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 when the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are used compared to the previously reported results for the PBE, PBEsol, LDA, and AM05 functionals; B3LYP, on the other hand, does not perform well for the considered system. Additionally, the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are more accurate for the density response properties than SCAN in the regime of partial degeneracy.

We present an analysis of the static exchange-correlation (XC) kernel computed from hybrid functionals with a single mixing coefficient such as PBE0 and PBE0–1/3. We break down the hybrid XC kernels into the exchange and correlation parts using the Hartree–Fock functional, the exchange-only PBE, and the correlation-only PBE. This decomposition is combined with exact data for the static XC kernel of the uniform electron gas and an Airy gas model within a subsystem functional approach. This gives us a tool for the non-empirical choice of the mixing coefficient under ambient and extreme conditions. Our analysis provides physical insights into the effect of the variation of the mixing coefficient in hybrid functionals, which is of immense practical value. The presented approach is general and can be used for other types of functionals like screened hybrids.

We present a proof-of-principle study demonstrating x-ray Raman Spectroscopy (XRS) from carbon samples at ambient conditions in conjunction with other common diagnostics to study warm dense matter, performed at the high energy density scientific instrument of the European x-ray Free Electron Laser (European XFEL). We obtain sufficient spectral resolution to identify the local structure and chemical bonding of diamond and graphite samples, using highly annealed pyrolytic graphite spectrometers. Due to the high crystal reflectivity and XFEL brightness, we obtain signal strengths that will enable accurate XRS measurements in upcoming pump-probe experiments with a high repetition-rate, where the samples will be pumped with high-power lasers. Molecular dynamics simulations based on density functional theory together with XRS simulations demonstrate the potential of this technique and show predictions for high-energy-density conditions. Our setup allows simultaneous implementation of several different diagnostic methods to reduce ambiguities in the analysis of the experimental results, which, for warm dense matter, often relies on simplifying model assumptions. The promising capabilities demonstrated here provide unprecedented insights into chemical and structural dynamics in warm dense matter states of light elements, including conditions similar to the interiors of planets, low-mass stars, and other celestial bodies.

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Linear-response time-dependent density functional theory (LR-TDDFT) simulations of disordered extended systems require averaging over different snapshots of ion configurations to minimize finite size effects due to the snapshot-dependence of the electronic density response function and related properties. We present a consistent scheme for the computation of the macroscopic Kohn–Sham (KS) density response function connecting an average over snapshot values of charge density perturbations to the averaged values of KS potential variations. This allows us to formulate the LR-TDDFT within the adiabatic (static) approximation for the exchange–correlation (XC) kernel for disordered systems, where the static XC kernel is computed using the direct perturbation method [Moldabekov et al., J. Chem. Theory Comput. 19, 1286 (2023)]. The presented approach allows one to compute the macroscopic dynamic density response function as well as the dielectric function with a static XC kernel generated for any available XC functional. The application of the developed workflow is demonstrated for the example of warm dense hydrogen. The presented approach is applicable for various types of extended disordered systems, such as warm dense matter, liquid metals, and dense plasmas.