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Preparation of a neutral nitrogen allotrope hexanitrogen C[2h]-N[6 ]
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  * Published: 11 June 2025

Preparation of a neutral nitrogen allotrope hexanitrogen C[2h]-N[6 ]

  * Weiyu Qian  (Qian Wei Yu )  ORCID: orcid.org/0000-0003-3275-1063^1,
  * Artur Mardyukov  ORCID: orcid.org/0000-0003-3908-6967^1 &
  * Peter R. Schreiner  ORCID: orcid.org/0000-0002-3608-5515^1 

Nature volume 642, pages 356-360 (2025)Cite this article

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Subjects

  * Chemical bonding
  * Materials chemistry
  * Chemical synthesis

Abstract

Compounds consisting only of the element nitrogen (polynitrogens or
nitrogen allotropes) are considered promising clean energy-storage
materials owing to their immense energy content that is much higher
than hydrogen, ammonia or hydrazine, which are in common use, and
because they release only harmless nitrogen on decomposition^1.
However, their extreme instability poses a substantial synthetic
challenge and no neutral molecular nitrogen allotrope beyond N[2] has
been isolated^2,3. Here we present the room-temperature preparation
of molecular N[6] (hexanitrogen) through the gas-phase reaction of
chlorine or bromine with silver azide, followed by trapping in argon
matrices at 10 K. We also prepared neat N[6] as a film at liquid
nitrogen temperature (77 K), further indicating its stability.
Infrared and ultraviolet-visible (UV-Vis) spectroscopy, ^15N-isotope
labelling and ab initio computations firmly support our findings. The
preparation of a metastable molecular nitrogen allotrope beyond N[2]
contributes to our fundamental scientific knowledge and possibly
opens new opportunities for future energy-storage concepts. 

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Main

Molecular nitrogen allotropes beyond N[2] are promising for the
development of high-energy-density materials^4 because they release
enormous energy on dissociation into gaseous N[2]. As the main
component of air, N[2] is inert, non-toxic and not a greenhouse
contributor^5,6,7. Unlike carbon, N[2] is the only nitrogen allotrope
found in nature and strategies for synthesizing higher neutral
molecular nitrogen allotropes are highly sought after^8,9,10,11,12,13
,14. However, they are deemed extremely unstable, especially when
uncharged and with an even electron count^15. Consequently, only two
examples have been reported. The azide radical (*N[3]) (Fig. 1a) was
identified in the gas phase through rotational spectroscopy in 1956
(refs. ^16,17). In 2002, N[4] was detected by gas-phase
neutralization-reionization mass spectrometry (NRMS); its structure
has not been revealed^18. The intermediacy of an N[6] species was
tentatively suggested in 1970 in the decay of azide radicals in
aqueous solution but no definitive spectroscopic evidence was
provided^19.

Fig. 1: All known neutral molecular nitrogen allotropes and
preparation of N[6].
figure 1

a, Discovery timeline (year given), composition and structure (the
structure of N[4] has not been determined). b, Reaction sequence used
in this study. r.t., room temperature.

Full size image

There are many computations proposing molecular allotropes spanning
from N[4] to N[120], including chains, rings and cages^7,20, most of
which have low dissociation barriers into N[2]. For example, hexazine
(cyc-N[6], the nitrogen analogue of benzene) exhibits a computed
barrier of only 4.2 kcal mol^-1 for decomposition into three N[2]
(ref. ^21). Quantum mechanical tunnelling (QMT) effects could further
reduce the lifetime of higher nitrogen allotropes, adding to their
difficulty of preparation^22.

Although the pursuit of higher neutral molecular nitrogen allotropes
is extremely challenging, several homonuclear polynitrogen ions have
been isolated. The synthesis and characterization of [N[5]]^+[PnF[6]]
^- (Pn = As, Sb) salts with a bent pentanitrogen cation represents a
milestone^23,24. 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 \(cyclo{{\rm{-N}}}_{5}^{-}\) anion^27. The
synthesis of various metal pentazolates was achieved through the
reaction of [Na(H[2]O)(N[5])]*2H[2]O with metal salts^28,29.

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 bonds^30,31. An aromatic
cyclic hexazine \({{\rm{N}}}_{6}^{4-}\) was identified through
solid-state X-ray diffraction of K[9]N[56] under pressures above
40 GPa and temperatures above 2,000 K (ref. ^32). Greschner et al.
predicted a new nitrogen molecular crystal comprising N[6] units with
an open-chain structure stabilized by electrostatic interactions^33,
in line with assessments for the molecular species^9.

