The lattice kinetic Monte Carlo method (LKMC) is an efficient approach for simulating dynamical evolution in microscopic systems such as point defect aggregation in crystals because it overcomes the primary temporal bottleneck in molecular dynamics simulations – the vibrational frequency. On the other hand, single atomic resolution LKMC, in which one lattice site is assigned per LKMC degree-of-freedom, is still highly constrained in scope and is limited to at most the micron scale for many problems of interest [1,2]. Recently, there has been much interest in the development of coarse-grained LKMC simulations in which multiple lattice sites are spatially grouped together into coarse-grained cells, which in turn evolve via a series of coarse-grained hops [1,2]. A key step in formulating such approaches is the so-called closure rule, which dictates how all the single-atom hopping rates are averaged within a coarse-grained cell.

In this paper we present a detailed analysis of LKMC coarse-graining approaches based on the overall framework published previously by Vlachos and coworkers [1,2]. The analysis is developed using a two-dimensional square lattice on which a system of strongly interacting particles is allowed to evolve (reversibly) into clusters. Effective closure methods are developed to account for the inhomogeneities that result in each coarse cell because of strong inter-particle interactions. Specifically, the limitations of the local mean-field approximation, which assumes that particles in a coarse cell are homogeneously distributed [1], are discussed and systematic computationally efficient approaches to improve it are presented. In each case, the overall cluster size distribution and individual cluster structures are used to assess the accuracy of the coarse-graining approach. Finally, the effects of the inter-particle interaction characteristics, such as interaction length and strength, on the accuracy of the coarse-graining schemes are described.

[1] M. A. Katsoulakis and D. G. Vlachos, Coarse-grained stochastic processes and kinetic Monte Carlo simulations for the diffusion of interacting particles. J. Chem. Phys., 119 (2003) 9412. [2] A. Chatterjee and D. G. Vlachos, Spatially adaptive lattice coarse-grained Monte Carlo simulations for diffusion of interacting molecules. J. Chem. Phys., 121 (2004) 11420.