  We develop a computationally efficient scheme to accurately determine
finite-temperature band gaps. We here focus on materials belonging to the class
ABX3 (A = Rb, Cs; B = Ge, Sn, Pb; and X = F, Cl, Br, I), which includes halide
perovskites. First, an initial estimate of the band gap is provided for the
ideal crystalline structure through the use of a range-separated hybrid
functional, in which the parameters are determined nonempirically from the
electron density and the high-frequency dielectric constant. Next, we consider
two kinds of band-gap corrections to account for spin-orbit coupling and
thermal vibrations including zero-point motions. In particular, the latter
effect is accounted for through the special displacement method, which consists
in using a single distorted configuration obtained from the vibrational
frequencies and eigenmodes, thereby avoiding lengthy molecular dynamics. The
sequential consideration of both corrections systematically improves the band
gaps, reaching a mean absolute error of 0.17 eV with respect to experimental
values. The computational efficiency of our scheme stems from the fact that
only a single calculation at the hybrid-functional level is required and that
it is sufficient to evaluate the corrections at the semilocal level of theory.
Our scheme is particularly convenient for large-size systems and for the
screening of large databases of materials.
