Phase space structures causing the reaction rate decrease in the collinear hydrogen exchange reaction

TL;DR

This paper investigates the phase space structures influencing the reaction rate decrease in the collinear hydrogen exchange reaction, revealing how invariant manifolds and energy transfer limitations cause this counterintuitive behavior.

Contribution

It introduces a phase space analysis using lobe dynamics to explain the reaction rate decrease and derives bounds for the reaction rate based on invariant manifold structures.

Findings

Invariant manifolds guide reaction trajectories.

Energy transfer limitations cause rate decrease.

Derived bounds for reaction rate.

Abstract

The collinear hydrogen exchange reaction is a paradigm system for understanding chemical reactions. It is the simplest imaginable atomic system with $2$ degrees of freedom modeling a chemical reaction, yet it exhibits behaviour that is still not well understood - the reaction rate decreases as a function of energy beyond a critical value. Using lobe dynamics we show how invariant manifolds of unstable periodic orbits guide trajectories in phase space. From the structure of the invariant manifolds we deduce that insufficient transfer of energy between the degrees of freedom causes a reaction rate decrease. In physical terms this corresponds to the free hydrogen atom repelling the whole molecule instead of only one atom from the molecule. We further derive upper and lower bounds of the reaction rate, which are desirable for practical reasons.