Electronic friction near metal surfaces: a case where molecule-metal couplings depend on nuclear coordinates

TL;DR

This paper derives a generalized form of electronic friction for molecules near metal surfaces, accounting for coordinate-dependent molecule-metal couplings, revealing significant effects on molecular dynamics beyond previous constant-coupling models.

Contribution

It extends previous models by deriving an explicit form of electronic friction that includes coordinate-dependent couplings using non-equilibrium Green's functions.

Findings

Coordinate-dependent couplings introduce new damping and stochastic forces.

Violating the Condon approximation significantly impacts molecular dynamics.

Numerical results show large effects compared to constant-coupling models.

Abstract

We derive an explicit form for the electronic friction as felt by a molecule near a metal surface for the general case that molecule-metal couplings depend on nuclear coordinates. Our work generalizes a previous study by von Oppen et al [Beilstein Journal of Nanotechnology, 3, 144, 2012], where we now go beyond the Condon approximation (i.e. molecule-metal couplings are not held constant). Using a non-equilibrium Green's function formalism in the adiabatic limit, we show that fluctuating metal-molecule couplings lead to new frictional damping terms and random forces, plus a correction to the potential of mean force. Numerical tests are performed and compared with a modified classical master equation; our results indicate that violating the Condon approximation can have a large effect on dynamics.