Evaluation of second and third dielectric virial coefficients for non-polarisable molecular models

The dielectric constant, ε, of a dilute vapour can be estimated from the dielectric virial equation of state (VEOS), but the long-ranged nature of the electrostatic interactions complicates the evaluation of coefficients of this series. We propose a formulation of the second and third dielectric coefficients of a general non-polarisable molecular model that permits their reliable calculation using Mayer sampling Monte Carlo. We demonstrate for three models: dipolar hard spheres, dipolar Lennard–Jones, and TIP4P water. The coefficients are used to compute ε for each model as a function of density, which are compared to molecular-simulation data. The form of the VEOS relating ε to density depends on the dielectric constant ε′ of the embedding medium. Three choices are examined: vacuum (ε′ = 1), self-consistent (ε′ = ε) and tin foil (ε′ = ∞). The vacuum-boundary form is found to be unreliable, losing accuracy at low density and yielding divergent results for ε at moderate densities. In contrast, the series formulated using the tin-foil boundary produces accurate and stable values of ε for almost all conditions and models examined here, even when truncated at second order (which itself is shown to be a large improvement over the first-order Clausius–Mossotti–Debye formula).