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Behaviours of hydrogen, such as fluidity and metallicity, are crucial for our understanding of planetary interiors and the emerging field of high-temperature superconducting hydrides. These behaviours were discovered in complex phase diagrams of hydrogen and hydrides, however, the transition mechanism of behaviours driven by temperature, pressure and chemical compression remain unclear, particularly in the processes of metallization. Until now, a comprehensive theoretical framework to quantify atomization and metallization of hydrogen in phase diagram of hydrides has been lacking. In this study, we address this gap by combining molecular dynamics and electronic structure analysis to propose a theoretical framework, which clarify the content and properties of atomic hydrogen under various temperature and pressure conditions and chemical compression exerted by non-hydrogen elements in hydrides. Applying this framework to the superconducting hydride LaBeH8, we identify three general hydrogen orderings within its phase diagram: molecular, sublattice and warm hydrogens. During the phase transition from molecule to sublattice, hydrogen exhibits different properties from three general hydrogen orderings, such as fast superionicity, metallicity and unusual atomic content response to temperature. These abnormal behaviours were defined as the critical metallization of hydrogen, which not only suggests a potential synthesis route for the metastable phase but also provides valuable insights into the complex synthetic products of superconducting hydrides.

Data driven methods have transformed the prospects of the computational chemical sciences, with machine learned interatomic potentials (MLIPs) speeding up calculations by several orders of magnitude. I reflect on theory driven, as opposed to data driven, discovery based on ab initio random structure searching (AIRSS), and then introduce two methods which exploit machine learning acceleration. I show how long high throughput anneals, between direct structural relaxation, enabled by ephemeral data derived potentials (EDDPs), can be incorporated into AIRSS to bias the sampling of challenging systems towards low energy configurations. Hot AIRSS (hot-AIRSS) preserves the parallel advantage of random search, while allowing much more complex systems to be tackled. This is demonstrated through searches for complex boron structures in large unit cells. I then show how low energy carbon structures can be directly generated from a single, experimentally determined, diamond structure. An extension to the generation of random sensible structures, candidates are stochastically generated and then optimised to minimise the difference between the EDDP environment vector and that of the reference diamond structure. The distance-based cost function is captured in an actively learned EDDP. Graphite, small nanotubes and caged, fullerene-like, structures emerge from searches using this potential, along with a rich variety of tetrahedral framework structures. Using the same approach, the pyrope, Mg$_3$Al$_2$(SiO$_4$)$_3$, garnet structure is recovered from a low energy AIRSS structure generated in a smaller unit cell with a different chemical composition. The relationship of this approach to modern diffusion model based generative methods is discussed., Comment: 13 pages, 9 figures, contributed to Data-driven discovery in the chemical sciences Faraday Discussion

Following long-standing predictions associated with hydrogen, high-temperature superconductivity has recently been observed in several hydride-based materials. Nevertheless, these high-$T_c$ phases only exist at extremely high pressures, and achieving high transition temperatures at ambient pressure remains a major challenge. Recent predictions of the complex hydride Mg$_{2}$IrH$_{6}$ may help overcome this challenge with calculations of high-$T_c$ superconductivity (65 K$~<~T_c~<~$ 170 K) in a material that is stable at atmospheric pressure. In this work, the synthesis of Mg$_{2}$IrH$_{6}$ was targeted over a broad range of $P$-$T$ conditions, and the resulting products were characterized using X-ray diffraction (XRD) and vibrational spectroscopy, in concert with first-principles calculations. The results indicate that the charge-balanced complex hydride Mg$_{2}$IrH$_{5}$ is more stable over all conditions tested up to ca 28 GPa. The resulting hydride is isostructural with the predicted superconducting Mg$_{2}$IrH$_{6}$ phase except for a single hydrogen vacancy, which shows a favorable replacement barrier upon insertion of hydrogen into the lattice. Bulk Mg$_{2}$IrH$_{5}$ is readily accessible at mild $P$-$T$ conditions and may thus represent a convenient platform to access superconducting Mg$_{2}$IrH$_{6}$ via non-equilibrium processing methods., Comment: 18 pages, 17 Figures

We investigate the pressure-temperature ($p$-$T$) phase diagram of elemental lithium (Li) up to multiterapascal (TPa) pressures using ab-initio random structure search (AIRSS) and density functional theory (DFT). At zero temperature, beyond the high-pressure $Fd\bar{3}m$ diamond structure predicted in previous studies, we find eleven solid-state phase transitions to structures of greatly varying complexity, in addition to two structures that we calculate will become stable with sufficient temperature. The full $p$-$T$ dependence of the phase boundaries are computed within the vibrational harmonic approximation, and the solid-liquid melting line is calculated using ab-initio molecular dynamics simulations. Notably, between 39.1 TPa and 55.7 TPa, Li adopts an elaborate monoclinic structure with 46 atoms in the primitive unit cell, and between 71.9 TPa and $103$ TPa, an incommensurate host-guest phase of the Ba-IV type. We find that Li, hitherto predicted to be an electride at TPa pressures, abruptly loses its electride character above 16 TPa, reverting back to normal metallic behaviour with a corresponding rise in the Fermi-level electronic density of states (eDOS) and broadening of the electronic bands.

