Evaluation and Meaning of Ionic and Dipolar Lattice Sums

Abstract

We discuss the lattice sums which arise in simulations of ionic and dipolar systems using periodic boundary conditions. The lattice sums are conditionally but not absolutely convergent and so the order of summation must be given. We sum them by spherical shells and discuss the role of an “external dielectric constant” ε′, the dielectric constant of a continuum outside the outermost shell becomes large. The lattice sums are converted into absolutely and rapidly convergent lattice sums and methods for rapid evaluation of these sums are discussed. The effect of ε′ on the Hamiltonian is discussed. The effect of changes in ε′ on the mean square dipole moment fluctuations is discussed and illustrated by reference to some Monte Carlo simulations of restricted primitive electrolyte.