  The electronic exchange-correlation (XC) kernel constitutes a fundamental
input for the estimation of a gamut of material properties such as the
dielectric characteristics, the thermal and electrical conductivity, or the
response to an external perturbation. In practice, no reliable method has been
known that allows to compute the kernel of real materials with arbitrary XC
functionals. In this work, we overcome this long-standing limitation by
introducing a new, formally exact methodology for the computation of the
material specific static XC kernel exclusively within the framework of density
functional theory (DFT) and without employing functional derivatives -- no
external input apart from the usual XC-functional is required. We compare our
new results with exact quantum Monte Carlo (QMC) data for the archetypical
uniform electron gas model at both ambient and warm dense matter conditions.
This gives us unprecedented insights into the performance of different
XC-functionals, and has important implications for the development of new
functionals that are designed for the application at extreme temperatures. In
addition, we obtain new DFT results for the XC kernel of warm dense hydrogen as
it occurs in fusion applications and astrophysical objects. The observed
excellent agreement to the QMC reference data demonstrates that our framework
is capable to capture nontrivial effects such as XC-induced isotropy breaking
in the density response of hydrogen at large wave numbers.
