Calculations Predict a Stable Molecular Crystal of N

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ARTICLES PUBLISHED ONLINE: 15 DECEMBER 2013 | DOI: 10.1038/NCHEM.1818

Calculations predict a stable molecular

crystal of N8 Barak Hirshberg1,R.BennyGerber1,2* and Anna I. Krylov3

Nitrogen, one of the most abundant elements in nature, forms the highly stable N2 molecule in its elemental state. In contrast, polynitrogen compounds comprising only nitrogen atoms are rare, and no molecular crystal made of these compounds has been prepared. Here, we predict the existence of such a molecular solid, consisting of N8 molecules, that is metastable even at ambient pressure. In the solid state, the N8 monomers retain the same structure and bonding pattern as those they adopt in the gas phase. The interactions that bind N8 molecules together are weak van der Waals and electrostatic forces. The solid is, according to calculations, more stable than a previously reported polymeric nitrogen solid, including at low pressure (below 20 GPa). The structure and properties of the N8 molecular crystal are discussed and a possible preparation strategy is suggested.

itrogen is one of the most abundant elements on Earth, Supplementary Fig. 1. A non-polymeric, molecular phase of nitrogen constituting 78% of the atmosphere in its elemental form consisting of a mixture of planar N6 and N2 has been considered 15 N(diatomic gas N2). Under cryogenic conditions it exists in theoretically . At pressures around 60 GPa, a barrierless trans- E the solid state as a crystalline solid in which N2 molecules, which formation of -N2 into a hybrid N6/N2 structure, in which the two feature a very strong intramolecular triple bond (225 kcal mol21), molecules appear in the unit cell, has been observed in calculations. are held together by weak van der Waals intermolecular forces. However, this structure has higher enthalpy than cg-N. A question of great fundamental interest is whether other molecular Experimentally, the cg-N form was characterized in 2004 (ref. 18). crystals made of pure nitrogen molecules may exist. Indeed, there has This single-bonded form of nitrogen was synthesized directly from been an intensive quest in recent years for new polyatomic molecules molecular nitrogen at temperatures above 2,000 K and pressures and ions only made of nitrogen1–7, and theoretical studies have played above 110 GPa. Such high temperature and pressure were required an important role in exploring the range and conditions of existence because of the large energy barrier associated with this phase tran- of different metastable nitrogen species8–13. sition, which involves significant rearrangement of bonds and a A major motivation for this pursuit is that polynitrogen molecules large change of volume per nitrogen atom (35%). This leads to large are expected to release large amounts of energy when decomposing hysteresis in the phase transition, which explains previous failures to into the very stable N2 molecules. Therefore, these species are poten- produce cg-N. It also suggests a wide range of metastability for this tially promising as high-energy-density materials (HEDM). Among polymeric form. At room temperature, cg-N was found to be meta- the different energetic nitrogen compounds (nitrates, ammonia, stable down to 42 GPa (ref. 18). Another experimentally observed nitramines, azides, polyazides and so on), pure polynitrogen form of nitrogen was a semiconducting dark amorphous form19 pro- molecules are particularly attractive, both because of the expected duced at 300 K and 240 GPa. It has been speculated that this form high energy density and because the sole product of their decompo- consists of a mixture of small clusters of non-molecular phases. sition is N2, which is inert, non-toxic and not a greenhouse gas. Here, we report a theoretical prediction of a molecular crystalline To date, most studies on polynitrogen species have involved iso- solid consisting of N8 molecules—a molecular form of solid nitro- lated compounds in the gas phase. These include the experimental gen that is not composed of N2 molecules. As will be discussed − detection of N3,N4 and N5 (refs 1–5). A notable discovery of nitro- below, the solid is predicted to be stable even at ambient pressure. þ gen-rich species in the condensed phase is that of the ion N5 It is computed to be highly energetic upon decomposition into (ref. 6). This can be stabilized with various counter ions (including nitrogen molecules. The crystalline solid was obtained spon- 2 nitrogen-rich ones) such as [B(N3)4] (ref. 7), and can be prepared on taneously (as discussed below) during the optimization of a tetramer a macroscopic scale. However, no molecular solid consisting purely of of N4 using periodic boundary conditions. The fact that N4 was Nn species has been detected or synthesized experimentally to date. detected experimentally may suggest a strategy (admittedly speculat- A number of nitrogen compounds have been predicted to be stable ive) for experimental preparation of this solid. in the gas phase8–10,12. In addition, several theoretical studies have also investigated different phases of solid nitrogen14–16. Several chain-like Results and discussion and three-dimensional solids have been predicted to be stable at For a molecular solid to be stable on a macroscopic scale, three high pressure, including the polymeric, cubic gauche (cg-N) structure, requirements must be satisfied. First, the molecular building which was first predicted in 1985 (ref. 17), which is the most stable blocks should be stable in the gas phase. In addition, the molecules below 170 GPa (ref. 16). Among the high-pressure phases, at pressures (or ions) should retain chemical stability in the crystal, that is, they E below 47 GPa, a molecular phase -N2 has been predicted to be the should not react with their neighbours. Finally, the interactions one with lowest enthalpy (at ambient pressure, the lowest enthalpy between molecules in the crystal should be of van der Waals and E phase is a-N2). The structures of a-N2, -N2 and cg-N are given in electrostatic types, such that the chemical identity of the constituting

