Spaces of mathematical chemistry

In an effort to expand the domain of mathematical chemistry and inspire research beyond the realms of graph theory and quantum chemistry, we explore five mathematical chemistry spaces and their interconnectedness. These spaces comprise the chemical space, which encompasses substances and reactions; the space of reaction conditions, spanning the physical and chemical aspects involved in chemical reactions; the space of reaction grammars, which encapsulates the rules for creating and breaking chemical bonds; the space of substance properties, covering all documented measurements regarding substances; and the space of substance representations, composed of the various ontologies for characterising substances.

Pressure Induces Six-fold Coordination for the Lighter Pnictides Phosphorus and Arsenic Triiodide

In this study, we employ an evolutionary algorithm in conjunction with first-principles density functional theory (DFT) calculations to comprehensively investigate the structural transitions, electronic properties, and chemical bonding behaviors of XI3 compounds, where X denotes phosphorus (P) and arsenic (As), across a range of elevated pressures. Our computational analyses reveal a distinctive phenomenon occurring under compression, wherein the initially trigonal structures of PI3 (P 63) and AsI3 (R-3) undergo an intriguing transformation, leading to the emergence of six-coordinated monoclinic phases (C2/m) at 6 GPa and 2 GPa for PI3 and AsI3, respectively. These high-pressure phases exhibit their stability up to 10 GPa for PI3 and 12 GPa for AsI3. Notably, the resulting structures at elevated pressures bear striking resemblance to the widely recognized six-coordinated octahedral BiI3 crystal configuration observed at ambient conditions. Our investigation further underscores the pivotal role of pressure-induced reactivity of the lone-pair electrons in PI3 and AsI3, facilitating their enhanced stereochemical reactivity and thereby enabling higher six-fold coordination. Complementary analyses employing electron localization function (ELF) and density of states (DOS) effectively delineate the progression towards augmented coordination in PI3 and AsI3 with increasing pressure. While the phenomenon of heightened coordination is conventionally associated with heavier pnictide iodides such as SbI3 and BiI3 under ambient conditions due to heightened ionic character and relativistic effects in bismuth (Bi) and antimony (Sb), our findings accentuate that analogous structural transformations can also be induced in lighter elements like phosphorus (P) and arsenic (As) under the influence of pressure.

Electron-Deficient Multicenter Bonding in Phase Change Materials: A Chance for Reconciliation

In the last few years, a controversy has been raised regarding the nature of the chemical bonding present in phase change materials (PCMs), many of which are minerals such as galena (PbS), clausthalite (PbSe), and altaite (PbTe). Two opposite bonding models have claimed to be able to explain the extraordinary properties of PCMs in the last decade: the hypervalent (electron-rich multicenter) bonding model and the metavalent (electron-deficient) bonding model. In this context, a third bonding model, the electron-deficient multicenter bonding model, has been recently added. In this work, we comment on the pros and cons of the hypervalent and metavalent bonding models and briefly review the three approaches. We suggest that both hypervalent and metavalent bonding models can be reconciled with the third way, which considers that PCMs are governed by electron-deficient multicenter bonds. To help supporters of the metavalent and hypervalent bonding model to change their minds, we have commented on the chemical bonding in GeSe and SnSe under pressure and in several polyiodides with different sizes and geometries.

Laser-induced voltage of table salt for deep ultraviolet pulsed laser detection

To meet the requirements of fast response and simple process of deep ultraviolet (UV) pulsed laser detector, table salt (TS) was used as laser detection material in combination with a variable resistor to achieve single-pulse laser detection. Under the irradiation of a KrF excimer laser, the laser-induced voltage (LIV) of TS was influenced by the dynamic process of laser-induced plasma, and the whole process was well fitted with the sum of the three exponential functions. As the applied bias voltage (Vb) and incident laser energy (Ein) increased, the LIV amplitude (Vp) increased and the response time decreased. When the variable resistor (R) was reduced to 14.7 Ω, the response time of LIV decreased from ∼300 μs to ∼20 ns, which is the same as the duration of laser pulse. This research provided a simple, low-cost, and fast method for the detection of UV single-pulse laser based on the laser-TS interaction.

Theoretical Study on the Structures and Electronic Properties of Tungsten Fluorides at High Pressures

Transition metal fluorides are a series of strong oxidizing agents. Tungsten (W) fluorides, particularly WF6, have shown broad applications such as luminescence and fluorinating agent. However, other stoichiometries of W fluorides have rarely been studied. It is well-known that pressure can induce structural phase transition, stabilize new compounds, and produce novel properties. In this work, the high-pressure phases of W-F were searched systematically at the pressure range of 0-200 GPa through first-principles swarm-intelligence structural search calculations. A new stoichiometry of WF4 has been predicted to be stable under high pressures. On the other hand, two new high-pressure phases of WF6 with the symmetries ofP 2 1 ${{P2}_{1}}$ /m and P ${P}$ -1 were found with decahedral structural units. The electronic properties of the W-F compounds were then investigated. The predicted stable WF6 high-pressure phases maintain semiconducting features, since the W atom provides all its valence electrons to fluorine. We evaluated the oxidizing ability of WF6 by calculating its electron affinity potential. The high pressureP 2 1 ${{P2}_{1}}$ /m WF6 molecular phase shows higher oxidation capacity than the ambient phase. The built pressure-composition phase diagram and the theoretical results of W-F system provide some useful information for experimental synthesis.

