Classical-Limit Polariton Chemistry

Abstract

The reaction dynamics of systems under strong vibrational coupling is an outstanding problem in chemistry. The reported experimental result is as follows: when molecules are placed inside an optical cavity resonant with a vibrational transition dipole, the rates of certain chemical reactions can be enhanced or reduced, dependent upon the cavity tuning. Describing the evolution of molecules strongly coupled to optical cavities has eluded theorists, as both traditional adiabatic and non-adiabatic rate theories fail to account for observed experiments. Certain classical dynamical schemes based on the cavity Born-Oppenheimer approximation have presented promising results to recover the frequency-dependent rate reduction. The theory draws heavily from the non-Markovian solvent coupling theory of Grote and Hynes.

This paper generalizes this classical-limit polariton chemistry scheme to a reactive system with an arbitrary number of coordinates, inspired by the collinear hydrogen atom exchange model. I provide my own derivation of the cavity Born-Oppenheimer approximation. Then, I demonstrate the formal equivalence of the time evolution of the reaction coordinates to a system of $d$ coupled stochastic differential equations, which exhibit generalized Langevin dynamics. I discuss the implications and limiting cases of this new model, and attempt some preliminary numerical investigations. Although not robust, the initial simulations suggest a strong dependence on the cavity and bath parameters of the transmission time of the reactive coordinate.