The dielectric constant of polar fluids and the distribution of the total dipole moment

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Abstract
This article examines the distribution of fluctuations of the total dipole moment M in polar fluids. Detailed results, including average energies, pressures, and dielectric constants, are reported from molecular dynamics simulations of a dipolar soft-sphere system in reaction field (RF) and periodic boundary conditions (PBC). Both cubic and truncated octahedral simulation cells are employed and we demonstrate that the properties of interest are insensitive to our choice of cell geometry. Some dependence upon RF cutoff is observed, particularly in results for the static dielectric constant. The distribution of instantaneous values of M shows no anisotropy, and we argue that the isotropic probability distribution function P(g), where g is the Kirkwood correlation factor and depends only upon the magnitude of M, is sufficient to fully characterize the fluctuations in the total moment for a large sample of a polar liquid. We demonstrate that the functional form for P(g) previously tested for a dipolar fluid in PBC [P. G. Kusalik, Mol. Phys. 80, 225 (1993)] holds for RF boundary conditions; we also find that this form is obeyed by other polar liquids such as water and methanol. The distribution function P(g) is found to be particularly effective at detecting finite size effects in simulations of polar liquids. We also show how knowledge of the functional form for P(g) can be efficaciously used to achieve significant reductions in the computational resources required to determine a static dielectric constant for a polar liquid.