A local superbasin kinetic Monte Carlo method.

We present a local superbasin kinetic Monte Carlo (LSKMC) method that efficiently treats multiple-time-scale problems in kinetic Monte Carlo (KMC). The method is designed to solve the small-barrier problem created by groups of recurrent free-energy minima connected by low free-energy barriers and separated from the full phase space of the system by high barriers. We propose an algorithm to detect, on the fly, groups of recurrent free-energy minima connected by low free-energy barriers and to consolidate them into "superbasins," which we treat with rate equations and/or absorbing Markov chains. We discuss various issues involved with implementing LSKMC simulations that contain local superbasins and non-superbasin events concurrently. These issues include the time distribution of superbasin escapes and interactions between superbasin and non-superbasin states. The LSKMC method is exact, as it introduces no new approximations into conventional KMC simulations. We demonstrate various aspects of LSKMC in several examples, which indicate that significant increases in computational efficiency can be achieved using this method.