Theory of vibrational energy relaxation in liquids: Vibrational–translational–rotational energy tranfer

Abstract

The concepts underlying a theoretical treatment of the vibrational energy relaxation (VER) time T1 of a solute normal mode in a molecular solvent are summarized, and results for T1, valid for VER processes mediated by vibrational–translational–rotational energy transfer, obtained from this treatment are presented. These results are based on the formula T1=βTR−1(ωl), where βTR(ω) is the translational–rotational branch of the friction kernel of the normal mode and where ωl is its liquid phase frequency. βTR(ω) is evaluated as the cosine transform of the autocorrelation function 〈ℱ̃(t)ℱ̃〉0 of the fluctuating generalized force exerted by the solvent on the solute normal mode coordinate conditional that this coordinate is fixed at its equilibrium value and that all solvent molecules are constrained to have their equilibrium geometries. The Gaussian model is utilized to evaluate 〈ℱ̃F(t)ℱ̃〉0 and molecular level expressions for ωl and for the Gaussian model parameters are presented for the infinitely dilute diatomic solution. The expressions involve site density integrals over the coordinates of a single solvent atomic site and over the coordinates 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 correlation functions of the liquid solution.