Main

Molecular nitrogen allotropes beyond N2 are promising for the development of high-energy-density materials4 because they release enormous energy on dissociation into gaseous N2. As the main component of air, N2 is inert, non-toxic and not a greenhouse contributor5,6,7. Unlike carbon, N2 is the only nitrogen allotrope found in nature and strategies for synthesizing higher neutral molecular nitrogen allotropes are highly sought after8,9,10,11,12,13,14. However, they are deemed extremely unstable, especially when uncharged and with an even electron count15. Consequently, only two examples have been reported. The azide radical (•N3) (Fig. 1a) was identified in the gas phase through rotational spectroscopy in 1956 (refs. 16,17). In 2002, N4 was detected by gas-phase neutralization-reionization mass spectrometry (NRMS); its structure has not been revealed18. The intermediacy of an N6 species was tentatively suggested in 1970 in the decay of azide radicals in aqueous solution but no definitive spectroscopic evidence was provided19.

Fig. 1: All known neutral molecular nitrogen allotropes and preparation of N6.
figure 1

a, Discovery timeline (year given), composition and structure (the structure of N4 has not been determined). b, Reaction sequence used in this study. r.t., room temperature.

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There are many computations proposing molecular allotropes spanning from N4 to N120, including chains, rings and cages7,20, most of which have low dissociation barriers into N2. For example, hexazine (cyc-N6, the nitrogen analogue of benzene) exhibits a computed barrier of only 4.2 kcal mol−1 for decomposition into three N2 (ref. 21). Quantum mechanical tunnelling (QMT) effects could further reduce the lifetime of higher nitrogen allotropes, adding to their difficulty of preparation22.

Although the pursuit of higher neutral molecular nitrogen allotropes is extremely challenging, several homonuclear polynitrogen ions have been isolated. The synthesis and characterization of [N5]+[PnF6]− (Pn = As, Sb) salts with a bent pentanitrogen cation represents a milestone23,24. Christe et al. initially identified the \(cyclo{{\rm{-N}}}_{5}^{-}\) anion using mass spectrometry in 2002 and 2003 (refs. 25,26) and Zheng et al. reported in 2017 the synthesis of a salt featuring the \(cyclo{{\rm{-N}}}_{5}^{-}\) anion27. The synthesis of various metal pentazolates was achieved through the reaction of [Na(H2O)(N5)]•2H2O with metal salts28,29.

In the realm of solid-state (non-molecular) structures, a breakthrough was the high-temperature (2,000 K), high-pressure (110 GPa) diamond-like solid-state cubic gauche nitrogen phase in which all atoms are connected by single bonds30,31. An aromatic cyclic hexazine \({{\rm{N}}}_{6}^{4-}\) was identified through solid-state X-ray diffraction of K9N56 under pressures above 40 GPa and temperatures above 2,000 K (ref. 32). Greschner et al. predicted a new nitrogen molecular crystal comprising N6 units with an open-chain structure stabilized by electrostatic interactions33, in line with assessments for the molecular species9.

In our analysis of the proposed molecular nitrogen allotropes, acyclic neutral N6 (hexaaza-1,2,4,5-tetraene, hexanitrogen, diazide) stands out because N2 moieties are not discernible (Fig. 1). The central N–N bond would lead to unproductive endothermic dissociation (ΔG298K theor. +26.1 kcal mol−1, vide infra) into two •N3. Furthermore, the computed dissociation barrier into three N2 molecules of ΔG‡298K = 14.8 kcal mol−1 makes N6 a promising candidate for synthesis. Here we show that N6 indeed can be prepared at room temperature through the reaction of Cl2 or Br2 with AgN3 under reduced pressure, followed by cryogenic trapping34. The characterization was accomplished by infrared (including 15N-isotope labelling) as well as UV-Vis spectroscopy and ab initio computations. We also demonstrate the preparation and stability of C2h-symmetric N6 (hereinafter referred to as N6) in neat form as a film at the temperature of liquid nitrogen (77 K).