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., Comment: 30 pages, 30 figures, including SM

The recent claim of room temperature superconductivity in a copper-doped lead apatite compound, called LK-99, has sparked remarkable interest and controversy. Subsequent experiments have largely failed to reproduce the claimed superconductivity, while theoretical works have identified multiple key features including strong electronic correlation, structural instabilities, and dopability constraints. A puzzling claim of several recent theoretical studies is that both parent and copper-doped lead apatite structures are dynamically unstable at the harmonic level, questioning decades of experimental reports of the parent compound structures and the recently proposed copper-doped structures. In this work, we demonstrate that both parent and copper-doped lead apatite structures are dynamically stable at room temperature. Anharmonic phonon-phonon interactions play a key role in stabilizing some copper-doped phases, while most phases are largely stable even at the harmonic level. We also show that dynamical stability depends on both volume and correlation strength, suggesting controllable ways of exploring the copper-doped lead apatite structural phase diagram. Our results fully reconcile the theoretical description of the structures of both parent and copper-doped lead apatite with experiment., Comment: 4 figures + Supplementary Information, published version

Controlling the formation and stoichiometric content of desired phases of materials has become a central interest for the study of a variety of fields, notably high temperature superconductivity under extreme pressures. The further possibility of accessing metastable states by initiating reactions by x-ray triggered mechanisms over ultra-short timescales is enabled with the development of x-ray free electron lasers (XFEL). Utilizing the exceptionally high brilliance x-ray pulses from the EuXFEL, we report the synthesis of a previously unobserved yttrium hydride under high pressure, along with non-stoichiometric changes in hydrogen content as probed at a repetition rate of 4.5\,MHz using time-resolved x-ray diffraction. Exploiting non-equilibrium pathways we synthesize and characterize a hydride with yttrium cations in an \textit{A}15 structure type at 125\,GPa, predicted using crystal structure searches, with a hydrogen content between 4.0--5.75 hydrogens per cation, that is enthalpically metastable on the convex hull. We demonstrate a tailored approach to changing hydrogen content using changes in x-ray fluence that is not accessible using conventional synthesis methods, and reveals a new paradigm in metastable chemical physics.

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., Comment: 22 pages, 15 figures

In the past decades many density-functional theory methods and codes adopting periodic boundary conditions have been developed and are now extensively used in condensed matter physics and materials science research. Only in 2016, however, their precision (i.e., to which extent properties computed with different codes agree among each other) was systematically assessed on elemental crystals: a first crucial step to evaluate the reliability of such computations. We discuss here general recommendations for verification studies aiming at further testing precision and transferability of density-functional-theory computational approaches and codes. We illustrate such recommendations using a greatly expanded protocol covering the whole periodic table from Z=1 to 96 and characterizing 10 prototypical cubic compounds for each element: 4 unaries and 6 oxides, spanning a wide range of coordination numbers and oxidation states. The primary outcome is a reference dataset of 960 equations of state cross-checked between two all-electron codes, then used to verify and improve nine pseudopotential-based approaches. Such effort is facilitated by deploying AiiDA common workflows that perform automatic input parameter selection, provide identical input/output interfaces across codes, and ensure full reproducibility. Finally, we discuss the extent to which the current results for total energies can be reused for different goals (e.g., obtaining formation energies)., Comment: Main text: 23 pages, 4 figures. Supplementary: 68 pages. Nature Review Physics 2023

Nitrogen-doped lutetium hydride has recently been proposed as a near-ambient-conditions superconductor. Interestingly, the sample transforms from blue to pink to red as a function of pressure, but only the pink phase is claimed to be superconducting. Subsequent experimental studies have failed to reproduce the superconductivity, but have observed pressure-driven colour changes including blue, pink, red, violet, and orange. However, discrepancies exist among these experiments regarding the sequence and pressure at which these colour changes occur. Given the claimed relationship between colour and superconductivity, understanding colour changes in nitrogen-doped lutetium hydride may hold the key to clarifying the possible superconductivity in this compound. Here, we present a full microscopic theory of colour in lutetium hydride, revealing that hydrogen-deficient LuH$_2$ is the only phase which exhibits colour changes under pressure consistent with experimental reports, with a sequence blue-violet-pink-red-orange. The concentration of hydrogen vacancies controls the precise sequence and pressure of colour changes, rationalising seemingly contradictory experiments. Nitrogen doping also modifies the colour of LuH$_2$ but it plays a secondary role compared to hydrogen vacancies. Therefore, we propose hydrogen-deficient LuH$_2$ as the key phase for exploring the superconductivity claim in the lutetium-hydrogen system. Finally, we find no phonon-mediated superconductivity near room temperature in the pink phase., Comment: 3 figures + Supplementary Information, published version

Motivated by the recent report of room-temperature superconductivity at near-ambient pressure in N-doped lutetium hydride by Dasenbrock et al. [Nature 615, 244 (2023)], we performed a comprehensive, detailed study of the phase diagram of the Lu-N-H system, looking for superconducting phases. We combined ab initio crystal structure prediction with ephemeral data-derived interatomic potentials to sample over 200,000 different structures. Out of the more than 150 structures predicted to be metastable within $\sim$ 50 meV from the convex hull we identify 52 viable candidates for conventional superconductivity, for which we computed their superconducting properties from Density Functional Perturbation Theory. Although for some of these structures we do predict a finite superconducting $T_{\text{c}}$, none is even remotely compatible with room-temperature superconductivity as reported by Dasenbrock et al. Our work joins the broader community effort that has followed the report of near-ambient superconductivity, confirming beyond reasonable doubt that no conventional mechanism can explain the reported $T_{\text{c}}$ in Lu-N-H.

