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The X$_2$MH$_6$ family, consisting of an electropositive cation X and a main group metal M octahedrally coordinated by hydrogen, has been predicted to hold promise for high-temperature conventional superconductivity. Herein, we analyze the electronic structure of two members of this family, Mg$_2$IrH$_6$ and Ca$_2$IrH$_6$, showing why the former may possess superconducting properties rivaling those of the cuprates, whereas the latter does not. Within Mg$_2$IrH$_6$ the vibrations of the IrH$_6^{4-}$ anions are key for the superconducting mechanism, and they induce coupling in the $e_g^*$ set, which are antibonding between the H 1$s$ and the Ir $d_{x^2-y^2}$ or $d_{z^2}$ orbitals. Because calcium possesses low-lying d-orbitals, $e_g^* \rightarrow$ Ca $d$ back-donation is preferred, quenching the superconductivity. Our analysis explains why high critical temperatures were only predicted for second or third row X metal atoms, and may hold implications for superconductivity in other systems where the antibonding anionic states are filled.

Experimentally obtained X-ray diffraction (XRD) patterns can be difficult to solve, precluding the full characterization of materials, pharmaceuticals, and geological compounds. Herein, we propose a method based upon a multi-objective evolutionary search that uses both a structure's enthalpy and similarity to a reference XRD pattern (constituted by a list of peak positions and their intensities) to facilitate structure solution of inorganic systems. Because the similarity index is computed for locally optimized cells that are subsequently distorted to find the best match with the reference, this process transcends both computational (e.g. choice of theoretical method, and 0 K approximation) and experimental (e.g. external stimuli, and metastability) limitations. We illustrate how the proposed methodology can be employed to successfully uncover complex crystal structures by applying it to a range of test cases, including inorganic minerals, pure elements ramp-compressed to extreme conditions, and molecular crystals. The results demonstrate that our approach not only improves the accuracy of structure prediction but also significantly reduces the time required to achieve reliable solutions, thus providing a powerful tool for the advancement of materials science and related fields.

Machine learning models are susceptible to being misled by biases in training data that emphasize incidental correlations over the intended learning task. In this study, we demonstrate the impact of data bias on the performance of a machine learning model designed to predict the synthesizability likelihood of crystal compounds. The model performs a binary classification on labeled crystal samples. Despite using the same architecture for the machine learning model, we showcase how the model's learning and prediction behavior differs once trained on distinct data. We use two data sets for illustration: a mixed-source data set that integrates experimental and computational crystal samples and a single-source data set consisting of data exclusively from one computational database. We present simple procedures to detect data bias and to evaluate its effect on the model's performance and generalization. This study reveals how inconsistent, unbalanced data can propagate bias, undermining real-world applicability even for advanced machine learning techniques., Comment: 8 pages, 4 figures, 3 appendices

Quantum nuclear effects and anharmonicity impact a wide range of functional materials and their properties. One of the most powerful techniques to model these effects is the Stochastic Self-Consistent Harmonic Approximation (SSCHA). Unfortunately, the SSCHA is extremely computationally expensive, prohibiting its routine use. We propose a protocol that pairs machine learning interatomic potentials, which can be tailored for the system at hand via active learning, with the SSCHA. Our method leverages an upscaling procedure that allows for the treatment of supercells of up to thousands of atoms with practically minimal computational effort. The protocol is applied to PdCuH$_x$ ($x = 0-2$) compounds, chosen because previous experimental studies have reported superconducting critical temperatures, $T_\text{c}$s, as high as 17~K at ambient pressures in an unknown hydrogenated PdCu phase. We identify a $P4/mmm$ PdCuH$_2$ structure, which is shown to be dynamically stable only upon the inclusion of quantum fluctuations, as being a key contributor to the measured superconductivity. For this system, our methodology is able to reduce the computational expense for the SSCHA calculations by $\sim$96\%. The proposed protocol opens the door towards the routine inclusion of quantum nuclear motion and anharmonicity in materials discovery.

High-temperature high-pressure superconducting hydrides are typically characterized by cage-like hydrogenic lattices filled with electropositive metal atoms. Here, density functional theory based evolutionary crystal structure searches find two phases that possess these geometric features and are related to the Type-II clathrate structure. In these $Fd\overline{3}m$ Li$_2$CaH$_{16}$ and $R\overline{3}m$ Li$_2$CaH$_{17}$ phases the calcium atom occupies the larger cage and the lithium atom the smaller one. The highest superconducting critical temperatures predicted within the isotropic Eliashberg formalism, 330~K at 350~GPa for $Fd\overline{3}m$ Li$_2$CaH$_{16}$ and 370~K at 300~GPa for $R\overline{3}m$ Li$_2$CaH$_{17}$, suggest these structures fall in the class of high-energy-density quantum materials known as hot superconductors. As pressure is lowered the cage-like lattices distort with the emergence of quasimolecular hydrogenic motifs; nonetheless Li$_2$CaH$_{17}$ is predicted to be superconducting down to 160~GPa at 205~K., Comment: 35 pages, 5 figures

