  Boltzmann transport calculations based on band structures generated with
density functional theory (DFT) are often used in the discovery and analysis of
thermoelectric materials. In standard implementations, such calculations
require dense ${\it k}$-point sampling of the Brillouin zone and are therefore
typically limited to the generalized gradient approximation (GGA), whereas more
accurate methods such as hybrid functionals would have been preferable. GGA
variants, however, generally underestimate the band gap. While premature onset
of minority carriers can be avoided with scissor corrections, the band gap also
affects the band curvature. In this study, we resolved the ${\it k}$-point
sampling issue in hybrid-functional based calculations by extending our
recently developed ${\it k}\cdot\tilde{{\it p}}$ interpolation scheme [Comput.
Mater. Sci. 134, 17 (2017)] to non-local one-electron potentials and spin-orbit
coupling. The Seebeck coefficient generated based on hybrid functionals were
found to agree better than GGA with experimental data for GaAs, InP, and PbTe.
For PbTe, even the choice of hybrid functional has bearing on the
interpretation of experimental data, which we attribute to the description of
valley convergence of the valence band.
