Coarse-Grained Lattice Monte Carlo Simulation of Continuous Systems

In this thesis, a coarse-grained lattice Metropolis Monte Carlo (CG-MMC) framework is presented for simulating atomic and molecular fluid systems described by standard molecular force-fields. The CG-MMC technique is demonstrated to be highly thermodynamically consistent with the underlying full resolution problem using a series of detailed comparisons, including vapor-liquid equilibrium phase envelopes and spatial density distributions for the square well, Lennard-Jones argon, and simple point charge (SPC) water models. The principal computational bottleneck associated with computing a coarse-grained interaction function for evolving particle positions on the discretized domain is addressed by the introduction of new closure approximations. It is shown that the coarse-grained potential can be computed at multiple temperatures and scales using a single set of free energy calculations. Theoretical underpinnings of CG-MMC are further discussed by addressing additional potential sources of error as well as computational advantages. Two important applications of CG-MMC model are presented. The first application explores the validity of CG-MMC model in non-equilibrium simulations. A variant of the CG-MMC method is developed that enables simulation of coarse-grained non-equilibrium trajectories. It is shown that the resulting NECG-MMC method generates trajectories that are consistent with coarse-grained Langevin dynamics. The second application explores the validity of CG-MMC model in large-scale simulation. Multi-particle move capability is developed and the scaling properties of the CG-MMC approach are studied. A non-equilibrium simulation at large scale is used as a demonstration.