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

The temperature (T) and density (rho) conditions at which hydrogen undergoes a molecular-to-atomic (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-rho regime, where the transition is largely T driven, and the low-T, high-rho regime, where the transition is largely rho 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 rho play an important role in the transition. The measurement results are found to be inconsistent with the semilocal 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 rho conditions. Together with previous comparisons at high-T, low-rho and low-T, high-rho these results provide a consistent picture for the MA transition over a wide T and rho 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.