ABSTRACT
Though the LSDA has successfully provided the insight for the ground state properties such as the cohesive properties and even the ground state magnetic moment in transition metals [4], the LSDA usually underestimates the band gaps in insulators and semiconductors and even the proper ground state for strongly correlated electron systems in, e.g. transition metal oxides. Perdew et al. [5] and Sham et al. [ 6] showed the discontinuity of the exchange-correlation potential with respect to an infinitesimal change of the electron number. It is now widely known that the underestimate of the band gaps in insulators and semiconductors is not due to the functional form of the exchange-correlation energy in the local approximation, but due to the DFT itself. Although there have been several attempts
Perdew and Zunger [8] proposed another treatment for this problem, by introducing the self-interaction correction term, which may be guided by the physical picture for the many-body effect. This approach loses its mathematical rigor but is easily manipulated in the LSDA formalism and applicable to many problems. Actually the problem of underestimating band gaps is essentially related to the localization/delocalization of valence electrons and this kind of improvement for the LSDA may help greatly for strongly correlated systems.
