The reactive flux method in the energy diffusion regime. II. Importance of the solvent’s spectral profile

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Abstract
The dependence of energy‐diffusion‐limited unimolecular‐rate constants upon the form of the solvent’s spectral profile is studied using generalized Langevin equation (GLE) dynamics. We find that the initial energy relaxation of the solute as it leaves the barrier region and the subsequent vibrational relaxation into the solute reactant well are governed by different frequency regions of the solvent’s spectral profile. Additionally, we find that for the case of a slowly relaxing bath the rate can depend quite dramatically upon the form of the friction kernel used in the GLE. Specifically, while the initial solute energy relaxation is observed to be similar for the Gaussian and exponential friction cases studied, there is a bottleneck to solute vibrational energy relaxation in the Gaussian friction case that is not present in the exponential friction case. In the Gaussian friction case, we find that neither the reactive flux method nor the Pollak–Grabert–Hänggi turnover theory (PGH) correctly predict the overall rate. As predicted in paper I [S. C. Tucker, J. Chem. Phys. 101, 2006 (1994)], the reactive flux in this case has two plateaus corresponding to two phenomenological rate constants. Mean first passage time calculations confirm that only the first of these two plateaus—which corresponds to the PGH estimate of the rate constant—is observed in the reactive flux simulations.