High-Pressure Bonding Mechanism of Selenium Nitrides - Inorganic

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High-Pressure Bonding Mechanism of Selenium Nitrides Wenjie Wang, Han Wang, Yue Liu, Da Li,* Fubo Tian, Defang Duan, Hongyu Yu, and Tian Cui* State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, China

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S Supporting Information *

ABSTRACT: The high-pressure phase diagrams of binary Se−N system have been constructed using the CALYPSO method and first-principles calculations. Four stable compounds (Cmc21-SeN2, P21/m-SeN3, P1̅-SeN4, and P1̅-SeN5) were identified at high pressures. Various peculiar nitrogen polymerization forms composed of single/double nitrogen−nitrogen bonds were found at the nitrogenrich condition, such as N∞-chains in P21/m-SeN3, oligomeric N8-chains in P1̅SeN4, and distorted N63− anion rings in P1̅-SeN5. Peculiar nitrogen polymerization forms make these compounds potential high-energy-density materials (HEDMs). Especially, P1̅-SeN5 has the highest energy density of 4.08 kJ g−1 among the selenium nitrides. The polymerization mechanism of nitrogen in the Se−N system has been explored using the “Lewis-like” two-center−two-electron and threecenter−two-electron bonding analysis. Using the nitrogen-rich P1̅-SeN5 as a prototype, it is found that the famous N6 distortion in the polymerized nitrogen HEDM can be explained by the interatomic mechanical unbalance which is induced by the three-center two-electron bonding between the metal atom and the two neighboring nitrogen atoms. try.30,31 (SN)x, a planar quasi-one-dimensional chain polymerized form of solid Se2N 2, was reported to be a superconductor with a critical temperature Tc of 0.26 K in 1975.32,33 However, the chemistry research of binary selenium−nitrogen progresses much more slowly.29 Se4N4 was not synthesized until 1992 due to its insolubility and instability.34 Later, two simple efficient synthesis approaches for the preparation of a small amount of Se4N4 are proposed by Siivari et al.35 NSe2, an unstable molecule, was produced in an argon/nitrogen/chalcogen microwave discharge situation and trapped in solid argon at 12 K.36. The electronic structures and molecular properties of Se2N2 were investigated by Tuononen et al. using different ab initio and density functional methods.37 The crystal phase of Se4N4 was first suggested by Dehnicke et al.38 in 1993. However, in our first-principles energy calculation, this structure is thermodynamically unstable. Up to now, many research studies about efficient synthetic methods, the role of starting material, and the preparation of cyclic and acyclic Se−N derivatives have been carried out. The study of the crystal structure and chemical bond interaction in the chalcogen−nitrogen compounds also attracts much attention.29 Meanwhile, it is of great significance to study the chemical reaction of selenium and nitrogen under high pressures, because high pressure is a good tool to obtain pure novel materials. In the present study, we performed a comprehensive crystal structure searching with various stoichiometries over a wide range of pressures (up to 150 GPa) in the Se−N system. Four stable phases were identified. Cmc21-SeN2 is constructed by

1. INTRODUCTION Recently, it has become popular to explore novel polymeric nitrogen in elemental nitrogen phases and nitrides theoretically and experimentally. Nitrogen-rich compounds attract vast interest because they are potential candidates as high-energydensity materials (HEDMs), which can be applied in the environmentally friendly explosives field.1 The high energy density of these materials originates from the remarkable gap of bond energy between the single/double bonds in the nonmolecular nitrogen (160/418 kJ mol−1) and triple bond in N2 molecule (954 kJ mol−1).2 High pressure has been proven to be a powerful approach which makes the nitrogen molecular phase transform to various types of nonmolecular phases.3−8 Exhilaratingly, various polymeric structures of nitrogen in a binary system had been found using high-pressure methods in the past decade. One-dimensional infinite polymeric nitrogen chains are found in N−H,9 Mg−N,10,11 CaN,12,13 Li−N,14 Hf−N,15 Rb−N,16 K−N,17 and boron nitride nanotubes.18 Various nitrogen rings are found in Mg−N,10,11 Ca−N,12,13 Li−N,14,19−21 Rb−N,16 K−N,17 and CsN.22,23 Besides infinite chains and rings, nitrogen can also form many special polymeric forms such as the oligomeric N-chains in Al−N,24 H−N,25 and Cs−N;23 2D network in K−N17 and Li−N;26 and 3D network in Be−N27 and He−N.28 These compounds composed of polymeric nitrogen all carry a higher energy density. The chemistry research of chalcogen−nitrogen (i.e., S/Se/ Te−N) systems spans more than 170 years and still receives great attention because many fascinating properties are found in the sulfur nitrides.29 For example, the S4N4 molecule with a cage-like structure, discovered in 1835, is a crucial starting material for various syntheses in sulfur−nitrogen chemis© XXXX American Chemical Society

