High-Pressure Electrides: The Chemical Nature of Interstitial Quasiatoms

Constructing Tunable Electrides on Monolayer Transition Metal Dichalcogenides

Electrides have emerged as promising materials with exotic properties due to the presence of localized electrons detached from all atoms. Despite the continuous discovery of many new electrides, most of them are based on atypical compositions, and their applications require an inert surface structure to passivate reactive excess electrons. Here, we demonstrate a different route to attain tunable electrides. We first report that monolayer transition metal dichalcogenides (TMDCs) exhibit weak electride characteristics, which is the remainder of the electride feature of the transition metal sublattice. By introducing chalcogen vacancies, the enhanced electride characteristics are comparable to those of known electrides. Since the precise tailoring of the chalcogen vacancy concentration has been achieved experimentally, we proposed that TMDCs can be used to build electrides with controllable intensities. Furthermore, we demonstrate that the electride states at the chalcogen vacancy of monolayer TMDCs will play an important role in catalyzing hydrogen evolution reactions.

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.

Noble Gas Anions: An Overview of Strategies and Bonding Motifs

This review article aims to provide an overview of the strategies employed to prepare noble gas anions under different environments and experimental conditions, and of the bonding motifs typically occurring in these species. Observed systems include anions fixed into synthesized salts, detected in the gas phase or in high-pressure devices. The major role of the theoretical calculations is also highlighted, not only in support of the experiments, but also as effective in predicting still unreported species. The chemistry of noble gas anions overall appears as a varied and rich paint, offering fascinating opportunities for both experimentalists and theoreticians.

Electride pureα-Zr: interstitial electrons induced type-II nodal line

Electrides have attracted significant attention in the fields of physics, materials science, and chemistry due to their distinctive electron properties characterized by weak nuclear binding. In this study, based on first-principles calculations and symmetry analysis, we report that the pure zirconium with alpha-phase (α-Zr) is expected to be the electrically neutral electride with topological nodal loop. Furthermore, the nodal loop located at thekz= 0 plane exhibits a clear drumhead-like surface state. The energy levels of the topological nodal loop can be regulated by applying uniaxial strain, resulting in the topological nodal loop being closer to the Fermi level. Remarkably, the work function of the electride Zr shows a significant anisotropy along the (001), (100), and (110) directions, particularly with a low work function of 3.14 eV along the (110) surface. Therefore, we predict thatα-Zr provides a promising platform for future research on topological electrides.

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.

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.

Predicted superconductivity in one-dimensional A3Hf2B3-type electrides

Inorganic electrides are considered potential superconductors due to the unique properties of their anionic electrons. However, most electrides require external high-pressure conditions to exhibit considerable superconducting transition temperatures (Tc). Therefore, searching for superconducting electrides under low or moderate external pressures is of significant research interest and importance. In this work, a series of A3Hf2B3-type compounds (A = Mg, Ca, Sr, Ba; B = Si, Ge, Sn, Pb) were constructed and systematically studied based on density functional theory calculations. According to the analysis of the electronic structures and phonon dispersion spectrums, stable one-dimensional electrides Ca3Hf2Ge3, Ca3Hf2Sn3, and Sr3Hf2Pb3, were screened out. Interestingly, the superconductivity of these electrides were predicted from electron phonon coupling calculations. It is highlighted that Sr3Hf2Pb3 showed the highest Tc, reaching 4.02 K, while the Tc values of Ca3Hf2Ge3 and Ca3Hf2Sn3 were 1.16 K and 1.04 K, respectively. Moreover, the Tc value of Ca3Hf2Ge3 can be increased to 1.96 K under 20 GPa due to the effect of phonon softening. This work enriches the types of superconducting electrides and has important guiding significance for the research on constructing electrides and related superconducting materials.

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

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

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.

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.

