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Hexacoordinated nitrogen(V) stabilized by high pressure

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In all of its known connections nitrogen retains a valence shell electron count of eight therefore satisfying the golden rule of chemistry - the octet rule. Despite the diversity of nitrogen chemistry (with oxidation states ranging from + 5 to −3), and despite numerous efforts, compounds containing nitrogen with a higher electron count (hypervalent nitrogen) remain elusive and are yet to be synthesized. One possible route leading to nitrogen’s hypervalency is the formation of a chemical moiety containing pentavalent nitrogen atoms coordinated by more than four substituents. Here, we present theoretical evidence that a salt containing hexacoordinated nitrogen(V), in the form of an NF6 anion, could be synthesized at a modest pressure of 40 GPa (=400 kbar) via spontaneous oxidation of NF3 by F2. Our results indicate that the synthesis of a new class of compounds containing hypervalent nitrogen is within reach of current high-pressure experimental techniques.


Since the first synthesis of the NF4+ cation in 19661 numerous experimental attempts have been made to synthesize its neutral parent molecule, NF52,3,4,5. All of these attempts turned out fruitless, eventually leading to the conclusion that the highest coordination number (CN) attainable for pentavalent nitrogen is 4, with higher CNs not possible due to steric hindrance around the nitrogen atom6. Obviously, it’s possible to find nitrogen in an environment with higher CNs, but only in salts containing the isolated, and non-hypervalent, N3− anion (e.g. Li3N exhibiting 8-fold N coordination)7, or in certain coordination complexes of trivalent nitrogen (e.g. [(Ph3PAu)5N]2+)8 in which, despite the high CNs, the valence shell electron count on nitrogen never exceeds eight.

Theoretical investigations into the properties of the nitrogen pentafluoride molecule (NF5) in the gas phase9,10,11,12,13 indicate that although it is a minimum on the potential energy surface (PES)11,12,13, its decomposition into NF3 and F2 is highly exothermic (+1.82 eV per NF5)12,13. Regarding the geometry of the molecule, the ground state structure of NF5 is a trigonal bipyramid with five covalent N–F bonds. Interestingly the energy of formation of the molecule is comparable with that of solid (NF4+)(F)14, making the NF5 system an interesting example of the interplay between covalent and ionic bonding.

In this communication we present results of a comprehensive computational investigation on the possibility of synthesizing solid NF5 from NF3 and F2 through the application of external pressure in the range of several dozens GPa (1 GPa = 10 kbar). At present pressures up to 200 GPa are routinely achieved in diamond anvil cells (DACs), and the large influence of such high-pressure (HP) conditions on the properties and reactivity of the elements and chemical compounds is well documented15,16,17,18. The potential of obtaining novel species through the application of HP is exemplified inter alia by the recent synthesis of nitrogen analogues of alkanes19, or by the theoretical predictions that hypervalent carbon species can be stabilized at large compression20.

Most importantly the oxidative strength of fluorine has been predicted to increase considerably at elevated pressures with calculations indicating that at such conditions F2 should oxidize Cs to CsF321,22, HgF2 to HgF323, and Ar to ArF224. Furthermore both theoretical25,26,27,28 and experimental19,29,30,31 high-pressure studies on the N/H system (analogous to the N/F system studied here) indicate that a wealth of exotic NxHy structures should, and indeed does stabilize at HP conditions.


Computational approach

Our solid-state calculations, performed within the Density Functional Theory, in the 0–300 GPa pressure range, utilized the hybrid HSE06 functional32,33,34. Importantly, benchmark calculations conducted for isolated molecules, indicate that this functional reproduces much better the gas-phase thermodynamic stability of nitrogen fluorides compared to the PBE functional35 typically used “by default” in HP solid-state calculations (for more details see sections I and II of the Supplementary Information, SI). Candidate structures of NF5 were identified through the application of the USPEX evolutionary algorithm36,37. The search for the enthalpically best structures revealed a surprising diversity of high-pressure NF5 polymorphs exhibiting numerous and versatile bonding patterns. All thermodynamic and structural parameters reported here are obtained with the use of the HSE06 functional.

