DFT, L(S)DA, LDA+U, LDA+DMFT..., whether we do approach to a proper description of optical response for strongly correlated systems?

I present a critical overview of so-called “{\it ab initio}” DFT (density fuctional theory) based calculation schemes for the description of the electronic structure, energy spectrum, and optical response for strongly correlated 3$d$ oxides, in particular, crystal-field and charge transfer transitions as compared with an “old”, cluster model that does generalize crystal-field and ligand-field theory. As a most instructive illustration of validity of numerous calculation techniques I address the prototypical 3$d$ insulator NiO predicted to be a metal in frames of a standard LDA (local density approximation) band theory.