High pressure electrides: a predictive chemical and physical theory

Diradicals as Topological Charge Carriers in Metal-Organic Toy Model Pt3(HIB)2

We explore the eclipsed stacking of a metal-organic Kagome lattice containing heavy-metal nodes. Our model is Pt3(HIB)2, a hypothetical but viable member of a well-known family of hexaaminobenzene based metal-organic frameworks (MOFs). Applying space group theory, it is shown how molecular diradicals, brought into play by a noninnocent ligand, become topologically nontrivial bands when moving in a periodic potential. Three factors are required to enable this: (1) eclipsed stacking, which shifts the Fermi level near a symmetry-protected band crossing (2) the emergence of an electride-like band that renders the topological Z 2 invariant equal to 1, thus nontrivial, and (3) Pt-induced spin-orbit coupling, to turn the crossing into a bulk band gap. The electride band, with its unforeseen role, bears kinship to the interlayer band in hexagonal superconductors. It places its charge density in the voids of the crystal, rather than around the atomic nuclei, and we name it a "pore band". While the synthesis of truly conductive MOFs has proven challenging, the analysis shows that intrinsically nonlocal physics may emerge from tunable molecular building blocks. With the richness of redox-active MOF chemistry, this offers a pathway to tailored topological electronics.

Superconducting Electride Li9S with a Transition Temperature above the McMillan Limit

An electride, characterized by unique interstitial anionic electrons (IAEs), offers promising avenues for modulating its superconductivity. The pressure-dependent coupling between IAEs and orbital electrons significantly affects the superconducting transition temperature (Tc). However, existing research has predominantly concentrated on pressures within 300 GPa. To advance the understanding, we propose investigating the Li-S system under ultrahigh pressure to unveil novel electride superconductors. Five stable Li-rich electrides with diverse IAE topologies, including one Li7S, three Li9S, and one Li12S phases, are identified through structural search calculations. Among the Li9S phases, in the C2/c phase (600 GPa), the IAEs are connected to the S atomic extra-nuclear electrons with the unconventional d orbital attribute due to the extreme pressure, while two low-pressure R-3 (25 GPa) and C2/m (400 GPa) phases have interconnected IAEs. Due to its unique IAE attributes, C2/c Li9S exhibits the highest Tc of 53.29 K at 600 GPa. Its superconductivity results from the coupling of the S d, Li p electrons, and IAEs with the low-frequency phonons associated with the attraction between IAEs and the Li-S framework. Our work enhances insights into IAEs within electrides and their role in facilitating superconductivity.

All-Single Bonds Fused N18 Macro-Rings and N8 Cagelike Building Blocks Stabilized in Lanthanum Supernitrides

Single-bonded polymeric nitrogen has gained tremendous research interest because of its unique physical properties and great potential applications. Despite much progress in theoretical predictions, it is still challenging to experimentally synthesize polynitrogen compounds with novel all-single-bonded units. Herein, we have synthesized two brand-new lanthanum supernitrides LaN8, through a direct reaction between La and N2 in laser-heated diamond anvil cells at megabar pressures. Our experiments and calculations revealed that two LaN8 phases had the R-3 and P4/n symmetry characterized by a unique 2D network with N18 macro-rings and cagelike N8 building blocks, respectively. Differing from known polynitrogen structures, these two polymers were composed of single-bonded nitrogen atoms belonging to sp3 and sp2 hybridizations. In particular, P4/n LaN8 possessed the longest N-N bond length among all of the experimentally reported metal nitrides, potentially being a high-energy-density material. The present study opens a fresh, promising avenue for the rational design and discovery of new supernitrides with unique nitrogen structures via the high-pressure treatment.

Symmetry-Shaped Singularities in High-Temperature Superconductor H3S

The superconducting critical temperature of H3S ranks among the highest measured, at 203 K. This impressive value stems from a singularity in the electronic density-of-states, induced by a flat-band region that consists of saddle points. The peak sits right at the Fermi level, so that it gives rise to a giant electron-phonon coupling constant. In this work, we show how atomic orbital interactions and space group symmetry work in concert to shape the singularity. The body-centered cubic Brillouin Zone offers a unique 2D hypersurface in reciprocal space: fully connecting squares with two different high-symmetry points at the corners, Γ and H, and a third one in the center, N. Orbital mixing leads to the collapse of fully connected 1D saddle point lines around the square centers, due to a symmetry-enforced s-p energy inversion between Γ and H. The saddle-point states are invariably nonbonding, which explains the unconventionally weak response of the superconductor's critical temperature to pressure. Although H3S appears to be a unique case, the theory shows how it is possible to engineer flat bands and singularities in 3D lattices through symmetry considerations.