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 compared to conventional finite difference methods. For these reasons, PROFESS-AD serves as an excellent prototyping tool and provides new opportunities for OFDFT.

Density functional theory in the local or semi-local density approximation is a powerful tool for materials simulation, yet it struggles in many cases to describe collective electronic order that is driven by electronic interactions. In this work it is shown how arbitrary, fluctuation-driven electronic order may be introduced into density functional theory using the quantum order-by-disorder framework. This is a method of calculating the free energy correction due to collective spin and charge fluctuations about a state that hosts static order, in a self-consistent manner. In practical terms, the quantum order-by-disorder method is applied to the Kohn-Sham auxiliary system of density functional theory to give an order-dependent correction to the exchange-correlation functional. Calculation of fluctuation propagators within density functional theory renders the result fully first-principles. Two types of order are considered as examples -- fluctuation-driven superconductivity and spin nematic order -- and implementation schemes are presented in each case., Comment: 20 pages, 2 figures; added Section V for context and added clarifying statements in Sections II A and IV A, C and E

Structure prediction has become a key task of the modern atomistic sciences, and depends on the rapid and reliable computation of the energy landscape. First principles density functional based calculations are highly reliable, faithfully describing the entire energy landscape. They are, however, computationally intensive and slow compared to interatomic potentials. Great progress has been made in the development of machine learning, or data derived, potentials, which promise to describe the entire energy landscape at first principles quality. However, compared to first principles approaches, their preparation can be time consuming and delay searching. Ab initio random structure searching (AIRSS) is a straightforward and powerful approach to structure prediction, based on the stochastic generation of sensible initial structures, and their repeated local optimisation. Here, a scheme, compatible with AIRSS, for the rapid construction of disposable, or ephemeral, data derived potentials (EDDPs) is described. These potentials are constructed using a homogeneous, separable manybody environment vector, and iterative neural network fits, sparsely combined through non-negative least squares. The approach is first tested on methane, boron nitride, elemental boron and urea. In the case of boron, an EDDP generated using data from small unit cells is used to rediscover the complex $\gamma$-boron structure without recourse to symmetry or fragments. Finally, an EDDP generated for silane (SiH$_4$) at 500 GPa enables the discovery of an extremely complex, dense, structure which significantly modifies silane's high pressure phase diagram. This has implications for the theoretical exploration for high temperature superconductivity in the dense hydrides, which have so far largely depended on searches in smaller unit cells., Comment: 17 pages, 12 figures

The choice of cathode material in Li-ion batteries (LIBs) underpins their overall performance. Discovering new cathode materials is a slow process, and all major commercial cathode materials are still based on those identified in the 1990s. Materials discovery using high-throughput calculations has attracted great research interest, however, reliance on databases of existing materials begs the question of whether these approaches are applicable for finding truly novel materials. In this work, we demonstrate that ab-initio random structure searching (AIRSS), a first-principles structure prediction methods that does not rely on any pre-existing data, can locate low energy structures of complex cathode materials efficiently based only on chemical composition. We use AIRSS to explore three Fe-containing polyanion compounds as low-cost cathodes. Using known quaternary LiFePO4 and quinary LiFeSO4F cathodes as examples, we easily reproduce the known polymorphs, in addition to predicting other, hitherto unknown, low energy polymorphs, and even finding a new polymorph of LiFeSO4F which is more stable than the known ones. We then explore the phase space for Fe-containing fluoroxalates, predicting a range of redox-active phases that have yet to be experimentally synthesized, demonstrating the suitability of AIRSS as a tool for accelerating the discovery of novel cathode materials., Comment: 24 pages, 10 figures. Supplementary information at the end of the main text

Computational searches for new materials are naturally turning from binary systems, to ternary and other multicomponent systems, and beyond. Here, we select the industrially-relevant metals titanium and aluminium and report the results of an extensive structure prediction study on the ternary titanium-carbon-oxygen (Ti-C-O) and aluminium-carbon-oxygen (Al-C-O) systems. We map out for the first time the full phase stability of Ti-C-O and Al-C-O compounds using first-principles calculations, through simple, efficient and highly parallel random structure searching in conjunction with techniques based on complex network theory. These phase stabilities emerge naturally from our `data agnostic' approach, in which we map stable compounds without recourse to structural databases or other prior knowledge. A surprising find is the predicted ambient pressure stability of octet-rule-fulfiling titanium and aluminium carbonate: Ti(CO3)$_2$ and Al$_2$(CO3)$_3$, neither of which has to our knowledge been synthesised before. These materials could potentially act as carbon sequestering compounds. Our searches discover several additional stable and metastable ternary compounds supported by the Ti-C-O and Al-C-O systems., Comment: 11 pages, 5 figures, plus Supplemental Material. Accepted for publication in Phys. Rev. Mat. (2021)

Titanium dioxide has been extensively studied in the rutile or anatase phases, 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 TiO$_2$ 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 stablities of the various polymorphs. To model the thermodynamic behaviors of ambient and high-pressure phases of TiO$_2$, 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 $\Delta$-learning potential contains long-range electrostatic interactions, and predicts the 0~K enthalpies of stable TiO$_2$ phases that are in good agreement with DFT. We construct a pressure-temperature phase diagram of TiO$_2$ in the range $0

