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A band structure description of the observed large band gaps and moments inboth the antiferromagnetic (AFM) and paramagnetic (PM) phases of the classicNaCl-structure Mott insulators MnO, FeO, CoO, and NiO is provided by ordinary,single-determinant density functional theory method. As noted by previousauthors, the ordered AFM phases already show in band theory significant bandgaps. However, for the disordered PM phases the commonly used band model hasbeen to assume the macroscopically observed, averaged NaCl structure, where alltransition metal sites are forced to be symmetry-equivalent (a monomorphousdescription); for the PM phase this forces zero moment on an atom by atombasis, thus producing a gapless PM state, in sharp conflict with experiment.Instead, we allow larger NaCl-type supercells where each TM site can havedifferent local bonding and spin environments (a polymorphous description) andthus the geometric flexibility to acquire symmetry-lowering distortions thatlower the total energy and can break the symmetry of the d orbitals. Theexistence of a distribution of different local spin and bonding environmentsallows large on-site magnetic moments to develop spontaneously in the DFT+Ucalculations leading to significant (1-3 eV) band gaps in the AFM, FM, and PMphases of the classic Mott insulators MnO, FeO, CoO, and NiO. We adapt to thespin disordered configurations in the PM phases the "special quasi-randomstructure" whereby supercell approximants which represent the best randomconfiguration average for finite supercells of a given lattice symmetry areconstructed. Thus, avoiding a monomorphous description of the disorderedmagnetic phases allows even ordinary DFT+U, which represents the N electronsystem with a single-determinant wavefunction, to describe the gapping not onlyin the AFM phases but also in the PM phases of MnO, FeO, CoO, and NiO.

A polymorphous band structure model of gapping in the anti-ferromagnetic and paramagnetic phases of the Mott insulators MnO, FeO, CoO, and NiO