We calculate surface-diffusion coefficients for hydrogen on the (100) face of nickel over a temperature range from 40 to 1000 K. The calculations include tunneling contributions from discrete-energy states. The results are in very good agreement with experiment. We find a dramatic leveling off of the Arrhenius plot at approximately 66 K, below which temperature the diffusion coefficient is virtually independent of temperature. The existence and magnitude of such a transition temperature agrees well with experimental findings and also with previous theoretical work based on path-integral transition-state theory. The present treatment provides insight into the origin of the effect. We evaluate the transition temperature analytically in terms of local quadratic approximations to the potential and find it to correspond approximately to the temperature at which the various low-energy bound-reactant states contribute equally to the diffusion coefficient. The nearly temperature-independent diffusion rate below the transition temperature corresponds to tunneling primarily from the ground state. The analytical expression for the transition temperature depends strongly on the magnitude of the frequency at the top of the potential barrier. We also demonstrate that this transition temperature does not correspond to a transition from over-barrier activated diffusion to tunneling diffusion, which has been previously proposed, and that the surface-diffusion process proceeds largely by a tunneling mechanism even well above the transition temperature.
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