We present an atomic-orbital-based approximate scheme for self-interaction correction (SIC) to the local-density approximation (LDA) of density-functional theory. The method, based on the idea of Filippetti and Spaldin [Phys. Rev. B 67, 125109 (2003)], is implemented in a code using localized numerical atomic-orbital basis sets and is now suitable for both molecules and extended solids. After deriving the fundamental equations as a nonvariational approximation of the self-consistent SIC theory, we present results for a wide range of molecules and insulators. In particular, we investigate the effect of re-scaling the self-interaction correction and we establish a link with the existing atomiclike corrective scheme $\mathrm{LDA}+U$. We find that when no re-scaling is applied, i.e., when we consider the entire atomic correction, the Kohn-Sham highest occupied molecular orbital (HOMO) eigenvalue is a rather good approximation to the experimental ionization potential for molecules. Similarly the HOMO eigenvalues of negatively charged molecules reproduce closely the molecular affinities. In contrast a re-scaling of about 50% is necessary to reproduce insulator band gaps in solids, which otherwise are largely overestimated. The method therefore represents a Kohn-Sham based single-particle theory and offers good prospects for applications where the actual position of the Kohn-Sham eigenvalues is important, such as quantum transport.

• Received 14 September 2006

DOI:https://doi.org/10.1103/PhysRevB.75.045101