  Accurately modeling the electronic structure of materials is a persistent
challenge to high-throughput screening. A promising means of balancing accuracy
against computational cost are non-self-consistent calculations with hybrid
density-functional theory, where the electronic band energies are evaluated
using a hybrid functional from orbitals obtained with a less demanding
(semi-)local functional. We have quantified the performance of this technique
for predicting the physical properties of sixteen tetrahedral semiconductors
with bandgaps from 0.2-5.5 eV. Provided the base functional predicts a
non-metallic electronic structure, bandgaps within 5 % of the PBE0 and HSE06
gaps can be obtained with an order of magnitude reduction in computing time.
The positions of the valence and conduction band extrema and the Fermi level
are well reproduced, further enabling calculation of the band dispersion,
density of states, and dielectric properties using Fermi's Golden Rule. While
the error in the non-self-consistent total energies is ~50 meV atom-1, the
energy-volume curves are reproduced accurately enough to obtain the equilibrium
volume and bulk modulus with minimal error. We also test the
dielectric-dependent scPBE0 functional and obtain bandgaps and dielectric
constants to within 2.5 % of the self-consistent results, which amount to a
significant improvement over self-consistent PBE0 for a similar computational
cost. We identify cases where the non-self-consistent approach is expected to
perform poorly, and demonstrate that partial self-consistency provides a
practical and efficient workaround. Finally, we perform proof-of-concept
calculations on CoO and NiO to demonstrate the applicability of the technique
to strongly-correlated open-shell transition-metal oxides.
