Density-functional theory for the energy of crystals: Test of the ionic model

A test of the ionic description of bonding is made for a wide variety of crystals. Self-consistent Hartree-Fock calculations provide the charge densities of the ions, from which the crystal energy is evaluated with a modified electron-gas energy functional. Thus, the crystal binding energy is found by a priori quantum-mechanical methods without fitting any adjustable parameters to experimental data. The theoretical crystal energies are minimized by varying the geometry of the crystals to predict the stable structures and equilibrium energies of the crystals. For the more highly ionic crystals, in which the electronegativity difference between atoms is larger than about one, this purely ionic theory predicts both crystal geometry and binding energy to an average accuracy of \ifmmode\pm\else\textpm\fi{}2%. For less ionic crystals, with electronegativity differences less than about one, the purely ionic theory gives larger errors, as expected, ranging up to about 8%. We conclude that the ionic description of bonding is quite accurate for a surprisingly wide range of crystals.