The effect of charge ordering in the octahedral sites of and on their electronic structure was investigated using DFT+U.82 A precise description of charge ordering was found to be crucial in determining the bandgaps of the compounds. GGA+U calculations of the electronic structure of antiferromagnetic yield an indirect bandgap of .83 The ionicity of has been determined using DFT calculations.84 Furthermore, a new developed quantum mechanical estimation method for the ionicity of spinel ferrites has been proposed and tested. On the basis of this, the ionicities of the spinel ferrites (M: Co, Cu, Fe, Mn, Ni) were calculated. The electronic structure of has been investigated using LSDA+U and hybrid-DFT in 2012.85 According to the theoretical results, the system is an indirect gap material in one of the minority channels and slightly larger direct bandgaps can be found both in the minority and majority channels. The electronic structure of (M: Ca, Mg, Zn) was investigated in a combined experimental and theoretical study.86 The DFT calculations reveal that the M-ion controllably affects the density of states of the Fe d-orbitals near the Fermi level. The electronic structure of was studied using GGA+U.87 Taking the effect of spin arrangement on symmetry into account, was classified as a semiconductor. The impact of cation distribution in on electronic structure and magnetic properties has been investigated by Feng et al.88 The lattice structure was optimized on the GGA level and the electronic structure was calculated with GGA+U. The calculated density of states shows that the distribution of Cu ions significantly impacts the electronic structure. Multilayer bispinel composites, in which one member is and the other is (M: Co, Mg, Mn, Ni), were modeled using GGA+U by Wells et al.89 It was found that substitution of the transition metal sites in the supercell produces cation charge transfers and magnetization modulation. Band shifts and gap modulation were comparable to the chemically similar bulk compounds. Two different distributions for the octahedral-site cations in and have been investigated using LDA and GGA, as well as LDA+U and GGA+U.90 It was shown that a different octahedral-site distribution impacts the density of states as well as the bandgaps in both the normal and inverse spinel configurations of these compounds. Magnetic properties and the electronic structure of have been studied using hybrid-DFT.91 The calculated density of states suggests that is an insulator. The electronic structure of normal and inverse spinel ferrites (M: Co, Fe, Mn, Ni) was investigated by self-interaction corrected LSDA.92 For both structures, all studied compounds were found to be insulating but with smaller gaps in the normal spinel structure. The calculated spin magnetic moments and exchange splitting of the conduction bands were dramatically increased when moving from the inverse spinel structure to the normal spinel. A first principle investigation of the electronic structure of (M: Co, Fe, Mn, Ni) compares the performance of LSDA and LSDA+U.93 For the LSDA+U approach, the charge ordering is stable in contrast to a metallic state given by the LSDA approach. Calculated x-ray absorption spectra as well as the x-ray magnetic circular dichroism spectra were in good agreement with the experiment. The electrical and magnetic properties of the normal and inverse spinel structures of were calculated with DFT by Zuo and Vittoria.94 The calculated bandgap suggests that is a complex insulator, in contrast to earlier LSDA and GGA calculations which suggest a half-metallic behavior. has been investigated theoretically at DFT level.95 The calculated band structure shows a low carrier density half-metal in the fully ordered state, in contrast to experimental characterizations. The computations yield a strong coupling of the energy bands at the Fermi energy to the internal structural parameter as well as strong effects on the electronic structure upon partial interchange of Fe and Mn atoms.