Umbrella sampling molecular dynamics study of the dielectric constant of water

Abstract

We have used a form of umbrella sampling with molecular dynamics to calculate the dielectric constant for a periodically replicated cubic system of the simple point charge (SPC) model for water. The dielectric constant is related to the average of the square of the total electric dipole. With standard sampling, the average is slowly converging due to slow diffusion of the dipole. Comparison between standard sampling and umbrella sampling is made to determine the improvement in convergence that can be obtained. Probability distributions are calculated as well as averages. The distributions are used to study the shape of the pertinent free energy surface and the anisotropy of a system of periodically replicated cubic boxes. For a system of 250 water molecules in the primary cell, there is substantial anisotropy that must be accounted for in an accurate calculation of the dielectric constant.