Energy of static electron lattices

Abstract

A new approach to evaluating the static lattice energy of any given Wigner lattice is proposed. The method is much simpler than the traditional one and the results are much faster to evaluate. The new approach is applied to two-dimensional triangular lattices where it is shown that the triangular lattice is more stable than the square lattice. Three-dimensional hexagonal lattices are also investigated. In addition, the authors place many of their considerations on a rigorous mathematical footing.