The first-principles phase diagram of monolayer nanoconfined water.

Water in nanoscale cavities is ubiquitous and of central importance to everyday phenomena in geology and biology. However, the properties of nanoscale water can be substantially different from those of bulk water, as shown, for example, by the anomalously low dielectric constant of water in nanochannels1, near frictionless water flow2 or the possible existence of a square ice phase3. Such properties suggest that nanoconfined water could be engineered for technological applications in nanofluidics4, electrolyte materials5 and water desalination6. Unfortunately, challenges in experimentally characterizing water at the nanoscale and the high cost of first-principles simulations have prevented the molecular-level understanding required to control the behaviour of water. Here we combine a range of computational approaches to enable a first-principles-level investigation of a single layer of water within a graphene-like channel. We find that monolayer water exhibits surprisingly rich and diverse phase behaviour that is highly sensitive to temperature and the van der Waals pressure acting within the nanochannel. In addition to multiple molecular phases with melting temperatures varying non-monotonically by more than 400 kelvins with pressure, we predict a hexatic phase, which is an intermediate between a solid and a liquid, and a superionic phase with a high electrical conductivity exceeding that of battery materials. Notably, this suggests that nanoconfinement could be a promising route towards superionic behaviour under easily accessible conditions.

Evidence for supercritical behaviour of high-pressure liquid hydrogen.

Hydrogen, the simplest and most abundant element in the Universe, develops a remarkably complex behaviour upon compression1. Since Wigner predicted the dissociation and metallization of solid hydrogen at megabar pressures almost a century ago2, several efforts have been made to explain the many unusual properties of dense hydrogen, including a rich and poorly understood solid polymorphism1,3-5, an anomalous melting line6 and the possible transition to a superconducting state7. Experiments at such extreme conditions are challenging and often lead to hard-to-interpret and controversial observations, whereas theoretical investigations are constrained by the huge computational cost of sufficiently accurate quantum mechanical calculations. Here we present a theoretical study of the phase diagram of dense hydrogen that uses machine learning to 'learn' potential-energy surfaces and interatomic forces from reference calculations and then predict them at low computational cost, overcoming length- and timescale limitations. We reproduce both the re-entrant melting behaviour and the polymorphism of the solid phase. Simulations using our machine-learning-based potentials provide evidence for a continuous molecular-to-atomic transition in the liquid, with no first-order transition observed above the melting line. This suggests a smooth transition between insulating and metallic layers in giant gas planets, and reconciles existing discrepancies between experiments as a manifestation of supercritical behaviour.

Chemical interactions that govern the structures of metals.

Most metals adopt simple structures such as body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed (HCP) structures in specific groupings across the periodic table, and many undergo transitions to surprisingly complex structures on compression, not expected from conventional free-electron-based theories of metals. First-principles calculations have been able to reproduce many observed structures and transitions, but a unified, predictive theory that underlies this behavior is not yet in hand. Discovered by analyzing the electronic properties of metals in various lattices over a broad range of sizes and geometries, a remarkably simple theory shows that the stability of metal structures is governed by electrons occupying local interstitial orbitals and their strong chemical interactions. The theory provides a basis for understanding and predicting structures in solid compounds and alloys over a broad range of conditions.

Feasible Route to High-Temperature Ambient-Pressure Hydride Superconductivity.

A key challenge in materials discovery is to find high-temperature superconductors. Hydrogen and hydride materials have long been considered promising materials displaying conventional phonon-mediated superconductivity. However, the high pressures required to stabilize these materials have restricted their application. Here, we present results from high-throughput computation, considering a wide range of high-symmetry ternary hydrides from across the periodic table at ambient pressure. This large composition space is then reduced by considering thermodynamic, dynamic, and magnetic stability before direct estimations of the superconducting critical temperature. This approach has revealed a metastable ambient-pressure hydride superconductor, Mg_{2}IrH_{6}, with a predicted critical temperature of 160 K, comparable to the highest temperature superconducting cuprates. We propose a synthesis route via a structurally related insulator, Mg_{2}IrH_{7}, which is thermodynamically stable above 15 GPa, and discuss the potential challenges in doing so.

Rules of formation of H-C-N-O compounds at high pressure and the fates of planetary ices.