1Institute of Chemistry and The Fritz Haber Center for Molecular Dynamics, The Hebrew University, Jerusalem 91904, Israel, 2Department of Chemistry, University of California, Irvine, California 92697, USA, 3Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, USA. *e-mail: [email protected]

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NATURE CHEMISTRY DOI: 10.1038/NCHEM.1818 ARTICLES

a c

EEE

EZE

b N N N N 45 N N 2 3 NN6 1 8 7

Figure 1 | Crystal structure of the predicted N8 solid and bonding pattern in N8 molecules. a, Unit cell of the crystalline solid N8 showing the two isomers EEE and EZE. b, Lewis structure of N8 as derived from NBO analysis. c, Crystalline lattice of the N8 solid, featuring the unit cell shown in a. The unit cell contains two different isomers of N8, EZE and EEE, 3.2 Å apart.

21 molecules is preserved. The study of the possible existence of solid (9.8 kcal mol ), which is substantially higher than that of N2 20 21 HArF is a dramatic example where this is not satisfied ; in this (the cohesive energy of the a-phase of N2 is 8.3 kJ mol ). This case, bringing together HArF molecules results in decomposition. stronger cohesive energy is due to considerable contribution of elec- On the other hand, a different compound, HXeCCH, was predicted trostatic interactions, as illustrated by the partial charges shown in to be stable as a crystalline solid, retaining the chemical identity of Fig. 2. Accordingly, a more reasonable comparison would be CO2 the isolated molecules21. and acetonitrile, which have cohesive energies of 26 and Initially, we intended to study the possibility of the formation of a 53 kJ mol21, respectively (Supplementary Table 4). Thus, cohesive crystal composed of N4 molecules by studying the stability of small energy of the predicted solid N8 is similar in magnitude to the cohe- clusters of N4. After finding a stable structure for a tetramer on the sive energy of a non hydrogen-bonded polar molecular solid such as potential energy surface, we initialized an optimization procedure acetonitrile. To validate the methodology, we computed the opti- using periodic boundary conditions. This procedure converged mized unit cell structures and cohesive energies of N2,CO2 and spontaneously to the crystal structure of solid N8 given in the fol- acetonitrile (Supplementary Table 4). We found that the method- lowing. Then, using plane-wave density functional theory ology used gave structures and cohesive energies within a few (PW-DFT) with periodic boundary conditions and the Perdew– percent of the experimental values. Burke–Ernzerhof (PBE) functional22 augmented by dispersion cor- To examine the robustness of the prediction made with the PBE rection23 (PBE-D), we found that a solid consisting of two isomers of functional we also re-optimized the structures and computed cohe- N8 is stable at low pressure. To examine the robustness of the equi- sive energies using another functional with empirical dispersion librium structure we carried out calculations using several different correction (BLYP-D) and a non-local VDW-DF (van der Waals initial structures, including one in which an N8 molecule in the unit density functional) designed for a more rigorous treatment of dis- 24 cell is separated to N3 and N5 fragments 2 Å apart, and one in persion within DFT . The variations in computed atomic which the terminal N3 group is rotated out of plane. The optimiz- volumes were less than 10%. We note that VDW-DF predicts an ation led in all cases to the same final structure. even larger cohesive energy than PBE-D (Supplementary Table 1). Enthalpy calculations were also carried out and revealed that this The similarity of the results obtained by three different functionals structure is more stable than the cg-N form below 20 GPa. At (and three different treatments of dispersion interactions) greatly ambient pressure, it shows 0.5274 eV per nitrogen atom stabiliz- strengthens the confidence in the prediction made here for the N8 ation relative to the cg-N form. For comparison, a-N2 is solid. To further validate the plane-wave DFT calculations, we opti- 1.4143 eV atom21 more stable than cg-N at ambient pressure. The mized the structures of the two isomers (EEE and EZE) and their corresponding cohesive energy is found to be 41.1 kJ mol21 dimer using plane-wave PBE-D, PBE-D and vB97X-D with the (9.8 kcal mol21), which is almost five times stronger than that in aug-cc-pVDZ basis set (see Supplementary Section II for full calcu- solid N2. In the following we describe the computed properties of lation details). The respective structural parameters and natural this material, analyse its electronic structure and bonding patterns, bond orbital (NBO) charges are given in Supplementary Table 2. and present vibrational spectra calculations that might be helpful for We found that the variations in structural parameters due to differ- experimental detection and characterization of this exotic material. ent levels of theory are relatively small, for example, a maximal Figure 1 shows the optimized unit cell structure of N8. The lattice change of 0.1 Å for N–N bond lengths. We also note that the parameters are given in Table 1. The atomic volume V0 of this structure is 14.89 Å3, which is significantly larger than that of cg-N 3 3 Table 1 | Unit cell parameters and lattice energy for (6.767 Å ) but lower than that of a-N2 (21.202 Å ). The structure is a true energy minimum, as verified by the fact that all computed crystalline N8. vibrational frequencies are positive. The structure is close to Parameter Value monoclinic and the unit cell contains two N8 molecules 3.2 Å a (Å) 10.72 apart (distance between N5 of EZE and N6 of EEE) (ref. 10). b (Å) 4.53 Interestingly, the solid is composed of two different isomers of c (Å) 6.90 N8, cis (Z) and trans (E) linear chains (using the notations from a 91.5 b 84.9 ref. 10, these are EEE and EZE isomers of N8). The cohesive energy of N (computed as the difference between g 45.9 8 3 V0 (Å )14.89 the energy of the solid divided by the number of molecules in the 21 unit cell and the monomer energy) is 41.1 kJ mol21 Lattice energy (kJ mol )41.1

