(113a) Coarse-Grained Lattice Monte Carlo Simulations of Continuous Systems

Monte Carlo and its dynamic variant, kinetic Monte Carlo, are used extensively to simulate an enormous range of material properties. In both cases, restricting particle positions to fixed lattice sites can substantially increase the computational efficiency of a simulation, and this benefit increases as the lattice becomes coarser. However, the confinement of particle positions to a rigid lattice necessarily reduces the available configurational degrees of freedom in a system and this constraint can become very important at elevated temperatures [1,2].

In this presentation, we discuss a new technique for performing Metropolis Monte Carlo (MMC) simulations of continuous systems on coarse rigid lattices, while preserving the phase-space contributions of the missing degrees-of-freedom. Previous Metropolis Monte Carlo modeling studies have shown that lattice representations are able to correctly capture the phase behavior of continuous fluids if the discretization is sufficiently fine [3], but the potential computational gains are limited by the required lattice resolution. The present approach relies on the pre-computation of coarse-grained potentials from equilibrium sampling of small systems. The potentials are generated in such a way so as to be scalable to different temperatures without the need for a new set of calculations. It is shown that the approach is able to capture both equilibrium (such as phase diagram features) and non-equilibrium (transport) features of the continuous system, even when the rigid lattice becomes highly coarse.

The approach then is extended to lattice kinetic Monte Carlo (LKMC) simulations by developing a method to map particle motions in a continuous system onto a finite set of discrete rate expressions. Both accuracy and performance are discussed with examples based on the Lennard-Jones potential.

[1] S. S. Kapur, M. Prasad, J. C. Crocker, T. Sinno, Role of configurational entropy in the thermo-dynamics of clusters of point defects in crystalline solids, Phys. Rev. B 72, 014119 (2005).

[2] J. Dai, W. D. Seider and T. Sinno, Lattice kinetic Monte Carlo simulations of defect evolution in crystals at elevated temperature. Molecular Simulation, 32, 305 (2006).

[3] A. Z. Panagiotopoulos, On the equivalence of continuum and lattice models for fluids. J. Chem. Phys., 112, 7132 (2000).