Structures of NF5

The lowest enthalpy structures of NF5 are shown in Fig. 1; for the purpose of this communication we label them with their respective space group symbols. The P1 structure is a molecular crystal consisting of NF3 and F2 molecules, and is the only polymorph containing trivalent nitrogen. Similarly, the P–1 structure is also a molecular crystal, but in contrast it is composed of isolated NF5 units. Both R3m and I–4 structures exhibit ionic character and both contain NF4+ cations and F anions. The I4/m and P4/n phases are also ionic, but apart from the NF4+ and/or F ions they both contain the NF6 anion in which pentavalent nitrogen is bonded to six fluorine atoms. This anion was first proposed by Ewig and Van Wazer11 who found it to be dynamically stable in the gas phase, and indeed thermodynamically more stable than NF5 + F. To our best knowledge there have been no prior reports on the stabilization of NF6 in the solid state.

Figure 1: Structures of solid NF5.
Figure 1

Nitrogen/fluorine atoms are marked by blue/red spheres (covalently bound F atoms are marked with smaller spheres while the F anions with larger ones).

The assignment of ionic/neutral NFnm+ fragments is based not only on the fact that the optimized geometry of these fragments agrees well with that predicted by the VSEPR model38 (NF3 – trigonal pyramid, NF4+ – tetrahedron, NF5 – trigonal bipyramid, NF6 – octahedron), but also on the excellent accordance between the bond lengths of these moieties at effectively 0 GPa and those obtained from gas-phase calculations (Table 1). It’s noteworthy to point that even at 300 GPa the NFnm+ fragments remain well-defined, although in some cases quite distorted (vide infra). This is best exemplified by the fact that at 300 GPa the secondary N···F contacts of all structures are more than 25% longer than the intramolecular N–F bonds, while F···F distances are more than 30% longer compared to the genuine F–F bond in a F2 molecular crystal optimized at the same pressure. As expected all of the studied NF5 polymorphs are wide-gap insulators with the band gap exceeding 5 eV even at 300 GPa.

Table 1: Comparison of calculated N–F bond lengths (in Å) of NFnm+ moieties in the gas phase and in various NF5 phases (ax – axial, eq – equatorial bonds).

The structures optimized with the PBE functional exhibit similar geometries to those described above (obtained with HSE06). Most importantly, we have compared the PBE and HSE06-optimized structure and found no evidence of a Peierls distortion ensuing after optimization of the PBE structures conducted with HSE06, in contrast to what was found for a polymeric phase of nitrogen39. We attribute it to the fact that the studied structures contain isolated ions or molecules, and do not exhibit extended motifs (chains, layers) for which one can expect a Peierls distortion. Finally, we note that while the resulting geometries remain essentially identical for the two functionals the relative enthalpies of various structures differ quite substantially; as already mentioned, in this report we focus on the HSE06 values (for details on the PBE/HSE06 enthalpy differences see Section II of SI).

Stability and pressure evolution of NF5 polymorphs

Surprisingly, despite the large diversity of bonding patterns exhibited by the structures containing pentavalent nitrogen their relative enthalpies at low pressure fall in a narrow range of 0.6 eV per NF5 unit (≈58 kJ/mol); see Fig. 2.

Figure 2: Pressure dependence of the relative enthalpy of NF5 polymorphs.
Figure 2

At each pressure point the enthalpies (obtained with HSE06 calculations) are referenced to that of I–4. The grey region marks the pressure range where the enthalpy change of the reaction NF3(s) + F2(s) → NF5(s) is positive (p < 40 GPa) indicating instability of NF5 towards decomposition into NF3 and F2.