The solar system's outer planets, and many of their moons, are dominated by matter from the H-C-N-O chemical space, based on solar system abundances of hydrogen and the planetary ices [Formula: see text]O, [Formula: see text], and [Formula: see text] In the planetary interiors, these ices will experience extreme pressure conditions, around 5 Mbar at the Neptune mantle-core boundary, and it is expected that they undergo phase transitions, decompose, and form entirely new compounds. While temperature will dictate the formation of compounds, ground-state density functional theory allows us to probe the chemical effects resulting from pressure alone. These structural developments in turn determine the planets' interior structures, thermal evolution, and magnetic field generation, among others. Despite its importance, the H-C-N-O system has not been surveyed systematically to explore which compounds emerge at high-pressure conditions, and what governs their stability. Here, we report on and analyze an unbiased crystal structure search among H-C-N-O compounds between 1 and 5 Mbar. We demonstrate that simple chemical rules drive stability in this composition space, which explains why the simplest possible quaternary mixture HCNO-isoelectronic to diamond-emerges as a stable compound and discuss dominant decomposition products of planetary ice mixtures.

Automatic differentiation for orbital-free density functional theory.

Differentiable programming has facilitated numerous methodological advances in scientific computing. Physics engines supporting automatic differentiation have simpler code, accelerating the development process and reducing the maintenance burden. Furthermore, fully differentiable simulation tools enable direct evaluation of challenging derivatives-including those directly related to properties measurable by experiment-that are conventionally computed with finite difference methods. Here, we investigate automatic differentiation in the context of orbital-free density functional theory (OFDFT) simulations of materials, introducing PROFESS-AD. Its automatic evaluation of properties derived from first derivatives, including functional potentials, forces, and stresses, facilitates the development and testing of new density functionals, while its direct evaluation of properties requiring higher-order derivatives, such as bulk moduli, elastic constants, and force constants, offers more concise implementations than conventional finite difference methods. For these reasons, PROFESS-AD serves as an excellent prototyping tool and provides new opportunities for OFDFT.

Developments and further applications of ephemeral data derived potentials.

Machine-learned interatomic potentials are fast becoming an indispensable tool in computational materials science. One approach is the ephemeral data-derived potential (EDDP), which was designed to accelerate atomistic structure prediction. The EDDP is simple and cost-efficient. It relies on training data generated in small unit cells and is fit using a lightweight neural network, leading to smooth interactions which exhibit the robust transferability essential for structure prediction. Here, we present a variety of applications of EDDPs, enabled by recent developments of the open-source EDDP software. New features include interfaces to phonon and molecular dynamics codes, as well as deployment of the ensemble deviation for estimating the confidence in EDDP predictions. Through case studies ranging from elemental carbon and lead to the binary scandium hydride and the ternary zinc cyanide, we demonstrate that EDDPs can be trained to cover wide ranges of pressures and stoichiometries, and used to evaluate phonons, phase diagrams, superionicity, and thermal expansion. These developments complement continued success in accelerated structure prediction.

Revisiting metal fluorides as lithium-ion battery cathodes.

Metal fluorides, promising lithium-ion battery cathode materials, have been classified as conversion materials due to the reconstructive phase transitions widely presumed to occur upon lithiation. We challenge this view by studying FeF3 using X-ray total scattering and electron diffraction techniques that measure structure over multiple length scales coupled with density functional theory calculations, and by revisiting prior experimental studies of FeF2 and CuF2. Metal fluoride lithiation is instead dominated by diffusion-controlled displacement mechanisms, and a clear topological relationship between the metal fluoride F- sublattices and that of LiF is established. Initial lithiation of FeF3 forms FeF2 on the particle's surface, along with a cation-ordered and stacking-disordered phase, A-LixFeyF3, which is structurally related to α-/ß-LiMn2+Fe3+F6 and which topotactically transforms to B- and then C-LixFeyF3, before forming LiF and Fe. Lithiation of FeF2 and CuF2 results in a buffer phase between FeF2/CuF2 and LiF. The resulting principles will aid future developments of a wider range of isomorphic metal fluorides.

Design Principles for High-Temperature Superconductors with a Hydrogen-Based Alloy Backbone at Moderate Pressure.

