Hidden Thermodynamic Ground State of Calcium Diazenide

Article pubs.acs.org/JPCC

Hidden Thermodynamic Ground State of Calcium Diazenide Hui Wang,†,‡ Yansun Yao,*,§,∥ Yanling Si,†,⊥ Zhijian Wu,*,† and G. Vaitheeswaran# †

State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China ‡ State Key Lab of Superhard Materials, Jilin University, Changchun 130012, Peoples Republic of China § Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E2, Canada ∥ Canadian Light Source, Saskatoon, Saskatchewan S7N 0X4, Canada ⊥ College of Resource and Environmental Science, Jilin Agricultural University, Changchun 130118, PR China # Advanced Center of Research in High Energy Materials (ACRHEM), University of Hyderabad, Prof. C. R. Rao Road, Gachibowli, Hyderabad 500 046, Andhra Pradesh, India ABSTRACT: A new member to the family of alkaline earth diazenides, calcium diazenide (CaN2), was recently synthesized by a controlled decomposition of calcium azide at highpressure/high-temperature conditions (Schneider et al. Inorg. Chem. 2012, 51, 2366− 2373). Isotypic to tetragonal calcium carbide, the synthesized CaN2 phase adopts a tI6 structure in which Ca2+ cations and [N2]2‑ anions are arranged in a distorted rocksalt structure. Using an unbiased structure searching method, we investigate the energy landscape of CaN2 at the first principles level and suggest that the tI6 structure is a metastable form of CaN2. A new orthorhombic oP12 structure, formed by a distorted bcc lattice of Ca2+ cations interpenetrated by [N2]2‑ anions, is predicted to be the thermodynamic ground state of CaN2. The energy of the oP12 structure is considerably lower than that of the synthesized phase, by ∼80 meV/CaN2, while it is also lower than the energies of the candidate structures previously considered. The oP12 structure remains as the thermodynamic ground state of CaN2 at high pressures up to 2.9 GPa, at where it undergoes a first-order phase transition to a higher density oP12′ structure. Above 2.9 GPa, the synthesized tI6 phase becomes the thermodynamic ground state of CaN2. The formation of the oP12 structure is predicted to be exothermic which suggests that this structure may be synthesized in future experiments with proper experimental conditions.

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specialized autoclave system.7−10 Since then, however, no other alkaline earth diazenides had been discovered for over a decade, probably due to the experimental difficulties, although theoretical prediction suggested that BeN2, MgN2, and CaN2 should all be thermodynamically stable at ambient conditions.11−14 New progress in the synthesis of alkaline earth diazenides has been made very recently. In 2012, Schneider et al. designed a new synthetic approach and successfully synthesized CaN2 in laboratory, using a controlled decomposition of the calcium azides at 800 °C and 12 GPa in a multianvil press.15 The crystal structure of the synthesized CaN2 has been determined from the powder X-ray diffraction data. The CaN2 structure is formed by Ca2+ cations and discrete [N2]2‑ anions arranged in a distorted NaCl lattice in which all [N2]2‑ anions are aligned along one 4-fold axis. This structure has a body-centered tetragonal unit cell with the space group I4/mmm (Pearson symbol tI6). Not exactly the first appearance in calcium compounds, the tI6 structure is known to exist in the polymorphs of calcium carbide CaC2 and calcium peroxide CaO2 in which [C2]2‑ and [O2]2‑ anions behave similarly as