At pressures lower than 11 GPa it is the P1 phase (Z = 1), containing molecular NIIIF3 mixed with F2, which is the lowest enthalpy structure. Interestingly upon compression of the P1 structure the F–F bond in F2 lengthens from 1.39 Å at 0 GPa to 1.44 Å at 39 GPa, while the shortest secondary N···F contact contracts from 3.14 Å to 1.89 Å. This points to a significant pressure-induced enhancement of the donor-acceptor interactions between the HOMO of NF3 and the antibonding LUMO of F2. In fact, upon compression to 40 GPa this interaction leads to heterolytic dissociation of the F2 molecules and formation of an ionic structure containing NF4+ cations separated by F anions. At 40 GPa the shortest F···F contact in P1 is 2.17 Å and the four N–F bonds have a length of 1.29 Å. Those changes clearly illustrate that compression of the P1 phase up to 40 GPa leads to spontaneous oxidation of NIIIF3 by F2 and subsequent formation of NVF4+ and F.

Note that at 40 GPa the oxidized P1 phase turns out to be identical in terms of geometry with another NF5 polymorph, R3m (Z = 3, Fig. 1). The coordination of the F anion in the latter structure is such that each F is surrounded by 11 F atoms originating from 7 NF4+ cations. In particular, the R3m polymorph becomes the ground state structure of the NF5 system already above 11 GPa. Our USPEX searches identify yet another (NF4+)(F) structure of the I–4 symmetry (Z = 2), which is even more densely packed than the R3m (F anions surrounded by 12 F atoms originating from 8 NF4+ cations). This structure is noteworthy since the I–4 phase becomes more stable than the R3m polymorph at 37 GPa. Nevertheless, already above 33 GPa both I–4 and R3m have a higher enthalpy than a more complex I4/m phase (Z = 6), which remains the lowest-enthalpy structure up to 151 GPa (see Fig. 2).

The I4/m phase is characterized by alternating (NF6)(F) and (NF4+)2 layers leading to a general formula of (NF4+)2(NF6)(F) = 3NF5. This structure bears many similarities to the HP phase of PCl5 (I2/m symmetry) which is best formulated as (PCl4+)2(PCl6)(Cl)40. The I2/m polymorph is also layered, but in contrast to the I4/m structure of NF5 it exhibits tilting of the complex ions about an axis lying in the plane of the layers. Geometry optimization of a NF5 polymorph isostructural with I2/m indicated that such a structure is not competitive with I4/m in terms of enthalpy.

The NF6 anion in I4/m exhibits a slight tetragonal distortion at the low pressure limit (effectively 0 GPa) with two axial N–F bonds shorter by 1.3% than the four equatorial ones. Still all the bond lengths are very close to those obtained in molecular calculation (Table 1). The difference between the axial and equatorial bonds in I4/m remains nearly constant with increasing pressure and does not exceed 1% at 300 GPa. Upon compression of I4/m the N–F bonds in NF4+ shorten by 5% (to 1.25 Å at 300 GPa), while in case of the axial/equatorial bonds of NF6 the contraction is approximately 8%.

Above 151 GPa I4/m is predicted to become thermodynamically less stable than a P4/n structure (Z = 4) containing a 1:1 ratio of NF4+ and NF6, and no F anions. This polymorph is isostructural with the ambient pressure phase of PCl5 = (PCl4+)(PCl6)41. In P4/n the NF6 anions are more distorted compared to I4/m with two unequal axial N–F bonds (Table 1 and Fig. 3). High pressure enhances this distortion with the difference between the two axial bonds reaching 10% at pressures above 20 GPa. This seems to indicate that in P4/n the NF6 anion could be also described as a complex of square pyramidal NF5 with an F anion (see Fig. 3). Unequivocal determination which of the two alternative descriptions (highly distorted NF6 vs NF5···F complex) is correct requires more elaborate calculations which are beyond the scope of this communication.

Figure 3: The geometry of the NF6 and NF5 fragments.
Figure 3

The NF6 fragment in P4/n at 0 and 300 GPa (left) and the NF5 fragment in P–1 at the same pressures (right). Bond distances (in Å) and angles between the axial and equatorial bonds are indicated.

