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The relative energetic stability of the structural phases of commonantiferromagnetic transition-metal oxides (MnO, FeO, CoO, and NiO) within thesemilocal and hybrid density functionals are fraught with difficulties. Inparticular, MnO is known to be the most difficult case for almost all commonsemilocal and hybrid density approximations. Here, we show that themeta-generalized gradient approximation (meta-GGA) constructed from thecuspless hydrogen model and Pauli kinetic energy density (MGGAC) can lead tothe 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 innice agreement with those obtained from high-level correlation methods like therandom phase approximation or quantum Monte Carlo techniques. Besides, we havealso applied the onsite hybrid functionals (closely related to DFT+U ) based onGGA and meta-GGA functionals, and it is shown that a relatively high amount ofHartree-Fock exchange is necessary to obtain the correct ground-statestructure. Our present investigation suggests that the semilocal MGGAC andonsite hybrids, both being computationally cheap, as methods of choice for thecalculation of the relative stability of antiferromagnetic transition-metaloxides having potential applications in solid-state physics and structuralchemistry.

Correct and accurate polymorphic energy ordering of transition-metal  monoxides obtained from semilocal and onsite-hybrid exchange-correlation  approximations