Electronic correlations and intrinsic magnetism of interstitial quasi-atomic states in Li8Au electride

We investigate the electronic sub-system of a recently designed Li8Au superconducting electride to reveal its many-body correlated nature and magnetic properties. Using maximally localized Wannier functions (MLWFs) to describe the interstitial anion electron (IAE) states, it was found that these states are partially occupied with a population of 1.5e- and have negligible hybridization with the almost completely filled p-Au states. The averaged interaction screened Hubbard parameter U for quasi-atomic IAE states evaluated by the constrained random-phase approximation (CRPA) method is 2 eV, comparable to the width of the electride band suggesting moderate electronic correlations. Using dynamical mean field theory (DMFT) approach we found that IAEs in Li8Au electride behave as magnetic centers and possess their own well localised magnetic moments of 0.5μB per quasi-atomic IAE. The obtained results deepen the understanding of the significance of many-body effects in the IAE subsystem of electronic states and reveal the mechanism for the formation of intrinsic magnetic moments on IAEs, which behave like ferromagnetic quasi-atoms in the Li8Au electride. Overall, the observed correlation effects in Li8Au emphasize their importance in materials with excess electrons confined in cavities.

Chemical Flexibility of Atomically Precise Metal Clusters

Ligand-protected metal clusters possess hybrid properties that seamlessly combine an inorganic core with an organic ligand shell, imparting them exceptional chemical flexibility and unlocking remarkable application potential in diverse fields. Leveraging chemical flexibility to expand the library of available materials and stimulate the development of new functionalities is becoming an increasingly pressing requirement. This Review focuses on the origin of chemical flexibility from the structural analysis, including intra-cluster bonding, inter-cluster interactions, cluster-environments interactions, metal-to-ligand ratios, and thermodynamic effects. In the introduction, we briefly outline the development of metal clusters and explain the differences and commonalities of M(I)/M(I/0) coinage metal clusters. Additionally, we distinguish the bonding characteristics of metal atoms in the inorganic core, which give rise to their distinct chemical flexibility. Section 2 delves into the structural analysis, bonding categories, and thermodynamic theories related to metal clusters. In the following sections 3 to 7, we primarily elucidate the mechanisms that trigger chemical flexibility, the dynamic processes in transformation, the resultant alterations in structure, and the ensuing modifications in physical-chemical properties. Section 8 presents the notable applications that have emerged from utilizing metal clusters and their assemblies. Finally, in section 9, we discuss future challenges and opportunities within this area.

Electride Formation of HCP-Iron at High Pressure: Unraveling the Origin of the Superionic State of Iron-Rich Compounds in Rocky Planets

Electride possesses electrons localized at interstitial sites without attracting nuclei. It brings outstanding material properties not only originating from its own loosely bounded characteristics but also serving as a quasiatom, which even chemically interacts with other elemental ions. In elemental metals, electride transitions have been reported in alkali metals where valence electrons can easily gain enough kinetic energy to escape nuclei. However, there are few studies on transition metals. Especially iron, the key element of human technology and geophysics, has not been studied in respect of electride formation. In this study, it is demonstrated that electride formation drives the superionic state in iron hydride under high-pressure conditions of the earth's inner core. The electride stabilizes the iron lattice and provides a pathway for hydrogen diffusion by severing the direct interaction between the metal and the volatile element. The coupling between lattice stability and superionicity is triggered near 100 GPa and enhanced at higher pressures. It is shown that the electride-driven superionicity can also be generalized for metal electrides and other rocky planetary cores by providing a fundamental interaction between the electride of the parent metal and doped light elements.

Exploring toroidal anvil profiles for larger sample volumes above 4 Mbar

With the advent of toroidal and double-stage diamond anvil cells (DACs), pressures between 4 and 10 Mbar can be achieved under static compression, however, the ability to explore diverse sample assemblies is limited on these micron-scale anvils. Adapting the toroidal DAC to support larger sample volumes offers expanded capabilities in physics, chemistry, and planetary science: including, characterizing materials in soft pressure media to multi-megabar pressures, synthesizing novel phases, and probing planetary assemblages at the interior pressures and temperatures of super-Earths and sub-Neptunes. Here we have continued the exploration of larger toroidal DAC profiles by iteratively testing various torus and shoulder depths with central culet diameters in the 30-50 µm range. We present a 30 µm culet profile that reached a maximum pressure of 414(1) GPa based on a Pt scale. The 300 K equations of state fit to our P-V data collected on gold and rhenium are compatible with extrapolated hydrostatic equations of state within 1% up to 4 Mbar. This work validates the performance of these large-culet toroidal anvils to > 4 Mbar and provides a promising foundation to develop toroidal DACs for diverse sample loading and laser heating.

Ground and excited electronic structures of electride and alkalide units: The cases of Metal-Tren, -Azacryptand, and -TriPip222 complexes

A systematic electronic structure analysis was conducted for M(L)n molecular electrides and their corresponding alkalide units M(L)n @M' (M/M' = Na, K; L = Tren, Azacryptand, TriPip222; n = 1, 2). All complexes belong to the "superalkali" category due to their low ionization potentials. The saturated molecular electrides display M+ (L)n - form with a greatly diffuse quasispherical electron cloud. They were identified as "superatoms" considering the contours of populating atomic-type molecular orbitals. The observed superatomic Aufbau order of M(Tren)2 is 1S, 1P, 1D, 1F, 2S, 2P, and 1G and it is consistent with those of M(Azacryptand) and M(TriPip222) up to the analyzed 1F level. Their excitation energies decrease gradually moving from M(Tren)2 to M(Azacryptand) and to M(TriPip222). The studied alkalide complexes carry [M(L)n ]+ @M'- ionic structure and their dissociation energies vary in the sequence of K(L)n @Na > Na(L)n @Na > K(L)n @K > Na(L)n @K. Similar to molecular electrides, the anions of alkalide units occupy electrons in diffuse Rydberg-like orbitals. In this work, excited states of [M(L)n @M']0/+/- and their trends are also analyzed.