Energy landscapes provide a conceptual framework for structure prediction, and a detailed understanding of their topological features is necessary to develop efficient methods for their exploration. The ability to visualise these surfaces is essential, but the high dimensionality of the corresponding configuration spaces makes this difficult. Here we present Stochastic Hyperspace Embedding and Projection (SHEAP), a method for energy landscape visualisation inspired by state-of-the-art algorithms for dimensionality reduction through manifold learning, such as t-SNE and UMAP. The performance of SHEAP is demonstrated through its application to the energy landscapes of Lennard-Jones clusters, solid-state carbon, and the quaternary system C+H+N+O. It produces meaningful and interpretable low-dimensional representations of these landscapes, reproducing well known topological features such as funnels, and providing fresh insight into their layouts. In particular, an intrinsic low dimensionality in the distribution of local minima across configuration space is revealed.

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 remarkably different from bulk, as shown e.g., by the anomalously low dielectric constant of water in nanochannels [1], near frictionless water flow [2], or the possible existence of a square ice phase [3]. Such properties suggest that nanoconfined water could be engineered for technological applications in nanouidics [4], electrolyte materials [5], and water desalination [6]. Unfortunately, challenges in experimentally characterising water on the nanoscale and the high cost of first-principles simulations have prevented the molecular level understanding required to control the behavior 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 behavior 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 over 400 degrees 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 behavior at easily accessible conditions., Comment: 33 pages, 8 figures

Single-crystal synchrotron X-ray diffraction, Raman spectroscopy, and first principles calculations have been used to identify the structure of the high-pressure (HP) phase of molecular methane above 20 GPa up to 71 GPa. The structure of HP phase is trigonal R3, which can be represented as a distortion of the cubic phase B, previously documented at 7-15 GPa and confirmed here. The positions of hydrogen atoms in HP phase have been 19 obtained from first principles calculations. The molecules occupy four different crystallographic sites in phases B and eleven sites in the HP phase, which result in splitting of molecular stretching modes detected in Raman spectroscopy and assigned here based on 22 a good agreement with the Raman spectra calculated from the first principles., Comment: 29 pages, 7 figures, 3 tables, supplemental material

Most elemental metals under ambient conditions adopt simple structures such as BCC, FCC and HCP in specific groupings across the Periodic Table, and on compression, many of these elements undergo transitions to surprisingly complex structures, including open and low-symmetry phases 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 of bonding that underlies this behavior is not yet in hand. We propose a remarkably simple theory based on large-scale high-throughput calculations of the elements over a broad range of thermodynamic conditions. The results broaden the conventional concept of metallic bonding with a new perspective that both explains the stability of different simple structures as well as lower symmetry phases arising from electron localization at interstitial sites in these structures. The success of this simple framework reveals the important role of chemical interactions in governing the structures and electronic properties of simple metals.

Helium is the second most abundant element in the universe, and together with silica, they are major components of giant planets. Exploring the reactivity and state of helium and silica under high pressure is of fundamental importance for developing and understanding of the evolution and internal structure of giant planets. Here, using first-principles calculations and crystal structure predictions, we identify four stable phases of a helium-silica compound with seven/eight-coordinated silicon atoms at pressure range of 600-4000 GPa, corresponding to the interior condition of the outer planets in the solar system. The density of HeSiO2 agrees with current structure models of the planets. This helium-silica compound exhibits a superionic-like helium diffusive state at the high pressure and high temperature conditions along the isentropes of Saturn, a metallic fluid state in Jupiter, and a solid state in the deep interiors of Uranus and Neptune. The reaction of helium and silica may lead to the erosion of the rocky core of giant planets and form a diluted core region. These results highlight the reactivity of helium under high pressure to form new compounds, and also provides evidence to help build more sophisticated interior models of giant planets., Comment: 20 pages, 5 figures

We use Density Functional Theory (DFT) and structure searching methods to show that the ground state of elemental sulfur is a Barium-IVa type incommensurate host-guest (HG) phase between $386$-$679$ GPa, becoming the first group-VI element predicted to possess such a structure. Within the HG phase, sulfur undergoes a series of transitions in which adjacent guest chains are not aligned but rather offset by different amounts, which can be described as a rearrangement of the stacking order of the chains. We show that these chain rearrangements are intimately coupled to modulations of the host and guest atoms which prove crucial to stabilising the HG structure. Unlike the high-pressure HG phases of other elements, sulfur does not exhibit interstitial charge localisation, and instead features strongly localised `voids' that are depleted of electronic charge. Prior to adopting the HG structure, we predict that sulfur possesses an orthorhombic structure of $Fdd2$ symmetry. We calculate the superconducting critical temperatures of these newly discovered phases, and show that $T_c$ is expected to peak between $24.8$ and $28.2$ K at $271$ GPa.