Interestingly there is no pressure region in which a structure containing NF5 molecules would be the most stable polymorph of NF5. The P–1 structure, which contains such units, becomes more stable than R3m/I–4 at 78/243 GPa, but still in the whole pressure region studied it remains less stable than the NF6-containing polymorphs (I4/m and P4/n). The coordination of NF5 molecules in the P1 phase changes from trigonal bipyramidal to square pyramidal above 40 GPa (Fig. 3). This transformation, which is in agreement with the predicted non-rigidness of the NF5 molecule12, is accompanied by a reduction in volume, and a change in the slope of the relative enthalpy (Fig. 2).


The enthalpy change associated with the reaction: NF3 + F2 → NF5 becomes negative already at 40 GPa, as indicated by the grey region in Fig. 2. This shows that NF5, containing hypervalent nitrogen, could be synthesized from NF3 and F2 already at relatively low pressure, in the form of a novel salt (NF4+)2(NF6)(F) (I4/m polymorph). Furthermore, we found NF5 to be stable against decomposition into NF4, another possible fluorine-rich phase of the N/F phase diagram (see Section III of the SI). Also, we emphasize that the calculated phonons remain positive within the whole Brillouin zone; a proof that the I4/m phase is dynamically stable both at the pressure of synthesis (40 GPa) as well as at higher pressures (see section IV in SI).

Our results hint that the high-pressure oxidation of NF3 by F2 is accompanied by the ionization of the reactants, that is formation of NF4+, NF6 and F ions in place of neutral NF5 molecules. The tendency for heterolytic, rather than homolytic splitting of the F–F bond in F2 reacting with NF3 is further exemplified by the molecular-ionic transition observed in the P1 polymorph of NF5.

On a side note, we here point that for the related N/H system Qian et al. also predict formation of ionic species at high pressure and at large hydrogen contents28. However these phases contain solely normal valent species (NH4+, H+, NH2, H), in contrast to the hypervalent NF5, NF6 species reported in this study. Another difference is that for the N/H system the NH5 composition is metastable with respect to decomposition into stable NH4 and H2 while we find NF4 to be unstable at both ambient and high pressure. The instability of hypervalent N/H molecules can be traced back to the large steric crowding around the nitrogen atom in NHn (n > 4) species. In fact, as calculated by Ewig and van Wazer, the NH5 molecule is not only thermodynamically but also dynamically unstable in the gas phase, in contrast to NF5 which is dynamically stable10.

The propensity for the formation of ionic phases at HP, observed also for other nitrogen compounds (NH3, N2O)25,29,42, can be explained by the pressure-induced increase of the lattice enthalpy (HL) of ionic phases which leads to additional stabilization of such structures with respect to molecular, van der Waals bonded polymorphs. The increase in HL is a consequence of the volume reduction upon compression, as the lattice enthalpy is proportional to the inverse cube root of the molecular volume (the so-called Bartlett’s relationship)43,44.

Interestingly in the case of the NF5 system the stabilization of ionic phases leads to larger than expected increase in hypervalency – the NF6 ion with a valence electron count of 12 is more stable at HP than the NF5 containing 10 electrons in the nitrogen valence shell. We note that this is not a general trend; in the case of hypervalent XeF2 the predicted pressure-induced ionization stabilizes a non-hypervalent salt of the (XeF+)(F) stoichiometry45.

In summary our calculations indicate that a compound containing nitrogen(V) covalently bound by six fluorine atoms can be synthesized via a HP reaction between NF3 and F2. A newly formed salt, of (NF4+)2(NF6)(F) stoichiometry, would constitute the first example of a compound containing hypervalent nitrogen atoms. Most interestingly, due to relatively low pressures involved and due to the involvement of strong ionic interactions this new species might be stable even upon decompression to ambient pressure, particularly at low temperatures. Due to the computer-intensive nature of phonon calculations a detailed study of the dynamic stability of various NF5 phases at low pressure is beyond the scope of this study.

