Dielectric constants from computer simulations

Abstract

Methods for obtaining a static dielectric constant ϵ from measurements of mean square dipole moment in a simulation are discussed. The simulations are seen as models of a macroscopic experiment to measure the dielectric constant. Such an experiment is usually carried out on a macroscopic sample of fixed shape. This sample is modelled by an array of copies of a microscopic simulation sample, the array having the appropriate shape. The different shapes correspond to different macroscopic experiments. The periodic boundary condition simulation sample hamiltonians appropriate to some different macroscopic geometries are described and appropriate fluctuation formulae for the dielectric constant obtained. The formulae are illustrated by simulations of fairly weakly dipolar molecules (which are rigid models of methyl chloride molecules) using samples of 27, 64, 125 and 216 molecules. All sample sizes give the same dielectric constant to within the error in the simulations, but the structure obtained for 27 molecules seems slightly distorted by small sample sizes. The measured wavevector dependent dielectric tensor ϵ(k) appears able to be extrapolated to k = 0 to agree with the values of ϵ obtained.