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 here that at least within the realm of classical mechanics, one can indeed talk about how specific molecular motions contribute to short-time solvation. Precisely how one should think about these motions depends on just how short a time interval one is considering. At the very shortest times, we use the fact that it is possible to express solvation time correlation functions rigorously as power series in time to confirm that the onset of solvation in unequivocally a matter of inertial (free-streaming) motion of individual solvent molecules. We allow for somewhat longer, but still short, time intervals by writing these same correlation functions in terms of the instantaneous normal modes of the solvent. The instantaneous-normal-mode expressions allow us to decompose the solvent dynamics into separate, well-defined collective motions, each with its own characteristic abilities to foster solvation. As distinctive as they appear, these two complimentary short-time views are, in fact, equally correct in the inertial regime, a point we establish by proving that two are simply different mathematical representations of the same underlying behavior.