In the last decade, there has been great progress in predicting and synthesizing polyhydrides that exhibit superconductivity when squeezed. Dopants allow these compounds to become metals at pressures lower than those required to metallize elemental hydrogen. Here, we show that by combining the fundamental planetary building blocks of molecular hydrogen and ammonia, conventional superconducting compounds can be formed at high pressure. Through extensive theoretical calculations we predict metallic metastable structures with NH$_n$ ($n=10,11,24$) stoichiometries that are based on NH$_4^+$ superalkali cations and complex hydrogenic lattices. The hydrogen atoms in the molecular cation contribute to the superconducting mechanism, and the estimated superconducting critical temperatures, $T_\text{c}$s, are comparable to the highest values computed for the alkali metal polyhydrides. The largest calculated (isotropic Eliashberg) $T_\text{c}$ is 179~K for $Pnma$-NH$_{10}$ at 300~GPa. Our results suggest that other molecular cations can be mixed with hydrogen under pressure yielding superconducting compounds.

Version 13 of XtalOpt, an evolutionary algorithm for crystal structure prediction, is now available for download from the CPC program library or the XtalOpt website, https://xtalopt.github.io. In the new version of the XtalOpt code, a general platform for multi-objective global optimization is implemented. This functionality is designed to facilitate the search for (meta)stable phases of functional materials through minimization of the enthalpy of a crystalline system coupled with the simultaneous optimization of any desired properties that are specified by the user. The code is also able to perform a constrained search by filtering the parent pool of structures based on a user-specified feature, while optimizing multiple objectives. Here, we present the implementation and various technical details, and we provide a brief overview of additional improvements that have been introduced in the new version of XtalOpt.

We explore electronic and structural properties of Fm$\overline{3}$m Lu-H-N structures with specific N,H ordering as plausible candidates for near-ambient superconductivity possibly originating from their remarkably narrow hydrogen-based bands at the Fermi level. Although LuH$_{2.875}$N$_{0.125}$ exhibits an instability persisting up to 17 GPa, it is anharmonically stable near ambient pressure when accounting for quantum nuclear effects. The presence of flat bands near $E_\text{F}$ is understood to arise from destructive\ quantum interference between N-p and surrounding H-s orbitals, with certain types of defects leaving the flat bands unaffected. The results suggest there is an optimal pressure near ambient where the superconducting $T_{\text{c}}$ is maximized in this structure by anharmonically-stabilized low-frequency and non-adiabatically coupled high-frequency hydrogen modes. Despite the metastability of this structure, its electronic properties and dynamical stability when calculated beyond a classical harmonic approach can explain the reported near-ambient superconductivity in Lu-H-N., Comment: Added significant supplemental information since previous version, revised main figures and text. Conclusions unchanged from previous version but additional insight uncovered regarding pressure dependence. 7 main figures and 11 SI figures

Large density functional theory (DFT) databases are a treasure trove of energies, forces and stresses that can be used to train machine learned interatomic potentials for atomistic modeling. Herein, we employ structural relaxations from the AFLOW database to train moment tensor potentials (MTPs) for four carbide systems: HfTaC, HfZrC, MoWC and TaTiC. The resulting MTPs are used to relax ~6300 random symmetric structures, and are subsequently improved via active learning to generate robust potentials (RP) that can relax a wide variety of structures, and accurate potentials (AP) designed for the relaxation of low-energy systems. This protocol is shown to yield convex hulls that are indistinguishable from those predicted by AFLOW for the HfTaC, HfZrC and TaTiC systems, and in the case of the MoWC system to predict thermodynamically stable structures that are not found within AFLOW, highlighting the potential of the employed protocol within crystal structure prediction. Relaxation of over three hundred Mo$_{1-x}$W$_x$C stoichiometry crystals first with the RP then with the AP yields formation enthalpies that are in excellent agreement with those obtained via DFT.

Inspired by the synthesis of the high-pressure Fm-3m LaH10 superconducting superhydride, systematic density functional theory (DFT) calculations are performed to study ternaries that could be derived from it by replacing two of the hydrogen atoms with boron or carbon and varying the identity of the electropositive element. Though many of the resulting alkali-metal and alkaline-earth MC2H8 phases are predicted to be dynamically stable at mild pressures, their superconducting critical temperatures (Tcs) are low because their metallicity results from the filling of an electride-like band. Substitution with a trivalent element leads to phases with substantial metal d-character at the Fermi level whose Tcs are typically above 40 K. Among the MB2H8 phases examined, KB2H8, RbB2H8 and CsB2H8 are predicted to be dynamically stable at very mild pressures, and their stability is rationalized by a DFT-Chemical Pressure analysis that elucidates the role of the M atom size. Quantum anharmonic effects strongly affect the properties of KB2H8, the highest predicted Tc compound, near 10 GPa, but molecular dynamics simulations reveal it would decompose below its Tc at this pressure. Nonetheless, at ca. 50 GPa KB2H8 is predicted to be thermally stable with a superconducting figure of merit surpassing that of the recently synthesized LaBeH8.