In our analysis of the proposed molecular nitrogen allotropes,
acyclic neutral N[6] (hexaaza-1,2,4,5-tetraene, hexanitrogen,
diazide) stands out because N[2] moieties are not discernible (Fig. 1
). The central N-N bond would lead to unproductive endothermic
dissociation (DG[298K] theor. +26.1 kcal mol^-1, vide infra) into two
*N[3]. Furthermore, the computed dissociation barrier into three N[2]
molecules of DG^++[298K] = 14.8 kcal mol^-1 makes N[6] a promising
candidate for synthesis. Here we show that N[6] indeed can be
prepared at room temperature through the reaction of Cl[2] or Br[2]
with AgN[3] under reduced pressure, followed by cryogenic trapping^34
. 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 C
[2h]-symmetric N[6] (hereinafter referred to as N[6]) in neat form as
a film at the temperature of liquid nitrogen (77 K).

Synthesis of N[6]

As AgN[3] is an excellent reagent for the synthesis of polyazides^35
and halogen azides both in the gas phase^36 and in solution^37,38, we
suggest that the reaction of AgN[3] with XN[3] (X = halogen) is a
viable route to N[6] (Fig. 1b). The reactions were conducted in
either a quartz tube or a U-trap by flowing gaseous Cl[2] through
solid AgN[3] under reduced pressure at room temperature (see the
'Synthesis details' section in Methods and Supplementary Fig. 1).
Apart from the known bands of ClN[3] (ref. ^39) and HN[3] (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 ClN[3]
(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 Br
[2] was used instead of Cl[2], indicating that the unidentified
species does not contain halogens (Fig. 2a upper trace and
Supplementary Fig. 6). Also, BrN[3] does not decompose on 436 nm
irradiation, providing clean decomposition spectra of the yet
unidentified species.

Fig. 2: Infrared spectra of N[6] isotopomers and side products.
figure 2

a, Lower trace: computed anharmonic infrared spectrum of N[6] at
B3LYP/def2-TZVP, including the n[8] + n[9] combination. Middle trace:
difference spectrum showing the changes after 8 min of 436 nm
irradiation of the products of the reaction of Cl[2] with AgN[3].
Upper trace: difference spectrum showing the changes after 6 min of
436 nm irradiation of the reaction products of Br[2] with AgN[3]. b,
Difference spectrum of a neat N[6] film at 77 K showing the changes
after 8 min of 436 nm irradiation. c, Bottom to top traces: computed
anharmonic infrared spectrum of N[6], ^15NNNNN^15N (1a), ^15NNN^15NNN
(1b) and NN^15N^15NNN (1c) at B3LYP/def2-TZVP, including the n[8] + n
[9] combination; difference spectrum showing the changes after 8 min
of 436 nm irradiation of the reaction products of Br[2] with AgN[3];
difference spectrum showing changes after 8 min of 436 nm irradiation
of the reaction products of Br[2] with Ag^15N^14N^14N. Matrix sites
from natural abundance and isotope-labelled HN[3] (#) and H[2]O (*)
are marked.

Full size image

The intensive vibrational band at 2,076.6 cm^-1 compares favourably
with the asymmetric stretching band of the azide moiety in
isoelectronic N[3]-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 N[6], 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 n[8] (a[g] symmetric N^3N^
4 stretching mode) and n[9] (b[u] asymmetric N^3N^2N^1 stretching
mode). The substantial anharmonic intensity contribution (219 km mol^
-1; Supplementary Table 2) of the fundamental n[11] at 2,143.5 cm^-1
and the n[8] + n[9] combination is notably stronger than its
fundamentals, suggesting that the combination n[8] + n[9] gains
energy through Fermi resonance from the adjacent strong fundamental n
[11] (ref. ^41).

To confirm our assignments, isotope-labelling experiments were
conducted using Ag^15N^14N^14N. Three groups of distinct peaks can be
discerned in the infrared spectra (Fig. 2c and Supplementary Fig. 8),
indicating the presence of two N[3] moieties in the molecule, which
can be attributed to three types of isotopomer (1a: ^15NNNNN^15N, 1b:
^15NNN^15NNN, 1c: NN^15N^15NNN), respectively. In particular, the
unsymmetric isotopic substitutions in 1b lower its point group from C
[2h] to C[s]. Computations delineate that the terminal (N^1 or N^6)
and internal (N^3 or N^4) ^15N substitutions mainly influence the
terminal (n[11]) and internal asymmetric stretching vibration (n[9])
of the N[3] moieties, respectively. This leads to a redshift of the n
[8] + n[9] combination and a blueshift of the n[11] fundamental in
going from 1a to 1c, resulting in their gradual separation. The
intensity ratio of the n[8] + n[9] combination and the n[11]
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 n[8]
 + n[9] combination to the strong n[11] 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 n
[7] in the experimental spectrum (Fig. 3). Furthermore, the computed
intensity of n[9] 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 n[9] observed in 1a and 1b
(approximately 1:2). The experimentally observed intensities agree
with these findings and show a slightly higher intensity of n[9] in
1c than in 1a.

