The paper presents evidence that within density-functional theory (DFT), orbital polarization must be treated on equal footing with spin and charge density for strongly interacting electron systems. Using a basis-set independent generalization of the LDA+U functional, the authors show that electronic orbital ordering is necessary to correctly describe the crystal structure and exchange interaction parameters of the Mott-Hubbard insulator KCuF₃. The failure of the local density approximation (LDA) in describing MHI is attributed to the neglect of orbital polarization, a key averaged quantity. The authors propose a generalization of the LDA+U functional that incorporates orbital ordering and the role of screened Coulomb interactions in driving both spin and orbital polarization. This functional is shown to be successful in describing various insulating 3d oxides and more complex systems like doped MHI. The functional is basis-set independent, with the only ambiguity being the choice of atomic spheres to identify orbital and exchange interactions. The paper uses KCuF₃ as a test case, where orbital degeneracy is only partially lifted by the lattice. Orbital polarization becomes evident in the ground state and is essential for the correct description of the crystal structure and lattice distortion. The authors show that LDA fails to reproduce the lattice deformation, while the LDA+U functional with orbital polarization correctly predicts the quadrupolar distortion and the spin-spin superexchange interactions. The results demonstrate that orbital polarization is a necessary condition for the correct description of the electronic structure and magnetic properties of KCuF₃. The authors also show that the LDA+U functional correctly reproduces the magnetic exchange interactions, with the antiferromagnetic exchange in CuF chains being much larger than the ferromagnetic exchange in the a-b planes, emphasizing the quasi-1D nature of the spin system. The results are consistent with neutron-scattering measurements, showing the Luttinger liquid nature of the spin system. The paper concludes that a basis-set independent generalization of the LDA+U method is essential for accurately describing the Jahn-Teller distortion and exchange interactions in Mott-Hubbard insulators.The paper presents evidence that within density-functional theory (DFT), orbital polarization must be treated on equal footing with spin and charge density for strongly interacting electron systems. Using a basis-set independent generalization of the LDA+U functional, the authors show that electronic orbital ordering is necessary to correctly describe the crystal structure and exchange interaction parameters of the Mott-Hubbard insulator KCuF₃. The failure of the local density approximation (LDA) in describing MHI is attributed to the neglect of orbital polarization, a key averaged quantity. The authors propose a generalization of the LDA+U functional that incorporates orbital ordering and the role of screened Coulomb interactions in driving both spin and orbital polarization. This functional is shown to be successful in describing various insulating 3d oxides and more complex systems like doped MHI. The functional is basis-set independent, with the only ambiguity being the choice of atomic spheres to identify orbital and exchange interactions. The paper uses KCuF₃ as a test case, where orbital degeneracy is only partially lifted by the lattice. Orbital polarization becomes evident in the ground state and is essential for the correct description of the crystal structure and lattice distortion. The authors show that LDA fails to reproduce the lattice deformation, while the LDA+U functional with orbital polarization correctly predicts the quadrupolar distortion and the spin-spin superexchange interactions. The results demonstrate that orbital polarization is a necessary condition for the correct description of the electronic structure and magnetic properties of KCuF₃. The authors also show that the LDA+U functional correctly reproduces the magnetic exchange interactions, with the antiferromagnetic exchange in CuF chains being much larger than the ferromagnetic exchange in the a-b planes, emphasizing the quasi-1D nature of the spin system. The results are consistent with neutron-scattering measurements, showing the Luttinger liquid nature of the spin system. The paper concludes that a basis-set independent generalization of the LDA+U method is essential for accurately describing the Jahn-Teller distortion and exchange interactions in Mott-Hubbard insulators.