(51d) Efficient Monte Carlo Algorithms for Simulation of Crystalline Solids

The nature of fluctuations in crystalline solids provides unique opportunities to improve the efficiency of molecular simulations.  In general, we seek to use our knowledge of the fluctuations to arrive at a more typical configuration after some change to the system.  We have previously described how the harmonic nature of the fluctuations can be used to scale coordinates relative to their lattice sites during free energy perturbation[1].  The result is precise estimates of the free energy differences between adjacent temperatures.  We have extended this idea to other contexts and have improved the sampling of volume within an isothermal-isobaric Monte Carlo simulation[2].  Here, the nature of the fluctuations provides an estimate of the appropriate coordinate scaling in order to increase the probability of volume change acceptance.  We find that the new volume change move allows for both a larger step size and faster convergence of calculated properties, in comparison to the conventional algorithm. The improvement is more dramatic for hard potentials, where compressing the system using the conventional algorithm (even a small amount) will almost always cause an overlap.  We also discuss additional applications of the coordinate scaling, including other free-energy perturbation methods.

1. T. B. Tan, A. J. Schultz, D. A. Kofke, “Efficient calculation of temperature dependence of solid-phase free energies by overlap sampling coupled with harmonically targeted perturbation”, J. Chem. Phys. 133, 134104 (2010).
2. A. J. Schultz, D. A. Kofke, "Algorithm for constant-pressure Monte Carlo simulation of crystalline solids", Phys. Rev. E, 84, 046712 (2011).