Pair potentials from band theory: Application to vacancy-formation energies

A method is presented for generating interatomic potentials in tight-binding models for metals. With the use of moment rules, the cohesive energy projected on a particular site is obtained as a function of the site's local atomic environment. It is then decomposed into a sum of one-body, two-body, and higher-order terms. The latter can be neglected if (1) the fractional deviations of the moments from their bulk values are small, and (2) contributions from connected four-atom clusters are negligible. As a test of the interatomic potentials, the ratio of the unrelaxed-vacancy---formation energy to the cohesive energy is calculated for two tight-binding model lattices and found to be within 10% of the exact model value. Predicted chemical trends in this ratio, as well as its overall magnitude, are also in reasonable agreement with experiment.