Random Force in Molecular Dynamics with Electronic Friction

Abstract

Originally conceived to describe thermal diffusion, the Langevin equation includes both a frictional drag and a random force, the latter representing thermal fluctuations first seen as Brownian motion. The random force is crucial for the diffusion problem as it explains why friction does not simply bring the system to a standstill. When using the Langevin equation to describe ballistic motion, the importance of the random force is less obvious and it is often omitted, for example, in theoretical treatments of hot ions and atoms interacting with metals. Here, friction results from electronic nonadiabaticity (electronic friction), and the random force arises from thermal electron–hole pairs. We show the consequences of omitting the random force in the dynamics of H-atom scattering from metals. We compare molecular dynamics simulations based on the Langevin equation to experimentally derived energy loss distributions. Despite the fact that the incidence energy is much larger than the thermal energy and the scattering time is only about 25 fs, the energy loss distribution fails to reproduce the experiment if the random force is neglected. Neglecting the random force is an even more severe approximation than freezing the positions of the metal atoms or modelling the lattice vibrations as a generalized Langevin oscillator. This behavior can be understood by considering analytic solutions to the Ornstein–Uhlenbeck process, where a ballistic particle experiencing friction decelerates under the influence of thermal fluctuations.

Effective medium theory for bcc metals: electronically non-adiabatic H atom scattering in full dimensions

“…On the other hand, there is a distinct difference in the energy loss distributions when comparing different surface facets or different temperatures. The effect of temperature has been reported previously 14 and arises from the reduced influence of the random force at low temperature.…”

“…We emphasize that neglecting the random force, as has sometimes been done, 44 can lead to spurious results. 14 The EMT-PES and the Langevin propagator integrating eqn (30) are implemented in our homemade program md_tian2 available at a public repository. 45…”

“…This introduces a temperature dependent random force that ensures detailed balance. 14 Despite the LDFA works well in modeling the ehp influence on the dynamics of atoms at metal surfaces, it is not applicable for molecule-surface scattering. The contribution due to the molecular electronic structure into the friction can be taken into account by the orbital-dependent friction approach.…”

Translational Inelasticity of Hydrogen Atoms Scattering off Hydrogen-Covered W(110) Surfaces

“…Within the LDFA, η el ( r i ) is taken as that of the same atom moving in a homogeneous free electron gas with the electronic density equal to that of the bare surface at the same position r i . ,,, The random force, F L ( t ), related to the friction force by the second fluctuation-dissipation theorem, accounts for electron temperature and is taken here as a Gaussian white noise . In the present calculations, electronic temperature is set at Ts = 300 K. The random force term has often been neglected when surface electron temperature is not high, as in the works rationalizing the relaxation of H hot atoms on a bare metallic surface, − or diatom recombination. ,, However, this term is crucial when elementary surface processes are triggered by intense laser pulses, causing electrons to be heated up to a few thousands of Kelvin. ,− Recently, this term has been also shown to sensibly alter the shape of specular energy loss spectra of hydrogen scattering from clean metal surfaces even at ambient temperatures.…”

“…18,19,31 However, this term is crucial when elementary surface processes are triggered by intense laser pulses, causing electrons to be heated up to a few thousands of Kelvin. 27,32−38 Recently, this term has been also shown to sensibly alter the shape of specular energy loss spectra of hydrogen scattering from clean metal surfaces 39 even at ambient temperatures. Dissipation to surface phonons is here neglected on the grounds that, as recently demonstrated, 3,4,28,29,40−42 dissipation to electrons largely dominates the relaxation of hydrogen on metals at short time scales.…”