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ARTICLES NATURE CHEMISTRY DOI: 10.1038/NCHEM.1818

a 1.255 1.239 1.126 EEE –0.22 1.389 0.25 –0.06 0.03

1.237

–0.04 1.256 1.126 1.405 EZE

–0.25 0.26 0.03

b 1.248

1.251 1.417 –0.03 1.139

1 –0.26 0.26 0.04 .382

1.266 1.251 1.138 –0.06 0.02 –0.21 0.25

1.127 1.257 1.236 1.406 1.241 –0.04 1.395 1.255 3.323 1.126 –0.25 –0.06 0.26 0.03 –0.22 0.25 0.02

Figure 2 | Structures and HOMOs of the components of the solid. The structures and data calculated by NBO are shown on the left, the corresponding

HOMOs on the right. a, EZE and EEE isomers of N8. b, EZE–EEE dimer from the optimized unit cell. c, Lowest-energy dimer of the two isomers. Black, bond lengths (Å); red, partial charges. Structures, molecular orbitals and charges are computed with vB97X-D/aug-cc-pVDZ. The unit cell geometry is the ﬁnal geometry from the PW-PBE-D optimization.

a 0.4 b 382.4 cg-N 0.2 382.5 N8

382.6

0.0 382.7

382.8 (eV per atom) –0.2 cg-N

cg-N N 8 E (eV per atom) 382.9 Cmcm H-H CH 383.0 –0.4 LB E 383.1 -N2 –0.6 383.2 0 102030405060 6 8 10 12 14 16 Pressure (GPa) Volume (Å3)

Figure 3 | Thermodynamic stability of different forms of solid nitrogen. a, Pressure dependence of the enthalpy (H ¼ E þ PV) difference with that of cg-N, per nitrogen atom, and comparisons with other high-pressure phases of solid nitrogen. It is seen that solid N8 is predicted to be more stable than other polymeric forms of nitrogen at low pressures (under 20 GPa). b, Computed energy versus volume dependence for cg-N and N8 solid, showing large differences in atomic volume.

+ − NBO charges computed by different methods are similar, which reaction between N5 and N3 . The structures and NBO charges provides additional support to the PBE calculations of the solid. (as well as molecular orbitals) of the EEE and EZE N8 molecules The electronic structure and energetics of N8 isomers have been as well as relevant dimers are shown in Fig. 2. Additional data are characterized in ref. 10, which investigated possible products of the summarized in Supplementary Section VI.

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NATURE CHEMISTRY DOI: 10.1038/NCHEM.1818 ARTICLES

× × × 21 equal to Ecoh ¼ 0.5 (Eb 8 2 2 Eb) ¼ 7.5 Eb ¼ 7.3 kcal mol .

