Understanding chemical reactions within a generalized Hamilton–Jacobi framework

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 Carathéodory plots or how trajectory-based quantum–classical analyses reveal unexpected discrepancies. As a working model, we consider the reaction dynamics associated with a Müller–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.