Observation of Iron with Eight Coordination in Iron Trifluoride under High Pressure

The chemistry of hypercoordination has been a subject of fundamental interest, especially for understanding structures that challenge conventional wisdom. The small ionic radii of Fe ions typically result in coordination numbers of 4 or 6 in stable Fe-bearing ionic compounds. While 8-coordinated Fe has been observed in highly compressed oxides, the pursuit of hypercoordinated Fe still faces significant challenges due to the complexity of synthesizing the anticipated compound with another suitable anion. Through first-principles simulation and advanced crystal structure prediction methods, we predict that an orthorhombic phase of FeF3 with exclusively 8-coordinated Fe is energetically stable above 18 GPa-a pressure more feasibly achieved compared to oxides. Inspired by this theoretical result, we conducted extensive experiments using a laser-heated diamond anvil cell technique to investigate the crystal structures of FeF3 at high-pressure conditions. We successfully synthesized the predicted orthorhombic phase of FeF3 at 46 GPa, as confirmed by in situ experimental X-ray diffraction data. This work establishes a new ionic compound featuring rare 8-coordinated Fe in a simple binary Fe-bearing system and paves the way for discovering Fe hypercoordination in similar systems.

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.

Pressure Induced Alteration and Stabilization of Intermolecular Stacking in Square-planar Osmium tetracarbonyl

Osmium carbonyls are well known to form stable 18-electron complexes like Os(CO)5 , Os2 (CO)9 and Os3 (CO)12 having both bridging and terminal carbonyls. For osmium tetra-carbonyl, Os(CO)4 solid-state packing significantly alters the ground-state structure. The gas-phase stable see-saw geometry converts to a square-planar structure in solid state. Highly efficient intermolecular stacking between Os(CO)4 units assists this transformation. Each Os(CO)4 molecule is stacked in a staggered orientation with respect to each other. Pressure induces a [Xe]4f14 5d6 6s2 (S=2)→[Xe]4f14 5d8 (S=0) electronic transition in osmium stabilize a square planar osmium tetra-carbonyl. Under the influence of isotropic pressure, the molecules not only come closer to each other but their relative orientations also get significantly altered. Calculations show that at P=1 GPa and above, the eclipsed orientation for the intermolecular stacking gets preferred over the staggered form. The staggered→eclipsed intermolecular stacking orientation under pressure is shown to be controlled by London dispersion interactions.

Pressure-Induced Phase Diagram and Electronic Structure Evolves during the Insulator-Metal Transition of Bulk BiFeO3

BiFeO3 is the most widely known multiferroic at room temperature, possessing both ferroelectricity and antiferromagnetism. It has high Curie temperature and Néel temperature, i.e., 1103 and 643 K, respectively. Despite these unique properties, the pressure-induced phase diagram of bulk BiFeO3 has remained controversial. Based on the ab initio evolutionary algorithm, we systematically searched for the potential stable structures of bulk BiFeO3 at 0-50 GPa. It is identified that there are five pressure-induced phase transition sequences R3c-G-AFM →(5GPa) C2/m-G-AFM →(15GPa) Pnma-G-AFM →(24GPa) Pnma-FM →(35GPa) Imma-FM →(45GPa) Cmcm-FM, which provided a comprehensive pressure-induced phase diagram. As the pressure increases, we discovered an interesting phenomenon: a pressure-induced magnetic sequence transition, i.e., BiFeO3 transitions from an antiferromagnetic to a ferromagnetic sequence. Concurrently, the electronic structure evolves during the insulator-metal transition, influenced not only by the pressure but also by the phase transition. Our research has elucidated the long-standing question of the phase transition sequence of the BiFeO3 system under pressure and provided theoretical support for the insulator-metal transition.

High-Yield Synthesis of Sodium Chlorides of Unconventional Stoichiometries

Abnormal salt crystals with unconventional stoichiometries, such as Na2 Cl, Na3 Cl, K2 Cl, and CaCl crystals that have been explored in reduced graphene oxide membranes (rGOMs) or diamond anvil cells, hold great promise in applications due to their unique electronic, magnetic, and optical properties predicted in theory. However, the low content of these crystals, only <1% in rGOM, limits their research interest and utility in applications. Here, a high-yield synthesis of 2D abnormal crystals with unconventional stoichiometries is reported, which is achieved by applying negative potential on rGOM. A more than tenfold increase in the abnormal Na2 Cl crystals is obtained using a potential of -0.6 V, resulting in an atomic content of 13.4 ± 4.7% for Na on rGOM. Direct observations by transmission electron microscopy and piezoresponse force microscopy demonstrates a unique piezoelectric behavior arising from 2D Na2 Cl crystals with square structure. The output voltage increases from 0 to ≈180 mV in the broad 0-150° bending angle regime, which meets the voltage requirement of most nanodevices in realistic applications. Density functional theory calculations reveal that the applied negative potential of the graphene surface can strengthen the effect of the Na+ -π interaction and reduce the electrostatic repulsion between cations, making more Na2 Cl crystals formed.

Calibration of local chemical pressure by optical probe

Chemical stabilization of a high-pressure metastable state is a major challenge for the development of advanced materials. Although chemical pressure (Pchem) can effectively simulate the effect of physical pressure (Pphy), experimental calibration of the pressure passed to local structural motifs, denoted as local chemical pressure (Pchem-Δ) which significantly governs the function of solid materials, remains absent due to the challenge of probing techniques. Here we establish an innovative methodology to experimentally calibrate the Pchem-Δ and build a bridge between Pchem and Pphy via an optical probe strategy. Site-selective Bi3+-traced REVO4 (RE = Y, Gd) is adopted as a prototype to introduce Bi3+ optical probes and on-site sense of the Pchem-Δ experienced by the REO8 motif. The cell compression of RE0.98Bi0.02VO4 under Pphy is chemically simulated by smaller-ion substitution (Sc3+ → RE3+) in RE0.98-xScxBi0.02VO4. The consistent red shift (Δλ) of the emission spectra of Bi3+, which is dominated by locally pressure-induced REO8 dodecahedral variation in RE0.98Bi0.02VO4 (Pphy) and RE0.98-xScxBi0.02VO4 (Pchem-Δ), respectively, is evidence of their similar pressure-dependent local structure evolution. This innovative Δλ-based experimental calibration of Pchem-Δ in the crystal-field dimension portrays the anisotropic transmission of Pchem to the local structure and builds a bridge between Pchem-Δ and Pphy to guide a new perspective for affordable and practical interception of metastable states.