) This estimate (which neglects molecular relaxation, many-body –1 35/33 (31/29) interactions and pairwise interactions beyond the nearest 24/22 (13/8) neighbours), is close to the computed cohesive energy of the solid (9.8 kcal mol21). Figure 3a shows enthalpy versus pressure for several forms of solid nitrogen (the results for solid N8 are computed with PW- PBE-D; the data for all other forms are from ref. 16 and 15/14 (14/13) Supplementary Section VIII presents details). Enthalpy calculations reveal that at ambient pressure N8 solid is considerably more stable than cg-N (the enthalpy stabilization per nitrogen atom is 2N + N 226/256 3 2 0.5274 eV atom21). It is also more stable than other forms N6 + N2 (except, of course, the most stable high-pressure form, E-N ). The Relevant energies ( Δ H / G , kcal mol 2 difference is sensitive to pressure, and at 20 GPa, cg-N becomes more stable. The atomic volumes of the two forms at this pressure 3 3 are 6.348 Å and 8.897 Å for cg-N and solid N8, respectively. Thus, 21 Figure 4 | Relevant energies (DH/DG,inkcalmol )oftheN8 isomers due to the large change in atomic volume ( 40%) we anticipate sig- and the barriers for decomposition (from ref. 10). The values for the EZE niﬁcant hysteresis for the transition between the two phases, as in isomer are shown in parentheses. thecaseoftheN2 to cg-N transition. Figure 3b, which presents the computed energy versus volume dependence of cg-N and N8,illus- Both the structures and NBO analysis suggest that the bonding in trates these large differences in atomic volume for the two forms linear N8 can be described as a terminal triple bond (N4–N5 and N7–N8, and that their relative stability can be reversed as a function of volume. bond lengths of 1.13 Å), a central double bond (N1–N2,1.24Å),a The relevant energetics and stability of N8 are summarized in weak single bond (N2–N3, 1.4 Å) and a bond with a strong ionic char- Fig. 4 using the values reported in ref. 10. The EEE and EZE 10 21 acter between N3 and N4 (1.26 Å) (N3 is assigned two lone pairs ) isomers are within 1 kcal mol of each other and are 21 (Fig. 1b). The structures of the two isomers (EEE and EZE) are very 15 kcal mol higher than the lowest-energy N8 isomer. The similar, and the structural parameters are not strongly affected by the barrier for EEE to EZE isomerization is 6 kcal mol21 (ref. 10). interactions between the fragments in the isolated dimer (Fig. 2c) Two possible decomposition pathways involve stretching of one 10 and in the solid (Fig. 2b). The comparison with reference molecules (or two) single bond(s) (N2–N3). As pointed in ref. 10, these barriers containing N–N bonds suggest that terminal bonds are stronger than are too low for linear N8 to be stable at ambient conditions. those in CH3N3, whereas inner bonds are slightly weaker. The However, stabilization in the solid should extend the stability of double bond is weaker than that in CH3N ¼ NCH3,andthesingle this compound to a broader range of conditions. Based on the ener- bonds are stronger than those in (CH3)2N–N(CH3)2.Arelatively gies from Fig. 4 and the cohesive energy of the solid, the energy that strong ionic character (charge separation of 0.2e between N3 and would be released by decomposing N8 solid into N2 molecules is 21 21 N4) suggests that the individual N8 molecules will be stabilized in the 260 kcal mol (or 32.5 kcal mol per N). lattice environment, consistent with relatively strong cohesive energy. We report the calculations of vibrational frequencies and infrared Figure 2 also shows molecular orbitals of the isolated N8 molecules intensities of solid N8 in Fig. 5. The most prominent feature is a and within the unit cell. We observe that the character of the highest strong transition at 2,169 cm21. The next strong transitions are at occupied molecular orbital (HOMO) does not change in the unit cell, 1,254 cm–1 and 1,231 cm–1. These vibrations can be described as as expected for a molecular, non-metallic solid. We note that the solid various combinations of the terminal NNN groups’ motions and HOMO is localized on a lower-energy EEE isomer. involve considerable amplitude of the polar N3–N4 bond stretch. It is instructive to compare the computed cohesive energy The fourth brightest transition is a bipedal-type vibration of the with the interaction energy of the isolated EZE–EEE dimer EZE moiety. Note that the frequency of this mode, which corre- 21 –1 (Eb ¼ 0.97 kcal mol ). If the solid was composed of unrelaxed sponds to EZE to EEE isomerization, is larger than 900 cm , EZE–EEE dimers (and assuming only pairwise interactions suggesting that the isomerization between the isomers is somewhat between the nearest neighbours), the cohesive energy would be suppressed in the solid. A complete list of frequencies and a

(i) (ii) (iii) 2,169 cm–1

) 160 –1

140

40 (ii) 1,254 cm–1 (iii)

20 (i) 923 cm–1 Infrared cross-section (km mol

0 0 500 1,000 1,500 2,000 Frequency (cm–1)

Figure 5 | Calculated infrared spectrum of N8 molecular solid and normal modes corresponding to the most intense transitions. The most intense 21 21 transitions correspond to motion of the terminal N3 groups (1,254 and 2,169 cm ). A bipedal mode is also shown at 923 cm .

