We present a systematic study that clarifies the validity and limitation of current hybrid functionals in density functional theory for structural and electronic properties of various semiconductors and insulators. The three hybrid functionals, PBE0 by Perdew, Ernzerhof, and Burke, HSE by Heyd, Scuseria, and Ernzerhof, and a long-range corrected (LC) functional, are implemented in a well-established plane-wave-basis-set scheme combined with norm-conserving pseudopotentials, thus enabling us to assess the applicability of each functional on an equal footing to the properties of the materials. The materials we have examined range from covalent to ionic materials as well as a rare-gas solid whose energy gaps determined by experiments are in the range of 0.6–14.2 eV, i.e., Ge, Si, BaTiO${}_3$, $\beta$-GaN, diamond, MgO, NaCl, LiCl, Kr, and LiF. We find that the calculated bulk moduli by the hybrid functionals show better agreement with the experiments than that provided by the generalized-gradient approximation (GGA), whereas the calculated lattice constants by the hybrid functionals and the GGA show comparable accuracy. The calculated energy band gaps and the valence-band widths for the ten prototype materials show substantial improvement using the hybrid functional compared with the GGA. In particular, it is found that the band gaps of the ionic materials as well as the rare-gas solid are well reproduced by the LC-hybrid functional, whereas those of covalent materials are well described by the HSE functional. We also examine exchange effects due to short-range and long-range components of the Coulomb interaction, and we propose an optimum recipe to the short-range and long-range separation in treating the exchange energy.

• Received 11 March 2011

DOI:https://doi.org/10.1103/PhysRevB.84.075205