MAGUS: machine learning and graph theory assisted universal structure searcher

Crystal structure predictions based on first-principles calculations have gained great success in materials science and solid state physics. However, the remaining challenges still limit their applications in systems with a large number of atoms, especially the complexity of conformational space and the cost of local optimizations for big systems. Here, we introduce a crystal structure prediction method, MAGUS, based on the evolutionary algorithm, which addresses the above challenges with machine learning and graph theory. Techniques used in the program are summarized in detail and benchmark tests are provided. With intensive tests, we demonstrate that on-the-fly machine-learning potentials can be used to significantly reduce the number of expensive first-principles calculations, and the crystal decomposition based on graph theory can efficiently decrease the required configurations in order to find the target structures. We also summarized the representative applications of this method on several research topics, including unexpected compounds in the interior of planets and their exotic states at high pressure and high temperature (superionic, plastic, partially diffusive state, etc.); new functional materials (superhard, high-energy-density, superconducting, photoelectric materials), etc. These successful applications demonstrated that MAGUS code can help to accelerate the discovery of interesting materials and phenomena, as well as the significant value of crystal structure predictions in general.

High-pressure synthesis of fully sp2-hybridized polymeric nitrogen layer in potassium supernitride

Searching for fully sp²-hybridized layered structures is of fundamental importance because of their fascinating physical properties and potential to host topologically non-trivial electronic states. However, the synthesis of fully sp²-hybridized layered polymeric nitrogen structures remains a challenging work because of their low stability. Here, we report the synthesis of a fully sp²-hybridized layered polymeric nitrogen structure featuring fused 18-membered rings in potassium supernitride (K₂N₁₆) under high-pressure and high-temperature conditions. Bader charge analysis reveals that the potassium atomic layer stabilizes the unique sp²-hybridized polymeric nitrogen layers through the charge transfer effect in K₂N₁₆. The calculation of electronic structure indicates that K₂N₁₆ is a topological semimetal with multiple Dirac points and hosts higher-order Dirac fermions with cubic dispersion, which are contributed by the sp²-hybridized polymeric nitrogen layers arranged in P6/mcc symmetry. The high-pressure synthesis of the fully sp²-hybridized polymeric nitrogen layered structure provides promising prospects for exploring novel topological materials with effective stabilization routes.

Unraveling the Bonding Complexity of Polyhalogen Anions: High-Pressure Synthesis of Unpredicted Sodium Chlorides Na2Cl3 and Na4Cl5 and Bromide Na4Br5

The field of polyhalogen chemistry, specifically polyhalogen anions (polyhalides), is rapidly evolving. Here, we present the synthesis of three sodium halides with unpredicted chemical compositions and structures (tP10-Na₂Cl₃, hP18-Na₄Cl₅, and hP18-Na₄Br₅), a series of isostructural cubic cP8-AX₃ halides (NaCl₃, KCl₃, NaBr₃, and KBr₃), and a trigonal potassium chloride (hP24-KCl₃). The high-pressure syntheses were realized at 41-80 GPa in diamond anvil cells laser-heated at about 2000 K. Single-crystal synchrotron X-ray diffraction (XRD) provided the first accurate structural data for the symmetric trichloride Cl₃^- anion in hP24-KCl₃ and revealed the existence of two different types of infinite linear polyhalogen chains, [Cl]_∞^n- and [Br]_∞^n-, in the structures of cP8-AX₃ compounds and in hP18-Na₄Cl₅ and hP18-Na₄Br₅. In Na₄Cl₅ and Na₄Br₅, we found unusually short, likely pressure-stabilized, contacts between sodium cations. Ab initio calculations support the analysis of structures, bonding, and properties of the studied halogenides.

Unexpected iron corrosion by excess sodium in two-dimensional Na-Cl crystals of abnormal stoichiometries at ambient conditions

At ambient conditions, we found salt crystals formed from unsaturated solutions on an iron surface; these salt crystals had abnormal stoichiometries (i.e. Na₂Cl and Na₃Cl), and these abnormal crystals with Cl:Na of 1/2-1/3 could enhance iron corrosion. Interestingly, we found that the ratio of abnormal crystals, Na₂Cl or Na₃Cl, with ordinary NaCl was relative to the initial NaCl concentration of the solution. Theoretical calculations suggest that this abnormal crystallisation behaviour is attributed to the different adsorption energy curves between Cl^--iron and Na⁺-iron, which not only promotes Na⁺ and Cl^- adsorbing on the metallic surface to crystallise at unsaturated concentration but also induces the formation of abnormal stoichiometries of Na-Cl crystals for different kinetic adsorptionprocess. These abnormal crystals could also be observed on other metallic surfaces, such as copper. Our findings will help elucidate some fundamental physical and chemical views, including metal corrosion, crystallisation and electrochemical reactions.

The six stages of the convergence of the periodic system to its final structure

The periodic system encodes order and similarity among chemical elements arising from known substances at a given time that constitute the chemical space. Although the system has incorporated new elements, the connection with the remaining space is still to be analysed, which leads to the question of how the exponentially growing space has affected the periodic system. Here we show, by analysing the space between 1800 and 2021, that the system has converged towards its current stable structure through six stages, respectively characterised by the finding of elements (1800-1826), the emergence of the core structure of the system (1826-1860), its organic chemistry bias (1860-1900) and its further stabilisation (1900-1948), World War 2 new chemistry (1948-1980) and the system final stabilisation (1980-). Given the self-reinforced low diversity of the space and the limited chemical possibilities of the elements to be synthesised, we hypothesise that the periodic system will remain largely untouched.

