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.


Introduction
Sodium and oxygen are among the most abundant elements in the solar system [1]. Sodium readily interacts with oxygen, typically producing Na 2 O, in which Na and O have oxidation states +1 and −2, respectively. Sodium can also react with oxygen to form sodium peroxide (Na 2 O 2 ), sodium superoxide (NaO 2 ), and sodium ozonide (NaO 3 ), in which peroxide (O 2 2− ), superoxide (O 2 − ), and ozonide (O 3 − ) groups, respectively, act as anions [2]. Na-O compounds have broad applications, e.g., as oxidizing agents, oxygen sources, and magnetic materials [3,4]. They are also the discharge products of Na-air batteries [5][6][7]. Therefore, obtaining an in-depth understanding of the structure and properties of Na-O compounds under different external conditions is of fundamental importance. The high-pressure structures and properties of these Na-O compounds have been widely investigated both experimentally and theoretically at 50 GPa [5,[8][9][10][11][12].
For instance, the observed anomalous insulativity in the first high-pressure electride Na-hP4 [29] led to a research boom on high-pressure electrides. Similarly, many novel stoichiometries and chemical properties have been found in the Na-Cl system under high pressure [22]; Na 3 Cl, Na 2 Cl, Na 3 Cl 2 , NaCl 3 , and NaCl 7 are theoretically stable and show unusual bonding and electronic properties. Remarkably, the most inert element, He, has shown the ability to form a compound, Na 2 He, at pressure greater than 113 GPa [30]. Oxygen also shows intriguing structures and oxidation states under compression. It is also the third most abundant element in the Earth s crust; hence, understanding its behavior under extreme pressures provides important insights into planetary interiors and oxidation chemistry [2]. A recent experimental and theoretical study found an unconventional pressure-stabilized divalent ozonide CaO 3 crystal with intriguing bonding; its existence has profound geological implications [31]. Recent discoveries of iron oxides with unusual oxidation states (FeO 2 [32], Fe 2 O 3 [33], and Fe 5 O 6 [34]) are also notable.
Considering The C2/c phase of Na 3 O is found to be a zero-dimensional (0D) electride with an insulating character. The Cmca phase of Na 4 O is a one-dimensional (1D) metallic electride.

Computational Methods and Details
Structure searching for the Na-O system was performed using Crystal Structure Analysis by Particle Swarm Optimization (CALYPSO) [35][36][37], an established method that has successfully predicted high-pressure structures in many systems [38][39][40][41]. The underlying structural relaxations and electronic structure calculations were performed using the Vienna ab initio Simulation Package (VASP) [42] with the Perdew-Burke-Ernzerhof generalized gradient approximation functional [43]. We used the projector augmented wave (PAW) [44] method to describe the valence electrons of the Na (2s 2 2p 6 3s 1 ) and O (2s 2 2p 4 ) atoms. We use a kinetic energy cutoff of 400 eV and k-point sampling with 0.3 Å −1 grid spacing. Each structure searching calculation generated 1200-1500 structures. After the structure searching, a kinetic energy cutoff of 1000 eV and dense k-point sampling with grid spacing of 0.1 Å −1 were used to ensure that enthalpy calculations were well converged to~1 meV/atom. Phonon calculations with a supercell were performed using the PHONOPY code [45]. Electron localization functions (ELFs) were drawn using VESTA software [46], and Bader's quantum theory was adopted to calculate charge transfer [47].

Stable Na-O Compounds at High Pressure
Our extensive searches for crystal structures of Na x O y (x = 1-4 and y = 1-5) considered pressures of 50, 100, 200, and 300 GPa with simulation cells having up to four formula units (f.u.) for each fixed composition using CALYPSO methodology, which allows efficiently finding stable structures given only the chemical composition [35][36][37]. All the candidate structures were relaxed using the VASP code [42], and thermodynamic stabilities were systematically investigated by calculating the formation enthalpies relative to Na and O at the corresponding pressure. The enthalpy of formation per atom is calculated as follows: Convex hull data at 0 K under different pressures (summarized in Figure 1a) show the stable compounds and phases as lying on the global stability line of the convex hull. The open symbols on the dotted lines represent unstable or metastable, and they decompose into other Na x O y compounds or elemental solid Na and O. Pressure range and structure of each stable compound. Na adopted the following structures: Na−bcc, Na−fcc, Na−cI16, Na−oP8, and Na−hP4 [29,[48][49][50][51], and O adopted ζ phases with C2/m symmetry [52].

