Canonical variational transition state theory for dissipative systems: Application to generalized Langevin equations

A numerical solution for the canonical variational dividing surface of two degree of freedom conservative systems is presented. The method is applied to reaction rates in dissipative systems whose dynamics is described by a generalized Langevin equation. Applications include a cubic and a quartic well using Ohmic and memory friction. For Ohmic friction, we find that in almost all cases, curvature of the optimal dividing surface may be neglected and the Kramers spatial diffusion limit for the rate is in practice an upper bound. For a Gaussian memory friction and a cubic oscillator, we compare the present theory with numerical simulations and other approximate theories presented by Tucker et al. [J. Chem. Phys. 95, 5809 (1991)]. For the quartic oscillator and exponential friction, we discover a strong suppression of the transmission coefficient and the reaction rate whenever the reduced static friction is of the same order of the reduced memory time. We also show that in this case, there is a strong suppression of the energy diffusion process in the reactants’ well.