Potential rules for stable transition metal hexafluorides with high oxidation states under high pressures

High pressure is a powerful tool in material sciences which can lead to the discovery of novel inorganic species in high oxidation states. Based on the prediction of the stability of PdF₆ with a high Pd oxidation state of +6, we propose three potential guiding rules for finding stable transition metal (TM) fluorides with high +6 oxidation states: (1) the existence of a large (>7 eV) valence orbitals energy differences of atoms between the TM d orbital and the F 2p orbital; (2) an appropriate number of valence electrons within the range of 6-11; and (3) suitable electronegativity values less than 2.3 on the Pauli scale. More importantly, by synergistically invoking all of these rules, we predict, by combining a particle swarm optimization algorithm with first-principles calculation on the phase stabilities of the various TM-F compounds, a collection of new TMF₆ species with the space group Pnma that have a +6 oxidation state. Subsequently, we develop an understanding of the high +6 oxidation state for the TM elements. These findings are expected to play a crucial role in the predictive discoveries of new fluorides with high oxidation states of +6.

Metal Halides for High-Capacity Energy Storage

High-capacity electrochemical energy storage systems are more urgently needed than ever before with the rapid development of electric vehicles and the smart grid. The most efficient way to increase capacity is to develop electrode materials with low molecular weights. The low-cost metal halides are theoretically ideal cathode materials due to their advantages of high capacity and redox potential. However, their cubic structure and large energy barrier for deionization impede their rechargeability. Here, the reversibility of potassium halides, lithium halides, sodium halides, and zinc halides is achieved through decreasing their dimensionality by the strong π-cation interactions between metal cations and reduced graphene oxide (rGO). Especially, the energy densities of KI-, KBr-, and KCl-based materials are 722.2, 635.0, and 739.4 Wh kg^-1 , respectively, which are higher than those of other cathode materials for potassium-ion batteries. In addition, the full-cell with 2D KI/rGO as cathode and graphite as anode demonstrates a lifespan of over 150 cycles with a considerable capacity retention of 57.5%. The metal halides-based electrode materials possess promising application prospects and are worthy of more in-depth researches.

Tracking structural phase transitions via single crystal x-ray diffraction at extreme conditions: advantages of extremely brilliant source

Highly brilliant synchrotron source is indispensable to track pressure-induced phenomena in confined crystalline samples in megabar range. In this article, a number of experimental variables affecting the quality high-pressure single-crystal x-ray diffraction data is discussed. An overview of the recent advancements in x-ray diffraction techniques at extreme conditions, in the frame of European Synchrotron Radiation Facility (ESRF)- Extremely Bright Source (EBS), is presented. Particularly, ID15b and ID27 beamlines have profited from the source upgrade, allowing for measurements of a few-micron crystals in megabar range. In case of ID27, a whole new beamline has been devised, including installation of double-multilayer mirrors and double crystal monochromator and construction of custom-made experimental stations. Two case studies from ID27 and ID15b are presented. Hypervalent CsI₃crystals, studied up to 24 GPa, have shown a series of phase transitions:Pnma → P-3c1→ Pm-3n. First transition leads to formation of orthogonal linear iodine chains made of I₃^-. Transformation to the cubic phase at around 21.7 GPa leads to equalization of interatomic I-I distances and formation of homoleptic I_n^m-chains. The second study investigates elastic properties and structure of jadarite, which undergoes isosymmetric phase transition around 16.6 GPa. Despite a few-micron crystal size, twinning and dramatic loss of crystal quality, associated with pressure-induced phase transitions, crystal structures of both compounds have been determined in a straightforward matter, thanks to the recent developments within ESRF-EBS.

Crystal Structures and Electronic Properties of BaAu Compound under High Pressure

The investigations of Au-bearing alloy materials have been of broad research interest as their relevant features exhibit significant advantages compared with pure Au. Here, we extensively investigate the compression behaviors of BaAu compounds via first-principles calculations and find that a high-pressure cubic phase is calculated to be stable above 12 GPa. Further electronic calculations indicate that despite the low electronegativity of Ba, Fd-3m-structured BaAu exhibits metallic characteristics, which is different from those of semiconducting alkali metal aurides that possess slight characteristics of an ionic compound. These findings provide a step toward a further understanding of the electronic properties of BaAu compounds and provide key insight for exploring the other Au-bearing alloy materials under extreme conditions.

Synthesis of rare-earth metal compounds through enhanced reactivity of alkali halides at high pressures

Chemical stability of the alkali halides NaCl and KCl has allowed for their use as inert media in high-pressure high-temperature experiments. Here we demonstrate the unexpected reactivity of the halides with metals (Y, Dy, and Re) and iron oxide (FeO) in a laser-heated diamond anvil cell, thus providing a synthetic route for halogen-containing binary and ternary compounds. So far unknown chlorides, Y2Cl and DyCl, and chloride carbides, Y2ClC and Dy2ClC, were synthesized at ~40 GPa and 2000 K and their structures were solved and refined using in situ single-crystal synchrotron X-ray diffraction. Also, FeCl2 with the HP-PdF2-type structure, previously reported at 108 GPa, was synthesized at ~160 GPa and 2100 K. The results of our ab initio calculations fully support experimental findings and reveal the electronic structure and chemical bonding in these compounds.

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 (H_a), 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.

