Instantaneous pair theory for high-frequency vibrational energy relaxation in fluids

Abstract

Notwithstanding the long and distinguished history of studies of vibrational energy relaxation, exactly how it is that high frequency vibrations manage to relax in a liquid remains somewhat of a mystery. Both experimental and theoretical approaches seem to say that there is a natural frequency range associated with intermolecular motion in liquids, typically spanning no more than a few hundred cm−1. Landau–Teller-type theories explain rather easily how a solvent can absorb any vibrational energy within this “band,” but how is it that molecules can rid themselves of superfluous vibrational energies significantly in excess of these values? In this paper we develop a theory for such processes based on the idea that the crucial liquid motions are those that most rapidly modulate the force on the vibrating coordinate — and that by far the most important of these motions are those involving what we have called the mutual nearest neighbors of the vibrating solute. Specifically, we suggest that whenever there is a single solvent molecule sufficiently close to the solute that the solvent and solute are each other’s nearest neighbors, then the instantaneous scattering dynamics of the solute–solvent pair alone suffices to explain the high-frequency relaxation. This highly reduced version of the dynamics has implications for some of the previous theoretical formulations of this problem. Previous instantaneous-normal-mode theories allowed us to understand the origin of a band of liquid frequencies, and even had some success in predicting relaxation within this band, but lacking a sensible picture of the effects of liquid anharmonicity on dynamics, were completely unable to treat higher frequency relaxation. When instantaneous-normal-mode dynamics is used to evaluate the instantaneous pair theory, though, we end up with a multiphonon picture of the relaxation which is in excellent agreement with the exact high-frequency dynamics — suggesting that the critical anharmonicity behind the relaxation is not in the complex, underlying liquid dynamics, but in the relatively easy-to-understand nonlinear solute–solvent coupling. There are implications, as well, for the independent binary collision (IBC) theory of vibrational relaxation in liquids. The success of the instantaneous-pair approach certainly provides a measure of justification for the IBC model’s focus on few-body dynamics. However, the pair theory neither needs nor supports the basic IBC factoring of relaxation rates into many-body and few-body dynamical components — into collision rates and relaxation rates per collision. Rather, our results favor taking an instantaneous perspective: the relaxation rate is indeed exercise in few-body dynamics, but a different exercise for each instantaneous liquid configuration. The many-body features therefore appear only in the guise of a purely equilibrium problem, that of finding the likelihood of particularly effective solvent arrangements around the solute. All of these results are tested numerically on model diatomic solutes dissolved in atomic fluids (including the experimentally and theoretically interesting case of I2 dissolved in Xe). The instantaneous pair theory leads to results in quantitative agreement with those obtained from far more laborious exact molecular dynamics simulations.