New kind of electride sandwich complexes based on the cyclooctatetraene ligand M12(η8-C8H8)2M22 (M1 = Na, K and M2 = Ca, Mg): a theoretical study

In the present study, the electronic structures of a series of binuclear sandwich complexes based on the cyclooctatetraene ligand M¹₂(η⁸-C₈H₈)₂M²₂ (M¹ = Na, K and M² = Ca, Mg) are studied theoretically. Each cyclooctatetraene ligand binds with the metal in the η⁸ binding mode. The M²-M² bond length agrees well with the reported bimetallic covalent Ca₂ and Mg₂ bond lengths. The Wiberg bond index (WBI) also indicates the presence of covalent M²-M² bonds, which gives additional stability to the complex. A non-nuclear attractor (NNA) is found in-between the M²-M² bond and the negative Laplacian of the electron density is found at the NNA. Noncovalent interaction (NCI) plot shows that electron density is localized at the M²-M² bond. Based on the performed analysis, we have concluded that the designed sandwich complexes are electrides. We herein report, for the first time, the electride sandwich complexes of the cyclooctatetraene ligand. Due to the presence of a diffuse electron system, the electride complexes exhibit higher values of the static second hyperpolarizability within the range of 2.6 × 10⁵ to 1.4 × 10⁶ a.u. Among the studied complexes, M¹₂(η⁸-C₈H₈)₂Ca₂ exhibit a higher value of static second hyperpolarizability.

Unveiling Interstitial Anionic Electron-Driven Ultrahigh K-Ion Storage Capacity in a Novel Two-Dimensional Electride Exemplified by Sc3Si2

Two-dimensional (2D) electrides, characterized by excess interstitial anionic electron (IAE) in a crystalline 2D material, offer promising opportunities for the development of electrode materials, in particular in rechargeable metal-ion batteries applications. Although a few such potential electride materials have been reported, they generally show low metal-ion storage capacity, and the effect of IAE on the ion storage performance remains elusive so far. Here we report a novel 2D electride, [Sc₃Si₂]¹⁺·1e^-, with fascinating IAE-driven high alkali metal-ion storage capacity. In particular, its K-ion specific capacity can reach up to 1497 mA h g^-1, higher than any previously reported 2D materials-based anodes in K-ion batteries (PIBs). The IAE in the [Sc₃Si₂]¹⁺·1e^- crystal accounts for such high capacity behavior, which can drift away and balance the charge on the metal-cation, playing a crucial role in stabilizing the metal-ion adsorption and enhancing multilayer-ions adsorption. This proposed IAE-driven storage mechanism provides an unprecedented avenue for the future design of high storage capacity electrode materials.

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.

Strain-induced multigap superconductivity in electrene Mo2N: a first principles study

Superconductivity in low dimensional materials and 2D electrides are topics of great interest with possible applications in next generation electronic devices. Using density functional theory (DFT) associated with Migdal-Eliashberg approach and maximally localized Wannier functions this study shows how biaxial strain affects superconductivity in a monolayer of Mo₂N. Results indicate that 2D Mo₂N presents strong electron-phonon coupling with large anisotropy in the superconducting energy gap. It is also proposed that, at low temperatures, a single layer of Mo₂N becomes an electride with localized electron gas pockets on the surface, resembling anions adsorbed on an atomic sheet. Calculations point to T_c = 24.7 K, a record high transition temperature for this class of material at ambient pressure. Furthermore, it is shown that when biaxial strain is applied to a superconducting Mo₂N monolayer, a new superconductivity gap starts at 2% strain and is enhanced by continuum strain, opening additional coupling channels.

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,...

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.

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.

Formation Mechanism of Chemically Precompressed Hydrogen Clathrates in Metal Superhydrides

Recently, the experimental discovery of high-T_c superconductivity in compressed hydrides H₃S and LaH₁₀ at megabar pressures has triggered searches for various superconducting superhydrides. It was experimentally observed that thorium superhydrides, ThH₁₀ and ThH₉, are stabilized at much lower pressures than LaH₁₀. Based on first-principles density functional theory calculations, we reveal that the isolated Th frameworks of ThH₁₀ and ThH₉ have relatively more excess electrons in interstitial regions than the La framework of LaH₁₀. Such interstitial excess electrons easily participate in the formation of the anionic H cage surrounding the metal atom. The resulting Coulomb attraction between cationic Th atoms and anionic H cages is estimated to be stronger than the corresponding one of LaH₁₀, thereby giving rise to larger chemical precompressions in ThH₁₀ and ThH₉. Such a formation mechanism of H clathrates can also be applied to other superhydrides such as CeH₉, PrH₉, and NdH₉. Our findings demonstrate that interstitial excess electrons in the isolated metal frameworks of high-pressure superhydrides play an important role in generating the chemical precompression of H clathrates.

Highs and Lows of Bond Lengths: Is There Any Limit?