Fig. 3: Measured and computed UV-Vis spectrum of N[6] 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 Br[2] with
AgN[3] in argon at 10 K. Inset, computed [TD-B3LYP/def2-TZVP]
electronic transitions for N[6] and molecular orbitals involved.

Full size image

To explore the intrinsic stability of N[6], we also prepared neat N
[6] 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 N[6] 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 N
[6] is sufficiently stable at the temperature of liquid nitrogen to
allow its direct identification.

Further evidence is provided by the UV-Vis spectrum of N[6]. After
6 min of 436 nm irradiation of the reaction products of Br[2] with
AgN[3], 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 N[6] 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 p - p* transition, which
aligns well with the observed photochemistry.

Computations

To better understand the structure and the potential energy landscape
of N[6], we computed its energy profile at CCSD(T)/cc-pVTZ (Fig. 4a
(DG[298K]) and Supplementary Fig. 10 (DH[0]); see the 'Computational
details' section in Methods). Only the C[2h]-N[6] trans-conformer is
a local minimum; the C[2v]-N[6] cis-conformer is a higher-order
stationary point and chemically not relevant^42,43. The formal double
bond lengths in the N[3] moieties are much longer than the triple
bond in N[2] (theor. 1.104 A; expt. 1.098 A)^44, indicating
double-bond character. Indeed, the computed N^2 = N^3/N^4 = N^5 bond
length (1.251 A) is close to that of trans-diazene (HN = NH, theor.
1.253 A; expt. 1.252 A)^45. The structure of N[6] is different from
the azide radical (*N = N = N, theor. 1.183 A; expt. 1.181 A)^46 but
comparable with the N[3] moiety in hydrazoic acid (HN[3], theor.
1.247 and 1.136 A; expt. 1.237 and 1.133 A for the N^1 = N^2 and N^2 
= N^3 bonds, respectively). The N^3-N^4 bond in N[6] (1.460 A)
compares favourably with that in hydrazine (H[2]N-NH[2], theor.
1.445 A; expt. 1.446 A). This geometric analysis is well captured by
the Lewis structure of N[6] (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 N^2 and N^5 (+0.2e) as
well as on N^3 and N^4 (-0.2e), respectively (Fig. 4a). Equally, N^
1-N^2/N^5-N^6 have the highest bond order (2.1), followed by N^2-N^3/
N^4-N^5 (1.4) and N^3-N^4 (1.1).

Fig. 4: Computational analyses for N[6].
figure 4

a, Potential energy profile (DG[298K], kcal mol^-1) for N[6] at CCSD
(T)/cc-pVTZ. The optimized parameters of N[6] are given in Angstrom
(normal font), degrees (italics), natural charges in bold and natural
bond orders in bold italics. Insets, computed NN bond lengths for N
[2], trans-HNNH, hydrazine and HN[3] at CCSD(T)/cc-pVTZ. b, Contour
line map of the Laplacian of the electron density of N[6]; solid and
dashed lines represent positive and negative regions, respectively. c
, ELF map.

Full size image

We visualized the Laplacian of the electron density to gauge where
the bonds in N[6] are likely to break (Fig. 4b) and why the computed
barrier for decomposition into three moles of N[2] is, compared with
other systems, rather high (DG^++[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 D
[2h]-N[4] dissociating into two N[2] is 6.5 kcal mol^-1 at MR-AQCC/
VTZ^47. With the electron density analysis, the 'Achilles' heel' was
discerned at the N^2-N^3/N^4-N^5 bonds, as evident from the vertex of
positive Laplacian of the in-plane electron density. This is
confirmed by the electron localization function (ELF) analysis^48
(Fig. 4c). Both the Laplacian of the electron density and the ELF
analysis indicate the electron density minimum around the N^2-N^3/N^
4-N^5 bonds. Hence, even though the Lewis structure would indicate N
[6] breaking into two *N[3] radicals, that is, breaking of the
central N^3-N^4 single bond, the computed barrier for this process
amounts to sizeable DG[298K] = 26.1 kcal mol^-1 and is unproductive.

