Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory

TL;DR

This paper introduces a modified flux correlation function for nonadiabatic rate calculations that reduces oscillations in the weak-coupling limit, enabling more accurate and efficient trajectory-based simulations of complex systems.

Contribution

It derives a new correlation function that remains non-oscillatory in the weak-coupling limit and links trajectory simulations to a generalized quantum transition-state theory.

Findings

The modified correlation function is non-oscillatory at weak coupling.

Trajectory simulations initialized near potential energy surface crossings.

Connection to Marcus theory in the classical harmonic limit.

Abstract

There is currently much interest in the development of improved trajectory-based methods for the simulation of nonadiabatic processes in complex systems. An important goal for such methods is the accurate calculation of the rate constant over a wide range of electronic coupling strengths and it is often the nonadiabatic, weak-coupling limit, which being far from the Born-Oppenheimer regime, provides the greatest challenge to current methods. We show that in this limit there is an inherent sign problem impeding further development which originates from the use of the usual quantum flux correlation functions, which can be very oscillatory at short times. From linear response theory, we derive a modified flux correlation function for the calculation of nonadiabatic reaction rates, which still rigorously gives the correct result in the long-time limit regardless of electronic coupling strength, but unlike the usual formalism is not oscillatory in the weak-coupling regime. In particular, a trajectory simulation of the modified correlation function is naturally initialized in a region localized about the crossing of the potential energy surfaces. In the weak-coupling limit, a simple link can be found between the dynamics initialized from this transition-state region and an generalized quantum golden-rule transition-state theory, which is equivalent to Marcus theory in the classical harmonic limit. This new correlation function formalism thus provides a platform on which a wide variety of dynamical simulation methods can be built aiding the development of accurate nonadiabatic rate theories applicable to complex systems.