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, can reach a critical temperature (Tc) 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 hydride superconductors with alloy backbones. We identify a hitherto unknown fluorite-type backbone in compositions of the form AXH8, which exhibit high temperature superconductivity at moderate pressures. The Fm-3m phase of LaBeH8, with a fluorite-type H-Be alloy backbone, is predicted to be metastable and superconducting with a Tc ~ 191 K at 50 GPa; a substantially lower pressure than that required by the geometrically similar clathrate hydride LaH10 (170 GPa). Our approach paves the way for finding high-Tc ternary hydride superconductors at conditions close to ambient pressures., Comment: 11 pages, 4 figures

We survey the landscape of binary hydrides across the entire periodic table from 10 to 500 GPa using a crystal structure prediction method. Building a critical temperature ($T_c$) model, with inputs arising from density of states calculations and Gaspari-Gyorffy theory, allows us to predict which energetically competitive candidates are most promising for high-$T_c$ superconductivity. Implementing optimisations, which lead to an order of magnitude speed-up for electron-phonon calculations, then allows us to perform an unprecedented number of "high-throughput" calculations of $T_c$ based on these predictions and to refine the model in an iterative manner. Converged electron-phonon calculations are performed for 121 of the best candidates from the final model. From these, we identify 36 above-100 K dynamically stable superconductors. To the best of our knowledge, superconductivity has not been previously studied in 27 of these. Of the 36, 18 exhibit superconductivity above 200 K, including structures of NaH$_6$ (248-279 K) and CaH$_6$ (216-253 K) at the relatively low pressure of 100 GPa.

Using spin-assisted ab-initio random structure searches, we explore an exhaustive quantum phase diagram of archetypal interfaced Mott insulators, i.e. lanthanum-iron and lanthanum-titanium oxides. In particular, we report that the charge transfer induced by the interfacial electronic reconstruction stabilises a high spin ferrous Fe2+ state. We provide a pathway to control the strength of correlation in this electronic state by tuning the epitaxial strain, yielding a manifold of quantum electronic phases, i.e. Mott-Hubbard, charge transfer and Slater insulating states. Furthermore we report that the electronic correlations are closely related to the structural oxygen octahedral rotations, whose control is able to stabilise the low spin state of Fe2+ at low pressure previously observed only under the extreme high pressure conditions in the Earth's lower mantle. Thus we provide avenues for magnetic switching via THz radiations which have crucial implications for next generation of spintronics technologies., Comment: 9 pages, 4 figures in main manuscript. 19 pages, 11 figures in supplementary

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.

Most water in the universe may be superionic, and its thermodynamic and transport properties are crucial for planetary science but difficult to probe experimentally or theoretically. We use machine learning and free energy methods to overcome the limitations of quantum mechanical simulations, and characterize hydrogen diffusion, superionic transitions, and phase behaviors of water at extreme conditions. We predict that a close-packed superionic phase with mixed stacking is stable over a wide temperature and pressure range, while a body-centered cubic phase is only thermodynamically stable in a small window but is kinetically favored. Our phase boundaries, which are consistent with the existing-albeit scarce-experimental observations, help resolve the fractions of insulating ice, different superionic phases, and liquid water inside of ice giants.

The make-up of the outer planets, and many of their moons, are dominated by matter from the H-C-N-O chemical space, commonly assumed to originate from mixtures of hydrogen and the planetary ices H$_2$O, CH$_4$, and NH$_3$. In their interiors, these ices 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. In turn, this determines planets' interior structure, thermal history, magnetic field generation, etc. Despite its importance, the H-C-N-O space has not been surveyed systematically. Asked simply: at high-pressure conditions, what compounds emerge within this space, and what governs their stability? Here, we report on results from an unbiased crystal structure search amongst H-C-N-O compounds at 5 Mbar to answer this question.

Superionic states are phases of matters that can simultaneously exhibit some of the properties of a fluid and of a solid. Superionic states of ice, H$_{3}$O, He-H$_{2}$O or He-NH$_{3}$ compounds have been reported in previous works. Silicon, sodium, and hydrogen are abundant elements inside the earth. Here, we use ab initio calculations to show that, at extreme conditions inside the earth, Na, Si, and H can form many hypervalent compounds that some of them can exist every close to ambient pressure, and surprisingly a previously unknown type of superionic state of $P\overline3m1 - $Na$_{2}$SiH$_{6}$ can form as well. Our work focused on new superionic state of Na$_{2}$SiH$_{6}$, and the results also reveal several different hypervalent Si-H anions discovered, which are different from individual SiH$_{5}^{\,-}$ and octahedral SiH$_{6}^{\,2-}$ in previous research of ternary alkali hypervalent silicon hydrides. Our work provides some advice on further investigations on potential ternary hydrides inside the earth.

Lanthanum hydrides, containing hydrogen framework structures under compression, display a superconducting state with a high observed critical temperature. However, this phenomenon has so far only been observed at very high pressures. Here, we computationally search for superconductors with very high critical temperatures, but at much lower pressures. We uncover two such sodalite-type clathrate hydrides, YbH6 and LuH6 (Tc =145 K at P=70 GPa for YbH6 and, especially, Tc =273 K at P=100 GPa for LuH6). These striking properties are a consequence of the strong interrelationship between the f states present at the Fermi surface, structural stability and Tc value. For example, TmH6, with unfilled 4f orbitals, is stable at 50 GPa, while it has a relatively low value of Tc of 25 K. As for the YbH6 and LuH6 compounds, they have filled f-shells and the decrease of the f-energy below the Fermi level leads to formation of the nesting regions on the Fermi surface and, as a result, to phonon "softening" and an increase in Tc., Comment: 14 pages ,4 figures