On the other hand, DG^++[298K] for the elementary decomposition into
three N[2] is 14.8 kcal mol^-1, implying a finite lifetime of N[6] at
room temperature. As N[6] decomposition may be accelerated by QMT^21,
22,49, we used canonical variational theory and small-curvature
tunnelling computations at B3LYP/def2-TZVP that reveal that N[6],
unlike hexazine (cyc-N[6])^21, is unlikely to decompose through QMT,
with an estimated half-life of N[6] 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 N[6] exists long
enough in the gas phase at ambient temperature to be trapped
subsequently in cryogenic matrices.

According to CCSD(T)/cc-pVTZ (DH[0]) computations, the decomposition
of N[6] into three N[2] is exothermic (DH[0]) 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 weight^50 (see
the 'Computational details' section in Methods).

We report here the facile synthesis and spectroscopic identification
of experimentally unreported hexanitrogen N[6]. This represents the
first, to our knowledge, experimentally realized neutral molecular
nitrogen allotrope beyond N[2] 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. Cl[2] or Br[2] was
evaporated (Cl[2]-CCl[4]: -140 degC, Br[2]: -85 degC) 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 (o 10 x 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 AgN[3] are
required for the straight quartz tube and U-trap, respectively. Na^
15N^14N^14N (>99% ^15N, Sigma-Aldridge) was used for isotope
labelling experiments. Chlorine gas was bubbled into CCl[4] at 0 degC
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-pVTZ^51,52,53 levels of theory using ORCA 5.0 (with
keywords verytightscf and verytightopt)^54. B3LYP^55,56 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 set^58. 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 Polyrate^68. Furthermore, local
stretching force constants were obtained by LModeA-nano^69 as a
plugin of the open-source version of the visualization program PyMOL.

Detonation calculation details

First, the density (r, in cm^3 per molecule) of the N[6] crystal was
determined using electrostatic interaction correction as suggested by
Politzer et al.^70 (equation (2)). M[m] (84.04/(6.02 x 10^23) g per
molecule) is the molecular mass. V[m] (610.52/(1.89 x 10^8)^3 cm^3
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 method^60,71. n is the parameter of balance between
positive and negative surface potentials^72 (equation (2)). \({\sigma
}_{{\rm{tot}}}^{2}\) (48.40 kcal^2 mol^-2) is the strengths and
variabilities of the overall surface potentials, which could be
derived from variance of positive (\({\sigma }_{+}^{2}\), 31.06 kcal^
2 mol^-2) and negative charges (\({\sigma }_{-}^{2}\), 17.34 kcal^
2 mol^-2) with equation (3). a (0.9183), b (0.0028) and g (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 equation^73 (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), DH[f] 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 C[2h]-N[6] and
3 moles of N[2]) 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 equation^
73, the CCSD(T)/cc-pVTZ level of theory predicts a lower density (r:
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 N[6] is 1.19 x 10^7 mol, which can release an energy of
2.20 x 10^9 kcal (9.21 terajoules) based on the enthalpy (DH[0]).
Considering that the standard kiloton TNT equivalent is
4.184 terajoules, N[6] 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, N[6] can release 1.9 times
the energy of HMX or RDX with the same weight.

References

 1. Christe, K. O. Polynitrogen chemistry enters the ring. Science
    355, 351-351 (2017).

    Article  ADS  CAS  PubMed  Google Scholar 

 2. Wang, Y. et al. Stabilization of hexazine rings in potassium
    polynitride at high pressure. Nat. Chem. 14, 794-800 (2022).

    Article  CAS  PubMed  Google Scholar 

 3. Ninet, S. Benzene-like N[6] hexazine rings. Nat. Chem. 15,
    595-596 (2023).

    Article  CAS  PubMed  Google Scholar 

 4. Yao, Y. & Adeniyi, A. O. Solid nitrogen and nitrogen-rich
    compounds as high-energy-density materials. Phys. Status Solidi B
    258, 2000588 (2021).

    Article  ADS  CAS  Google Scholar 

 5. Klapotke, T. M. & Witkowski, T. G. Nitrogen-rich energetic
    1,2,5-oxadiazole-tetrazole-based energetic materials. Propellants
    Explos. Pyrotech. 40, 366-373 (2015).

    Article  Google Scholar 

 6. Nguyen, M. T. Polynitrogen compounds: 1. Structure and stability
    of N[4] and N[5] systems. Coord. Chem. Rev. 244, 93-113 (2003).

    Article  CAS  Google Scholar 

 7. Zarko, V. E. Searching for ways to create energetic materials
    based on polynitrogen compounds (review). Combust. Explos. Shock
    Waves 46, 121-131 (2010).

    Article  Google Scholar 

 8. Larson, A., Larsson, M. & Ostmark, H. Theoretical study of
    rectangular (D[2h]) N[4]. J. Chem. Soc. Faraday Trans. 93,
    2963-2966 (1997).

