  A band structure description of the observed large band gaps and moments in
both the antiferromagnetic (AFM) and paramagnetic (PM) phases of the classic
NaCl-structure Mott insulators MnO, FeO, CoO, and NiO is provided by ordinary,
single-determinant density functional theory method. As noted by previous
authors, the ordered AFM phases already show in band theory significant band
gaps. However, for the disordered PM phases the commonly used band model has
been to assume the macroscopically observed, averaged NaCl structure, where all
transition metal sites are forced to be symmetry-equivalent (a monomorphous
description); for the PM phase this forces zero moment on an atom by atom
basis, thus producing a gapless PM state, in sharp conflict with experiment.
Instead, we allow larger NaCl-type supercells where each TM site can have
different local bonding and spin environments (a polymorphous description) and
thus the geometric flexibility to acquire symmetry-lowering distortions that
lower the total energy and can break the symmetry of the d orbitals. The
existence of a distribution of different local spin and bonding environments
allows large on-site magnetic moments to develop spontaneously in the DFT+U
calculations leading to significant (1-3 eV) band gaps in the AFM, FM, and PM
phases of the classic Mott insulators MnO, FeO, CoO, and NiO. We adapt to the
spin disordered configurations in the PM phases the "special quasi-random
structure" whereby supercell approximants which represent the best random
configuration average for finite supercells of a given lattice symmetry are
constructed. Thus, avoiding a monomorphous description of the disordered
magnetic phases allows even ordinary DFT+U, which represents the N electron
system with a single-determinant wavefunction, to describe the gapping not only
in the AFM phases but also in the PM phases of MnO, FeO, CoO, and NiO.
