Hydrogen motion on a rigid Cu surface: The calculation of the site to site hopping rate by using flux–flux correlation functions

Abstract

We use the quantum flux–flux correlation function theory to calculate the rate coefficient for site-to-site hopping by a single hydrogen atom absorbed on a rigid Cu(100) surface. We investigate hydrogen dynamics during barrier crossing and determine the time scales on which the hydrogen atom crosses or recrosses the barrier, as well as the time scale on which double jumps occur. We define two kinds of transition state theory rate coefficients: one (Miller and Tromp) which assumes that only the short time dynamics contributes to the rate coefficient and another which includes the effect of the earliest recrossing. We examine numerically the accuracy of these approximations and compare them to other transition state theory calculations and to our ‘‘exact’’ calculations. The simulations are also used to study the contribution of multiple jumps to the diffusion coefficient, to calculate the isotope effect on the rate coefficient and to determine the role of dimensionality in modeling surface diffusion. We find that the motion of the adsorbed atom perpendicular to the surface influences strongly the migration dynamics because the energy is very rapidly transferred back and forth between motion parallel and perpendicular to the surface. In particular this energy exchange process enhances the frequency of recrossing events and diminishes the frequency of the multiple jumps. We also make an extensive comparison between classical and quantum simulations.