    Article  CAS  Google Scholar 

 9. Glukhovtsev, M. N. & von Rague Schleyer, P. Structures, bonding
    and energies of N[6] isomers. Chem. Phys. Lett. 198, 547-554
    (1992).

    Article  ADS  CAS  Google Scholar 

10. Glukhovtsev, M. N., Jiao, H. & von Rague Schleyer, P. Besides N
    [2], what is the most stable molecule composed only of nitrogen
    atoms? Inorg. Chem. 35, 7124-7133 (1996).

    Article  CAS  PubMed  Google Scholar 

11. Strout, D. L. Acyclic N[10] fails as a high energy density
    material. J. Phys. Chem. A 106, 816-818 (2002).

    Article  CAS  Google Scholar 

12. Hirshberg, B., Gerber, R. B. & Krylov, A. I. Calculations predict
    a stable molecular crystal of N[8]. Nat. Chem. 6, 52-56 (2014).

    Article  CAS  PubMed  Google Scholar 

13. Strout, D. L. Cage isomers of N[14] and N[16]: nitrogen molecules
    that are not a multiple of six. J. Phys. Chem. A 108, 10911-10916
    (2004).

    Article  CAS  Google Scholar 

14. Samartzis, P. C. & Wodtke, A. M. All-nitrogen chemistry: how far
    are we from N[60]? Int. Rev. Phys. Chem. 25, 527-552 (2010).

    Article  Google Scholar 

15. Mikhailov, O. V. Molecular and electronic structures of neutral
    polynitrogens: review on the theory and experiment in 21st
    century. Int. J. Mol. Sci. 23, 2841 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

16. Thrush, B. A. & Norrish, R. G. W. The detection of free radicals
    in the high intensity photolysis of hydrogen azide. Proc. R. Soc.
    Lond. A 235, 143-147 (1956).

    Article  ADS  Google Scholar 

17. Beaman, R. A., Nelson, T., Richards, D. S. & Setser, D. W.
    Observation of azido radical by laser-induced fluorescence. J.
    Phys. Chem. 91, 6090-6092 (1987).

    Article  CAS  Google Scholar 

18. Cacace, F., de Petris, G. & Troiani, A. Experimental detection of
    tetranitrogen. Science 295, 480-481 (2002).

    Article  ADS  CAS  PubMed  Google Scholar 

19. Hayon, E. & Simic, M. Absorption spectra and kinetics of the
    intermediate produced from the decay of azide radicals. J. Am.
    Chem. Soc. 92, 7486-7487 (1970).

    Article  CAS  Google Scholar 

20. Zhou, H., Wong, N.-B., Zhou, G. & Tian, A. Theoretical study on
    "multilayer" nitrogen cages. J. Phys. Chem. A 110, 3845-3852
    (2006).

    Article  CAS  PubMed  Google Scholar 

21. Sedgi, I. & Kozuch, S. Quantum tunneling instability of the
    mythical hexazine and pentazine. Chem. Commun. 60, 2038-2041
    (2024).

    Article  CAS  Google Scholar 

22. Schreiner, P. R. Quantum mechanical tunneling is essential to
    understanding chemical reactivity. Trends Chem. 2, 980-989
    (2020).

    Article  CAS  Google Scholar 

23. Christe, K. O., Wilson, W. W., Sheehy, J. A. & Boatz, J. A. N[5]^
    +: a novel homoleptic polynitrogen ion as a high energy density
    material. Angew. Chem. Int. Ed. 38, 2004-2009 (1999).

    Article  CAS  Google Scholar 

24. Vij, A. et al. Polynitrogen chemistry. Synthesis,
    characterization, and crystal structure of surprisingly stable
    fluoroantimonate salts of N[5]^+. J. Am. Chem. Soc. 123,
    6308-6313 (2001).

    Article  CAS  PubMed  Google Scholar 

25. Vij, A., Pavlovich, J. G., Wilson, W. W., Vij, V. & Christe, K.
    O. Experimental detection of the pentaazacyclopentadienide
    (pentazolate) anion, cyclo-N[5]^-. Angew. Chem. Int. Ed. 41,
    3051-3054 (2002).

    Article  CAS  Google Scholar 

26. Ostmark, H. et al. Detection of pentazolate anion (cyclo-N[5]^-)
    from laser ionization and decomposition of solid p
    -dimethylaminophenylpentazole. Chem. Phys. Lett. 379, 539-546
    (2003).

    Article  ADS  Google Scholar 

27. Zhang, C. et al. Synthesis and characterization of the
    pentazolate anion cyclo-N[5]- in (N[5])[6](H[3]O)[3](NH[4])[4]Cl.
    Science 355, 374-376 (2017).

