Statistical mechanics of isomerization dynamics in liquids and the transition state approximation

TLDR

The form of rate equations for isomerization depends on the ensemble used for averaging, and the validity of the resulting physical expression relies on time‑scale separation and the plateau value problem. The study uses time‑correlation function methods to analyze classical isomerization of small nonrigid molecules in liquids and predicts that transmission coefficients will deviate from unity depending strongly on solvent thermodynamic state. Time‑correlation function methods are applied to classical isomerization in liquids, and the approximations required for transition‑state theory are outlined with error estimates. Molecular expressions for a macroscopic rate constant are derived, yielding a single ensemble‑independent physical expression; coupling to the liquid provides dissipation that enables a plateau rate but also causes violations of Wigner’s assumption in transition‑state theory.

Abstract

In this article, time correlation function methods are used to discuss classical isomerization reactions of small nonrigid molecules in liquid solvents. Molecular expressions are derived for a macroscopic phenomenological rate constant. The form of several of these equations depend upon what ensemble is used when performing averages over initial conditions. All of these formulas, however, reduce to one final physical expression whose value is manifestly independent of ensemble. The validity of the physical expression hinges on a separation of time scales and the plateau value problem. The approximations needed to obtain transition state theory are described and the errors involved are estimated. The coupling of the reaction coordinate to the liquid medium provides the dissipation necessary for the existence of a plateau value for the rate constant, but it also leads to failures of Wigner’s fundamental assumption for transition state theory. We predict that for many isomerization reactions, the transmission coefficient will differ significantly from unity and that the difference will be a strong function of the thermodynamic state of the liquid solvent.