INTRODUCTION Progressive developments of high-pressure technology for the synthesis of new materials have substantially expanded the class of binary metal nitrides in recent years, and stimulated the study of nitrogen in new and sometimes unusual bonding environments. In the past decade, a series of noble metal pernitrides have been successfully synthesized in laboratory using laser-heated diamond anvil cell techniques.1−6 Noble metal pernitrides have a simple chemical composition of MNM4+[N2]4‑ (MNM = Os, Ir, Pd, and Pt), in which the 4-fold negatively charged and single bonded dinitrogen anion represents a deprotonated hydrazine N2H4. Many of the synthesized pernitrides exhibit remarkable mechanical properties (e.g., superconductivity, low compressibility comparable to that of cubic boron nitride) and, therefore, are often considered as potentially technologically important materials. A chemically related group, alkaline earth nitrides MAE2+[N2]2‑, also attracted considerable attention due to their analogue formula type and similar structures to the pernitrides. Unlike the pernitrides, alkaline earth nitrides contain 2-fold negatively charged and double bonded dinitrogen anions. These anions represent deprotonated diazene N2H2 units and were therefore named as diazenides. The first members of the alkaline earth diazenides, SrN2 and BaN2, were synthesized as early as 2001 using a © 2013 American Chemical Society

Received: October 17, 2013 Revised: December 7, 2013 Published: December 10, 2013 650

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Figure 1. Supercell views of (a) the tI6 structure at 0 GPa, (b) the oP12′ structure at 5 GPa, and (c) the oP12 structure at 0 GPa. The dark lines denote the unit cells, while the large and small spheres represent Ca and N atoms, respectively. The solid cyan lines are used to highlight the coordination environment between Ca atoms. The coordination numbers of 12 (a and b) and 8 (c) correspond to a fcc-like and a bcc-like sublattice of Ca, respectively.

[N2]2‑ anions. The measured N−N distance is 1.202 Å in CaN2, very close to the C−C distance of 1.191 Å in CaC2.16,17 Interestingly, according to an earlier theoretical prediction,12 the synthesized tI6 structure is not the thermodynamic ground state of CaN2. At least four other structures, including the proposed ground state (a δ-ZnCl2 structure), have been suggested to be more stable than the tI6 structure for CaN2. All four candidate structures have similar energies, that is, within the variation of 10 meV/CaN2, which may indicate a rather flat energy landscape near the energy minima. It should not be a surprise that the high-pressure synthesis reaches a metastable phase, in this case the tI6 phase, following a particular synthesis route.18−20 A further question to ask, however, is whether hitherto unknown but more stable CaN2 phases can also form, maybe through different synthesis routes, under high pressure. Could we survey the energy landscape using the state-of-the-art theoretical tools and provide suggestions on the synthesis conditions? After all, the structural diversity of CaN2 has yet to be examined. The previous theoretical study of the structures of CaN2 is limited on only 15 known AB2 structural types.7 There is a possibility that other structural types are more thermodynamically stable, perhaps also quench recoverable, awaiting to be discovered. For this purpose, we studied the thermodynamic stability of the crystalline CaN2 from the atmosphere pressure up to 12 GPa by means of an unbiased structure searching method in combination with first-principles density functional calculations. We predicted an orthorhombic structure, with Ca2+ cations arranged in a distorted body centered cubic (bcc) lattice in which [N2]2‑ anions occupy one-third of the octahedral sites, as the thermodynamic ground state. The predicted structure has significantly lower total energy than the tI6 structure, by nearly 80 meV/CaN2. As well, this structure is more stable than all theoretical models considered previously. We also predicted that the orthorhombic structure stays as the thermodynamic ground state at high pressures up to 2.9 GPa, before it transforms to the tI6 structure. The phonon calculations reveal that the orthorhombic structure is mechanically stable, and therefore may be quenching recoverable to ambient conditions.

effectiveness of our method has been demonstrated by recent successes in predicting high-pressure structures of various systems, ranging from elements to binary and ternary compounds.23−29 We searched the structures of stoichiometric CaN2 with simulation cell sizes of 1−4 formula units (f. u.) at pressure of 0 and 12 GPa. The local structural relaxations and electronic band structure calculations were performed in the framework of density functional theory30 within the generalized gradient approximation and frozen-core all-electron projectoraugmented wave (PAW) method,31 as implemented in the VASP code.32,33 The adopted PAW pseudopotentials of Ca and N treat 2p3s and 2s2p electrons as valence electrons. The cutoff energy of 520 eV and appropriate Monkhorst−Pack k-meshes34 were chosen to ensure that all the enthalpy calculations were well converged to within 1 meV/atom. The phonon calculations were carried out by using a finite displacement approach35 through the PHONOPY program.36