We present theoretical and experimental studies of superconductivity and low temperature structural phase boundaries in lithium. We mapped the structural phase diagram of 6Li and 7Li under hydrostatic conditions between 5 top 55GPa and within the temperature range of 15 to 75K, observing the FCC-hR1-cI16 phase transitions. 6Li and 7Li show some differences at the structural boundaries, with a potential shift of the phase boundaries of 6Li to lower pressures. Density functional theory calculations and topological analysis of the electron density elucidates the superconducting properties and interatomic interactions within these phases of lithium., Comment: (24 pages, 10 figures, 2 tables, 2 parts including main manuscript and the supplementary information section)

Spinodal decomposition can improve a number of essential properties in materials, especially hardness. Yet, the theoretical prediction of the onset of this phenomenon (e.g., temperature) and its microstructure (e.g., wavelength) often requires input parameters coming from costly and time-consuming experimental efforts, hindering rational materials optimization. Here, we present a procedure where such parameters are not derived from experiments. First, we calculate the spinodal temperature by modeling nucleation in the solid solution while approaching the spinode boundary. Then, we compute the spinodal wavelength self-consistently using a few reasonable approximations. Our results show remarkable agreement with experiments and, for NiRh, the calculated yield strength due to spinodal microstructures surpasses even those of Ni-based superalloys. We believe that this procedure will accelerate the exploration of the complex materials experiencing spinodal decomposition, critical for their macroscopic properties., Comment: 10 pages, 4 figures

Early quantum mechanical models suggested that pressure drives solids towards free-electron metal behavior where the ions are locked into simple close-packed structures. The prediction and subsequent discovery of high-pressure electrides (HPEs), compounds assuming open structures where the valence electrons are localized in interstitial voids, required a paradigm shift. Our quantum chemical calculations on the iconic insulating Na-hP4 HPE show that increasing density causes a 3s -> 3pd electronic transition due to Coulomb repulsion between the 1s2s and 3s states, and orthogonality of the 3pd states to the core. The large lobes of the resulting Na-pd hybrid orbitals point towards the center of an 11-membered penta-capped trigonal prism and overlap constructively, forming multi-centered bonds, which are responsible for the emergence of the interstitial charge localization in Na-hP4. These multi-centered bonds facilitate the increased density of this phase, which is key for its stabilization under pressure.

Using first principles calculations, {111} intrinsic stacking fault (ISF) energies in Group IVB, VB, and VIB high-entropy transition metal carbides are shown to be predictable from an optimized rule of mixtures based on the properties of the single metal carbide constituents present near the stacking fault. A composition-independent linear relationship is demonstrated between the ISF energies and the unstable stacking fault (USF) energies along the <112>{111} gamma surface slip path. Treating the ISF and USF energies as analogous to the heat of reaction and transition state barrier in chemical reactions, this linear relationship represents a new application of the Evans-Polanyi-Semenov principle. Further, a full defect energy distribution can be obtained from the predicted ISF energies with only the composition as an input for the mixed early-transition metal carbides. Applying a model that balances the elastic repulsion between partial dislocations with the distribution of ISF energies, we show that Shockley partial edge dislocations should remain bound for all valence electron concentration values up to about 9.6, even when the average stacking fault energy is negative., Comment: 10 pages

Metastable materials are abundant in nature and technology, showcasing remarkable properties that inspire innovative materials design. However, traditional crystal structure prediction methods, which rely solely on energetic factors to determine a structure's fitness, are not suitable for predicting the vast number of potentially synthesizable phases that represent a local minimum corresponding to a state in thermodynamic equilibrium. Here, we present a new approach for the prediction of metastable phases with specific structural features, and interface this method with the XtalOpt evolutionary algorithm. Our method relies on structural features that include the local crystalline order (e.g., the coordination number or chemical environment), and symmetry (e.g., Bravais lattice and space group) to filter the parent pool of an evolutionary crystal structure search. The effectiveness of this approach is benchmarked on three known metastable systems: XeN$_8$, with a two-dimensional polymeric nitrogen sublattice, brookite TiO$_2$, and a high pressure BaH$_4$ phase that was recently characterized. Additionally, a newly predicted metastable melaminate salt, $P$-1 WC$_{3}$N$_{6}$, was found to possess an energy that is lower than two phases proposed in a recent computational study. The method presented here could help in identifying the structures of compounds that have already been synthesized, and developing new synthesis targets with desired properties.

The structure of the material responsible for the room temperature and near ambient pressure superconductivity reported in an N-doped lutetium hydride [Nature, 615, 244 (2023)] has not been conclusively determined. Herein, density functional theory calculations are performed in an attempt to uncover what it might be. Guided by a range of strategies including crystal structure prediction and modifications of existing structure types, we present an array of Lu-N-H phases that are dynamically stable at experimentally relevant pressures. Although none of the structures found are thermodynamically stable, and none are expected to remain superconducting above 17 K at 10 kbar, a number of metallic compounds with fcc Lu lattices -- as suggested by the experimental X-ray diffraction measurements of the majority phase -- are identified. The system whose calculated equation of states matches best with that measured for the majority phase is fluorite-type LuH2, whose 10 kbar superconducting critical temperature was estimated to be 0.09 K using the Allen-Dynes modified McMillan equation., Comment: 11 pages, 8 figures

