Article pubs.acs.org/JPCA
A New Allotrope of Nitrogen as High-Energy Density Material Michael J. Greschner,†,‡ Meng Zhang,*,§ Arnab Majumdar,† Hanyu Liu,∥ Feng Peng,⊥,# John S. Tse,† and Yansun Yao*,†,‡ †
Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E2, Canada Canadian Light Source, Saskatoon, Saskatchewan S7N 2V3, Canada § Department of Physics, East China University of Science and Technology, Shanghai 200237, China ∥ Geophysical Laboratory, Carnegie Institution of Washington, NW, Washington, D.C. 20015, United States ⊥ College of Physics and Electronic Information, Luoyang Normal University, Luoyang 471022, China # Beijing Computational Science Research Center, Beijing 10084, China ‡
S Supporting Information *
ABSTRACT: A new allotrope of nitrogen in which the atoms are connected to form a novel N6 molecule is predicted to exist at ambient conditions. The N6 molecule is a charge-transfer complex with an open-chain structure containing both single and triple bonds. The charge transfer induces ionic characteristics in the intermolecular interactions and leads to a much higher cohesive energy for the predicted crystal compared to solid N2. The N6 solid is also more stable than a previously reported polymeric solid of nitrogen. Because of the kinetic stability of the molecules and strong intermolecular interactions, the N6 crystal is shown by metadynamics simulations to be dynamically stable around room temperature and to only dissociate to N2 molecules above 700 K. The N6 crystal can likely be synthesized under high-pressure high-temperature conditions, and the considerable metastability may allow for an ambientpressure recovery of the crystal. Because of the large energy difference between the single and triple bonds, the dissociation of the N6 crystal is expected to release a large amount of energy, placing it among the most efficient energy materials known today.
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Theoretical predictions9−14 have been demonstrated to be very successful in leading to the discovery of new nitrogen allotropes. In recent years, several hypothetical structures have made their real-world appearance in laboratory, including the N3 and N4 molecules,1 N5 ions,4,5 as well as the polymeric crystal.7 In a recent study, Hirshberg et al.15 predicted the existence of a molecular crystal of nitrogen consisting of novel N8 molecules. This solid contains two different isomers of N8, where the two N4 units are connected in either cis (Z) or trans (E) configuration with respect to the central double bond. This crystal was predicted to be metastable at ambient conditions and to have a large energy content (∼260 kcal mol−1), which is superior to many modern HEDMs. The N8 crystal was suggested to be formed from a crystal composed of the N4 molecules, while the synthesis of this precursor is still ongoing. This therefore motivated us to explore the possibility of finding crystals with polynitrogen molecules that may be directly formed from N2. In this study we focus on the N6 molecules. As per the Lewis structures, the N6 and N8 molecules have a similar number of single bonds and therefore have comparable energy content. As well, it may be possible to form N6 molecules directly from N2. The N2 to N6 transition is associated with a large energy barrier, which inhibits the
INTRODUCTION Allotropic modifications of nitrogen, that is, compounds consisting of endothermic nitrogen molecules, have been actively investigated as high-energy-density materials (HEDM). Under ambient conditions, nitrogen exists as a diatomic N2 form with a triple bond. This bonding is recognized as the strongest in nature, making N2 chemically inert. At cryogenic conditions, N2 crystallizes into a solid in which the molecules are held together by van der Waals (vdW) forces. Allotropic modification of nitrogen is achieved by transforming N2 into single- or double-bonded metastable forms, such as polynitrogen molecules or polymeric crystals.1−5 Because of the large energy difference between the single (∼40 kcal mol−1) and triple bonds (∼225 kcal mol−1), nitrogen allotropes are efficient energy carriers, which, if metastable at ambient conditions, would be placed among the most powerful HEDMs known today. The decomposition of nitrogen allotropes is environmentally friendly, producing only nontoxic N2. In 1992, Mailhiot et al. made a ground-breaking prediction,6 that a solely single-bonded phase of nitrogen (the “cubic gauche” (cg) phase) could be thermodynamically stable under high pressure. Remarkably, after overcoming substantial experimental difficulties, the cg phase was successfully synthesized in 2004 via high-pressure (>120 GPa) high-temperature (>2500 K) techniques.7 Along with the cg phase, amorphous nitrogen was also synthesized, which contains nonmolecular nitrogen clusters.8 © 2016 American Chemical Society
Received: February 18, 2016 Revised: April 13, 2016 Published: April 18, 2016 2920
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ensemble using VASP and optPBE-vdW functional38,39 to take into account the vdW interactions.