Received: October 11, 2018

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DOI: 10.1021/acs.inorgchem.8b02889 Inorg. Chem. XXXX, XXX, XXX−XXX

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Se4N4 is identified to be thermodynamically unstable because of its positive formation enthalpy (0.7 eV/atom) in our calculation. From convex schema in Figure 1a, there is no

layers that consisted of the nitrogen dimers and selenium atoms. Significantly, different polymeric nitrogen forms were observed in the other three phases, P21/m-SeN3, P1̅-SeN4, and P1̅-SeN5. Nitrogen atoms form infinite chains in P21/m-SeN3, peculiar oligomeric chains in P1̅-SeN4, and abnormal infinite chains plus a twisted N63− anion ring in P1̅-SeN5. It is exciting that these three nitrogen-rich phases are expected to be highenergy-density materials with energy density of 3.27 kJ g−1 (P21/m-SeN3), 3.26 kJ g−1 (P1̅-SeN4), and 4.08 kJ g−1 (P1̅SeN5). Furthermore, we combine the electron localization function (ELF)39,40 with the quantitative information from periodic natural bond orbital (periodic NBO) analysis41 on the study of a “Lewis-like” two-center−two-electron chemical bond. In addition, supplemental information about the threecenter−two-electron chemical bonds is studied using the solid state adaptive natural density partitioning (SSAdNDP)42 method. In this way, we found the alternation of single and weak double bonding modes in the N∞-chains of P21/m-SeN3 and P1̅-SeN5. We also found that the abnormal twisted N63− anion rings in the P1̅-SeN5 structure originate from the interatomic mechanical unbalance induced by the threecenter−two-electron bonding mode between N and neighboring Se atoms. We also explain the origin of the semiconductivity of Cmc21-SeN2 and the metallicity of P21/m-SeN3 from chemical perspective.

2. COMPUTATIONAL METHOD In order to identify the possible ground-state structures of the binary Se−N system, extensive structural searches are performed for various stoichiometries of SeNx (x = 1/2, 2/3, 1, 2, 3, 4, and 5) within 1−4 formula units (f.u.) in the simulation cell using the particle swarm optimization (PSO) algorithm43 as implemented in the crystal structure analysis by particle swarm optimization (CALYPSO) code.44 Density functional energy calculations about energy calculations, geometry optimizations, electronic structure, and partial charge density were performed within the Vienna ab initio simulation package (VASP) with the Perdew−Burke−Ernzerhof generalized gradient approximation (GGA) exchange and correlation function. Projector-augmented wave (PAW) pseudopotentials are used, and the Se 4s24p4 electrons and N 2s22p3 electrons are treated as valence electrons. An energy cutoff of 700 eV for the plane-wave basis sets and a reciprocal space resolution of 2π × 0.03 Å−1 for the electronic Brillouin zone (BZ) integration were used to ensure that the error bars of the total energies were less than 1 meV/atom. The NBO45−47 analysis for the periodic system was performed by Periodic NBO developed by the Schmidt group.41 The research for three-center− two-electron-type bonds was performed by SSAdNDP.42 In both the Periodic NBO program and the SSAdNDP program, the basis set is 6311G (with polarization) for projection to obtain PW DFT representation to ensure the total spillover is less than 1.0 × 10−3. The phonon frequencies of all structures were calculated by the supercell finite displacement method performed in the PHONOPY code.48

