  In this paper we assess the predictive power of the self-consistent hybrid
functional scPBE0 in calculating the band gap of oxide semiconductors. The
computational procedure is based on the self-consistent evaluation of the
mixing parameter $\alpha$ by means of an iterative calculation of the static
dielectric constant using the perturbation expansion after discretization
(PEAD) method and making use of the relation $\alpha = 1/\epsilon_{\infty}$.
Our materials dataset is formed by 30 compounds covering a wide range of band
gaps and dielectric properties, and includes materials with a wide spectrum of
application as thermoelectrics, photocatalysis, photovoltaics, transparent
conducting oxides, and refractory materials. Our results show that the scPBE0
functional provides better band gaps than the non self-consistent hybrids PBE0
and HSE06, but scPBE0 does not show significant improvement on the description
of the static dielectric constants. Overall, the scPBE0 data exhibit a mean
absolute percentage error of 14 \% (band gaps) and 10 \% ($\epsilon_\infty$).
For materials with weak dielectric screening and large excitonic biding
energies scPBE0, unlike PBE0 and HSE06, overestimates the band gaps, but the
value of the gap become very close to the experimental value when excitonic
effects are included (e.g. for SiO$_2$). However, special caution must be given
to the compounds with small band gaps due to the tendency of scPBE0 to
overestimate the dielectric constant in proximity of the metallic limit.
