Hydrogen and helium are the most abundant elements in the universe and, in principle, are the simplest elements. Nonetheless, they display remarkable properties under pressure that have fascinated theoreticians and experimentalists for over a century. Recent advances in computational methods have made it possible to elucidate many of these properties. We review some of the computational methods that have been applied to dense hydrogen and helium in recent years, mainly those that perform a simulation directly from the physical picture of electrons and ions; primarily, those based on density functional theory and quantum Monte Carlo methods. We then discuss the predictions from such methods as applied to the phase diagram of hydrogen, including the solid and fluid phases, with particular focus on the crystal structures, the liquidliquid transition and comparison of the results with experimental shock-wave data. We then discuss predictions of ordered quantum states, including a possible low-temperature fluid and high-temperature superconductivity in the atomic state. We also briefly discuss pure helium, and then focus on hydrogen-helium mixtures, with particular focus on properties of relevance to planetary science.
Using quantum simulation techniques based on either density functional theory or quantum Monte Carlo, we find clear evidence of a first-order transition in liquid hydrogen, between a low conductivity molecular state and a high conductivity atomic state. Using the temperature dependence of the discontinuity in the electronic conductivity, we estimate the critical point of the transition at temperatures near 2,000 K and pressures near 120 GPa. Furthermore, we have determined the melting curve of molecular hydrogen up to pressures of 200 GPa, finding a reentrant melting line. The melting line crosses the metalization line at 700 K and 220 GPa using density functional energetics and at 550 K and 290 GPa using quantum Monte Carlo energetics.phase transition | quantum Monte Carlo | density functional theory | plasma phase transition | melting S ince the pioneering work of Wigner and Huntington (1), on the metallization of solid molecular hydrogen by pressure, there has been a great effort to understand the molecular dissociation process in high-pressure hydrogen from both experiment and theory. In the solid, at low temperatures, metallization has been expected to occur in conjunction with a transition to a solid atomic state, although a transition to exotic phases such as quantum fluids (2) or metallic molecular phases may also be possible (3-5).For dense hydrogen in the liquid phase, metallization (probably accompanied by molecular dissociation) can occur either through a continuous process (a crossover) or through a sharp, first-order transition, often called the plasma phase transition. Numerous experiments have been performed in the liquid phase using dynamic compression techniques to measure both the principal Hugoniot in hydrogen and deuterium [using for example: gas guns (6), laser-driven compression (7-9), magnetically driven flyers (10, 11), and converging explosives (12)] and to measure off-Hugoniot properties at lower temperatures [electrical conductivity measurements using shock reverberation (13) and multiple shocks (14), compressibility measurements using explosive-driven generators (15), to mention a few]. The conductivity measurements by Nellis and coworkers (13) produced the first evidence of minimum metallic conductivity in fluid hydrogen at a pressure of 140 GPa and temperatures on the order of 3,000 K. Until recently, there were no experimental indications of a first-order liquid-liquid transition (LLT) in hydrogen. Even though results could not rule out the existence of the transition and most studies had been performed at fairly high temperatures, there was no sign of a sharp, first-order behavior. The only direct experimental evidence of a LLT is from the work of Fortov et al. (15) where reverberating shocks produced with high explosives were used to ramp compress hydrogen, presumably reaching temperatures in the range of 3-8 × 10 3 K. Using highly resolved flash X-ray diagnostics, they were able to measure the compressibility of the liquid and found a 20% increase in density in the regime wher...
Using first-principles molecular dynamics, we study the influence of nuclear quantum effects (NQEs) and nonlocal exchange-correlation density functionals (DFs) near molecular dissociation in liquid hydrogen. NQEs strongly influence intramolecular properties, such as bond stability, and are thus an essential part of the dissociation process. Moreover, by including DFs that account for either the self-interaction error or dispersion interactions, we find a much better description of molecular dissociation and metallization than previous studies based on classical protons and/or local or semi-local DFs. We obtain excellent agreement with experimentally measured optical properties along pre-compressed Hugoniots, and while we still find a first-order liquid-liquid transition at low temperatures, transition pressures are increased by more than 100 GPa.
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