Ab initio density functional theory approach to warm dense hydrogen: from density response to electronic correlations

Abstract

Understanding the properties of warm dense hydrogen is of key importance for the modeling of compact astrophysical objects and to understand and further optimize inertial confinement fusion (ICF) applications. The work horse of warm dense matter theory is given by thermal density functional theory (DFT), which, however, suffers from two limitations: (i) its accuracy can depend on the utilized exchange--correlation (XC) functional, which has to be approximated and (ii) it is generally limited to single-electron properties such as the density distribution. Here, we present a new ansatz combining time-dependent DFT results for the dynamic structure factor $S_{ee}(\mathbf{q},ω)$ with static DFT results for the density response. This allows us to estimate the electron--electron static structure factor $S_{ee}(\mathbf{q})$ of warm dense hydrogen with high accuracy over a broad range of densities and temperatures. In addition to its value for the study of warm dense matter, our work opens up new avenues for the future study of electronic correlations exclusively within the framework of DFT for a host of applications.

Figures (4)

• Figure 1: Electronic static structure factor $S_{ee}(\mathbf{q})$ of hydrogen at $\rho=0.08\,$g/cc [$r_s=3.23$] and $T=4.8\,$eV [$\Theta=1$] for $N=32$ (circles) and $N=14$ (plusses) atoms. Black crosses: quasi-exact PIMC reference data Dornheim_JCP_2024; red symbols: direct TDDFT; green symbols: TDDFT + $\chi_A$-correction [Eq. (\ref{['eq:correction']})]; yellow symbols: TDDFT + $\chi_A(\mathbf{q})$ and $\Delta\chi_l$ [Eq. (\ref{['eq:quantum_correction']})] corrections; dashed blue: chemical model bellenbaum2025estimatingionizationstatescontinuum, see Supplemental Material supplement. The inset shows the relative deviation of TDDFT data sets with respect to PIMC.
• Figure 2: (a) Inelastic ITCF $F_\textnormal{inel}(\mathbf{q},\tau)$ (top curves) and elastic ITCF $F_\textnormal{el}(\mathbf{q},\tau)=W_R(\mathbf{q})$ (horizontal lines) computed from PIMC (dashed black), direct TDDFT (solid red) and TDDFT + $\chi_A$ correction [Eq. (\ref{['eq:correction']})] (solid green) for $T=4.8\,$eV, $\rho=0.08\,$g/cc and $q=1.892$Å$^{-1}$. (b) Corresponding dynamic structure factor $S_\textnormal{inel}(\mathbf{q},\omega)$, with the inset showing a magnified segment around $\omega\to0$.
• Figure 3: (a) Static electron density response function $\chi_\textnormal{inel}(\mathbf{q})$ [Eq. (\ref{['eq:static_chi']})] of hydrogen at $\rho=0.08\,$g/cc and $T=4.8\,$eV. Black crosses: quasi-exact PIMC reference data Dornheim_MRE_2024Dornheim_JCP_2024; red symbols: direct TDDFT; green symbols: direct perturbation approach, $\chi_A(\mathbf{q})$. (b) and (c): electronic isosurfaces of the perturbed and unperturbed systems; see the Supplemental Material supplement for details.
• Figure 4: Electron static structure factor $S_{ee}(\mathbf{q})$ of hydrogen at $\rho=0.33\,$g/cc [$r_s=2$] and $T=12.5\,$eV [$\Theta=1$, red], $T=6.27\,$eV [$\Theta=0.5$, green] and $T=3.13\,$eV [$\Theta=0.25$, blue]. Symbols show fully corrected TDDFT data [Eq. (\ref{['eq:final_final']})] and the curves have been computed based on a chemical model bellenbaum2025estimatingionizationstatescontinuum, see the Supplemental Material supplement for details. The black crosses show quasi-exact PIMC reference data Dornheim_JCP_2024 for $\Theta=1$.