Hydrogen is rarely observed as ligand in hypervalent species, however, we find that high-pressure hydrogenation may stabilise hypervalent hydrogen-rich materials. Focussing on ternary silicon hydrides via lithium doping, we find anions composed of hypervalent silicon with H ligands formed under high pressure. Our results reveal two new hypervalent anions: layered-SiH$_{5}^{-}$ and tricapped trigonal prismatic SiH$_{6}^{2-}$. These differ from octahedral SiH$_{6}^{2-}$ described in earlier studies. In addition, there are further hydrogen-rich structures Li$_{3}$SiH$_{10}$ and Li$_{2}$SiH$_{6+\delta}$ which may be stabilised at high pressure. Our work provides pointers to future investigations on hydrogen-rich materials., Comment: 6 pages, 4 figures

In spite of their importance for understanding phonon transport phenomena in thin films and polycrystalline solids, the effects of boundary roughness scattering on phonon specularity and coherence are poorly understood because there is no general method for predicting their dependence on phonon momentum, frequency, branch and boundary morphology. Using the recently formulated atomistic S-matrix method, we develop a theory of boundary roughness scattering to determine the mode-resolved phonon coherence and specularity parameters from the scattering amplitudes. To illustrate the theory, we apply it to phonon scattering in realistic nonsymmetric graphene grain boundary (GB) models derived from atomic structure predictions. The method is validated by comparing its predictions with frequency-resolved results from lattice dynamics-based calculations. We prove that incoherent scattering is almost perfectly diffusive. We show that phonon scattering at the graphene GB is not diffuse although coherence and specularity are significantly reduced for long-wavelength flexural acoustic phonons. Our approach can be generalized to other atomistic boundary models., Comment: 7 pages, 5 figures

Nuclear Magnetic Resonance (NMR) is one of the most powerful experimental techniques to characterize the structure of molecules and confined liquids. Nevertheless, the complexity of the systems under investigation usually requires complementary computational studies to interpret the NMR results. In this work we focus on polycyclic aromatic hydrocarbons (PAHs), an important class of organic molecules which have been commonly used as simple analogues for the spectroscopic properties of more complex systems, such as porous disordered carbons. We use Density Functional Theory (DFT) to calculate 13C chemical shifts and Nucleus Independent Chemical Shifts (NICS) for 34 PAHs. The results show a clear molecular size dependence of the two quantities, as well as the convergence of the 13C NMR shifts towards the values observed for graphene. We then present two computationally cheap models for the prediction of NICS in simple PAHs. We show that while a simple dipolar model fails to produce accurate values, a perturbative tight-binding approach can be successfully applied for the prediction of NICS in this series of molecules, including some non-planar ones containing 5- and 7-membered rings. This model, one to two orders of magnitudes faster than DFT calculations, is very promising and can be further refined in order to study more complex systems.

Rare-earth hydrides can exhibit high-temperature superconductivity under high pressure. Here, we apply a crystal structure prediction method to the current record-holding $T_c$ material, LaH$_{10}$, and a candidate for even higher $T_c$, YH$_{10}$. We find a pressure-induced phase transition from the experimentally observed cubic LaH$_{10}$ phase to a new hexagonal phase at around 420 GPa. This hexagonal phase could explain experimental observations of hcp impurities in fcc samples. We find that YH$_{10}$ forms similar structures to LaH$_{10}$ and discuss the sensitivity of superconductivity calculations to the computational parameters used.

The recent discovery of H3S and LaH10 superconductors with record high superconducting transition temperatures, Tc, at high pressure, has fueled the search for room-temperature superconductivity in the compressed superhydrides. Here we predict the existence of an unprecedented hexagonal HfH10, with an extraordinarily high Tc of around 213-234 K at 250 GPa. In HfH10, the H atoms are arranged in clusters to form a planar "penta-graphene-like" sublattice, in contrast to the covalent sixfold cubic structure in H3S and clathrate-like structure in LaH10. The Hf atom acts as a "precompressor" and electron donor to the hydrogen sublattice. This "penta-graphene-like" H10 structure is also found in ZrH10, ScH10 and LuH10 at high pressure, each material showing a high Tc ranging from 134 to 220 kelvin. Our study of dense superhydrides with "penta-graphene-like" layered structures opens the door to the exploration and exploitation of a new class of high Tc superconductors.

The measurement of superconductivity at above 200K in compressed samples of hydrogen sulfide and lanthanum hydride at 250K is reinvigorating the search for conventional high temperature superconductors. At the same time it exposes a fascinating interplay between theory, computation and experiment. Conventional superconductivity is well understood, and theoretical tools are available for accurate predictions of the superconducting critical temperature. These predictions depend on knowing the microscopic structure of the material under consideration, and can now be provided through computational first principles structure predictions. The experiments at the megabar pressures required are extremely challenging, but for some groups at least, permit the experimental exploration of materials space. We discuss the prospects for the search for new superconductors, ideally at lower pressures., Comment: 29 pages, 9 figures, submitted version

Predicting phase stabilities of crystal polymorphs is central to computational materials science and chemistry. Such predictions are challenging because they first require searching for potential energy minima and then performing arduous free-energy calculations to account for entropic effects at finite temperatures. Here, we develop a framework that facilitates such predictions by exploiting all the information obtained from random searches of crystal structures. This framework combines automated clustering, classification and visualisation of crystal structures with machine-learning estimation of their enthalpy and entropy. We demonstrate the framework on the technologically important system of TiO2, which has many polymorphs, without relying on prior knowledge of known phases. We find a number of new phases and predict the phase diagram and metastabilities of crystal polymorphs at 1600 K, benchmarking the results against full free-energy calculations.

