Dynamics of liquid state chemical reactions: Modeling of R-dependent correlation functions

Abstract

Methods for the simplified construction of those reagent configuration point r₀‐dependent static and dynamic solvent correlation functions required to implement the molecular time scale generalized Langevin equation (MTGLE) approach to problems in liquid state chemical reaction dynamics [S. A. Adelman, J. Chem. Phys. 73, 3145 (1980)] are presented. These methods permit one to bypass straightforward but laborious construction of the correlation functions via molecular dynamics simulations of the solvent motion about the solute for many solute configurations r₀. The methods are based on two approximations: (i) The matrix r₀‐dependent friction kernel of the reagents β₁(t;r₀) is modeled via a matrix generalization of the conventional Gaussian approximation for scalar time correlation functions. This modeling permits one to reduce the problem of constructing β₁(t;r₀) to an equilibrium calculation which may be carried out by Monte Carlo as opposed to molecular dynamics techniques. (ii) The equilibrium r₀‐dependent solvent correlation functions required to construct the Gaussian approximation to β₁(t;r₀) are calculated using the superposition approximation. This permits one to construct β₁ (t;r₀), and hence the MTGLE chain models, from equilibrium solute–solvent and solvent–solvent pair correlation functions. For simple liquids, the pair correlation functions may be obtained as solutions to the Percus–Yevick integral equation. The simplified methods are applied to construct the MTGLE chain models for three Lennard‐Jones systems designed to simulate infinitely dilute solutions of molecular iodine in: liquid carbon tetrachloride, dense gaseous ethane, and liquid ethane. The results are tested against molecular dynamics for the I₂ in CCl₄ model solution.