Understanding chemical reactions within a generalized Hamilton-Jacobi framework

TL;DR

This paper introduces a generalized Hamilton-Jacobi framework to analyze chemical reactions, integrating topology and dynamics, and applies it to a model reaction to compare classical and quantum trajectories.

Contribution

It develops a unified approach for studying reaction paths and trajectories, revealing discrepancies between classical and quantum analyses in chemical reactivity.

Findings

High-dimensional problems can be addressed with Caratheodory plots.

Quantum-classical trajectory analyses show unexpected discrepancies.

Reaction probabilities are computed from both classical and quantum trajectories.

Abstract

Reaction paths and classical and quantum trajectories are studied within a generalized Hamilton-Jacobi framework, which allows to put on equal footing topology and dynamics in chemical reactivity problems. In doing so, we show how high-dimensional problems could be dealt with by means of Caratheodory plots or how trajectory-based quantum-classical analyses reveal unexpected discrepancies. As a working model, we consider the reaction dynamics associated with a Mueller-Brown potential energy surface, where we focus on the relationship between reaction paths and trajectories as well as on reaction probability calculations from classical and quantum trajectories.