Barium-Nitrogen Phases Under Pressure: Emergence of Structural

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Barium-Nitrogen Phases Under Pressure: Emergence of Structural Diversity and Nitrogen-Rich Compounds Bowen Huang, and Gilles Frapper Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b02907 • Publication Date (Web): 15 Oct 2018 Downloaded from http://pubs.acs.org on October 17, 2018

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Chemistry of Materials

Barium-Nitrogen Phases Under Pressure: Emergence of Structural Diversity and Nitrogen-Rich Compounds Bowen Huang†,‡ and Gilles Frapper*,‡ †College ‡IC2MP

of Materials Science and Engineering, Hunan University, Changsha 410082, PR China

UMR 7285, Université de Poitiers - CNRS, 4, rue Michel Brunet TSA 51106 - 86073 Poitiers Cedex 9, France.

ABSTRACT: Although the potential of polynitrogen as a high-energy density material (HEDM) has attracted attention, the difficulty of preserving polynitrogen thwarts attempts to discover molecular and extended nitrogen structures. Mixing nitrogen with electropositive elements to obtain viable solid-state compounds represents one approach to overcome thermodynamic/kinetic instability. In pursuit of barium nitrides within the Ba−N family, we theoretically explored the ground/meta-stable structures from ambient pressure up to 100 GPa. Crystal structure prediction (CSP) based on evolutionary algorithms and density functional theory identified 13 stoichiometries and 24 stable structures; several metastable phases were dynamically stable. Pressure and barium/nitrogen ratio represent controllable factors for polynitrogen net preparation. Four types of phases could be classified based on nitrogen structural dimensionality: isolated nitrogen atom; nitrogen molecules, e.g. N2 dumbbells, linear N3 azides, N4 zigzag units, N5 pentazolate, N6 six-membered rings; 1D polythiazyl S2N2-like nitrogen chains; and 2D polymeric nitrogen layers. Interestingly, P63/mcm-Ba3N, R-3m-Ba2N, and C2/m-Ba3N2 have predicted electride properties. Notably, we observe electronic property changes in the chargebalanced Ba3N2 compound as pressure increases. Solid-state Ba3N2 changes from a conducting electride at ambient pressure with encapsulated anionic N2 dumbbells and isolated N atoms to a nitride semiconductor above 5 GPa in which isolated N3ions are trapped within a Ba2+ ocean–as expected for text-book charge-balanced structures–and is metallic above 25 GPa. In addition, ab initio molecular dynamics analysis indicate nitrogen-rich BaN2, BaN4, and bis-pentazolate Ba(N5)2 are quenchable to ambient pressure, suggesting these polymeric nitrogen networks can be preserved up to at least 600 K; these quenchable phases are promising candidate HEDMs.

1. Introduction Nitrogen constitutes about 78% of the earth’s atmosphere, making it the most abundant uncombined element accessible to man and a potential natural resource in chemistry. However, dinitrogen N2 is mostly unreactive at atmospheric pressure and room temperature, mainly due to its strong triple N≡N bond, which has a short bond length of 1.10 Å and high dissociation energy of 945 kJ/mol. The N ≡ N triple bond is much stronger than the N=N double bond (418 kJ/mol) or N–N single bond (160 kJ/mol).1,2 Molecules and ions containing nitrogen atoms connected by unstable single or double bonds have been proposed to decompose to very stable N2 molecules with the release of large amounts of energy. Therefore, potential applications of molecules and ions containing nitrogen atoms as propellants, explosives and pyrotechnics have been envisaged.3–5 Unfortunately, neutral polynitrogen compounds are metastable and are expected to have a small energy barrier towards decomposition (Scheme 1), such as the long-sought but still unobtained tetrahedrane.6 Therefore, these predicted Nn species are very reactive. Nevertheless, the quest for materials with a high nitrogen content is still considered a ‘Holy Grail’ in science, due to

their chemical interest and potential as environmentally friendly high-energy density materials (HEDMs). In an attempt to overcome these kinetic and thermodynamic issues, chemists and physicists have proposed various conceptual and experimental strategies to obtain polynitrogen-containing compounds in molecular and solid states.7–20 We recently proposed that mixing an electropositive element A or molecular species with nitrogen may lead to stable solid-state AxNy compounds.13 In the nitrogen-rich crystalline phases, the polynitrogen anionic (N)xq- nets would be stabilized by a sea of cations. To the best of our knowledge, only two ionic nitrogen-based species have been experimentally characterized: the well-established metastable azide N3-, finite N5+ chain,21,22 and the cyclo-pentazolate anion N5-.16,23– 25

Another strategy to obtain “polymerized nitrogen” is to modulate the pressure to overcome the high kinetic barriers encountered in such processes and to thermodynamically stabilize the AxNy products, as illustrated in Scheme 1. Then, the resulting high-pressure compound may be quenchable to ambient conditions.

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In previous research (Mg13, Ti26, Mo27, Zr28), we combined these concepts – mixing an electropositive element A or molecular species with nitrogen and modulating the pressure – to predict novel polynitrogen-based materials. In this study, we focused on the pressure range from 0 up to 100 GPa, as these pressures can now be easily reached experimentally in diamond anvil cells. We investigated the possible formation and stability of molecular and polymeric nitrogen motifs in the Ba-N binary system under pressure, following our work on Mg-N binary phase diagrams.13 Compared to Mg2+, the larger size of Ba2+ should allow more nitrogen atoms around the cation. Moreover, the peculiar properties of barium under high pressure, such as its electronegativity, polarizability, and the so-called s-d transition,29 may lead to some interesting electronic properties in the Ba-N binary system. Structure searches for (meta)stable Ba-N compounds were performed using an unbiased structure prediction method, based on the evolutionary algorithm, in conjunction with first principles density-functional approaches to evaluate total energies and forces. We predicted the emergence of several (meta)stable nitrogen networks in thirteen different compositions upon compression, namely Ba:N = 3:1, 2:1, 3:2, 1:1, 2:3, 1:2, 3:8, 1:3, 1:4, 1:5, 2:11, 1:6 and 1:10. To the best of our knowledge, only four of these stoichiometries are experimentally known (3:1, 2:1, 1:2, 1:6).7,30–32

Scheme 1. Schematic energy profile of molecular N2 to polynitrogen compound reactions. The stabilizing effects of pressure and/or s-block element mixing are highlighted. Our calculations indicated that nitrogen atoms would form at high pressure, in addition to isolated nitrides, N2 dumbbells, linear N3 azides, N4 zigzag units, pentazolate N5 rings, 5-membered rings with terminal nitrogen N6 motifs, benzene-like N6 rings, infinite nitrogen-based chains, and nitrogen layers. We rationalized the shapes of these nitrogen structures through chemical bonding analysis and thus explained the electronic properties of the identified compounds. Interestingly, a metal electride to semiconductor to metal sequence is observed in charge-balanced Ba3N2

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under pressure. Moreover, a nitrogen-rich pentazolatebased phase, Ba(N5)2, is located at the ground state. Finally, we explore the properties and potential applications of BaN compounds as HEDMs. 2. Computational Details To identify stable ground-state structures and compositions within the binary Ba-N system, a variablecomposition evolutionary algorithm (VC-EA) implemented in the USPEX code33–35 was employed to scan the configurational, structural and composition spaces of BaxNy (where x and y are positive integers) and seek the local minima on the energy landscape. Thus, the VC-EA enabled identification of specific compositions in the binary Ba-N system at given pressures; in this case, atmospheric pressure and 10, 50 and 100 GPa (see Figure 1). Finally, fixed composition EA structural searches were undertaken for given (x, y) compositions and pressures to check the lowest energetic phase on the potential energy surface (PES) had been found. The variable- and fixedcomposition EA have previously been described in detail, 24–26. In our study, the total number of atoms in the primitive cell was up to 30. Technical details of the USPEX evolutionary structural searches are given in the Supporting Information section S1.1. Structure relaxations (shape, volume, atomic positions) were performed according to density functional theory (DFT) within the framework of the all-electron projector augmented wave (PAW) method,36 as implemented in the VASP code.37 We adopted the Perdew-Burke-Ernzerhof (PBE) functional38 at the generalized gradient approximation (GGA)39 level of theory, with PAW potentials for barium and nitrogen atoms with radii of 2.8 a.u. for Ba ([Kr] core) and 1.5 a.u. for N ([He] core), a planewave kinetic energy cutoff of 600 eV, and a uniform, Γcentered grid with 2π × 0.03 Å-1 spacing for reciprocal space sampling. All of the (meta)stable structures were optimized at pressures from 1 atm up to 100 GPa until the net forces on atoms were below 1 meV Å−1 and the total stress tensor deviated from the target pressure by ≤ 0.01 GPa, resulting in enthalpies that converged to better than 1 meV per atom (lower than a chemical accuracy of 1 kcal/mol, i.e., 0.04 eV/atom).40 Computed structural parameters and energies are given in the Supporting Information sections S2 and S3, respectively. The dynamic stability of the statically relaxed structures was established by the absence of imaginary phonon frequencies, which were computed using the finite displacement method implemented in the PHONOPY code41 (see phonon dispersion curves of BaxNy phases in the Supporting Information section S4). In addition, the effect of zero-point energy (ZPE) on the stability of Ba-N compounds was studied. The inclusion of ZPE only moderately shifted the fields of stability, but did not change the topology of the phase diagram. Thus, the energies presented are non-ZPE corrected. The thermodynamic stability of the BaxNy system was examined using the enthalpies of formation over the pressure range


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of 0-100 GPa. At 0 K, the ground-state enthalpy of formation ∆rHf is defined as: ∆rHf(BaxNy) = H(BaxNy) – xH(Ba) – yH(N) where H = Ee + PV and H, Ee, P, and V are enthalpy, total electronic energy, pressure, and volume, respectively. As references, the body-centered cubic (bcc, Im-3m) and hexagonal-closed packed (hcp, P63/mmc) barium structures and Pa-3, Pbcn, P21/c, P41212, I213, Pba2 and I-43m structures for nitrogen at their respective stability ranges were used. To perform chemical bonding analysis, we carried out single-point calculations (using the geometries obtained from VASP) to calculate the density of states (DOS, displayed in the Supporting Information section S5), crystal overlap Hamilton population (COHP, LOBSTER package), and electron localization function (ELF). DOS, crystal overlap orbital population (COOP), and molecular orbital diagrams are also obtained using the extended Hückel theory (eHT) Yaehmop code42. CRYSTAL 17,43 a quantum code in which the Bloch functions of periodic systems are expanded as linear combinations of atomcentered Gaussian functions, was employed to analyze the electride properties of barium-rich crystalline compounds in more detail (band structures, DOS). The technical details of the CRYSTAL17 periodic calculations are given in the Supporting Information section 1.3. Images of the crystalline structures were produced using VESTA software.44

to cover majority of metastable phases with affordable calculation cost. Other metastable nitrides might lie well above this limit,8,45 but our metastable structure exploration of 13 BaxNy compositions is obviously limited by computational resource as a tremendous effort is needed nowadays to get the phonon curves of each selected structure. These structures are metastable in the binary Ba-N phase diagram, but may appear experimentally as so-called viable structures for kinetic reasons.46 Metastable structures are of great significance, and in practice can often be synthesized by choosing the appropriate precursors and carefully controlling the reaction conditions (pressure, temperature, quench rate, etc.). Moreover, we checked the quenchability of selected high-pressure nitrogen-rich structures, e.g., BaN4 and BaN10, by examining their kinetic and thermal properties. We performed ab initio molecular dynamics simulations up to 1000 K. A crystalline structure is definitively termed viable if no structural transformations are observed in the nitrogen network, i.e., an absence of nitrogen bond breaking after a long simulation (10 ps), indicating the existence of a substantial kinetic barrier that facilitates formation and trapping of viable (meta)stable structures.

