Electrostatic interactions in three-dimensional solids. Self-consistent Madelung potential (SCMP) approach

A revised formulation of the self-consistent Madelung potential method in terms of a nonlinear Schrödinger equation, analogous to that used in solvent effect theories, is presented. It is shown that the corresponding Hartree–Fock equations can be derived from a description of the crystal wave function by a Hartree product, involving single determinental wave functions of unit motifs, related by symmetry. Earlier calculations using a point charge approximation to the Madelung potential, instead of to the electrostatic interaction energy, lead to variationally incorrect electronic wave functions. An improved method is presented where the Coulomb interactions with the environment are approximated either by Mulliken, or by Löwdin net atomic charges in a consistent manner. The method has been applied to hydrogen fluoride and carbon dioxide molecular crystals.