Surface self-diffusion of hydrogen on a model potential: Quantum aspects and correlated jumps

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Abstract
We have included the proper quantum effects into the theory for thermal rate constants between any two sites of a multisite system by Voter and Doll [J. Chem. Phys. 8 2, 80 (1985)]. The thermal rate constants are expressed in terms of quantum flux correlation functions and we apply the formalism to surface self‐diffusion. Using a potential energy function that previously has been used in order to describe hydrogen adsorbed on a coppersurface, we determine the quantum corrections to the classical transition state theory, both those associated with bound degrees of freedom and those associated with tunneling and nonclassical reflexion. Our results agree quite well with previous calculations. To evaluate the temperature and time propagators necessary for the quantum dynamics we use a fast Fourier transform technique and we demonstrate that it is feasible to study the probability of correlated jumps in the case of surface diffusion. By solving for the three‐dimensional and classical motion for the hydrogen atom it is shown that it is crucial to go beyond a one‐dimensional treatment in order to study the possibility of correlated jumps. In this preliminary study we have neglected the motion of the substrate degrees of freedom, but the main aim with the presented approach is to be able to treat quantitatively the multidimensional case.