transition at ambient conditions. The energy barrier may be overcome by applying external pressure. As shown previously by molecular dynamics (MD) simulations,16 crystalline N2 (εphase) can be transformed without a barrier to a crystalline mixture containing N2 and N6 molecules near 60 GPa. Experimentally, evidence of a cyclic N6 molecule (benzene analogue) has been observed in an elimination reaction of a diazido platinum complex at 77 K.17 Different synthetic routes to N6 isomers18−20 have been theoretically investigated, while the crystalline phases21 have been experimentally attempted using the photolysis of compressed sodium azide (NaN3). Recently, crystals containing ionized N6 molecules were predicted to form in alkali metal nitrides under high pressure.22−28 Crystals consisting of neutral N6 molecules, however, are a relatively new territory yet to be explored, both theoretically and experimentally. In the present study, we investigated the possible existence of crystalline N6 using state-of-the-art first-principles computational methods. The global minimum geometry of the N6 molecule is identified to have a charge-transfer open chain structure. Because of the charge disparity of the N6 molecules, in the solid state, the N6 molecules are stabilized by strong electrostatic attractions from four nearest-neighbor molecules. These ionic interactions resulted in a fairly high cohesive energy (7.09 kcal mol−1) making the crystal structure metastable at ambient conditions. This is supported by metadynamics simulations showing that the new allotrope of nitrogen is dynamically stable around room temperature, and only dissociates to pure N2 above 700 K. The dissociation is highly exothermic with a large energy release (estimated as 185 kcal mol−1). Because of the stability of the N6 molecule and strong electrostatic interactions in the crystalline environment, the predicted crystal has considerable kinetic stability and may be recoverable once it is produced under high pressure.
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RESULTS AND DISCUSSION The N6 Molecule: Diazide or Benzene Analogue? There have been many theoretical studies40−45 addressing the stability of the N6 isomers, either regarding it as an open-chain diazide (e.g., C2h, C2v) or as a benzene analogue (e.g., D6h, D2h, D2). The swarm-intelligence structure search and vibrational analysis identified a number of N6 isomers in both categories (for details see Supporting Information). From this, it appears that the open chain structures are more energetically favorable than the ring structures. The diazide C2h geometry was found to be the global minimum, while the benzene analogue D6h and its Jahn−Teller variation C2 are at 1.30 and 1.19 eV above, respectively. This suggests that the triple bonding in open-chain structures are substantially more favorable than the π bonding in benzene analogues. The geometry of the C2h isomer is consistent with a N3−− N3+ adduct (Figure 1a), which could dissociate into a (N2)3
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METHODS The search for the global minimum geometry of the N6 molecule was performed using the swarm-intelligence Crystal structure Analysis by Particle Swarm Optimization (CALYPSO) algorithm.29,30 More than 400 distinct N6 isomers were generated in the search and fully relaxed using all-electron, spinunrestricted relativistic calculations, with the Perdew−Burke− Ernzerhof (PBE) functional31 and double-numerical basis sets including d polarization functions implemented in the DMoL3 program.32 After the relaxation, the low-energy isomers were selected for more refined optimization and vibrational analysis, using the MP2 calculations with a larger cc-pVDZ basis set and the Gaussian09 package.33 Crystal structures were constructed from random distributions of the lowest energy N6 molecules. Five hundred stacking patterns were generated in unit cells of arbitrary shapes containing up to four N6 molecules. Crystal structures were fully optimized using the Vienna Ab initio Simulation Package (VASP).34 A projector augmented wave potential35 with the PBE functional and a cutoff energy of 400 eV were used. Phonons were calculated on a 2 × 2 × 2 supercell using the finite displacement method.36 Enthalpy and electronic structure calculations were performed with the VASP code. A dense 12 × 12 × 12 k-point grid was used to sample the Brillouin zone (BZ), which was shown to yield convergence for total energies within 1 meV atom−1. Metadynamics simulations37 were performed in supercells with eight N6 molecules with a 2 × 2 × 2 k-point mesh for BZ sampling. Each metastep consisted of an MD simulation in an NVT