Evolutionary searches were employed to predict the most stable structures of perovskites with helium atoms on their A-sites up to pressures of 10 GPa. The thermodynamics associated with helium intercalation into [CaZr]F6, structure that [He]2[CaZr]F6 adopts under pressure, and the mechanical properties of the parent perovskite and helium-bearing phase were studied via density functional theory (DFT) calculations. The pressure-temperature conditions where the formation of HeAlF3, HeGaF3, HeInF3, HeScF3 and HeReO3 from elemental helium and the vacant A-site perovskites is favored were found. Our DFT calculations show that entropy can stabilize the helium-filled perovskites provided that the volume that the noble gas atom occupies within their pores is larger than within the elemental solid at that pressure. We find that helium incorporation will increase the bulk modulus of AlF3 from a value characteristic of tin to one characteristic of steel, and hinders rotations of its octahedra that occur under pressure.

An overview of the behavior of materials at high pressure is presented, starting from the effects on single atoms driving electronic transitions and changes in periodic trends. A range of high-pressure-induced phenomena in the solid state are then discussed building on the atomic changes, including bizarre electronic structures, electrides, compounds of noble gases, changes in elemental miscibility, and strange structural and bonding configurations. In the final section, the field of high pressure superconductivity is discussed, as high pressure phases have generated immense study and excitement as some of their critical superconducting temperatures approach room temperature., Comment: Written for Comprehensive Inorganic Chemistry III (2023)

Inspired by the synthesis of XB3C3 (X= Sr, La) compounds in the bipartite sodalite clathrate structure, density functional theory (DFT) calculations are performed on members of this family containing up to two different metal atoms. A DFT-chemical pressure analysis on systems with X= Mg, Ca, Sr, Ba reveals that the size of the metal cation, which can be tuned to stabilize the B-C framework, is key for their ambient-pressure dynamic stability. High-throughput density functional theory calculations on 105 Pm-3 symmetry XYB6C6 binary-guest compounds (where X, Y are electropositive metal atoms) find 22 that are dynamically stable at 1 atmosphere, expanding the number of potentially synthesizable phases by 19 (18 metals and 1 insulator). The density of states at the Fermi level and superconducting critical temperature, Tc, can be tuned by changing the average oxidation state of the metal atoms, with Tc being highest for an average valence of +1.5. KPbB6C6, with an ambient-pressure Eliashberg Tc of 88 K, is predicted to possess the highest-Tc among the studied Pm-3n XB3C3 or Pm-3 XY B6C6 phases, and calculations suggest it may be synthesized using high-pressure high-temperature techniques then quenched to ambient conditions.

The high critical superconducting temperatures ($T_c$s) of metal hydride phases with clathrate-like hydrogen networks have generated great interest. Herein, we employ the Density Functional Theory-Chemical Pressure (DFT-CP) method to explain why certain electropositive elements adopt these structure types, whereas others distort the hydrogenic lattice, thereby decreasing the $T_c$. The progressive opening of the H$_{24}$ polyhedra in MH$_6$ phases is shown to arise from internal pressures exerted by large metal atoms, some of which may favor an even higher hydrogen content that loosens the metal atom coordination environments. The stability of the LaH$_{10}$ and LaBH$_8$ phases is tied to stuffing of their shared hydrogen network with either additional hydrogen or boron atoms. The predictive capabilities of DFT-CP are finally applied to the Y-X-H system to identify possible ternary additions yielding a superconducting phase stable to low pressures., Comment: 13 pages, 3 figures

Ab initio evolutionary structure searches coupled with quasiharmonic calculations predict that the insulating Na hP4 phase transitions to a novel P63/m phase between 200 GPa at 150 K, and 350 GPa at 1900 K. P63/m Na is a topological semimetal with a Dirac nodal surface that is protected by a non-symmorphic symmetry, S2z . It is characterized by localized non-nuclear charge within 1D honeycomb channels and 0D cages rendering it an electride. These results highlight the complexity of warm dense sodiums electronic structure and free energy landscape that emerges at conditions where ionic cores overlap.

A metallic covalently bonded carbon allotrope is predicted via first principles calculations. It is composed of an $sp^3$ carbon framework that acts as a diamond anvil cell by constraining the distance between parallel cis-polyacetylene chains. The distance between these $sp^2$ carbon atoms renders the phase metallic, and yields two well-nested nearly parallel bands that span the Fermi level. Calculations show that this phase is a conventional superconductor, with the motions of the $sp^2$ carbons being key contributors to the electron phonon coupling. The $sp^3$ carbon atoms impart superior mechanical properties, with a predicted Vickers hardness of 48~GPa. This phase, metastable at ambient conditions, could be made via cold compression of graphite to 40~GPa. A family of multifunctional materials with tunable superconducting and mechanical properties could be derived from this phase by varying the $sp^2$ versus $sp^3$ carbon content and by doping.

