  We assess the accuracy of common hybrid exchange-correlation (XC) functionals
(PBE0, PBE0-1/3, HSE06, HSE03, and B3LYP) within Kohn-Sham density functional
theory (KS-DFT) for the harmonically perturbed electron gas at parameters
relevant for the challenging conditions of warm dense matter. Generated by
laser-induced compression and heating in the laboratory, warm dense matter is a
state of matter that also occurs in white dwarfs and planetary interiors. We
consider both weak and strong degrees of density inhomogeneity induced by the
external field at various wavenumbers. We perform an error analysis by
comparing to exact quantum Monte-Carlo results. In the case of a weak
perturbation, we report the static linear density response function and the
static XC kernel at a metallic density for both the degenerate ground-state
limit and for partial degeneracy at the electronic Fermi temperature. Overall,
we observe an improvement in the density response for partial degeneracy when
the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are used compared to the
previously reported results for the PBE, PBEsol, LDA, AM05, and SCAN
functionals; B3LYP, on the other hand, does not perform well for the considered
system. Together with the reduction of self-interaction errors, this seems to
be the rationale behind the relative success of the HSE03 functional for the
description of the experimental data on aluminum and liquid ammonia at WDM
conditions.
