Nucleation free-energy barriers with Hybrid Monte-Carlo/Umbrella Sampling

Abstract

The aim of this work is to evaluate nucleation free-energy barriers using molecular dynamics (MD). More specifically, we use a combination of Hybrid Monte Carlo (HMC) and an Umbrella Sampling scheme, and compute the crystallisation barrier of NaCl from its melt. Firstly the convergence and performance of HMC for different time-steps and the number of MD steps within a HMC cycle are assessed. The calculated potential energies and densities converge regardless of the chosen time-step. However the acceptance ratio of the Metropolis step within the HMC scheme strongly depends on the time-step and affects the performance. It is shown that the acceptance ratio is close to 100% for time-steps of the order of those commonly used in molecular dynamics runs. We then explore the results obtained with a “non-Metropolised” version of HMC where the MD trajectories are always accepted (omitting the Metropolis criteria) and conclude that they are satisfactory for time-steps below 5 fs. Next, HMC is combined with Umbrella Sampling (HMC/US) to compute the nucleation free-energy for both the standard and the “non-Metropolised” HMC (using a small time-step) and in both cases find excellent agreement with the reported values. To conclude, we explore approximations to the HMC/US technique implementing HMC with isothermal–isobaric MD trajectories. The computed nucleation free-energy curve is coincident, within the statistical error, with previous calculations.