Benchmarking exchange-correlation functionals in the spin-polarized inhomogeneous electron gas under warm dense conditions

Warm dense matter is a highly active research area both at the frontier and interface of material science and plasma physics. We assess the performance of the commonly used exchange-correlation (XC) approximation (LDA, PBE, PBEsol, and AM05) in the spin-polarized inhomogeneous electron gas under warm dense conditions based on exact path-integral quantum Monte Carlo calculations. This extends our recent analysis on the relevance of inhomogeneities in the spin-unpolarized warm dense electron gas [Moldabekov et al., J. Chem. Phys. 155, 124116 (2021)]. We demonstrate that the predictive accuracy of these XC functionals deteriorates with (1) a decrease in density (corresponding to an increase in the interelectronic correlation strength) and (2) an increase of the characteristic wave number of the density perturbation. We provide recommendations for the applicability of the considered XC functionals at conditions typical for warm dense matter. Furthermore, we hint at future possibilities for constructing more accurate XC functionals under these conditions.

Figure 1

Electron density along the perturbation direction for $r_s=2$ and a perturbation with $A=0.1$ where $q_{\min }=2\pi /L$ (top), $2q_{\min }$, and $3q_{\min }$ (bottom).

Figure 2

Electron density along the perturbation direction for $r_s=2$ and a perturbation with $A=0.5$ where $q_{\min }=2\pi /L$ (top), $2q_{\min }$, and $3q_{\min }$ (bottom).

Figure 3

Relative deviation of the electron density at $r_s=2$ in response to an external perturbation with $A=0.1$ and increasing wave numbers $q$. From top to bottom: $q_{\min }, 2q_{\min }$, and $3q_{\min }$.

Figure 4

Relative deviation of the electron density at $r_s=2$ in response to an external perturbation with $A=0.5$ and increasing wave numbers $q$. From top to bottom: $q_{\min }, 2q_{\min }$, and $3q_{\min }$.

Figure 5

Electron density along the perturbation direction for $r_s=6$ and a perturbation with $A=0.01$ where $q_{\min }=2\pi /L$ (top), $2q_{\min }$, and $3q_{\min }$ (bottom).

Figure 6

Relative deviation of the electron density at $r_s=6$ in response to an external perturbation with $A=0.01$ and increasing wave numbers $q$. From top to bottom: $q_{\min }, 2q_{\min }$, and $3q_{\min }$.

Figure 7

Electron density along the perturbation direction for $r_s=6$ and a perturbation with $A=0.1$ at $2q_{\min }$ and $3q_{\min }, q_{\min }=2\pi /L$.

Figure 8

Relative deviation of the electron density at $r_s=6$ in response to an external perturbation with $A=0.1$ and increasing wave numbers $q$. From top to bottom: $2q_{\min }$ and $3q_{\min }$.

Figure 9

Electron density along the perturbation direction for a double harmonic perturbation with wave numbers $q_1=q_{\min }$ and $q_2=2q_{\min }$ and amplitudes $A=0.1$ and $A=0.01$ for moderate coupling $r_s=2$ (top) and strong coupling $r_s=6$ (bottom).

Figure 10

Relative deviation of the electron density in response to an external double harmonic perturbation with wave numbers $q_1=q_{\min }$ and $q_2=2q_{\min }$ and amplitudes $A=0.1$ and $A=0.01$ for moderate coupling $r_s=2$ (top) and strong coupling $r_s=6$ (bottom).

Figure 11

Comparing the electron density in the spin-polarized electrons gas with the spin-unpolarized case. The density is shown along the perturbation direction for $A=0.1$ and $r_s=2$ at $q_1=q_{\min }$ (top) and $q_1=3q_{\min }$ (bottom).

Figure 12

Comparison of CPU hours required to obtain converged results using different XC functionals at $r_s=2$ for weakly (top) and strongly (bottom) perturbed spin-polarized electrons.

Figure 13

Comparison of CPU hours required to obtain converged results using different XC functionals at $r_s=6$ for weakly (top) and strongly (bottom) perturbed spin-polarized electrons.