Overlap interactions and bonding in ionic solids

The virial theorem is used with tight-binding theory to show that the overlap repulsion should vary as 1/$d^4$ in covalent solids, as 1/$d^8$ in ionic solids, and as 1/$d^{12}$ in inert-gas solids. The 1/$d^8$ form is used to predict equilibrium spacings in alkali-metal halides and alkaline-earth chalcogenides. It is then combined with the equilibrium condition to obtain analytic formulas in terms of the tight-binding parameters for the cohesive energy, bulk modulus, and Grüneisen constant for these systems.