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RESULTS AND DISCUSSION

The equilibrium state of CaN2 at 12 GPa revealed by our ab initio structural search is exactly the synthesized tI6 structure.15 Other theoretical models have much higher enthalpies than the tI6 phase, at this pressure, which explains why the tI6 structure is more accessible in the synthesis experiments. The tI6 structure is situated in a distorted NaCl lattice in which Ca2+ cations and [N2]2− anions form two interpenetrating face centered cubic (fcc) sublattices, with the octahedral voids of one type filled by the other type of ions, and with [N2]2− anions uniformly aligned along a fcc lattice vector (Figure 1a). The molecular alignments modify the force field and considerably elongate the lattice vector parallel to [N2]2− anions. At the atmospheric pressure, the calculated lattice vectors of the fcc sublattice are 5.09, 5.09, and 5.98 Å, respectively, clearly representing a tetragonal distortion. The distortion of the unit cell breaks down the ideal octahedral environment in the tI6 structure and reduces the coordination number from 6 to 4 + 2. In this specific arrangement, Ca2+ cations are coordinated “sideon” by four and “end-on” by two diazenide units (Figure 1a), giving a loosely defined coordination number of 8 + 2 = 10. In Table 1, we listed the optimized structural parameters of the tI6 structure, and made a comparison with previously reported theoretical and experimental data, which yields a good agreement.

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METHODS We performed structure predictions through CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) methodology as implemented in the CALYPSO code.21,22 The 651

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neither the triclinic CaN2 nor the monoclinic CaN2 is energetically competitive compared with the undistorted tI6 structure, so we will not discuss them further. On the other hand, we were able to obtain an energetically competitive modification of the tI6 structure from our ab initio structural search; that is, an orthorhombic distortion in which half of [N2]2− anions are aligned along the c-axis of the NaCl lattice while the other half aligned along the a-axis (Figure 1b). This orthorhombic structure adopts the Pnma space group and in this paper we refer it as the oP12′ structure (the prime here stands for a metastable form). At 12 GPa, the calculated enthalpies of the oP12′ and tI6 structures only differ by about 25 meV/CaN2, and this difference continuously reduces at lower pressures (Figure 2a). Notably, the oP12′ structure is structurally related to the predicted thermodynamic ground state of CaN2; we will come back to this later. The predicted thermodynamic ground state of CaN2 also possesses a Pnma space group; here we note it as the oP12 structure (the absence of the prime indicates a ground state). The optimized structural parameters for the oP12 structure are as follows: Ca 4c 0.375, 0.25, 0.721; N 4c 0.133, 0.25, 0.435; and N 4c 0.521, 0.25, 0.261, with a = 8.284, b = 4.742, and c = 4.252 Å. Significantly, the oP12 structure has much lower energy than the tI6 structure, by more than 80 meV/CaN2, at the atmospheric pressure (Figure 2a). The energy of the oP12 structure is also lower than that of the previously proposed thermodynamic ground state, the δ-ZnCl2 structure, by more than 60 meV/CaN2. In the oP12 structure, Ca2+ cations form a distorted bcc lattice in which each cation is neighbored by another eight cations (Figure 1c). At the atmospheric pressure, the nearest and second nearest Ca−Ca distances in the oP12 structure are 3.67 and 3.94 Å, respectively, comparable to the values of 3.60 and 3.91 Å in the tI6 structure. In the bcc lattice, a half of [N2]2− anions occupy the face-sharing octahedral sites on the (100) planes, while the other half occupy the edgesharing octahedral sites on the (010) and (001) planes. The orientations of [N2]2− anions are aligned parallel to a bcc face

Table 1. Lattice Parameters a, b, and c (Å), Bond Length of the Diazenide Unit dNN (Å), Volume V (Å3/CaN2), Total Energy E0, Zero-Point Energy EZP, and Formation Energy ΔE (eV/CaN2) for Different Structures of CaN2 tI6 calcd a b c dNN V E0 EZP ΔER1 ΔER2 ΔER3 a

calcd

a

expt

b

3.604

3.620

3.575

5.978 1.257 38.83 −20.19 0.20 −1.530 −0.209 −0.395

6.010 1.258 39.41

5.984 1.202 38.24

oP12

oP12′

0 GPa

5 GPa

8.284 4.742 4.252 1.246 41.75 −20.28 0.22 −1.614 −0.293 −0.479

7.587 5.011 3.909 1.251 37.15

From ref 14. bFrom ref 15.

