THE SHORT-TIME DYNAMICS OF SOLVATION

At long enough times, the idiosyncratic motions of individual solvent molecules have long since ceased to matter to the process of solvation ; the fact that a real solvent is not a featureless continuum just has no bearing on the dynamics. However, at short times, typically times well under a picosecond, the situation is quite different. We show her e that at least within the realm of classical mechanics, one can indee d talk about how specific molecular motions contribute to short-time s olvation. Precisely how one should think about these motions depends o n just how short a time interval one is considering. At the very short est times, we use the fact that it is possible to express solvation ti me correlation functions rigorously as power series in time to confirm that the onset of solvation in unequivocally a matter of inertial (fr ee-streaming) motion of individual solvent molecules. We allow for som ewhat longer, but still short, time intervals by writing these same co rrelation functions in terms of the instantaneous normal modes of the solvent. The instantaneous-normal-mode expressions allow us to decompo se the solvent dynamics into separate, well-defined collective motions , each with its own characteristic abilities to foster solvation. As d istinctive as they appear, these two complimentary short-time views ar e, in fact, equally correct in the inertial regime, a point we establi sh by proving that two are simply different mathematical representatio ns of the same underlying behavior.