A saddle in a corner - a model of collinear triatomic chemical reactions

TL;DR

This paper introduces a geometrical model for collinear triatomic chemical reactions that explains reaction rate dependencies and phase space transition state theory applicability using advanced dynamical systems analysis.

Contribution

It presents a novel geometrical model capturing key features of atom-diatom reactions, analyzing phase space structures near equilibrium points.

Findings

Reaction rates depend nontrivially on parameters, initial conditions, and energy.

Conditions for validity and failure of phase space transition state theory are identified.

The model is neither near-integrable nor hyperbolic but still analyzable.

Abstract

A geometrical model which captures the main ingredients governing atom-diatom collinear chemical reactions is proposed. This model is neither near-integrable nor hyperbolic, yet it is amenable to analysis using a combination of the recently developed tools for studying systems with steep potentials and the study of the phase space structure near a center-saddle equilibrium. The nontrivial dependence of the reaction rates on parameters, initial conditions and energy is thus qualitatively explained. Conditions under which the phase space transition state theory assumptions are satisfied and conditions under which these fail are derived.