Neutral binary chalcogen–nitrogen and ternary S,N,P molecules: new structures, bonding insights and potential applications

Abstract

Early theoretical and experimental investigations of inorganic sulfur–nitrogen compounds were dominated by (a) assessments of the purported aromatic character of cyclic, binary S,N molecules and ions, (b) the unpredictable reactions of the fascinating cage compound S₄N₄, and (c) the unique structure and properties of the conducting polymer (SN)_x. In the last few years, in addition to unexpected developments in the chemistry of well-known sulfur nitrides, the emphasis of these studies has changed to include nitrogen-rich species formed under high pressures, as well as the selenium analogues of well-known S,N compounds. Novel applications have been established or predicted for many binary S/Se,N molecules, including their use for fingerprint detection, in optoelectronic devices, as high energy-density compounds or as hydrogen-storage materials. The purpose of this perspective is to evaluate critically these new aspects of the chemistry of neutral, binary chalcogen–nitrogen molecules and to suggest experimental approaches to the synthesis of target compounds. Recently identified ternary S,N,P compounds will also be considered in light of their isoelectronic relationship with binary S,N cations.

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Tristram Chivers

Tristram Chivers, a native of Bath, England, received his BSc, PhD (with Prof. R. D. Chambers FRS) and DSc degrees all from the University of Durham (UK). He joined the University of Calgary in 1969 and served as Head of the Chemistry Department from 1977 to 1982. He is currently Professor Emeritus of Chemistry. His research interests are in the area of main group element chemistry with an emphasis on chalcogen compounds and inorganic ring systems. He is the author of two books: “A Guide to Chalcogen–Nitrogen Chemistry” and (with I. Manners) “Inorganic Rings and Polymers of the p-Block Elements: From Fundamentals to Applications”.

Risto S. Laitinen

Risto S. Laitinen received his Ph. D. (eng) in 1982 from Helsinki University of Technology (Finland). He joined University of Oulu in 1988 and is currently Professor Emeritus of inorganic chemistry. He has been the Head of Chemistry Department in 1993–2013 and the head of Research Unit of Environmental and Chemical Engineering in 2017–2019. His research activities comprise experimental and computational main group chemistry, in particular chemistry of chalcogens. He has edited two books: “Selenium and Tellurium Chemistry: From Small Molecules to Biomolecules and Materials” (with J. D. Woollins) and “Selenium and Tellurium Reagents in Chemistry and Materials Science” (with R. Oilunkaniemi).

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1. Introduction

In contrast to the oxides of nitrogen NO, NO₂, and N₂O_x (x = 1, 3, 5), which all have acyclic structures, sulfur and nitrogen form a variety of neutral binary compounds with cyclic, polycyclic or polymeric structures.¹ These include the intriguing, orange cage molecule E₄N₄ (1, E = S) with D_2d symmetry,^2a the colourless, planar four-membered ring E₂N₂ (2, E = S),^2b and the blue-black polymer (SN)_x (3),^2c which becomes superconducting at 0.26 K. Less well-known are the red, six-membered ring 1,3-S₄N₂ (4),^2d which adopts a half-chair conformation, and the explosive S₅N₆ (5),^2e an orange compound with a cradle-like structure (Scheme 1). A labile –N=S=N– bridging unit is a common feature of both 4 and 5. The extremely hazardous selenium nitride Se₄N₄ (1, E = Se)^3a has a cage structure similar to that of the sulfur analogue as does the mixed chalcogen nitride 1,5-Se₂S₂N₄.^3b The binary selenium nitride Se₂N₂ (2, E = Se) has not been identified as the free ligand, but both main-group metal and transition–metal complexes have been structurally characterised.^3c,d The six-membered ring 1,3-Se₄N₂ (4, E = Se) is unknown,⁴ consistent with ab initio molecular orbital calculations for the S_xSe_4−xN₂ ring systems. The stability of these ternary chalcogen nitrides is estimated to decrease with increasing selenium content and those that contain an –N=Se=N– fragment were found to be less stable than those that incorporate an –N=S=N– moiety.⁵

Scheme 1 Structures of E₄N₄ (E = S, Se), E₂N₂ (E = S, Se), (SN)_x, S₄N₂ and S₅N₆.

