Generalized Langevin theory for many-body problems in chemical dynamics: Explicit coordinate motion in molecular solvents

Abstract

A practically useful and physically realistic generalized Langevin equation of motion that governs the dynamics of a small number of chemically relevant explicit solute generalized coordinates, e.g., a reaction coordinate or a normal mode coordinate, in a molecular solvent is developed. This equation of motion, which can be made the basis of analytical treatments of spectra and rate constants in molecular solvents, naturally represents the physics of the ultrafast relaxation regime in which cage effects governed by the instantaneous cage restoring force exerted on the explicit coordinates play a dominant role. This equation of motion realistically describes both indirect (explicit coordinate implicit coordinate solvent) and direct (explicit coordinate solvent) energy exchange processes as well as frequency modulation (dephasing) processes. This equation of motion also describes energy exchange with solvent vibrational as well as solvent translational-rotational degrees of freedom in a useful manner. The generalized Langevin equation for explicit coordinate motion in molecular solvents is based on the partial clamping model, which in turn assumes that (1) the liquid state motion of the explicit coordinates may be realistically approximated by small amplitude excursions from an initial point, and (2) the fluctuations in the local solvent density field are sufficiently small that the fluctuations of the perturbation density field induced by the small amplitude excursions may be ignored.