Simulation of electrostatic systems in periodic boundary conditions. II. Equivalence of boundary conditions

Abstract We consider simulations of dipolar systems under periodic boundary conditions in which a large sphere consisting of periodic replications of a central simulation cell is surrounded by a continuum of dielectric constant ε'. We develop a perturbation theory expressing correlation functions with ε" in terms of correlation functions with ε' exactly to order N*1, N being the number of particles in the sample. In the thermodynamic limit, the correlation functions and internal energy density are independent of e The Kirkwood g-factor is strongly dependent on ε ' but in such a way as to make the dielectric constant independent of ε'. The dependence upon ε' of hA{r) at large r, described in paper I, is explained in terms of the perturbation series.