Adsorbate migration on a solid surface: The connection between hopping dynamics and the atom-surface interaction energy

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Abstract
The migration of an adsorbed atom at moderate temperatures is described in terms of uncorrelated jumps between lattice sites which lead to diffusion. It is widely believed that a jumping rate coefficient and therefore a diffusion coefficient can be defined only if energy exchange with the moving lattice or collisions with randomly distributed impurities give the motion of the adsorbate a random character. In this paper we examine systematically a suggestion of Haug, Wanhstrom, and Metiu, who conjectured that coupling between the adsorbate motion along the surface and its motion perpendicular to it can provide the necessary randomization and, in particular, make possible the definition of a hopping rate coefficient. We calculate the flux–flux correlation functions needed for describing the dynamics of single and double jumps by using a set of simple, but reasonably realistic, adsorbate-surface interactions. In all these calculations the lattice atoms are held fixed. We show that in spite of this, the correlation functions converge and rate constants can be defined for many of the potentials. We study in detail those features of the potential energy surface (PES) that lead to convergence and also how the shape of the PES influences the amount of recrossing (i.e., the accuracy of the transition state theory) and multiple jumping. Our results indicate that it is possible to develop a correction to the transition state theory which includes the effect of thermal fluctuations and calculates the recrossing correction by holding the lattice atoms fixed. This saves substantial computer time.