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.

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We used molecular dynamics simulations based on density functional theory to study the thermophysical properties of warm dense helium. The influence of different exchange-correlation (XC) functionals was analyzed. We calculated the equation of state at high pressures up to several Mbar and temperatures up to 100 000 K in order to reconstruct recent static, single shock, and quasi-isentropic compression experiments. Furthermore, we calculated the dynamic electrical conductivity and determined the reflectivity and DC conductivity. We compared our results with experimental data and found good agreement between our calculations and the high-pressure experiments. The different XC functionals give similar results in the equation of state calculations, but have a strong impact on the reflectivity and the DC conductivity.

The Kubo-Greenwood (KG) formula is often used in conjunction with Kohn-Sham (KS) density functional theory (DFT) to compute the optical conductivity, particularly for warm dense mater. For applying the KG formula, all KS eigenstates and eigenvalues up to an energy cutoff are required and thus the approach becomes expensive, especially for high temperatures and large systems, scaling cubically with both system size and temperature. Here, we develop an approach to calculate the KS conductivity within the stochastic DFT (sDFT) framework, which requires knowledge only of the KS Hamiltonian but not its eigenstates and values. We show that the computational effort associated with the method scales linearly with system size and reduces in proportion to the temperature unlike the cubic increase with traditional deterministic approaches. In addition, we find that the method allows an accurate description of the entire spectrum, including the high-frequency range, unlike the deterministic method which is compelled to introduce a high-frequency cut-off due to memory and computational time constraints. We apply the method to helium-hydrogen mixtures in the warm dense matter regime at temperatures of ∼ 60kK and find that the system displays two conductivity phases, where a transition from non-metal to metal occurs when hydrogen atoms constitute ∼ 0.3 of the total atoms in the system. well as their formation and evolution characteristics [4][5][6]. Generally, EOS and properties are calculated for various materials using first-principle methods, specifically the Kohn-Sham density functional theory (KS-DFT) at finite temperatures [7-10], often showing good agreement with experiments [10][11][12]. Within the KS-DFT framework, WDM conductivity is often obtained by using the Kubo-Greenwood (KG) formalism [13][14][15][16] with good results when compared to experiment. The KS-DFT and the KG electrical conductivity equation when applied to WDM requires large computational effort which increases dramatically with temperature and system size, because of the need to construct and propagate all the occupied KS eigenstates, as well as a sufficient number of unoccupied states, the number of which grows as T 3 , where T is the temperature [17]).Recently, stochastic DFT (sDFT) approaches that circumvent the computational difficulties mentioned above have been developed [17][18][19][20][21][22] for ground/thermal state calculations. These have also served as a basis for devel-arXiv:1906.03346v1 [cond-mat.mtrl-sci]

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