Search

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 〈F(t)F〉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 〈FF(t)F〉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. [ABSTRACT FROM AUTHOR]

A theoretical treatment of the vibrational–vibrational (VV) contribution to the vibrational energy relaxation time T1 of a solute normal mode in a molecular solvent, which extends a previous treatment [S. A. Adelman, R. H. Stote, and R. Muralidhar, J. Chem. Phys. 99, 1320 (1993), henceforth called Paper I] of the vibrational–translational–rotational (VTR) contribution to T1, is outlined and expressions for this VV contribution, valid for the infinitely dilute diatomic solution, are presented. The treatment is based on the formula T1=β-1(ωl), where β(ω) is the friction kernel of the relaxing solute mode and where ωl is its liquid phase frequency. β(ω) is evaluated as the cosine transform of the autocorrelation function 〈F(t)Fĩ〉0v of the fluctuating generalized force exerted by the vibrating solvent on the solute normal mode coordinate conditional that this coordinate is fixed at its equilibrium value. 〈F(t)F〉0v is expressed as a superposition of the rigid solvent autocorrelation function 〈F(t)F〉0 and a correction which accounts for solvent vibrational motion. For diatomic solvents one has 〈F(t)F〉0v= 〈F(t)F〉0+NSMD(t) cos ωDt F(ΩD), where NS=number of solvent molecules, MD(t) is the vibrational force gradient autocorrelation function, ωD and ΩD are solvent molecule liquid phase frequencies, and F(Ω)=1/2hΩ-1 coth[hΩ/2kBT].The Gaussian model is assumed for 〈F(t)F〉0 and MD(t) yielding β(ω) as a superposition of a Gaussian centered at ω=0 which mediates VTR processes and a Gaussian centered at ω=ωD which mediates VV processes. Vector integral expressions for MD(t), ωD, and ΩD are presented which are similar to the expressions for ωl and 〈F(t)F〉0 given in Paper I. These expressions permit the evaluation of the VV contribution to T1 from the atomic masses, bondlengths, vibrational frequencies, and site–site interaction... [ABSTRACT FROM AUTHOR]

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 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 〈F2>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)[bar_over_tilde:_approx._equal_to]ρ0kgas(T)... [ABSTRACT FROM AUTHOR]