3. Results and Discussion All of the proposed solid-state BaxNy compounds are stationary points on the potential energy surface, located on or above the Ba-N convex hull. We verified that each phase meets two criteria of stability: (i) Dynamical criterion: each structure is dynamically stable, as indicated by the absence of imaginary frequencies in all phonon dispersion curves. The corresponding stationary point on the PES is a local enthalpy minimum, i.e., a stable or metastable crystalline solid. (ii) Thermodynamic criterion: a thermodynamically stable BaxNy compound must be more stable than any isochemical mixture of the elements or other BaxNy stoichiometries at a given pressure. Thus, a stable structure must lie on the convex hull constructed on the plot of the formation enthalpy versus composition N/(Ba+N). If not located on the convex hull, strictly speaking, the phase is thermodynamically unstable and might decompose into other BaxNy stoichiometries and/or elements, unless the kinetic barrier is sufficiently high – as encountered in metastable phases such as the experimental Ba(N3)2 azide.30 We also considered metastable phases with different covalent nitrogen nets, and selected the metastable phases with exothermic formation reactions (∆rHf < 0 meV/atom) that are close to the convex hull (∆rHf < 150 meV/atom) or which have been experimentally synthesized. The 150 meV/atom arbitrary criterion is aim

Figure 1. Convex hulls for the Ba-N system at selected pressures. Solid squares denote stable structures, empty squares represent metastable structures. The space group is indicated for each novel stable structure. 3.1. Thermodynamic stability. Stable compounds, which form at the thermodynamic convex hull (Figure 1), were identified at selected pressures, and their stability fields are shown in the pressure-composition phase diagram (Figure 2). It is noteworthy that our EA searches successfully reproduced the experimentally known Ba3N,32 Ba2N,31 BaN247 and BaN630,48 structures at atmospheric pressure. When the pressure was increased from 0 to 100 GPa, 13 stable stoichiometries emerged, including ten Nrich stoichiometries, namely BaN, Ba2N3, BaN2, BaN3, Ba3N8, BaN4, BaN5, Ba2N11, BaN6 and BaN10, and three Ba-rich compositions, Ba3N2, Ba2N and Ba3N. Several stable Ae-N



stoichiometries have been predicted within the same pressure range for Be,14 Mg,13,49 and Ca50. The diversity of stable stoichiometries in Ae-N phases increases as Z(Ae) increases. The increase in cation size between Be to Ba allows more nitrogen atoms around each cation center. Note that the expected charge-balanced 3:2 composition has not yet been characterized in the Ba-N phase diagram, while our EA searches locate this Ba3N2 composition on the convex hull up to 100 GPa.

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Figure 2. Pressure-composition phase diagram for the Ba-N system from 0 to 100 GPa. The stable phases are indicated by bold lines, and metastable phases are depicted by thin, red, dashed lines. The blue italic numbers represent the thermodynamic stability ranges, while the black, non-italic numbers denote the phase transition pressures. As shown in Figure 2, these BaxNy compounds undergo a series of phase transitions in their stability domains. Twenty-four stable phases were predicted; their covalent nitrogen-nitrogen nets are displayed in Table 1, followed by the energetics of the phases, and their structural and bonding properties. Moreover, four metastable phases were located and are discussed thereafter (see Table 2 and Table S1).Note that we recalculated our binary convex hulls using the recently released SCAN (strongly constrained and appropriately-normalized) meta-GGA functional, known to be theoretically superior than PBE-GGA for calculation of energies in solids.51,52 The results are given in SI section S7. We show that the energetic trends are preserved, with SCAN enthalpies lower than the PBE-GGA values, in validation of our methodological approach.

Table 1. Chemical features of predicted stable barium-nitrogen BaxNy compounds. Structure information Single atom Single atom and N2 dumbbells

N2 dumbbells

N2 dumbbells and linear N3 units Linear N3 units Finite N4 chains Five-membered rings

Nitrogen network

Composition Ba3N Ba2N Ba3N2 Ba3N2

VECa 11 9 8 8

Space group and associated pressure stability rangeb P63/mcm, 0-1 R-3m, 0-8; P-3m1, 1-57; I4/mmm, >57 P-1, 5-25; C2/c, >25 C2/m, 0-5

BaN Ba2N3 BaN2 Ba3N8 BaN4 BaN6 Ba2N11

7 6.3 6 5.8 5.5 5.3 5.4

P21/c, 13-47; P21/m, 47-70; C2/m, >70 C2/m, 14-83 C2/c, 0-24; C2/m, 24-63 Cmmm, 6-64 P6/mmm, 4-30 Fmmm, 0-5 P-1, 6-14

BaN6

5.3

P21/m, 5-9

BaN2

6

P21/c, >63

BaN5 BaN10

5.4 5.2

Imma, 25-80 P-1, >12


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Chemistry of Materials 1D armchair chains; 1D chains linked by non‐planar cis‐bent N4 units 1D infinite helical chains

aValence

BaN4

5.5

P41212, 30-48; C2/c, > 48

BaN3

5.7

C2/c, 99-100

electron concentration of BaxNy is given in brackets; VEC = (2x+5y)/(y).

bPressure

in GPa. The pressure range corresponds to the domain of thermodynamic stability.

Studied pressure range: [0 to 100 GPa] 3.2. Structure and bonding in BaxNy phases. Based on the structural arrangement and dimensionality of the covalent nitrogen network, the variety of crystal structures could be classified into four different categories (see Tables 1 and 2): structures with (1) isolated nitrogen atoms, as found in Ba3N, Ba2N, and Ba3N2; (2) encapsulated moleculelike covalent anionic units, such as N2 dumbbells, linear triatomic N3 units, bent N4 finite chain, five-membered rings N5 and N5-N, and six-membered rings N6 as found in Ba3N2, BaN, BaN2, Ba2N11, Ba5N7, BaN5, or BaN6 or BaN10; (3) 1D infinite nitrogen chains (BaN3, BaN4 and BaN5); and finally (4) 2D covalent nitrogen layers alternating with barium sheets (BaN6). This structural classification can also be applied to other alkaline and alkaline earth nitride AxNy compounds. The electronic and geometric structures of the BaxNy phases were examined to better understand their chemical bonding. Throughout this article, electron transfer is considered to occur from electropositive barium atoms into the polynitrogen sublattice. Thus, a Ny network bears 2x valence electrons (ve) per formula unit. Nevertheless, under pressure, the 6s orbital – as well as the low-lying 5d levels of barium – may also participate in bonding crystal orbitals. Therefore, a thorough exploration of the electronic properties of BaxNy is required through a careful analysis of the computed DOS, COHP, ELF plots, charge density, and Bader charges, as well as via a molecular orbital approach. As a first guide, a useful parameter for rationalizing structural properties is the valence electron concentration (VEC), which is defined as VEC = (2x+5y)/y for BaxNy compounds. For VEC = 8, the octet rule is verified for each nitrogen, i.e., N3-, as in the charge-balanced Ae3N2 compound. Thus, in barium-rich phases, in which VEC > 8, the N ions remain isolated. In nitrogen-rich phases (VEC < 8), the nitrogen anions can be viewed as nuclei with unpaired electrons. Therefore, nitrogen-nitrogen bonds are expected to fill the octet; molecular or extended covalent nitrogen networks are encountered. Indeed, this is what we observed and will describe in detail. Nevertheless, remember that the formal charge distribution does not reflect the actual charge transfer.

covalent high-pressure cubic gauche cg-N (I213) phase at 0, 10, 50 and 100 GPa are 1.41 Å, 1.40 Å, 1.37 Å, and 1.34 Å, respectively. These values help us to guide assignment of nitrogen-nitrogen bonds with the help of Lewis rules to rationalize the local structural environments in nitrogen motifs using VSEPR theory. 3.2.1. A pressure-induced conducting electridesemiconductor transition in Ba3N2. The solid-state alkaline earth nitride Ae3N2 is a textbook case of a chargebalanced compound in which ions follow the octet rule, [3 Ae2+, 2N3-]. However, based on our current knowledge, there is no experimental evidence of a 3:2 composition in the barium-nitrogen binary phase diagram. Interestingly, our theoretical investigation shows the Ba3N2 compound is thermodynamically stable from ambient pressure up to 100 GPa (see Figure 2). This finding invites experimentalists to search for this 3:2 composition, which is experimentally known in isoelectronic Ae3N2 (Ae = Be, Mg, Ca).13,49,50 According to our calculations, C2/m Ba3N2 is the lowest enthalpy structure between 0 to 5 GPa. Above 5 GPa, a P-1 high-pressure phase becomes lower in enthalpy than C2/m; 5 GPa is easily accessible in today’s high-pressure experimental setups. P-1 remains thermodynamically stable up to 25 GPa, when C2/c comes into existence (see Figure 2). Our computed phase transition sequence for Ba3N2, C2/m → P-1 → C2/c, does not follow the sequences proposed for isoelectronic Be3N214, Mg3N2,9 and Ca3N240. Moreover, our predicted Ba3N2 phases are all lower in energy than the previously published phases53 (see the E(P) curves of selected Ba3N2 phases in Figure S18).

