Assessing the accuracy of hybrid exchange-correlation functionals for the density response of warm dense electrons

Abstract

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.

Non-empirical Mixing Coefficient for Hybrid XC Functionals from Analysis of the XC Kernel

“…This is also the case for the HSE06 and HSE03 kernels, which are screened versions of PBE0. 11 A relevant observation is that AM05 performs as well as PBE0 and HSE06 and much better than PBE for solids and surfaces. 39 The success of AM05 is due to a subsystem functional approach.…”

“… 8 Additionally, hybrid XC functionals enable thermal XC effects 9 , 10 to be treated more accurately than usual ground-state functionals due to the inherent use of thermally smeared occupation numbers. 11 − 13 This is particularly important for warm dense matter (WDM), 14 − 16 which is a state of matter generated for example by laser heating or shock compression at facilities such as the European X-ray Free-Electron Laser (XFEL) 17 and Linac coherent light source (LCLS) at SLAC 18 and naturally occurs in astrophysical objects like the interior of giant planets. 18 , 19 Important technological applications of WDM include the discovery of novel materials under extreme conditions 20 − 22 and hot-electron chemistry.…”

“… 45 It becomes exact in the limit of q → 0. The results for K xc ( q ) based on various LDA, GGA, meta-GGA, and hybrid XC functionals, including the data for the PBE, PBE0, PBE0–1/3, and AM05 functionals, were reported in refs ( 11 ) and ( 45 ). In this work, we break down the PBE0-type functionals into exchange and correlation parts with the aim of obtaining physical insight into how the results change as we vary the mixing coefficient.…”

“…Commonly used orbital-dependent XC functionals belong to the class of hybrid functionals that mix exact Hartree–Fock (HF) exchange with the exchange energy obtained from a density functional approximation, e.g., on the level of the local density approximation (LDA) and the generalized density approximation (GGA). , The success of hybrid XC functionals stems from the reduction of the infamous self-interaction (or delocalization) error, which often hinders explicit density XC functionals like LDA and GGA from reaching chemical accuracy . Additionally, hybrid XC functionals enable thermal XC effects , to be treated more accurately than usual ground-state functionals due to the inherent use of thermally smeared occupation numbers. − This is particularly important for warm dense matter (WDM), − which is a state of matter generated for example by laser heating or shock compression at facilities such as the European X-ray Free-Electron Laser (XFEL) and Linac coherent light source (LCLS) at SLAC and naturally occurs in astrophysical objects like the interior of giant planets. , Important technological applications of WDM include the discovery of novel materials under extreme conditions − and hot-electron chemistry . Therefore, a rigorous understanding of hybrid XC functionals within the generalized KS-DFT approach is of immense importance for physics and quantum chemistry under both ambient and extreme conditions.…”

“…The perturbation amplitude is set to A = 0.01. For a detailed discussion of the convergence with respect to the simulation parameters, see our recent papers. , …”