Synthesis of N6

As AgN3 is an excellent reagent for the synthesis of polyazides35 and halogen azides both in the gas phase36 and in solution37,38, we suggest that the reaction of AgN3 with XN3 (X = halogen) is a viable route to N6 (Fig. 1b). The reactions were conducted in either a quartz tube or a U-trap by flowing gaseous Cl2 through solid AgN3 under reduced pressure at room temperature (see the ‘Synthesis details’ section in Methods and Supplementary Fig. 1). Apart from the known bands of ClN3 (ref. 39) and HN3 (ref. 40), a distinct group of bands at 2,076.6, 2,049.0, 1,177.6 and 642.1 cm−1 was recorded (Supplementary Fig. 2). After irradiating the matrices with 436 nm light (Fig. 2a middle trace and Supplementary Fig. 3), all bands vanish. However, the rates of decomposition of the newly observed infrared bands differ from those attributed to ClN3 (Supplementary Figs. 4 and 5). There were no discernible products other than chloronitrene (ClN) detected in the difference spectrum after irradiation. Furthermore, identical bands were detected when Br2 was used instead of Cl2, indicating that the unidentified species does not contain halogens (Fig. 2a upper trace and Supplementary Fig. 6). Also, BrN3 does not decompose on 436 nm irradiation, providing clean decomposition spectra of the yet unidentified species.

Fig. 2: Infrared spectra of N6 isotopomers and side products.
figure 2

a, Lower trace: computed anharmonic infrared spectrum of N6 at B3LYP/def2-TZVP, including the ν8 + ν9 combination. Middle trace: difference spectrum showing the changes after 8 min of 436 nm irradiation of the products of the reaction of Cl2 with AgN3. Upper trace: difference spectrum showing the changes after 6 min of 436 nm irradiation of the reaction products of Br2 with AgN3. b, Difference spectrum of a neat N6 film at 77 K showing the changes after 8 min of 436 nm irradiation. c, Bottom to top traces: computed anharmonic infrared spectrum of N6, 15NNNNN15N (1a), 15NNN15NNN (1b) and NN15N15NNN (1c) at B3LYP/def2-TZVP, including the ν8 + ν9 combination; difference spectrum showing the changes after 8 min of 436 nm irradiation of the reaction products of Br2 with AgN3; difference spectrum showing changes after 8 min of 436 nm irradiation of the reaction products of Br2 with Ag15N14N14N. Matrix sites from natural abundance and isotope-labelled HN3 (#) and H2O (*) are marked.

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The intensive vibrational band at 2,076.6 cm−1 compares favourably with the asymmetric stretching band of the azide moiety in isoelectronic N3–NCO (2,099.1 cm−1, Ar matrix)41. Compared with the computed harmonic vibrations at CCSD(T)/cc-pVTZ, the four bands noted above could be attributed to N6, except the band at 2,049.0 cm−1 of moderate intensity, although it disappeared together with the other bands following photolysis (Supplementary Figs. 4 and 7). To determine the origin of the band at 2,049.0 cm−1, anharmonic vibrational frequencies were computed at B3LYP/def2-TZVP (Supplementary Table 1). This analysis indicates that this band derives from a combination of fundamentals ν8 (ag symmetric N3N4 stretching mode) and ν9 (bu asymmetric N3N2N1 stretching mode). The substantial anharmonic intensity contribution (219 km mol−1; Supplementary Table 2) of the fundamental ν11 at 2,143.5 cm−1 and the ν8 + ν9 combination is notably stronger than its fundamentals, suggesting that the combination ν8 + ν9 gains energy through Fermi resonance from the adjacent strong fundamental ν11 (ref. 41).