A polymeric nitrogen N[Formula: see text]-N[Formula: see text] system with enhanced stability at low pressure

Postulated in 1992 and synthesized in 2004 above 2000 K and 110 GPa, the singly-bonded nitrogen cubic gauche crystal (cg-PN) is still considered to be the ultimate high energy density material (HEDM). The search however has continued for a method to synthesize cg-PN at more ambient conditions or find HEDMs which can be synthesized at lower pressure and temperature. Here, using ab initio evolutionary crystal prediction techniques, a simpler nitrogen-based molecular crystal consisting of N[Formula: see text] and N[Formula: see text] molecules is revealed to be a more favorable polynitrogen at lower pressures. The energetic gain of  534 meV/atom over cg-PN and  138 meV/atom over the N[Formula: see text] molecular crystal at zero pressure makes the N[Formula: see text]-N[Formula: see text] system more appealing. Dynamical and mechanical stabilities are investigated at 5 and 0 GPa, and vibrational frequencies are assessed for its Raman and IR spectra. The prospects of an experimental synthesis of the N[Formula: see text]-N[Formula: see text] polymeric system compared to cg-PN is higher because the C[Formula: see text] symmetry of N[Formula: see text] within this crystal would be easier to target from the readily available N[Formula: see text] azides and the observed N[Formula: see text] and N[Formula: see text] radicals.

Conceptual density functional theory under pressure: Part I. XP-PCM method applied to atoms

High pressure chemistry offers the chemical community a range of possibilities to control chemical reactivity, develop new materials and fine-tune chemical properties. Despite the large changes that extreme pressure brings to the table, the field has mainly been restricted to the effects of volume changes and thermodynamics with less attention devoted to electronic effects at the molecular scale. This paper combines the conceptual DFT framework for analyzing chemical reactivity with the XP-PCM method for simulating pressures in the GPa range. Starting from the new derivatives of the energy with respect to external pressure, an electronic atomic volume and an atomic compressibility are found, comparable to their enthalpy analogues, respectively. The corresponding radii correlate well with major known sets of this quantity. The ionization potential and electron affinity are both found to decrease with pressure using two different methods. For the electronegativity and chemical hardness, a decreasing and increasing trend is obtained, respectively, and an electronic volume-based argument is proposed to rationalize the observed periodic trends. The cube of the softness is found to correlate well with the polarizability, both decreasing under pressure, while the interpretation of the electrophilicity becomes ambiguous at extreme pressures. Regarding the electron density, the radial distribution function shows a clear concentration of the electron density towards the inner region of the atom and periodic trends can be found in the density using the Carbó quantum similarity index and the Kullback-Leibler information deficiency. Overall, the extension of the CDFT framework with pressure yields clear periodic patterns.

An Observation Related to the Pressure Dependence of Ionic Radii

Here it is shown that the crystal radii of ions are represented by a simple relation rcryst = rB3√(10 m)/N, where m and N are small integer numbers determined by the principal and orbital quantum numbers and valence, and rB is the Bohr radius. The relation holds to within 5%. This finding elucidates that despite their original definition crystal- and ionic radii are not classical but represent the limiting case of spherically symmetric spatial averages of the valence electron states and, therefore, are able to reflect changes in the valence electron configuration with pressure and temperature. The relation is used to show general pressure-effects on the radii, in particular the increase of bond coordination with pressure and metallization as limiting state. The pressure-effect is exemplified for the elements Mg and Si as major constituent cations in the Earth’s mantle, and for Ba as a large ionic lithophile element. It is found that at least to about 140 GPa the radii depend linearly on pressure. Further, if a generalization is permitted for just three elements, the pressure-dependence is lesser the higher the charge of the ion. The three elements exhibit a much weaker pressure-dependence than previously calculated non-bonding radii. For mantle geochemistry this finding implies that elements incompatible in the upper mantle remain so for the main lower mantle minerals bridgmanite and periclase and are hosted by davemaoite.

A first-principles study on crystal structures and metallization of sodium-rich sulfides under high pressure

We performed systematical theoretical simulations on phase diagrams, crystal structures, electron properties, and phonon features of Na-S system under high pressures. NaS, Na₂S, and Na₄S, were found to be stable under pressures. The superconducting transition critical temperature was estimated to nearly 0 K at 100 GPa in Na₃S due to the weak electron-phonon coupling. Furthermore, by the comparison on the structures, the electron features, and alkali metal ions of stoichiometric proportion, we found that not only the pressure but also the number of sodium atoms in the formula unit of alkali metal atoms can promote the insulator-metal transformation in the alkali metal sulfides, such as Li-S, Na-S, and K-S systems.

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.

Formation of Unconventional Stoichiometric Na-Cl Magic-Number Nanoclusters and 2D Assembly on Ir(111)

Sodium chlorides in non-1:1 stoichiometry are counterintuitive but recently their existence has been found under the high pressure condition or in the confined space between graphene sheets. Here the direct observation of the formation of Na₃ Cl nanoclusters, a stable magic-number structure, is reported on an Ir(111) surface using scanning tunneling microscopy and noncontact atomic force microscopy. The stability of Na₃ Cl nanoclusters in the free and adsorbed state is corroborated by density functional theory calculations. It is also found that a density of nanoclusters together with Cl adatoms may further aggregate and self-assemble into a Na₃ Cl₄ monolayer, forming a novel metastable phase of NaCl(111) with a honeycomb lattice. Further calculations suggest that charge transfer between the polar nanoclusters and the metal substrate stabilizes NaCl of non-1:1 stoichiometry. The work exhibits the possibility of exploring unconventional ionic crystals on the surface with atomically precise control of structure and composition.

