A flux-flux cross-correlation function approach to self-diffusion of hydrogen atom on a Cu(111) surface

We have employed a flux-flux cross-correlation function approach (CCFA) to calculate quantum thermal rate constants of reactions for which an auto-correlation function approach (ACFA) is not adequate. In CCFA, two dividing surfaces partition a system into three regions, while in ACFA, two channels are defined by a dividing surface. Therefore, the CCFA method is appropriate for multi-channel reactions. In this paper, we show the efficiency of CCFA for multi-channel reactions. For example, we have examined self-diffusion of a hydrogen atom on a rigid Cu(111) surface. We introduce closed dividing surfaces that subdivide the potential energy surface for each channel. A combination of the closed dividing surfaces and CCFA allows us to calculate rate constants for both single and multi-hopping modes directly. Then, we calculate a diffusion constant without the usual uncorrelated hops approximation, using instead the calculated site-to-site hopping rates, thus showing the importance of multihops.