We recall that the lengths of N-N bonds are roughly 1.10 Å for the triple bond, 1.25 Å for the double bond and 1.45 Å for the single bond at ambient conditions. For calibration, the N-N single bond distances in the three-dimensional



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atmospherically stable C2/m Ba3N2 phase, namely (Ba2+)6(N24-)(N3-)2(2e-), an electron-rich structure. To trace these “free” electrons in the layered Ba3N2 structure, we computed the partial electron charge density of this phase and looked for high values in the plots displayed in Figure 4.

Figure 3. Calculated structures of Ba3N2. (a) C2/m Ba3N2 at 1 atm (b) viewing the Ba3N2 slab based on two hexagonal Ba monolayers with (c) encapsulated N2 units and N atoms in octahedral sites. (d) P-1 Ba3N2 at 10 GPa and (e) C2/c Ba3N2 at 50 GPa. Ba and N are represented by large green and small grey spheres, respectively. Remarkably, the C2/m phase present at atmospheric pressure contains encapsulated N2 dumbbells and isolated N in distorted Ba6 octahedral sites, as shown in Figure 3, while the experimentally known Ae3N2 phases present only N3- anions surrounded by six metal ions. The C2/m structure contains stacked hexagonal layers of Ba3N2 separated by an interlayer region of 3.85 Å. Within the Ba3N2 slab, the shortest Ba-Ba separations are computed at 3.71-3.99 Å, compared with the Ba-Ba nearest neighbor distances of 3.92 Å in ionic solid BaO.54 Thus, Ba3N2 can be viewed as containing divalent barium, (Ba2+)6(2N, N2)12-. The Ba-N separations are 2.67-2.91 Å and 2.51-2.84 Å for NBa6 and N2Ba6, respectively. The encapsulated nitrogen ions are N3- nitrides stabilized by Ba2+ cations through ionic bonds. What charge has diatomic N2? The crystallographic independent N2 unit has a N-N bond length of 1.35 Å. This distance is greater than that of the experimentally reported diazenide BaN2, 1.24 Å7 (1.25 Å in HHN=NH), and smaller than that of pernitride [N2]4- ions which have N-N bond lengths of about 1.40 Å55,56 (1.45 Å in hydrazine H2N-NH2).57 The COHP and MO analysis for the N2 unit allows us to assign a formal charge of -4 per N2 (see Figure 4); the filling of the two antibonding π* orbitals of N2 is computed at 100%, resembling the expected value of 100% for pernitride N24-. The shortened single bond observed in [N2]4- is due to a nitrogen 2p orbital and barium 5d orbital overlap (see the projected Ba and N DOS in Figure S13). Fewer than four electrons are transferred from barium to nitrogen. Therefore, the following formulation is proposed for the

Figure 4. (a) Total and projected DOS and (b) -COHP for C2/m Ba3N2 at 0 GPa. Schematic molecular orbitals of N2 are displayed (see the MO diagram in Figure S8). Partial charge density maps for the (010) plane of C2/m Ba3N2 calculated using energy ranges of (c) -0.5 eV ≤ E ≤ 0.0 eV and (d) -2.0 eV ≤ E ≤ -1.0 eV. The Fermi level is located at E = 0.0 eV. The contour map of the partial electron density, just below the Fermi level, is very informative: we observe electron density maxima in the interlayer space between cationic (Ba3N2)+ slabs. In the -2 to -1 eV energy range, the electrons are localized at the isolated nitrogen. High electron density is observed in the interstitial regions and N2 units in the energy window of -0.5 eV, i.e., up to the Fermi level, which is a typical signature of an electride. Combining the DOS and partial charge density analysis, we conclude that Ba3N2 is a conducting 2D electride. Nonatom-centered electrons act as intercalated anions, holding the cationic Ba3N2 layers together via Coulomb attraction. Unexpectedly, at ambient pressure, Ba3N2 belongs to the layered subnitride family, such as Ba2N, and is not a charge-balanced Zintl Ae3N2 compound (Ae = Be, Mg, Ca). Finally, we hypothesized that a layer of [Ba3N2]+(e-) could be separated from the bulk material. Our DFT calculations predict an exfoliation energy of 125 meV/atom for Ba3N2, which can be compared with 264 meV/atom for [Ca2N]+(e-).58 Above 5 GPa, a P-1 polymorph appears as the lowest enthalpy structure and is thermodynamically stable. This phase features isolated nitrogen nuclei that occupy cavities inside a barium sublattice, as depicted in Figure 3d. Each N atom has five nearest Ba2+ neighbors located at a distance less than 2.76 Å, while Ba is 3- and 4-coordinated to nitrogen. Interestingly, the Ba cages contain empty sites in this P-1 structure, and 1D tunnels are formed, running along the (100) direction. High ELF values correspond to well-localized electrons and are found in the region around nitrogen atoms, in this case, the N3- nitride ions. Zintl phases, such as (Ba2+)3(N3-)2, would be expected to be


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semiconductors or insulators. As the PBE functional is known to underestimate band gaps, we employed the HSE06 calculation, which calculated a band gap of 1.8 eV between the valence and conduction band of P-1 Ba3N2 at 10 GPa (1.1 eV at PBE level). Thus, the C2/m → P-1 phase transition represents a novel example of a pressureinduced metallic 2D electride → semiconducting transition. The ultimate high-pressure phase, which was found for Ba3N2, adopts a C2/c structure (Z = 4) above 25 GPa (Figure 3e). In the C2/c layered structure, each slab consists of two condensed layers of face-sharing NBa8 polyhedra. A separation of 2.24 Å is calculated between two stacked Ba3N2 slabs (shortest Ba-Ba distance of ~3.06 Å). C2/c Ba3N2 undergoes pressure-induced band gap closure around 40 GPa. When pressure increases, the Ba 5d bands broaden and mix with the Ba 6s bands, which is comparable to the s → d transition observed in elemental alkaline earth metals.59 These Ba s-d hybridized states overlap with the occupied N 2p states of isolated N3- anions, conferring conductivity to C2/c Ba3N2 at high pressure, regardless of the weak density of states at the Fermi level. To summarize, we predict the Ba3N2 compound goes from: Conducting electride→Semiconductor→Metal over the pressure range from 0 to 100 GPa; this is an interesting feature for experimentalists. 3.2.2. Ba-rich electrides: Ba3N and Ba2N. Two stable Ba-rich compositions are proposed at ambient pressure, namely, Ba3N and Ba2N, but only Ba2N is thermodynamically stable up to 100 GPa (see Figures 1 and 2). One of the common features of these compositions is the presence of isolated nitrogen nuclei trapped inside barium sublattice cavities, as depicted in Figure 5. Ba3N and Ba2N have VEC values of 11 and 9, respectively, higher than the 8 expected for the octet rule. Therefore, an extra electron, e-, is expected over the whole structure. 3.2.2.1. Ba3N. In Ba3N, the anti-TlI3-type structure (space group P63/mcm) is most enthalpically stable at 1 atm, in good agreement with experimental findings.32 The calculated lattice constants are also consistent with experimental data (see Table S1). The Ba and N atoms are arranged in an infinite chain of face-sharing barium octahedra, centered with nitrogen atoms (Figure 5). P63/mcm exhibits hexagonal close packing of [Ba6/2N] chains. The calculated Ba-N distance within the chains is 2.75 Å, slightly lower than the sum of the ionic radii of 2.9 (Ba2+ N3-).60 The closest N-N separation is 3.55 Å. Such short distances can be explained by assuming strong ionic interactions within the chain, according to [(Ba2+)3(N3-)]3+. This electron repartition leaves an excess of three electrons for metallic bonding between chains, or for ionic interstitial electrons with (Ba3N)3+ chain interactions. The latter bonding mode explains the long inter-chain Ba-Ba separations of 4.9-5.0 Å, which can be compared with the calculated Ba-Ba distance of 4.3 Å in Ba bcc metal. ELF analysis confirmed the existence of a high-density of interstitial electrons (Figure 5). The cationic (Ba3N)3+

chains/rods interact with interstitial electrons localized in the one-dimensional void of the P63/mcm structure. Also, Ba3N is a 1-D electride at 1 atm (Similar results have been confirmed by Park et al.,61 recently). Above 1 GPa, Ba3N is thermodynamically unstable and undergoes disproportionation to Ba + Ba2N.

Figure 5. P63/mcm structure of Ba3N at 1 atm. (a) Isosurface of ELF with a value of 0.6. Face-sharing Ba6 octahedra centered with N atoms are highlighted. (b) ELF contours in the (001) plane; hexagonal close-packed [Ba6/2N] chains are shown. Bonds between Ba (large green) and N (small grey) are outlined. 3.2.2.2. Ba2N phases. Our structure searches correctly identified the experimental R-3m Ba2N structure as the global minimum at 1 atm.31 At 8 GPa, a new phase of P-3m1 symmetry becomes most stable. The calculated transition pressure is in agreement with the experimental value of 2 GPa.62 The P-3m1 phase remains the minimum enthalpy structure up to 57 GPa, where another phase of I4/mmm symmetry emerges as the ground state; these crystal structures are given in Figure 6. Note that the transition phase sequence is not in agreement with the recently proposed R-3m (4 GPa)  P-3m1 (9.5 GPa)  Cc  I4/mmm sequence.63 This discrepancy is discussed in the Supporting Information section S8.2. Atmospheric R-3m Ba2N has an anti-CdCl2-type structure. The hexagonal layered unit is composed of Ba6/3 edge-sharing octahedra centered by a nitrogen atom with a Ba-N distance of 2.79 Å, typical of ionic bonding. In this phase, nitrogen exists as N3-: the closest N-N separation is 4.06 Å, much longer than the typical 1.45 Å N-N bond length, as in H2N-NH2 hydrazine.57 Thus, each Ba2N unit can be regarded as a positively charged ionic slab, [(Ba2+)2(N3-)]+. These cationic [Ba2N]+ layers are separated by a vacuum of 4.60 Å, and stacked in an ABC fashion along the [001] direction, as shown in Figure 6d. To balance the cationic charge of the [Ba2N]+ layer, the interlayer spacing confines the extra electrons, resulting in a [Ba2N]+ plus econfiguration. This assumption applies in isoelectronic and isostructural Ca2N64 and Li4N.65 The ELF profile of R3m Ba2N in Figure 6a illustrates the unshared electron interaction between interstitial electrons X- (X is a void) and the Ba2N+ layers and reflects the ionic bonding property. The DOS in Figure 6d indicates Ba2N is a metal. The broad DOS peak around EF is mainly composed of a non-atom-centered orbital located at X (voids) with small contributions from Ba and N, as shown in the total and projected DOS. The integrated electron density of the conduction band from -2 eV to 0 eV is equal to 0.45 e/f.u.,



is consistent with the chemical view of the [(Ba2+)2(N3-)]+eelectride. To summarize, this R-3m dibarium nitride crystal may be viewed as cationic Ba2N+ layers alternating with confined anionic electrons, which is the signature of a twodimensional conducting electride.