Finally, it is also worth to remark that the phase transitions of NF5 bear many similarities to those exhibited by PCl5, which serves as good example on the rule of thumb that at HP elements tend to resemble their heavier congeners15. We hope that the results presented here, which offer an intriguing extension of the palette of N/F binary compounds46, will motivate experiments aimed at stabilizing the first genuine hexacoordinated binary compound of pentavalent nitrogen.


Hybrid potential calculations

Periodic DFT calculations utilized the HSE06 hybrid potential32,33,34, while the PBE exchange correlation functional35 was used in evolutionary searches, phonon calculations, and for comparative calculations. The projector augmented-wave (PAW) method was used, as implemented in the VASP 5.2 code47,48,49. The cut-off energy of the plane waves was set to 1000 eV with a self-consistent-field convergence criterion of 10−6 eV. Valence electrons were treated explicitly, while standard VASP pseudopotentials were used for the description of core electrons. The k-point mesh was set at  × 0.06 Å−1. All structures were optimized using a conjugate gradient algorithm until the forces acting on the atoms were smaller than 10 meV/Å. The abovementioned parameters ensured convergence of the calculated enthalpy within 2 meV per atom.

Structure searches

The candidate structures of NF3, F2, NF5, as well as NF4 (see SI) were identified with the use of the USPEX evolutionary algorithm coupled with the PBE functional. Evolutionary searches were conducted for Z = 1, 2, 3, and 4 at P = 50, 100, 200 and 300 GPa. Due to the large computational cost of the HSE06 functional we were not able to employ it during the USPEX runs. Therefore, all of the best candidate structures obtained with USPEX were fully re-optimized (i.e. optimization of lattice parameters and internal coordinates) using the HSE06 functional. Beside the best structures identified at PBE level, we also used a number of enthalpically low lying meta-stable structures in the HSE06 re-optimization. For NF3 our structure search identified the Pnma, Pnma (2), and P212121 molecular phases proposed in an earlier study50, and did not find any new phases which would be competitive in terms of enthalpy with those three. The enthalpy change of the reaction NF3(s)  + F2(s) → NF5(s) was calculated taking (at each pressure) the lowest enthalpy polymorph of NF5 and NF3, as well as the ambient-pressure α polymorph of F251. We note that above 50 GPa α-F2 (C2/c space group) symmetrizes spontaneously to a Cmca structure which is analogous to the high-pressure polymorph of Cl252. Even at 300 GPa F2 remains in the form of a molecular crystal.

Dispersion corrections

In order to determine the influence of dispersion-type interactions on the relative stability of NF5 polymorphs we have calculated dispersion corrections (in the form of D3 correction proposed by Grimme and co-workers53,54,55) for structures optimized at the HSE06 level of theory. We found that the D3 correction has very little to no influence on the relative stability of different NF5 polymorphs (changes of transition pressures do not exceed 2 GPa upon inclusion of D3 corrections).

Structure visualization was performed with the VESTA 3.1 software56. Symmetry recognition was performed with the online program FINDSYM57.

Additional Information

How to cite this article: Kurzydłowski, D. and Zaleski-Ejgierd, P. Hexacoordinated nitrogen(V) stabilized by high pressure. Sci. Rep. 6, 36049; doi: 10.1038/srep36049 (2016).

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D.K. and P.Z.-E. acknowledge the support from the Polish National Science Centre (NCN) within grants no. UMO-2014/13/D/ST5/02764, and UMO-2012/05/B/ST3/02467. This research was carried out with the support of the Interdisciplinary Centre for Mathematical and Computational Modelling (ICM) University of Warsaw under grant no GA65–26.

Author information


  1. Centre of New Technologies, University of Warsaw, Warsaw 02-097, Poland

    • Dominik Kurzydłowski
  2. Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszyński University in Warsaw, Warsaw 01-938, Poland

    • Dominik Kurzydłowski
  3. Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw 01-224, Poland

    • Patryk Zaleski-Ejgierd


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D.K. conceived the idea of stabilizing NF5 at high-pressure. D.K. and P.Z.-E. designed the research and carried out the calculations. Both authors analysed the results and wrote the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Dominik Kurzydłowski or Patryk Zaleski-Ejgierd.

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