It was recalled that, although theories (transition state, jump diffusion) which were commonly used to describe surface diffusion could not provide information concerning the motion of adsorbed particles within potential wells, interesting results had been obtained by means of molecular dynamics simulations. The latter revealed enhanced oscillations in the mean-square displacement before the linear time behavior was reached. Evidence was also found for long correlated jumps. Here, single-particle diffusion on surfaces was studied within the framework of the continuous Brownian model (Klein-Kramers equation). The Klein-Kramers dynamics were first analyzed by making qualitative assumptions concerning the dissipation integral, and by obtaining necessary and sufficient conditions for typical time scales in order to obtain various migration mechanisms. In the case of high barriers, conditions were found for multiple jumps to be inhibited or to occur with low or high probabilities. Starting from the dynamic structure factor, the relevant correlation functions (velocity self-correlation spectrum, mean-square displacement) were then evaluated; together with the jump probabilities. Given these values of the parameters, diffusion proceeded via a considerable fraction of multiple correlated jumps, and many oscillations were found in the mean-square displacement; in good agreement with molecular dynamics results.

R.Ferrando, R.Spadacini, G.E.Tommei, G.Caratti: Surface Science, 1994, 311[3], 411-21