Evolutionary structure searches revealed a plethora of stable and low-enthalpy metastable phases in the S-P-H ternary phase diagram under pressure. A wide variety of crystalline structure types were uncovered ranging from those possessing one-dimensional chains, two-dimensional sheets based on S-H or S-P-H square lattices as well as S-H or P-H honeycombs, and cage-like structures. Some of the cage-like structures could be derived from doping the high-pressure high-temperature superconducting $Im\bar{3}m$ H$_3$S phase with phosphorous. Most of the discovered compounds were metallic, however those derived from $Im\bar{3}m$ H$_3$S lattices with low levels of P-doping were predicted to possess the highest superconducting critical temperatures ($T_c$s). The propensity for phosphorous to assume octahedral coordination, as well as the similar radii of sulfur and phosphorous are key to maintaining a high density of states at the Fermi level in $Im\bar{3}m$ S$_{0.875}$P$_{0.125}$H$_3$, whose $T_c$ was estimated to be similar to that of H$_3$S at 200~GPa.

At high pressure, the typical behavior of elements dictated by the periodic table - including oxidation numbers, stoichiometries in compounds, and reactivity, to name but a few - is altered dramatically. As pressure is applied, the energetic ordering of atomic orbitals shifts, allowing core orbitals to become chemically active, atypical electron configurations to occur, and in some cases, non-atom-centered orbitals to form in the interstices of solid structures. Strange stoichiometries, structures, and bonding motifs result. Crystal structure prediction tools, not burdened by preconceived notions about structural chemistry learned at atmospheric pressure, have been applied to great success to explore phase diagrams at high pressure, identifying novel structures in diverse chemical systems. Several of these have been subsequently observed by experimental investigations, whose access to high-pressure regimes is bolstered by advances in diamond anvil cell and dynamic compression techniques. The joint efforts of experiment and theory have led to particular success in the realm of high-temperature superconductors, identifying many novel phases whose superconducting transition approaches room temperature., Comment: 17 pages (35 with references), 6 figures

First-principles calculations and analysis of the thermodynamic, structural, and electronic properties of liquid SiO$_2$ characterize the bonded-to-atomic transition at 0.1--1.6 TPa and 10$^4$--10$^5$ K (1--7 eV), the high-energy-density regime relevant to understanding planetary interiors. We find strong ionic bonds that become short-lived due to high kinetics during the transition, with sensitivity of the transition temperature to pressure, and our calculated Hugoniots agree with past experimental data. These results reconcile previous experimental and theoretical findings by clarifying the nature of the bond dissociation process in early Earth and "rocky" (oxide) constituents of large planets., Comment: 11 pages, 11 figures

Over the past decade, a combination of crystal structure prediction techniques and experimental synthetic work has thoroughly explored the phase diagrams of binary hydrides under pressure. The fruitfulness of this dual approach is demonstrated in the recent identification of several superconducting hydrides with $T_c$s approaching room temperature. We start with an overview of the computational procedures for predicting stable structures and estimating their propensity for superconductivity. A survey of phases with high $T_c$ reveals some common structural features that appear conducive to the strong coupling of the electronic structure with atomic vibrations that leads to superconductivity. We discuss the stability and superconducting properties of phases containing two of these -- molecular H$_2$ units mixed with atomic H and hydrogenic clathrate-like cages -- as well as more unique motifs. Finally, we argue that ternary hydride phases, which are far less-explored, are a promising route to achieving simultaneously superconductivity at high temperatures and stability at low pressures. Several ternary hydrides arise from the addition of a third element to a known binary hydride structure through site mixing or onto a new site -- and several more are based on altogether new structural motifs., Comment: 19 pages, 4 tables, 5 figures

First-principles calculations were carried out to provide a chemical basis for proposed structures associated with the recently reported room-temperature superconductivity in a carbonaceous sulfur hydride material under pressure. Calculations were performed on supercells of H$_3$S doped with 1.85-25\% carbon, corresponding to SH$_3$~$\rightarrow$~CH$_3$ or SH$_3$~$\rightarrow$~CH$_4$ substitutions, primarily at pressures of 270 GPa where the maximum critical temperature, $T_c$, has been reported. In the first type of substitution, the carbon atoms can be six-fold coordinated, stabilizing a CH$_6$ configuration within the cubic H$_3$S framework structure that forms under pressure. In the second, the carbon can be four-fold coordinated as methane intercalated into the H-S lattice, with or without an additional hydrogen in the framework. The results indicate that unusual local bonding configurations with respect to carbon can be stabilized under pressure. The doping breaks degenerate bands, lowering the density of states at the Fermi level ($N_F$), and localizing electrons in C-H bonds. Low levels of CH$_4$ doping do not increase $N_F$ to values as high as those calculated for $Im\bar{3}m$ H$_3$S, but they do result in a larger logarithmic average phonon frequency, and an electron-phonon coupling parameter comparable to that of $R3m$ H$_3$S. The $T_c$s estimated for carbon doping levels ranging from 1.85-5.7\% are compatible with experimental measurements for the C-S-H superconductor.