Where are the Excess Electrons in Subvalent Compounds? The Case of Ag7Pt2O7

Subvalent compounds raise the question of where those valence electrons not belonging to chemical bonds are. In the limiting case of Ag7Pt2O7, there is just one-electron excess in the chemical formula requiring the presence of Ag atoms with oxidation states below +1, assuming conventional Pt4+ and O2- ions. Such a situation challenges the understanding of the semiconducting and diamagnetic behavior observed in this oxide. Previous explanations that localize pairwise the electron excess in tetrahedral Ag4 interstices do not suffice in this case, since there are six silver tetrahedral voids and only an excess of nine electrons in the unit cell. Here, we provide an alternative explanation for the subvalent nature of this compound by combining interatomic distances, electron density-based descriptors, and orbital energetic analysis criteria. As a result, Ag atoms that do not participate in their valence electron are revealed. We identify excess electrons located in isolated subvalent silver clusters with electron-deficient multicenter bonds resembling pieces of metallic bonding in fcc-Ag and Ag7Pt2 alloy. Our analysis of the electronic band structure also supports the multicenter bonding picture. This combined approach from the real and reciprocal spaces reconciles existing discrepancies and is key to understanding the new chemistry of silver subvalent compounds.

Counting Electrons in Electrides

The selection and design of charge integration methods remain an outstanding challenge in materials chemistry. In complex materials like electrides, this challenge is amplified by the small charge and complex shape of electride wave functions. For these reasons, popular integration methods, such as the Bader method, usually fail to assign any charge to the bare electrons in an electride. To address this challenge, we developed an algorithm that instead partitions the charge based on the electron localization function (ELF), a popular scheme for visualizing chemically important features in molecules and solids. The algorithm uses Bader segmentation of the ELF to find the electride electrons and Voronoi segmentation of the ELF to identify atoms. We apply this method, "BadELF", to the quantification of atomic radii and oxidation states in both ionic compounds and electrides. For ionic compounds, we find that the BadELF method yields radii that agree closely with Shannon crystal radii, while the oxidation states agree closely with the Bader method. When they are applied to electrides, however, only the BadELF algorithm yields chemically meaningful charges. We argue that the BadELF method provides a useful strategy to identify electrides and obtain new insight into their most essential property: the quantity of electrons within them.

On the Electride Nature of Na-hP4

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 Pauli 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 multicentered bonds, which are responsible for the emergence of the interstitial charge localization in Na-hP4. These multicentered bonds facilitate the increased density of this phase, which is key for its stabilization under pressure.

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.

Magnetic quasi-atomic electrons driven reversible structural and magnetic transitions between electride and its hydrides

In electrides, interstitial anionic electrons (IAEs) in the quantized energy levels at cavities of positively charged lattice framework possess their own magnetic moment and interact with each or surrounding cations, behaving as quasi-atoms and inducing diverse magnetism. Here, we report the reversible structural and magnetic transitions by the substitution of the quasi-atomic IAEs in the ferromagnetic two-dimensional [Gd2C]2+·2e- electride with hydrogens and subsequent dehydrogenation of the canted antiferromagnetic Gd2CHy (y > 2.0). It is demonstrated that structural and magnetic transitions are strongly coupled by the presence or absence of the magnetic quasi-atomic IAEs and non-magnetic hydrogen anions in the interlayer space, which dominate exchange interactions between out-of-plane Gd-Gd atoms. Furthermore, the magnetic quasi-atomic IAEs are inherently conserved by the hydrogen desorption from the P[Formula: see text] 1m structured Gd2CHy, restoring the original ferromagnetic state of the R[Formula: see text]m structured [Gd2C]2+·2e- electride. This variable density of magnetic quasi-atomic IAEs enables the quantum manipulation of floating electron phases on the electride surface.

Coexistence of ferromagnetism and charge density waves in monolayer LaBr2

Charge density waves (CDWs), a common phenomenon of periodic lattice distortions, often suppress ferromagnetism in two-dimensional (2D) materials, hindering their magnetic applications. Here, we report a novel CDW that generates 2D ferromagnetism instead of suppressing it, through the formation of interstitial anionic electrons as the charge modulation mechanism. Via first-principles calculations and a low-energy effective model, we find that the highly symmetrical monolayer LaBr2 undergoes a 2 × 1 CDW transition to a magnetic semiconducting T' phase. Concurrently, the delocalized 5d1 electrons of La in LaBr2 redistribute and accumulate within the interstitial space in the T' phase, forming anionic electrons, also known as 2D electride or electrene. The strongly localized nature of anionic electrons promotes a Mott insulating state and full spin-polarization, while the overlap of their extended tails yields ferromagnetic direct exchange between them. Such transition introduces a new magnetic form of CDWs, offering promising opportunities for exploring novel fundamental physics and advanced spintronics applications.

