Nonequilibrium reaction rate theory: Formulation and implementation within the hierarchical equations of motion approach

TL;DR

This paper develops a fully quantum mechanical, numerically exact method to calculate chemical reaction rates under nonequilibrium conditions, such as in molecular junctions, using an extended flux correlation function formalism and hierarchical equations of motion.

Contribution

It introduces a novel extension of the flux correlation function formalism combined with hierarchical equations of motion for nonequilibrium reaction rate calculations.

Findings

Successfully applied to current-induced proton transfer in molecular junctions.

Demonstrates how bias voltage and coupling affect reaction rates.

Provides a new tool for studying reactions in nonequilibrium quantum environments.

Abstract

The study of chemical reactions in environments under nonequilibrium conditions has been of interest recently in a variety of contexts, including current-induced reactions in molecular junctions and scanning tunneling microscopy experiments. In this work, we outline a fully quantum mechanical, numerically exact approach to describe chemical reaction rates in such nonequilibrium situations. The approach is based on an extension of the flux correlation function formalism to nonequilibrium conditions and uses a mixed real and imaginary time hierarchical equations of motion approach for the calculation of rate constants. As a specific example, we investigate current-induced intramolecular proton transfer reactions in a molecular junction for different applied bias voltages and molecule-lead coupling strengths.