Compressed superhydrides: the road to room temperature superconductivity

Room-temperature superconductivity has been a long-held dream and an area of intensive research. The discovery of H₃S and LaH₁₀under high pressure, with superconducting critical temperatures (T_c) above 200 K, sparked a race to find room temperature superconductors in compressed superhydrides. In recent groundbreaking work, room-temperature superconductivity of 288 K was achieved in carbonaceous sulfur hydride at 267 GPa. Here, we describe the important attempts of hydrides in the process of achieving room temperature superconductivity in decades, summarize the main characteristics of high-temperature hydrogen-based superconductors, such as hydrogen structural motifs, bonding features, electronic structure as well as electron-phonon coupling etc. This work aims to provide an up-to-date summary of several type hydrogen-based superconductors based on the hydrogen structural motifs, including covalent superhydrides, clathrate superhydrides, layered superhydrides, and hydrides containing isolated H atom, H₂and H₃molecular units.

Microwave-assisted synthesis of defective Ca1-xAgxTi1-yCoyO3 with high photoelectrocatalytic activity for organic pollutant removal from water

CaTiO₃ is considered to be one of the most promising catalysts for the degradation of organic pollutants, but its application is limited by the wide band gap and low catalytic activity. Element doping is an effective strategy to solve these problems. Herein, a novel CaTiO₃ co-doped with Ag and Co (Ca_1-xAg_xTi_1-yCo_yO₃) was synthesized by combining co-precipitation and the microwave hydrothermal method for the first time. The crystal structure, microstructure and light absorption of the material were systematically investigated. The results showed that Ca_1-xAg_xTi_1-yCo_yO₃ had higher light absorption than pure CaTiO₃, and the band gap was reduced to 2.78 eV. First-principles calculations indicated that Ag-Ca and Co-Ti tended to form donor-acceptor defect pairs in the doping process. These defect states not only enhanced the adsorption properties, but also could be used as carrier traps to optimize the dielectric properties of CaTiO₃. In the photoelectrocatalytic system, with 0.01 g of catalyst, 98% of methylene blue in 100 mL solution (10 mg L^-1) was degraded in 150 min. In addition, Ca_1-xAg_xTi_1-yCo_yO₃ showed strong stability and excellent recyclability. The double ion co-doping technology will provide an effective strategy for improving the catalytic activity of traditional wide-band gap semiconductors.

Stability of hypothetical AgIICl2 polymorphs under high pressure, revisited: a computational study

A comparative computational study of stability of candidate structures for an as-yet unknown silver dichloride AgCl2 is presented. It is found that all considered candidates have a negative enthalpy of formation, but are unstable towards charge transfer and decomposition into silver(I) chloride and chlorine within the DFT and hybrid-DFT approaches in the entire studied pressure range. Within SCAN approach, several of the "true" AgIICl2 polymorphs (i.e. containing Ag(II) species) exhibit a region of stability below ca. 20 GPa. However, their stability with respect to aforementioned decomposition decreases with pressure by account of all three DFT methods, which suggests a limited possibility of high-pressure synthesis of AgCl2. Some common patterns in pressure-induced structural transitions observed in the studied systems also emerge, which further testify to an instability of hypothetical AgCl2 towards charge transfer and phase separation.

Formation of twelve-fold iodine coordination at high pressure

Halogen compounds have been studied widely due to their unique hypercoordinated and hypervalent features. Generally, in halogen compounds, the maximal coordination number of halogens is smaller than eight. Here, based on the particle swarm optimization method and first-principles calculations, we report an exotically icosahedral cage-like hypercoordinated IN6 compound composed of N6 rings and an unusual iodine-nitrogen covalent bond network. To the best of our knowledge, this is the first halogen compound showing twelve-fold coordination of halogen. High pressure and the presence of N6 rings reduce the energy level of the 5d orbitals of iodine, making them part of the valence orbital. Highly symmetrical covalent bonding networks contribute to the formation of twelve-fold iodine hypercoordination. Moreover, our theoretical analysis suggests that a halogen element with a lower atomic number has a weaker propensity for valence expansion in halogen nitrides.

Pressure-stabilized hexafluorides of first-row transition metals

Fluorine chemistry was demonstrated to show the importance of stretching the limits of chemical synthesis, oxidation state, and chemical bonding at ambient conditions. Thus far, the highest fluorine stoichiometry of a neutral first-row transition-metal fluoride is five, in VF₅ and CrF₅. Pressure can stabilize new stoichiometric compounds that are inaccessible at ambient conditions. Here, we attempted to delineate the fluorination limits of first-row transition metals at a high pressure through first-principles swarm-intelligence structure searching simulations. Besides reproducing the known compounds, our extensive search has resulted in a plethora of unreported compounds: CrF₆, MnF₆, FeF₄, FeF₅, FeF₆, and CoF₄, indicating that the application of pressure achieves not only the fluorination limit (e.g., hexafluoride) but also the long-sought bulky tetrafluorides. Our current results provide a significant step forward towards a comprehensive understanding of the fluorination limit of first-row transition metals.

Crystal Structure Prediction and Lattice Dynamical Calculations for the Rare Platinum-Group Mineral Zaccariniite (RhNiAs)

The crystal structures of newly found minerals are routinely determined using single-crystal techniques. However, many rare minerals usually form micrometer-sized aggregates that are difficult to study with conventional structural methods. This is the case for numerous platinum-group minerals (PGMs) such as, for instance, zaccariniite (RhNiAs), the crystal structure of which was first obtained by studying synthetic samples. The aim of the present work is to explore the usefulness of USPEX, a powerful crystal structure prediction method, as an alternative means of determining the crystal structure of minerals such as zaccariniite, with a relatively simple crystal structure and chemical formula. We show that fixed composition USPEX searches with a variable number of formula units, using the ideal formula of the mineral as the only starting point, successfully predict the tetragonal structure of a mineral. Density functional theory (DFT) calculations can then be performed in order to more tightly relax the structure of the mineral and calculate different fundamental properties, such as the frequency of zone-center Raman-active phonons, or even their pressure behavior. These theoretical data can be subsequently compared to experimental results, which, in the case of newly found minerals, would allow one to confirm the correctness of the crystal structure predicted by the USPEX code.