Room-Temperature Solid-State Synthesis of Cs3Cu2I5 Thin Films and Formation Mechanism for Its Unique Local Structure

Blue-emitting Cs₃Cu₂I₅ has attracted attention owing to its near-unity PL quantum yield and applications in DUV photodetectors and scintillators. Its PL properties originate from the unique local structure around the luminescent center, the [Cu₂I₅]^3- polyhedron iodocuprate anion consisting of the edge-shared CuI₃ triangle and the CuI₄ tetrahedron dimer, which is isolated by Cs⁺ ions. We found that solid-state reactions between CsI and CuI occur near room temperature (RT) to form Cs₃Cu₂I₅ and/or CsCu₂I₃ phases. High-quality thin films of these phases were obtained by the sequential deposition of CuI and CsI by thermal evaporation. We elucidated that the formation of interstitial Cu⁺ and the antisite of I^- at the Cs⁺ site in the CsI crystal through Cu⁺ and I^- diffusion results in the RT synthesis of Cs₃Cu₂I₅. The unique structure formation of the luminescent center was revealed using a model based on the low packing density of the CsCl-type crystal structure, similar sizes of Cs⁺ and I^- ions, and the high diffusivity of Cu⁺. The self-aligned patterning of the luminous regions on thin films was demonstrated.

Emerging d-d orbital coupling between non-d-block main-group elements Mg and I at high pressure

d-d orbital coupling, which increases anisotropic and directional bonding, commonly occurs between d-block transition metals. Here, we report an unexpected d-d orbital coupling in the non-d-block main-group element compound Mg2I based on first-principles calculations. The unfilled d orbitals of Mg and I atoms under ambient conditions become part of the valence orbitals and couple with each other under high pressures, resulting in the formation of highly symmetric I-Mg-I covalent bonding in Mg2I, which forces the valence electrons of Mg atoms into the lattice voids to form interstitial quasi-atoms (ISQs). In turn, the ISQs highly interact with the crystal lattice, contributing to lattice stability. This study greatly enriches the fundamental understanding of chemical bonding between non-d-block main-group elements at high pressures.

Recent Developments of High-Pressure Spark Plasma Sintering: An Overview of Current Applications, Challenges and Future Directions

Spark plasma sintering (SPS), also called pulsed electric current sintering (PECS) or field-assisted sintering technique (FAST) is a technique for sintering powder under moderate uniaxial pressure (max. 0.15 GPa) and high temperature (up to 2500 °C). It has been widely used over the last few years as it can achieve full densification of ceramic or metal powders with lower sintering temperature and shorter processing time compared to conventional processes, opening up new possibilities for nanomaterials densification. More recently, new frontiers of opportunities are emerging by coupling SPS with high pressure (up to ~10 GPa). A vast exciting field of academic research is now using high-pressure SPS (HP-SPS) in order to play with various parameters of sintering, like grain growth, structural stability and chemical reactivity, allowing the full densification of metastable or hard-to-sinter materials. This review summarizes the various benefits of HP-SPS for the sintering of many classes of advanced functional materials. It presents the latest research findings on various HP-SPS technologies with particular emphasis on their associated metrologies and their main outstanding results obtained. Finally, in the last section, this review lists some perspectives regarding the current challenges and future directions in which the HP-SPS field may have great breakthroughs in the coming years.

Pressure Stabilized Lithium-Aluminum Compounds with Both Superconducting and Superionic Behaviors

Superconducting and superionic behaviors have physically intriguing dynamic properties of electrons and ions, respectively, both of which are conceptually important and have great potential for practical applications. Whether these two phenomena can appear in the same system is an interesting and important question. Here, using crystal structure predictions and first-principle calculations combined with machine learning, we identify several stable Li-Al compounds with electride behavior under high pressure, and we find that the electronic density of states of some of the compounds has characteristics of the two-dimensional electron gas. Among them, we estimate that Li_{6}Al at 150 GPa has a superconducting transition temperature of around 29 K and enters a superionic state at a high temperature and wide pressure range. The diffusion in Li_{6}Al is found to be affected by an electride and attributed to the atomic collective motion. Our results indicate that alkali metal alloys can be effective platforms to study the abundant physical properties and their manipulation with pressure and temperature.

Oxidative Addition of Methane and Reductive Elimination of Ethane and Hydrogen on Surfaces: From Pure Metals to Single Atom Alloys

Oxidative addition of CH₄ to the catalyst surface produces CH₃ and H. If the CH₃ species generated on the surface couple with each other, reductive elimination of C₂H₆ may be achieved. Similarly, H's could couple to form H₂. This is the outline of nonoxidative coupling of methane (NOCM). It is difficult to achieve this reaction on a typical Pt catalyst surface. This is because methane is overoxidized and coking occurs. In this study, the authors approach this problem from a molecular aspect, relying on organometallic or complex chemistry concepts. Diagrams obtained by extending the concepts of the Walsh diagram to surface reactions are used extensively. C-H bond activation, i.e., oxidative addition, and C-C and H-H bond formation, i.e., reductive elimination, on metal catalyst surfaces are thoroughly discussed from the point of view of orbital theory. The density functional theory method for structural optimization and accurate energy calculations and the extended Hückel method for detailed analysis of crystal orbital changes and interactions play complementary roles. Limitations of monometallic catalysts are noted. Therefore, a rational design of single atom alloy (SAA) catalysts is attempted. As a result, the effectiveness of the Pt₁/Au(111) SAA catalyst for NOCM is theoretically proposed. On such an SAA surface, one would expect to find a single Pt monatomic site in a sea of inert Au atoms. This is desirable for both inhibiting overoxidation and promoting reductive elimination.