Two distinct points on the potential energy curve (PEC) of a pairwise interaction, the zero‐energy crossing point and the point where the stretching force constant vanishes, allow us to anticipate the range of possible distances between two atoms in diatomic, molecular moieties and crystalline systems. We show that these bond‐stability boundaries are unambiguously defined and correlate with topological descriptors of electron‐density‐based scalar fields, and can be calculated using generic PECs. Chemical databases and quantum‐mechanical calculations are used to analyze a full set of diatomic bonds of atoms from the s‐p main block. Emphasis is placed on the effect of substituents in C−C covalent bonds, concluding that distances shorter than 1.14 Å or longer than 2.0 Å are unlikely to be achieved, in agreement with ultra‐high‐pressure data and transition‐state distances, respectively. Presumed exceptions are used to place our model in the correct framework and to formulate a conjecture for chained interactions, which offers an explanation for the multimodal histogram of O−H distances reported for hundreds of chemical systems.

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.

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.

Ab initio Gibbs ensemble Monte Carlo simulations of the liquid-vapor equilibrium and the critical point of sodium

The ab initio (ai) Gibbs ensemble (GE) Monte Carlo (MC) method coupled with Kohn-Sham density functional theory is successful in predicting the liquid-vapour equilibrium of insulating systems. Here we show that the aiGEMC method can be used to study also metallic systems, where the excited electronic states play an important role and cannot be neglected. For this we include the electronic free energy in the formulation of the effective energy of the system to be used in the acceptance criteria for the MC moves. The application of this aiGEMC method to sodium yields a good agreement with available experimental data on the liquid-vapour equilibrium densities. We predict a critical point for sodium at 2338 ± 108 K and 0.24 ± 0.03 g cm-3. The liquid structure stemming from aiGEMC simulations is very similar to the one from ab initio molecular dynamics. Since this method can determine phase transition without computing the Gibbs free energy, it may offer a new possibility to study other materials with a reasonable computational cost.

Prediction of Stable Ground-State Binary Sodium-Potassium Interalkalis under High Pressures

The complex structures and electronic properties of alkali metals and their alloys provide a natural laboratory for studying the interelectronic interactions of metals under compression. A recent theoretical study (J. Phys. Chem. Lett. 2019, 10, 3006) predicted an interesting pressure-induced decomposition-recombination behavior of the Na₂K compound over a pressure range of 10-500 GPa. However, a subsequent experiment (Phys. Rev. B 2020, 101, 224108) reported the formation of NaK rather than Na₂K at pressures above 5.9 GPa. To address this discordance, we study the chemical stability of different stoichiometries of Na_xK (x = 1/4, 1/3, 1/2, 2/3, 3/4, 4/3, 3/2, and 1-4) by an effective structure searching method combined with first-principles calculations. Na₂K is calculated to be unstable at 5-35 GPa due to the decomposition reaction Na₂K → NaK + Na, coinciding well with the experiment. NaK undergoes a combination-decomposition-recombination process accompanied by an opposite charge-transfer behavior between Na and K with pressure. Besides NaK, two hitherto unknown compounds NaK₃ and Na₃K₂ are uncovered. NaK₃ is a typical metallic alloy, while Na₃K₂ is an electride with strong interstitial electron localization.

Ferromagnetic Weyl Fermions in Two-Dimensional Layered Electride Gd_{2}C

Recently, two-dimensional layered electrides have emerged as a new class of materials which possess anionic electrons in the interstitial spaces between cationic layers. Here, based on first-principles calculations, we discover a time-reversal-symmetry-breaking Weyl semimetal phase in a unique two-dimensional layered ferromagnetic (FM) electride Gd_{2}C. It is revealed that the crystal field mixes the interstitial electron states and Gd-5d orbitals near the Fermi energy to form band inversions. Meanwhile, the FM order induces two spinful Weyl nodal lines (WNLs), which are converted into multiple pairs of Weyl nodes through spin-orbit coupling. Further, we not only identify Fermi-arc surface states connecting the Weyl nodes but also predict a large intrinsic anomalous Hall conductivity due to the Berry curvature produced by the gapped WNLs. Our findings demonstrate the existence of Weyl fermions in the room-temperature FM electride Gd_{2}C, therefore offering a new platform to investigate the intriguing interplay between electride materials and magnetic Weyl physics.

