts to promote the relaxation. Through suitable projections we show that the average influence spectrum is dominated by longitudinal motion of the solvent atoms in the first solvation shell. We go further, however, and examine the nature of the instantaneous relaxation promoted by individual liquid configurations. The number of instantaneous modes that contribute significantly fluctuates strongly from configuration to configuration, and the number of solvent atoms strongly coupled to the solute has a certain amount of variation as well, but invariably each significant mode ends up promoting the relaxation by moving just one or two significant solvent atoms—a feature we explore in a companion paper.