Studying and exploring potential energy surfaces of compressed molecules: a fresh theory from the eXtreme Pressure Polarizable Continuum Model

We present a new theory for studying and exploring the potential energy surface of compressed molecular systems as described within the XP-PCM framework. The effective potential energy surface is defined by the sum of the electronic energy of the compressed system and the pressure-volume work that is necessary in order to create the compression cavity at the given condition of pressure. We show that the resulting total energy Gt is related to the electronic energy by a Legendre transform, in which the pressure and volume of the compression cavity are the conjugate variables. We present an analytical expression for the evaluation of the gradient of the total energy ∇Gt to be used for the geometry optimization of equilibrium geometries and transition states of compressed molecular systems. We also show that, as a result of the Legendre transform property, the potential energy surface can be studied explicitly as function of the pressure, leading to an explicit connection with the well-known Hammond postulate. As a proof of concept, we present the application of the theory to studying and determining of the optimized geometry of compressed methane and the transition state of electrocyclic ring-closure of hexatriene and of H-transfer between two methyl 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.

Molecular Electrides: An In Silico Perspective

Electrides are defined as the ionic compounds where the electron(s) serves as an anion. These electron(s) is (are) not bound to any atoms, bonds, or molecules rather than they are localized into the space, crystal voids, or interlayer between two molecular slabs. There are three major categories of electrides, known as organic electriades, inorganic electrides, and molecular electrides. The computational techniques have proven as a great tool to provide emphasis on the electride materials. In this review, we have focused on the computational methodologies and criteria that help to characterize molecular electrides. A detailed account of the computational methods and basis sets applicable for molecular electrides have been discussed along with their limitation(s) in this field. The main criterion for the identification of the electrides has also been discussed thoroughly with proper examples. The molecular electrides presented here have been justified with all the required criteria that support and proved their electride characteristics. We have also presented a few systems which have similar properties but are not considered as molecular electrides. Moreover, the applicability of the electrides in catalytic processes has also been presented.

Predicted crystal structures of xenon and alkali metals under high pressures

The pressure-induced reaction between xenon (Xe) and other non-inert gas elements and the resultant crystal structures have attracted great interest. In this work, we carried out extensive simulations on the crystal structures of Xe-alkali metal (Xe-AM) systems under high pressures. Among all predicted compounds, KXe and RbXe are found to become stable at a pressure of ∼16 GPa by adopting a cubic symmetry of space group Pm3̄m. The stabilization of KXe and RbXe requires slightly lower pressure compared with that of previously reported CsXe (25 GPa), interestingly, which is in contrast to the electronegativity order of the AMs and unexpected. Our simulations also indicate that all predicted Xe compounds contain negatively charged Xe. Moreover, our in-depth analysis indicates that the occupation of AM d-orbitals plays a critical role in stabilizing these Xe-bearing compounds. These results shed light on the understanding of the reaction between Xe and AMs and the formation mechanism of the resultant crystal structures.

Theoretical methods for structural phase transitions in elemental solids at extreme conditions: statics and dynamics

In recent years, theoretical studies have moved from a traditionally supporting role to a more proactive role in the research of phase transitions at high pressures. In many cases, theoretical prediction leads the experimental exploration. This is largely owing to the rapid progress of computer power and theoretical methods, particularly the structure prediction methods tailored for high-pressure applications. This review introduces commonly used structure searching techniques based on static and dynamic approaches, their applicability in studying phase transitions at high pressure, and new developments made toward predicting complex crystalline phases. Successful landmark studies for each method are discussed, with an emphasis on elemental solids and their behaviors under high pressure. The review concludes with a perspective on outstanding challenges and opportunities in the field.

Unique Conduction Band Minimum of Semiconductors Possessing a Zincblende-Type Framework

Tetrahedral semiconductors such as Si adopt a diamond-type crystal structure with low packing density arising from open cavities in the crystallographic space. By taking LiAlGe as an example, we propose a zincblende-type framework as a platform for semiconductors possessing electroactive cavities. LiAlGe adopts a half-Heusler-type crystal structure including an ordered diamond-type sublattice (zincblende-type) (AlGe) and is an indirect semiconductor with a band gap of ∼0.1 eV. The conduction band minimum (CBM) is uniquely located at the cavity space surrounded by four cations (Al₄) in real space. The bond ionicity and cation (Al) p orbitals located around the Fermi energy are requisite for the CBM to float in the cavity space. DFT calculations indicate the conversion of the semiconductor to a semimetallic electride under a pressure of ∼8 GPa, which is accompanied by band gap collapse due to electron transfer from valence band maximum to the cavity space. The high-pressure electride of LiAlGe formed under a very small critical pressure is derived from the presence of inherent crystallographic cavities having deep orbital levels energetically. This finding suggests the possible utilization of electroactive cavity spaces in tetrahedral semiconductors, which are widely used in modern electronic devices.