O-Rich Compounds
The O-rich compounds showed a remarkable feature of having all O atoms as quasimolecular O2 units. In addition to the previously proposed structures, new structures and stoichiometries were found, as discussed below in detail. To analyze these new structures, we calculated the O-O bond lengths and Bader charges in established structures of C/2m O2 [52], Pbam Na2O2 [9], P4/mbm NaO2 [5], and P63/mmc Na2O [10] at pressures of 50-300 GPa for comparison (Table S2).
The calculated formation enthalpies of Na x O y compounds in Figure 1a show that already known compounds of Na 2 O, Na 2 O 2 , NaO 2 , and NaO 3 lie on the convex hulls at the whole pressure range. NaO 3 is known to possess an Im2m phase at ambient pressure [11]. Yang [5] reported NaO 2 to have three stable high-pressure phases (Pnnm, Immm, and P4/mbm) between 0 and 50 GPa. It has been reported that Na 2 O 2 is stable in Amm2 (distorted P6 2 m) and P2 1 /c phases at low temperature [8]. However, the P6 2 m and Pbam structures become the most stable at elevated temperature under pressures up to 300 GPa [9]. Na 2 O undergoes phase transition from a cubic antifluorite (Fm3m) structure to an orthorhombic anticotunnite structure (Pnma), and then to a Ni 2 In-type (P6 3 /mmc) structure [10].
At elevated pressures, four new phases (P2/m and Cmc2 1 NaO 2 , Immm and C2/m NaO 3 ) of the compounds with known stoichiometry were found. Moreover, new stoichiometries NaO 5 , NaO 4 , Na 4 O, and Na 3 O became thermodynamically stable. An Immm phase of NaO 5 stabilized at 50 GPa, and then transformed to a P-1 phase at 107.6 GPa. NaO 4 stabilized in a P2 1 /c phase above 66.8 GPa, and then transformed to a P-1 phase at 127 GPa. Na 3 O stabilized at 217 GPa in a C/2c structure, and Na 4 O stabilized at 205 GPa in a Cmca structure. To provide further information potentially useful for experimental synthesis, Figure 1b shows calculated pressure-composition diagrams of the stable Na-O compounds. All of the predicted compounds were dynamically stable without any imaginary phonon modes in the whole Brillouin zone ( Figure S1 in the Supplementary Materials). Table S1 gives detailed structural information, and auxiliary POSCAR files are added below Table S1 in the Supplementary Materials.

O-Rich Compounds
The O-rich compounds showed a remarkable feature of having all O atoms as quasimolecular O 2 units. In addition to the previously proposed structures, new structures and stoichiometries were found, as discussed below in detail. To analyze these new structures, we calculated the O-O bond lengths and Bader charges in established structures of C/2m O 2 [52], Pbam Na 2 O 2 [9], P4/mbm NaO 2 [5], and P6 3 /mmc Na 2 O [10] at pressures of 50-300 GPa for comparison (Table S2).
For NaO 2 , in addition to three previously proposed structures (Pnnm, Immn, and P 4 /mbm) [5], two new structures were found: P2/m (2 f.u./cell) and  (Table S2). These results confirm that the O3-O4 quasimolecular O 2 units can be viewed as O 2 2units, which were first observed in superoxide. This indicates that the superoxide group is not maintained in NaO 2 with increasing pressure.
An Im2m phase of NaO 3 containing unusual ozone anions at ambient pressure was previously reported [11]. Our calculations found two new NaO 3 phases (Immm (2 f.u./cell) and C2/m (2 f.u./cell)) whose O atoms existed as quasimolecular O 2 units rather than ozone anions. The Immm structure contained one Na atom at the 4e position and two inequivalent O atoms at the 8 m and 4f sites (Figure 2c). The Na was coordinated with 10 O atoms; O1 was coordinated with three Na atoms, whereas O2 was coordinated with two Na atoms and one O2 atom (Figure 2c) (Table S2). These results confirm that the O3-O4 quasimolecular O2 units can be viewed as O2 2-units, which were first observed in superoxide. This indicates that the superoxide group is not maintained in NaO2 with increasing pressure. An Im2m phase of NaO3 containing unusual ozone anions at ambient pressure was previously reported [11]. Our calculations found two new NaO3 phases (Immm (2 f.u./cell)  (Table S1) indicate that all quasimolecular O 2 units in P2 1 /c and P-1 NaO 4 phases had an intermediate bonding situation that did not coincide with that shown by any known O 2 functional group. Previous studies of lithium oxides at high pressure [53,54] reported LiO 4 phases with space groups of Ibam or I4/mcm at 50 GPa. The more accurate calculation used here for the Na-O system found the P2 1 /c structure to be energetically favorable at 50 GPa.
Our calculations for NaO 5 , the most O-rich Na-O composition, found two crystal structures with Immm (2 f.u./cell) and P-1 (2 f.u./cell) symmetries. The Immm contained one Na atom at the 4i position and two inequivalent O atoms at the 16o and 4j sites (Figure 2g [55][56][57], whereas the high-oxygen-content Na-O compounds of the present study did not give these groups. To understand the electronic structures of O-rich compounds, we calculated the projected density of states (PDOS). All the O-rich compounds shared similar features. Thus, we present the PDOS of the lower-pressure structures for each compound in Figure 3 as representatives and provide the PDOS of higher-pressure structures in Figure S2 in the Supplementary Materials. As can be seen form Figure 3, the O 2p states dominated the valance bands, while the contribution of Na to the valance states was negligible since electrons were transferred from Na to O. However, there were insufficient Na atoms to donate their electrons to fully occupy the O 2p states. All these O-rich compounds were electron-deficient, and the partially occupied O 2p electronic bands led to metallicity. All the metallic O-rich compounds were nonmagnetic, similar to YO 3 [55], LiO 2 [54], and NaO 2 [5]. This can be attributed to pressure-induced magnetic collapse [58].

