Calculation of the vacancy formation energy in aluminium

This paper addresses the problem of calculating the vacancy formation energy in simple metals and presents results for aluminium. The calculations are based on the pseudopotential method, the local-density approximation for exchange and correlation, and periodically repeating geometry. The approach used is similar to that proposed by Car and Parrinello, and allows the simultaneous relaxation of the electrons and the ionic positions. Problems peculiar to metals in this approach are discussed and a way of overcoming them is presented. The calculated vacancy energy (0.56 eV) in aluminium is in quite good agreement with experiment (0.66 eV). Comparisons with perturbation theory show that the calculated value is subject to a technical error of only approximately 0.03 eV and that corrections due to periodic boundary conditions are also of this order. The contribution to the vacancy energy from non-linear effects is similar to the jellium estimate of Evans and Finnis.