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.

Compression Produces a Square-Planar Iron Tetracarbonyl

Iron carbonyls are known to form 18-electron complexes like Fe(CO)₅, Fe₂(CO)₉, and Fe₃(CO)₁₂ having terminal or bridged Fe-CO bonding. Based on genetic algorithm-assisted density functional theory (DFT) calculations, it is predicted that at pressures above 2 GPa, iron tetracarbonyl, Fe(CO)₄, attains a square-planar geometry with a 16-electron count. Compression overcomes the [Ar]4s²3d⁶ (S = 2) → [Ar]4s⁰3d⁸ (S = 0) excitation energy to stabilize a closed-shell Fe(CO)₄ with a d⁸-configuration. Strong σ(4CO) → Fe (d_x²_-y²) bonding along with Fe(d_xz, d_yz) and Fe(d_xy) → π (CO)₄* back-bonding assists the formation of square-planar Fe(CO)₄ under pressure. Compression progressively flattens and destabilizes the ambient pressure C_2v structure of Fe(CO)₄, and beyond 2 GPa, it undergoes a sharp C_2v → D_4h transition with ΔV_unit-cell = 2.1% and trans-θ(OC-Fe-CO) = 180°. Realizing a square-planar geometry in a four-coordinated Fe-carbonyl complex shows the rich prospects of the new chemistry under pressure.

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.

Superatomic Au25(SC2H5)18 Nanocluster under Pressure

The past decade has witnessed significant advances in the synthesis and structure determination of atomically precise metal nanoclusters. However, little is known about the condensed matter properties of these nanosized metal nanoclusters packed in a crystal lattice under high pressure. Here using density functional theory calculations, we simulate the crystal of a representative superatomic gold cluster, Au₂₅(SR)₁₈ ⁰ (R = C₂H₅), under various pressures. At ambient conditions, Au₂₅(SC₂H₅)₁₈ ⁰ clusters are packed in a crystal via dispersion interactions; being a 7e superatom, each cluster carries a magnetic moment of 1 μ_B or one unpaired electron. Upon increasing compression (from 10 to 110 GPa), we observe the formation of intercluster Au-Au, Au-S, and S-S covalent bonds between staple motifs, thereby linking the clusters into a network. The pressure-induced structural change is accompanied by the vanishment of the magnetic moment and the semiconductor-to-metal transition. Our work shows that subjecting crystals of atomically precise metal nanoclusters to high pressures could lead to new crystalline states and physical properties.

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.

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.

Predicted Stable Electrides in Mg-Al System under High Pressure

Magnesium and aluminum, as the adjacent light metal elements, are difficult to form the stable stoichiometries compounds under ambient conditions. In this work, using evolutionary ab initio structural prediction approaches,...

Metallic Aluminum Suboxides with Ultrahigh Electrical Conductivity at High Pressure

Aluminum, as the most abundant metallic elemental content in the Earth's crust, usually exists in the form of alumina (Al₂O₃). However, the oxidation state of aluminum and the crystal structures of aluminum oxides in the pressure range of planetary interiors are not well established. Here, we predicted two aluminum suboxides (Al₂O, AlO) and two superoxides (Al₄O₇, AlO₃) with uncommon stoichiometries at high pressures using first-principle calculations and crystal structure prediction methods. We find that the P4/nmm Al₂O becomes stable above ~765 GPa and may survive in the deep mantles or cores of giant planets such as Neptune. Interestingly, the Al₂O and AlO are metallic and have electride features, in which some electrons are localized in the interstitials between atoms. We find that Al₂O has an electrical conductivity one order of magnitude higher than that of iron under the same pressure-temperature conditions, which may influence the total conductivity of giant planets. Our findings enrich the high-pressure phase diagram of aluminum oxides and improve our understanding of the interior structure of giant planets.

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.

Environmental modifications of atomic properties: The ground and 1s2p excited states of compressed helium

Atoms remaining as recognizably distinct constituents of bulk condensed phases can have properties modified from those of the isolated species. Dense helium bubbles at high pressures are a common form of radiation damage degrading the mechanical and electrical properties of host materials. Detailed knowledge is critical for predicting their long term performance. Modifications of the ground and first singlet excited states of confined compressed helium are investigated using an entirely non-empirical theory based on the results of ab initio self-consistent field calculations with corrections for the effects of electron correlation. For finite sized portions representing bulk condensed fcc and bcc phases of helium atoms, Hartree-Fock wavefunctions, energies, and charge distributions were computed as a function of different atomic densities using two models. The first model for the first excited state localizes the excitation on the central atom; in the second model, this is partially delocalized over the closest atomic neighbors. Total energies for the finite size portions are derived by adding the inter-atomic dispersive attractions and a density functional description of the short-range inter-atomic correlation energy. The experimental energy of the first allowed electronic transition increases with density being larger than in an isolated atom. The intra-atomic correlation energy does not contribute to this energy shift. The calculated energy shifts agree well with experiment for both bulk solid and liquid helium. The 2p orbital is increasingly compressed by density enhancement, thus generating the energy shifts. Consequently, calculations of the inelastic electron scattering cross sections are substantially incorrect if the compression of the final 1s2p state is not included. The character of the excitations is examined, and it is argued that these are of Frenkel rather than the Wannier type.

