  The relative energetic stability of the structural phases of common
antiferromagnetic transition-metal oxides (MnO, FeO, CoO, and NiO) within the
semilocal and hybrid density functionals are fraught with difficulties. In
particular, MnO is known to be the most difficult case for almost all common
semilocal and hybrid density approximations. Here, we show that the
meta-generalized gradient approximation (meta-GGA) constructed from the
cuspless hydrogen model and Pauli kinetic energy density (MGGAC) can lead to
the correct ground state of MnO. The relative energy differences of zinc-blende
(zb) and rock-salt (rs) structures as computed using MGGAC are found to be in
nice agreement with those obtained from high-level correlation methods like the
random phase approximation or quantum Monte Carlo techniques. Besides, we have
also applied the onsite hybrid functionals (closely related to DFT+U ) based on
GGA and meta-GGA functionals, and it is shown that a relatively high amount of
Hartree-Fock exchange is necessary to obtain the correct ground-state
structure. Our present investigation suggests that the semilocal MGGAC and
onsite hybrids, both being computationally cheap, as methods of choice for the
calculation of the relative stability of antiferromagnetic transition-metal
oxides having potential applications in solid-state physics and structural
chemistry.