An unambiguous crystallographic structure solution for the observed phases II-VI of high pressure hydrogen does not exist due to the failure of standard structural probes at extreme pressure. In this work we propose that nuclear magnetic resonance spectroscopy provides a complementary structural probe for high pressure hydrogen. We show that the best structural models available for phases II, III, and IV of high pressure hydrogen exhibit markedly distinct nuclear magnetic resonance spectra which could therefore be used to discriminate amongst them. As an example, we demonstrate how nuclear magnetic resonance spectroscopy could be used to establish whether phase III exhibits polymorphism. Our calculations also reveal a strong renormalisation of the nuclear magnetic resonance response in hydrogen arising from quantum fluctuations, as well as a strong isotope effect. As the experimental techniques develop, nuclear magnetic resonance spectroscopy can be expected to become a useful complementary structural probe in high pressure experiments., Comment: Accepted manuscript; 7 pages, 3 figures; contains Supplemental Material

Anticipating the low energy arrangements of atoms in space is an indispensable scientific task. Modern stochastic approaches to searching for these configurations depend on the optimisation of structures to nearby local minima in the energy landscape. In many cases these local minima are relatively high in energy, and inspection reveals that they are trapped, tangled, or otherwise frustrated in their descent to a lower energy configuration. Strategies have been developed which attempt to overcome these traps, such as classical and quantum annealing, basin/minima hopping, evolutionary algorithms and swarm based methods. Random structure search makes no attempt to avoid the local minima, and benefits from a broad and uncorrelated sampling of configuration space. It has been particularly successful in the first principles prediction of unexpected new phases of dense matter. Here it is demonstrated that by starting the structural optimisations in a higher dimensional space, or hyperspace, many of the traps can be avoided, and that the probability of reaching low energy configurations is much enhanced. Excursions into the extra dimensions are progressively eliminated through the application of a growing energetic penalty. This approach is tested on hard cases for random search - clusters, compounds, and covalently bonded networks. The improvements observed are most dramatic for the most difficult ones. Random structure search is shown to be typically accelerated by two orders of magnitude, and more for particularly challenging systems. This increase in performance is expected to benefit all approaches to structure prediction that rely on the local optimisation of stochastically generated structures., Comment: 10 pages, 11 figures, Accepted Manuscript

A two-dimensional carbon allotrope, Stone-Wales graphene, is identified in stochastic group and graph constrained searches and systematically investigated by first-principles calculations. Stone-Wales graphene consists of well-arranged Stone-Wales defects, and it can be constructed through a 90$^\circ$ bond-rotation in a $\sqrt{8}$$\times$$\sqrt{8}$ super-cell of graphene. Its calculated energy relative to graphene, +149 meV/atom, makes it more stable than the most competitive previously suggested graphene allotropes. We find that Stone-Wales graphene based on a $\sqrt{8}$ super-cell is more stable than those based on $\sqrt{9} \times \sqrt{9}$, $\sqrt{12} \times \sqrt{12}$ and $\sqrt{13} \times \sqrt{13}$ super-cells, and is a "magic size" that can be further understood through a simple "energy splitting and inversion" model. The calculated vibrational properties and molecular dynamics of SW-graphene confirm that it is dynamically stable. The electronic structure shows SW-graphene is a semimetal with distorted, strongly anisotropic Dirac cones., Comment: Accepted;5 pages;5 figures;53 references and 8 pages of supplementary file

Faithful representations of atomic environments and general models for regression can be harnessed to learn electron densities that are close to the ground state. One of the applications of data-derived electron densities is to orbital-free density functional theory. However, extrapolations of densities learned from a training set to dissimilar structures could result in inaccurate results, which would limit the applicability of the method. Here, we show that a non-Bayesian approach can produce estimates of uncertainty which can successfully distinguish accurate from inaccurate predictions of electron density. We apply our approach to density functional theory where we initialise calculations with data-derived densities only when we are confident about their quality. This results in a guaranteed acceleration to self-consistency for configurations that are similar to those seen during training and could be useful for sampling based methods, where previous ground state densities cannot be used to initialise subsequent calculations.

Cazorla et al. [preceding comment] criticize our recent results on the high-PT phase diagram of CaF2 (Phys. Rev. B 95, 054118 (2017)). According to our analysis, Cazorla et al. have not converged their calculations with respect to simulation cell size, undermining the comment's conclusions about both the high-T behaviour of the P-62m-CaF2 polymorph, and the use of the QHA in our work. As such, we take this opportunity to emphasise the importance of correctly converging molecular dynamics simulations to avoid finite-size errors. We compare our quasiharmonic phase diagram for CaF2 with currently available experimental data, and find it to be entirely consistent and in qualitative agreement with such data. Our prediction of a superionic phase transition in P-62m-CaF2 (made on the basis of the QHA) is shown to be accurate, and we argue that simple descriptors, such as phonon frequencies, can offer valuable insight and predictive power concerning superionic behaviour., Comment: 5 pages, 3 figures

Superionic hydrogen was previously thought to be an exotic state predicted and confirmed only in pure H2O ice. In Earth's deep interior, H2O exists in the form of O-H groups in ultra-dense hydrous minerals, which have been proved to be stable even at the conditions of the core-mantle boundary (CMB). However, the superionic states of these hydrous minerals at high P-T have not been investigated. Using first-principles calculations, we found that pyrite structured FeO2Hx (0 <= x <= 1) and d-AlOOH, which have been proposed to be major hydrogen-bearing phases in the deep lower mantle (DLM), contain superionic hydrogen at high P-T conditions. Our observations indicate a universal pathway of the hydroxyl O-H at low pressure transforming to symmetrical O-H-O bonding at high-P low-T, and a superionic state at high-P high-T. The superionicity of hydrous minerals has a major impact on the electrical conductivity and hydrogen transportation behaviors of Earth's lower mantle as well as the CMB.