Figure 1. (a) Convex hulls of the Se−N system at selected pressures. Solid points connected by the solid line denote stable structures, while empty points connected by the dotted line represent unstable/ metastable structures. (b) Predicted pressure−composition phase diagram of the Se−N crystal phases.

stable phase found at low pressures until 80 GPa. Also, we found that only the N-rich compounds are thermodynamically stable at the selected pressure range. This situation is similar to that of the S−N system49 which has close electronegativity between S and N atoms. However, most binary systems have a large electronegativity gap between two elements. This makes them form many stable phases at low pressures and even in ambient conditions. So, the low reaction activity in the Se−N system may originate from the stable Se6 rings in the elemental Se crystal, the high dissociation energy (945.41 kJ mol−1) of nitrogen gas with N−N triple bond, and the close electronegativity between Se and N. The P21/m-SeN3 is the most thermodynamically stable phase at relatively low pressure, but as the pressure increases, the Cmc21-SeN2 becomes more advantageous in energy. The formation enthalpy deviation of P1̅-SeN4 with respect to the convex solid line at 130 GPa is extremely small and finally disappears at 140 GPa, while nitrogen-rich P1̅-SeN5 becomes stable at 130 GPa. The phonon dispersion curves of these thermodynamically stable phases indicate their dynamical stability (see Figure S5). Crystal structure information on the considered structures and elementary Se/N structures is shown in the Appendices A1 and A2 of the Supporting Information. NBO analysis is widely applied in promoting the interpretation of complex electronic structures.45−47 Schmidt et al. generalized the NBO analysis to bulk materials and/or periodic surface models for which a majority of computational studies utilize plane-wave (PW) density functional theory (DFT) by using the Periodic NBO program.41 ELF50,51 is a

3. RESULTS AND DISCUSSION 3.1. Phase Diagram and Stability of the Se−N System. The convex schema is a widely recognized criterion in judging the thermodynamic stability of compounds with special stoichiometries at high pressures. It suggests that the point in the solid convex line is stable while the point in the dotted convex line is unstable. An extensive structural search of the Se−N compounds is performed. The SeNx (x = 1/2, 2/3, 1, 2, 3, 4, and 5) stoichiometries were optimized at zero temperature and selected pressures of 0, 20, 50, 100, and 150 GPa. As mentioned above, the only reported compound P21/cB