Recent Advances and Applications of Inorganic Electrides

Electrides, accommodating excess electrons in lattice voids as anions, have attracted considerable attention in both fundamental research and application development because of their interesting properties, such as ultralow work functions, high electronic mobility, high catalytic activity, and anisotropic electronic and optical properties. Recently, much research progress has been made in both types and applications of inorganic electrides because of the high stability. In this Perspective, we aim to summarize the recent development of inorganic electrides discovered and proposed by experiment and theoretical calculations, highlighting the main applications, including catalysis, metal-ion batteries, superconductivity, magnetism, and organic light-emitting diodes. We provide insights into the role of anionic electrons in electrides playing in the stability and properties. Finally, the problems, challenges, and opportunities are presented, which provide an outlook for future research.

Ferromagnetic quasi-atomic electrons in two-dimensional electride

An electride, a generalized form of cavity-trapped interstitial anionic electrons (IAEs) in a positively charged lattice framework, shows exotic properties according to the size and geometry of the cavities. Here, we report that the IAEs in layer structured [Gd₂C]²⁺·2e⁻ electride behave as ferromagnetic elements in two-dimensional interlayer space and possess their own magnetic moments of ~0.52 μ_B per quasi-atomic IAE, which facilitate the exchange interactions between interlayer gadolinium atoms across IAEs, inducing the ferromagnetism in [Gd₂C]²⁺·2e⁻ electride. The substitution of paramagnetic chlorine atoms for IAEs proves the magnetic nature of quasi-atomic IAEs through a transition from ferromagnetic [Gd₂C]²⁺·2e⁻ to antiferromagnetic Gd₂CCl caused by attenuating interatomic exchange interactions, consistent with theoretical calculations. These results confirm that quasi-atomic IAEs act as ferromagnetic elements and trigger ferromagnetic spin alignments within the antiferromagnetic [Gd₂C]²⁺ lattice framework. These results present a broad opportunity to tailor intriguing ferromagnetism originating from quasi-atomic interstitial electrons in low-dimensional materials.

Ferromagnetic quasi-atomic behavior of interstitial anionic electrons (IAEs) in practical electrides is yet to be discovered experimentally. Here, the authors reveal that IAEs in two-dimensional electride [Gd₂C]²⁺⋅2e^- behave as magnetic elements with their own magnetic moment.

Pressure-induced unexpected -2 oxidation states of bromine and superconductivity in magnesium bromide

Finding novel compounds with unusual crystal structures and physical properties is always an important goal for the materials and chemistry community. Pressure becomes attractive due to its unique ability to break down many fundamental rules by modifying the chemical properties of elements, overcoming reaction barriers and shortening interatomic distances, leading to the formation of some novel materials with unexpected properties. In this work, for the first time we have analyzed the high-pressure phase diagram, crystal structures and electron properties of the Mg-Br system up to 200 GPa using unbiased structure searching techniques. Besides the already known MgBr₂, here we report that three unusual stoichiometries of Mg-Br compounds can be stabilized at high pressures as MgBr₃, MgBr and Mg₄Br. Firstly, among the predicted stable compounds, we find that the Mg₄Br in the I4/mmm structure stabilized at 178 GPa behaves as a typical electride, indicating that the formation pressure of an electride for Mg can be significantly reduced by bonding with Br atoms. Secondly, it is surprising that the unexpected oxidation states of Br approaching -2 are observed in the predicted I4/mmm Mg₄Br and Pm3[combining macron]m MgBr compounds. Furthermore, P2₁/m MgBr₃ and I4[combining macron]2m MgBr₃ phases are predicted as superconductors with an estimated T_c of 23.2 and 0.49 K, respectively. Our work represents a significant step toward understanding the high pressure behaviors of alkaline earth halides and searching for novel high temperature superconductors.

