A velocity reset method of simulating thermal motion and damping in gas–solid collisions

Abstract

We present a velocity reset procedure for the approximate description of the molecular dynamics of a tractable subset of the atoms composing a macroscopic solid which is subjected to collisions. The coupling of the subset to the remainder (the reservoir) is taken into account in a stochastic manner by periodically resetting the velocities of subset particles which interact with the reservoir. The Cartesian velocity components are reset to vnew =(1−θ)1/2vold +θ1/2vT, where vold is the previous velocity, vT is a random velocity chosen from a Maxwellian distribution at temperature T, and θ is a parameter which controls the strength of the reset. In the limit θ=1 and all subset particles are reset, the method is similar to Andersen’s thermostat procedure [J. Chem. Phys. 72, 2384 (1980)]. In the double limit that θ→0 and the interval between resets Δtrs →0 such that β=θ/2Δtrs is fixed, the equations of motion for the subset reduce to Langevin form, where β is the frictional damping rate. This partial velocity reset method is a computational procedure allowing for (1) relaxation dynamics which are equivalent to the frictional damping theories, (2) inclusion of nonzero temperature effects on damping, (3) rapid generation of initial states selected from a canonical ensemble in preparation for individual transient scattering events, and, (4) simulations akin to molecular dynamics. We show that the velocity reset method reproduces previous calculations of the energy accommodation for the collision of an atom with a simple cubic lattice. Two new simulations of the Ag fcc 111 crystal face are done using a pairwise Lennard-Jones interaction. These involve thermostating to a fixed temperature and computation of spectral densities and autocorrelations.