Hydrogen-based superconductors provide a route to the long-sought goal of room-temperature superconductivity, but the high pressures required to metallize these materials limit their immediate application. For example, carbonaceous sulfur hydride, the first room-temperature superconductor made in a laboratory, can reach a critical temperature (T_{c}) of 288 K only at the extreme pressure of 267 GPa. The next recognized challenge is the realization of room-temperature superconductivity at significantly lower pressures. Here, we propose a strategy for the rational design of high-temperature superconductors at low pressures by alloying small-radius elements and hydrogen to form ternary H-based superconductors with alloy backbones. We identify a "fluorite-type" backbone in compositions of the form AXH_{8}, which exhibit high-temperature superconductivity at moderate pressures compared with other reported hydrogen-based superconductors. The Fm3[over ¯]m phase of LaBeH_{8}, with a fluorite-type H-Be alloy backbone, is predicted to be thermodynamically stable above 98 GPa, and dynamically stable down to 20 GPa with a high T_{c}∼185 K. This is substantially lower than the synthesis pressure required by the geometrically similar clathrate hydride LaH_{10} (170 GPa). Our approach paves the way for finding high-T_{c} ternary H-based superconductors at conditions close to ambient pressures.

Structural diversity and hydrogen storage properties in the system K-Si-H.

KSiH3 exhibits 4.1 wt% experimental hydrogen storage capacity and shows reversibility under moderate conditions, which provides fresh impetus to the search for other complex hydrides in the K-Si-H system. Here, we reproduce the stable Fm3̄m phase of K2SiH6 and uncover two denser phases, space groups P3̄m1 and P63mc at ambient pressure, by means of first-principles structure searches. We note that P3̄m1-K2SiH6 has a high hydrogen content of 5.4 wt% and a volumetric density of 88.3 g L-1. Further calculations suggest a favorable dehydrogenation temperature Tdes of -20.1/55.8 °C with decomposition into KSi + K + H2. The higher hydrogen density and appropriate dehydrogenation temperature indicate that K2SiH6 is a promising hydrogen storage material, and our results provide helpful and clear guidance for further experimental studies. We found three further potential hydrogen storage materials stable at high pressure: K2SiH8, KSiH7 and KSiH8. These results suggest the need for further investigations into hydrogen storage materials among such ternary hydrides at high pressure.

Quantum hydrogen-bond symmetrization in the superconducting hydrogen sulfide system.

The quantum nature of the proton can crucially affect the structural and physical properties of hydrogen compounds. For example, in the high-pressure phases of H2O, quantum proton fluctuations lead to symmetrization of the hydrogen bond and reduce the boundary between asymmetric and symmetric structures in the phase diagram by 30 gigapascals (ref. 3). Here we show that an analogous quantum symmetrization occurs in the recently discovered sulfur hydride superconductor with a superconducting transition temperature Tc of 203 kelvin at 155 gigapascals--the highest Tc reported for any superconductor so far. Superconductivity occurs via the formation of a compound with chemical formula H3S (sulfur trihydride) with sulfur atoms arranged on a body-centred cubic lattice. If the hydrogen atoms are treated as classical particles, then for pressures greater than about 175 gigapascals they are predicted to sit exactly halfway between two sulfur atoms in a structure with Im3m symmetry. At lower pressures, the hydrogen atoms move to an off-centre position, forming a short H-S covalent bond and a longer H···S hydrogen bond in a structure with R3m symmetry. X-ray diffraction experiments confirm the H3S stoichiometry and the sulfur lattice sites, but were unable to discriminate between the two phases. Ab initio density-functional-theory calculations show that quantum nuclear motion lowers the symmetrization pressure by 72 gigapascals for H3S and by 60 gigapascals for D3S. Consequently, we predict that the Im3m phase dominates the pressure range within which the high Tc was measured. The observed pressure dependence of Tc is accurately reproduced in our calculations for the phase, but not for the R3m phase. Therefore, the quantum nature of the proton fundamentally changes the superconducting phase diagram of H3S.

High-pressure phase behaviors of titanium dioxide revealed by a Δ-learning potential.