Early studies of cyclic S,N species, including cations and anions as well as neutral molecules, focussed on the proposed aromatic character of planar ring systems as well as the properties and possible applications of the conducting polymer (SN)_x. For example, the following species were considered to be aromatic on the basis of the Hückel 4n + 2π-electron rule: S₂N₂ (6π), S₃N₃⁻ (10π), S₄N₃⁺ (10π) and S₅N₅⁺ (14π).^1a A fuller understanding of (a) the nature of the transannular E⋯E interactions in E₄N₄ (1, E = S, Se) and related bicyclic sulfur–nitrogen molecules,^6,7 (b) the electronic structures of the chalcogen nitrides E₂N₂ (2, E = S, Se), and (c) the mechanism of the topochemical polymerisation of S₂N₂ rings to generate the polymer (SN)_x continues to occupy the attention of computational chemists.⁸ Furthermore, the serendipitous finding by Kelly and co-workers ca. 12 years ago that S₂N₂ vapour interacts with fingerprints on a glass vial to give a visible image of (SN)_x has now reached the stage of potential commercial applications in forensic science.⁹ This development has generated impetus to the search for practical uses of other binary chalcogen–nitrogen species both known and unknown.

In the foregoing context nitrogen-rich chalcogen nitrides have been neglected, undoubtedly as a result of the difficulty in handling these energy-rich systems. However, recent experimental and computational studies of sulfur–nitrogen and selenium–nitrogen species under high pressure have revealed the formation or prediction of a number of novel binary chalcogen nitrides with unique structures and properties. In a similar vein optoelectronic or mechanical applications have been predicted for the as-yet-unknown sulfur-rich nitride S₃N₂.¹⁰ The focus of this perspective is an appraisal of recent experimental and computational studies of the structures and properties of both known and new binary chalcogen nitrides with an emphasis on the potential applications of these materials.¹¹ The chemistry of the less well-studied selenium nitrides will be compared with that of sulfur nitrides throughout the discussion.

The article is organised by considering sulfur-rich nitrides S_xN₂ (x = 3, 4) initially, followed by new developments in the chemistry of molecules containing equal numbers of chalcogen and nitrogen atoms as exemplified by compounds 1–3. The treatise then focusses on the synthesis, unusual structures and predicted properties of nitrogen-rich chalcogen nitrides. Finally, the significance of the recent characterisation of both acyclic and cyclic S,N,P molecules^12a,b will be evaluated in the context of the isoelectronic relationship of these ternary species with known binary S,N cations.^1a,b

2. Sulfur-rich sulfur nitrides S₃N₂ and S₄N₂

The structures and properties of the sulfur–rich nitrides 1,3-S₃N₂ and 1,3-S₄N₂ (4) provide an interesting comparison. The putative five-membered ring cyclo-1,3-S₃N₂ is an antiaromatic (8π-electron) system, whereas the known six-membered ring cyclo-1,3-S₄N₂ is formally a 10π-electron molecule, which adopts a half-chair conformation in the solid state.^2d The optimised geometries for 4 ¹³ gave values of S–S and S–N bond lengths that are in close agreement with the experimental data.^2d For example, the calculated S–S bond length is 2.090 Å,¹³cf. 2.061 Å from the X-ray structure.^2d This congruence establishes confidence in the calculated S–S bond length of 2.302 Å for cyclo-1,3-S₃N₂.¹³ The elongated S–S bond is presumably a result of inherent strain in the five-membered ring, as suggested by the predicted value of the internal bond angle < NSS = 94.5°, cf. 105.2° in the six-membered ring 4.^2d

As an alternative to a cyclic structure, in 2018 Chen and co-workers have proposed a stable two-dimensional trisulfur dinitride with three polymorphs comprised solely of σ bonds.^10a The crystal structure of the most stable form, α-S₃N₂ (space group Pmn21), consists of condensed 12-membered (S₆N₆) rings (Fig. 1). The S₃N₂ crystal is predicted to be dynamically, thermally and chemically stable on the basis of the computed phonon spectrum and ab initio molecular dynamics simulations. The predicted “chemical stability” is surprising in view of the known susceptibility of sulfur–nitrogen compounds to degradation by both nucleophiles and electrophiles.^1a,b Calculations also indicate that α-S₃N₂ will be a wide, direct band gap (3.92 eV) semiconductor with possible optoelectronic applications such as blue or UV light-emitting diodes and photodetectors.

Fig. 1 The PBE-predicted 2D crystal structure of α-S₃N₂: a = 4.24, b = 8.89 Å; d₁ = 1.81, d₂ = 1.72, d₃ = 1.66 Å; θ₁ = 116.8°, θ₂ = 119.3°, θ₃ = 119.2°, θ₄ = 106.1°, θ₅ = 103.7°.^10a Bonding is depicted by an isosurface of the electron density.^10a (Reproduced with permission from H. Xiao, X. Shi, X. Liao, Y. Zhang and X. Chen, Phys. Rev. Mater., 2018, 2, 024002. @ 2018 American Physical Society.)

