Long-range contributions to the total energy of an impurity in an extended substrate

A study of the total energy of an isolated impurity in an extended substrate is presented. The approach is based on the Green's function embedding method within the density functional theory framework. We explicitly take care of the influence of an infinite substrate and introduce the contributions to the total energy of an isolated impurity deriving from long range charge density oscillations. Total energies for a substitutional Al atom in Mg and Na bulks calculated in this way are compared with those obtained by expressions limited to smaller regions, focusing on accuracy and convergence as function of the self-consistent calculation volume. A faster and variational (monotonic) convergence is obtained by using the energy expression proposed in this paper.