Color centers in NaCl by hybrid functionals

We present in this work the electronic structure and transition energies (both thermodynamic and optical) of Cl vacancies in NaCl by hybrid density functionals. The underestimated transition energies by the semilocal functional inherited from the band-gap problem are recovered by the PBE0 hybrid functional through the nonlocal exact exchange, whose amount is adjusted to reproduce the experimental band gap. The hybrid functional also gives a better account of the lattice relaxation for the defect systems arising from the reduced self-interaction. On the other hand, the quantitative agreement with experimental vertical transition energy cannot be achieved with hybrid functionals due to the inaccurate descriptions of the ionization energies of the localized defect and the positions of the band edges.