Multiphonon vibrational relaxation in liquids: An exploration of the idea and of the problems it causes for molecular dynamics algorithms

Abstract

The basic solid-state perspective on energy relaxation—that a solute transfers large amounts of energy to its surroundings by exciting overtones of the solid’s phonons—is sufficiently beguiling that it is tempting to try to apply it to high-frequency vibrational energy relaxation in liquids. We suggest that when the phonon concept is suitably adapted this picture does provide a surprisingly realistic and quantitative portrait of vibrational energy dispersal in solution. Within the nonlinear instantaneous-normal-mode/instantaneous-pair theory of vibrational relaxation, relaxation rates can be formally written as a sum over the contributions of successively higher overtones of fundamental solvent frequencies. However the presence of a significant width to the band of fundamental frequencies in the liquid state means that there could, in principle, be complex interferences between multiple contributing overtones, rendering the overtone picture no more than a formal construct. What we find is that such interferences do not occur. Despite the fact the band shape is log normal—with a relatively long band tail—the relaxation is invariably dominated by a single overtone. This same perspective also helps us understand one of the failings of the common velocity-Verlet molecular dynamics algorithm in predicting high-frequency energy relaxation.