Harmonically-Mapped Averaging Applied to Lennard-Jones Crystal Phase

Mapped averaging is a technique we developed to improve ensemble averages during a molecular simulation¹. When applied to crystals, we map based on the behavior of a harmonic description of the solid and compute the anharmonic contribution to properties of interest with high precision. We can then add in the harmonic contribution and obtain the actual property value. The anharmonic contribution is insensitive to system size and truncation effects while the harmonic contribution can be computed for very large systems with long truncation. The resulting property values are both very precise and accurate with relatively small computational effort.

We have applied mapped averaging to collect potential energy and pressure data for the Lennard-Jones model in the FCC and HCP phases. We fit an equation of state to each set of data to obtain a description of both phases from low to high density (the soft-sphere limit) and up to melting temperatures. We find the HCP phase to be more stable at low temperatures and densities. Coupled with the virial equation of state for the vapor and an equation of state fit to more limited simulation data for the liquid phase, we predict the phase boundaries including the triple point with unprecedented accuracy and precision. We also discuss the effect of vacancies on the properties and phase diagram.

(1) Moustafa, S. G.; Schultz, A. J.; and Kofke, D. A. Very fast averaging of thermal properties of crystals by molecular simulation, Phys. Rev. E 2015, 92, 043303.