Electronegativity under Confinement

The electronegativity concept was first formulated by Pauling in the first half of the 20th century to explain quantitatively the properties of chemical bonds between different types of atoms. Today, it is widely known that, in high-pressure regimes, the reactivity properties of atoms can change, and, thus, the bond patterns in molecules and solids are affected. In this work, we studied the effects of high pressure modeled by a confining potential on different definitions of electronegativity and, additionally, tested the accuracy of first-order perturbation theory in the context of density functional theory for confined atoms of the second row at the Hartree–Fock level. As expected, the electronegativity of atoms at high confinement is very different than that of their free counterparts since it depends on the electronic configuration of the atom, and, thus, its periodicity is modified at higher pressures.

Proposed Superconducting Electride Li_{6}C by sp-Hybridized Cage States at Moderate Pressures

The combination of electride state and superconductivity within the same compound, e.g., [Ca_{24}Al_{28}O_{6}]^{4+}(4e^{-}), opens up a new category of conventional superconductors. However, neither the underlying causations to explain superconducting behaviors nor effects of interstitial quasiatoms (ISQs) on superconductivity remain unclear. Here we have designed an efficient and resource-saving method to identify superconducting electrides only by chemical compositions and bonding characteristics. A representative superconducting electride Li_{6}C with a noteworthy T_{c} of 10 K below 1 Mbar among the known binary electrides has been revealed. Our first-principles studies unveil that the anomalous sp-hybridized cage-state ISQs, as a guest in Li_{6}C, exhibit unexpected ionic and covalent bonds, which act as a chemical precompression to lower dynamically stable pressure. More importantly, we uncover that, contrary to common expectations, the high T_{c} is attributed to the strong electron-phonon coupling derived from the synergy of interatomic coupling effect, phonon softening caused by Fermi surface nesting, and phonon-coupled bands, which are mainly dominated by host sp-hybridized electrons, rather than the ISQs. Our present results elucidate a new superconducting mechanism of electrides and shed light on the way for seeking a high-T_{c} superconductor at lower pressures in cage-state electrides.

High-Pressure Phase Diagram of the Ti-O System

Titanium oxides are technologically important compounds. The chemistry of the Ti-O system is quite rich, largely because of the multiple oxidation states that titanium atoms can take. In this work, using a combination of variable-composition evolutionary crystal structure prediction (USPEX code) and data mining (Materials Project), we predicted all of the stable titanium oxides in the pressure range 0-200 GPa and found that 27 compounds can be stable at different pressures. We resolved contradictions between previous works and predicted four hitherto-unknown stable phases: P2₁/c-TiO₃, I4/mmm-Ti₃O₂, Imm2-Ti₅O₂, and R3̅-Ti₁₂O₅. We also showed that the high-pressure P6̅m2-TiO phase is an electride.

Electron-Deficient-Type Electride Ca5Pb3: Extension of Electride Chemical Space

Electrides have been identified so far by two major routes: one is conversion of elemental metals and stoichiometric compounds by high pressure; the other is to search for electron-rich compounds, and this approach is more general. In contrast, few electron-deficient structures in existing databases have been revealed as potential electride candidates. In this work, we found an electron-deficient compound Ca₅Pb₃ could be transformed into electrides upon applying external pressure or strain along the c-axis, which induces the electron immigration from Pb to interstitial sites. Furthermore, the electron doping via Hf substitution of Ca atoms for Ca₅Pb₃ was found to be capable of tuning the interstitial electron density under ambient pressure, resulting in a new stable ternary electride Ca₃Hf₂Pb₃, Hf-substituted Ca₅Pb₃. The electron-deficient electride discovered here is of novel type and can largely expand the research scope of electrides. Considering a recently reported neutral electride Na₃N and the present finding, it is now clarified that electrides can be identified irrespective of stoichiometry (electron-rich, -neutral, or -poor) for compounds.

How Many Electrons Does a Molecular Electride Hold?

Electrides are very peculiar ionic compounds where electrons occupy the anionic positions. In a crystal lattice, these isolated electrons often form channels or surfaces, furnishing electrides with many traits with promising technological applications. Despite their huge potential, thus far, only a few stable electrides have been produced because of the intricate synthesis they entail. Due to the difficulty in assessing the presence of isolated electrons, the characterization of electrides also poses some serious challenges. In fact, their properties are expected to depend on the arrangement of these electrons in the molecule. Among the criteria that we can use to characterize electrides, the presence of a non-nuclear attractor (NNA) of the electron density is both the rarest and the most salient feature. Therefore, a correct description of the NNA is crucial to determine the properties of electrides. In this paper, we analyze the NNA and the surrounding region of nine molecular electrides to determine the number of isolated electrons held in the electride. We have seen that the correct description of a molecular electride hinges on the electronic structure method employed for the analyses. In particular, one should employ a basis set with sufficient flexibility to describe the region close to the NNA and a density functional approximation that does not suffer from large delocalization errors. Finally, we have classified these nine molecular electrides according to the most likely number of electrons that we can find in the NNA. We believe this classification highlights the strength of the electride character and will prove useful in designing new electrides.