Figure 1. Structure and electronic structure of the global-minimum N6 molecule. (a) Optimized C2h geometry and (b) dissociation to N2. Numbers are NBO charges (e−, red) and bond lengths (Å, black), respectively. (c) The Lewis structure and (d) deformation electron density. (e, f) Isosurfaces of two HOMOs plotted using the isovalue of 0.01 e− Å−3. All calculations were completed at the MP2/cc-pVDZ level.
trimer (Figure 1b). Natural bond orbital (NBO) analysis46 reveals that the two identical terminal bonds, N1−N5 and N3− N6, have strong triple bond character with the bond length of 1.16 Å, which is only slightly longer than the bond length in N2 (1.11 Å). Between the N4 and N2 atoms the bond is a single bond, with the bond length of 1.46 Å. The bond length for the two internal bonds, N5−N4 and N2−N3, is 1.26 Å, which is similar to the bond length in diazene N2H2 (1.25 Å). The NBO analysis reveals that the N5−N4 and N2−N3 are polar bonds, with an amount of charge (∼0.2 e−) being transferred from the N5 (N3) atom to the N4 (N2) atom. The Lewis structure and Voronoi deformation density of the C2h isomer are shown in Figure 1c,d. This molecule is stabilized by several resonance structures, namely, NN+−N−−N−−N+N ↔ NN+N− N−−N−N+. Molecular orbitals (MO) analysis (Figure 1e,f) 2921
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Such an arrangement therefore favors attractions between atoms with the opposite charges, and minimizes repulsions between lone pairs. Calculated cohesive energy for the (N6)2 dimer is 5.54 kcal mol−1, suggesting strong interactions between N6 molecules. The N6 Crystal: Maximized Electrostatic Stabilization. The lowest-energy crystal structure has a monoclinic unit cell with the C2/m space group (Figure 3a; see structural parameters in Supporting Information). The number of nearest neighbors is maximized in the crystalline phase. In this structure, the N6 molecules are only slightly distorted from their gas-phase geometry. The bond lengths for the N1−N5, N5−N4, and N2−N4 bonds are 1.15, 1.24, and 1.42 Å, respectively, very close to the gas-phase values. In the C2/m structure, the N6 molecules are arranged in slabs, while the slabs are held together by vdW interactions (Figure 3b). Within the slab, the intermolecular N···N interactions are maximized through electrostatic attractions from four nearest neighbors, which results in a cohesive energy of ∼7.09 kcal mol−1 (calculated as the difference between the average energy of a N6 unit in solid and the energy of a gas-phase N6 at T = 0 K). The cohesive energy of the N6 solid is substantially higher than the cohesive energy of the N2 solid (∼1.98 kcal mol−1). The difference can be attributed to the enhanced intermolecular interactions due to the charge disparity of the N6 molecules. Using the energy difference between the N2 and N6 molecules, and the cohesive energy of the N6 crystal, the energy release in the dissociation of the N6 crystal to N2 molecules is estimated to be ∼185 kcal mol−1 (or 61.6 kcal mol−1 per N2) at T = 0 K. Such a high energy density, if realized, would place the N6 crystal among the best performing high-energy materials known today. To examine the energetics of the N6 crystal, the enthalpy of the C2/m structure was calculated and compared with other crystalline forms of nitrogen (Figure 3c). The vdW interactions were taken into account using nonlocal optPBE-vdW density functional. The calculation was also repeated using semiempirical DFT-D2 corrections,47 and the standard PBE functional (see details in Supporting Information). In the
