Phase space structures governing reaction dynamics in rotating molecules

TL;DR

This paper extends the understanding of phase space structures that govern reaction dynamics to include rotating molecules, using geometric Hamiltonian methods and normal form theory, which is crucial for molecular reaction analysis.

Contribution

It generalizes the construction of phase space structures to rotationally symmetric N-body systems, enhancing the applicability to molecular reaction dynamics.

Findings

Generalized phase space structure construction for rotating systems

Applicable to reaction dynamics in molecules with rotational symmetry

Provides a framework for analyzing reaction pathways 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{\'e}-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.