A subsequent study of 2D monolayer crystals of E₃N₂ (E = S, Se) employing DFT calculations predicted α-heart and β-heart structures, which exhibit different mechanical and electrical properties.^10b The former structure resembles that depicted for α-S₃N₂ in Fig. 1. The E₃N₂ materials are predicted to have unusual mechanical properties as indicated by the values of Negative Poisson's Ratios indicating auxetic behaviour.^10c

The recent computational predictions of the unique structure and mechanical properties of S₃N₂ provide a strong incentive for pursuing experimental approaches to this unknown binary sulfur nitride. A carefully controlled cyclocondensation reaction of ClSSCl with Me₃SiNSNSiMe₃ under high-dilution conditions is a plausible first attempt.¹⁴ An alternative route is the one-electron chemical or electrochemical reduction of the known radical cation [S₃N₂]˙⁺, which is prepared by oxidation of S₄N₄ with AsF₅ in liquid SO₂.^1a The reaction of 1,3-S₄N₂ (4) with one equivalent of PPh₃ is likely to result in attack of the nucleophile at the S(IV) centre rather than the required removal of a single sulfur atom from the –S–S–S– unit.

3. Molecules with equal numbers of chalcogen and nitrogen atoms

3.1. Tetrasulfur and tetraselenium tetranitride E₄N₄ (1, E = S, Se)

The S₄N₄ (1, E = S) molecule is regarded as the quintessential binary sulfur–nitrogen compound in view of its multifarious applications as a reagent in inorganic and organic chemistry, despite a tendency to detonate under the influence of heat or friction.^1a Notwithstanding the availability of simple synthetic procedures, the selenium analogue 1 (E = Se) has undergone limited use for the preparation of selenium–nitrogen compounds owing to the explosive nature of this reagent.^1a,b Some new aspects of the chemical reactivity of 1 (E = S), including the electrochemical reduction and photochemical behaviour, are discussed in a recent book chapter.^1b This section will consider more recent developments in the chemistry of S₄N₄, especially those involving an understanding of the electronic structure and unusual reaction chemistry of this cage compound.

3.1.1. Electronic structure of 1 (E = S, Se); transannular E⋯E interactions. The strength of the intramolecular S⋯S interaction in 1 (E = S) has been estimated to be of the order of a hydrogen bond on the basis of the noncovalent interaction index.¹⁵ Tuononen et al., have investigated the nature of this interaction in 1 (E = S, Se) with high-level theoretical methods.⁶ Their results showed that the elongation of the transannular E⋯E bonds compared to a typical single-bond value can be attributed to surprisingly large correlation effects. Furthermore, there is some singlet diradical character associated with each E⋯E interaction. Although the consequences of this feature of the electronic structure of 1 (E = S) have not been investigated intentionally by experimentalists, an early report by Mews described the preparation of the di-substituted derivative S,S′-1,5-S₄N₄[ON(CF₃)₂]₂ upon reaction of S₄N₄ with two equivalents of the nitroxide radical (CF₃)₂NO˙.¹⁶ The reaction of S₄N₄ with molecular H₂ is worthy of investigation computationally and experimentally in view of this diradical character and the potential use of sulfur–nitrogen compounds as hydrogen-storage materials as discussed in section 3.2.5.

A different aspect of the bonding interactions in 1 (E = S) was reported in 2016 by Jenkins and co-workers.¹⁷ By applying QTAIM (quantum theory of atoms in molecules) methodology to all 18 modes of vibration of the cage molecule, these authors found a considerable degree of metallicity in the S–S and S–N bonding interactions, on the basis of the delocalisation of the electron density away from the atoms. In particular, considerable metallic behaviour was apparent in the S–S bond critical points for all modes.¹⁷ The experimental implications of this finding are yet to be investigated.

3.1.2. Unusual reaction chemistry involving S₄N₄. Numerous complexes of S₄N₄ with Lewis acids have been structurally characterised and the bonding trends in these N-bonded adducts have been investigated.^1b,18 In 2018 Si and Ganguly described first principles calculations of the interaction of S₄N₄ with benzene and naphthalene.¹⁹ These authors found that the σ hole of the sulfur atoms of S₄N₄ engages in non-covalent interactions with these aromatic π-systems. For example, the interaction energy of S₄N₄ with three naphthalene rings was estimated to be ca. 20 kcal mol⁻¹.¹⁹ The S⋯π interaction is the main driving force in these complexes of S₄N₄ with only a marginal contribution from the N atoms. The reactions of S₄N₄ with alkynes have been investigated in considerable details and shown to cause cleavage of the cage molecule to form the heterocycle 1,2,5-thiadiazole as the major product along with the 7-membered rings (RC)₂S₃N₃ and RCS₃N₃.^1a The only example of adduct formation between S₄N₄ and an organic compound was reported more than 20 years ago by Konarev et al.²⁰ These authors determined the single crystal X-ray structural analysis of the non-stoichiometric complex C₆₀(S₄N₄)_1.33(C₆H₆)_0.67 and found that only the sulfur atoms participate in bonding to the fullerene.²⁰ A more detailed experimental investigation of complexes of S₄N₄ with aromatic systems is warranted in view of the computational predictions.¹⁹

