Simulation of electrostatic systems in periodic boundary conditions. I. Lattice sums and dielectric constants

TLDR

The study simulates a dense hard‑sphere fluid with embedded dipoles to investigate how the Kirkwood g‑factor and long‑range correlation functions depend on the surrounding dielectric constant ε′. Effective interactions under periodic boundary conditions are calculated by treating the infinite array of replicas as a sphere surrounded by vacuum or a dielectric continuum, and the authors simulate the hard‑sphere fluid with embedded dipoles, varying ε′ to examine its influence on the net dipole term, Kirkwood g‑factor, and long‑range correlations. The authors resolve discrepancies among calculation methods, demonstrate that the system’s dielectric constant is independent of ε′, and confirm that Clausius‑Mosotti and Kirkwood formulas yield consistent values.

Abstract

The effective interactions of ions, dipoles and higher-order multipoles under periodic boundary conditions are calculated where the array of periodic replications forms an infinite sphere surrounded by a vacuum. Discrepancies between the results of different methods of calculation are resolved and some shape-dependent effects are discussed briefly. In a simulation under these periodic boundary conditions, the net Hamiltonian contains a positive term proportional to the square of the net dipole moment of the configuration. Surrounding the infinite sphere by a continuum of dielectric constant ε.' changes this positive term, the coefficient being zero as ε' ->∞ . We report on the simulation of a dense fluid of hard spheres with embedded point dipoles; simulations are made for different values of showing how the Kirkwood gr-factor and the long-range part of hA (r) depend on ε' in a finite simulation. We show how this dependence on ε' nonetheless leads to a dielectric constant for the system that is independent of ε . In particular, the Clausius-Mosotti and Kirkwood formulae for the dielectric constant e of the system give consistent ε values.