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

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 the Keldysh nonequilibrium Green’s function treatment of electrons, Fokker–Planck description of the reaction coordinate, and Kramers first-passage time calculations. The nonequilibrium Green’s functions (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 is shown to be the determining factors when considering chemical reaction rates, each of which results from highly tunable parameters within the system.

Emergence of negative viscosities and colored noise under current-driven Ehrenfest molecular dynamics

“…It is instead convenient to adopt a quasi-classical approach in which the nuclei are assumed to behave according to classical equations of motion under the effects of the quantum tunneling electrons. This enables the description of arbitrary molecular potentials for systems along with being able to capture experimentally observed phenomena such as current-induced heating [32][33][34][35][36][37] along with bond rupture and electronically induced chemical reactions [38][39][40][41], at the cost of a fully quantum description.…”

“…A common accompanying assumption is the clear separation of time-scales between the classically described nuclei and the electronic environment, which through the use of a perturbative approximation allows for a Langevin description of the classical particle [32][33][34][35][36][41][42][43][44][45][46][47]. In this regime, the particle dynamics are described by stochastic differential equations in which nuclei evolve under the influence of a frictional force which acts to subdue nuclear vibrations, and a stochastic force which delivers energy to the nuclei; the balance of these two forces yielding the temperature of the molecule.…”

“…In this regime, the particle dynamics are described by stochastic differential equations in which nuclei evolve under the influence of a frictional force which acts to subdue nuclear vibrations, and a stochastic force which delivers energy to the nuclei; the balance of these two forces yielding the temperature of the molecule. In addition, the influence of the electronic environment on the molecular potential is captured by an additional renormalization term which can naturally describe switching phenomena and bond-stability [32,35,41,44]. The Langevin approach has had great success in the description and simulation of large-scale systems corresponding to real molecular electronic junction configurations, such as for graphene nanoribbons [48,49].…”

“…In an exact theory, the stochastic force at a given time should have some dependency on the history of the classical coordinate; this corresponds to colored noise [58]. However, it is often computationally infeasible to account for this and it becomes necessary to employ the white-noise approximation; this states that the stochastic force is entirely uncorrelated at different times [32,33,39,41,42,44]. While the white-noise approximation proves to be applicable in regimes showing a clear time-scale separation between electronic and classical coordinates, we show here that it must be called into question in cases where the time-scale separation becomes less defined.…”

Unraveling current-induced dissociation mechanisms in single-molecule junctions

“…11,43 Similarly, the study of mechanical instabilities of molecular junctions under the influence of nonconservative current-induced forces has so far been based on classical treatments of the nuclei and/or used the harmonic approximation for the description of the nuclear potentials. [44][45][46][47][48] It is also noted that the theoretical framework to study the related process of dissociative electron attachment in the gas phase is well established, [49][50][51][52] but this problem is conceptually simpler because only a single electron that is scattered from the molecule has to be considered. Moreover, the processes of light-induced dissociation or desorption of molecules at surfaces has also been studied in great detail theoretically.…”