First-principles definition of ionicity and covalency in molecules and solids.

The notions of ionicity and covalency of chemical bonds, effective atomic charges, and decomposition of the cohesive energy into ionic and covalent terms are fundamental yet elusive. For example, different approaches give different values of atomic charges. Pursuing the goal of formulating a universal approach based on firm physical grounds (first-principles or non-empirical), we develop a formalism based on Wannier functions with atomic orbital symmetry and capable of defining these notions and giving numerically robust results that are in excellent agreement with traditional chemical thinking. Unexpectedly, in diamond-like boron phosphide (BP), we find charges of +0.68 on phosphorus and -0.68 on boron atoms, and this anomaly is explained by the Zintl-Klemm nature of this compound. We present a simple model that includes energies of the highest occupied cationic and lowest unoccupied anionic atomic orbitals, coordination numbers, and strength of interatomic orbital overlap. This model captures the essential physics of bonding and accurately reproduces all our results, including anomalous BP.

Lithiation of phosphorus at the nanoscale: a computational study of LinPm clusters.

Systematic structure prediction of LinPm nanoclusters was performed for a wide range of compositions (0 ≤ n ≤ 10, 0 ≤ m ≤ 20) using the evolutionary global optimization algorithm USPEX coupled with density functional calculations. With increasing Li concentration, the number of P-P bonds in the cluster reduces and the phosphorus backbone undergoes the following transformations: elongated tubular → multi-fragment (with mainly P5 rings and P7 cages) → cyclic topology → branched topology → P-P dumbbells → isolated P ions. By applying several stability criteria, we determined the most favorable LinPm clusters and found that they are located in the compositional area between m ≈ n/3 and m ≈ n/3 + 6. For instance, the Li3P7 cluster has the highest stability and is known to be the structural basis of the corresponding bulk crystal. The obtained results provide valuable insights into the lithiation mechanism of nanoscale phosphorus which is of interest for development of novel phosphorus-based anode materials.

Exploring correlation effects and volume collapse during electride dimensionality change in Ca2N.

We investigate the role of interstitial electronic states in the metal-to-semiconductor transition and the origin of the volume collapse in Ca2N during the pressure-induced phase transitions accompanied by changes of electride subspace dimensionality. Our findings highlight the importance of correlation effects in the electride subsystem as an essential component of the complex phase transformation mechanism. By employing a simplified model that incorporates the distortion of the local environment surrounding the interstitial quasi-atom (ISQ) which emerges under pressure and solving this model by Dynamical Mean Field Theory (DMFT), we successfully reproduced the evolution between the metallic and semiconducting phases and captured the remarkable volume collapse. Central to this observation is a significant enhancement of the localization of excess electrons and the emergence of antiferromagnetic pairing among them, leading to a spin-state transition with a notable reduction in the magnetic moment on the interstitial states.

Prediction and Rationalization of Abundant C-N-H Molecules in Different Environments.

The extreme chemical diversity of CmNnHk molecules is at the same time very important (central in organic chemistry) and difficult to rationalize in the sense that some molecules are abundant and easy to synthesize, while others are rare and difficult to make. Using the recently developed criteria of molecular "magicity", combined with evolutionary structure prediction and quantum-chemical calculations, we study these molecules in a wide range of compositions (0 ≤ m ≤ 13, 0 ≤ n ≤ 4, and 0 ≤ k ≤ 14). "Magic" molecules are defined as those that are lower in energy than any isochemical mixture of molecules with the nearest compositions. The predicted "magic" molecules are in good agreement with compounds found in versatile environments (interstellar and circumstellar media, Titan's lower atmosphere, and crude oil fractions) and in experimental chemistry. This work shows the predictive power of our approach, capable of predicting and explaining stable molecules in complex systems.

Order-Disorder Phase Transition and Ionic Conductivity in a Li2B12H12 Solid Electrolyte.

