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

## TL;DR

This paper extends a Lagrangian descriptor-based method to construct time-dependent, multi-dimensional dividing surfaces that eliminate recrossings, enabling exact transition state theory rates in complex, time-dependent systems.

## Contribution

It introduces a formalism for constructing recrossing-free, time-dependent dividing surfaces in systems with multiple degrees of freedom using Lagrangian descriptors.

## Key findings

- Dividing surfaces are recrossing-free in numerical simulations.
- The method yields exact transition state theory rates.
- Extension to systems with bath degrees of freedom is demonstrated.

## Abstract

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.