The complex crystal chemistry of elemental boron has led to numerous proposed structures with distinctive motifs as well as contradictory findings. Herein, evolutionary structure searches performed at 100 GPa have uncovered a series of potential new metastable phases of boron, and bonding analyses were carried out to elucidate their electronic structure. These polymorphs, dynamically stable at 100 GPa, were grouped into two families. The first was derived from the thermodynamic minimum at these conditions, $\alpha$-Ga, whereas channels comprised the second. Two additional intergrowth structures were uncovered, and it was shown they could be constructed by stacking layers of $\alpha$-Ga-like and channel-like allotropes on top of each other. A detailed bonding analysis revealed networks of four-center $\sigma$-bonding functions linked by two-center B-B bonds in the $\alpha$-Ga based structures, and networks that were largely composed of three-center $\sigma$-bonding functions in the channel-based structures. Seven of these high pressure phases were found to be metastable at atmospheric conditions, and their Vickers hardnesses were estimated to be $\sim$36 GPa., Comment: 14 pages, 12 figures, 3 tables

Evolutionary crystal structure prediction searches have been employed to explore the ternary Li-F-H system at 300 GPa. Metastable phases were uncovered within the static lattice approximation, with LiF$_3$H$_2$, LiF$_2$H, Li$_3$F$_4$H, LiF$_4$H$_4$, Li$_2$F$_3$H and LiF$_3$H lying within 50 meV/atom of the 0 K convex hull. All of these phases contain H$_n$F$_{n+1}^-$ ($n$ = 1; 2) anions, and Li$^+$ cations. Other structural motifs such as LiF slabs, H$_3^+$ molecules, and F$^{\delta -}$ ions are present in some of the low enthalpy Li-F-H structures. The bonding within the H$_n$F$_{n+1}^-$ molecules, which may be bent or linear, symmetric or asymmetric, is analyzed. The five phases closest to the hull are insulators, while LiF$_3$H is metallic and predicted to have a vanishingly small superconducting critical temperature. This study lays the foundation for future investigations of the role of temperature and anharmonicity on the stability and properties of compounds and alloys in the Li-F-H ternary system., Comment: 11 pages, 4 figures, 1 table

Evolutionary searches predicted a number of ternary phases that could be synthesized at pressures of 100-300~GPa. $P6_3/mmc$ CaSH$_2$, $Pnma$ CaSH$_2$, $Cmc2_1$ CaSH$_6$, and $I\bar{4}$ CaSH$_{20}$ were composed of a Ca-S lattice along with H$_2$ molecules coordinated in a ``side-on'' fashion to Ca. The H-H bond lengths in these semiconducting phases were elongated because of H$_2$ $\sigma\rightarrow$ Ca d donation, and Ca d$\rightarrow$ H$_2$ $\sigma^*$ back-donation, via a Kubas-like mechanism. $P\bar{6}m2$ CaSH$_3$, consisting of two-dimensional HS and CaH$_2$ sheets, was metastable and metallic above \edit{128~GPa}. The presence of van Hove singularities increased its density of states at the Fermi level, and concomitantly the superconducting critical temperature, which was estimated to be as high as \edit{$\sim$100~K at 128~GPa}. This work will inspire the search for superconductivity in materials based upon \edit{honeycomb HX (X=S, Se, Te), and MH$_2$ (M=Mg, Ca, Sr, Ba) layers} under pressure.

Room temperature superconductivity has been achieved under high pressure in an organically derived carbonaceous sulfur hydride with a critical superconducting transition temperature (Tc) of 288 kelvin. This development is part of a new class of dense, hydrogen rich materials with remarkably high critical temperatures. Metal superhydrides are a subclass of these materials that provide a different and potentially more promising route to very high Tc superconductivity. The most promising binary metal superhydrides contain alkaline or rare earth elements, and recent experimental observations of LaH10 have shown them capable of Tc s up to 250 to 260 kelvin. Predictions have shown yttrium superhydrides to be the most promising with an estimated Tc in excess of 300 kelvin for YH10. Here we report the synthesis of an yttrium superhydride that exhibits superconductivity at a critical temperature of 262 kelvin at 182 gigapascal. A palladium thin film assists the synthesis by protecting the sputtered yttrium from oxidation and promoting subsequent hydrogenation. Phonon mediated superconductivity is established by the observation of zero resistance, an isotope effect and the reduction of Tc under an external magnetic field. The upper critical magnetic field is 103 tesla at zero temperature. We suggest YH9 is the synthesized product based on comparison of the measured Raman spectra and Tc to calculated Raman results.

The silver-fluorine phase diagram has been scrutinized as a function of external pressure using theoretical methods. Our results indicate that two novel stoichiometries containing Ag+ and Ag2+ cations (Ag3F4 and Ag2F3) are thermodynamically stable at ambient and low pressure. Both are computed to be magnetic semiconductors at ambient pressure conditions. For Ag2F5, containing both Ag2+ and Ag3+, we find that strong 1D antiferromagnetic coupling is retained throughout the pressure-induced phase transition sequence up to 65 GPa. Our calculations show that throughout the entire pressure range of their stability the mixed valence fluorides preserve a finite band gap at the Fermi level. We also confirm the possibility of synthesizing AgF4 as a paramagnetic compound at high pressure. Our results indicate that this compound is metallic in its thermodynamic stability region. Finally, we present general considerations on the thermodynamic stability of mixed valence compounds of silver at high pressure.

