Trajectory analysis of a kinetic theory for isomerization dynamics in condensed phases

Abstract

We use an exact microscopic formalism to study the implications of a stochastic model of isomerization dynamics in liquids. In the model, a reaction coordinate moves in a multistable potential and is coupled to a thermal bath via random collisions which occur with a specified average collision frequency. The nonlinear dynamics for this system is solved numerically. It is found that the usual linear rate law for isomerization is valid for any nonzero collision frequency if the activation barrier to reaction is sufficiently high. The reasons for this behavior are discussed at length. With appropriate parameter choices, we can draw conclusions concerning the trans–gauche isomerization of n-butane in liquids. Transition state theory is found to overestimate the rate constant by at least a factor of 2 to 3 at any collision frequency. The collisional contribution to the volume of activation is calculated. At 1 atm, the result is an order of magnitude larger in size than the transition state theory activation volume. Furthermore, this collisional contribution has a strong pressure dependence that should be observable experimentally.