  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 semi-local
functional inherited from the band gap problem are recovered by the PBE0 hybrid
functional through the non-local 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.
