Self-consistency in total energy calculations: implications for empirical and semi-empirical schemes

Abstract

The authors assess the viability of nonself-consistent total energy calculations using the Harris-Foulkes energy functional. The self-consistent electron density in 11 aluminium structures is resolved into components that are qualitatively similar to the free pseudo-atomic density. For many of the structures the components display significant anisotropies, whilst between the structures there are also important differences. By studying the sensitivity of the Harris-Foulkes energy functional to perturbations in the input electron density, they are able to relate these differences in atomic-like densities to differences in energy. They conclude that no estimate for the electron density based on the superposition of spherical densities can be expected to give errors in the energy of less than 0.03 eV per atom. Given the significant variation in atomic-like electron densities from structure to structure, any transferable density scheme is also prone to energy errors. By constructing a least-squares fit of electron density data to a given functional form, they conclude that the errors in the absolute energies per atom are typically of the order of 0.05 eV whilst for energy differences they drop to 0.01 eV.