To confirm our assignments, isotope-labelling experiments were conducted using Ag15N14N14N. Three groups of distinct peaks can be discerned in the infrared spectra (Fig. 2c and Supplementary Fig. 8), indicating the presence of two N3 moieties in the molecule, which can be attributed to three types of isotopomer (1a: 15NNNNN15N, 1b: 15NNN15NNN, 1c: NN15N15NNN), respectively. In particular, the unsymmetric isotopic substitutions in 1b lower its point group from C2h to Cs. Computations delineate that the terminal (N1 or N6) and internal (N3 or N4) 15N substitutions mainly influence the terminal (ν11) and internal asymmetric stretching vibration (ν9) of the N3 moieties, respectively. This leads to a redshift of the ν8 + ν9 combination and a blueshift of the ν11 fundamental in going from 1a to 1c, resulting in their gradual separation. The intensity ratio of the ν8 + ν9 combination and the ν11 fundamental in 1a is nearly 1:1, which is much higher than that in 1c (about 1:17). These findings align well with the anharmonic infrared intensities computed by density functional theory (Supplementary Table 3), which are attributed to the closer proximity of the ν8 + ν9 combination to the strong ν11 fundamental in 1a, resulting in an increase of the Fermi resonance and vice versa in 1c. Statistically, the anticipated ratio of the three isotopomers should be 1a:1b:1c = 1:2:1, which is reflected in the observed fundamental ν7 in the experimental spectrum (Fig. 3). Furthermore, the computed intensity of ν9 in 1c (107 km mol−1; Supplementary Table 3) is higher than that in 1a (92 km mol−1) and 1b (98 km mol−1), which matches the intensity ratios of ν9 observed in 1a and 1b (approximately 1:2). The experimentally observed intensities agree with these findings and show a slightly higher intensity of ν9 in 1c than in 1a.

Fig. 3: Measured and computed UV-Vis spectrum of N6 and molecular orbitals involved in the electronic transitions.
figure 3

Experimental difference UV-Vis spectrum reflecting changes following 4 min of 436 nm irradiation of the reaction products of Br2 with AgN3 in argon at 10 K. Inset, computed [TD-B3LYP/def2-TZVP] electronic transitions for N6 and molecular orbitals involved.

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To explore the intrinsic stability of N6, we also prepared neat N6 at room temperature and condensed it at liquid nitrogen temperature (77 K) as a film on the surface of the matrix window without using argon as a host gas. Irradiation of such N6 films resulted in very similar spectral changes as those observed in argon matrices at 10 K (Fig. 2b and Supplementary Fig. 9). That is, neat N6 is sufficiently stable at the temperature of liquid nitrogen to allow its direct identification.

Further evidence is provided by the UV-Vis spectrum of N6. After 6 min of 436 nm irradiation of the reaction products of Br2 with AgN3, we observed the disappearance of the transitions at 190 and 249 nm and, consistent with the infrared experiments, no new transitions appeared (Fig. 3). All transitions correlate well with the values for the electronic excitations of N6 at 186 nm (f = 0.8512) and 248 nm (f = 0.0078) computed at [TD-B3LYP/def2-TZVP]. Furthermore, the computations reveal a weak electronic excitation at 422 nm (f = 0.0004), corresponding to a π → π* transition, which aligns well with the observed photochemistry.

