# A simplified self-interaction correction applied to atoms, insulators, and metals (density, functional, energy bands)

## Description

One of the principal aims of theoretical solid state physics is to use an effective one-body Schrodinger equation to predict the energies of various states in atoms, molecules, and solids. The most common procedure involves incorporating the many-body effects of the electrons into a local 'exchange-correlation' potential. Comparison of the resulting one-particle eigenvalues to experimental photoemission data, though, reveals that this local potential happens to place the one-particle energies too high. For insulators and semiconductors, it predicts anomalously small band gaps. And in the case of transition metals, it predicts valence d bands which are too high and too disperse at the end of the transition series One of the problems with the local density approximation is a spurious self-interaction of the electrons which is present due to the approximate nature of its local exchange-correlation potential. This effect can be corrected, resolving the discrepancy for atoms mentioned above. In other words the one-particle eigenvalues agree with experimental removal energies. The self-interaction correction terms, though, are not invariant under unitary transformations of the orbitals. In particular, for a Bloch state in a crystal, they are zero. Previous applications of the self-interaction correction, therefore, usually involved atomic-like schemes or Wannier-orbital methods In this paper, we propose a size-consistent approximation to the self-interaction correction. It reproduces the original SIC results for the energy levels of atoms fairly closely, and also corrects the band gaps in the insulators which were tested, Neon and Sodium Chloride. The method fails in the case of transition metals. Further analysis, though, indicates the necessity to incorporate metallic screening effects into the problem. A crude screened method yields d band positions and dispersions in Copper and Zinc which are a large improvement over their local density counterparts The basic conclusion, then, is that there exists non-zero self-interaction terms in solids in many cases. This implies that in these cases there is a certain degree of localization of the states involved, which is contrary to much of established energy band lore