Analytical reaction dynamics: Origin and implications of trapped periodic trajectories

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Abstract
An analytical theory for the origin and dynamical implications of multiple trapped periodic trajectories on reactive surfaces is developed, and compared with numerical calculations. The dynamical motion is visualized in an orthogonal curvilinear coordinate system determined by the forms of the trapped trajectories, a device which leads naturally to the introduction of a generating function to determine the number and positions of possible trapped trajectories at any given energy. The connection between this function and the potential surface is examined in detail. This shows that the pattern of trapped trajectories may be deduced from knowledge of the combined variation of the potential energy and the transverse vibrational frequency along the reaction coordinate. This generating function is used to show that the lines of the trapped trajectories correspond to turning points of dynamical flux with respect to position along the reaction coordinate. It also provides a static explanation for the recently observed alternate repulsive and attractive character of successive trapped trajectories.