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ARTICLES NATURE CHEMISTRY DOI: 10.1038/NCHEM.1818 comparison of the spectra of the solid and the isolated monomers 5. Hansen, N. et al. Photofragment translation spectroscopy of ClN3 at 248 nm: are given in Supplementary Section XI. determination of the primary and secondary dissociation pathways. J. Chem. Phys. 123, 104305 (2005). Finally, we would like to point out that the structure of N8 solid þ 6. Christe, K. O., Wilson, W. W., Sheehy, J. A. & Boatz, J. A. N5 : a novel was first obtained in a calculation starting from a tetramer structure homoleptic polynitrogen ion as a high energy density material. Angew. Chem. of N4 molecules (our initial goal was to investigate the possible stab- Int. Ed. 38, 2004–2009 (1999). 7. Haiges, R., Schneider, S., Schroer, T. & Christe, K. O. High energy density ility of a molecular solid composed of N4 moieties). We observed þ 2 þ 2 materials. 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I. will be an exciting challenge to attempt its preparation. Van der Waals density functional for general geometries. Phys. Rev. Lett. 92, 246401 (2004). Methods 25. Giannozzi, P. et al. Quantum Espresso: a modular and open-source software project for quantum simulations of materials. J. Phys. 21, 395502 (2009). For solid periodic boundary conditions calculations, we used Quantum Espresso25. 26. Chai, J-D. & Head-Gordon, M. Long-range corrected hybrid density functionals The calculations made use of PW-DFT with the PBE-D functional22,23 and were with damped atom–atom dispersion interactions. Phys. Chem. Chem. Phys. 10, performed at ambient pressure (1 atm). To investigate the relative thermodynamic 6615–6620 (2008). stability, we also computed the enthalpies of the N solid and cg-N form at pressures 8 27. Shao, Y. et al. Advances in methods and algorithms in a modern quantum up to 50 GPa. To validate the PW-PBE-D results, we performed additional chemistry program package. Phys. Chem. Chem. Phys. 8, 3172–3191 (2006). calculations, not using periodic boundary conditions, with vB97X-D26 and MP2 (Moller–Plesset perturbation theory) methods using Q-Chem27. In addition, we investigated the sensitivity of the computed structures and cohesive energies to Acknowledgements different functionals (BLYP-D) and dispersion treatment (that is, non-local DFT) as Research at the Hebrew University of Jerusalem was supported under the auspices of the well as initial structures used for optimization. The details of the calculations are Saerree K. and Louis P. Fiedler Chair in Chemistry (R.B.G.). A.I.K. acknowledges support given in Supplementary Section II. from the Army Research Office (grant W911NF-12-1-0543). B.H. and R.B.G. wishes to thank S. Aflalo for her help with the artwork for the manuscript. Received 30 July 2013; accepted 7 November 2013; published online 15 December 2013 Author contributions B.H. performed the calculations. A.I.K. provided advice on electronic structure References calculations. R.B.G. proposed the research topic. B.H., A.I.K. and R.B.G. contributed to the 1. Vij, A. et al. Experimental detection of the pentaazacyclopentadienide (pentazolate) interpretation of the results and co-wrote the manuscript. 2 anion, cyclo-N5 . Angew. Chem. Int. Ed. 114, 3177–3180 (2002). 2. Cacace, F., de Patris, G. & Troiani, A. Experimental detection of tetranitrogen. Additional information Science 295, 480–481 (2002). 2 Supplementary information is available in the online version of the paper. Reprints and 3. Ostmark, H. et al. Detection of pentazolate anion (cyclo-N5 ) from laser ionization and decomposition of solid p-dimethylaminophenylpentazole. Chem. permissions information is available online at www.nature.com/reprints. Correspondence and Phys. Lett. 379, 539–546 (2003). requests for materials should be addressed to R.B.G. 2 4. Samartzis, P. C. et al. Two photoionization thresholds of N3 produced by ClN3 2 photodissociation at 248 nm: further evidence for cyclic N3 . J. Chem. Phys. Competing financial interests 123, 051101 (2005). The authors declare no competing financial interests.

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