Static Dielectric Constant from Simulations Revisited: Fluctuations or External Field?

We compare two methods-the fluctuation formula and the application of an external electric field-for determining the static relative permittivity (static dielectric constant) from molecular simulations in the Ewald dielectric boundary conditions. We express both the systematic and statistical errors in terms of a dimensionless saturation (dielectric polarization reduced by its maximum) and show that both methods possess the same efficiency. Saturation in the fluctuation route depends on the number of particles and the permittivity of the surrounding medium, where a value of infinity (tinfoil) for the latter is usually reasonable but not necessarily optimum. Saturation in the external field route is easily controlled by the field intensity; hence, we develop an extrapolation scheme and apply it to several water models, specifically, nonpolarizable (SPC/E, TIP4P/2005, NE6) and polarizable (POL3, DC97, BK3). In addition, we discuss the Clausius-Mossotti approximation for the optical permittivity; this quantity is needed in the fluctuation formula for polarizable models.