28. Xu, Y. et al. A series of energetic metal pentazolate hydrates.
    Nature 549, 78-81 (2017).

    Article  ADS  CAS  PubMed  Google Scholar 

29. Xu, Y., Tian, L., Li, D., Wang, P. & Lu, M. A series of energetic
    cyclo-pentazolate salts: rapid synthesis, characterization, and
    promising performance. J. Mater. Chem. A 7, 12468-12479 (2019).

    Article  CAS  Google Scholar 

30. Eremets, M. I., Gavriliuk, A. G., Trojan, I. A., Dzivenko, D. A.
    & Boehler, R. Single-bonded cubic form of nitrogen. Nat. Mater. 3
    , 558-563 (2004).

    Article  ADS  CAS  PubMed  Google Scholar 

31. Benchafia, E. M. et al. Cubic gauche polymeric nitrogen under
    ambient conditions. Nat. Commun. 8, 930 (2017).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

32. Laniel, D. et al. Aromatic hexazine [N[6]]^4- anion featured in
    the complex structure of the high-pressure potassium nitrogen
    compound K[9]N[56]. Nat. Chem. 15, 641-646 (2023).

    Article  CAS  PubMed  Google Scholar 

33. Greschner, M. J. et al. A new allotrope of nitrogen as
    high-energy density material. J. Phys. Chem. A 120, 2920-2925
    (2016).

    Article  CAS  PubMed  Google Scholar 

34. Qian, W. Y., Mardyukov, A. & Schreiner, P. R. Hexanitrogen (N
    [6]): a synthetic leap towards neutral nitrogen allotropes.
    Preprint at https://doi.org/10.26434/chemrxiv-2024-90vvx (2024).

35. Zeng, X. et al. Reaction of AgN[3] with SOCl[2]: evidence for the
    formation of thionyl azide, SO(N[3])[2]. Inorg. Chem. 43,
    4799-4801 (2004).

    Article  CAS  PubMed  Google Scholar 

36. Raschig, F. Uber Chlorazid N[3]Cl. Ber. Dtsch. Chem. Ges. 41,
    4194-4195 (1908).

    Article  Google Scholar 

37. Lyhs, B., Blaser, D., Wolper, C., Schulz, S. & Jansen, G. A
    comparison of the solid-state structures of halogen azides XN[3]
    (X=Cl, Br, I). Angew. Chem. Int. Ed. 51, 12859-12863 (2012).

    Article  CAS  Google Scholar 

38. Buzek, P., Klapotke, T. M., von Rague Schleyer, P.,
    Tornieporth-Oetting, I. C. & White, P. S. Iodine azide. Angew.
    Chem. Int. Ed. 32, 275-277 (1993).

    Article  Google Scholar 

39. Shurvell, H. F. & Hyslop, D. W. Infrared spectrum of cyanogen
    azide. J. Chem. Phys. 52, 881-887 (1970).

    Article  ADS  CAS  Google Scholar 

40. Pimental, G. C. & Charles, S. W. Infrared spectral perturbations
    in matrix experiments. Pure Appl. Chem. 7, 111-124 (1963).

    Article  Google Scholar 

41. Zeng, X., Beckers, H. & Willner, H. Matrix isolation of two
    isomers of N[4]CO. Angew. Chem. Int. Ed. Engl. 50, 482-485
    (2011).

    Article  CAS  PubMed  Google Scholar 

42. Tobita, M. & Bartlett, R. J. Structure and stability of N[6]
    isomers and their spectroscopic characteristics. J. Phys. Chem. A
    105, 4107-4113 (2001).

    Article  CAS  Google Scholar 

43. Gagliardi, L., Evangelisti, S., Barone, V. & Roos, B. O. On the
    dissociation of N[6] into 3 N[2] molecules. Chem. Phys. Lett. 320
    , 518-522 (2000).

    Article  ADS  CAS  Google Scholar 

44. Huber, K. P. & Herzberg, G. in Molecular Spectra and Molecular
    Structure (eds Huber, K. P. & Herzberg, G.) Ch. 2, 8-689
    (Springer, 1979).

45. Carlotti, M., Johns, J. W. C. & Trombetti, A. The n[5]
    fundamental bands of N[2]H[2] and N[2]D[2]. Can. J. Phys. 52,
    340-344 (1974).

    Article  ADS  CAS  Google Scholar 

46. Brazier, C. R., Bernath, P. F., Burkholder, J. B. & Howard, C. J.
    Fourier transform spectroscopy of the n[3] band of the N[3]
    radical. J. Chem. Phys. 89, 1762-1767 (1988).

