The ab-initio self-interaction corrected (SIC) local-spin-density (LSD) approximation is elaborated upon, with emphasis on the ability to describe localization phenomena in solids. Two methods for minimizing the SIC-LSD total energy functional are considered, one using an unified Hamiltonian for all electron states, thus having the advantages of Bloch's theorem, the other one employing an iterative scheme in real space. Moreover, an extension of the formalism to the relativistic case is discussed. Results for NiO, cerium and cerium compounds are presented. For NiO a significant charge transfer gap is produced, in contrast to the near vanishing band gap seen in the LSD approximation. Also, the magnetic moment is larger in the SIC-LSD approach than in the LSD approach. For the cerium compounds, the intricate isostructural phase transitions in elemental cerium and cerium pnictides may be accurately described. A sizeable orbital moment for elemental cerium metal is obtained which, upon lattice expansion, is seen to reach the atomic limit.
Temmerman, W. M., Svane, A., Szotek, Z., Winter, H., & Beiden, S. V. (2007). On the Implementation of the Self-Interaction Corrected Local Spin Density Approximation for d- and f-Electron Systems. In Electronic Structure and Physical Properies of Solids (pp. 286–312). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-46437-9_8