Calculations were based upon the pseudopotential method, the local-density approximation for exchange and correlation, and periodically repeating geometry. The approach was similar to that proposed by Car and Parrinello, and allowed the simultaneous relaxation of the electrons and the ionic positions. Problems peculiar to metals in this approach were considered, and a way of overcoming them was presented. The calculated vacancy energy (0.56eV) in aluminium was in quite good agreement with experiment (0.66eV). Comparisons with perturbation theory showed that the calculated value was subject to a technical error of approximately 0.03eV and that corrections due to periodic boundary conditions were also of this order.

Calculation of the Vacancy Formation Energy in Aluminium. M.J.Gillan: Journal of Physics - Condensed Matter, 1989, 1[4], 689-711