A convenient synthesis of S₄N₄ involves the cyclocondensation reaction of [(Me₃Si)₂N]₂S with an equimolar mixture of SCl₂ and SO₂Cl₂.²¹ The complexity of the reaction pathway for this transformation is highlighted on the cover page of a recent textbook with a focus on “arrow-pushing” in inorganic chemistry.²² Ghosh and Berg propose a twelve-step process with the sequential participation of the reagents SCl₂ followed by SO₂Cl₂. However, the combination of SCl₂ and SO₂Cl₂ generates SCl₄ (+SO₂) spontaneously, so a cyclocondensation pathway involving this in situ reagent is more likely. The formation of an acyclic –SNSNS– intermediate and, subsequently, an eight-membered S₄N₄ ring via a series of thermodynamically favoured eliminations of Me₃SiCl is suggested (Scheme 2).

Scheme 2 Formation of S₄N₄via cyclocondensation of [(Me₃Si)₂N]₂S with SCl₄.

Kumar and Muralidharan have reported the hexamethyldisilazane (HMDS)-assisted synthesis of β-In₂S₃, CuS and Ag₂S nanoparticles via reactions of sulfur with an appropriate metal salt in the presence of HMDS.²³ In order to explain the role of HMDS in the synthesis of these metal sulfides, the formation of a novel polymeric intermediate [SN(SiMe₃)]_n, was invoked.^23c,d The characterization of this purported polymer was based upon GPC (gel permeation chromatography) analysis of the distilled material, as well as ²⁹Si NMR spectra and HRMS (high resolution mass spectrometry) data.^23a The fact that this intermediate could not be isolated as a pure compound was attributed by the authors to the similarity of its boiling point with that of HMDS. Since the boiling point of HMDS is only 125 °C, this explanation is highly unlikely. Orange crystals obtained as a minor by-product in the synthesis of Ag₂S were identified by XRD as S₄N₄ as a minor by-product;^23b however, the formation of this binary sulfur nitride from the purported sulfur imide polymer is not readily explained.

3.2. Disulfur and diselenium dinitride E₂N₂ (2, E = S, Se)

In contrast to the numerous applications of S₄N₄ as a source of novel inorganic and organic sulfur–nitrogen compounds,^1a,b the use of S₂N₂ in synthesis is rare owing to its highly labile nature. However, both electrochemical and chemical reduction produce the [S₃N₃]⁻ anion, which can be isolated as ion-separated salts.^1b,24 This section will consider recent developments in our understanding of the chemistry of S₂N₂ and its heavier chalcogen homologues, including electronic structures, spectroscopic characterisation, the isomers formed upon photolysis, topochemical polymerization to give (SN)_x, and possible use as a hydrogen-storage material.

3.2.1. Electronic structures. The square-planar structure of S₂N₂ (2, E = S), a volatile white crystalline solid, was established 45 years ago.^1a Despite this longevity, the electronic structure of this four-membered ring and its heavier chalcogen analogues continues to generate controversy centred around their aromaticity and diradical character.²⁵ The most recent developments are discussed below.

In 2004 Head-Gordon et al. concluded that the diradical character of S₂N₂ is not significant on the basis of a large HOMO–LUMO gap (5.1 eV), a large singlet–triplet vertical transition energy (3.6 eV), and the lack of a spin-unrestricted solution at the level of DFT using the B3LYP functional.²⁶ They asserted, however, that S₂N₂ is aromatic based on its negative NICS value (−26.2 ppm), albeit with a small aromatic stabilisation energy, since only two of the six π electrons contribute to the bonding.

Concurrently, Tuononen and co-workers investigated the electronic structures and molecular properties of S₂N₂,^27a as well as the unknown heavier chalcogen analogues Se₂N₂, SSeN₂ and Te₂N₂,^27b by employing various computational methods. These authors agreed that all of these four-membered rings can be described as 2π-electron aromatics, but with minor singlet diradical character ranging from 6% in S₂N₂ to 10% Te₂N₂ located solely on the two nitrogen atoms.^27b

In 2012 Braida et al. carried out an ab initio valence bond study of E₂N₂ which confirmed that the diradical sites are the two nitrogen atoms (E = Se, Te), however they estimated that the contribution from diradical structures is close to 50%.²⁸ Their calculations of vertical resonance energies gave values of about 80% of the predicted value of benzene for S₂N₂ with somewhat lower values for Se₂N₂ and Te₂N₂, consistent with the notion of aromatic character for S₂N₂ based on magnetic criteria. An important conclusion from these results is that diradical character and aromaticity are not mutually exclusive.²⁸ In a sequel to his earlier work on valence bond structures for S₂N₂, Harcourt²⁹ postulated that the six Lewis structures assumed by Braida et al.²⁸ are equivalent to resonance between two increased-valence structures with one-electron and fractional electron-pair π bonds.

