THEORY OF VIBRATIONAL-ENERGY RELAXATION IN LIQUIDS - VIBRATIONAL TRANSLATIONAL-ROTATIONAL ENERGY-TRANSFER

The concepts underlying a theoretical treatment of the vibrational ene rgy relaxation (VER) time T1 of a solute normal mode in a molecular so lvent are summarized, and results for T1, valid for VER processes medi ated by vibrational-translational-rotational energy transfer, obtained from this treatment are presented. These results are based on the for mula T1 = beta(TR)-1 (omega(l)), where beta(TR)(omega) is the translat ional-rotational branch of the friction kernel of the normal mode and where omega, is its liquid phase frequency. Beta(TR)(omega) is evaluat ed as the cosine transform of the autocorrelation function [F(t)F]0 of the fluctuating generalized force exerted by the solvent on the solut e normal mode coordinate conditional that this coordinate is fixed at its equilibrium value and that all solvent molecules are constrained t o have their equilibrium geometries. The Gaussian model is utilized to evaluate [F(t)F]0 and molecular level expressions for omega(l) and fo r the Gaussian model parameters are presented for the infinitely dilut e diatomic solution. The expressions involve site density integrals ov er the coordinates of a single solvent atomic site and over the coordi nates of a pair of solvent atomic sites located on the same molecule. The results permit the evaluation of T1 in terms of the atomic masses and gas phase bondlengths of the solute and the solvent molecules, the solute gas phase vibrational frequency, the solute-solvent site-site interaction potentials, and specified equilibrium site-site pair corre lation functions of the liquid solution.