indicates that the two degenerate highest occupied molecular orbitals (HOMOs) are derived from the N5−N4 and N2−N3 bonding orbitals, where the π characters are clearly visible (additional MOs are provided in Supporting Information). In the N6 molecule the 2pπ orbital has higher energy than the 2pσ orbital, which differs from the situation of N2, where the two orbitals have an energy crossover. The absence of the crossover in the N6 molecule is due to the elongated NN bond length, which results in a lower bond order for the 2pσ orbital and less antibonding mixing with the 2sσ orbital. The dissociation of the N6 molecule involves simultaneous breaking of the N5−N4 and N2−N3 bonds (Figure 1b), with a calculated energy release of 8.33 eV/N6 at T = 0 K. The (N6)2 Dimer: Electrostatic Stabilization by Molecular Charge Disparity. In the crystalline environment, N6 molecules are expected to preserve their chemical integrity. The intermolecular interactions are mainly vdW and electrostatic in origin. This bonding environment was analyzed on the globalminimum (N6)2 dimer (Figure 2). In the dimer, the two N6
Figure 2. Structure of the global-minimum (N6)2 dimer. Numbers in red and black indicate the NBO charges (e−) and N−N distances (Å), respectively.
molecules are identical and suited in a way that the closest N··· N contact (2.89 Å, less than the sum of two vdW radii) connects the N3(N5) and N2(N4) atoms of the two molecules.
Figure 3. Structure and energetics of the crystalline nitrogen. (a) Unit cell of the crystalline N6 structure with the C2/m space group. (b) Network of the intermolecular N···N contacts shown in a slab of N6 molecules in the structure. (c) Calculated enthalpies per atom for different forms of crystalline nitrogen. The enthalpy of the cg structure is used as the zero-energy reference level. 2922
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character are located in lower energy regions, in particular, between −5 and −10 eV, where the 2pσg orbital mixes with 2sσg orbital. Phonon dispersion relations for the N6 crystal were calculated at ambient pressure (Supporting Information). Notably, all vibrational modes were found to be positive, suggesting this crystal is mechanically stable and might be quench recoverable at ambient pressure. The metastability is due to the intrinsic stability of the N6 molecule and the nearestneighbor electrostatic interactions in the solid phase. Thermal Effect on the N6 Crystal: Dissociation and Energy Release. Metadynamics simulations were employed to provide insight into the thermodynamic behavior of the N6 crystal. Calculations were performed at 1 atm and different temperatures, namely, 300, 500, 700, 1200, 1500, and 2000 K, with a simulation time over 40 ps (0.4 ps for each metastep). At 300 K, the crystal was found to be stable, where the thermal fluctuation of the volume is clear (Figure 5a). The dissociation of the crystal started at 700 K, and it became more dramatic at elevated temperatures (Figure 5a,b). At 700 and 1200 K, the enthalpy evolution in the simulation shows a stepwise path, where the plateau regions represent progressive dissociations of the N6 molecules. At 1200 K, plateaus in the enthalpy were observed at metasteps 5−7, metasteps 8−16, and metasteps 18−29, corresponding to the dissociation of 1/2, 5/8, and 7/8 of N6 molecules in the crystal, respectively, until, eventually, pure N2 is observed at the 30th metastep (Figure 5c). The entire dissociation process at 1200 K lasted 12 ps, or 30 metasteps, which is substantially shorter than what is required at 700 K, for example, 41.2 ps (103 metasteps). Heating further, to 1500 K and above, the enthalpy evolution proceeds straight downhill with no outstanding intermediate stages. The enthalpy release in the thermal dissociation is enormously large, that is, 0.9 eV/atom, along with a considerable volume expansion of ∼46% (Figure 5a,b). These values, however, are still likely to be underestimated since the actual N2 product is expected to be in the gas phase, while metadynamics simulation was performed in the crystalline phase. Regardless, the metadynamics simulations employed here reveal a kinetically stable range for the N6 crystal under ambient conditions, which is critical for the practical application of this novel material.
