Lagrangian Descriptors of Thermalized Transition States on Time-Varying Energy Surfaces

Thermalized chemical reactions driven under dynamical load are characteristic of activated dynamics for arbitrary nonautonomous systems. Recent generalizations of transition state theory to obtain formally exact rates have required the construction of a time-dependent transition state trajectory. Here, we show that Lagrangian descriptors can be used to obtain this structure directly. By developing a phase space separatrix that is void of recrossings, these constructs allow for the principal criterion in the implementation of modern rate theories to be satisfied. Thus, the reactive flux over a time-varying barrier can be determined without ambiguity in chemical reactions. The generality of the formalism suggests that this approach is applicable to any activated system subjected to arbitrary driving and thermal fluctuations.