The tI6 structure represents a local minimum in the potential energy surface of CaN2. To examine the energy landscape near this minimum, we generated several modifications of the tI6 structure by applying different relative orientations of [N2]2− anions. For the first trials, we examined two known modifications, the triclinic and monoclinic ones, which were previously observed in the polymorphs of CaC2 at low temperatures. Starting from the tI6 structure, a triclinic modification is introduced by aligning half of [N2]2− anions parallel to two of the body diagonals, and aligning the other half parallel to two of the face diagonals, of the distorted NaCl lattice. The triclinic modification of the tI6 structure has been observed in CaC2 in presence of cyanamide anions (CN22‑).37 The monoclinic modification is very similar to the lowtemperature modification of sodium cyanide in which all [N2]2− anions are tiled a small angle with respect to the c axis of the distorted NaCl lattice.38 Our enthalpy calculations revealed that

Figure 2. (a) Calculated enthalpy curves of the oP12−oP12′ structure and the δ-ZnCl2 structure with respect to that of the tI6 structure. A single curve is used for the oP12 and oP12′ structures in which the structural transition occurs near 2.9 GPa. (b) Shortest (violet blocks) and second shortest (pink dash) distances between the center of [N2]2− anion to six neighboring Ca2+ cations in a ([N2]2−)(Ca2+)6 octahedron within the oP12 structure or the oP12′ structure as functions of pressure. The nearest distance block contains five [N2]2−−Ca2+ contacts that vary a little in their lengths. The oP12−oP12′ phase transition is clearly shown by a sudden decrease of the second nearest distance near 2.9 GPa, which brings the [N2]2− anion from the pyramidal void (c) back to the octahrdal void (d) in the ([N2]2−)(Ca2+)6 octahedron. The Ca and N atoms are shown as big and small spheres, respectively. (e) Calculated volume and energy for the oP12 and oP12′ structures as functions of pressure (symbol curves). A large discontinuity occurs at the phase transition point (ΔV and ΔE). The volume and energy of the tI6 structure (dash and solid curves) are presented for a comparison. 652

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Figure 3. Prototypic view of the oP12 structure in (a) a bcc unit cell and in (b) a bcc supercell illustrating its structural relations to (c) the oP12′ structure and (d) the tI6 structure, both shown in a fcc unit cell. For a clear presentation, the distortions of the unit cell and the deviations of the atomic positions are not shown.

