Linear-response time-dependent density functional theory approach to warm dense matter with adiabatic exchange-correlation kernels

We present a methodology for the linear-response time-dependent density functional theory (LR-TDDFT) calculation of the dynamic density response function of warm dense matter in the adiabatic approximation that can be used with any available exchange-correlation (XC) functional across Jacob's ladder and across temperature regimes. The uniqueness of the presented approach is that it can go beyond the adiabatic local density approximation and adiabatic generalized gradient approximation while preserving the self-consistency between the Kohn-Sham (KS) response function and adiabatic XC kernel for extended systems. The key ingredient to 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 random phase approximation result, the total density response function, and of the adiabatic XC kernel. The analysis is performed using local density approximation, generalized gradient approximation, and meta-generalized gradient approximation 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.