Molecular electronic junctions with stochastic structural transitions

TL;DR

This paper introduces a theoretical method to incorporate stochastic molecular structural fluctuations into electron transport calculations using nonequilibrium Green's functions, accounting for dynamic transitions like hydrogen bond formation and breaking.

Contribution

The authors develop a novel approach employing stochastic calculus to derive equations for averaged Green's functions, enabling analysis of dynamical molecular transitions in transport properties.

Findings

Derived closed-form equations for stochastically averaged Green's functions.

Provided expressions for current that include transition probabilities and dynamics.

Illustrated the approach with several example applications.

Abstract

We present a theoretical approach to include dynamical aspects of molecular structural fluctuations, such as, for example, forming and breaking hydrogen bonds, isomerizations, and dynamical supramolecular structures, in nonequilibrium Green's functions electron transport calculations. Structural transitions are treated as a stochastic telegraph process, and the primary quantity of interest is a retarded Green's function averaged over realizations of a stochastic process. Using the Novikov-Furutsu functional stochastic calculus method, we derive equations of motion for stochastically averaged retarded Green's function in closed form. Consequently, we obtain the expression for electric current averaged over transitions, which depends not only on probabilities of observing particular molecular structures but also on the dynamics. However, the proposed method has a significant limitation - we have to assume that the imaginary parts of retarded self-energies produced by left and right electrodes are proportional to each other; this significantly restricts possible applications of the theory. Several examples illustrate the proposed approach.