Classical mechanics of a collinear exchange reaction: A direct evaluation of the reaction probability and product distribution

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Abstract
Instead of finding regions of reactivity in the asymptotic reactants (products) phase space, involving a two dimensional search, one may directly evaluate the boundary of reactivity bands. Here we provide a practical method, for the regime in which transition state theory is not exact, for directly evaluating such boundaries. The method is iterative, convergent and at each iteration step provides improved upper and lower bounds to the reaction probability. A numerical application to the hydrogen exchange reaction giving product distributions and reaction probabilities over a wide range of energies is provided. We find that the existence of two bounded trajectories that are not periodic is crucial to understanding the dynamics of the system.