Temperature-induced phase transitions and ionic conductivities of Li2B12H12 and LiCB11H12 were simulated with the use of machine learning interatomic potentials based on van der Waals-corrected density functional theory (rev-vdW-DF2 functional). The simulated temperature of order-disorder phase transition, lattice parameters, diffusion, ionic conductivity, and activation energies are in good agreement with experimental data. Our simulations of Li2B12H12 uncover the importance of the reorientational motion of the [B12H12]2- anion. In the ordered α-phase (T < 625 K), these anions have well-defined orientations, while in the disordered ß-phase (T > 625 K), their orientations are random. In vacancy-rich systems, its complete rotation was observed, while in the ideal crystal, the anions display limited vabrational motion, indicating the static nature of the phase transition without dynamic disordering. The use of machine learning interatomic potentials has allowed us to study large systems (>2000 atoms) in long (nanosecond-scale) molecular dynamics runs with ab initio quality.

Ultralow reaction barriers for CO oxidation in Cu-Au nanoclusters.

Systematic structure prediction of CunAum nanoclusters was carried out for a wide compositional area (n + m ≤ 15) using the evolutionary algorithm USPEX and DFT calculations. The obtained structural data allowed us to assess the local stability of clusters and their suitability for catalysis of CO oxidation. Using these two criteria, we selected several most promising clusters for an accurate study of their catalytic properties. The adsorption energies of reagents, reaction paths, and activation energies were calculated. We found several cases with low activation energies and explained these cases using the patterns of structural change at the moment of CO2 desorption. The unique case is the Cu7Au6 cluster, which has extremely low activation energies for all transition states (below 0.05 eV). We thus showed that higher flexibility due to the binary nature of nanoclusters makes it possible to achieve the maximum catalytic activity. Considering the lower price of copper, Cu-Au nanoparticles are a promising new family of catalysts.

Enhancement of superconducting properties in the La-Ce-H system at moderate pressures.

Ternary hydrides are regarded as an important platform for exploring high-temperature superconductivity at relatively low pressures. Here, we successfully synthesized the hcp-(La,Ce)H9-10 at 113 GPa with the initial La/Ce ratio close to 3:1. The high-temperature superconductivity was strikingly observed at 176 K and 100 GPa with the extrapolated upper critical field Hc2(0) reaching 235 T. We also studied the binary La-H system for comparison, which exhibited a Tc of 103 K at 78 GPa. The Tc and Hc2(0) of the La-Ce-H are respectively enhanced by over 80 K and 100 T with respect to the binary La-H and Ce-H components. The experimental results and theoretical calculations indicate that the formation of the solid solution contributes not only to enhanced stability but also to superior superconducting properties. These results show how better superconductors can be engineered in the new hydrides by large addition of alloy-forming elements.

Novel Topological Motifs and Superconductivity in Li-Cs System.

In this work, we determined the phase diagram and electronic properties of the Li-Cs system by using an evolutionary crystal structure prediction algorithm coupled with first-principles calculations. We found that Li-rich compounds are more easily formed in a wide range of pressures, while the only predicted Cs-rich compound LiCs3 is thermodynamically stable at pressures above 359 GPa. A topological analysis of crystal structures concludes that both Li6Cs and Li14Cs have a unique topology that has not been reported in existing intermetallics. Of particular interest is the fact that four Li-rich compounds (Li14Cs, Li8Cs, Li7Cs, and Li6Cs) are found to be superconductors with a high critical temperature (∼54 K for Li8Cs at 380 GPa), due to their peculiar structural topologies and notable charge transfer from Li to Cs atoms. Our results not only extend an in-depth understanding of the high-pressure behavior of intermetallic compounds but also provide a new route to design new superconductors.

Stability of sulfur molecules and insights into sulfur allotropy.