Computations

To better understand the structure and the potential energy landscape of N6, we computed its energy profile at CCSD(T)/cc-pVTZ (Fig. 4a (ΔG298K) and Supplementary Fig. 10 (ΔH0); see the ‘Computational details’ section in Methods). Only the C2h-N6 trans-conformer is a local minimum; the C2v-N6 cis-conformer is a higher-order stationary point and chemically not relevant42,43. The formal double bond lengths in the N3 moieties are much longer than the triple bond in N2 (theor. 1.104 Å; expt. 1.098 Å)44, indicating double-bond character. Indeed, the computed N2 = N3/N4 = N5 bond length (1.251 Å) is close to that of trans-diazene (HN = NH, theor. 1.253 Å; expt. 1.252 Å)45. The structure of N6 is different from the azide radical (•N = N = N, theor. 1.183 Å; expt. 1.181 Å)46 but comparable with the N3 moiety in hydrazoic acid (HN3, theor. 1.247 and 1.136 Å; expt. 1.237 and 1.133 Å for the N1 = N2 and N2 = N3 bonds, respectively). The N3–N4 bond in N6 (1.460 Å) compares favourably with that in hydrazine (H2N–NH2, theor. 1.445 Å; expt. 1.446 Å). This geometric analysis is well captured by the Lewis structure of N6 (Fig. 1). These conclusions are supported by natural bond orbital computations, which indicate that the terminal nitrogen atoms are electronically neutral, whereas small positive and negative charges are located at N2 and N5 (+0.2e) as well as on N3 and N4 (−0.2e), respectively (Fig. 4a). Equally, N1–N2/N5-N6 have the highest bond order (2.1), followed by N2–N3/N4–N5 (1.4) and N3–N4 (1.1).

Fig. 4: Computational analyses for N6.
figure 4

a, Potential energy profile (ΔG298K, kcal mol−1) for N6 at CCSD(T)/cc-pVTZ. The optimized parameters of N6 are given in Ångstrom (normal font), degrees (italics), natural charges in bold and natural bond orders in bold italics. Insets, computed NN bond lengths for N2, trans-HNNH, hydrazine and HN3 at CCSD(T)/cc-pVTZ. b, Contour line map of the Laplacian of the electron density of N6; solid and dashed lines represent positive and negative regions, respectively. c, ELF map.

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We visualized the Laplacian of the electron density to gauge where the bonds in N6 are likely to break (Fig. 4b) and why the computed barrier for decomposition into three moles of N2 is, compared with other systems, rather high (ΔG‡298K = 14.8 kcal mol−1). This barrier implies appreciable kinetic stability that is mirrored by our observations. For comparison, the computed barrier of hypothetical D2h-N4 dissociating into two N2 is 6.5 kcal mol−1 at MR-AQCC/VTZ47. With the electron density analysis, the ‘Achilles’ heel’ was discerned at the N2–N3/N4–N5 bonds, as evident from the vertex of positive Laplacian of the in-plane electron density. This is confirmed by the electron localization function (ELF) analysis48 (Fig. 4c). Both the Laplacian of the electron density and the ELF analysis indicate the electron density minimum around the N2–N3/N4–N5 bonds. Hence, even though the Lewis structure would indicate N6 breaking into two •N3 radicals, that is, breaking of the central N3–N4 single bond, the computed barrier for this process amounts to sizeable ΔG298K = 26.1 kcal mol−1 and is unproductive.

On the other hand, ΔG‡298K for the elementary decomposition into three N2 is 14.8 kcal mol−1, implying a finite lifetime of N6 at room temperature. As N6 decomposition may be accelerated by QMT21,22,49, we used canonical variational theory and small-curvature tunnelling computations at B3LYP/def2-TZVP that reveal that N6, unlike hexazine (cyc-N6)21, is unlikely to decompose through QMT, with an estimated half-life of N6 of more than 132 years at 77 K (Supplementary Table 4). At 298 K, the computed half-life still amounts to 35.7 ms. This supports our finding that N6 exists long enough in the gas phase at ambient temperature to be trapped subsequently in cryogenic matrices.

According to CCSD(T)/cc-pVTZ (ΔH0) computations, the decomposition of N6 into three N2 is exothermic (ΔH0) by 185.2 kcal mol−1, which is 2.2 and 1.9 times higher than the decomposition enthalpies of TNT (2,4,6-trinitrotoluene) and HMX (1,3,5,7-tetranitro-1,3,5,7-tetrazocane, octogen) by weight50 (see the ‘Computational details’ section in Methods).

