  We present a new methodology for the linear-response time-dependent density
functional theory (LR-TDDFT) calculation of the dynamic density response
function of warm dense matter in an adiabatic approximation that can be used
with any available exchange-correlation (XC) functional across Jacob's Ladder
and across temperature regimes. The main novelty of the presented approach is
that it can go beyond the adiabatic local density approximation (ALDA) and
generalized LDA (AGGA) while preserving the self-consistence between the
Kohn-Sham (KS) response function and adiabatic XC kernel for extended systems.
The key ingredient for the presented method is the combination of the adiabatic
XC kernel from the direct perturbation approach with the macroscopic dynamic KS
response from the standard LR-TDDFT method using KS orbitals. We demonstrate
the application of the method for the example of warm dense hydrogen, for which
we perform a detailed analysis of the KS density response function, the RPA
result, the total density response function and of the adiabatic XC kernel. The
analysis is performed using LDA, GGA, and meta-GGA level approximations for the
XC effects. The presented method is directly applicable to disordered systems
such as liquid metals, warm dense matter, and dense plasmas.