Using ab initio evolutionary algorithm USPEX, we predict structures of sulfur molecules Sn (n = 2 - 21). It is shown that for n ≥ 5 stable structures of sulfur molecules are closed helical rings, which is in agreement with the experimental data and previous calculations. We investigate the stability of molecules using the following criteria: second-order energy difference (Δ2E), fragmentation energy (Efrag) and HOMO-LUMO gaps. The S8 molecule has the highest value of Δ2E and forms the most common allotropic form of sulfur (orthorhombic α-S), into which all other modifications convert over time at room temperature. Commonly found molecules S12 and S6 also have strongly positive Δ2E. Another well-known molecule, S7, has negative Δ2E, but at temperatures above 900 K has positive second-order free energy difference Δ2G. Generally, Δ2E (or Δ2G at finite temperatures) is a quantitative measure of the stability allowing one to predict the ease of formation of molecules and corresponding molecular crystals. Temperature dependence of the above-mentioned measures of stability explains a wide range of facts about sulfur crystalline allotropes, molecules in the gas phase, etc.

Protein structure prediction using the evolutionary algorithm USPEX.

Protein structure prediction is one of major problems of modern biophysics: current attempts to predict the tertiary protein structure from amino acid sequence are successful mostly when the use of big data and machine learning allows one to reduce the "prediction problem" to the "problem of recognition". Compared with recent successes of deep learning, classical predictive methods lag behind in their accuracy for the prediction of stable conformations. Therefore, in this work we extended the evolutionary algorithm USPEX to predict protein structure based on global optimization starting with the amino acid sequence. Moreover, we compared frequently used force fields for the task of protein structure prediction. Protein structure relaxation and energy calculations were performed using Tinker (with several different force fields) and Rosetta (with REF2015 force field) codes. To create new protein structure models in the USPEX algorithm, we developed novel variation operators. The test of the new method on seven proteins having (for simplicity) no cis-proline (with ω ≈ 0°) residues, and a length of up to 100 residues, revealed that our algorithm predicts tertiary structures of proteins with high accuracy. The comparison of the final potential energies of the predicted protein structures obtained using the USPEX and the Rosetta Abinitio approach showed that in most cases the developed algorithm found structures with close or even lower energy (Amber/Charmm/Oplsaal) and scoring function (REF2015). While USPEX has clearly demonstrated its ability to find very deep energy minima, our study showed that the existing force fields are not sufficiently accurate for accurate blind prediction of protein structures without further experimental verification.

Phosphorus nanoclusters and insight into the formation of phosphorus allotropes.

Elemental phosphorus has a striking variety of allotropes, which we analyze by looking at stable phosphorus clusters. We determine the ground-state structures of Pn clusters in a wide range of compositions (n = 2-50) using density functional calculations and global optimization techniques. We explain why the high-energy white phosphorus is so easily formed, compared to the much more stable allotropes - the tetrahedral P4 cluster is so much more stable than nearby compositions that only by increasing the size to P10 one can get a more stable non-P4-based structure. Starting from 17 atoms, phosphorus clusters have a single-stranded structure, consisting of a set of well-resolved structural units connected by P2 linking fragments. The investigation of relative stability has revealed even-odd alternations and structural magic numbers. The former are caused by the higher stability of clusters with even numbers of atoms due to closed electronic shells. The structural magic numbers are associated with the presence of particular stable structural units and lead to enhanced stability of P18+12k (k = 0, 1, 2) clusters. We also compare the energies of the obtained ground-state structures with clusters of different phosphorus allotropes. Clusters of fibrous phosphorus are energetically the closest to the ground states, white phosphorus clusters are found to be less stable, and the least stable allotrope at the nanocluster scale is black phosphorene.

PNO: a promising deep-UV nonlinear optical material with the largest second harmonic generation effect.

In this work, the polar tetrahedron [PN2O2] was revealed as a new deep-ultraviolet (deep-UV) nonlinear optically active unit. Accordingly, a thermodynamically stable compound (PNO) consisting of the polar [PN2O2] units was predicted and suggested as a promising candidate for deep-UV nonlinear optical (NLO) materials. Compared with other deep-UV materials known to date, PNO possesses the strongest second harmonic generation (SHG) coefficient (about 6 times that of KH2PO4 (KDP)). Moreover, its three-dimensional connectivity endows it with good mechanical and thermal properties. Therefore, PNO should be a new option for non-π-conjugated deep-UV NLO materials.

Computational prediction of new magnetic materials.

