Evaluation of exchange-correlation functionals with multiple-shock conductivity measurements in hydrogen and deuterium at the molecular-to-atomic transition

Abstract

The temperature (T) and density (ρ) conditions at which hydrogen undergoes a molecular-toatomic (MA) transition is crucial to our understanding of the gas-giant planets such as Jupiter and Saturn. First-principles (FP) calculations suggest that this transition is coincident with metallization and acts as a catalyst for hydrogen-helium demixing, which has significant consequences for models of planetary interiors. Prediction of this transition boundary has proven to be difficult using FP methods. In particular, detailed comparisons of finite temperature density functional theory (FT-DFT) calculations of the MA transition in both the high-T , low-ρ regime, where the transition is largely T-driven, and the low-T , high-ρ regime, where the transition is largely ρ-driven, suggest that the transition is very sensitive to the exchange-correlation (xc) functional used in the calculation. Here we present a detailed comparison of previous multiple-shock electrical conductivity measurements with FT-DFT calculations employing various xc functionals to probe a regime where both T and ρ play an important role in the transition. The measurement results are found to be inconsistent with the semi-local xc functional PBE, and are in much better agreement with the nonlocal xc functionals vdW-DF1 and vdW-DF2. Furthermore, we show that the inconsistency with PBE likely stems from pressure errors associated with the PBE xc functional, resulting in calculated pressures that are too low at these T and ρ conditions. Together with previous comparisons at high-T , low-ρ and low-T , high-ρ these results provide a consistent picture for the MA transition over a wide T and ρ range. This picture may also provide insight into differences in experimental observations of the metallization of liquid hydrogen and deuterium in the low-T regime.

Benchmarking vdW‐DF first‐principles predictions against Coupled Electron–Ion Monte Carlo for high‐pressure liquid hydrogen

“…Analysis of the conductivities in terms of the Drude–Smith model provides σ dft ( ω = 0) = 5, 450(50), σ qmc ( ω = 0) = 7, 280(70)(Ω cm) −1 at T = 1, 500 K r s = 1.40 and σ dft ( ω = 0) = 4, 600 (40), σ qmc ( ω = 0) = 5, 900(40)(Ω cm) −1 at T = 3, 000 K r s = 1.52 for vdW‐DF and CEIMC, respectively. In Figure b, we also report a recent result for the DC conductivity from FPMD with the vdW‐DF XC approximation at a state point close to our present one…”

Plasma phase transition (by the fiftieth anniversary of the prediction)

“…[40] Totally, the combination of these effects increases the pressure and densities of the phase transition. [54] The approach based on the path integral molecular dynamics and DFT with non-local exchange correlation functionals gives good agreement with the experimental data obtained in Sandia Z-machine, [33] National Ignition Facility (NIF) [25] and some optical measurements from the DAC experiments. [54] The approach based on the path integral molecular dynamics and DFT with non-local exchange correlation functionals gives good agreement with the experimental data obtained in Sandia Z-machine, [33] National Ignition Facility (NIF) [25] and some optical measurements from the DAC experiments.…”

“…[33,54] At the same time, contribution of the zero vibrations or nuclear quantum effects decreases the pressure and density of the phase transition. [33,54] At the same time, contribution of the zero vibrations or nuclear quantum effects decreases the pressure and density of the phase transition.…”

“…[33,54] At the same time, contribution of the zero vibrations or nuclear quantum effects decreases the pressure and density of the phase transition. [33,40,54] Theoretically, combination of such effects gives more accurate description of the equation of state and structural properties of dense hydrogen. [33,40,54] Theoretically, combination of such effects gives more accurate description of the equation of state and structural properties of dense hydrogen.…”

Metastable molecular fluid hydrogen at high pressures

“…[1][2][3][4][5][6][7][8][9][10][11] The methods also include density functional theory (DFT), [12] path-integral molecular dynamics (PIMD) based on DFT, coupled electron-ion Monte Carlo (CEIMC), [13] and the quantum Monte Carlo molecular dynamics (QMCMD). [1][2][3][4][5][6][7][8][9][10][11] The methods also include density functional theory (DFT), [12] path-integral molecular dynamics (PIMD) based on DFT, coupled electron-ion Monte Carlo (CEIMC), [13] and the quantum Monte Carlo molecular dynamics (QMCMD).…”