Good agreement was found between experimental Vickers hardnesses, $H_\text{v}$, of a wide range of materials and those calculated by three macroscopic hardness models that employ the shear and/or bulk moduli obtained from: (i) first principles via AFLOW-AEL (AFLOW Automatic Elastic Library), and (ii) a machine learning (ML) model trained on materials within the AFLOW repository. Because $H_\text{v}^\text{ML} $ values can be quickly estimated, they can be used in conjunction with an evolutionary search to predict stable, superhard materials. This methodology is implemented in the XtalOpt evolutionary algorithm. Each crystal is minimized to the nearest local minimum, and its Vickers hardness is computed via a linear relationship with the shear modulus discovered by Teter. Both the energy/enthalpy and $H_\text{v, Teter}^{\text{ML}}$ are employed to determine a structure's fitness. This implementation is applied towards the carbon system, and 43 new superhard phases are found. A topological analysis reveals that phases estimated to be slightly harder than diamond contain a substantial fraction of diamond and/or lonsdaleite.

The theoretical exploration of the phase diagrams of binary hydrides under pressure using \emph{ab initio} crystal structure prediction techniques coupled with first-principles calculations has led to the \emph{in silico} discovery of numerous novel superconducting materials. This Perspective article focuses on the alkaline earth and rare earth polyhydrides whose superconducting critical temperature, $T_c$, was predicted to be above the boiling point of liquid nitrogen. After providing a brief overview of the computational protocol used to predict the structures of stable and metastable hydrides under pressure, we outline the equations that can be employed to estimate $T_c$. The systems with a high $T_c$ can be classified according to the motifs found in their hydrogenic lattices. The highest $T_c$s are found for cages that are reminiscent of clathrates, and the lowest for systems that contain atomic and molecular hydrogen. A wide variety of hydrogenic motifs including 1- and 2-dimensional lattices, as well as H$_{10}^{\delta-}$ molecular units comprised of fused H$_5^{\delta-}$ pentagons are present in phases with intermediate $T_c$s. Some of these phases are predicted to be superconducting at room temperature. Some may have recently been synthesized in diamond anvil cells., Comment: 12 pages, 5 figures, 3 tables, perspective

Evolutionary algorithms and the particle swarm optimization method have been used to predict stable and metastable high hydrides of iron between 150-300 GPa that have not been discussed in previous studies. Cmca FeH5, Pmma FeH6 and P2/c FeH6 contain hydrogenic lattices that result from slight distortions of the previously predicted I4/mmm FeH5 and Cmmm FeH6 structures. Density functional theory calculations show that neither the I4/mmm nor the Cmca symmetry FeH5 phases are superconducting. A P1 symmetry FeH7 phase, which is found to be dynamically stable at 200 and 300 GPa, adds another member to the set of predicted nonmetallic transition metal hydrides under pressure. Two metastable phases of FeH$_8$ are found, and the preferred structure at 300 GPa contains a unique 1-dimensional hydrogenic lattice., Comment: 24 pages, 7 figures

The computational and experimental exploration of the phase diagrams of binary hydrides under high pressure has uncovered phases with novel stoichiometries and structures, some which are superconducting at quite high temperatures. Herein we review the plethora of studies that have been undertaken in the last decade on the main group and transition metal hydrides, as well as a few of the rare earth hydrides at pressures attainable in diamond anvil cells. The aggregate of data shows that the propensity for superconductivity is dependent upon the species used to "dope" hydrogen, with some of the highest values obtained for elements that belong to the alkaline and rare earth, or the pnictogen and chalcogen families., Comment: 73 pages, 18 figures, and 1 table

The traditional paradigm for materials discovery has been recently expanded to incorporate substantial data driven research. With the intent to accelerate the development and the deployment of new technologies, the AFLOW Fleet for computational materials design automates high-throughput first principles calculations, and provides tools for data verification and dissemination for a broad community of users. AFLOW incorporates different computational modules to robustly determine thermodynamic stability, electronic band structures, vibrational dispersions, thermo-mechanical properties and more. The AFLOW data repository is publicly accessible online at aflow.org, with more than 1.7 million materials entries and a panoply of queryable computed properties. Tools to programmatically search and process the data, as well as to perform online machine learning predictions, are also available., Comment: 14 pages, 8 figures

Machine learning approaches, enabled by the emergence of comprehensive databases of materials properties, are becoming a fruitful direction for materials analysis. As a result, a plethora of models have been constructed and trained on existing data to predict properties of new systems. These powerful methods allow researchers to target studies only at interesting materials $\unicode{x2014}$ neglecting the non-synthesizable systems and those without the desired properties $\unicode{x2014}$ thus reducing the amount of resources spent on expensive computations and/or time-consuming experimental synthesis. However, using these predictive models is not always straightforward. Often, they require a panoply of technical expertise, creating barriers for general users. AFLOW-ML (AFLOW $\underline{\mathrm{M}}$achine $\underline{\mathrm{L}}$earning) overcomes the problem by streamlining the use of the machine learning methods developed within the AFLOW consortium. The framework provides an open RESTful API to directly access the continuously updated algorithms, which can be transparently integrated into any workflow to retrieve predictions of electronic, thermal and mechanical properties. These types of interconnected cloud-based applications are envisioned to be capable of further accelerating the adoption of machine learning methods into materials development., Comment: 10 pages, 2 figures