Figure 6. Ba2N crystal structures (a, c, e) and total and projected DOS and associated ELF contours (isosurface value = 0.8) (b, d, f) of R-3m at 0 GPa (a, d), P-3m1 at 10 GPa (b, e) and the I4/mmm phase at 100 GPa (c, f). The anti-CdI2-type P-3m1 structure is computed to be the most stable phase up to 57 GPa. The crystal structure is closely related to that of the atmospheric phase (see Figure 6b) and presents /AA/ stacking of Ba2N layers based on Ba6/3 edge-sharing octahedra centered by a nitrogen atom. At 10 GPa, the Ba-N distance is 2.62 Å, reflecting ionic bonding character, while the interlayer Ba-Ba separation is computed at 3.57 Å, analogous to that of BaO (Ba2+Ba2+=3.83 Å at 10 GPa). P-3m1 Ba2N maintains the 2D metallic electride property (See Figures 6b and 6e). Above 57 GPa, a tetragonal phase becomes the groundstate structure (space group I4/mmm, MoSi2-type), in which the coordination number of nitrogen increases from six to eight. Ba2N presents a bcc-substructure as displayed in Figure 6c. This phase may be alternatively described as AB-stacked Ba2N layers, composed of fused distorted Ba8/4 cubes centered by N atoms. In the distorted NBa8 cubes, the Ba-Ba distance is 2.72 Å and 3.00 Å, and Ba-N distance is 2.52 Å at 100 GPa. The slab interspacing is computed at 2.94 Å. No localized electrons are located in the void layer. Moreover, DOS analysis identified a s → d transition in I4/mmm Ba2N; this a well-characterized feature in solid alkaline and earth alkaline metals under high pressure. A metallic bond character is present in high-pressure I4/mmm Ba2N. To summarize, the 2D electride property of Ba2N is not maintained in the high-pressure metallic

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I4/mmm phase, although its Ca2N analog has been claimed to be a 2D electride over the range between 0 to 100 GPa with a predicted R-3m → Fm-3m → I4/mmm sequence.50 3.2.3. Molecular-like units and extended nets in nitrogen-rich BaxNy compounds. 3.2.3.1. BaN with pernitride N24-. Above 13 GPa and up to 100 GPa, the 1:1 stoichiometry is computed to be a thermodynamically stable system (see Figures 1 and 2). Phase transitions occur as pressure increases: P-1 (metastable)  P21/c  P21/m  C2/m. All structures are given in Table S1. In BaN, each N is formally N2-, leaving one unpaired electron, thus is capable of forming one bond. This structural requirement is observed in all stable phases in the 13-100 GPa range; their respective structures contain encapsulated N2 dumbbells with N-N separations of 1.41 Å (P21/c, 10 GPa), 1.41 Å (P21/m, 50 GPa) and 1.38 Å (C2/m, 100 GPa). These values indicate N-N single bond character, as expected for a 14-ve diatomic A2. The N24- dumbbell is a solid-state equivalent of molecular F2, with fully occupied πg* levels (See the N2 MO diagram in Figure S8). All atoms obey the octet rule in (Ba2+)2(N24-), and the Zintl stable P21/c phase would be expected to be semiconducting, at least at low pressure; this feature was observed in the HSE06 DOS in Figure S6. However, at higher pressure, the calculated DOS for P21/m at 50 GPa and C2/m at 100 GPa show these BaN phases are all metallic in character (See DOS in Figure S7). In fact, close inspection of the DOS shows the 6s/5d Ba orbitals contribute significantly to the occupied nitrogen levels, a signature of partial covalent BaN character in BaN. Back-donation occurs from the occupied N2 π* levels to the empty Ba levels, explaining the metallic character of BaN. This finding illustrates the limitation of the Zintl rule in the Ba-N system under high pressure; not all valence electrons in electropositive alkaline earth metals are localized in the nitrogen networks. Valence electrons may participate in covalent cation-anion bonds or metallic cation-cation bonds, as found in metallic CaSi66 or K5Sb367. Indeed, the following text shows that such Zintl violation is a consistent feature of the behavior of several Ba/N phases under pressure. 3.2.3.2. Ba2N3 with N2 dumbbells. From 14 to 83 GPa, the C2/m phase is the thermodynamic ground state phase. The structure of this phase is displayed in Figure 7, and can be thought of as being composed of isolated N2 units embedded in the barium framework. Two non-equivalent N2 dumbbells are observed in Ba2N3.


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Figure 7. (a) Structure of C2/m Ba2N3 at 50 GPa (b) and projected DOS. At 50 GPa, the shortest interatomic N-N distance is 1.25 Å, indicating a double bond character. Thus, a formal charge of -2 may be attributed. The other non-equivalent N2 dimer has a N-N separation of 1.34 Å, which lies between that of single (1.41 Å) and double (1.25 Å) bonds. Thus, one may attribute a formal charge of -3 to this dimer, which is isoelectronic to the superoxide O2- species encountered in the experimental paramagnetic KO2 salt (O-O distance of 1.28 Å). To explain the bonding mode in Ba2N3, this compound could be assigned as (Ba2+)4(N22-)(N23-)2. With a charge of -2/-3 per N2, the two antibonding πg* orbitals of N22-/3- are partially filled. Thus, a bond order of 2 is expected in N22- and 1.5 in N23-, which correlate well with the structural properties of the N2 units. In addition, Ba2N3 is a metal between 14 and 100 GPa. 3.2.3.3. BaN2 under pressure, a formal N2+N2 coupling. The 1:2 stoichiometry is stable over the entire pressure range. This 1:2 composition presents a phase sequence of C2/c (24 GPa)  C2/m (63 GPa)  P21/c. The C2/c and C2/m structures consist of N2 dimers sitting in the four-fold channels of a 3D barium network (Figure 8). Up to 63 GPa, the shortest N-N separation is below 1.24 Å, indicating N-N double bond character. According to the Zintl-Klemm concept, BaN2 can be described as Ba2+N22-, and contains 12-electron N2 dimers isovalent to paramagnetic O2. The calculated DOS corroborates these findings (Figure 8): the Fermi level crosses a region mainly based on nitrogen π antibonding states, i.e., the π* of N22-. Half of the π* band is filled. C2/c and C2/m BaN2 are metallic up to 63 GPa. Above 63 GPa, the stoichiometry of BaN2 stabilizes into the P21/c structure shown in Figure 8c. This structure consists of planar zigzag N4 units (with two outer N-N distances of 1.30 Å, and a central distance of 1.32 Å at 100 GPa) along the a direction and contained in the bc plane. These finite chains are separated by isolated Ba2+ atoms. Following ZKC, one may assign a formal charge of -4 to the N4 group, leading to the 24 ve tetraatomic species isoelectronic to the solid-state Bi44- unit in CaBi2.68 Molecular orbital analysis of the zigzag N4 species revealed a substantial energy gap separates the bonding πx level (HOMO) and antibonding πx* level (LUMO), thus one may expect P21/c BaN2 to be a semiconductor. This assumption is verified at ambient pressure (band gap of 0.7 eV) and up to ~20 GPa, but P21/c BaN2 is metallic at higher pressures. When pressure rises, involvement of the Ba 5d states in the Ba-N bonding interaction is observed, a d(Ba) - p(N) band mixing occurs around the Fermi level (see Figure 8f).

Figure 8. Crystal structures (a, c, e) and DOS (b, d, f) for BaN2 phases: (a, d) C2/c at 0 GPa, (b, e) C2/m at 50 GPa, and (c, f) P21/c at 100 GPa. In BaN2, pressure-induced cross-linking of N2 may be evocated: two open-shell N22- bond to give a closed-shell N44- unit. Note that P21/c BaN2 is quenchable up to ambient pressure. The structure and phonon dispersion curve are presented in Figure S4. 3.2.3.4. Ba3N8: alternating Ba2N2 monolayers and Ba(N2)3 slab. Our evolutionary searches uncovered the Nrich Mg3N8 stoichiometry as a thermodynamic ground state at pressures as low as 6 GPa, which are easily achievable in high-pressure synthesis. This phase is stable thermodynamically from 6 to 64 GPa (Cmmm space group, Z = 2). This structure (Figure 9) may be viewed as follows: a hexagonal layer of barium atoms (4 Ba/unit cell) with a N2 dumbbell seated in the hole of each Ba6 hexagon (2 N2/unit cell), and one Ba filling the six-fold channel perpendicular to the 2D hexagonal Ba layers (2 Ba/unit cell) with six N2 units surrounding each isolated Ba (6 N2/unit cell). Within the Ba4(N2)2 monolayer, the NN distance is computed at 1.23 Å, typical of double N=N bonds (see BaN2 in section 3.2.3.3). An electronic structure analysis leads to the conclusion that two electrons occupy the two antibonding π* levels of N2. Thus, N2 is formally N22-, isoelectronic to O2, explaining the expected double bond character. Moreover, unusually short Ba-Ba contacts of 2.97 Å and 3.14 Å are computed within the 6-membered ring Ba6 (at 50 GPa, the Ba-Ba contact is longer than 3.18 Å in hcp-Ba). Looking at the DOS and COHP, we see the Ba states are occupied by ~2 electrons (Ba-Ba and Ba-N bonding). Therefore, one may conclude each monolayer is a formally cationic [(Ba2+)4(N22-)2-2e-]2+ layer in Cmmm Ba3N8. Let us now consider the Ba2(N2)6 slab intercalated between two Ba4(N2)2 monolayers (see Figure 9b). A N-N separation of 1.16-1.18 Å is calculated for the six N2 units, which can be compared to 1.11 Å in free N2. A deep analysis of the DOS and COHP in Figure 9 revealed the two antibonding π* levels of each N2 are occupied by roughly one electron, given an MO explanation of the observed slight N2 elongation. Thus, one may assign a formal charge of -1 per N2 unit. Therefore, each Ba2(N2)6 slab may be viewed as



[(Ba2+)2(N2-)6]2-. To conclude, the Cmmm Ba3N8 phase may be viewed as an alternating anionic [Ba2(N2)6]2- slab and cationic [Ba4(N2)2]2+ monolayer stacked along the [001] direction. As expected from our electronic structure analysis, Ba3N8 is a metal.

