Generalized Langevin theory for many-body problems in chemical dynamics: Reactions in liquids

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Abstract
A general theoretical framework for classical trajectory simulations of chemical reactions in liquids is presented. This framework is a development of the molecular timescale generalized Langevin equation (MTGLE) theory [S. A. Adelman, Adv. Chem. Phys. 44, 143 (1980)] for condensed phase chemical reaction dynamics. This generalization permits one to treat solute configuration (r0) dependent generalized damping forces in a computationally straightforward manner. Thus, for example, dynamical effects of common caging of reagents are realistically accounted for in the present theory. The theory is based on the following method. The nonequilibrium solvent density induced by small displacements Δr0(t) of the solute (chemical system) from a configuration point r0 is computed by linear response theory. The time dependent reaction force that the solvent exerts on the solute is then computed from the nonequilibrium solvent density. This leads to a set of solute configuration dependent MTGLE parameters {ωep2(r0), ωp+12(r0)}, p=0,1,2,⋅⋅⋅, which account for dynamical effects of solvent–solute interaction. These parameters may be generated as a function of r0 by performing molecular dynamics simulations of the solvent for a number of solute configurations r0. A generalized equivalent harmonic chain representation for solute dynamics is then developed. The force constants of the equivalent chain are the MTGLE parameters. Techniques for approximating the non‐Markovian chain equations by Markovian model chain equations are presented. These Markovian equations are directly applicable to simulation of liquid state reactions.

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