We report here the facile synthesis and spectroscopic identification of experimentally unreported hexanitrogen N6. This represents the first, to our knowledge, experimentally realized neutral molecular nitrogen allotrope beyond N2 that exhibits unexpected stability. This discovery challenges the long-held belief of the elusiveness of neutral molecular nitrogen allotropes.

Methods

Matrix apparatus design

For the matrix isolation studies, we used an APD Cryogenics HC-2 cryostat with a closed-cycle refrigerator system, equipped with an inner CsI window for infrared measurements. Spectra were recorded at the temperature of the matrix (10 K) with a Bruker VERTEX 70 FT-IR spectrometer with a spectral range of 4,000–400 cm−1 and a resolution of 0.7 cm−1 and UV-Vis spectra were recorded with a Jasco V-670 spectrophotometer equipped with an inner sapphire window. A high-pressure mercury lamp (HBO 200, Osram) with a monochromator (Bausch & Lomb) was used for irradiation. Cl2 or Br2 was evaporated (Cl2-CCl4: −140 °C, Br2: −85 °C) from a storage bulb into the quartz tube or U-trap. Although not directly measured, all reaction products were co-condensed with a large excess of argon (typically 60–120 mbar from a 2,000-ml storage bulb) onto the surface of the matrix window at 10 K in several milliseconds.

Synthesis details

Warning! Silver azide and halogen azides are extremely hazardous and explosive. Such compounds should be handled with utmost care and only in very small quantities (<5 mmol). Appropriate safety precautions (blast screens, face shields, Kevlar gloves, soundproof earmuffs and protective leather clothing) are necessary. Make sure to eliminate static electricity before handling. It is also crucial to avoid friction and light exposure and prevent any contact with metals during sample handling to ensure safety.

Silver azide was synthesized by adding a stoichiometric amount of a silver nitrate–water solution to a sodium azide–water solution in the dark. The precipitate was washed three times with anhydrous ethanol. The resulting slurry was loosely dispersed on one side of the inner surface of a straight quartz tube (ø 10 × 1) or the inner surface of a U-trap (inside diameter 10 mm) and then brought to reduced pressure to remove the solvent. Typically, 0.6 mmol and 2.5 mmol of AgN3 are required for the straight quartz tube and U-trap, respectively. Na15N14N14N (>99% 15N, Sigma-Aldridge) was used for isotope labelling experiments. Chlorine gas was bubbled into CCl4 at 0 °C and degassed before use. Bromine was purified by vacuum distillation before use. Typically, 3 mmol of halogen were stored in the storage bulb for the reaction.

Computational details

Geometry optimizations and energy computations were carried out at the CCSD(T)/cc-pVTZ51,52,53 levels of theory using ORCA 5.0 (with keywords verytightscf and verytightopt)54. B3LYP55,56 computations (geometry optimizations, energy computations (all free energies were computed at 298 K), harmonic vibrational analysis and DVPT2 anharmonic vibrational analysis) were performed using Gaussian 16 (ref. 57) with a def2-TZVP basis set58. Local minima were confirmed by vibrational frequencies analyses and transition states were further confirmed by intrinsic reaction coordinate computations. Harmonic vibrational analysis at CCSD(T)/cc-pVTZ was performed using CFOUR v2.1 (ref. 59). Wavefunction analysis (Laplacian of electron density and electron localization function) results were obtained from Multiwfn 3.8 (ref. 60) at CCSD(T)/cc-pVTZ. Natural bond order analysis and resonance structures were computed with NBO 7.0 (refs. 61,62). CVT/SCT (canonical variational transition state theory with small-curvature tunnelling) and CVT/ZCT (canonical variational transition state theory with zero-curvature tunnelling) computations were carried out with Gaussrate 17 (refs. 27,63,64,65,66,67) as an interface between Gaussian 16 and Polyrate68. Furthermore, local stretching force constants were obtained by LModeA-nano69 as a plugin of the open-source version of the visualization program PyMOL.

