Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators

Evidence is presented that within the density-functional theory orbital polarization has to be treated on an equal footing with spin polarization and charge density for strongly interacting electron systems. Using a basis-set independent generalization of the LDA+U functional, we show that electronic orbital ordering is a necessary condition to obtain the correct crystal structure and parameters of the exchange interaction for the Mott-Hubbard insulator ${\mathrm{KCuF}}_3$.