studied pressure range, the most stable crystalline phase is the one consisting of solely N2 molecules; its overwhelming stability is owed to the strong NN bonds. At ambient pressure, the cg phase7 is energetically the least favorable due to the high energy of the N−N bonds. The nonmolecular structure that contains extended chains of alternating single and double bonds16 has lower energy than the cg phase. Both the N6 crystal and the N8 crystal15 have a mixture of single and triple bonds, so their enthalpies are comparable. Clearly the energetic order at ambient pressure is determined by the stability of the constituent nitrogen forms, but nonmolecular crystals (cg and extended chain structures) are denser than molecular ones, and therefore they are favored by virtue of smaller pV works at high pressure. Most importantly, the N6 crystal is calculated to be more stable than the cg phase below 22 GPa and more stable than the extended chain structure below 5.2 GPa, so it is the most preferred nonmolecular N2 structure. The bonding pattern in the N6 crystal was analyzed through the electron localization function48 (ELF; Figure 4a,b). A σ
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SUMMARY As potential high-energy density materials, allotropic modifications of nitrogen have been actively investigated by both experiment and theory. Here we predict a new molecular crystal of nitrogen consisting of novel N6 molecules, instead of ordinary N2. The constituent N6 molecule has a charge-transfer open-chain structure that is stabilized by strong electrostatic interactions in the solid. Metadynamics simulations revealed this crystal to be metastable at ambient conditions, and to dissociate to N2 molecules at temperatures above 700 K. Because of the large energy difference between the N−N and NN bonds, dissociation of the N6 crystal is expected to release a large amount of energy (∼185 kcal mol−1). At ambient conditions, the N6 crystal is thermodynamically much more stable than the previously synthesized cubic gauche phase of nitrogen. The N6 crystal also has considerable kinetic stability around room temperature, which may be sufficient for an ambient-pressure recovery. The results obtained in this study provide new insight into the understanding of nitrogen allotropes, and we hope these new results will stimulate future experimental exploration into the synthesis of this material.
Figure 4. Electronic structure of the crystalline N6. (a) Three dimensional ELF isosurface (value = 0.7) and (b) the ELF contours drawn in the plane that contains the N6 molecules. “LP” indicates the lone pairs. (c) Electronic band structure and projected DOS calculated at ambient pressure.
bond is clearly identified between N4 and N2 atoms as well as the lone pairs outside the molecule. Between N5(N3) and N4(N2) the bonding is predominately σ type with admixture of π bonding. The bonding between N1(N6) and N5(N3) has both σ and π characters, consistent with a triple bond description. The band structure and density of states (DOS; Figure 4c) show that the N6 crystal has an insulating ground state with a pseudodirect band gap of ∼1.7 eV, approximately at the energy lower limit for visible light spectrum (Note that the band gap is likely underestimated in generalized gradient approximation (GGA)). The projected DOS shows that the energy bands located around the band gap are characteristic of the 2pπu (below) and 2pπg* (above) orbitals. Orbitals with s2923
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Figure 5. Dissociation of the crystalline N6. Evolutions of the (a) volume and (b) enthalpy of the N6 crystal at ambient pressure and T = 300, 700, 1200, and 1500 K. (c) Instantaneous simulation cell at selected metasteps from the simulation at T = 1200 K. The N6 and N2 molecules are colored blue and red, respectively.
