The phase diagram of high-pressure hydrogen is of great interest for fundamental research, planetary physics, and energy applications. A first-order phase transition in the fluid phase between a molecular insulating fluid and a monoatomic metallic fluid has been predicted. The existence and precise location of the transition line is relevant for planetary models. Recent experiments reported contrasting results about the location of the transition. Theoretical results based on density functional theory are also very scattered. We report highly accurate coupled electron-ion Monte Carlo calculations of this transition, finding results that lie between the two experimental predictions, close to that measured in diamond anvil cell experiments but at 25-30 GPa higher pressure. The transition along an isotherm is signaled by a discontinuity in the specific volume, a sudden dissociation of the molecules, a jump in electrical conductivity, and loss of electron localization.high pressure | phase transitions | quantum Monte Carlo | hydrogen metallization | molecular dissociation H ydrogen is the simplest element of the periodic table and a paradigmatic element in developing general physical theories of condensed matter. Despite the simple electronic structure, its phase diagram is unexpectedly rich, ranging from the normal three-phase equilibria (solid-liquid-gas) of the lowpressure molecular system to the fully dissociated and ionized plasma states at extreme conditions of temperature and pressure. Accurate knowledge of its phase diagram is highly relevant as testified by the continuing intense research activity over the last half century (1-5). Its relevance in nature arises because it is the most abundant element in the universe and, together with the next simplest element helium, constitutes 70-90% of the atmosphere of the giant planets, Jupiter and Saturn, and of the many, recently discovered, exoplanets. Also, it is the putative element for nuclear fusion for energy applications.The longest outstanding issue concerns the metal-insulator transition and its interplay with molecular dissociation. Molecular dissociation can occur either upon increasing temperature in the low-pressure fluid or upon increasing pressure in the low-temperature crystalline phase, or even as a combined action of temperature and pressure in the denser molecular fluid (5). The first prediction of metallization at zero temperature suggested that the molecular crystal would become atomic and transform to a simple metal above 25 GPa (1). Later experiments with higher pressures up to at least 360 GPa have found no convincing evidence of the metallic state at least below room temperature. However, they have revealed a rich phase diagram with a sequence of phase transformations in the molecular solid and the possibility of a semimetallic state (3, 6-13).The metallic state has been unequivocally observed in the dense fluid in the range of 100-200 GPa and estimated temperatures of 2,000-3,000 K by dynamical compression experiments (5, 14-16). Using the ...

We performed simulations for solid molecular hydrogen at high pressures (250GPa≤P≤500GPa) along two isotherms at T=200 K (phases III and VI) and at T=414 K (phase IV). At T=200K we considered likely candidates for phase III, the C2c and Cmca12 structures, while at T=414K in phase IV we studied the Pc48 structure. We employed both Coupled Electron-Ion Monte Carlo (CEIMC) and Path Integral Molecular Dynamics (PIMD) based on Density Functional Theory (DFT) using the vdW-DF approximation. The comparison between the two methods allows us to address the question of the accuracy of the xc approximation of DFT for thermal and quantum protons without recurring to perturbation theories. In general, we find that atomic and molecular fluctuations in PIMD are larger than in CEIMC which suggests that the potential energy surface from vdW-DF is less structured than the one from Quantum Monte Carlo. We find qualitatively different behaviors for systems prepared in the C2c structure for increasing pressure. Within PIMD the C2c structure is dynamically partially stable for P≤250GPa only: it retains the symmetry of the molecular centers but not the molecular orientation; at intermediate pressures it develops layered structures like Pbcn or Ibam and transforms to the metallic Cmca-4 structure at P≥450GPa. Instead, within CEIMC, the C2c structure is found to be dynamically stable at least up to 450GPa; at increasing pressure the molecular bond length increases and the nuclear correlation decreases. For the other two structures the two methods are in qualitative agreement although quantitative differences remain. We discuss various structural properties and the electrical conductivity. We find these structures become conducting around 350GPa but the metallic Drude-like behavior is reached only at around 500GPa, consistent with recent experimental claims.

Optical properties of compressed fluid hydrogen in the region where dissociation and metallization is observed are computed by ab-initio methods and compared to recent experimental results. We confirm that above 3000 K both processes are continuous while below 1500K the first order phase transition is accompanied by a discontinuity of the DC conductivity and the thermal conductivity, while both the reflectivity and absorption coefficient vary rapidly but continuously. Our results support the recent analysis of NIF experiments (P. Celliers et al, Science 361, 677-682 (2018)) which assigned the inception of metallization to pressures where the reflectivity is about 0.3. Our results also support the conclusion that the temperature plateau seen in laser-heated DAC experiments at temperatures higher than 1500 K corresponds to the onset of of optical absorption, not to the phase transition.

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We analyze in detail the electronic properties of high pressure hydrogen around the liquid-liquid phase transition based on Coupled Electron-Ion Monte Carlo calculations. Computing the off-diagonal single particle density matrix and the momentum distribution we discuss localization properties of the electrons. The abrupt changes of these distributions indicate a metal to insulator transition occurring together with the structural transition from the atomic to molecular fluid. We further discuss the electron-proton and electron-electron pair correlation functions, which also change abruptly at the transition.