In 2018 Karadakov et al. employed magnetic criteria to study the bonding and aromaticity in the ground, first singlet excited and lowest triplet electronic states of S₂N₂.²⁵ Their results indicate that (a) the S₀ electronic state is aromatic, but less so than the electronic ground state of benzene, (b) S₁ is strongly antiaromatic, and (c) T₁ is moderately antiaromatic to a similar extent to that observed in the electronic ground state of square cyclobutadiene. Thus, they assert that S₂N₂ is the first example of an inorganic ring for which theory predicts substantial changes in aromaticity upon vertical transition from the ground state to the first singlet or lowest triplet electronic states.²⁵

3.2.2. Spectroscopic characterisation. Tuononen et al.,^27b found that coupled cluster and multiconfigurational approaches, as well as density functional methods, were the most reliable for the prediction of spectroscopic properties such as vibrational frequencies, ¹⁴N, ¹⁵N and ⁷⁷Se NMR chemical shifts, and excitation energies of sulfur and selenium nitrides. The congruence between the computational results and experimental data for S₂N₂ provides some confidence in the predictions for selenium-containing analogues SSeN₂ and Se₂N₂.

The calculated IR-active vibrational frequencies^27b are in reasonable agreement with experimental data from the IR and Raman spectra of S₂N₂ obtained as a solid condensate and in N₂ or CH₄ matrices at 15–35 K, which were reported by Downs et al.³⁰ By using 30% ¹⁵N-enrichment, these authors confirmed that the isolated S₂N₂ molecule has essentially the same square-planar geometry as the crystalline solid; calculations of the S–N stretching force constant indicated a bond order only slightly greater than 1.³⁰ In 2014 the high-resolution gas-phase FTIR spectrum of S₂N₂ together with a re-investigation of the IR spectrum in solid argon at 16 K were reported by Perrin, Beckers and co-workers.³¹ The main difference between the gas-phase and solid-state structures of S₂N₂ involves the bond angles; in the gas phase the angle at nitrogen <SNS is smaller than <NSN, whereas the opposite is true in the solid-state structures.³¹ These small disparities may be the consequence of the intermolecular interactions that occur between S₂N₂ rings in the plane of the chain of rings in the solid state. Cremer et al. have computed a pseudorotation barrier of <2 kJ mol⁻¹ for S₂N₂ indicative of a floppy molecule, however these authors maintain that this characteristic does not alter the electronic structure of the four-membered ring.³²

The predicted IR and Raman spectra of the selenium-containing systems Se₂N₂ and SSeN₂ are depicted in Fig. 2.^27b The band at ∼590 cm⁻¹ in the IR spectrum of Se₂N₂ should be considerably less intense than the other two bands. In a similar vein, the intensity of the band at 822 cm⁻¹ is estimated to be more than twice those of the other two bands.

Fig. 2 (a) IR/Raman spectra of S₂N₂.³⁰ (Adapted with permission from R. Evans, A. J. Downs, R. Köppe and S. C. Peake, J. Phys. Chem. A, 2011, 115, 5127–5137. @ 2011 American Chemical Society), and the theoretically predicted IR/Raman spectra of (b) and Se₂N₂ and (c) SeSN₂ ^27b (adapted with permission from H. M. Tuononen, R. Suontamo, J. Valkonen and R. S. Laitinen, J. Phys. Chem. A, 2005, 109, 6309–6317. @ 2005 American Chemical Society).

Tuononen et al., have also calculated the ¹⁴N, ¹⁵N and ⁷⁷Se NMR chemical shifts for the chalcogen nitrides S₂N₂, SeSN₂, Se₂N₂, S₄N₄ and Se₂S₂N₄.^27b Surprisingly, no experimental NMR data are available for S₂N₂. However, the calculated ¹⁴N and ¹⁵N NMR chemical shifts for S₄N₄ and the known mixed selenium–sulfur nitride Se₂S₂N₄ are in excellent agreement with the experimental data^3c providing some confidence in the predicted values of 95 ± 20, 125 ± 20 and 185 ± 20 ppm for S₂N₂, SeSN₂ and Se₂N₂, respectively. The calculated ⁷⁷Se chemical shifts for 1,5-Se₂S₂N₄ at different levels of theory are ca. 200 ppm lower than experimental values.^3c,27b By contrast, the calculated PBEPE and CAS ⁷⁷Se chemical shifts of 1906 and 1886 ppm for Se₄²⁺ are only slightly lower than the experimental value of 1936 ppm. Assuming a similar error for SeSN₂ and Se₂N₂, ⁷⁷Se chemical shifts of 1820 ± 20 and 1780 ± 20 ppm, respectively, are estimated for these structurally analogous four-membered rings.^27b The ternary chalcogen nitride SeSN₂ has been proposed as an intermediate in the formation of 1,5-Se₂S₂N₄ from reactions of (Me₃SiNSN)₂E (E = S, Se) with E′Cl₂ (E′ = S, Se),^3c but this potential precursor of a mixed sulfur–selenium nitride polymer (SNSeN)_x has eluded isolation.

