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We examine the phase space structures that govern reaction dynamics in theabsence of critical points on the potential energy surface. We show that in thevicinity of hyperbolic invariant tori it is possible to define phase spacedividing surfaces that are analogous to the dividing surfaces governingtransition from reactants to products near a critical point of the potentialenergy surface. We investigate the problem of capture of an atom by a diatomicmolecule and show that a normally hyperbolic invariant manifold exists at largeatom-diatom distances, away from any critical points on the potential. Thisnormally hyperbolic invariant manifold is the anchor for the construction of adividing surface in phase space, which defines the outer or loose transitionstate governing capture dynamics. We present an algorithm for sampling anapproximate capture dividing surface, and apply our methods to therecombination of the ozone molecule. We treat both 2 and 3 degree of freedommodels with zero total angular momentum. We have located the normallyhyperbolic invariant manifold from which the orbiting (outer) transition stateis constructed. This forms the basis for our analysis of trajectories for ozonein general, but with particular emphasis on the roaming trajectories.

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone