  The electronic structure, magnetic moment, and volume collapse of MnO under
pressure are obtained from four different correlated band theory methods; local
density approximation + Hubbard U (LDA+U), pseudopotential self-interaction
correction (pseudo-SIC), the hybrid functional (combined local exchange plus
Hartree-Fock exchange), and the local spin density SIC (SIC-LSD) method. Each
method treats correlation among the five Mn 3d orbitals (per spin), including
their hybridization with three O $2p$ orbitals in the valence bands and their
changes with pressure. The focus is on comparison of the methods for rocksalt
MnO (neglecting the observed transition to the NiAs structure in the 90-100 GPa
range). Each method predicts a first-order volume collapse, but with variation
in the predicted volume and critical pressure. Accompanying the volume collapse
is a moment collapse, which for all methods is from high-spin to low-spin (5/2
to 1/2), not to nonmagnetic as the simplest scenario would have. The specific
manner in which the transition occurs varies considerably among the methods:
pseudo-SIC and SIC-LSD give insulator-to-metal, while LDA+U gives
insulator-to-insulator and the hybrid method gives an insulator-to-semimetal
transition. Projected densities of states above and below the transition are
presented for each of the methods and used to analyze the character of each
transition. In some cases the rhombohedral symmetry of the
antiferromagnetically ordered phase clearly influences the character of the
transition.