DOI: 10.1021/acs.inorgchem.8b02889 Inorg. Chem. XXXX, XXX, XXX−XXX

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find all “Lewis-like” two-center−two-electron bonds in all stable phases. From Table S1, we can see that Se3 forms a polar (σ, Se-p, N-sp3, 0.79) bond with N3 and 2 equivalent (σ, Se-p, N-sp3, 0.8) bonds with nearby N7, while Se3 has no covalent interaction with the nearby N2. The situation in Se1, Se2, and Se4 is the same as that in Se3. N2 has a nonpolar (σ, N-sp2, N-sp3, 0.99) bond with N7, as does that between N3 and N6. The covalent interaction, described by periodic NBO, is consistent with the chemical picture of the ELF. Actually, by giving a “Lewis-like” chemical picture of the solid, we can not only look inside into the real space property of material, such as hardness, but also get a deep and intuitive understanding of the property in reciprocal space, such as energy band structure. For example, from the energy fat-band (see Figure 3e) and the partial charge density of the highest valence and the lowest conduction band in k-point Γ (see Figure 3a,c), we found that the highest conduction band and the lowest valence band are largely contributed by the polar bonding interaction of bonds (σ, Se-p, N-sp3) and the antibonding interaction of bonds (σ*, Se-p, N-sp3), respectively. Therefore, it is expected that the state in the high-symmetry k-point S, of which the wave vector corresponds to the direction along Se3−N7−Se3, will have a great change in the strength of these bonds and then in the energy of state. That is true for the valence band. By comparing the partial charge density of k-point Γ and k-point S of the highest valence band (see Figure 3a,b), we find that the bonding interaction of (σ, Se3-p, N7-sp3) along the X axis direction increases, which is consistent with the large reduction in the energy in the k-point S relative to the k-point Γ in the highest valence band. However, the situation in the lowest conduction band is unexpected in that the energy is almost the same in k-point Γ and k-point S as compared with the partial charge density of k-point Γ and S in the lowest conduction band (see Figure 3c,d). In a comparison with k-point Γ, it is found that in k-point S the bonding interaction of (σ, Se3-p, N3-sp3) in the Y axis direction increases while the antibonding action of (σ*, Se3-p, N7-sp3) in the X direction increases. These two effects cancel out each other making the energy almost unchanged. As a result, this phase exhibits semiconductivity. 3.3. SeN3: Layers with Covalent and Noncovalent Interaction plus N∞-Chains with Alternation of Single and Weak Double Bonds. The P21/m-SeN3 shown in Figure 2b consists of the alternation of layers and N∞-chains. From the ELF in Figure S10b, we found that the N and Se atoms were combined by covalent interactions to form infinite chains and then form a layered structure through noncovalent interactions. From Table S2, it is found that the Se1 has two slightly different bonds (σ, Se-p, N-sp2, 0.83) and (σ, Se-p, Nsp, 0.78) with the two nearby N6 atoms. In N∞-chains, N1 has a (σ, N-sp3, N-sp3, 0.99) bond with N2 and two bonds with N4. The former is a (σ, N-sp2, N-sp2 0.98) bond and the latter is a weak (π, N-p, N-p, 0.44) bond. This π bond is so weak for the reason that the antibonding NBO of this bond has a large occupation number 1.01, which means that this bond may correspond to some energy levels between that of complete π bonding interaction and complete π antibonding interaction. In other words, it may result in metallicity. In Figure 4a, the 21th and 22th bands overlap along the directions of k-point Y to A and k-point E to C. Also, through the partial charge density of all these four high-symmetry k-points, we found that they are controlled by the weak π bonding interaction or weak

suitable tool for a relative qualitative characterization of chemical bonds combined with topological analysis in molecules and is first systematically investigated in solids by Nesper and Schnering et al.39,40 Both of these two methods have a strong connection with the Lewis structure which remains the basic concept for chemical bond classification and a powerful way to recognize the atomic interactions in materials. Here, we combine them together to seek insight into the chemical properties in the stable phases of the Se−N system at high pressures. The ELF diagrams of these stable phases are integrated into Figure S6. The key information on the “Lewis-like” two-center−two-electron bonds from the Periodic NBO program, such as the exact component of each bond, was integrated into Tables S1−S4. However, in order to simplify our analysis, if the percentage of the s orbital falls in the range 0−15%, 15−30%, 30%−40%, and 40%−50%, the type of this hybrid orbital will be simply divided into p, sp3, sp2, and sp, respectively. To simplify the description of the two-center−two-electron chemical bonds, when we say atom A has a (σ, A-sp, B-sp2, 0.89) natural bond with atom B, it means that atom A uses an sp hybrid orbital to combine with an sp2 hybrid orbital of atom B to form a σ bond of which the bond order is 0.89 (equal to 0.5 × (n1 − n2); n1 is the occupied number of the bonding NBO while n2 is the occupied number the antibonding NBO). All bonds between Se and N atoms are polar with nearly 70% polarizability. Therefore, there will be no more tautology for it. 3.2. SeN 2 : Layered with Covalent Interaction. Obviously, Cmc21-SeN2 shown in Figure 2a has a layer structure, and its ELF shown in Figure S6a indicates that the interaction between two neighboring layers is a noncovalent interaction. As mentioned, in order to comprehend the covalent interaction in the Se−N system, we are going to

Figure 2. Crystal structure of the predicted stable Se−N compounds: (a) Cmc21-SeN2 at 90 GPa, (b) P21/m-SeN3 at 80 GPa, (c) P1̅-SeN4 at 140 GPa, and (d) P1̅-SeN5 at 130 GPa. The sticks represent covalent bonds. The large and small spheres denote selenium and nitrogen atoms, respectively. C