Figure 9. Cmmm Ba3N8 phase at 50 GPa. (a) Ba2(N2) monolayer and (b) alternating Ba2(N2) monolayer and Ba2(N6) slab. Distances are given in angstroms. The large spheres indicate barium atoms, and small spheres indicate nitrogen atoms. Green and blue spheres lie in the ab planes, while N2 units (in brown) lie along the c direction. Green contacts are drawn as an visual guide. (c) COHP of the BaBa and Ba-N interactions and (d) pDOS for the monolayer plane. 3.2.3.5. BaN3 containing helical polynitrogen -Nchains. Above 56 GPa, C2/c phase is the lowest structure, and becomes thermodynamically stable above 99 GPa. The structure of the C2/c phase at 100 GPa is depicted in Figure 10. One-dimensional infinite helical chains run into barium channels along [001], with N-N bond lengths of 1.34-1.39 (single/double character), and N-N-N valence angles of ~109° (sp2/sp3 N). As shown in Figure 10c, a resonant structure – among others, and VSEPR rules help to understand the structural features of this anionic helical chain -(N64-)n-. The structure contains bent nitrogen atoms (AX2E2 and AX2E1), single N-N bonds with delocalized π electrons, and repulsive lone pairs that explain its helical form (dihedral angle of 35.4°). At 100 GPa, BaN3 presents a metallic character.

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Figure 10. (a) C2/m BaN3 structure at 100 GPa, (b) structural parameters, and (c) Lewis structure and VSEPR notation of the N6 repeating unit. Distances are shown in Å, dihedral angles in °. 3.2.3.6. BaN4: from molecular to polymeric nitrogen net. BaN4 is thermodynamically stable above 4 GPa, and exhibits three phase transitions up to 100 GPa, the first phase occurring at 4 GPa (P6/mmm), the second at 30 GPa (P41212), and the last at 48 GPa (C2/c). The stable P6/mmm structure contains N2 dumbbells in the prismatic sites of a hexagonal barium network (See Figure S9). At 10 GPa, the Ba-Ba separations are longer than 4.1 Å, and the shortest Ba-N contact is at 2.91 Å, typical of ionic bonds. Thus, N2 dimers formally have a minus charge, (Ba2+)(N2-)2. From this assumption, the N2- MO diagram presents a singly occupied antibonding πg*. Therefore, elongation of the NN bond is expected in respect of neutral N2. Indeed, this is what we observed: at 10 GPa, the NN separation is 1.17 Å in P6/mmm and 1.11 Å in neutral N2. N2- is a radical, as in isovalent nitric oxide NO. These assumptions are validated by the computed electrical conducting property of P6/mmm BaN4; P6/mmm is a metal (See Figure S9). A phase transition occurs at 30 GPa. P41212 becomes the lowest structure in the 30-48 GPa pressure range. The structure features infinite planar 1D armchair-shaped nitrogen chains, intercalated by barium atoms. Such polymeric chains have been recently proposed in CaN4,50 and MgN413 at high pressure. The N-N bond lengths along the nitrogen chain are around 1.33 Å, which is longer than a double bond (1.25 Å), but shorter than a single bond (1.40 Å) at 50 GPa. This intermediate distance is consistent with the bonding picture, in which six π electrons are distributed along the polymeric -(N42-)x- chain. We invite the reader to look at our discussion of the isostructural and isovalent Cmmm MgN4 structure in our recent publication.13 Standard application of the VSEPR theory to this planar chain enabled rationalization of the structural and bonding properties of the poly-N42- chains: each nitrogen atom is bent. The planarity of the entire armchair chain is the result of delocalization, and also of the strong ionic interactions between Ba2+ ions and poly-N42- chains. The DOS for P41212 BaN4 indicates metallic character. At ambient pressure, P41212 BaN4 is dynamically stable, lying 236 meV above the ground state C2/m structure.

Figure 11. C2/c BaN4 structure at 100 GPa. (a) View of the infinite nitrogen chain in Ba channels, (b) selected structural parameters and (c) Lewis structure of poly-N44chain (distances in Å, angles in °; VSEPR AXnEn notation).


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A C2/c phase emerges above 48 GPa, and also contains 1D nitrogen chains running in Ba channels. Each chain is non-planar and may be viewed as two linked, non-planar cis-bent N4 units with a torsional angle of 28.3° at 100 GPa (See Figure 11). The NN bond lengths along the chain lie between that of a double and a single bond (1.28-1.37 Å), and the valence angles are 106.2°-111.2°, typical for bent nitrogen. A small band gap is calculated using the HSE06 method, which indicates semiconductor behavior at 100 GPa. The 1-D polynitrogen net is maintained when pressure is released to ambient conditions, and C2/c is quenchable and lies at 236 meV/atm above the ground state C2/m. In the 1:4 Ba:N composition, pressure may polymerize nitrogen into 1D chains, thus the synthesized highpressure compounds – P41212 and C2/c – may be recoverable at 1 atm. 3.2.3.7. BaN5 with pentazolate rings. The stability range for BaN5 is 25-80 GPa (space group Imma). The structure of this phase is displayed in Figure 12 and is built from hcp Ba layers, with 5-membered N5 rings between layers. Such pentazole rings have been predicted in alkaline and alkaline earth metals MN5 (M = Ca,50 Li,69 Cs,70 Na,16 etc.), and have also recently been observed experimentally in the high-pressure phase CsN5.71 At 50 GPa, the N-N distances range from 1.30 Å to 1.35 Å in the planar pentazolate unit, signaling a delocalized system. The average N-N bond length in the pentazolate N5- is 1.30 Å in LiN5 (40 GPa), 1.30 Å in NaN5 (20 GPa), and 1.33 Å in CsN5 (1 atm) and 1.33 Å in the gas phase. Therefore, it is tempting to assign a formal charge of minus one per N5 ring. This N5- ring, isolobal to C5H5- cyclopentadienyl, has six delocalized π electrons, and follows the Hückel aromaticity (4n+2) and octet rules. Nevertheless, following ZKC, Ba should give two electrons to each N5, as Zhu et al.50 concluded in their study of the electronic properties of predicted CaN5 structure. Note that, with a 2- charge, N52- is a radical species. Thus, a closer look at the bonding is needed. In Imma BaN5, inspection of the DOS shows extensive participation of barium 5d orbitals in the filled levels of the system (See Figure 12). A significant d-orbital population of approximatively 0.55 at the barium atom is computed at 50 GPa. Moreover, a -ICOHP of 0.218 eV/pair is computed for Ba-N contacts. Therefore, the cation-anion interactions cannot be described as purely ionic, and must also have partially covalent character. We propose that the extra electron is delocalized over the Ba-(N5-)-Ba network, which explains the relatively short cation-anion separation of 2.59 Å at 50 GPa.

Figure 12. (a) Structure of Imma BaN5. Ba-Ba green lines are drawn as a visual guide. (b) Lewis structure of N5pentazolate. (c) Projected and total DOS. To summarize, Ba gives one electron to a N5 ring, then N5- follows the 4n+2 Hückel and octet rules, while the remaining electron is delocalized over the whole Ba net via partially covalent Ba-N interactions. This proposed picture explains the metallic property of Imma BaN5 well. 3.2.3.8. Ba2N11 with N3 azide and N2 dumbbells. From 8 to 14 GPa, the P-1 phase of Ba2N11 is stable. Its structure is displayed in the Supplementary Information. One linear N3 and four N2 motifs per f.u. fill the void between two Ba layers. Ba-Ba and Ba-N separation are longer than 4.03 Å and 2.69 Å, respectively, at 10 GPa. The calculated NN separation is 1.18 Å in centrosymmetric N3, typical of the double bonds in azide N3- structures72,73. Thus, it remains formally three electrons to four N2, (Ba2+)2(N3-)[(N2)4]3-. A distance of 1.15-1.16 Å is found for N2 units, i.e., a slightly elongated triple bond induced by partial occupation of antibonding nitrogen π* bands. Ba2N11 is a metal. 3.2.3.9. BaN6: a stable azide crystal. This 1:6 stoichiometry has a small range of thermodynamic stability between 0 to 9 GPa (See Figure 2). At ambient pressure, the Fmmm structure presents eight N2 units coordinated to each barium cation and can be described as a metal-inorganic framework with channels. A Ba(η1N2)6(ηδ2-N2)2 motif is encountered with NN distances of 1.13-1.17 Å, slightly longer that of free N2. Ba-Ba contacts are larger than 4.5 Å, a signature of the presence of isolated Ba2+ cations. Two electrons are transferred from Ba to three N2 units, leading to partial occupation of the antibonding π* nitrogen-nitrogen levels: N-N bonds are activated in this nitrogen-rich compound. Fmmm BaN6 is a metal (see SI). Above 5 GPa, a novel BaN6 phase appears as the thermodynamically ground-state structure up to 9 GPa. This monoclinic P21/m phase has been experimentally proposed at ambient pressure as a metastable azide crystal. As shown in Figure S1, P21/m BaN6 presents two independent azide N3- units, with NN distances of ~1.18-1.19 Å (double bonds) and valence angles of 179.0°-179.9°. Our calculated crystallographic parameters are in perfect agreement with the experimental values (see Supplementary Information). This solid-state compound is an insulator, as expected for Zintl phase (Ba2+)(N3-)2. P21/m diazide barium is quenchable, a metastable phase at ambient pressure lying 33 meV/atom above the N2-based ground-state Fmmm structure.



