Electrostatic energies of crystals in space of arbitrary dimension

We present a new method to evaluate electrostatic energies under periodic boundary conditions. The lattice sum of Coulomb potentials is expressed through the elliptic Q function of the third kind. This enables us to evaluate electrostatic energies of ionic crystals very accurately and with very rapid convergence. In particular, we study the dimensionality of the electrostatic energies of NaCl-type and CsCl-type crystals, whose expressions are functions of the spatial dimension treated as a real number. Furthermore, the expressions we obtain are applicable to computational simulations using molecular dynamics and Monte Carlo methods. We generate random distributions of point charges under periodic boundary conditions, and we analyze the randomness and its anisotropy on the basis of potential distributions. (author)