Simulation of electrostatic systems in periodic boundary conditions. III. Further theory and applications

This paper makes some developments and clarifications of the theory for the application of periodic boundary conditions to the numerical simulation of the statistical mechanics of a cubic sample of dipolar particles. The reaction-field effect is treated rigorously. The anisotropies inherent in the periodic boundary condition Hamiltonian are allowed for in the derivation of a new fluctuation formula. A perturbation theory to account for anisotropic long-ranged terms is described, giving two dielectric constant estimates from one simulation. These new results are illustrated with Monte Carlo simulations of the Stockmayer system at reduced density 0.8, reduced square dipole moment 2.0 and scaled temperature 1.35, giving a dielectric constant estimate of 25 $\pm$ 2 from all the data, and showing that the perturbation theories are very accurate. It appears possible to claim that periodic boundary conditions should be used with infinite external dielectric constant in almost all circumstances, because they then give a chain of configurations that provide comparatively very stable estimates of dielectric constant.