We briefly present the theoretical framework of a hierarchical multi-scale approach, which is an ab initio-based stochastic method, and its applications to several chemical/physical kinetic processes on metallic surfaces. We first introduce necessary theoretical basis of ab initio and Monte Carlo (MC) methods, and then illustrate different Monte Carlo algorithms for important ensembles, including canonical and grand canonical ensembles. In the following section, we describe two important protocols which are essential to integrate ab initio data and MC models. Two examples are presented in order to elucidate the power of this multi-scale approach. The first example focuses on the combination of kinetic Monte Carlo and transition state theory. We discuss the detailed processes of performing kinetic Monte Carlo simulation on atomic diffusion on alloyed surface, including some technical aspects. In the second example, we presents a different way to account for the local environment-sensitive metal-catalyzed O2 dissociation reactions using combinatory techniques including cluster expansion and grand canonical Monte Carlo methods. This approach provides steady-state rates and rate derivatives that are comparable with experiments. Moreover, the connection between the feasible mechanisms and the observed kinetic behaviors can now be built.
Quantifying the multi-scale kinetic processes in soil environments: frontiers and challenges