The energy landscape of carbon is exceedingly complex, hosting diverse and important metastable phases, including diamond, fullerenes, nanotubes and graphene. Searching for structures, especially those with large unit cells, in this landscape is challenging. Here we use a combined stochastic search strategy employing two algorithms (AIRSS and RG2) to apply connectivity constraints to unit cells containing up to 100 carbon atoms. We uncover three low energy carbon polymorphs (Pbam-32, P6/mmm and I-43d) with new topologies, containing 32, 36 and 94 atoms in their primitive cells, respectively. Their energies relative to diamond are 96 meV/atom, 131 meV/atom and 112 meV/atom, respectively, which suggests potential metastability. These three carbon allotropes are mechanically and dynamically stable, insulating carbon crystals with superhard mechanical properties. The I43d structure possesses a direct band gap of 7.25 eV, which is the widest gap in the carbon allotrope family. Silicon, germanium and tin versions of Pbam-32, P6/mmm and I-43d also show energetic, dynamical and mechanical stability. The computed electronic properties show that they are potential materials for semiconductor and photovoltaic applications., Comment: Accepted; 6 pages; 3 figures; 11 pages of supplementary

A new phase V of hydrogen was recently claimed in experiments above 325 GPa and 300 K. Due to the extremely small sample size at such record pressures the measurements were limited to Raman spectroscopy. The experimental data on increase of pressure shows decreasing Raman activity and darkening of the sample, which suggests band-gap closure and impending molecular dissociation, but no definite conclusions could be reached. Furthermore, the available data is insufficient to determine the structure of phase V, which remains unknown. Introducing saddle-point $ab$ $initio$ random structure searching (sp-AIRSS), we find several new structural candidates of hydrogen which could describe the observed properties of phase V. We investigate hydrogen metallisation in the proposed candidate structures, and demonstrate that smaller band gaps are associated with longer bond lengths. We conclude that phase V is a stepping stone towards metallisation., Comment: 7 pages, 3 figures, includes Supplemental Material

We investigate the binary phase diagram of helium and iron using first-principles calculations. We find that helium, which is a noble gas and inert at ambient conditions, forms stable crystalline compounds with iron at terapascal pressures. A FeHe compound becomes stable above 4 TPa, and a FeHe$_2$ compound above 12 TPa. Melting is investigated using molecular dynamics simulations, and a superionic phase with sublattice melting of the helium atoms is predicted. We discuss the implications of our predicted helium-iron phase diagram for interiors of giant (exo)planets and white dwarf stars., Comment: 5 pages, 3 figures, includes Supplemental Material

High-throughput computational materials searches generate large databases of locally-stable structures. Conventionally, the needle-in-a-haystack search for the few experimentally-synthesizable compounds is performed using a convex hull construction, which identifies structures stabilized by manipulation of a particular thermodynamic constraint (for example pressure or composition) chosen based on prior experimental evidence or intuition. To address the biased nature of this procedure we introduce a generalized convex hull framework. Convex hulls are constructed on data-driven principal coordinates, which represent the full structural diversity of the database. Their coupling to experimentally-realizable constraints hints at the conditions that are most likely to stabilize a given configuration. The probabilistic nature of our framework also addresses the uncertainty stemming from the use of approximate models during database construction, and eliminates redundant structures. The remaining small set of candidates that have a high probability of being synthesizable provide a much needed starting point for the determination of viable synthetic pathways., Comment: Accepted Manuscript

Evaluating the total energy of an extended distribution of point charges, which interact through the Coulomb potential, is central to the study of condensed matter. With near ubiquity, the summation required is carried out using Ewald's method, which splits the problem into two separately convergent sums; one in real space and the other in reciprocal space. Density functional based electronic structure methods require the evaluation of the ion-ion repulsive energy, neutralised by a uniform background charge. Here a purely real-space approach is described. It is straightforward to implement, computationally efficient and offers linear scaling. When applied to the evaluation of the electrostatic energy of neutral ionic crystals, it is shown to be closely related to Wolf's method., Comment: 16 pages, 4 figures

We introduce two-dimensional borane, a single-layered material of BH stoichiometry, with promising electronic properties. We show that, according to Density Functional Theory calculations, two-dimensional borane is semimetallic, with two symmetry-related Dirac cones meeting right at the Fermi energy $E_f$. The curvature of the cones is lower than in graphene, thus closer to the ideal linear dispersion. Its structure, formed by a puckered trigonal boron network with hydrogen atoms connected to each boron atom, can be understood as distorted, hydrogenated borophene (Science \textbf{350}, 1513 (2015)). Chemical bonding analysis reveals the boron layer in the network being bound by delocalized four-center two-electron ${\sigma}$ bonds. Finally, we suggest high-pressure could be a feasible route to synthesise two-dimensional borane., Comment: 5 pages, 3 figures, 1 table