Corrected spherical model for vacancies in simple metals

The energy required to create a vacancy in a simple metal is written, apart from the lattice relaxation energy, as the sum of two terms. One is the binding energy $E_b$ of an atom in the perfect solid; the other represents the difference between the energies of the defected and perfect crystals in the same volume. This second term is estimated, using the spherical-solid model, as the difference of two self-consistent calculations of total energies within the local-density formalism. The ions surrounding the defect are simulated by pseudopotentials. The spherical approximation of the perfect lattice is obtained by adding the "exact" ionic potential at the center of the defected lattice. This exact potential results from a self-consistent augmented-plane-wave calculation of the perfect solid, which also gives the binding energy $E_b$. The magnitude of the nonspherical ionic potential contribution to the vacancy energy is then investigated, using different linear-response functions for the perfect and defected systems. Satisfying agreement with experiment is obtained for the alkali metals Li, Na, and K, but the model fails for high-electron-density metals as Al.