  The development of novel materials for vacuum electron sources in particle
accelerators is an active field of research that can greatly benefit from the
results of \textit{ab initio} calculations for the characterization of the
electronic structure of target systems. As state-of-the-art many-body
perturbation theory calculations are too expensive for large-scale material
screening, density functional theory offers the best compromise between
accuracy and computational feasibility. The quality of the obtained results,
however, crucially depends on the choice of the exchange-correlation potential,
$v_{xc}$. To address this essential point, we systematically analyze the
performance of three popular approximations of $v_{xc}$ (PBE, SCAN, and HSE06)
on the structural and electronic properties of bulk Cs$_3$Sb and Cs$_2$Te, two
representative materials of Cs-based semiconductors employed in photocathode
applications. Among the adopted approximations, PBE shows expectedly the
largest discrepancies from the target: the unit cell volume is overestimated
compared to the experimental value, while the band gap is severely
underestimated. On the other hand, both SCAN and HSE06 perform remarkably well
in reproducing both structural and electronic properties. Spin-orbit coupling,
which mainly impacts the valence region of both materials inducing a band
splitting and, consequently, a band-gap reduction of the order of 0.2 eV, is
equally captured by all functionals. Our results indicate SCAN as the best
trade-off between accuracy and computational costs, outperforming the
considerably more expensive HSE06.
