Some Comments on the Quantum-Mechanical Treatment of Defects in Ionic Crystals

Abstract

Per-Olov Lowdin’s thesis1) “A theoretical investigation into some properties of ionic crystals”, constitutes a landmark in the theory of the electronic structure of ionic crystals. By combining mathematical ingenuity and an enormous amount of numerical work without the help of electronic computers Lowdin was able to get not only very good agreement between experimental and theoretical values for a number of physical parameters for nearly all the alkali halides, but also and of greater importance to introduce a new physical concept. His calculations of cohesive energies and equilibrium lattice constants gave a quantum mechanical background and “explanation” of the Born-Mayer theory. But his quantum mechanical treatment went far beyond the Born-Mayer model, since it contained ingredients, which could explain the deviations from the Cauchy relations for the elastic constants. It is particularly interesting to notice that the effective many-ion forces, which are responsible for these deviations, actually came out of the calculations as a result of the careful treatment of the overlap between the ions. Lowdin’s alkali halide work shows what in a favourable case can be achieved by an “ab initio” calculation.