Kramers theory of chemical reactions in a slowly adjusting environment

Abstract

When describing the reaction dynamics in a slowly relaxing environment, one has to include slow nonreactive modes of the environment in an explicit consideration along with the “chemical” mode intrinsically responsible for the chemical transformation. This is done within the framework of the Kramers approach to condensed phase chemical reaction dynamics. The problem is studied under the condition of high friction of the nonreactive mode (slow adjustment) while friction of the chemical mode covers the whole range from weak to high friction. It is found that the reaction dynamics and, hence, the kinetics depend strongly on the strength of the coupling of the reactive and the nonreactive modes. For strong mode coupling the rate constant monotonically decreases with the increase of the friction of the chemical mode. Such behavior is quite distinctive from one for fast adjustment of the environment when the rate constant demonstrates a turnover behavior. Turnover behavior takes place for moderate strength mode coupling. This case has its own interesting specific features: (1) When friction of the chemical mode tends towards zero, the reaction rate remains finite due to the energy diffusion of the chemical mode induced by the motion of the nonreactive mode. (2) For a certain range of the friction coefficients particles escape the reactant domain on a path that avoids the saddle on the potential surface. This saddle-point avoidance is accompanied by violation of the Arrhenius law in the sense that the activation energy becomes a function of the friction intensity. (3) There is a range of the friction coefficients, where the kinetics is multiexponential. Analytical expressions for the rate constant are obtained for those conditions when the kinetics is single exponential. They show how the rate constant depends on the friction coefficients as well as on the parameters of the potential surface.