Detonation calculation details

First, the density (ρ, in cm3 per molecule) of the N6 crystal was determined using electrostatic interaction correction as suggested by Politzer et al.70 (equation (2)). Mm (84.04/(6.02 × 1023) g per molecule) is the molecular mass. Vm (610.52/(1.89 × 108)3 cm3 per molecule) is the volume of the isolated gas-phase molecule, which was determined by the 0.001 a.u. density envelope using the marching tetrahedron method60,71. ν is the parameter of balance between positive and negative surface potentials72 (equation (2)). \({\sigma }_{{\rm{tot}}}^{2}\) (48.40 kcal2 mol−2) is the strengths and variabilities of the overall surface potentials, which could be derived from variance of positive (\({\sigma }_{+}^{2}\), 31.06 kcal2 mol−2) and negative charges (\({\sigma }_{-}^{2}\), 17.34 kcal2 mol−2) with equation (3). α (0.9183), β (0.0028) and γ (0.0443) are coefficients.

$$\rho =\alpha \left(\frac{{M}_{{\rm{m}}}}{{V}_{{\rm{m}}}}\right)+\beta (\nu {\sigma }_{{\rm{tot}}}^{2})+\gamma $$
(1)
$$\nu =\frac{{\sigma }_{+}^{2}{\sigma }_{-}^{2}}{{({\sigma }_{+}^{2}+{\sigma }_{-}^{2})}^{2}}$$
(2)
$${\sigma }_{{\rm{tot}}}^{2}={\sigma }_{+}^{2}+{\sigma }_{-}^{2}$$
(3)

The detonation velocity (D) and detonation pressure (P) were calculated using the Kamlet–Jacobs equation73 (equations (4) and (5)). N is the number of moles of the gas generated per gram (equation (6)), \(\bar{M}\) is the average molecular weight of the gaseous product (equation (7)), Q is the heat of detonation (equation (8)), M is the molecular weight (84.04 g mol−1), ΔHf is the standard heat of formation (774.88 kJ mol−1, which was derived from the energy difference of the computed enthalpy at 298 K between C2h-N6 and 3 moles of N2) and a (0), b (0), c (0) and d (6) represent the number of C, H, O, and N atoms in the molecule, respectively.

$$D=1.01{(N\sqrt{\bar{M}Q})}^{\frac{1}{2}}(1+1.3\rho )$$
(4)
$$P=1.558{\rho }^{2}N\sqrt{\bar{M}Q}$$
(5)
$$N=\frac{b+2c+2d}{4M}$$
(6)
$$\bar{M}=\frac{4M}{b+2c+2d}$$
(7)
$$Q=\frac{28.9b+94.05a+0.239\Delta {H}_{{\rm{f}}}}{M}$$
(8)

Assessing the energetic performance using the Kamlet–Jacobs equation73, the CCSD(T)/cc-pVTZ level of theory predicts a lower density (ρ: 1.51 g cm−3) than that of TNT (1.65 g cm−3) and an excellent detonation performance (detonation velocity D: 8,930 m s−1; detonation pressure P: 31.7 GPa). This compares favourably with several well-known explosives, for example, TNT (D: 6,900 m s−1; P: 21.0 GPa), RDX (1,3,5-trinitro-1,3,5-triazinane; D: 8,750 m s−1; P: 34.5 GPa) and FOX-7 (1,1-diamino-2,2-dinitroethylene; D: 8,870 m s−1; P: 34.5 GPa)74.

Energy-releasing equivalent calculation details

A kiloton of N6 is 1.19 × 107 mol, which can release an energy of 2.20 × 109 kcal (9.21 terajoules) based on the enthalpy (ΔH0). Considering that the standard kiloton TNT equivalent is 4.184 terajoules, N6 can release 2.2 times the energy of TNT of the same weight. On the basis of the documented TNT equivalent based on weight for HMX (1.15) and RDX (1.15)50, N6 can release 1.9 times the energy of HMX or RDX with the same weight.