Quantum effect of solvent on molecular vibrational energy relaxation of solute based upon path integral influence functional theory

Abstract

Path integral influence functional theory has been applied to the investigation of the quantum effect of the solvent on vibrational relaxation of the solute. A classical bath approximation was attained by taking the ℏ→0 limit with respect to the solvent degrees of freedom. A comparison of the calculated relaxation time for the quantum solvent with that for the classical one showed that the quantum effect is very large and, at the same time, it depends much upon the process, i.e., single-phonon process, two-phonon process, or three-phonon process. This indicates that the so-called quantum correction does not work since the relaxation is usually a mixture of these multiphonon processes. A numerical example for CN− in water also demonstrates that, although the classical approximation for the solvent significantly overestimates the relaxation time, it presents reliable energy transfer pathways or relaxation mechanism.