Obtaining time-dependent multi-dimensional dividing surfaces using Lagrangian descriptors

Highlights: • Lagrangian Descriptors lead to rates in driven higher-dimensional chemical reactions. • Multi-dimensional non-recrossing dividing surfaces can be constructed without recourse to perturbation theory. • Rates and mechanisms are benchmarked on a 4-dimensional model of a chemical reaction. Dynamics between reactants and products are often mediated by a rate-determining barrier and an associated dividing surface leading to the transition state theory rate. This framework is challenged when the barrier is time-dependent because its motion can give rise to recrossings across the fixed dividing surface. A non-recrossing time-dependent dividing surface can nevertheless be attached to the TS trajectory resulting in recrossing-free dynamics. We extend the formalism—constructed using Lagrangian Descriptors—to systems with additional bath degrees of freedom. The propagation of reactant ensembles provides a numerical demonstration that our dividing surface is recrossing-free and leads to exact TST rates.