    Article  ADS  CAS  Google Scholar 

47. Bittererova, M., Ostmark, H. & Brinck, T. Ab initio study of the
    ground state and the first excited state of the rectangular (D
    [2h])N[4] molecule. Chem. Phys. Lett. 347, 220-228 (2001).

    Article  ADS  Google Scholar 

48. Lu, T. & Chen, F. Multiwfn: a multifunctional wavefunction
    analyzer. J. Comput. Chem. 33, 580-592 (2012).

    Article  PubMed  Google Scholar 

49. Schreiner, P. R. Tunneling control of chemical reactions: the
    third reactivity paradigm. J. Am. Chem. Soc. 139, 15276-15283
    (2017).

    Article  CAS  PubMed  Google Scholar 

50. Weggel, D. C. in Blast Protection of Civil Infrastructures and
    Vehicles Using Composites (ed. Uddin, N.) 3-43 (Woodhead
    Publishing, 2010).

51. Pople, J. A., Head-Gordon, M. & Raghavachari, K. Quadratic
    configuration interaction. A general technique for determining
    electron correlation energies. J. Chem. Phys. 87, 5968-5975
    (1987).

    Article  ADS  CAS  Google Scholar 

52. Bartlett, R. J. & Purvis, G. D. Many-body perturbation theory,
    coupled-pair many-electron theory, and the importance of
    quadruple excitations for the correlation problem. Int. J. Mol.
    Sci. 14, 561-581 (1978).

    CAS  Google Scholar 

53. Pople, J. A., Krishnan, R., Schlegel, H. B. & Binkley, J. S.
    Electron correlation theories and their application to the study
    of simple reaction potential surfaces. Int. J. Mol. Sci. 14,
    545-560 (1978).

    CAS  Google Scholar 

54. Neese, F. Software update: the ORCA program system--version 5.0.
    WIREs Comput. Mol. Sci. 12, e1606 (2022).

    Article  Google Scholar 

55. Becke, A. D. Density-functional thermochemistry. III. The role of
    exact exchange. J. Chem. Phys. 98, 5648-5652 (1993).

    Article  ADS  CAS  Google Scholar 

56. Stephens, P. J., Devlin, F. J., Chabalowski, C. F. & Frisch, M.
    J. Ab initio calculation of vibrational absorption and circular
    dichroism spectra using density functional force fields. J. Phys.
    Chem. 98, 11623-11627 (1994).

    Article  CAS  Google Scholar 

57. Frisch, M. J. et al. Gaussian 16, Revision B.01 (Gaussian, Inc.,
    2016).

58. Weigend, F. & Ahlrichs, R. Balanced basis sets of split valence,
    triple zeta valence and quadruple zeta valence quality for H to
    Rn: design and assessment of accuracy. Phys. Chem. Chem. Phys. 7,
    3297-3305 (2005).

    Article  CAS  PubMed  Google Scholar 

59. Stanton, J. F. et al. CFOUR, coupled-cluster techniques for
    computational chemistry, a quantum-chemical program package with
    the integral packages MOLECULE (J. Almlof and PR Taylor), PROPS
    (PR Taylor) (2014).

60. Lu, T. & Chen, F. Quantitative analysis of molecular surface
    based on improved Marching Tetrahedra algorithm. J. Mol. Graph.
    Model. 38, 314-323 (2012).

    Article  PubMed  Google Scholar 

61. Glendening, E. D., Landis, C. R. & Weinhold, F. NBO 7.0: new
    vistas in localized and delocalized chemical bonding theory. J.
    Comput. Chem. 40, 2234-2241 (2019).

    Article  CAS  PubMed  Google Scholar 

62. Glendening, E. D., Landis, C. R. & Weinhold, F. Natural bond
    orbital methods. WIREs Comput. Mol. Sci. 2, 1-42 (2012).

    Article  CAS  Google Scholar 

63. Zheng, J. et al. Gaussrate 17-B (Univ. Minnesota, 2017).

64. Garrett, B. C. & Truhlar, D. G. Generalized transition state
    theory. Bond energy-bond order method for canonical variational
    calculations with application to hydrogen atom transfer
    reactions. J. Am. Chem. Soc. 101, 4534-4548 (1979).

    Article  CAS  Google Scholar 

65. Garrett, B. C. & Truhlar, D. G. Criterion of minimum state
    density in the transition state theory of bimolecular reactions.
    J. Chem. Phys. 70, 1593-1598 (1979).

    Article  ADS  CAS  Google Scholar 

66. Garrett, B. C., Truhlar, D. G., Grev, R. S. & Magnuson, A. W.
    Improved treatment of threshold contributions in variational
    transition-state theory. J. Phys. Chem. 84, 1730-1748 (1980).