Na-Rich Compounds
Compression stabilized Na 3 O at 217 GPa with a C2/c structure and Na 4 O at 205 GPa with a Cmca structure. In the C2/c Na 3 O structure, the O atom was surrounded by 11 Na atoms, forming a 17-faced polyhedron. The distance between neighboring oxygen atoms was 2.65 Å at 300 GPa (Figure 4a). In Cmca Na 4 O, the coordination number of O increased to 12, and neighboring oxygen atoms were 2.73 Å apart at 300 GPa (Figure 4d). Both phases had all O atoms as oxide ions rather than quasimolecular O 2 units. The Na-rich Na-O materials are naturally electron-rich systems, making them potential candidate electride materials. Electrides have some electrons localized at interstitial regions, rather than being attached to atoms, and these electrons behave as anions [59]. According to the dimensionality of the anionic electrons and corresponding interstitial spaces where the electrons are trapped, electrides can be classified into zero-dimensional (0D), onedimensional (1D), two-dimensional (2D), and three-dimensional (3D) electrides [60]. Miao and Hoffmann attributed the formation of high-pressure electrides to external pressure inducing changes in energy between the interstitial space and the valence orbitals of atoms [15,61].

Na-Rich Compounds
Compression stabilized Na3O at 217 GPa with a C2/c structure and Na4O at 20 with a Cmca structure. In the C2/c Na3O structure, the O atom was surrounded by atoms, forming a 17-faced polyhedron. The distance between neighboring oxygen was 2.65 Å at 300 GPa (Figure 4a). In Cmca Na4O, the coordination number of O inc to 12, and neighboring oxygen atoms were 2.73 Å apart at 300 GPa (Figure 4d) phases had all O atoms as oxide ions rather than quasimolecular O2 units. The N Na-O materials are naturally electron-rich systems, making them potential can electride materials. Electrides have some electrons localized at interstitial regions, than being attached to atoms, and these electrons behave as anions [59]. According dimensionality of the anionic electrons and corresponding interstitial spaces whe electrons are trapped, electrides can be classified into zero-dimensional (0D), one-d sional (1D), two-dimensional (2D), and three-dimensional (3D) electrides [60]. Mia Hoffmann attributed the formation of high-pressure electrides to external pressure ing changes in energy between the interstitial space and the valence orbitals of [15,61].
The calculated Bader charges for the C2/c Na3O and Cmca NaO4 phases sho charge was transferred from Na to both O and interstitial spaces (Table S1). The ele provided by Na atoms were first captured by O atoms to reach a stable eight-el closed-shell configuration. Further electrons from the Na were then trapped in the stitial spaces, favoring electride formation. Subsequent ELF analysis characterized calization of the excess electrons. The ELF maps for C2/c Na3O and Cmca Na4O w isosurface value of 0.7 at 300 GPa (Figure 4b,e) clearly show electrons localized in terstices of the crystal, suggesting electride formation. Anionic electrons in the C2/c electride were limited to 0D (Figure 4b). The anionic electrons in 0D electrides ar pletely localized in the void of the crystal and do not contribute to the conductivity system. Thus, 0D electrides tend to form semiconductors or insulators, such as the insulating phase of Na-hP4 [29] at 320 GPa and semiconductor phase of Li-aba2-40 [39] at 70 GP. The other structure, Cmca Na4O, was a 1D electride in which anionic electrons were delocalized in a channel, in which the electrons could move along the channel, leading to a metallic nature. The electronic properties of both structures were explored through PDOS calculations (Figure 4c,f). C2/c Na3O was clearly insulating due to Na-O ionic bonding and the localized 0D interstitial electrons. However, Cmca Na4O was metallic; the states around the Fermi level were all mainly contributed by the Na 3p and 3s orbitals and O 2p orbitals (Figure 4f). Similar electride suboxides, Li6O [54] and Mg3O2 [62], have also been reported at high pressure. Na4O is a non-superconducting metal electride.
To show the general trend of electronic properties of the Na-O compounds, we summarize the DOSs at the Fermi level for various Na-O compounds at 300 GPa as a function of Na content in Figure S3 in the Supplementary Materials. It can be seen that all the Orich compounds were metallic due to their electron-deficient character as aforementioned. For the Na2O2 and Na2O compounds, the octet rule was achieved as the peroxide O2 2− group or O 2− anions acquired exactly two electrons from the two Na atoms, leading to an insulating character. The Na-rich compounds, Na3O and Na4O, should be metallic due to the existence of excess electrons. However, the formation of the 0D electride made Na3O an insulator.