The discovery of new magnetic materials is a big challenge in the field of modern materials science. We report the development of a new extension of the evolutionary algorithm USPEX, enabling the search for half-metals (materials that are metallic only in one spin channel) and hard magnetic materials. First, we enabled the simultaneous optimization of stoichiometries, crystal structures, and magnetic structures of stable phases. Second, we developed a new fitness function for half-metallic materials that can be used for predicting half-metals through an evolutionary algorithm. We used this extended technique to predict new, potentially hard magnets and rediscover known half-metals. In total, we report five promising hard magnets with high energy product (|BH|MAX), anisotropy field (Ha), and magnetic hardness (κ) and a few half-metal phases in the Cr-O system. A comparison of our predictions with experimental results, including the synthesis of a newly predicted antiferromagnetic material (WMnB2), shows the robustness of our technique.

"Magic" Molecules and a New Look at Chemical Diversity of Hydrocarbons.

We address the question why among the multitude of imaginable CnHm compositions some are easily synthesizable and abundant in nature, while others are not. To shed light on this problem we borrow approaches from nanocluster study, where stability with respect to neighboring compositions is used as a criterion of "magic" (particularly stable) clusters. By merging this criterion with predictions of lowest-energy structures of all CnHm molecules in a wide range of compositions (n ≤ 20, m ≤ 42) we provide guidelines for predicting the presence or absence of certain hydrocarbon molecules in various environments, their relative abundance and reactivity/inertness. The resulting maps of stability show the increased stability of C2nH2 compounds, polyaromatic hydrocarbons, and diamondoids, which is supported by experimental studies of the interstellar medium, flames, and petroleum fractions. This approach can be applied to any other molecular system, rationalizing the diversity of known compounds and predicting new potentially synthesizable molecules.

Effect of Magnetic Impurities on Superconductivity in LaH10.

Polyhydrides are a novel class of superconducting materials with extremely high critical parameters, which is very promising for sensor applications. On the other hand, a complete experimental study of the best so far known superconductor, lanthanum superhydride LaH10 , encounters a serious complication because of the large upper critical magnetic field HC2 (0), exceeding 120-160 T. It is found that partial replacement of La atoms by magnetic Nd atoms results in significant suppression of superconductivity in LaH10 : each at% of Nd causes a decrease in TC by 10-11 K, helping to control the critical parameters of this compound. Strong pulsed magnetic fields up to 68 T are used to study the Hall effect, magnetoresistance, and the magnetic phase diagram of ternary metal polyhydrides for the first time. Surprisingly, (La,Nd)H10 demonstrates completely linear HC2 (T) âˆ |T - TC |, which calls into question the applicability of the Werthamer-Helfand-Hohenberg model for polyhydrides. The suppression of superconductivity in LaH10 by magnetic Nd atoms and the robustness of TC with respect to nonmagnetic impurities (e.g., Y, Al, C) under Anderson's theorem gives new experimental evidence of the isotropic (s-wave) character of conventional electron-phonon pairing in lanthanum decahydride.

Localization Mechanism of Interstitial Electronic States in Electride Mayenite.

Electrides contain interstitial electrons with the states that are spatially separated from the crystal framework states and form a detached electronic subsystem. In mayenite [Ca12Al14O32]2+(e-)2 interstitial electrons form a unique charge network where localization and delocalization coexist, pointing to the importance of investigating the many-body nature of electride states. Using density functional theory and dynamical mean-field theory, we show a tendency toward electron localization and antiferromagnetic pairing, which leads to the formation of an experimentally observed peak under the Fermi level. The effect is associated with strong hybridization between interstitial electronic states, which removes the degeneracy and leads to the formation of a singlet state on a bonding molecular orbital as well as with the Coulomb interaction between interstitial electrons. Our work provides a fundamental understanding of the localization mechanism of interstitial electrons in mayenite and proposes a new approach for a proper description of the electronic subsystem of mayenite and other electrides.

Stabilization of hexazine rings in potassium polynitride at high pressure.