DOI: 10.1021/acs.inorgchem.8b02889 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 3. Partial charge density diagrams for Cmc21-SeN2 of different high-symmetry k-points in the highest valence band and the lowest conduction band: (a) k-point Γ in the highest valence band, (b) k-point S in highest valence band, (c) k-point Γ in the lowest conduction band, and (d) k-point S in the lowest conduction band. The values of these isosurfaces are all 0.015. (e) The energy fat-band diagram of Cmc21-SeN2 on 90 GPa. The circles with the colors pink, blue, and green denote the p state in N, s state in N, and p state in Se, respectively. (f) BZ and highly symmetrical k-points of the lattice of Cmc21 phase.

electron interactions with N1 and N8 in the adjacent cells (see Figure 5a). In a comparison of the partial charge density in k-

Figure 4. (a) Energy fat-band diagram of P21/m-SeN3 on 80 GPa. The circles with colors pink, blue, and green denote the p orbital of N, s orbital of N, and p orbital of Se, respectively. (b) Partial charge density diagram for P21/m-SeN3 on 80 GPa on k-point Y in the 21th band. The value of this isosurface is 0.015.

Figure 5. (a) Three-center−two-electron bond combining Se1 with N1, and N8 in the adjacent cell in P1̅-SeN4. (b) The three-center− two-electron bond combining Se2 and N1, N7 in P1̅-SeN5. (c) The projection drawing of N63− and its nearest two Se atoms in P1̅-SeN5. The values of these isosurfaces are all 0.02.

π antibonding interaction in the N∞-chains (see Figure 4b and Figure S2), proving our conjecture above. 3.4. SeN4: Oligomeric N-Chains. P1̅-SeN4 shown in Figure 2c has a 3D distorted nitrogen backbone chain in which eight nitrogen atoms combine into a finite chain with two terminated Se atoms. From Table S3, both Se1−N7 and Se2− N8 combine to form (σ, Se-p, N-sp3, 0.78) bonds. The bonds of N7−N6, N5−N8, and N3−N4 are all (σ, N-sp2, N-sp2, 0.88) bonds. The other covalent bonds are all (σ, N-sp3, N-sp3, 0.88) bonds. It is worth noting that the Periodic NBO program divides two p orbitals of Se into Natural Rydberg orbitals, which means that these orbitals are too dispersed and cannot be divided into any two-center−two-electron bonds. So, we use the program SSAdNDP to deal with the multicenter twoelectron local interaction, as a supplement for the chemical picture of Periodic NBO and ELF. Using the SSAdNDP program, it is found that Se1 has some three-center−two-

point Γ of the highest occupied band and the lowest empty band (see Figure S3), this three-center−two-electron local interaction can be confirmed. In Figure S1(a), the energy fatband shows that the P1̅-SeN4 with the oligomeric nitrogen backbone phase is metallic, which is not due to the crossing of the energy band as in P21/m-SeN3 but the total valence electron number in this phase. The conductivity is almost determined by the p orbital of N. 3.5. SeN5: Distorted N6-Rings plus N∞-Chains with Alternation of Single and Weak Double Bonds. P1̅-SeN5 shown in Figure 2d has N∞-chains and distorted N6 anion rings with −3 charges. This phase is a semiconductor with a small band gap as shown in Figure S1b. From Table S4, in the infinite chain, N3 has two bonds with N4 of which the first one D

DOI: 10.1021/acs.inorgchem.8b02889 Inorg. Chem. XXXX, XXX, XXX−XXX

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is due to the weak π bond in the N∞-chains. The present study fills the research vacancy in the chemical reaction of Se and N under high pressure theoretically and gives guidance to further experiments on the new high-pressure phases or high-energydensity materials in the Se−N system.

