Multiple hops in multidimensional activated surface diffusion

Kramers' theory is used to derive simple expressions for the hopping distribution in multidimensional activated surface diffusion. The expressions are tested against one- and two-dimensional numerically exact simulations. The present expressions are valid provided that the average energy loss of the particle as it goes from one barrier to the next is of the order of k(B)T or more. The ratio of double hops to single hops is shown to obey an Arrhenius-like behavior, with a prefactor that is proportional to root T The added activation energy is proportional to the average energy loss of the diffusing particle. The magnitude of the energy loss depends on the coupling between modes: the stronger the coupling, the larger the energy loss and the smaller is the multiple hopping probability. The theory is used to analyze recent experiments on the diffusion of the Pt atom on a Pt(110)-(1 x 2) missing row reconstructed surface. (C) 1999 Elsevier Science B.V. All rights reserved.