Generalized Langevin theory for many-body problems in chemical dynamics: The equivalent chain equations for solute motion in molecular solvents

Abstract

A generalized Langevin equation framework for the treatment of liquid state influence on solute dynamics in molecular solvents, which generalizes an earlier framework restricted to monatomic solvents [S. A. Adelman, Adv. Chem. Phys. 53, 61 (1983)], is developed. This framework permits one to realistically treat energy exchange between the solute atoms and the solvent vibrational (V) degrees of freedom. This energy exchange can qualitatively influence the rates of liquid state processes when the solute frequencies relevant to the process of interest (e.g., a solute normal mode frequency if one is interested in the vibrational energy relaxation of that mode) substantially overlap the V bands of the frequency spectrum describing local solvent density fluctuations. The main result of the present analysis is an infinite set of equivalent chain equations governing the dynamics of the solute configuration point in molecular solvents. These are equations of motion for the solute configuration point and for the coordinates of an infinite set of abstract chain ‘‘molecules’’. Each molecule is composed of r+1 ‘‘atoms’’ where r is the number of normal modes of a real solvent molecule. The nearest neighbor chain of fictitious molecules may alternatively be regarded as a set of r+1 nearest neighbor cross-linked ‘‘atomic’’ chains. Atomic chain 1 executes low frequency ‘‘acoustical’’ motions which simulate the influence of local solvent translational–rotational (TR) density fluctuations. Atomic chains 2,3,. . .,r+1 execute high frequency ‘‘optical’’ motions which simulate the influence of normal mode V local solvent density fluctuations. The coupling of the optical and acoustical branches of the chain by the crosslinks is the chain formalism equivalent of the physical coupling, due to liquid state effects, of the temporal development of the TR and V modes of motion. The theory presented in this paper provides a conceptual foundation for the treatment of liquid state reactions occuring in molecular solvents by stochastic dynamics techniques. This conceptual foundation may be made the basis of practical simulation methods for treating reactions of diatomic solutes in molecular solvents and may be further developed to provide practical simulation methods for polyatomic solutes in molecular solvents.