Off-Lattice Kinetic Monte Carlo Methods
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Exact modeling of the dynamics of chemical and material systems over experimentally relevant time scales still eludes us even with modern computational resources. Fortunately, many systems can be described as rare event systems where atoms vibrate around equilibrium positions for a long time before a transition is made to a new atomic state. For those systems, the kinetic Monte Carlo (KMC) algorithm provides a powerful solution. In traditional KMC, mechanism and rates are computed beforehand, limiting moves to discretized positions and largely ignoring strain. Many systems of interest, however, are not well-represented by such lattice-based models. Moreover, materials often evolve with complex and concerted mechanisms that cannot be anticipated before the start of a simulation. In this chapter, we describe a class of algorithms, called off-lattice or adaptive KMC, which relaxes both limitations of traditional KMC, with atomic configurations represented in the full configuration space and reaction events are calculated on-the-fly, with the possible use of catalogs to speed up calculations. We discuss a number of implementations of off-lattice KMC developed by different research groups, emphasizing the similarities between the approaches that open modeling to new classes of problems.
This work was supported in part by a grant from the Natural Science and Engineering Research Council of Canada. MT and NM are grateful to Calcul Québec and Compute Canada for providing extensive computer time and computer access. The work in Austin was supported by the National Science Foundation (CHE-0645497, CHE-1152342, and CHE-1534177) and the Welch Foundation (F-1841). Sustained computational resources have been provided by the Texas Advanced Computing Center.
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