Au with sp3 Hybridization in Li5AuP2

The achievement of new bonding patterns of atoms in compounds is of great importance, which usually induces interesting physical and chemical properties. Rich oxidation states, diverse bonding types, and unique aurophilic attraction endow gold (Au) as a distinctive element. Here we report that a pressure-induced Li₅AuP₂, identified by a swarm intelligence-based structural prediction, becomes the first example of Au with sp³ hybridization. The most remarkable feature of Li₅AuP₂ is that it contains various frameworks made by AuP₄, AuLi₄, LiP₄, and blende-like Li-P units, exhibiting noncentrosymmetry. The charge transfer from Li to Au makes Au 6p orbitals activate and hybridize with the 6s one. On the other hand, Li donating electrons to P and polar Au-P covalence make the constituent atoms satisfy the octet rule, rendering Li₅AuP₂ with a semiconducting character and a large second-order nonlinear optical response in the near-infrared region. Our work represents a significant step toward extending the understanding of gold chemistry.

Materials by design at high pressures

Pressure, a fundamental thermodynamic variable, can generate two essential effects on materials. First, pressure can create new high-pressure phases via modification of the potential energy surface. Second, pressure can produce new compounds with unconventional stoichiometries via modification of the compositional landscape. These new phases or compounds often exhibit exotic physical and chemical properties that are inaccessible at ambient pressure. Recent studies have established a broad scope for developing materials with specific desired properties under high pressure. Crystal structure prediction methods and first-principles calculations can be used to design materials and thus guide subsequent synthesis plans prior to any experimental work. A key example is the recent theory-initiated discovery of the record-breaking high-temperature superhydride superconductors H3S and LaH10 with critical temperatures of 200 K and 260 K, respectively. This work summarizes and discusses recent progress in the theory-oriented discovery of new materials under high pressure, including hydrogen-rich superconductors, high-energy-density materials, inorganic electrides, and noble gas compounds. The discovery of the considered compounds involved substantial theoretical contributions. We address future challenges facing the design of materials at high pressure and provide perspectives on research directions with significant potential for future discoveries.

Unconventional Stoichiometries of Na-O Compounds at High Pressures

It has been realized that the stoichiometries of compounds may change under high pressure, which is crucial in the discovery of novel materials. This work uses systematic structure exploration and first-principles calculations to consider the stability of different stoichiometries of Na-O compounds with respect to pressure and, thus, construct a high-pressure stability field and convex hull diagram. Four previously unknown stoichiometries (NaO5, NaO4, Na4O, and Na3O) are predicted to be thermodynamically stable. Four new phases (P2/m and Cmc21 NaO2 and Immm and C2/m NaO3) of known stoichiometries are also found. The O-rich stoichiometries show the remarkable features of all the O atoms existing as quasimolecular O2 units and being metallic. Calculations of the O-O bond lengths and Bader charges are used to explore the electronic properties and chemical bonding of the O-rich compounds. The Na-rich compounds stabilized at extreme pressures (P > 200 GPa) are electrides with strong interstitial electron localization. The C2/c phase of Na3O is found to be a zero-dimensional electride with an insulating character. The Cmca phase of Na4O is a one-dimensional metallic electride. These findings of new compounds with unusual chemistry might stimulate future experimental and theoretical investigations.

Pressure Gradient Squeezing Hydrogen out of MnOOH: Thermodynamics and Electrochemistry

Pressure of gigapascal (GPa) is a robust force for driving phase transitions and chemical reactions with negative volume change and is intensely used for promoting combination/addition reactions. Here, we find that the pressure gradient between the high-pressure region and the ambient-pressure environment in a diamond anvil cell is an even stronger force to drive decomposition/elimination reactions. A pressure difference of tens of GPa can "push" hydrogen out from its compounds in the high-pressure region to the environment. More importantly, in transition metal hydroxides such as MnOOH, the protons and electrons of hydrogen can even be separated via different conductors, pushed out by the high pressure, and recombine outside under ambient conditions, producing continuous current. A pressure-gradient-driven battery is hence proposed. Our investigation demonstrated that a pressure gradient is a special and powerful force to drive decomposition and electrochemical reactions.

Laser heating system at the Extreme Conditions Beamline, P02.2, PETRA III

A laser heating system for samples confined in diamond anvil cells paired with in situ X-ray diffraction measurements at the Extreme Conditions Beamline of PETRA III is presented. The system features two independent laser configurations (on-axis and off-axis of the X-ray path) allowing for a broad range of experiments using different designs of diamond anvil cells. The power of the continuous laser source can be modulated for use in various pulsed laser heating or flash heating applications. An example of such an application is illustrated here on the melting curve of iron at megabar pressures. The optical path of the spectroradiometry measurements is simulated with ray-tracing methods in order to assess the level of present aberrations in the system and the results are compared with other systems, that are using simpler lens optics. Based on the ray-tracing the choice of the first achromatic lens and other aspects for accurate temperature measurements are evaluated.

Novel 2D CaCl crystals with metallicity, room-temperature ferromagnetism, heterojunction, piezoelectricity-like property and monovalent calcium ions

Under ambient conditions, the only known valence state of calcium ions is +2, and the corresponding crystals with calcium ions are insulating and nonferromagnetic. Here, using cryo-electron microscopy, we report direct observation of two-dimensional (2D) CaCl crystals on reduced graphene oxide (rGO) membranes, in which the calcium ions are only monovalent (i.e. +1). Remarkably, metallic rather than insulating properties are displayed by those CaCl crystals. More interestingly, room-temperature ferromagnetism, graphene-CaCl heterojunction, coexistence of piezoelectricity-like property and metallicity, as well as the distinct hydrogen storage and release capability of the CaCl crystals in rGO membranes are experimentally demonstrated. We note that such CaCl crystals are obtained by simply incubating rGO membranes in salt solutions below the saturated concentration, under ambient conditions. Theoretical studies suggest that the formation of those abnormal crystals is attributed to the strong cation-π interactions of the Ca cations with the aromatic rings in the graphene surfaces. The findings highlight the realistic potential applications of such abnormal CaCl material with unusual electronic properties in designing novel transistors and magnetic devices, hydrogen storage, catalyzers, high-performance conducting electrodes and sensors, with a size down to atomic scale.