Density Functional Theory calculations using the quasi-harmonic approximation have been used to calculate the solid Hugoniot of two polytypes of boron carbide up to 100 GPa. Under the assumption that segregation into the elemental phases occurs around the pressure that the B11Cp(CBC) polytype becomes thermodynamically unstable with respect to boron and carbon, two discontinuities in the Hugoniot, one at 50 GPa and one at 90-100 GPa, are predicted. The former is a result of phase segregation, and the latter a phase transition within boron. First principles molecular dynamics (FPMD) simulations were employed to calculate the liquid Hugoniot of B4C up to 1.5 TPa, and the results are compared to recent experiments carried out at the Omega Laser Facility up to 700 GPa [Phys. Rev. B 94, 184107 (2016)]. A generally good agreement between theory and experiment was observed. Analysis of the FPMD simulations provides evidence for an amorphous, but covalently bound, fluid below 438 GPa, and an atomistic fluid at higher pressures and temperatures., Comment: 10 pages, 6 figures

Evolutionary algorithms (EA) coupled with Density Functional Theory (DFT) calculations have been used to predict the most stable hydrides of phosphorous (PHn, n = 1-6) at 100, 150 and 200 GPa. At these pressures phosphine is unstable with respect to decomposition into the elemental phases, as well as PH2 and H2. Three metallic PH2 phases were found to be dynamically stable and superconducting between 100-200 GPa. One of these contains five formula units in the primitive cell and has C2/m symmetry (5FU-C2/m). It is comprised of 1D periodic PH3-PH-PH2-PH-PH3 oligomers. Two structurally related phases consisting of phosphorous atoms that are octahedrally coordinated by four phosphorous atoms in the equatorial positions and two hydrogen atoms in the axial positions (I4/mmm and 2FU-C2/m) were the most stable phases between ~160-200 GPa. Their superconducting critical temperatures (Tc) were computed as being 70 and 76 K, respectively, via the Allen-Dynes modified McMillan formula and using a value of 0.1 for the Coulomb pseudopotential, u*. Our results suggest that the superconductivity recently observed by Drozdov, Eremets and Troyan when phosphine was subject to pressures of 207 GPa in a diamond anvil cell may result from these, and other, decomposition products of phosphine., Comment: 9 pages, 5 figures, 2 tables

Evolutionary structure searches predict three new phases of iodine polyhydrides stable under pressure. Insulating P1-H5I, consisting of zigzag chains of HI (delta+)and H2(delta-) molecules, is stable between 30-90 GPa. Cmcm-H2I and P6/mmm-H4I are found on the 100, 150 and 200 GPa convex hulls. These two phases are good metals, even at 1 atm, because they consist of monoatomic lattices of iodine. At 100 GPa the Tc of H2I and H4I are estimated to be 7.8 and 17.5 K, respectively. The increase in Tc relative to elemental iodine results from a larger omega-log from the light mass of hydrogen, and an enhanced lambda from modes containing H/I and H/H vibrations., Comment: 5 pages, 4 figures

Evolutionary structure searches are used to predict stable phases with unique stoichiometries in the hydrogen-rich region of the magnesium/hydrogen phase diagram under pressure. MgH$_4$, MgH$_{12}$ and MgH$_{16}$ are found to be thermodynamically stable with respect to decomposition into MgH$_2$ and H$_2$ near 100 GPa, and all lie on the convex hull by 200 GPa. MgH$_4$ contains two H$^-$ anions and one H$_2$ molecule per Mg$^{2+}$ cation, whereas the hydrogenic sublattices of MgH$_{12}$ and MgH$_{16}$ are composed solely of H$_2^{\delta -}$ molecules. The high-hydrogen content stoichiometries have a large density of states at the Fermi level, and the $T_c$ of MgH$_{12}$ at 140 GPa is calculated to be nearly three times greater than that of the classic hydride, MgH$_2$, at 180 GPa.

Evolutionary structure searches are used to predict a new class of compounds in the lithium--rich region of the lithium/hydrogen phase diagram under pressure. First principles computations show that LimH, 4

The structures of compressed rubidium polyhydrides, RbHn with n>1, and their evolution under pressure are studied using density functional theory calculations. These phases, which start to stabilize at only P=2 GPa, consist of Rb+ cations and one or more of the following species: H- anions, H2 molecules, and H3- units. The latter motif, the simplest example of a three-center four-electron bond, is found in the most stable structures, RbH5 and RbH3. Pressure induces the symmetrization of H3-. The thermodynamically most stable polyhydrides metallize above 200 GPa. At the highest pressures studied, our evolutionary searches find an RbH6 phase which contains polymeric (H3-)$_\infty$ chains that show signs of one-dimensional liquid-like behavior.