Embedded-cluster model for the effect of phonons on hydrogen surface diffusion on copper

We treat surface diffusion of H on a (100) plane of copper by a model involving 21 degrees of freedom, three for the H and three each for six surface atoms. The six movable surface atoms are embedded on the surface of a bulk crystal. The interaction potential consists of pairwise H–Cu and Cu–Cu interactions, and the dynamics are treated by variational transition state theory with a small-curvature-approximation semiclassical adiabatic ground-state transmission coefficient. The classical barrier height for surface diffusion on the assumed potential energy surface is 11.7 kcal/mol, and we find an Arrhenius activation energy that increases from about 6 kcal/mol, below 160 K, to about 11 kcal/mol, above 400 K. The rate is dominated by tunneling at and below about 200 K. As compared to a treatment with a rigid surface the rate is increased by factors of 16, 3.1, 2.4, 1.6, and 1.3 at 110, 160, 200, 400, and 1000 K, respectively.