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+U for strongly correlated materials with rectified band gaps, but for non-strongly-correlated semiconductors one has to resort to expensive methods like hybrid functionals or GW. In spite of the state-of-the-art meta-GGA functionals like TB09 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+U are explained. Applications, issues and limitations of DFT-1/2 are comprehensively included in this review.

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Surface passivation is proved to be an effective way to adjust material properties or to explore new two-dimensional (2D) materials. Herein, we proposed three hydrocarbons with high stability for the first time via hydrogenation on the Kagome graphene, namely, C6H4, C6H6-I, and C6H6-II. Unlike the Kagome graphene, which is metallic, all these 2D monolayers are wide-bandgap semiconductors (4.06–4.81 eV). Among them, C6H4 is an indirect bandgap semiconductor, but both C6H6-I and C6H6-II possess the direct bandgap feature. Considerable carrier mobilities (102 to 103 cm2 V–1 s–1) have been further confirmed in the three hydrocarbons on the basis of modified deformation potential theory. Specifically, for C6H4, the hole mobilities are as high as 104 to 105 cm2 V–1 s–1, comparable to those of graphene and black phosphorus. The intrinsic vertical electric field induced by the asymmetric crystal structures in C6H4 and C6H6-I will be beneficial to the spatial separation of electrons and holes in semiconductors, promising in the field of optoelectronics. In addition, hydrogenation has a great influence on the mechanical properties of Kagome graphene, no matter whether it is Young’s modulus, Poisson’s ratio, or ideal tensile strength. Particularly, in-plane axial negative Poisson’s ratios (−0.011/–0.018 along the a-/b-direction) were found in C6H6-I, mainly originated from the interaction of carbon pentagons and octagons. These interesting findings in our work may pave the way for the application of hydrogenated Kagome graphene in the future.