Beside this azide phase, our CSP searches found several dynamically stable BaN6 phases that do not lie on the convex hull but possess thermodynamically metastable and novel topologies; we will discuss these in the next section. 3.2.3.10. BaN10: a nitrogen-rich phase with two pentazolate rings. Above 12 GPa, a thermodynamically stable BaN10 phase emerges (space group P-1, Z = 2). This phase has the highest nitrogen content in our explored binary Ba-N phase diagram, and also – to the best of our knowledge – of other s-block element nitrides. Two N5 rings per barium cation are stacked along the [001] direction, as displayed in Figure 13. At 50 GPa, NN distances of 1.28-1.31 Å are calculated within the 5membered ring, typical of the six π electron 5-membered ring N5- (delocalized single/double bonds). A large HOMO (π3)-LUMO(π4) gap of 3.4 eV is calculated in isolated pentazolate. In solid-state P-1 BaN10, a large gap separates the valence from the conduction bands, as expected for a Zintl compound.

Figure 13. BaN10 phases. (a) P-1 at 50 GPa and (b) I-42d at 1 atm. (c) Local geometry in the I-42d phase (distances in Å). The green Ba-Ba lines are drawn as a visual guide. Owing to the potential application of this predicted Ba(N5)2 phase as a HEDM, we explored the quenchability of P-1 BaN10, and found that this phase remains dynamically stable at ambient pressure. Nevertheless, a lower pentazolate-containing structure (space group I-42d, Z = 4, see Figure 13b) was located on the PES during our molecular evolutionary search74 and lies 57 meV/atom below the P-1 phase at 1 atm. The I-42d  P-1 phase transition is computed at 8 GPa. Each N5 ring is bonded to four Ba2+ through ionic Ba-N bonds of ~3.01 Å, leaving a free lone-pair per N5 (see Figure 13c), thus each Ba2+ is coordinated to eight pentazolate units. The typical pentazolate N-N bond lengths were calculated (~1.32 Å). We checked the thermal stability of I-42d Ba(N5)2 by running AIMD simulations up to 1000 K for 10 ps (see technical details in Supplementary Information). The 5membered N5- ring motif persisted up to 1000 K. Our findings invite us to search for other nitrogen-rich bispentazolate crystals M(N5)2 where M is a divalent metal

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such as the alkaline earth elements Be, Mg, Ca, Sr or transition metals Fe, Cu, Cd and Zn. These are dynamically, mechanically and thermodynamically stable materials, and we will report the structural and electronic properties of the resulting nitrogen-rich bis-pentazolate crystals in a forthcoming dedicated article. 3.3. Metastable nitrogen-rich phases with novel polynitrogen structures. Metastable polymorphs are routinely observed during material synthesis, e.g., synthesis of azides such as Ba(N3)2, and are currently of great interest as they may possess superior properties for some applications. Depending on the precursors, such as very reactive atomic nitrogen instead of unreactive N2, these thermodynamically metastable compounds may lie on or above the “new” convex hull (see Figure 2 of Ceder et al.8). Remember that EA searches for ground-state crystalline structures generate numerous ‘high-energy’ optimized structures. Therefore, we identified new structures on the potential energy surface of a given BaxNy composition, looking at nitrogen-rich phases, original nitrogen nets, and for structures having a (ΔHconvex hull – ΔHstructure) energy difference lower than 150 meV/atom. All of our selected metastable phases are dynamically stable (no imaginary phonons) and have a negative enthalpy of formation. Moreover, all of these metastable candidates may persist kinetically, as they possess strong delocalized nitrogen-nitrogen bonds. Selected metastable nitrogenrich BaxNy are listed in Table 2. Moreover, beside the following selected metastable nitrogen-rich phases, we have investigated also the 4:3 stoichiometry, a reported experimental one.75 Three metastable Ba4N3 polymorphs are located on the PES, and contain N2 units and isolated N in octahedral voids. We discussed their structural and electronic properties in the Supporting Information section S8. These predicted Ba4N3 are electrides and will be the subject of a dedicated publication. Let discuss on the nitrogen-rich metastable phases, BaN5 and BaN6 phases. 3.3.1. Infinite chains in BaN5. At 100 GPa, our CSP searches lead to a metastable polymorph of BaN5 that contains infinite zigzagging polynitrogen chains encapsulated in barium channels (see Figure 14). NN bond lengths run from 1.27 to 1.36 (single/double character), characteristic of a p-delocalized system. Each nitrogen atom is bent, and the chains are distorted helixes with dihedral angles of 17°-175° along the skeleton. Looking at the DOS, we see that the Ba levels are substantially occupied; thus we propose an ionic picture in which one electron is attributed per linear N5 fragment, as in pentazolate BaN5, leading to [(Ba2+)(N5-)-1e-]. A Lewis structure of linear N5- is given in Figure 14b. This metallic nitrogen-rich phase is not quenchable, and higher in energy by 130 meV/atom than pentazolate at 1 atm.

Table 2. Chemical features of predicted metastable barium-nitrogen BaxNy compounds Structure information

Nitrogen network

Composition


VECa

Space group

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Chemistry of Materials 1D infinitely twisted chains, 2-coordinated N

BaN5

5.4

P1

6-membered ring

BaN6

5.3

P-1(II)

5-membered ring with terminal N

BaN6

5.3

P-1(I)

2D nitrogen network

BaN6

5.3

C2/m

aValence

electron concentration of BaxNy is given in brackets; VEC = (2x+5y)/(y).

Studied pressure range: [0 to 100 GPa] 3.3.2. Rings in BaN6. In the 1:6 stoichiometry, a thermodynamically metastable P-1 phase is the lowest phase above 21 GPa, as shown in Figure 2. Its structure is displayed in Figure 14. Isolated planar N5-N units fill the space between two corrugated barium layers. To the best of our knowledge, such a N6 motif represents a new topology in nitrogen-based compounds. If one assigns a 2charge to N6 (see the Lewis structures in Figure 14d), (N5N)2- is reminiscent of an isoelectronic closed-shell pentazole N5-F molecule. Eight π electrons are delocalized over the planar N5-N ring, explaining the double/single bond character (NN = 1.24-1.37 Å) and the stability of this motif that obeys the Hückel rule with 4n+2π electrons in the 5-membered ring. At 50 GPa, the second lowest metastable phase, BaN6, contains 6-membered nitrogen rings (See Figure 14e). This P-1 (II) structure lies 115 meV/atom above the ground-state N5-N BaN6 phase and 145 meV above the convex hull. Stable 8-π electron N62anions have also been found in AN6 (A = Mg,13,49 Ca,50 …). 3.3.3. C2/m BaN6 with a 2D nitrogen net. A layered BaN6 structure C2/m is observed at 100 GPa, as depicted in Figure 15, with the phonon dispersion curve and DOS shown in Figure S4 and S5. This phase lies 16 meV/atom above the ground-state structure and is located 21 meV/atom from the convex hull. Each bidimensional nitrogen slab >(N4/2N-2)< is intercalated between two barium monolayers (dBa-N = 2.56 Å, dBa-Ba=3.14 Å), and contains covalent single N-N bonds (dN-N = 1.35-1.41). The 6-membered ring N6 has a chair conformation, and all nitrogen atoms follow the octet rule as depicted by the Lewis structure in Figure 15c. (Ba2+)(poly-N62-) follows the ZKC and – as expected – is a semiconductor at 100 GPa (HSE06 level).

Figure 14. Metastable BaxNy phases: (a) P1 BaN5 at 100 GPa, (c) P-1 (I) BaN6 at 50 GPa, and (e) P-1 (II) BaN6 at 50 GPa. Selected Lewis structures of (b) the N5- chain, (d) (N5N)2- ring, and (f) N62- rings. Distances are indicated in angstroms, angles in degrees. VSEPR AXnEm notation is given.



Figure 15. (a) Metastable C2/m BaN6 phase at 100 GPa, (b) view of its nitrogen layer perpendicular to the net, and (c) Lewis structure of its repeating unit. 3.4 High energy-density BaxNy? We investigated the HEDM properties of selected BaxNy compounds and report their energy density and velocity of detonation (VOD) values calculated using the Kamlet-Jacobs empirical equation76 in Table 3 (details of the calculations are given in the Supporting Information section S1.4). We assume that the decomposition products are BaN2(s) and N2(g). The quenchability of nitrogen-rich high-pressure phases was investigated by assessing their dynamic stability at ambient conditions (T = 0 K). None of the proposed phases have imaginary vibrational modes at 1 atm. Moreover, the proposed phases are thermally stable – in the sense that their nitrogen nets are maintained – up to 1000 K (AIMD simulations, see in the Supporting Information section S9). Table 3. Explosive properties for potential HEDMs

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crystalline forms were achieved, ranging from small molecular units composed of a few atoms (azenide and pernitride N2, azide N3, N4, rings N5, and N6) to 1D and 2D nets. Here, barium gives its valence electrons to the nitrogen net, leading to occupation of the antibonding nitrogen states and thus decreasing the dimensionality of the covalent nitrogen sublattice from 3D (pure highpressure nitrogen phase), to 2D (in BaN6), to 1D (in BaNx, x=3,4,6) and 0D (molecular anionic Nx species). These anionic polynitrogen nets are stabilized by ionic interactions under high pressure. The nitrogen-rich highpressure BaN2, BaN4, and bis-pentazolate Ba(N5)2 phases are quenchable to ambient pressure based on our ab initio molecular dynamics analysis, revealing their nitrogen networks can be preserved up to at least 1000 K. Thus, these quenchable phases are promising candidate HEDMs. Finally, we predict the ground-state bis-pentazolate Ba(N5)2 phase, which is the highest theoretically viable nitrogen-rich solid-state compound. We expect our findings will motivate the material science community to transform our in silico proposed BaxNy structures into the real world, e.g. by synthesizing solid-state barium-nitrogen materials.

Phase Space group

Energy density kJ/g

VoD km/s

Detonation pressure kPa

BaN4 P41212

0.623

5.9

234

SUPPORTING INFORMATION

0.626

5.7

213

The supporting information is available free of charge on the ACS publication website at: DOI:

0.577

6.1

204

Methodology details; lattice parameters for all predicted structures; formation enthalpies, density of states and phonon frequency; electride analysis detail; comparison between GGA-PBE and Meta-GGA SCAN calculations; AIMD simulation results.

