GENERALIZED LANGEVIN MODEL FOR MOLECULAR-DYNAMICS OF AN ACTIVATED REACTION IN SOLUTION

The molecular dynamics (MD) by which an A + BC --> AB + C atom exchange reaction takes place in rare gas solvent are modeled using the generalized Langevin equation (GLE) and are compared in terms of energy flow to the results of full deterministic MD. A simple single atom model is used for the force-force correlation function and the corresponding fluctuation-response derived memory kernel. We model both the generation from an equilibrium ensemble of the specific fluctuation by which the reactants climb the barrier to the transition state and the dissipation of the fluctuation as the reagents descend the barrier to equilibrated products. This model of the generation and decay of the fluctuation by which an activated process emerges from and returns to equilibrium is an extension beyond the usual use of the GLE to model the dynamics of equilibrium systems, barrier recrossings in the vicinity of a barrier top (Grote-Hynes), or the decay of nonequilibrium systems toward equilibrium. An analysis of reagent translational motion for this reaction in terms of the GLE shows that there are several identifiable epochs in the time history of this reaction: (1) a +/- 10 fs time period (the recrossing epoch) immediately before and after the transition state at t = 0 during which the reaction coordinate dynamics are dominated by the random forces; (2) periods of +/- (10-60) fs (intrinsic potential epochs) during which the mutual forces among the reagents dominate; (3) periods of +/- (60-300) fs (generative-dissipative epochs) in which the generative-dissipative forces dominate; and (4) initial and final periods < - 300 and > 300 fs (equilibrium epochs) during which the generative-dissipative and random forces are in balance. This example calculation illustrates that in favorable cases a simple GLE approach can be useful in modeling and understanding both the reactant and product time histories of the MD of activated solution reactions.