First-passage time theory of activated rate chemical processes in electronic molecular junctions

TL;DR

This paper develops a comprehensive reaction-rate theory for current-activated chemical reactions in molecular junctions, integrating nonequilibrium Green's functions, Fokker-Planck dynamics, and first-passage time analysis to understand reaction kinetics under electrical bias.

Contribution

It introduces a novel theoretical framework combining NEGF, Fokker-Planck, and Kramers' theory to analyze reaction rates in electronically driven molecular systems, revealing effects like Landauer's blowtorch.

Findings

Localized heating influences reaction rates.

Configuration-dependent viscosity affects reaction dynamics.

Landauer's blowtorch effect emerges naturally in the model.

Abstract

Confined nanoscale spaces, electric fields and tunneling currents make the molecular electronic junction an experimental device for the discovery of new, out-of-equilibrium chemical reactions. Reaction-rate theory for current-activated chemical reactions is developed by combining a Keldysh nonequilibrium Green's functions treatment of electrons, Fokker-Planck description of the reaction coordinate, and Kramers' first-passage time calculations. The NEGF provide an adiabatic potential as well as a diffusion coefficient and temperature with local dependence on the reaction coordinate. Van Kampen's Fokker-Planck equation, which describes a Brownian particle moving in an external potential in an inhomogeneous medium with a position-dependent friction and diffusion coefficient, is used to obtain an analytic expression for the first-passage time. The theory is applied to several transport scenarios: a molecular junction with a single, reaction coordinate dependent molecular orbital, and a model diatomic molecular junction. We demonstrate the natural emergence of Landauer's blowtorch effect as a result of the interplay between the configuration dependent viscosity and diffusion coefficients. The resultant localized heating in conjunction with the bond-deformation due to current-induced forces are shown to be the determining factors when considering chemical reaction rates; each of which result from highly tunable parameters within the system.