Limitations of the DFT–1/2 method for covalent semiconductors and transition-metal oxides

The DFT-1/2 method in density functional theory [L. G. Ferreira et al., Phys. Rev. B 78, 125116 (2008)] aims to provide accurate band gaps at the computational cost of semilocal calculations. The method has shown promise in a large number of cases, however some of its limitations or ambiguities on how to apply it to covalent semiconductors have been pointed out recently [K.-H. Xue et al., Comput. Mater. Science 153, 493 (2018)]. In this work, we investigate in detail some of the problems of the DFT-1/2 method with a focus on two classes of materials: covalently bonded semiconductors and transition-metal oxides. We argue for caution in the application of DFT-1/2 to these materials, and the condition to get an improved band gap is a spatial separation of the orbitals at the valence band maximum and conduction band minimum.