Diffusion of hydrogen, deuterium, and tritium on the (100) plane of copper: Reaction-path formulation, variational transition state theory, and tunneling calculations

We have applied variational transition state theory in a reaction-path formulation, using semiclassical methods of calculating multidimensional tunneling probabilities, to the surface diffusion of H, D, and T on the (100) surface of fcc Cu cover the temperature range 100-1000 K using the empirical pairwise interaction potential of Gregory, Gelb, and Silbey. We show that the reaction-path formalism offers a tractable way to deal with multidimensional motion of an adsorbate across a many-atom substrate. Our calculations show that the variational transition states for these systems are located at the saddle point for all temperatures studied. We find very large quantal effects, due to zero point quantization and tunneling, with the largest effects, over four orders of magnitude, for H at 100 K. At this temperature, tunneling alone increases the surface diffusion coefficient by three orders of magnitude. Even at 140 K, the tunneling effect increases the surface diffusion coefficients of H, D, and T by factors 3.0, 1.6, 1.3, respectively. Unfortunately, there are no experimental data available for this system for comparison, but in light of the very large quantal effects, we are encouraged by the reasonably good agreement of our results for T ≥ 110 K with those of Valone, Voter, and Doll, who included quantal effects by a completely different method.