diagonal, either to the [001] direction or to the [011̅] direction, while the anion centers are shifted away from ideal octahedral sites. In view of an local ([N2]2−)(Ca2+)6 octahedral vertex, [N2]2− anion moves away from the vertex center toward a pyramid void below (Figure 2c). Thus, one of six Ca2+ cations sited on the vertex is farther away from [N2]2− anion and therefore the nearest distances from [N2]2− anions to Ca2+ cations fall into two groups: one is considerably longer as 3.64 Å and the other five ones range from 2.28 Å to 2.56 Å (Figure 2b). Correspondingly, the Ca2+ ion is coordinated “end-on” by two and “side-on” by three [N2]2− anions (Figure 1c), resulting in a loosely defined coordination number of 2 + 6 = 8. We observed an important structural feature of the oP12 structure; that is, under high pressure, Ca2+ cations and [N2]2− anions tend to rearrange themselves toward a more closepacked oP12′ structure. According to the enthalpy calculations, the oP12 structure would complete a phase transition to the oP12′ structure at 2.9 GPa, and beyond this point it becomes less stable than the tI6 structure (Figure 2a). Quite interestingly, the oP12 and oP12′ structures belong to the same Pnma space group, but this phase transition is not an isostructural one.39 The oP12 and oP12′ structures represent two different structural motifs, bcc vs fcc, and thus, this phase transition is classified as the first-order. At 5 GPa, the optimized structural parameters for the oP12′ structure are: Ca 4c 0.363, 0.25, 0.813; N 4c 0.159, 0.25, 0.383; and N 4c 0.55, 0.25, 0.358, with a = 7.587, b = 5.011, and c = 3.909 Å. As a typical feature of a first-order phase transition, the volume of the oP12 structure collapses by 7% (ΔV = 2.81 Å3/CaN2) in the vicinity of 2−3 GPa, and at the same time the total energy of the oP12 structure experiences an abrupt jump (Figure 2e). The oP12− oP12′ transition consists two major distortions in the bcc lattice of Ca2+ cations, that are (1) compressing two of the three 4fold axes, which transforms the (001) bcc layers into the (001) fcc layers, and (2) stretching the rest 4-fold axis, which yields the [001] fcc vector (Figure 3a−c). In view of local ([N2]2−)(Ca2+)6 coordination, [N2]2− anion is brought back from the pyramidal void to the center of the (Ca2+ ) 6 octahedron after the phase transition (Figure 2d). This

coordination change is clearly shown by a large reduction of the second nearest anion−cation distances at the phase transition point (Figure 2b). Correspondingly, the Ca2+ cation in the oP12′ structure is coordinated “end-on” by two and “side-on” by four diazenide units, presenting a loosely defined coordination number of 2 + 8 = 10. The large volume collapse at the oP12−oP12′ phase transition is therefore consistent with the bcc−fcc transition of the Ca2+ sublattice and the increment of the coordination number, that is, from 5 to 6 for [N2]2− anions and from 8 to 10 for Ca2+ cations. It should be noted here that the oP12−oP12′ transition in CaN2 differs fundamentally from an ordinary Bain’s deformation.40 Usually used to characterize the bcc−fcc martensitic transformations, the Bain’s deformation is composed of a homogeneous shear of three successive (011) bcc planes along the ±[110] directions which transforms the ABAB... stacking into the fcc phase with ABCABC... staking along the [111] fcc direction. The Bain’s deformation is less energetically favorable, for the present case, because the relative shifting of planes would enhance nonbonded N−N interactions and therefore requires additional energy to complete the transition. Thus, in the oP12−oP12′ transition, no plane shearing is involved. The orientations of [N2]2− anions are essentially unchanged, which, in the final oP12′ structure, are parallel to two orthogonal lattice vectors (Figure 3c). The tI6 structure differs from the oP12′ structure mainly in the relative orientations of [N2]2− anions. In the tI6 structure, all anions are aligned along one of the lattice vectors (Figure 3d), and this ordering yields a smaller crystal volume. For example, close to 3 GPa, the volume of the tI6 structure is nearly ∼1.8% smaller than the volume of the oP12′ structure. Thus, the tI6 structure would be thermodynamically more stable than the oP12′ phase, at elevated pressures, taking advantage of the more favorable PV contribution to the enthalpy. The transition from the oP12 structure to the tI6 structure, on the other hand, requires additional reorientation of the [N2]2− anions, and therefore, would be less energetically favorable compared with a direct transition to the oP12′ structure. In view of the energetics, this may explains why the synthesized tI6 phase is locked in its 653

