Electron-gas theory of ionic crystals, including many-body effects

The electron-gas theory of ionic crystals is extended to include nonadditive (many-body) interactions arising from the simultaneous overlap of the densities of several ions. The theory is used to predict equilibrium geometries, lattice energies, and pressure-induced phase transitions for the fluorides and oxides of the alkali and alkaline earth metals. The results are in good agreement with electron-gas calculations assuming additive, two-body interactions between pairs of ions. This comparison shows that the simultaneous overlap of three or more ions has only a small effect on these crystals, and that for many purposes the simpler two-body approximation is adequate. The predictions of lattice distances and energies agree with experiment to a typical accuracy of 1 or 2%. In order to obtain this accuracy, it is necessary to calculate the electron densities for the anions in a stabilizing potential well whose size is determined self-consistently by the electrostatic potential of the crystal at the anion site. This shrinkage of the anion by the crystal is also a kind of many-body interaction, but it can be handled within the framework of an effective two-body interaction involving the stabilized anions. The corresponding cation expansion effect is also calculated, and shown to be negligible for the alkali and alkaline earth metal ions.