Non-local Exchange and Correlation

Abstract

Despite the general success of the local and semilocal approximations for exchange and correlation, limitations or even failures of the density functional theory become obvious for subsystems of localized d or f electrons. In particular, the correlation is not correctly described. One speaks about ‘strongly correlated’ electrons and materials. One idea to solve the correlation problem is the description of the missing effect by on-site Coulomb interactions. The implementation of this idea is illustrated and explicitly presented for the case, where the interaction beyond the local or semilocal treatment is described by an empirical Hubbard-like parameter U. For the resulting DFT+ U approach a special scheme of application and the influence on some properties of atoms with partially filled 3 d shells are presented. The localization of some electronic states also ask for a better treatment of the non-locality inherent in the exchange interaction and therefore for a generalized density functional theory. The local or semilocal exchange-correlation functional is replaced by a ‘hybrid’ one, that is a combination of the orbital-dependent Hartree-Fock and a common density functional. Meanwhile, many hybrid functionals exist. They are not only more accurate as far as energetics is concerned but also open the fundamental gaps in the electronic structure of non-metals. The implementation of the adiabatic-connection fluctuation-dissipation theorem is a promising way to describe explicitly the van der Waals interaction.