is the (σ, N-sp3, N-sp3, 0.98) bond and the second one is the (π, N-p, N-p, 0.42) bond. Analogously, there are two bonds between N5 and N6 which are the (σ, N-sp3, N-sp3, 0.98) bond and (π, Se-p, N-p, 0.30) bond, respectively. N4 combines with N6 through a (σ, N-sp3, N-sp2, 0.98). N3 and N4 have two lone pair electrons (N-sp, 0.89), while N5 and N6 have two lone pair electrons (N-sp2, 0.85). It is different from the situation in P21/m-SeN3, in which the nitrogen atoms in the chains have the same natural lone pair orbitals and occupation number. This subtle difference from the quantitative information given by the Periodic NBO program can be accounted for by the ionic interaction between these N0.5− anions and Se2+ cation, of which the strength and direction are influenced by the spatial position of these N0.5− anions. What is more attractive is that the N63− ring in this structure contains an astonishing distortion, which is so different from the planar or slightly puckered N rings in the binary nitride system with highly different electronegativities, such as Li−N,20 Rb−N,16 and CaN.12 From Table S4, we found that all the N atoms in N6−3 are connected only by the single bonds (σ, N-sp3, N-sp3, 0.98) which means that the N-p orbital could not form a delocalized π bond as a normal situation in the plane rings. From the ELF (see Figure S6d), it is clear that the lone pair electrons’ space distributions are all affected by the Se2+cation nearby. Is this the complete cause of the distortion in the N63−? We found that the Periodic NBO program divides all p orbitals of Se into natural Rydberg states, which means that these orbitals could not be divided into any two-center−two-electron bonds. However, using the SSAdNDP program we found that Se1 has three three-center−two-electron bonds with N1 and N7, or N1 and N10, or N7 and N10, while Se2 has similar bonds with N2 and N8, or N2 and N9, or N8 and N9. One of these orbital wave function of these bonds is shown in Figure 5b. We can imagine that all these three-center−two-electron bonds on the N63− will clearly drag the N atom to the corresponding Se atoms, and then the consequence undoubtedly is consistent with the real structure in N63− (see Figure 5c). In addition, if we compare the partial charge density of P1̅-SeN5 on k-point Γ between the highest valence band and the lowest conduction band (see Figure S4), this three-center−two-electron bond can be confirmed.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b02889.

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Orbital component, energy fat-band curves, partial charge density, phonon dispersion curves, electron localization function, and crystal structures of the Se− N system (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Da Li: 0000-0002-0041-9181 Tian Cui: 0000-0002-9664-848X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Key R&D Program of China (2018YFA0305900), National Natural Science Foundation of China (91745203, 11404134, 51572108, 11574109, 11674122), Program for Changjiang Scholars and Innovative Research Team in University (IRT_15R23), National Fund for Fostering Talents of Basic Science (J1103202), and Jilin Provincial Science and Technology Development Project of China (20160520016JH). Parts of the calculations were performed in the High Performance Computing Center (HPCC) of Jilin University.

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4. CONCLUSIONS In summary, combining the crystal structure searching method with the first-principles total energy minimization calculations, we explore the new high-pressure phase of SeNx (x = 1/2, 2/3, 1, 2, 3, 4, 5) up to 150 GPa. Four new stable phases Cmc21SeN2, P21/m-SeN3, P1̅ -SeN4, and P1̅ -SeN5 have been identified. Note that nitrogen atoms polymerize in P21/mSeN3, P1̅-SeN4, and P1̅-SeN5 to form a variety of structures. Meanwhile, these phases all have higher energy density of 3.27, 3.26, and 4.08 kJ g−1, respectively. With the help of quantitative information offered by the Periodic NBO and SSAdNDP program, we describe the bonding modes of all the stable phases in detail in terms of a “Lewis-like” two-center− two-electron bond and a three-center−two-electron bond and construct a complete chemical picture about the covalence interaction in these compounds. On this basis, the distortion of the N63− ring in P1̅-SeN5, which is nonaromatic, can be explained by the three-center−two-electron bond between Se and N atoms. The origination of the semiconductor-type band structure of Cmc21-SeN2 has been discussed through the view of a covalence interaction, while the metallicity in P21/m-SeN3

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DOI: 10.1021/acs.inorgchem.8b02889 Inorg. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.inorgchem.8b02889 Inorg. Chem. XXXX, XXX, XXX−XXX