Theoretical Study on the Electronic Structure of Heavy Alkali-Metal Suboxides

On the metal-rich side of the phase diagrams of the Rb-O, Cs-O, and Rb-Cs-O systems, one can find a variety of stoichiometries: for example, Rb₉O₂, Rb₆O, Cs₄O, Cs₇O, Cs₁₁O₃, RbCs₁₁O₃, and Rb₇Cs₁₁O₃. They may be termed heavy alkali-metal suboxides. The application of the standard electron-counting scheme to these compounds suggests the presence of surplus electrons. This motivated us to carry out a theoretical study using the first-principles density functional theory (DFT) method. The structures of these compounds are based on either a formally cationic Rb₉O₂ or Cs₁₁O₃ cluster. The analyses of the partial charge density just below the Fermi level and the electron localization function (ELF) have revealed that there exist surplus electrons in interstitial regions of all the investigated suboxides so that the excess positive charge of the cluster can be compensated. Density of states (DOS) calculations suggest that all of the compounds are metallic. Therefore, the suboxides listed above may be regarded as a new family of metallic electrides, where coreless electrons reside in interstitial spaces and provide a conduction channel. Except for the phases of Rb₉O₂ and Cs₁₁O₃, the suboxide structures include both the cationic clusters and alkali-metal matrix. Several charge analyses indicate that the interstitial surplus-electron density can be assigned to the alkali-metal atoms in the metal matrix, leading to the possibility of the presence of negatively charged alkali-metal atoms, namely Rb^- (rubidide) and Cs^- (caeside) ions, a.k.a. alkalides. In Rb₆O, Rb^-, Rb⁰, and Rb⁺ are found to coexist in the same crystal structure. Similarly, in Cs₇O, one can find the three types of Cs atoms. However, in Cs₄O, no Cs⁰ state is identified. In the Rb-Cs-O ternary suboxides, Rb takes a negatively charged anion state or neutral state, while all of the Cs atoms are found to be cationic because they get involved in the Cs₁₁O₃ cluster and all the Rb atoms exist in interstitial sites. Orbital interactions between the clusters are analyzed to understand how the condensation of the clusters into the solid happens and how the electride nature ensues. These clusters are found to have some superatomic character.

A chemical perspective on high pressure crystal structures and properties

The general availability of third generation synchrotron sources has ushered in a new era of high pressure research. The crystal structure of materials under compression can now be determined by X-ray diffraction using powder samples and, more recently, from multi-nano single crystal diffraction. Concurrently, these experimental advancements are accompanied by a rapid increase in computational capacity and capability, enabling the application of sophisticated quantum calculations to explore a variety of material properties. One of the early surprises is the finding that simple metallic elements do not conform to the general expectation of adopting 3D close-pack structures at high pressure. Instead, many novel open structures have been identified with no known analogues at ambient pressure. The occurrence of these structural types appears to be random with no rules governing their formation. The adoption of an open structure at high pressure suggested the presence of directional bonds. Therefore, a localized atomic hybrid orbital description of the chemical bonding may be appropriate. Here, the theoretical foundation and experimental evidence supporting this approach to the elucidation of the high pressure crystal structures of group I and II elements and polyhydrides are reviewed. It is desirable and advantageous to extend and apply established chemical principles to the study of the chemistry and chemical bonding of materials at high pressure.

Generalized Stress-Redox Equivalence: A Chemical Link between Pressure and Electronegativity in Inorganic Crystals

The crystal structure of many inorganic compounds can be understood as a metallic matrix playing the role of a host lattice in which the nonmetallic atomic constituents are located, the Anions in Metallic Matrices (AMM) model stated. The power and utility of this model lie in its capacity to anticipate the actual positions of the guest atoms in inorganic crystals using only the information known from the metal lattice structure. As a pertinent test-bed for the AMM model, we choose a set of common metallic phases along with other nonconventional or more complex structures (face-centered cubic (fcc) and simple cubic Ca, CsCl-type BaSn, hP4-K, and fcc-Na) and perform density functional theory electronic structure calculations. Our topological analysis of the chemical pressure (CP) scalar field, easily derived from these standard first-principles electronic computations, reveals that CP minima appear just at the precise positions of the nonmetallic elements in typical inorganic crystals presenting the above metallic subarrays: CaF₂, rock-salt and CsCl-type phases of CaX (X = O, S, Se, Te), BaSnO₃, K₂S, and NaX (X = F, Cl, Br, I). A theoretical basis for this correlation is provided by exploring the equivalence between hydrostatic pressure and the oxidation (or reduction) effect induced by the nonmetallic element on the metal structure. Indeed, our CP analysis leads us to propose a generalized stress-redox equivalence that is able to account for the two main observed phenomena in solid inorganic compounds upon crystal formation: (i) the expansion or contraction experienced by the metal structure after hosting the nonmetallic element while its topology is maintained and (ii) the increasing or decreasing of the effective charge associated with the anions in inorganic compounds with respect to the charge already present in the interstices of the metal network. We demonstrate that a rational explanation of this rich behavior is provided by means of Pearson-Parr's electronegativity equalization principle.