The experimental UV spectrum of S₂N₂ consists of a broad band in the range 4.5–5.8 eV comprised of two overlapping absorptions centred at approximately 5.0 eV (∼250 nm) which is attributed to the π → π* electronic transition.³³ The calculated band-gap energies decrease as the selenium content in the ring increases as illustrated by colourless S₂N₂ (3.32 eV, ∼375 nm) the predicted orange-yellow colour of SSeN₂ (2.50 eV, ∼495 nm) and red colour of Se₂N₂ (2.20 eV, ∼560 nm).^27b This information should be valuable for the identification of the selenium-containing four-membered rings.

3.2.3. Photolysis: isomers of S₂N₂. In 2015 Zeng, Beckers and co-workers investigated the UV photolysis of S₂N₂ in solid argon matrices using two different light sources (λ = 248 or 255 nm).³⁴ Although calculations predict both linear SNNS (6) and cyclic 1,2,3,4-dithiadiazete (C_2v) (7) to be lower in energy than the familiar cyclic S₂N₂ (D_2h) (2, E = S),¹⁴ neither of these two isomers has been observed experimentally. Instead, by employing IR spectra of both natural abundance and ¹⁵N-enriched S₂N₂, these authors were able to identify two open shell isomers, trans-SNSN (8) and cis-SNSN (9), as well as a closed shell C_2v dimer (SN)₂ (10), as the primary photolysis products (Scheme 3).³⁴ The identification of the open shell isomers is relevant to the mechanism of polymerisation of S₂N₂ into (SN)_x, which is discussed in the next section.

Scheme 3 Structural arrangements of planar cyclic and acyclic isomers of S₂N₂.³⁴

3.2.4. Topochemical polymerisation to (SN)_x: applications in forensic science. The spontaneous topochemical polymerisation of S₂N₂ into (SN)_x, a polymer with fascinating conducting properties, has been known for more than 40 years.^2c Kelly et al., have demonstrated that this process can be achieved in the zeolite Na-ZSM-5, which has a pore size that is able to accommodate S₂N₂ as well as infinite channels along the b-axis to allow for polymer growth.^9a The same group also reported that the exposure of fingerprints on various surfaces, e.g. glass, metal, paper or ceramic surfaces, to S₂N₂ vapour generated an image of the fingerprint due to the formation of blue-black (SN)_x polymer (Fig. 3a).^9b,c It was suggested that this serendipitous observation could have applications in forensic science, although the design of a practical and portable apparatus for the production of S₂N₂ was recognised as a major impediment. However, in 2019 a collaborative effort with industrial and government laboratories described a comparison of the S₂N₂ process with other methods for fingerprint detection and found it to be effective with the potential for improvements over existing processes. Crucially, this study relied on a safe-to-handle, but unidentified, precursor that is rapidly decomposed to S₂N₂. The experimental set-up is illustrated in Fig. 3b.^9d

Fig. 3 (a) Formation of (SN)_x over latent fingermarks on metallic surfaces^9c (reproduced with permission from S. M. Bleay, P. F. Kelly, R. S. B. King, J. Mater. Chem., 2010, 20, 10100–10102. @ 2010 The Royal Society of Chemistry.). (b) Diagram of S₂N₂ processing equipment^9d (reprinted with permission from S. M. Bleay, P. F. Kelly, R. S. P. King and S. G. Thorngate, Sci. Justice, 2019, 59, 606–621. @ 2019 Elsevier B. V.).

In 2013 Takaluoma et al. carried out molecular dynamics simulations of the topochemical polymerisation of S₂N₂ in the solid state using DFT methods and periodic functions.⁸ The calculations involved both high pressures and slightly elevated temperatures in order to increase the reaction rate. The formation of (SN)_x is initiated by cleavage of one S–N bond in S₂N₂ followed by a very rapid attack of the resulting open-chain isomer, e.g.8 in Scheme 3, on a neighbouring ring (Fig. 4). Propagation occurs along the a axis throughout the lattice. The packing changes from the herringbone structure of the S₂N₂ lattice to the layered structure of (SN)_x. Although the metrical data for the polymer chain are in good agreement with the experimental crystal structure, there is less long-range order between neighbouring chains, possibly due to the influence of pressure or the poor description of dispersion by density functional theory.⁸

Fig. 4 Simulated energy profile of the topochemical polymerisation of S₂N₂ rings to (SN)_x at 50 GPa and 600 K. Sulfur atoms are indicated by yellow spheres and nitrogen atoms by blue spheres (b axis is directed away from the reader).⁸ (Reproduced with permission from T. T. Takaluoma, K. Laasonen and R. S. Laitinen, Inorg. Chem., 2013, 52, 4648–4657. @ 2013 American Chemical Society.)

