The magnetic properties of the transition metal monoxides MnO and NiO are
investigated at equilibrium and under pressure via several advanced
first-principles methods coupled with Heisenberg Hamiltonian MonteCarlo. The
comparative first-principles analysis involves two promising beyond-local
density functionals approaches, namely the hybrid density functional theory and
the recently developed variational pseudo-self-interaction correction method,
implemented with both plane-wave and atomic-orbital basis sets. The advanced
functionals deliver a very satisfying rendition, curing the main drawbacks of
the local functionals and improving over many other previous theoretical
predictions. Furthermore, and most importantly, they convincingly demonstrate a
degree of internal consistency, despite differences emerging due to
methodological details (e.g. plane waves vs. atomic orbitals