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To examine the role of ZP motion, the ZP energies were estimated within a harmonic approximation for both tI6 and oP12 phases (Table 1). The calculated ZP energies are very similar for the tI6 and oP12 structures, that are 0.20 and 0.22 eV/CaN2, respectively. Slightly higher ZP energy of the oP12 structure is resulted from a shorter intermolecular N−N distances, and therefore higher stretching frequencies, of [N2]2− anions. It is important to note, that even with the inclusion of the ZP motions, the oP12 phase remains as the thermodynamic ground state of CaN2. The thermodynamic stability of the oP12 phase at zero pressure was examined in terms of the formation energies of three possible reaction routes:

crystal structure, rather than transforming to the thermodynamic ground state oP12, upon annealing to the ambient conditions. The mechanic stability of a crystalline structure requires the eigen frequencies of its lattice vibrations be real for all wavevectors in the Brillouin zone. To examine the stability of the oP12 structure, the phonon frequencies were calculated at atmospheric pressure. Imaginary frequency was not observed in the entire Brillouin zone (Figure 4), indicating that the

ΔE R1 = ECaN2 − ECa − E N2

(1)

ΔE R2 = ECaN2 −

1 2 ECa N − E N2 3 3 2 3

(2)

ΔE R3 = ECaN2 −

1 3 ECa 2N − E N2 2 4

(3)

The ambient structures for the reaction products, namely, the fcc-Ca, α-Ca3N2, anti-CdCl2-type Ca2N, and α-N2, were chosen as the reference phases. As shown in Table 1, the calculated formation energies obtained by the three reaction routes indicate that the formation of the CaN2 is exothermic and the oP12 structure is stable against the decomposition into the mixture of Ca + N2, Ca2N3 + N2, or Ca2N + N2. A potential challenge for a direct high-pressure synthesis of the oP12 phase is its narrow pressure range of stability. The oP12 phase is only thermodynamic stable from the atmospheric pressure to approximate 3 GPa. One may, however, be able to obtain the oP12 phase through other approaches; for example, by rapidly heating and quenching the CaN2 sample at higher pressures, thereby providing the condition for the CaN2 to energetically overcome the energy barriers between the tI6 and oP12 phases.

Figure 4. Total phonon density of states of the oP12 and tI6 structures calculated at the atmospheric pressure.

predicted oP12 structure is mechanically stable and, if synthesized, might be quenchable to atmospheric pressure. A relatively small mass of the diazenide unit gives rise to large zero-point (ZP) motion of the nuclei, which might be strong enough to affect the relative stabilities of the CaN2 structures.

Figure 5. (a) Total density of states and the integration of the total density of states of the oP12 structure at the atmospheric pressure. The Fermi level is shown by vertical dot line at 0 eV. (b) Molecular orbital scheme for [N2]2‑ anion. For a pedagogical visualization, the energy levels are not scaled. (c−f) Band decomposed charge densities within the energy range of −23 to −20 eV, −11 to −10 eV, −8 to −5 eV, and −2 to 2 eV, respectively. The Ca and N atoms are shown as big and small balls, respectively. The golden isosurface has a charge density of 0.3 electron/Å3. 654

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remains as the ground state of CaN2 from the atmospheric pressure up to 2.9 GPa, at where it undergoes a first-order phase transition to a higher density oP12′ structure. A large volume drop and an increment of coordination numbers are suggested to occur for this phase transition. Above 2.9 GPa, the tI6 phase becomes the thermodynamic ground state of CaN2, while the oP12′ phase is metastable. The tI6 and oP12′ phases both have a NaCl motif in which Ca2+ cations and [N2]2‑ anions form two interpenetrating fcc sublattices. The relative orientations of [N2]2‑ anions, however, are different in the two structures, and they may correspond to different synthesis routes. The oP12 structure is predicted to be exothermic and metallic at equilibrium. Phonon calculations reveal that the oP12 structure is mechanically stable and therefore perhaps can be quenched to ambient conditions. This study therefore provides a timing examination of the structures of CaN2, and the results obtained will hopefully provide insight and guidance to future experiments on CaN2, as well as to experiments on other alkaline earth diazenides.