    Article  CAS  Google Scholar 

67. Truhlar, D. G., Issacson, A., Skodje, R. & Garrett, B. C.
    Additions and corrections - incorporation of quantum effects in
    generalized-transition-state theory. J. Phys. Chem. 87, 4554-4554
    (1983).

    Article  Google Scholar 

68. Zheng, J. et al. Polyrate-version 2017-C (Univ. Minnesota, 2017).

69. Tao, Y., Zou, W., Nanayakkara, S. & Kraka, E. LModeA-nano: a
    PyMOL plugin for calculating bond strength in solids, surfaces,
    and molecules via local vibrational mode analysis. J. Chem.
    Theory Comput. 18, 1821-1837 (2022).

    Article  CAS  PubMed  Google Scholar 

70. Politzer, P., Martinez, J., Murray, J. S., Concha, M. C. &
    Toro-Labbe, A. An electrostatic interaction correction for
    improved crystal density prediction. Mol. Phys. 107, 2095-2101
    (2009).

    Article  ADS  CAS  Google Scholar 

71. Bader, R. F. W., Carroll, M. T., Cheeseman, J. R. & Chang, C.
    Properties of atoms in molecules: atomic volumes. J. Am. Chem.
    Soc. 109, 7968-7979 (1987).

    Article  CAS  Google Scholar 

72. Murray, J. S., Concha, M. C. & Politzer, P. Links between surface
    electrostatic potentials of energetic molecules, impact
    sensitivities and C-NO[2]/N-NO[2] bond dissociation energies.
    Mol. Phys. 107, 89-97 (2009).

    Article  ADS  CAS  Google Scholar 

73. Kamlet, M. J. & Jacobs, S. J. Chemistry of detonations. I. A
    simple method for calculating detonation properties of C-H-N-O
    explosives. J. Chem. Phys. 48, 23-35 (1968).

    Article  ADS  CAS  Google Scholar 

74. Prazyan, T. L. & Zhuravlev, Y. N. Computer simulation of the
    structure and electronic and detonation properties of energy
    materials. Combust. Explos. Shock Waves 53, 718-723 (2017).

    Article  Google Scholar 

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Acknowledgements

Financial support by the Deutsche Forschungsgemeinschaft (DFG)
through grant MA 8773/3-1 (A.M.) is gratefully acknowledged. We
sincerely thank X. Bi (Northeast Normal University), T. M. Klapotke
(Ludwig Maximilian University of Munich) and Y. Ning (Northeast
Normal University) for their valuable suggestions for the synthesis
of silver azide and T. Lu (Beijing Kein Research Center for Natural
Sciences) for advice about the detonation performance computations.
We also thank W. D. Allen (University of Georgia) and X. Zeng (Fudan
University) for carefully reading and commenting on the manuscript.

Funding

Open access funding provided by Justus-Liebig-Universitat Giessen.

Author information

Authors and Affiliations

 1. Institute of Organic Chemistry, Justus Liebig University Giessen,
    Giessen, Germany

    Weiyu Qian  (Qian Wei Yu ), Artur Mardyukov & Peter R. Schreiner

Authors

 1. Weiyu Qian  (Qian Wei Yu )
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 2. Artur Mardyukov
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 3. Peter R. Schreiner
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Contributions

W.Q., A.M. and P.R.S. conceived the project. W.Q. and A.M. designed
and conducted the experiments, performed computations and collected
all data. W.Q. wrote the original manuscript. W.Q., A.M. and P.R.S.
revised the manuscript. A.M. and P.R.S. supervised the project.

Corresponding authors

Correspondence to Artur Mardyukov or Peter R. Schreiner.

Ethics declarations

Competing interests

W.Q., A.M., and P.R.S. are inventors on European patent application
EP24194869 (16 August 2024), submitted by the Justus Liebig
University Giessen, which covers a method for producing molecular
polynitrogens.

Peer review

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Nature thanks Chunlin He, Thomas Klapotke and the other, anonymous,
reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

This file contains a note for the synthesis, Supplementary Figs.
1-15, Supplementary Tables 1-4 as well as xyz-coordinates of all
computed species.

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Cite this article

Qian, W., Mardyukov, A. & Schreiner, P.R. Preparation of a neutral
nitrogen allotrope hexanitrogen C[2h]-N[6 ]. Nature 642, 356-360
(2025). https://doi.org/10.1038/s41586-025-09032-9

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  * Received: 18 September 2024

  * Accepted: 16 April 2025

  * Published: 11 June 2025

  * Issue Date: 12 June 2025

  * DOI: https://doi.org/10.1038/s41586-025-09032-9

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