Efficiency Comparison of Single- and Multiple-Macrostate Grand Canonical Ensemble Transition-Matrix Monte Carlo Simulations

Abstract

Recent interest in parallelizing flat-histogram transition-matrix Monte Carlo simulations in the grand canonical ensemble, due to its demonstrated effectiveness in studying phase behavior, self-assembly and adsorption, has led to the most extreme case of single-macrostate simulations, where each macrostate is simulated independently with ghost particle insertions and deletions. Despite their use in several studies, no efficiency comparisons of these single-macrostate simulations have been made with multiple-macrostate simulations. We show that multiple-macrostate simulations are up to 3 orders of magnitude more efficient than single-macrostate simulations, which demonstrates the remarkable efficiency of flat-histogram biased insertions and deletions, even with low acceptance probabilities. Efficiency comparisons were made for supercritical fluids and vapor–liquid equilibrium of bulk Lennard-Jones and a three-site water model, self-assembling patchy trimer particles and adsorption of a Lennard-Jones fluid confined in a purely repulsive porous network, using the open source simulation toolkit FEASST. By directly comparing with a variety of Monte Carlo trial move sets, this efficiency loss in single-macrostate simulations is attributed to three related reasons. First, ghost particle insertions and deletions in single-macrostate simulations incur the same computational expense as grand canonical ensemble trials in multiple-macrostate simulations, yet ghost trials do not reap the sampling benefit from propagating the Markov chain to a new microstate. Second, single-macrostate simulations lack macrostate change trials that are biased by the self-consistently converging relative macrostate probability, which is a major component of flat histogram simulations. Third, limiting a Markov chain to a single macrostate reduces sampling possibilities. Existing parallelization methods for multiple-macrostate flat-histogram simulations are shown to be more efficient than parallel single-macrostate simulations by approximately an order of magnitude or more in all systems investigated.

Flat-Histogram Monte Carlo Simulation of Water Adsorption in Metal–Organic Frameworks

“…The second move is another canonical move, based on an extension of the AVBMC3 move, which we label AVBMC4. A full description of this AVB move is given in ref and described in Section SI.3 of the SI but may be summarized as a move that selects two target, nonbonded SPC/E molecules and then attempts to move a third bonded molecule from one target molecule to the other. The AVB GC transfer move is simply a GC transfer move that preferentially inserts (deletes) an SPC/E molecule in (from) the bonded region of a target molecule .…”

“…The chemical potentials were chosen to yield local maxima in ln Π(N;μ) that aid explanatory discussion. The macrostate domains were divided into windows using an exponential strategy, 43 with exponent 1.5, 48 windows for CO 2 , and 80 windows for SPC/E water (roughly the same number of windows relative to N max ). The simplest MC move set was used (unbiased translations, rotations, and GC transfer moves, with relative weights 3:2:5) and no lookup tables or cell lists were utilized to speed up calculations for the preliminary simulations; this is a basic implementation of TMMC in FEASST.…”

“…This by itself targets a key concern of previous water simulations: the tendency of the simulation to get “stuck” in configurations that contain a certain number of water molecules. Simulations of adsorption in simple models of pores with purely repulsive interactions showed that FHMC with grand canonical ensemble trial moves may be up to 3 orders of magnitude more efficient than simulations with only canonical ensemble trials . Biased MC trial moves separately address low trial acceptance ratios by generating higher-quality trial moves.…”

“…Simulations of adsorption in simple models of pores with purely repulsive interactions showed that FHMC with grand canonical ensemble trial moves may be up to 3 orders of magnitude more efficient than simulations with only canonical ensemble trials. 43 Biased MC trial moves separately address low trial acceptance ratios by generating higher-quality trial moves.…”

Efficient Modeling of Water Adsorption in MOFs Using Interpolated Transition Matrix Monte Carlo

“…Consequently, the total number of molecules remains constant through simulation. Hatch et al 46 demonstrated that single-macrostate simulations are less efficient than multiple-macrostate simulations, mainly due to the lack of microstate sampling. However, we show that with single-macrostate simulations, it is possible to skip sampling certain macrostates and interpolate transition probabilities to obtain the full MPD with reduced simulation cost.…”