On the self-consistency of DFT-1/2.

Density functional theory (DFT)-1/2 is an efficient bandgap rectification method for DFT under local density approximation (LDA) or generalized gradient approximation. It was suggested that non-self-consistent DFT-1/2 should be used for highly ionic insulators like LiF, whereas self-consistent DFT-1/2 should still be used for other compounds. Nevertheless, there is no quantitative criterion prescribed for which implementation should work for an arbitrary insulator, which leads to severe ambiguity in this method. In this work, we analyze the impact of self-consistency in DFT-1/2 and shell DFT-1/2 calculations in insulators or semiconductors with ionic bonds, covalent bonds, and intermediate cases and show that self-consistency is required even for highly ionic insulators for globally better electronic structure details. The self-energy correction renders electrons more localized around the anions in self-consistent LDA-1/2. The well-known delocalization error of LDA is rectified, but with strong overcorrection, due to the presence of additional self-energy potential. However, in non-self-consistent LDA-1/2 calculations, the electron wave functions indicate that such localization is much more severe and beyond a reasonable range because the strong Coulomb repulsion is not counted in the Hamiltonian. Another common drawback of non-self-consistent LDA-1/2 is that the ionicity of the bonding gets substantially enhanced, and the bandgap can be enormously high in mixed ionic-covalent compounds like TiO2.

DFT-1/2 and shell DFT-1/2 methods: electronic structure calculation for semiconductors at LDA complexity.

It is known that the Kohn-Sham eigenvalues do not characterize experimental excitation energies directly, and the band gap of a semiconductor is typically underestimated by local density approximation (LDA) of density functional theory (DFT). An embarrassing situation is that one usually uses LDA+Ufor strongly correlated materials with rectified band gaps, but for non-strongly-correlated semiconductors one has to resort to expensive methods like hybrid functionals orGW. In spite of the state-of-the-art meta-generalized gradient approximation functionals like TB-mBJ and SCAN, methods with LDA-level complexity to rectify the semiconductor band gaps are in high demand. DFT-1/2 stands as a feasible approach and has been more widely used in recent years. In this work we give a detailed derivation of the Slater half occupation technique, and review the assumptions made by DFT-1/2 in semiconductor band structure calculations. In particular, the self-energy potential approach is verified through mathematical derivations. The aims, features and principles of shell DFT-1/2 for covalent semiconductors are also accounted for in great detail. Other developments of DFT-1/2 including conduction band correction, DFT+A-1/2, empirical formula for the self-energy potential cutoff radius, etc, are further reviewed. The relations of DFT-1/2 to hybrid functional, sX-LDA,GW, self-interaction correction, scissor's operator as well as DFT+Uare explained. Applications, issues and limitations of DFT-1/2 are comprehensively included in this review.