Exponentiating trajectories and statistical behavior in collinear atom–diatom collisions

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Abstract
The dynamic basis for statistical behavior in classical collinear bimolecular collisions is explored using an approach suggested by recent studies in nonlinear mechanics. Studies of the dynamics on three model potential energy surfaces including the Karplus–Porter H+H2 system indicate that statistical product distributions evolve from regions of the initial phase space characterized by trajectories which exponentially separate in time from nearby neighbors by more than 3 orders of magnitude. The time scale required to achieve this degree of exponential separation and associated statistical behavior is substantially shorter than that expected from arguments based on rates of intramolecular energy transfer. Our computational results also provide evidence for the validity of several assumptions implicit in the variational equations approach to determining the critical energy for energy randomization in molecular systems.