BaN4 C2/c BaN10 I-42d

The energy density values for P41212-BaN4, C2/c-BaN4, and I-42d-BaN10 are 0.62 kJ·g−1, 0.63 kJ·g−1, and 0.58 kJ·g-1, respectively. Thus, their detonation velocity ranges from 5.7 to 6.1 km/s, which is lower than the secondary explosive cyclotetramethylene tetranitramine (CH2)4(NNO2)4 HMX (VOD ∼ 9.1 km/s), but comparable than the detonation velocity of the explosive 2,4,6-trinitrotoluene (TNT) (VOD ∼ 6.9 km/s) and primary explosive lead azide Pb(N3)2 (VOD ∼ 3.8 km/ s). Moreover, the stabilization pressure for P-1 BaN10 is only 12 GPa, which is much lower than the pressure required to synthesize polymeric cg-N2 (>100 GPa). High energy density, low stabilization pressure and quenchability make P−1 BaN10, a candidate HEDM. 4. Conclusion We performed crystal structure predictions to investigate the stable ground states of barium nitrides at ambient pressure and pressures up to 100 GPa. Along with the experimentally reported Ba3N, Ba2N, BaN2, and BaN6, we predicted nine new stoichiometries – namely, Ba3N2, BaN, Ba2N3, Ba3N8, Ba2N11, and BaNx (x = 3, 4, 5, 6 and 10) – that become stable at specific pressure ranges. Interestingly, Ba3N, Ba2N and Ba3N2 possess electride properties. Interstitial electrons were predicted to exist in the channel and layer forms. By adjusting the barium ratio in the BaxNy phase diagram, a series of polynitrogen

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected]

ORCID Bowen Huang: 0000-0002-2682-9584 Gilles Frapper: 0000-0001-5177-6691

Author Contributions The manuscript was written in collaboration by both authors. All authors have given approval to the final version of the manuscript.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT We thank the GDRI RFCCT CNRS (DNM-evol program) and Hubert Curien Partnerships PHC XU GUANGQI 2015 (No. 34455PE) program of the French Ministry of Foreign Affairs, Région Poitou-Charentes (France) for financial support for a Ph.D. fellowship. We also acknowledge the High-Performance


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Computing Centers of Poitiers University (Mesocentre SPIN, France) and the TGCC/ Curie GENCI (France) under project no. X2016087539 for allocation of computing time. We are grateful to Pr. John Akapulco for the drawings. Dr. Shuyin Yu and Mr. Le Wang (Northwestern Polytechnical University, Xi'an, China; training research in Poitiers U. with GF) are acknowledged for their participation in preliminary data collection in 2016.

(18)

REFERENCES

(21)

(1) (2) (3) (4) (5) (6) (7)

(8)

(9) (10)

(11)

(12)

(13)

(14)

(15)

(16) (17)

Parker, V. B. Thermal Properties of Aqueous Uni-Univalent Electrolytes; US Government Printing Office Washington: DC, 1965. Cottrell, T. L. The strengths of chemical bonds; Butterworths: London 1958. Klapötke, T. M. High Energy Density Materials; Springer: Berlin, 2007. Singh, R. P. P.; Verma, R. D. D.; Meshri, D. T. T.; Shreeve, J. M. M. Energetic Nitrogen-Rich Salts and Ionic Liquids. Angew. Chemie Int. Ed. 2006, 45, 3584–3601. Brinck, T. Green Energetic Materials; Wiley, 2014. Jursic, B. S. Structures and Properties of Nitrogen Derivatives of Tetrahedrane. J. Mol. Struct. THEOCHEM 2001, 536, 143–154. Vajenine, G. V.; Auffermann, G.; Prots, Y.; Schnelle, W.; Kremer, R. K.; Simon, A.; Kniep, R. Preparation, Crystal Structure, and Properties of Barium Pernitride, BaN2. Ingo. Chem. 2001, 40, 4866-4870. Sun, W.; Holder, A.; Orvañanos, B.; Arca, E.; Zakutayev, A.; Lany, S.; Ceder, G. Thermodynamic Routes to Novel Metastable Nitrogen-Rich Nitrides. Chem. Mater. 2017, 29, 6936–6946. Laniel, D.; Dewaele, A.; Garbarino, G. High Pressure and High Temperature Synthesis of the Iron Pernitride FeN2. Inorg. Chem. 2018, 57, 6245–6251. Bykov, M.; Bykova, E.; Aprilis, G.; Glazyrin, K.; Koemets, E.; Chuvashova, I.; Kupenko, I.; McCammon, C.; Mezouar, M.; Prakapenka, V.; et al. Fe-N System at High Pressure Reveals a Compound Featuring Polymeric Nitrogen Chains. Nat. Commun. 2018, 9, 2756-2763. Bhadram, V. S.; Liu, H.; Xu, E.; Li, T.; Prakapenka, V. B.; Hrubiak, R.; Lany, S.; Strobel, T. A. Semiconducting cubic titanium nitride in the Th3P4 structure. Phys. Rev. Mater. 2018, 2, 011602-011606. Laniel, D.; Weck, G.; Loubeyre, P. Direct Reaction of Nitrogen and Lithium up to 75 GPa: Synthesis of the Li3N, LiN, LiN2 , and LiN5 Compounds. Inorg. Chem. 2018, 57, 10685–10693. Yu, S.; Huang, B.; Zeng, Q.; Oganov, A. R.; Zhang, L.; Frapper, G. Emergence of Novel Polynitrogen Molecule-like Species, Covalent Chains, and Layers in MagnesiumNitrogen MgxNy Phases under High Pressure. J. Phys. Chem. C 2017, 121, 11037–11046. Wei, S.; Li, D.; Liu, Z.; Wang, W.; Tian, F.; Bao, K.; Duan, D.; Liu, B.; Cui, T. A Novel Polymerization of Nitrogen in Beryllium Tetranitride at High Pressure. J. Phys. Chem. C 2017, 121, 9766–9772. Yu, H.; Duan, D.; Tian, F.; Liu, H.; Li, D.; Huang, X.; Liu, Y.; Liu, B.; Cui, T. Polymerization of Nitrogen in Ammonium Azide at High Pressures. J. Phys. Chem. C 2015, 119, 25268– 25272. Steele, B. A.; Oleynik, I. I. Sodium Pentazolate: A Nitrogen Rich High Energy Density Material. Chem. Phys. Lett. 2016, 643, 21–26. Clark, W. P.; Steinberg, S.; Dronskowski, R.; McCammon, C.; Kupenko, I.; Bykov, M.; Dubrovinsky, L.; Akselrud, L. G.; Schwarz, U.; Niewa, R. High-Pressure NiAs-Type Modification of FeN. Angew. Chemie - Int. Ed. 2017, 56, 7302–7306.

(19) (20)

(22)

(23) (24)

(25) (26)

(27)

(28)

(29) (30) (31) (32) (33) (34) (35)

(36) (37) (38) (39)

Bhadram, V. S.; Kim, D. Y.; Strobel, T. A. High-Pressure Synthesis and Characterization of Incompressible Titanium Pernitride. Chem. Mater. 2016, 28, 1616–1620. Niwa, K.; Ogasawara, H.; Hasegawa, M. Pyrite Form of Group-14 Element Pernitrides Synthesized at High Pressure and High Temperature. Dalt. Trans. 2017, 46, 9750–9754. Niwa, K.; Terabe, T.; Kato, D.; Takayama, S.; Kato, M.; Soda, K.; Hasegawa, M. Highly Coordinated Iron and Cobalt Nitrides Synthesized at High Pressures and High Temperatures. Inorg. Chem. 2017, 56, 6410–6418. Christe, K. O.; Wilson, W. W.; Sheehy, J. A.; Boatz, J. A. N5+: A Novel Homoleptic Polynitrogen Ion as a High Energy Density Material. Angew. Chemie Int. Ed. 2001, 40, 2947– 2947. Vij, A.; Wilson, W. W.; Vij, V.; Tham, F. S.; Sheehy, J. A.; Christe, K. O. Polynitrogen Chemistry. Synthesis, Characterization, and Crystal Structure of Surprisingly Stable Fluoroantimonate Salts of N5+. J. Am. Chem. Soc. 2001, 123, 6308–6313. Steele, B. A.; Stavrou, E.; Crowhurst, J. C.; Zaug, J. M.; Prakapenka, V. B.; Oleynik, I. I. High-Pressure Synthesis of a Pentazolate Salt. Chem. Mater. 2017, 29, 735–741. Laniel, D.; Weck, G.; Gaiffe, G.; Garbarino, G.; Loubeyre, P. High-Pressure Synthesized Lithium Pentazolate Compound Metastable under Ambient Conditions. J. Phys. Chem. Lett. 2018, 9, 1600–1604. Prasad, D. L. V. K.; Ashcroft, N. W.; Hoffmann, R. Evolving Structural Diversity and Metallicity in Compressed Lithium Azide. J. Phys. Chem. C 2013, 117, 20838–20846. Yu, S.; Zeng, Q.; Oganov, A. R.; Frapper, G.; Zhang, L. Phase Stability, Chemical Bonding and Mechanical Properties of Titanium Nitrides: A First-Principles Study. Phys. Chem. Chem. Phys. 2015, 17, 11763–11769. Yu, S.; Huang, B.; Jia, X.; Zeng, Q.; Oganov, A. R.; Zhang, L.; Frapper, G. Exploring the Real Ground-State Structures of Molybdenum Dinitride. J. Phys. Chem. C 2016, 120, 11060– 11067. Yu, S.; Zeng, Q.; Oganov, A. R.; Frapper, G.; Huang, B.; Niu, H.; Zhang, L. First-Principles Study of Zr–N Crystalline Phases: Phase Stability, Electronic and Mechanical Properties. RSC Adv. 2017, 7, 4697–4703. Kenichi, T. High-Pressure Structural Study of Barium to 90 GPa. Phys. Rev. B 1994, 50, 16238–16246. Choi, C. S. Neutron Diffraction Study of Ba(N3)2. Acta Crystallogr. Sect. B Struct. Crystallogr. Cryst. Chem. 1969, 25, 2638–2644. Reckeweg, O.; DiSalvo, F. J. Crystal Structure of Dibarium Mononitride, Ba2N, an Alkaline Earth Metal Subnitride. Z. Kristallogr. - New Cryst. Struct. 2005, 220, 519–520. Steinbrenner, U.; Simon, A. Ba3N - a New Binary Nitride of an Alkaline Earth Metal. Zeitschrift für Anorg. und Allg. Chemie 1998, 624, 228–232. Oganov, A. R.; Glass, C. W. Crystal Structure Prediction Using Ab Initio Evolutionary Techniques: Principles and Applications. J. Chem. Phys. 2006, 124, 244704. Oganov, A. R.; Lyakhov, A. O.; Valle, M. How Evolutionary Crystal Structure Prediction Works—and Why. Acc. Chem. Res. 2011, 44, 227–237. Lyakhov, A. O.; Oganov, A. R.; Stokes, H. T.; Zhu, Q. New Developments in Evolutionary Structure Prediction Algorithm USPEX. Comput. Phys. Commun. 2013, 184, 1172– 1182. Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953–17979. Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169–11186. Perdew, J. P.; Burke, K.; Ernzerhof, M. Perdew, Burke, and Ernzerhof Reply: Phys. Rev. Lett. 1998, 80, 891–891. Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient



