Nonempirical generalized gradient approximation free-energy functional for orbital-free simulations

We report a purely nonempirical generalized gradient approximation for the noninteracting free energy functional of orbital-free density functional theory obtained via a novel constraint-based parametrization scheme. We use that functional to provide forces for finite-temperature molecular dynamics simulations in the warm dense matter (WDM) regime and demonstrate good-to-excellent agreement with reference Kohn-Sham calculations under WDM conditions at a minuscule fraction of the computational cost of corresponding orbital-based simulations.

Figure 1

VT84F and APBEF Pauli term enhancement factors $F_{\tau }\left(s\right)-(5s^2/3)$ as a function of $s$ ($T=0$ K).

Figure 2

Electronic heat capacity, $C_{\mathrm{V}}^{\mathrm{el}}$, as a function of electronic $T$ for sc-H at material density ${\rho }_{\mathrm{H}}=0.60$ and 2.0 g/cm${}^3$.

Figure 3

Upper panel: Pressures for OFDFT and KS AIMD, both with explicitly $T$-dependent XC (Ref. 34) compared with PIMC (Ref. 12) results for deuterium at ${\rho }_{\mathrm{D}}=1.964$ g/cm${}^3$ ($r_{\mathrm{s}}=1.40$ bohrs). Lower panel: Relative differences of OFDFT and PIMC pressures with respect to KS values.

Figure 4

Excess pressure relative to the TF model for OFDFT (APBEK and VT84F functionals), KS and PIMC (Ref. 12), for deuterium at material density ${\rho }_{\mathrm{D}}=1.964$ g/cm${}^3$ ($r_{\mathrm{s}}=1.40$ bohrs).

Figure 5

Pressure vs material density for selected temperatures calculated by OFDFT and KS AIMD for deuterium.

Figure 6

The OFDFT and KS ion pair-correlation function for $T=31250$ K (upper panel) and $T=62500$ K (lower panel).

Figure 7

CPU time per AIMD step as a function of $T$ for OFDFT-MD calculations compared to the KS-MD data. Deuterium at ${\rho }_{\mathrm{D}}=1.964$ g/cm${}^3$ ($r_{\mathrm{s}}=1.40$ bohrs), 128 atoms in simulation cell.