Path Integral Approach to the Calculation of Reaction Rates for a Reaction Coordinate Coupled to a Dual Harmonic Bath

TL;DR

This paper introduces a path integral method for calculating reaction rates in complex molecular systems, effectively handling a dual harmonic bath environment with both intramolecular modes and an external spectral density.

Contribution

It develops a novel numerical approach based on path integrals and influence functionals for reaction rate calculations in systems with dual harmonic baths, combining reaction surface Hamiltonian and spectral density models.

Findings

Applied to H-transfer in 6-Aminofulvene-1-aldimine, demonstrating the method's effectiveness.

Derived general equations linking rate constants to influence functionals.

Implemented approximations for efficient numerical computation.

Abstract

We present a new method for the numerical calculation of canonical reaction rate constants in complex molecular systems, which is based on a path integral formulation of the flux-flux correlation function. Central is the partitioning of the total system into a relevant part coupled to a dual bath. The latter consists of two parts: First, a set of strongly coupled harmonic modes, describing, for example, intramolecular degrees of freedom. They are treated on the basis of a reaction surface Hamiltonian approach. Second, a set of bath modes mimicking an unspecific environment modeled by means of a continuous spectral density. After deriving a set of general equations expressing the canonical rate constant in terms of appropriate influence functionals, several approximations are introduced to provide an efficient numerical implementation. Results for an initial application to the H-transfer in 6-Aminofulvene-1-aldimine are discussed.