Meta-GGA dielectric-dependent and range-separated screened hybrid functional for reliable prediction of material properties

We propose a range-separated hybrid exchange-correlation functional to calculate solid-state material properties. The functional mixes Hartree-Fock exchange with the semilocal exchange of the meta-generalized gradient approximation (meta-GGA) and the fraction of Hartree-Fock exchange is determined from the dielectric function. First-principles calculations and comparison with other meta-GGA approximations show that the functional leads to reasonably good performance for the band gap and optical properties. We also show that the present functional also successfully resolves the well-known ``band gap problem'' of narrow gap Cu-based semiconductors, such as Cu3SbSe4 and Cu3AsSe4, where, in general, a considerably large band inversion energy leads to a ``false'' negative or metallic band gap for all other methods. Furthermore, reasonable accuracy for the occupied d-bands and transition energies is also obtained for bulk solids. Thus, overall, our results demonstrate the predictive power of range-separated meta-GGA hybrid functionals for quantum materials simulations.