Metallic and anti-metallic properties of strongly covalently bonded energetic AlN5 nitrides

High pressure can stimulate numerous novel physical effects which are not observed under ambient conditions, such as the electronic redistribution and delocalization phenomenon in strongly covalently bonded nitrides. Through first principles simulations, we report a new N-rich aluminum nitride AlN5, which crystallizes with the space group P1[combining macron] at 20 GPa and then transforms into the I4[combining macron]2d phase at 60 GPa. We have identified and proved the delocalization effects of π electrons in the strongly covalent Lewis poly-nitrogen structure via the one-dimensional particle in a box mechanism, which contributes to the metallization and stability of the system. This implies that not all strongly covalently bonded systems with highly localized electrons exhibit nonmetallic properties in III-V main group nitrides. Furthermore, pressure results in the hybridization configuration mutation from sp2 in the P1[combining macron] phase to a mixture of sp2 and sp3 hybridization in the I4[combining macron]2d phase, which leads to phase transition from metal to insulator. With increasing pressure, the band gap increases abnormally, exhibiting anti-metallization induced by the strong hybridization. Interestingly, the P1[combining macron] and I4[combining macron]2d structures are simultaneously accompanied by a high energy density and hardness, which enable them to have a greater ability to resist elasticity, plastic deformation and external force destruction in potential applications. Their energy density and hardness are up to 3.29 kJ g-1 and 15.2 GPa in the P1[combining macron] phase but especially 6.14 kJ g-1 and 31.7 GPa in the I4[combining macron]2d phase.

Single step synthesis of highly conductive room-temperature stable cation-substituted mayenite electride target and thin film

Novel approaches to synthesize efficient inorganic electride [Ca24Al28O64]4+(e-)4 (thereafter, C12A7:e-) at ambient pressure under nitrogen atmosphere, are actively sought out to reduce the cost of massive formation of nanosized powder as well as compact large size target production. It led to a new era in low cost industrial applications of this abundant material as Transparent Conducting Oxides (TCOs) and as a catalyst. Therefore, the present study about C12A7:e- electride is directed towards challenges of cation doping in C12A7:e- to enhance the conductivity and form target to deposit thin film. Our investigation for cation doping on structural and electrical properties of Sn- and Si-doped C12A7:e- (Si-C12A7:e, and Sn-C12A7:e-) reduced graphene oxide (rGO) composite shows the maximum achieved conductivities of 5.79 S·cm-1 and 1.75 S·cm-1 respectively. On the other hand when both samples melted, then rGO free Sn-C12A7:e- and Si-C12A7:e- were obtained, with conductivities ~280 S.cm-1 and 300 S·cm-1, respectively. Iodometry based measured electron concentration of rGO free Sn-C12A7:e- and Si-C12A7:e-, 3 inch electride targets were ~2.22 × 1021 cm-3, with relative 97 ± 0.5% density, and ~2.23 × 1021 cm-3 with relative 99 ± 0.5% density, respectively. Theoretical conductivity was already reported excluding any associated experimental support. Hence the above results manifested feasibility of this sol-gel method for different elements doping to further boost up the electrical properties.

Predicted Pressure-Induced Superconducting Transition in Electride Li_{6}P

Electrides are unique compounds where most of the electrons reside at interstitial regions of the crystal behaving as anions, which strongly determines its physical properties. Interestingly, the magnitude and distribution of interstitial electrons can be effectively modified either by modulating its chemical composition or external conditions (e.g., pressure). Most of the electrides under high pressure are nonmetallic, and superconducting electrides are very rare. Here we report that a pressure-induced stable Li_{6}P electride, identified by first-principles swarm structure calculations, becomes a superconductor with a predicted superconducting transition temperature T_{c} of 39.3 K, which is the highest among the already known electrides. The interstitial electrons in Li_{6}P, with dumbbell-like connected electride states, play a dominant role in the superconducting transition. Other Li-rich phosphides, Li_{5}P, Li_{11}P_{2}, Li_{15}P_{2}, and Li_{8}P, are also predicted to be superconducting electrides, but with a lower T_{c}. Superconductivity in all these compounds can be attributed to a combination of a weak electronegativity of phosphorus (P) with a strong electropositivity of lithium (Li), and opens up the interest to explore high-temperature superconductivity in similar binary compounds.

