Comparison of rate theories for generalized Langevin dynamics

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Abstract
Rate constants evaluated from (1) the energy-loss turnover theory of Pollak, Grabert, and Hänggi (PGH), (2) the Grote–Hynes extension of Kramers theory (GH), and (3) the microcanonical variational transition state theory for dissipative systems of Tucker and Pollak (μVTST) are compared with rate constants determined from direct computer simulations of generalized Langevin dynamics. The comparisons are made for a cubic oscillator under the influence of a slow bath characterized by a Gaussian friction kernel. In the μVTST calculations, which are based on an effective two degree of freedom Hamiltonian, barrier crossing due to energy transfer from the bath to the effective Hamiltonian is neglected. This neglect is significant only at very strong coupling, where it causes the μVTST results to drop below the simulation results. Both GH and μVTST theories fail (as expected) in the energy diffusion regime, while PGH theory is only moderately successful. The μVTST results agree extremely well with the simulation results in the spatial diffusion regime, providing a significant improvement over the GH results at intermediate coupling strengths and over the PGH results at strong coupling strengths. This improvement is a result of nonlinear effects which are included in the μVTST approach but neglected in the PGH and GH theories.