Abstract
AbstractThe vacancy‐formation energy in aluminium is calculated up to second order in electron–ion interaction within the density‐functional formalism, where the explicit gradient‐expansion of the kinetic energy is used. The ground state for the defect corresponds to an uniform positive background with a spherical hole and an electron density profile represented by an analytical (Gaussian) form which minimizes the total energy. An entirely analytical expression is obtained for zero‐and first‐order energies. The density induced by the perturbative ionic potential (superposition of pseudopotentials minus positive background) is calculated using a linear‐response function which, in the defect, takes into account the charge depletion around the vacancy. The following conclusions are drawn: the perturbation series is convergent, the vacancy‐formation energy is very sensitive to the choice of the (local) pseudopotential.
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