The predicted oP12 phase of CaN2 exhibits metallic characters, as illustrated by the calculated electronic densityof-states (DOS) shown in Figure 5a. The subset of electronic bands located around the Fermi level is characteristic of the 2pπg* antibonding orbital of [N2]2− anions. This subset is half occupied by two electrons. In the valence region, the occupied electronic bands are largely separated from each other and thus grouped into three subsets, which, in the order of increasing energy, are characteristic of 2sσg, 2sσu*, 2pσg/2pπu molecular orbitals. The inert 3p orbital of Ca2+ cations overlaps with the 2sσg bonding states in energy, and therefore, it contributes additional six electrons to the first subset (below −20 eV). The second subset of the valence bands near −11 eV is composed from primarily the antibonding 2sσu* states. The 2pσg and 2pπu bonding orbitals are located next to each other in energy (below −5.5 eV) and, respectively, contribute two and four electrons to the third subset of the valence bands. The partition of the electronic DOS in energy corresponds to the molecular orbital scheme shown in Figure 5b. Clearly, in the molecular orbital of [N2]2− anion, the 2pσg state still has lower energy than the double-degenerated 2pπu states, which is, in fact, in contrast to the neutralized N2 molecule. It is perhaps well known that the N2 molecule has strong s−p mixing between the 2sσg and 2pσg orbtials such that the antibonding interaction is able to push the 2pσg orbital up in energy to above that of the 2pπu orbital (and also pushes down the energy of the 2sσg orbital). This energy crossover is not observed in [N2]2− anions, primarily due to the enhanced 2pσg bonding by the introduction of two additional electrons. In this respect, the analogy of the [N2]2− anion to the O2 molecule is clear, and this can be explained by the Zintl−Klemm rule.41 If the N− anion is viewed as isoelectronic to oxygen, it makes complete sense that the [N2]2− would adopt the molecular orbital of O2 and formally fulfills the electronic octet. The integration of electronic DOS of the occupied states yields a total electron count of 8 + 2 + 6 + 2 = 18. A slight orbital mixing between the [N2]2− molecular orbitals and Ca2+ valences states (4s, 4p, and 3d), is observed in some of the valence bands. Information about the spatial localization of the four subsets of occupied bands was obtained by analyzing the partial (or band decomposed) charge density. The main character of the [N2]2− molecular orbital can be clearly seen in Figure 5c−f. The bonding structure of the oP12 structure thus exhibits great similarity to that of an isolated [N2]2− anion. The contribution of calcium to the electronic DOS is hardly seen in the valence regime, indicating that electrons are almost depleted from its’ 4s orbital. The oP12′, δ-ZnCl2, and tI6 structures,15 as well as other alkali earth diazenides,12 share the same bonding motif with the oP12 structure, and therefore, their electronic DOS follow the same partition pattern as shown in Figure 5a.

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AUTHOR INFORMATION

Corresponding Authors

*(Y.Y.) Phone: 1-306-966-6430. E-mail: [email protected]. *(Z.W.) Phone: 86-431-85262801. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS H.W. appreciatively acknowledges the financial support by Natural Science Foundation of China (NSFC) under 11104104 and China Postdoctoral Science Foundation (Nos. 2012M510893). Y.Y. gratefully acknowledges the Information and Communications Technology group at the University of Saskatchewan for providing computing resource, the Plato cluster, which is part of the High Performance Computing Training and Research Facilities at the University of Saskatchewan. Part of the calculations have been performed by the use of computing resources provided by WestGrid and Compute Canada. The work at the University of Saskatchewan was supported by a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant.

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REFERENCES

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SUMMARY In the present study, an unbiased structure searching method in combination with first-principles calculations was employed to investigate the phase stabilities, structural and electronic properties of CaN2. Recently synthesized tI6 phase of CaN2 was suggested as a metastable form at the atmospheric pressure. A new orthorhombic oP12 phase was predicted as the thermodynamic ground state of CaN2, which has considerably lower energy than the synthesized tI6 phase, as well as than the theoretical models considered before. The oP12 structure is formed by a distorted bcc lattice of Ca2+ cations with [N2]2‑ anions populated in the octahedral voids. The oP12 structure 655

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dx.doi.org/10.1021/jp410281q | J. Phys. Chem. C 2014, 118, 650−656