Energy landscapes of perfect and defective solids: from structure prediction to ion conduction

The energy landscape concept is increasingly valuable in understanding and unifying the structural, thermodynamic and dynamic properties of inorganic solids. We present a range of examples which include (i) structure prediction of new bulk phases including carbon nitrides, phosphorus carbides, LiMgF3 and low-density, ultra-flexible polymorphs of B2O3, (ii) prediction of graphene and related forms of ZnO, ZnS and other compounds which crystallise in the bulk with the wurtzite structure, (iii) solid solutions, (iv) understanding grossly non-stoichiometric oxides including the superionic phases of δ-Bi2O3 and BIMEVOX and the consequences for the mechanisms of ion transport in these fast ion conductors. In general, examination of the energy landscapes of disordered materials highlights the importance of local structural environments, rather than sole consideration of the average structure.

New Two-Dimensional Wide Band Gap Hydrocarbon Insulator by Hydrogenation of a Biphenylene Sheet

Based on first-principles calculations, the ground state configuration (Cmma-CH) of a hydrogenated biphenylene sheet ( Science 2021, 372, 852) is carefully identified from hundreds of possible candidates generated by RG² code ( Phys. Rev. B. 2018, 97, 014104). Cmma-CH contains four inequivalent benzene molecules in its crystalline cell due to its Cmma symmetry. Hydrogen atoms bond to carbon atoms in each benzene with a boat-like (DDUDDU) up/down sequence and reversed boat-1 (UUDUUD) sequence in adjacent benzene rings. Cmma-CH is energetically less stable than the proposed allotropes of hydrogenated graphene, but the formation energy for hydrogenating a biphenylene sheet is remarkably lower than that for hydrogenating graphene to graphane. Our results of mechanical and dynamical stability also confirm that Cmma-CH is a stable 2D hydrocarbon, which is expected to be realized experimentally. Especially, biphenylene undergoes a transition from normal metal to a wide band gap insulator (4.645 eV) by hydrogenation to Cmma-CH, which has potential applications in nanodevices at elevated temperatures and high voltages.

Design and Fabrication of a Sandwichlike Zn/Cu/Al-Zr Coating for Superior Anticorrosive Protection Performance of ZM5 Mg Alloy

A new three-layered film was fabricated on magnesium (Mg) alloy via electroplating to guard against corrosion in a chloride aqueous environment, which consisted of an underlying double-layered zinc/copper (Zn/Cu) and a top aluminum-zirconium (Al-Zr) layer. The Zn/Cu underlayers not only impeded the galvanic corrosion between the Al-Zr coating and Mg alloy but also improved the adhesive ability between the substrate and the upper Al-Zr layer. Herein, we discussed the nucleus sizes of Al-Zr coatings at the stage of nucleation carried out with different contents of ZrCl₄ in AlCl₃-1-butyl-3-methylimidazolium chloride ionic liquid. The sandwichlike three-layered Zn/Cu/Al-Zr coatings were systematically investigated by surface morphology, phase structure, hardness, anticorrosion performances, and first-principles calculations. The corrosion current density declined from 1.461 × 10^-3 A·cm^-2 of bare Mg to 4.140 × 10^-7 A·cm^-2 of the Zn/Cu/Al-Zr3 sample. Neutral salt spray testing demonstrated that the Zn/Cu/Al-Zr3 sample showed no evident signs of corrosion after 6 days of exposure. The enhancement of the corrosion protection property was related to the fact that the application of the Cu layer changed the corrosion direction from initial longitudinal corrosion to extended lateral corrosion and the top Al-Zr coating hindered the transmission of aggressive ions. In addition, upon increasing the Zr content in the alloy films, the Fermi energy reduced initially and then increased. The Al-Zr3 alloy with 8.3 atom % Zr showed the lowest Fermi energy (-3.0823 eV), which exhibited the most efficient corrosion protection. These results showed that the prepared three-layered coating provided reliable corrosion protection to Mg alloy and may thus promote its practical applications.

Pretreatment to Leaching for a Primary Copper Sulphide Ore in Chloride Media

The dissolution of copper sulphide ores continues to be a challenge for the copper industry. Several media and leaching alternatives have been proposed to improve the dissolution of these minerals, especially for the leaching of chalcopyrite. Among the alternatives, pretreatment prior to leaching was proposed as an option that increases the dissolution of copper from sulphide ores. In this study, a mineral sample from a copper mining company was used. The copper grade of the sample was 0.79%, and its main contributor was chalcopyrite (84%). The effect of curing time (as pretreatment) in a chloride media on copper sulphide ore was evaluated at various temperatures: 25, 50, 70 and 90 °C. The pretreated sample and leaching residues were characterized by X-ray diffraction, scanning electron microscopy, and reflected light microscopy. Pretreatment products such as CuSO4, NaFe3(SO4)2(OH)6, and S0 were identified although with difficulty, due to the low presence of chalcopyrite in the initial sample (1.99%). Under the conditions of 15 kg/t of H2SO4, 25 kg/t of NaCl, and 15 days of curing time, a copper extraction of 93.1% was obtained at 90 °C with 50 g/L of Cl− and 0.2 M of H2SO4.