Accuracy of atomic-sphere approximation in electronic-structure calculations for transition-metal systems

The simple atomic-sphere approximation (ASA) is used very often for the first-principles calculations based on density-functional theory, in order to study the electronic structure of complex transition-metal systems. We clarify the accuracy of ASA, comparing with the full-potential (FP) calculation results. We show that the ASA calculations reproduce very well the bulk properties, obatined by the FP calculations, while its accuracy decreases significantly for the non-periodic transition-metal system properties, such as vacancy formation energies and solution energies of 3d impurities. It is discussed that the ASA error worsens together with the anisotropic part of FP and the charge transfer between defect and host atoms. It is also discussed that the ASA error may become larger with the generalized-gradient approximation than with the local-spin-density approximation.