Titanium dioxide has been extensively studied in the rutile or anatase phase, while its high-pressure phases are less well-understood, despite that many are thought to have interesting optical, mechanical, and electrochemical properties. First-principles methods, such as density functional theory (DFT), are often used to compute the enthalpies of TiO2 phases at 0 K, but they are expensive and, thus, impractical for long time scale and large system-size simulations at finite temperatures. On the other hand, cheap empirical potentials fail to capture the relative stabilities of various polymorphs. To model the thermodynamic behaviors of ambient and high-pressure phases of TiO2, we design an empirical model as a baseline and then train a machine learning potential based on the difference between the DFT data and the empirical model. This so-called Δ-learning potential contains long-range electrostatic interactions and predicts the 0 K enthalpies of stable TiO2 phases that are in good agreement with DFT. We construct a pressure-temperature phase diagram of TiO2 in the range 0 < P < 70 GPa and 100 < T < 1500 K. We then simulate dynamic phase transition processes by compressing anatase at different temperatures. At 300 K, we predominantly observe an anatase-to-baddeleyite transformation at about 20 GPa via a martensitic two-step mechanism with a highly ordered and collective atomic motion. At 2000 K, anatase can transform into cotunnite around 45-55 GPa in a thermally activated and probabilistic manner, accompanied by diffusive movement of oxygen atoms. The pressures computed for these transitions show good agreement with experiments. Our results shed light on how to synthesize and stabilize high-pressure TiO2 phases, and our method is generally applicable to other functional materials with multiple polymorphs.

Anataselike Grain Boundary Structure in Rutile Titanium Dioxide.

The formation of nanoscale phases at grain boundaries in polycrystalline materials has attracted much attention, since it offers a route toward targeted and controlled design of interface properties. However, understanding structure-property relationships at these complex interfacial defects is hampered by the great challenge of accurately determining their atomic structure. Here, we combine advanced electron microscopy together with ab initio random structure searching to determine the atomic structure of an experimentally fabricated Σ13 (221) [11̅0] grain boundary in rutile TiO2. Through careful analysis of the atomic structure and complementary electron energy-loss spectroscopy analysis we identify the existence of a unique nanoscale phase at the grain boundary with striking similarities to the bulk anatase crystal structure. Our results show a path to embed nanoscale anatase into rutile TiO2 and showcase how the atomic structure of even complex internal interfaces can be accurately determined using a combined theoretical and experimental approach.

Computationally Directed Discovery of MoBi2.

Incorporating bismuth, the heaviest element stable to radioactive decay, into new materials enables the creation of emergent properties such as permanent magnetism, superconductivity, and nontrivial topology. Understanding the factors that drive Bi reactivity is critical for the realization of these properties. Using pressure as a tunable synthetic vector, we can access unexplored regions of phase space to foster reactivity between elements that do not react under ambient conditions. Furthermore, combining computational and experimental methods for materials discovery at high-pressures provides broader insight into the thermodynamic landscape than can be achieved through experiment alone, informing our understanding of the dominant chemical factors governing structure formation. Herein, we report our combined computational and experimental exploration of the Mo-Bi system, for which no binary intermetallic structures were previously known. Using the ab initio random structure searching (AIRSS) approach, we identified multiple synthetic targets between 0-50 GPa. High-pressure in situ powder X-ray diffraction experiments performed in diamond anvil cells confirmed that Mo-Bi mixtures exhibit rich chemistry upon the application of pressure, including experimental realization of the computationally predicted CuAl2-type MoBi2 structure at 35.8(5) GPa. Electronic structure and phonon dispersion calculations on MoBi2 revealed a correlation between valence electron count and bonding in high-pressure transition metal-Bi structures as well as identified two dynamically stable ambient pressure polymorphs. Our study demonstrates the power of the combined computational-experimental approach in capturing high-pressure reactivity for efficient materials discovery.

Multistep Dissociation of Fluorine Molecules under Extreme Compression.

All elements that form diatomic molecules, such as H_{2}, N_{2}, O_{2}, Cl_{2}, Br_{2}, and I_{2}, are destined to become atomic solids under sufficiently high pressure. However, as revealed by many experimental and theoretical studies, these elements show very different propensity and transition paths due to the balance of reduced volume, lone pair electrons, and interatomic bonds. The study of F under pressure can illuminate this intricate behavior since F, owing to its unique position on the periodic table, can be compared with H, with N and O, and also with other halogens. Nevertheless, F remains the only element whose solid structure evolution under pressure has not been thoroughly studied. Using a large-scale crystal structure search method based on first principles calculations, we find that, before reaching an atomic phase, F solid transforms first into a structure consisting of F_{2} molecules and F polymer chains and then into a structure consisting of F polymer chains and F atoms, a distinctive evolution with pressure that has not been seen in any other elements. Both intermediate structures are found to be metallic and become superconducting, a result that adds F to the elemental superconductors.

