Rotational energy relaxation of individual rotational states in liquids

Abstract

The manner in which most molecules reorient in liquids bears little resemblance to the process in the gas phase. For small-moment-of-inertia species such as the hydrides, however, the observation of discrete spectroscopic lines corresponding to individual isolated-molecule quantum transitions suggests that one is actually seeing single-molecule dynamics perturbed only weakly by the environment—just as one sees with solution-phase vibrational behavior. We examine here the degree to which such individual rotational quantum states remain well defined in liquids by considering the rates of discrete energy-level-to-energy-level transitions in solution. For rotational quantum states that do preserve their free-rotor character in a liquid, we find that the transition rate between angular momentum states obeys a rotational Landau–Teller relation strikingly similar to the analogous expression for vibration: the rate is proportional to the liquid’s rotational friction evaluated at the transition frequency. Subsequent evaluation of this friction by classical linearized instantaneous-normal-mode theory suggests that we can understand this relationship by regarding the relaxation as a kind of resonant energy transfer between the solute and the solution modes. On specializing to the particular cases of H2 and D2 in Ar(l), we find that the most critical modes are those that move the light solute’s center of mass with respect to a single nearby solvent. This observation, in turn, suggests a generalization of instantaneous-normal-mode ideas that transcends both linear coupling and harmonic dynamics: an instantaneous-pair theory for the relaxation of higher-lying levels. By employing a linearized instantaneous-normal-mode theory of relaxation within the liquid band and an instantaneous-pair theory for higher-frequency relaxation, we find that the resonant-transfer paradigm is reasonably successful in reproducing molecular dynamics results spanning a wide range of different rotational states.