(40) (41)

(42)

(43)

(44) (45) (46) (47)

(48) (49)

(50) (51) (52)

(53)

(54) (55) (56)

(57) (58)

Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865–3868. Pople, J. A. Nobel Lecture: Quantum Chemical Models. Rev. Mod. Phys. 1999, 71, 1267–1274. Togo, A.; Oba, F.; Tanaka, I. First-Principles Calculations of the Ferroelastic Transition between Rutile-Type and CaCl2-Type SiO2 at High Pressures. Phys. Rev. B 2008, 78, 134106-134114. A Landrum, G. A. viewkel (ver 3.0). viewkel is distributed as part of the YAeHMOP extended Hückel molecular orbital package and is freely available at http://yaehmop.sourceforge.net. Dovesi, R.; Erba, A.; Orlando, R.; Zicovich-Wilson, C. M.; Civalleri, B.; Maschio, L.; Rérat, M.; Casassa, S.; Baima, J.; Salustro, S.; Kirtman, B. Quantum-Mechanical Condensed Matter Simulations with CRYSTAL. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2018, e1360-e1395. Momma, K.; Izumi, F. VESTA 3 for Three-Dimensional Visualization of Crystal, Volumetric and Morphology Data. J. Appl. Crystallogr. 2011, 44, 1272–1276. Aykol, M.; Dwaraknath, S. S.; Sun, W.; Persson, K. A. Thermodynamic Limit for Synthesis of Metastable Inorganic Materials. Sci. Adv. 2018, 4, eaaq0148- eaaq0154. Hoffmann R. Unstable. AmSci. 1987, 75, 61-621 Zhang, L. Q.; Cheng, Y.; Niu, Z. W.; Piao, C. G.; Ji, G. F. Theoretical Calculations of Mechanical, Electronic, and Chemical Bonding in CaN2, SrN2, and BaN2. Z. Naturforsch. A. 2014, 69, 619–628. Reckeweg, O.; Simon, A. Azide Und Cyanamide – Ähnlich Und Doch Anders/Azides and Cyanamides – Similar and Yet Different. Z. Naturforsch. B. 2003, 58, 1097–1104. Wei, S.; Li, D.; Liu, Z.; Li, X.; Tian, F.; Duan, D.; Liu, B.; Cui, T. Alkaline-Earth Metal (Mg) Polynitrides at High Pressure as Possible High-Energy Materials. Phys. Chem. Chem. Phys. 2017, 1–11. Zhu, S.; Peng, F.; Liu, H.; Majumdar, A.; Gao, T.; Yao, Y. Stable Calcium Nitrides at Ambient and High Pressures. Inorg. Chem. 2016, 55, 7550–7555. Sun, J.; Ruzsinszky, A.; Perdew, J. Strongly Constrained and Appropriately Normed Semilocal Density Functional. Phys. Rev. Lett. 2015, 115, 036402. Sun, J.; Remsing, R. C.; Zhang, Y.; Sun, Z.; Ruzsinszky, A.; Peng, H.; Yang, Z.; Paul, A.; Waghmare, U.; Wu, X.; et al. Accurate First-Principles Structures and Energies of Diversely Bonded Systems from an Efficient Density Functional. Nat. Chem. 2016, 8, 831–836. Römer, S. R.; Dörfler, T.; Kroll, P.; Schnick, W. Group II Element Nitrides M3N2 under Pressure: A Comparative Density Functional Study. Phys. status solidi 2009, 246, 1604–1613. Taylor, D. Thermal Expansion Data. I: Binary Oxides with the Sodium Chloride and Wurtzite Structures, MO. Trans. J. Br. Ceram. Soc. 1984, 83, 5–9. Salamat, A.; Hector, A. L.; Kroll, P.; McMillan, P. F. Nitrogen-Rich Transition Metal Nitrides. Coord. Chem. Rev. 2013, 257, 2063–2072. Wessel, M.; Dronskowski, R. Nature of N−N Bonding within High-Pressure Noble-Metal Pernitrides and the Prediction of Lanthanum Pernitride. J. Am. Chem. Soc. 2010, 132, 2421– 2429. Miessler, G. L.; Tarr, D. A. Inorganic Chemistry; Prentice Hall, 2004. Druffel, D. L.; Kuntz, K. L.; Woomer, A. H.; Alcorn, F. M.; Hu, J.; Donley, C. L.; Warren, S. C. Experimental

(59)

(60) (61)

(62)

(63) (64) (65)

(66)

(67) (68) (69) (70) (71)

(72) (73) (74)

(75)

(76)

Page 16 of 17

Demonstration of an Electride as a 2D Material. J. Am. Chem. Soc. 2016, 138, 16089–16094. Tal, A. A.; Katsnelson, M. I.; Ekholm, M.; Jönsson, H. J. M.; Dubrovinsky, L.; Dubrovinskaia, N.; Abrikosov, I. A. Pressure-induced crossing of the core levels in 5d metals. Phys. Rev. B 2016, 93, 205150-205155. Radii, D. of I. http://abulafia.mt.ic.ac.uk/shannon/ Park, C.; Kim, S. W.; Yoon, M. First-Principles Prediction of New Electrides with Nontrivial Band Topology Based on One-Dimensional Building Blocks. Phys. Rev. Lett. 2018, 120, 026401. Vajenine, G. V.; Grzechnik, A.; Syassen, K.; Loa, I.; Hanfland, M.; Simon, A. Interplay of Metallic and Ionic Bonding in Layered Subnitrides AE2N (AE=Ca, Sr, or Ba) under High Pressure. Comptes Rendus Chim. 2005, 8, 1897– 1905. Zhang, Y.; Wu, W.; Wang, Y.; Yang, S. A.; Ma, Y. PressureStabilized Semiconducting Electrides in Alkaline-EarthMetal Subnitrides. J. Am. Chem. Soc. 2017, 139, 13798–13803. Lee, K.; Kim, S. W.; Toda, Y.; Matsuishi, S.; Hosono, H. Dicalcium Nitride as a Two-Dimensional Electride with an Anionic Electron Layer. Nature 2013, 494, 336–340. Tsuji, Y.; Dasari, P. L. V. K.; Elatresh, S. F.; Hoffmann, R.; Ashcroft, N. W. Structural Diversity and Electron Confinement in Li4N: Potential for 0-D, 2-D, and 3-D Electrides. J. Am. Chem. Soc. 2016, 138, 14108–14120. Kurylyshyn, I. M.; Fässler, T. F.; Fischer, A.; Hauf, C.; Eickerling, G.; Presnitz, M.; Scherer, W. Probing the ZintlKlemm Concept: A Combined Experimental and Theoretical Charge Density Study of the Zintl Phase CaSi. Angew. Chemie Int. Ed. 2014, 53, 3029–3032. Alemany, P.; Llunell, M.; Canadell, E. Concerning the Different Roles of Cations in Metallic Zintl Phases: Ba7Ga4Sb9 as a Test Case. Inorg. Chem. 2006, 45, 7235–7241. Dong, X.; Fan, C. Rich Stoichiometries of Stable Ca-Bi System: Structure Prediction and Superconductivity. Sci. Rep. 2015, 5, 9326. Shen, Y.; Oganov, A. R.; Qian, G.; Zhang, J.; Dong, H.; Zhu, Q.; Zhou, Z. Novel Lithium-Nitrogen Compounds at Ambient and High Pressures. Nat. Publ. Gr. 2015, 5, 1–8. Peng, F.; Han, Y.; Liu, H.; Yao, Y. Exotic Stable Cesium Polynitrides at High Pressure. Sci. Rep. 2015, 5, 16902. Steele, B. A.; Stavrous, E.; Prakapenka, V. B.; Radousky, H.; Zaug, J.; Crowhurst, J. C.; Oleynik, I. I. Cesium Pentazolate: A New Nitrogen-Rich Energetic Material. AIP Conf. Proc. 2017; 1793, 040016-040020. Wang, X.; Li, J.; Botana, J.; Zhang, M.; Zhu, H.; Chen, L.; Liu, H.; Cui, T.; Miao, M. Polymerization of Nitrogen in Lithium Azide. J. Chem. Phys. 2013, 139, 1–6. Zhang, M.; Yan, H.; Wei, Q.; Liu, H. A New High-Pressure Polymeric Nitrogen Phase in Potassium Azide. RSC Adv. 2015, 5, 11825–11830. Zhu, Q.; Oganov, A. R.; Glass, C. W.; Stokes, H. T. Constrained Evolutionary Algorithm for Structure Prediction of Molecular Crystals: Methodology and Applications. Acta Crystallogr. Sect. B Struct. Sci. 2012, 68, 215–226. Prots, Y.; Auffermann, G.; Tovar, M.; Kniep, R. Sr4N3: A Hitherto Missing Member in the Nitrogen Pressure Reaction Series Sr2N→Sr4N3→SrN→SrN2. Angew. Chemie Int. Ed. 2002, 41, 2288–2290. Kamlet, M. J.; Jacobs, S. J. Chemistry of Detonations. I. A Simple Method for Calculating Detonation Properties of C– H–N–O Explosives. J. Chem. Phys. 1968, 48, 23–35.


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Barium-Nitrogen Phases Under Pressure: Emergence of Structural

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