Transition states, trapped trajectories, and classical bound states embedded in the continuum

We show that the best choice of transition state, for the atom exchange reaction in a classical collinear collision of an atom with a diatomic, is a classical bound state embedded in the continuum: a periodic vibration of the triatomic system across the interaction region of the potential surface. These unstable bound states also serve as limit sets of the trapped trajectories that form the boundary of reactivity bands in molecular collisions, and we comment on the implications of this result for calculation of product state distributions. Numerical calculations of transition states are presented for the collinear H+H2 and F+H2 reactions.

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