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(3) Olah, G. A.; Surya Prakash, G. K.; Rasul, G. N62+ and N42+ Dications and Their N12 and N10 Azido Derivatives: DFT/GIAO-MP2 Theoretical Studies. J. Am. Chem. Soc. 2001, 123, 3308−3310. (4) 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. Chem., Int. Ed. 1999, 38, 2004−2009. (5) Vij, A.; Pavlovich, J. G.; Wilson, W. W.; Vij, V.; Christe, K. O. Experimental Detection of the Pentaazacyclopentadienide (Pentazolate) Anion, cyclo-N5−. Angew. Chem. 2002, 114, 3177−3180. (6) Mailhiot, C.; Yang, L. H.; McMahan, A. K. Polymeric Nitrogen. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 46, 14419−14435. (7) Eremets, M. I.; Gavriliuk, A. G.; Trojan, I. A.; Dzivenko, D. A.; Boehler, R. Single-Bonded Cubic Form of Nitrogen. Nat. Mater. 2004, 3, 558−563. (8) Eremets, M. I.; Hemley, R. J.; Mao, H.-k.; Gregoryanz, E. Semiconducting Non-Molecular Nitrogen up to 240 GPa and Its LowPressure Stability. Nature 2001, 411, 170−174. (9) Alemany, M.; Martins, J. L. Density-Functional Study of Nonmolecular Phases of Nitrogen: Metastable Phase at Low Pressure. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 68, 024110. (10) Zahariev, F.; Hu, A.; Hooper, J.; Zhang, F.; Woo, T. Layered Single-Bonded Nonmolecular Phase of Nitrogen from First-Principles Simulation. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 72, 214108. (11) Oganov, A. R.; Glass, C. W. Crystal Structure Prediction Using Ab initio Evolutionary Techniques: Principles and Applications. J. Chem. Phys. 2006, 124, 244704. (12) Yao, Y.; Tse, J. S.; Tanaka, K. Metastable High-Pressure SingleBonded Phases of Nitrogen Predicted via Genetic Algorithm. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, 052103. (13) Ma, Y.; Oganov, A.; Li, Z.; Xie, Y.; Kotakoski, J. Novel High Pressure Structures of Polymeric Nitrogen. Phys. Rev. Lett. 2009, 102, 065501. (14) Wang, X.; Wang, Y.; Miao, M.; Zhong, X.; Lv, J.; Cui, T.; Li, J.; Chen, L.; Pickard, C. J.; Ma, Y. Cagelike Diamondoid Nitrogen at High Pressures. Phys. Rev. Lett. 2012, 109, 175502. (15) Hirshberg, B.; Gerber, R. B.; Krylov, A. I. Calculations Predict a Stable Molecular Crystal of N8. Nat. Chem. 2013, 6, 52−56.
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b01655. Details of optimized geometries of the gas-phase N6 isomers; molecular orbitals, thermodynamic stability and Natural bond orbital analysis of the C2h isomer; structure parameters of the predicted crystalline N6 phase; phonon dispersion relations for the crystalline N6 structure; analysis of the van der Waals interactions in nitrogen crystals. (PDF)
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AUTHOR INFORMATION
Corresponding Authors
*Phone: 86-21-64253964. E-mail:
[email protected]. (M.Z.) *Phone: 1-306-9666430. E-mail:
[email protected]. (Y.Y.) Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS M.J.G., A.M., and Y.Y. thank the ICT group at the Univ. of Saskatchewan, WestGrid, and Compute Canada for providing computing resource. This project was supported by Natural Sciences and Engineering Research Council of Canada (NSERC), and by National Natural Science Foundation of China (Grant No. 11204079).
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DOI: 10.1021/acs.jpca.6b01655 J. Phys. Chem. A 2016, 120, 2920−2925