Random Structure Searching with Orbital-Free Density Functional Theory.

The properties of a material depend on how its atoms are arranged, and predicting these arrangements from first principles is a longstanding challenge. Orbital-free density functional theory provides a quantum-mechanical model based solely on the electron density, not individual wave functions. The resulting speedups make it attractive for random structure searching, whereby random configurations of atoms are relaxed to local minima in the energy landscape. We use this strategy to map the low-energy crystal structures of Li, Na, Mg, and Al at zero pressure. For Li and Na, our searching finds numerous close-packed polytypes of almost-equal energy, consistent with previous efforts to understand their low-temperature forms. For Mg and Al, the searching identifies the expected ground state structures unambiguously, in addition to revealing other low-energy structures. This new role for orbital-free density functional theory-particularly as continued advances make it accurate for more of the periodic table-will expedite crystal structure prediction over wide ranges of compositions and pressures.

Ab initio random structure searching for battery cathode materials.

Cathodes are critical components of rechargeable batteries. Conventionally, the search for cathode materials relies on experimental trial-and-error and a traversing of existing computational/experimental databases. While these methods have led to the discovery of several commercially viable cathode materials, the chemical space explored so far is limited and many phases will have been overlooked, in particular, those that are metastable. We describe a computational framework for battery cathode exploration based on ab initio random structure searching (AIRSS), an approach that samples local minima on the potential energy surface to identify new crystal structures. We show that by delimiting the search space using a number of constraints, including chemically aware minimum interatomic separations, cell volumes, and space group symmetries, AIRSS can efficiently predict both thermodynamically stable and metastable cathode materials. Specifically, we investigate LiCoO2, LiFePO4, and LixCuyFz to demonstrate the efficiency of the method by rediscovering the known crystal structures of these cathode materials. The effect of parameters, such as minimum separations and symmetries, on the efficiency of the sampling is discussed in detail. The adaptation of the minimum interatomic distances on a species-pair basis, from low-energy optimized structures to efficiently capture the local coordination environment of atoms, is explored. A family of novel cathode materials based on the transition-metal oxalates is proposed. They demonstrate superb energy density, oxygen-redox stability, and lithium diffusion properties. This article serves both as an introduction to the computational framework and as a guide to battery cathode material discovery using AIRSS.

High-temperature phase transitions in dense germanium.

Through a series of high-pressure x-ray diffraction experiments combined with in situ laser heating, we explore the pressure-temperature phase diagram of germanium (Ge) at pressures up to 110 GPa and temperatures exceeding 3000 K. In the pressure range of 64-90 GPa, we observe orthorhombic Ge-IV transforming above 1500 K to a previously unobserved high-temperature phase, which we denote as Ge-VIII. This high-temperature phase is characterized by a tetragonal crystal structure, space group I4/mmm. Density functional theory simulations confirm that Ge-IV becomes unstable at high temperatures and that Ge-VIII is highly competitive and dynamically stable at these conditions. The existence of Ge-VIII has profound implications for the pressure-temperature phase diagram, with melting conditions increasing to much higher temperatures than previous extrapolations would imply.

Hydrogen Pentagraphenelike Structure Stabilized by Hafnium: A High-Temperature Conventional Superconductor.

The recent discovery of H_{3}S and LaH_{10} superconductors with record high superconducting transition temperatures T_{c} at high pressure has fueled the search for room-temperature superconductivity in the compressed superhydrides. Here we introduce a new class of high T_{c} hydrides with a novel structure and unusual properties. We predict the existence of an unprecedented hexagonal HfH_{10}, with remarkably high value of T_{c} (around 213-234 K) at 250 GPa. As concerns the novel structure, the H ions in HfH_{10} are arranged in clusters to form a planar "pentagraphenelike" sublattice. The layered arrangement of these planar units is entirely different from the covalent sixfold cubic structure in H_{3}S and clathratelike structure in LaH_{10}. The Hf atom acts as a precompressor and electron donor to the hydrogen sublattice. This pentagraphenelike H_{10} structure is also found in ZrH_{10}, ScH_{10}, and LuH_{10} at high pressure, each material showing a high T_{c} ranging from 134 to 220 K. Our study of dense superhydrides with pentagraphenelike layered structures opens the door to the exploration of a new class of high T_{c} superconductors.