Transition Path Sampling Study of Classical Rate-promoting Vibrations

It is now widely accepted that there is a class of enzymatic proton transfer reactions, which proceed through quantum tunneling. In a series of papers we have argued that some experimental features of these reactions can be explained by assuming the presence of a "rate-promoting" vibration which brings donor and acceptor closer together, thus leading to rate enhancement. There has never been a study of this effect for classical systems. We used transition path sampling to study the equivalent classical problem and found a complicated dynamical behavior that cannot be captured by transition state theory. Slow promoting vibrations lead to reactive trajectories that overshoot the saddle point, but on the other hand the short period of fast oscillations allows the reactants to stay only briefly in a low-barrier regime. There is a competition between these effects, which results to an intermediate value for the frequency of the rate-promoting vibration that is optimal for enhancing the rate.