title: Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone.
abstract: We examine the phase space structures that govern reaction dynamics in the absence of critical points on the potential energy surface. We show that in the vicinity of hyperbolic invariant tori, it is possible to define phase space dividing surfaces that are analogous to the dividing surfaces governing transition from reactants to products near a critical point of the potential energy surface. We investigate the problem of capture of an atom by a diatomic molecule and show that a normally hyperbolic invariant manifold exists at large atom-diatom distances, away from any critical points on the potential. This normally hyperbolic invariant manifold is the anchor for the construction of a dividing surface in phase space, which defines the outer or loose transition state governing capture dynamics. We present an algorithm for sampling an approximate capture dividing surface, and apply our methods to the recombination of the ozone molecule. We treat both 2 and 3 degrees of freedom models with zero total angular momentum. We have located the normally hyperbolic invariant manifold from which the orbiting (outer) transition state is constructed. This forms the basis for our analysis of trajectories for ozone in general, but with particular emphasis on the roaming trajectories.
authors: School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom.
authors: Frédéric A L
authors: FA
authors: Mauguière
authors: School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom.
authors: Peter
authors: P
authors: Collins
authors: Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA.
authors: Zeb C
authors: ZC
authors: Kramer
authors: School of Chemistry, Cardiff University, Cardiff CF10 3AT, United Kingdom.
authors: Barry K
authors: BK
authors: Carpenter
authors: Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA.
authors: Gregory S
authors: GS
authors: Ezra
authors: Institute of Electronic Structure and Laser, Foundation for Research and Technology - Hellas, and Department of Chemistry, University of Crete, Iraklion 711 10, Crete, Greece.
authors: Stavros C
authors: SC
authors: Farantos
authors: School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom.
authors: Stephen
authors: S
authors: Wiggins