Phase space structures governing reaction dynamics in rotating molecules

Abstract

Recently the phase space structures governing reaction dynamics in Hamiltonian systems have been identified and algorithms for their explicit construction have been developed. These phase space structures are induced by saddle type equilibrium points which are characteristic for reaction type dynamics. Their construction is based on a Poincar{é}-Birkhoff normal form. Using tools from the geometric theory of Hamiltonian systems and their reduction we show in this paper how the construction of these phase space structures can be generalized to the case of the relative equilibria of a rotational symmetry reduced $N$-body system. As rotations almost always play an important role in the reaction dynamics of molecules the approach presented in this paper is of great relevance for applications.

28 pages, 7 figures, pdflatex

References in corpus (3)

• Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum
• Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry
• Stability transitions for axisymmetric relative equilibria of Euclidean symmetric Hamiltonian systems

Cited by in corpus (7)

• Bifurcations of transition states: Morse bifurcations
• Reaction dynamics through kinetic transition states
• Reactivity Boundaries to Separate the Fate of a Chemical Reaction Associated with Multiple Saddles
• Reactivity Boundaries to Separate the Fate of a Chemical Reaction Associated with an Index-two saddle
• Morse bifurcations of transition states in bimolecular reactions
• Identifying Reaction Pathways in Phase Space via Asymptotic Trajectories
• Stabilization of reacting systems