Nuclear quantum effects influence the structure and dynamics of hydrogen bonded systems, such as water, which impacts their observed properties with widely varying magnitudes. This review highlights the recent significant developments in the experiment, theory and simulation of nuclear quantum effects in water. Novel experimental techniques, such as deep inelastic neutron scattering, now provide a detailed view of the role of nuclear quantum effects in water's 2 properties. These have been combined with theoretical developments such as the introduction of the competing quantum effects principle that allows the subtle interplay of water's quantum effects and their manifestation in experimental observables to be explained. We discuss how this principle has recently been used to explain the apparent dichotomy in water's isotope effects, which can range from very large to almost nonexistent depending on the property and conditions. We then review the latest major developments in simulation algorithms and theory that have enabled the efficient inclusion of nuclear quantum effects in molecular simulations, permitting their combination with on-the-fly evaluation of the potential energy surface using electronic structure theory. Finally, we identify current challenges and future opportunities in the area.3

The MB-pol many-body potential has recently emerged as an accurate molecular model for water simulations from the gas to the condensed phase. In this study, the accuracy of MB-pol is systematically assessed across the three phases of water through extensive comparisons with experimental data and high-level ab initio calculations. Individual many-body contributions to the interaction energies as well as vibrational spectra of water clusters calculated with MB-pol are in excellent agreement with reference data obtained at the coupled cluster level. Several structural, thermodynamic, and dynamical properties of the liquid phase at atmospheric pressure are investigated through classical molecular dynamics simulations as a function of temperature. The structural properties of the liquid phase are in nearly quantitative agreement with X-ray diffraction data available over the temperature range from 268 to 368 K. The analysis of other thermodynamic and dynamical quantities emphasizes the importance of explicitly including nuclear quantum effects in the simulations, especially at low temperature, for a physically correct description of the properties of liquid water. Furthermore, both densities and lattice energies of several ice phases are also correctly reproduced by MB-pol. Following a recent study of DFT models for water, a score is assigned to each computed property, which demonstrates the high and, in many respects, unprecedented accuracy of MB-pol in representing all three phases of water.

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.