3.2.5. A hydrogen-storage material?. Datta has described quantum chemical investigations of the interaction of H₂ molecules with binary S,N rings including S₂N₂.³⁵ An adduct of S₂N₂ with two molecules of H₂ located in an eclipsed fashion above and below the ring was found to have only dispersive interactions with a low binding energy (<−1.5 kcal mol⁻¹). However, when the ring is doped with a transition metal such as Ni(0), Pd(0) or Pt(0), complexes that incorporate three H₂ molecules for each metal centre were found to have binding energies of −67.75, −18.73 and −81.75 kcal mol⁻¹ for M = Ni, Pd and Pt, respectively. As illustrated in Fig. 5, the binding modes of H₂ to the metal centre are markedly different. In the Ni and Pd complexes four H atoms appear as hydrides while one H₂ molecule is η²-coordinated to the metal. By contrast, in the most stable Pt complex all six hydrogen atoms exist as hydrides with five of them forming an almost regular pentagon.³⁵ Although the practicality of using binary S,N compounds as hydrogen-storage materials may be questioned by experimentalists, investigations of the interaction of extended systems similar to (SN)_x may be worthy of experimental interrogation.

Fig. 5 B3LYP/6-31G(d,p) optimised structures of H₂-absorbed metal-doped S₂N₂ (a) M = Ni (b) M = Pd (c) M = Pt (redrawn from computational data in ref. 35).

4. Nitrogen-rich chalcogen nitrides

Early work on nitrogen-rich sulfur nitrides such as SN₂ and SN₄ was mainly limited to the purported involvement of these species as fleeting intermediates. However, recent experimental and theoretical investigations of the formation and structures of this class of sulfur nitrides and their selenium analogues under high pressure have revealed fascinating properties with potential applications in optoelectronics and as high-energy-density materials. This section is organised according to increasing nitrogen content of these binary molecular species. Nitrogen-rich selenium nitrides are discussed in section 4.4.

4.1. The isomers NNS and NSN

The lowest energy isomer NNS, a heavier analogue of the stable molecule N₂O, decomposes above 160 K. It is generated by flash photolysis of 5-phenyl-1,2,3,4-thiatriazole and has been characterised by high-resolution mass spectrometry and IR spectroscopy.³⁶ The symmetrical isomer NSN has been invoked as an elimination product during the transformations of polycyclic S–N compounds,^1a but the synthesis and structure of this simple sulfur nitride remained elusive until very recently (vide infra).

In 2016 Zhang and co-workers investigated the stability, electronic structure and optical properties of a P3m1 phase of 1T-EN₂ (E = S, Se, Te) by means of DFT calculations (the prefix 1T refers to one layer per trigonal unit cell).³⁷ The calculated crystal structure of the two-dimensional material 1T-SN₂ is comprised of six-coordinated S atoms and three-coordinate N centres (Fig. 6a). These chalcogen nitrides 1T-EN₂ (E = S, Se, Te) are endothermic materials. 1T-SN₂ has dynamical stability based on phonon spectra and calculated cohesive energies, but the thermal and mechanical stabilities have yet to be determined. Band-structure calculations revealed indirect band gaps of 2.825, 2.351, and 2.336 eV for 1T-SN₂, 1T-SeN₂, and 1T-TeN₂, respectively. Furthermore, the application of biaxial strain induced a transition from a wide-band-gap semiconductor to a metal. These findings suggest that the binary chalcogen nitrides 1T-EN₂ are promising materials for applications in optoelectronic devices.³⁷

Fig. 6 Optimised structures of (a) 1T-SN₂ ³⁷ (reproduced with permission from J.-H. Lin, H. Zhang, X.-L. Cheng and Y. Miyamoto, Phys. Rev. B, 2016, 94, 195404. @ 2016 American Physical Society), and (b) S-SN₂ ³⁸ (reproduced with permission from F. Li, X. Lv, J. Gu, K. Tu, J. Gong, P. Jin and Z. Chen, Nanoscale, 2020, 12, 85–92. @ 2020 The Royal Society of Chemistry).

Earlier this year Chen and co-workers proposed a new phase of the SN₂ monolayer, namely S-SN₂, by using first-principles calculations combined with the particle-swarm optimisation method.³⁸ The structure of S-SN₂ belongs to the space group P4M2 and incorporates four-coordinate S atoms and two-coordinate nitrogen centres (Fig. 6b); the prefix S is used to indicate its square lattice and, hence, distinguish this new structure from 1T-SN₂. The S-SN₂ monolayer is a remarkably stable semi-conductor with an indirect band gap of 2.79 eV, cf. 2.825 eV for 1T-SN₂.³⁷ The co-existence of both out-of-plane and in-plane negative Poisson's ratios indicates 3D auxetic properties for this new material,^10c which may have applications in mechanical or optoelectronics devices.

