Theory of vibrational energy relaxation in liquids: Diatomic solutes in monatomic solvents.

A numerical study of the solute, solvent, and energy flow pathway dependence of the vibrational energy relaxation (VER) time T1 of a harmonic solute vibrational mode is presented for the prototype case of diatomic solutes in monatomic solvents. This study is based on formulas for T1 developed in the preceding paper, especially the relationship T1=β-1(ωl) where β(ω) is the frequency-dependent friction kernel of the solute normal mode and where ωl is its liquid state frequency. These formulas permit evaluation of T1 and its energy flow pathway dependence from equilibrium solute–solvent pair correlation functions. Applications are made to VER of ground electronic state molecular iodine and bromine in the fluids xenon and argon and in model Lennard-Jones solvents designed to simulate ethane and carbon tetrachloride. Satisfactory agreement between the present treatment and experimental and computer simulation results for 15 thermodynamic states is found. The VER rates (∼T-11) were found to increase with increase in the degree of resonance overlap between ωl and the solvent frequency spectrum ρF(ω)∼β(ω). Moreover indirect energy flow pathways, i.e., those which involve solute vibration ↔ solute translation–rotation ↔ solvent energy transfer, are found to play a qualitatively essential role for many of the systems studied here. Finally a study of the temperature and density dependence of T1 for iodine in xenon in the experimentally accessible range is presented. [ABSTRACT FROM AUTHOR]