THE SHORT-TIME INTRAMOLECULAR DYNAMICS OF SOLUTES IN LIQUIDS .2. VIBRATIONAL POPULATION RELAXATION

Events such as the vibrational relaxation of a solute are often well d escribed by writing an effective equation of motion-a generalized Lang evin equation-which expresses the surrounding medium's influence on th e intramolecular dynamics in terms of a friction and a fluctuating for ce acting on the solute. These quantities, though, can be obtained fro m the instantaneous normal modes (INMs) of the system when the relaxat ion takes place in a fluid, suggesting that we should be able to analy ze in some detail the solvent motions driving the relaxation, at least for short times. In this paper we show that this promise can indeed b e realized for the specific case of a vibrating diatomic molecule diss olved 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 appropriat e to INMs (a few hundred femtoseconds) often suffices to predict T-1 t imes. We use this observation to probe the dependence of these relaxat ion rates on thermodynamic conditions and to look at the molecular mec hanisms underlying the process. We find that raising the temperature a t any given density or raising the density at any given temperature wi ll invariably increase the rate of energy relaxation. However, since t hese two trends may be in conflict in a typical constant-pressure labo ratory experiment, we also find that it is possible to make sense of t he ''anomalous'' inverted temperature dependence recently seen experim entally. We find, as well, that the INM theory-which has no explicit c ollisions built into it-predicts exactly the same density dependence a s the venerable independent-binary-collision (IBC) theory (an intrigui ng result in view of recent claims that experimental observations of t his kind of dependence provide support for the IBC theory). The actual mechanisms behind vibrational population relaxation are revealed by l ooking in detail at the vibrational friction ''influence spectrum''-th e spectrum of INMs weighted by how efficiently each mode acts to promo te the relaxation. Through suitable projections we show that the avera ge influence spectrum is dominated by longitudinal motion of the solve nt atoms in the first solvation shell. We go further, however, and exa mine the nature of the instantaneous relaxation promoted by individual liquid configurations. The number of instantaneous modes that contrib ute significantly fluctuates strongly from configuration to configurat ion, and the number of solvent atoms strongly coupled to the solute ha s a certain amount of variation as well, but invariably each significa nt mode ends up promoting the relaxation by moving just one or two sig nificant solvent atoms-a feature we explore in a companion paper. (C) 1997 American Institute of Physics.