Time correlation function approach to vibrational energy relaxation in liquids: Revised results for monatomic solvents and a comparison with the isolated binary collision model

Abstract

A refined version of a molecular theory of liquid phase vibrational energy relaxation (VER) [S. A. Adelman and R. H. Stote, J. Chem. Phys. 88, 4397, 4415 (1988)] is presented and compared to the isolated binary collision (IBC) model. The theory is based on the Gaussian model for the fluctuating force autocorrelation function of the solute vibrational coordinate. Within the Gaussian model, the VER rate constant may be constructed in terms of solute–solvent site–site potential energy and equilibrium pair correlation functions. In the present refined treatment, crossfrictional contributions to the fluctuating force autocorrelation function are retained and its initial value 〈F̃2〉0 is evaluated from an exact rather than an approximate formula. Applications of the theory are made to model Lennard-Jones systems designed to simulate molecular iodine dissolved in liquid xenon at T=298 K and molecular bromine dissolved in liquid argon at T=295 K and T=1500 K. The refinements, along with an improved polynomial fitting procedure for the solute–solvent pair correlation functions, are found to yield significant changes in both the absolute VER rates and in their isothermal density dependencies. Moreover, it is found for all three solutions that the Gaussian decay time is nearly independent of density from ideal gas to the dense fluid regimes. This condition is sufficient for the emergence of an IBC-like factorization of the VER rate constant kliq(T) into a liquid phase structural contribution proportional to 〈F̃2〉0 and a dynamical contribution which is nearly density independent. The liquid structural contribution is, in general, not well-approximated by a contact collisional assumption but rather depends on a range of solute–solvent interatomic separations. For the Br2/Ar solutions, the rate constant isotherms show a superlinear deviation from the low density extrapolation kliq(T)≂ρ0kgas(T) which is qualitatively similar to that observed for a number of cryogenic and pressurized fluids. For the I2/Xe solution a qualitatively different sublinear rate isotherm is found. This ‘‘nonclassical’’ isotherm is correlated with the nonmonotonic density dependence of the magnitudes of the solute–solvent pair correlation function in the region important for the determination of 〈F̃2〉0 found for the I2/Xe system.