Chaotic Dynamics in Multidimensional Transition States

TL;DR

This paper investigates how the transition state in a multidimensional reactive system exhibits chaotic behavior and how its phase space structures evolve with energy, particularly in the hydrogen exchange reaction.

Contribution

It demonstrates that the transition state can regain normal hyperbolicity at higher energies, ensuring the persistence of phase space structures crucial for transition state theory.

Findings

Transition state dynamics become more chaotic with increasing energy.

The transition state initially loses, then regains normal hyperbolicity.

Phase space structures remain valid at most energies above the threshold.

Abstract

The crossing of a transition state in a multidimensional reactive system is mediated by invariant geometric objects in phase space: An invariant hyper-sphere that represents the transition state itself and invariant hyper-cylinders that channel the system towards and away from the transition state. The existence of these structures can only be guaranteed if the invariant hyper-sphere is normally hyperbolic, i.e., the dynamics within the transition state is not too strongly chaotic. We study the dynamics within the transition state for the hydrogen exchange reaction in three degrees of freedom. As the energy increases, the dynamics within the transition state becomes increasingly chaotic. We find that the transition state first looses and then, surprisingly, regains its normal hyperbolicity. The important phase space structures of transition state theory will therefore exist at most energies above the threshold.