Metal-to-Semiconductor Transition and Electronic Dimensionality Reduction of Ca2N Electride under Pressure

The discovery of electrides, in particular, inorganic electrides where electrons substitute anions, has inspired striking interests in the systems that exhibit unusual electronic and catalytic properties. So far, however, the experimental studies of such systems are largely restricted to ambient conditions, unable to understand their interactions between electron localizations and geometrical modifications under external stimuli, e.g., pressure. Here, pressure-induced structural and electronic evolutions of Ca2N by in situ synchrotron X-ray diffraction and electrical resistance measurements, and density functional theory calculations with particle swarm optimization algorithms are reported. Experiments and computation are combined to reveal that under compression, Ca2N undergoes structural transforms from R3 ¯ m symmetry to I4 ¯ 2d phase via an intermediate Fd3 ¯ m phase, and then to Cc phase, accompanied by the reductions of electronic dimensionality from 2D, 1D to 0D. Electrical resistance measurements support a metal-to-semiconductor transition in Ca2N because of the reorganizations of confined electrons under pressure, also validated by the calculation. The results demonstrate unexplored experimental evidence for a pressure-induced metal-to-semiconductor switching in Ca2N and offer a possible strategy for producing new electrides under moderate pressure.

Insights into Antibonding Induced Energy Density Enhancement and Exotic Electronic Properties for Germanium Nitrides at Modest Pressures

Here, the electronic and bonding features in ground-state structures of germanium nitrides under different components that not accessible at ambient conditions have been systematically studied. The forming essence of weak covalent bonds between the Ge and N atom in high-pressure ionic crystal Fd-3 m-Ge₃N₄ is induced by the binding effect of electronic clouds originated from the Ge_ p orbitals. Hence, it helps us to understand the essence of covalent bond under high pressure, profoundly. As an excellent reducing agent, germanium transfer electrons to the antibonding state of the N₂ dimer in Pa-3-GeN₂ phase at 20 GPa, abnormally, weakening the bonding strength considerably than nitrogen gap (N≡N) at ambient pressure. Furthermore, the common cognition that the atomic distance will be shortened under the high pressures has been broken. Amazingly, with a lower range of synthetic pressure (∼15 GPa) and nitrogen contents (28%), its energy density is up to 2.32 kJ·g^-1, with a similar order of magnitude than polymeric LiN₅ (nonmolecular compound, 2.72 kJ·g^-1). It breaks the universal recognition once again that nitrides just containing polymeric nitrogen were regarded as high energy density materials. Hence, antibonding induced energy density enhancement mechanism for low nitrogen content and pressure has been exposed in view of electrons. Both the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO) are usually the separated orbitals of N_π* and N_σ*, which are the key to stabilization. Besides, the sp² hybridizations that exist in N₄ units are responsible for the stability of the R-3 c-GeN₄ structure and restrict the delocalization of electrons, exhibiting nonmetallic properties.

TiC3 Monolayer with High Specific Capacity for Sodium-Ion Batteries

Sodium-ion batteries (SIBs) have attracted considerable attention due to the intrinsic safety and high abundance of sodium. However, the lack of high-performance anode materials becomes a main obstacle for the development of SIBs. Here, we identify an ideal anode material, a metallic TiC₃ monolayer with not only remarkably high storage capacity of 1278 mA h g^-1 but also low barrier energy and open-circuit voltage, through first-principles swarm-intelligence structure calculations. TiC₃ still keeps metallic after adsorbing two-layer Na atoms, ensuring good electrical conductivity during the battery cycle. Besides, high melting point and superior dynamical stability are in favor of practical application. Its excellent performance can be mainly attributed to the presence of an unusual n-biphenyl unit in the TiC₃ monolayer. High cohesive energy, originating from multibonding coexistence (e.g., covalent, ionic, and metal bonds) in the TiC₃ monolayer, provides strong feasibility for experimental synthesis. In comparison with TiC₃, functionalized TiC₃ with oxygen shows a higher storage capacity; meanwhile, it keeps nearly the same barrier energy. This is in sharp contrast with metal-rich MXenes. These intriguing properties make the TiC₃ monolayer a promising anode material for SIBs.