Pressure-induced electrides and metallic phases in the Y-Cl system

Pressure can profoundly change the electronic structure, leading to the formation of new phases and materials with exotic properties. Herein, using evolutionary algorithms and density functional theory, we systematically investigate the behaviour of materials in the yttrium-chlorine binary system under pressure. Electrons are found to be spatially confined at low pressures in yttrium chlorides and tend to form new electrides. In particular, a novel yttrium chloride, Y₃Cl₂, is predicted to be thermodynamically and lattice dynamically stable at approximately 10 GPa. Further analyses of the electron localization function and partial charge density identify trigonal Y₃Cl₂as a new 2D high-pressure electride with partially localized electrons contributing to the conduction. By further increasing the pressure, electrons in the yttrium-chlorine binary system tend to delocalize with the electrides decomposing into two new compounds (Y₂Cl and YCl₂) and a new YCl phase (space groupP6₃/mmc) above 20 GPa. These newly discovered phases are all metallic in their stable pressure range according to band structure simulations without interstitial electron localization. The discovery of these unconventional yttrium chlorides may inspire strategies to search for low-pressure electrides in other rare-earth halogenide systems.

Stoner enhancement from interstitial electrons in Y2C toward a spontaneous ferromagnetic electride

The evolutionary magnetism associated with the interlayer spacing in two-dimensional (2D) Y₂C electrides has been investigated by first-principles total-energy calculations based on density functional theory. Several structures with different c-axis parameters around the optimized value were taken into our consideration. Mapping of the electron localization function shows that the interstitial electron is strongly localized at the body center position (denoted as the X-site) in the primitive rhombohedral unit cell, serving as an anion which is ionically bonded with the cationic framework of the Y₂C layer. As the c-axis parameter decreases, the volume of the X-site is systematically reduced while both the charge and magnetization density for X are increased. It indicates that the compressed inter-layer space effectively increases the degree of localization of interstitial anionic electrons (IAEs) correlated with their enhanced local magnetic moments. We have found that the exchange splitting of the density of states for Y₂C becomes more prominent with a decrease in the c-axis parameter as predicted from a pressurized alkali metal system. Accompanied by the calculated magnetization values, it can be concluded that the increased degree of localization for IAEs between cationic framework layers has greatly influenced the Stoner parameter leading to the increased magnetic moment based on the Stoner enhancement mechanism; hence, it plays a key role in the emergence of a spontaneous ferromagnetic electride.

Pressure-induced Na-Au compounds with novel structural units and unique charge transfer

The exploration of novel intermetallic compounds is of great significance for basic research and practical application. Considering the interesting and diverse attributes of Na and Au, their large electronegative difference, and the unresolved high-pressure Na-Au structures, first-principles swarm-intelligence structural search calculations are employed to explore the potential Na-Au compounds at high pressures. Besides reproducing the known Na-Au compounds, eleven new phases are disclosed, exhibiting several unprecedented Au atomic arrangements, such as rectangular ladder, layer formed by edge-sharing squares, hexahedron framework, and diamond-like skeleton, enriching the understanding of Au chemistry. Moreover, the coordination number of Au can be effectively modulated by controlling Na composition. In the Na-rich compounds (Na₄Au, Na₅Au, and Na₆Au), Au shows a formal charge beyond -2, acting as a 6p-block element, originating from pressure-induced unusual Na 3s or 3p → Au 6p charge transfer. These compounds are metallic, but not superconductive. Moreover, the good agreement between the experimental XRD patterns and the simulated ones allows us to assign the predicted P6/mmm Na₂Au and Fm3[combining macron]m Na₃Au as the experimental structures at 59.6 GPa. Our work indicates that the modulation of pressure and chemical composition is a useful way to stabilize novel intermetallic compounds.

Interplay of Anionic Quasi-Atoms and Interstitial Point Defects in Electrides: Abnormal Interstice Occupation and Colossal Charge State of Point Defects in Dense fcc-Lithium

Electrides are an emerging class of materials with highly localized electrons in the interstices of a crystal that behave as anions. The presence of these unusual interstitial quasi-atom (ISQ) electrons leads to interesting physical and chemical properties and wide potential applications for this new class of materials. Crystal defects often have a crucial influence on the properties of materials. Introducing impurities has been proved to be an effective approach to improve the properties of a material and to expand its applications. However, the interactions between the anionic ISQs and the crystal defects in electrides are yet unknown. Here, dense fcc-Li was employed as an archetype to explore the interplay between anionic ISQs and interstitial impurity atoms in this electride. This work reveals strong coupling among the interstitial impurity atoms, the ISQs, and the matrix Li atoms near to the defects. This complex interplay and interaction mainly manifest as the unexpected tetrahedral interstitial occupation of impurity atoms and the enhancement of electron localization in the interstices. Moreover, the Be impurity occupying the octahedral interstice shows the highest negative charge state (Be^8-) discovered thus far. These results demonstrate the rich chemistry and physics of this emerging material and provide a new basis for enriching their variants for a wide range of applications.