Joint Theoretical Study on Quantum Rate Processes

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We have employed a flux-flux cross-correlation function approach (CCFA) to calculate the quantum thermal rate constants of reactions for which an auto-correlation function, approach (ACFA) is not adequate. In the former approach, two dividing surfaces partition a system into three regions, while in the latter approach, 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 the CCFA to multi-channel reactions, and extend it to surface reactions, where there are an infinite number of localized channels. For example, we have adapted a model that forms a stable complex in a well between two barriers, and have investigated the self-diffusion of a hydrogen atom on a Cu(111) surface. In the former reaction, in addition to defining the complex channel, the cross-correlation function can avoid the oscillations seen in the ACFA. In the latter reaction, we introduce closed dividing surfaces that subdivide the potential energy surface for each channel. The combination of closed dividing surfaces and the CCFA provides well-defined rate constants for both single and multi-hopping rates.