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Vacancy-ordered halide perovskite Cs2BX6 semiconductors are attracting an increasing level of interest for optoelectronic applications due to their high chemical stability and unique light emission properties. Here, we performed first-principles calculations to determine the energy positions and atomic orbital hybridization features of band edge states in Cs2BX6 (B = Ge, Sn, Te, Ti, Zr, Hf; X = Cl, Br, I). Our results revealed that all the Cs2BX6 perovskites, except for Cs2TeX6, have direct bandgaps at the Γ point. The indirect bandgaps of Cs2TeX6 originate from the symmetry-forbidden Te p–X p coupling at the Γ point. Both energy positions and dispersions of the band edge states of Cs2BX6 can be well modulated by varying X- and B-site ions. Our work provides a comprehensive understanding of electronic structures and optoelectronic properties of Cs2BX6 perovskites, shedding light on the design rules for high-performance perovskite optoelectronics. [ABSTRACT FROM AUTHOR]

High-hardness metal compounds have huge potential applications in multifunctional devices used under extreme conditions. Here, an ab initio evolutionary algorithm was used to systematically search for structures in the Re3C system with high hardness and metallicity under the pressure of 0–300 gigapascal (GPa). We discovered a structure (namely, C2/m) with the lowest enthalpy at 154 GPa and two metastable phases (namely, P63/mmc and C2/m- α), which could maintain thermodynamic and mechanical stability at zero pressure, and they could be quenched to ambient conditions. More importantly, the hardness of the metal compounds (21.4 GPa for C2/m, 25.2 GPa for P63/mmc) exceeds that of TiN (18.7 GPa), the material for commercial machine tools. In addition, our analysis shows that the coexistence of Re–C bond and Re–Re bond with strong coupling, and avoiding the antibonding state of 5d-electron of Re–Re bond near the Fermi level, could be the reasons why the structure has high hardness and metal properties at the same time. [ABSTRACT FROM AUTHOR]