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We discuss a general approach to a realistic theory of the electronicstructure in materials containing correlated d- or f- electrons. The mainfeature of this approach is the taking into account the energy dependence ofthe electron self-energy with the momentum dependence being neglected (localapproximation). In the case of strong interactions (U/W>>1 - rare-earth system)the Hubbard-I approach is the most suitable. Starting from an exact atomicGreen function with the constrained density matrix the band structure problemis formulated as the functional problem on Nmm' for f-electrons and thestandard LDA-functional for delocalized electrons. In the case of moderatecorrelations (U/W=1 metal-insulator regime) we start from the dynamical meanfield iterative perturbation scheme (IPS) of G. Kotliar et. al. and also makeuse of our multiband atomic Green function. Finally for the weak interactions(U/W<1 -transition metals) the self-consistent diagrammatic fluctuation-exchange (FLEX)-approach of N. Bickers and D. Scalapino is generalized to therealistic multiband case. We presents two-band, two-dimensional modelcalculations for all three regimes. A realistic calculation in Hubbard-I schemewith the exact solution of the on-site multielectron problem for f(d)- shellswas performed for mixed-valence 4f compound TmSe, and for the classical Mottinsulator NiO.Comment: 14 pages, Latex, 9 Postscript figures, submitted to Phys. Rev.

Ab initiocalculations of quasiparticle band structure in correlated systems: LDA++ approach