Polynitrogen molecules are attractive for high-energy-density materials due to energy stored in nitrogen-nitrogen bonds; however, it remains challenging to find energy-efficient synthetic routes and stabilization mechanisms for these compounds. Direct synthesis from molecular dinitrogen requires overcoming large activation barriers and the reaction products are prone to inherent inhomogeneity. Here we report the synthesis of planar N62- hexazine dianions, stabilized in K2N6, from potassium azide (KN3) on laser heating in a diamond anvil cell at pressures above 45 GPa. The resulting K2N6, which exhibits a metallic lustre, remains metastable down to 20 GPa. Synchrotron X-ray diffraction and Raman spectroscopy were used to identify this material, through good agreement with the theoretically predicted structural, vibrational and electronic properties for K2N6. The N62- rings characterized here are likely to be present in other high-energy-density materials stabilized by pressure. Under 30 GPa, an unusual N20.75--containing compound with the formula K3(N2)4 was formed instead.

Sr-Doped Superionic Hydrogen Glass: Synthesis and Properties of SrH22.

Recently, several research groups announced reaching the point of metallization of hydrogen above 400 GPa. Despite notable progress, detecting superconductivity in compressed hydrogen remains an unsolved problem. Following the mainstream of extensive investigations of compressed metal polyhydrides, here small doping of molecular hydrogen by strontium is demonstrated to lead to a dramatic reduction in the metallization pressure to ≈200 GPa. Studying the high-pressure chemistry of the Sr-H system, the formation of several new phases is observed: C2/m-Sr3 H13 , pseudocubic SrH6 , SrH9 with cubic F 4 ¯ 3 m $F\bar{4}3m$ -Sr sublattice, and pseudo tetragonal superionic P1-SrH22 , the metal hydride with the highest hydrogen content (96 at%) discovered so far. High diffusion coefficients of hydrogen in the latter phase DH  = 0.2-2.1 × 10-9 m2 s-1 indicate an amorphous state of the H-sublattice, whereas the strontium sublattice remains solid. Unlike Ca and Y, strontium forms molecular semiconducting polyhydrides, whereas calcium and yttrium polyhydrides are high-TC superconductors with an atomic H sublattice. The discovered SrH22 , a kind of hydrogen sponge, opens a new class of materials with ultrahigh content of hydrogen.

Electronegativity and chemical hardness of elements under pressure.

SignificanceOver the years, many unusual chemical phenomena have been discovered at high pressures, yet our understanding of them is still very fragmentary. Our paper addresses this from the fundamental level by exploring the key chemical properties of atoms-electronegativity and chemical hardness-as a function of pressure. We have made an appropriate modification to the definition of Mulliken electronegativity to extend its applicability to high pressures. The change in atomic properties, which we observe, allows us to provide a unified framework explaining (and predicting) many chemical phenomena and the altered behavior of many elements under pressure.

Ultrahigh-Pressure Magnesium Hydrosilicates as Reservoirs of Water in Early Earth.

The origin of water on the Earth is a long-standing mystery, requiring a comprehensive search for hydrous compounds, stable at conditions of the deep Earth and made of Earth-abundant elements. Previous studies usually focused on the current range of pressure-temperature conditions in the Earth's mantle and ignored a possible difference in the past, such as the stage of the core-mantle separation. Here, using ab initio evolutionary structure prediction, we find that only two magnesium hydrosilicate phases are stable at megabar pressures, α-Mg_{2}SiO_{5}H_{2} and ß-Mg_{2}SiO_{5}H_{2}, stable at 262-338 GPa and >338 GPa, respectively (all these pressures now lie within the Earth's iron core). Both are superionic conductors with quasi-one-dimensional proton diffusion at relevant conditions. In the first 30 million years of Earth's history, before the Earth's core was formed, these must have existed in the Earth, hosting much of Earth's water. As dense iron alloys segregated to form the Earth's core, Mg_{2}SiO_{5}H_{2} phases decomposed and released water. Thus, now-extinct Mg_{2}SiO_{5}H_{2} phases have likely contributed in a major way to the evolution of our planet.