On the equilibrium approach to isomerization dynamics in liquids

Abstract

Following Kramers, we describe the dynamics of an isomerization reaction A ⇆ B as a diffusion process in a bistable intramolecular potential. In order to calculate the chemical relaxation time t r, we rely on a purely equilibrium approach, introduced by Chandler, and we focus on the properties of the time correlation function C(t) = ⟨δNA (0) δNA (t)⟩, and of its derivatives. A plateau formalism permits the extraction of the long relaxation time t r from the short time dynamics of a molecule which starts at t = 0 from the activated region between A and B. The calculation makes it possible to encompass in a unified way the low and high friction limits, which are usually treated differently. It involves the definition of a species specification function σ A , which indicates microscopically if a molecule is A or B. Most of the time, σ A is taken as a Heaviside function, although its definition should be experiment-dependent. We examine the possibility of taking a wide species specification, presenting a smooth variation in the activated region.