Conclusions
In summary, we used systematic structure exploration and first-principles calculations to construct a high-pressure stability field and convex hull diagram of the Na-O system with different stoichiometries at pressures of 50-300 GPa. Four previously unknown stoichiometries (NaO5, NaO4, Na4O, and Na3O) and four new phases of known The calculated Bader charges for the C2/c Na 3 O and Cmca NaO 4 phases show that charge was transferred from Na to both O and interstitial spaces (Table S1). The electrons provided by Na atoms were first captured by O atoms to reach a stable eight-electron closedshell configuration. Further electrons from the Na were then trapped in the interstitial spaces, favoring electride formation. Subsequent ELF analysis characterized the localization of the excess electrons. The ELF maps for C2/c Na 3 O and Cmca Na 4 O with an isosurface value of 0.7 at 300 GPa (Figure 4b,e) clearly show electrons localized in the interstices of the crystal, suggesting electride formation. Anionic electrons in the C2/c Na 3 O electride were limited to 0D (Figure 4b). The anionic electrons in 0D electrides are completely localized in the void of the crystal and do not contribute to the conductivity of the system. Thus, 0D electrides tend to form semiconductors or insulators, such as the insulating phase of Na-hP4 [29] at 320 GPa and semiconductor phase of Li-aba2-40 [39] at 70 GP. The other structure, Cmca Na 4 O, was a 1D electride in which anionic electrons were delocalized in a channel, in which the electrons could move along the channel, leading to a metallic nature. The electronic properties of both structures were explored through PDOS calculations (Figure 4c,f). C2/c Na 3 O was clearly insulating due to Na-O ionic bonding and the localized 0D interstitial electrons. However, Cmca Na 4 O was metallic; the states around the Fermi level were all mainly contributed by the Na 3p and 3s orbitals and O 2p orbitals (Figure 4f). Similar electride suboxides, Li 6 O [54] and Mg 3 O 2 [62], have also been reported at high pressure. Na 4 O is a non-superconducting metal electride.
To show the general trend of electronic properties of the Na-O compounds, we summarize the DOSs at the Fermi level for various Na-O compounds at 300 GPa as a function of Na content in Figure S3 in the Supplementary Materials. It can be seen that all the O-rich compounds were metallic due to their electron-deficient character as aforementioned. For the Na 2 O 2 and Na 2 O compounds, the octet rule was achieved as the peroxide O 2 2− group or O 2− anions acquired exactly two electrons from the two Na atoms, leading to an insulating character. The Na-rich compounds, Na 3 O and Na 4 O, should be metallic due to the existence of excess electrons. However, the formation of the 0D electride made Na 3 O an insulator.

Conclusions
In summary, we used systematic structure exploration and first-principles calculations to construct a high-pressure stability field and convex hull diagram of the Na-O system with different stoichiometries at pressures of 50-300 GPa. Four previously unknown stoichiometries (NaO 5 , NaO 4 , Na 4 O, and Na 3 O) and four new phases of known stoichiometries (P2/m and Cmc2 1 NaO 2 and Immm and C2/m NaO 3 ) were predicted to be thermodynamically stable. Remarkably, the O-rich stoichiometries showed all O atoms to exist in quasimolecular O 2 units in a metallic state. Calculated O-O bond lengths and Bader charges were 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) as electrides with strong interstitial electron localization. Electrons in C2/c Na 3 O localized to 0D, making the compound an insulator. In contrast, Cmca Na 4 O was revealed as a 1D electride with metallic features. This work provides guidance for further experimental studies of the properties of the Na-O system.

Supplementary Materials:
The following are available online at https://www.mdpi.com/article/ 10.3390/ma14247650/s1: Figure S1. Phonon dispersion curves of the predicted Na-O compounds at the respective stable pressures; Figure S2. The PDOS of the predicted O-rich Na-O compounds; Figure S3. The DOS at the Fermi level versus sodium content of Na-O compounds at 300 GPa; Table S1. Structure details of the conventional unit cell of Na x O y from the CALYPSO structure searches at different pressures and auxiliary POSCAR files; Table S2. Calculated O-O bond lengths and Bader charges.