The Harris functional applied to surface and vacancy formation energies in aluminium

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Abstract
Non-self-consistent calculations of total energies using the Hohenberg-Kohn-Sham functional and the approximate functional of Harris have been made for a three-layer (111) slab of aluminium and compared to fully self-consistent calculations. The norm-conserving pseudopotential of Bachelet, Hamann and Schluter was used. The Harris total energy for the slab, which is calculated from an input charge density constructed by superimposing free atomic charge densities, is closer to the self-consistent energy for reasons which are discussed in detail. Nevertheless, the corresponding Harris surface energies are not sufficiently accurate to be useful. By renormalising the atomic charge densities which are superimposed to form the input charge density, in particular by pushing charge from the tails towards the cores, the surface energy from a self-consistent calculation can be accurately reproduced by the Harris functional. Furthermore the Harris functional with the same renormalised atoms accurately reproduces the surface-layer contraction and also the formation energy of a vacancy (to within 0.01 eV) obtained from self-consistent calculations.