In 2017 Cui and co-workers performed particle-swarm optimisation calculations on the sulfur–nitrogen system up to 200 GPa.³⁹ Three binary sulfur–nitrogen solids were determined to be thermodynamically stable: Pnma (SN)_x, Pnnm SN₂, and C2/c SN₄ at pressures of 37, 43 and 48 GPa, respectively. Their crystal structures are depicted in Fig. 7. A polymeric 3D arrangement was predicted for SN₂ (Fig. 8c). Partial density of states calculations indicated that SN₂ is a semiconductor with a direct band gap of 0.66 eV at 60 GPa.

Fig. 7 Crystal structures of (a) Pnma (SN)_x, (b) Immm (SN)_x, (c) Pnnm SN₂, and (d) C2/c SN₄.³⁹ (Reproduced with permission from D. Li, F. Tian, Y. Z. Lv, S. Wei. D. Duan, B. Liu and T. Cui, J. Phys. Chem. C, 2017, 121, 1515–1520. @ 2017 The American Chemical Society.)

Fig. 8 Crystal structure of SN₂ formed at 81.6 GPa showing (a) the cross-linked octahedra and (b) the edge-sharing octahedra and apical S–N bonds.⁴⁰ (Reproduced with permission from D. Laniel, M. Bykov, T. Fedotenko, A. V. Ponomareva, I. A. Abrikosov, K. Glazyrin, V. Svitlyk, L. Dubrovinsky and N. Dubrovinskaia, Inorg. Chem., 2019, 58, 9195–9204. @ 2019 The American Chemical Society.)

Last year a seminal experimental investigation of the formation of sulfur nitrides in the S–N₂ system at high pressures by Laniel and co-workers confirmed the predictions for SN₂. These authors found that the reaction of elemental sulfur and N₂ gas in a diamond anvil cell at pressures above 60 GPa with laser heating produces an orthorhombic (P_nnm) SN₂ compound.⁴⁰ The lattice parameters of this material obtained from powder diffraction data match closely the theoretically predicted crystalline structure of SN₂.³⁷ Single crystal X-ray diffraction analysis revealed a CaCl₂-type structure composed of edge-sharing SN₆ octahedra with N atoms that are triply coordinated by S atoms (Fig. 8).⁴⁰ The SN₂ solid was found to be metastable down to ca. 20 GPa, at which point it dissociates into its elements.⁴⁰

4.2. Thiatetrazole SN₄

The nitrogen-rich thiatetrazole SN₄ has attracted the attention of both experimental and theoretical chemists for more than 20 years. Klapötke and Schulz attempted to prepare SN₄ from the reaction of the cation [NS]⁺ in [NS][AsF₆] with the azide ion [N₃]⁻ in cesium azide. The final product was a black precipitate identified as the polymer (SN)_x; no experimental evidence (¹⁴N NMR) could be found for the expected SN₄ intermediate.⁴¹ Furthermore, no spectroscopic evidence for the formation of SN₄ was garnered from the recent study of the S–N₂ system at high pressures, which led to the characterisation of metastable SN₂ (section 4.1).⁴⁰

The main focus of early theoretical investigations of SN₄ was an estimate of the aromaticity of the cyclic isomer, which is a 6π-electron five-membered ring formally related to thiophene by the replacement of four CH units by four nitrogen atoms. Schleyer and co-workers calculated NICS (nucleus independent chemical shift) and NICS(1) values of −18.40 and −17.48 for cyclo-SN₄; the large negative values are indicative of substantial aromatic character in the ring.^42a This conclusion is supported by the calculated value of 18.56 for the ASE (aromatic stabilisation energy).^42b

Nitrogen-rich sulfur nitrides are of considerable interest as high energy-density materials. The energy content of cyclo-SN₄ was first computed by Wang and co-workers using DFT methods at the B3LYP/6-311+G** level.⁴³ It was found that cyclo-SN₄ is ca. 100 kcal mol⁻¹ higher in energy than the decomposition products 1/8S₈ + N₂. However, the low dissociation barrier of 7.0 kcal mol⁻¹ for the decomposition of SN₄ into N₂ + N₂S (Scheme 4) precludes the isolation of this sulfur nitride under ambient conditions.⁴⁴

Scheme 4 The most facile dissociation pathway for cyclo-SN₄.⁴⁴

4.3. Dithiatetrazine S₂N₄

A planar six-membered ring cyclo-S₂N₄ would be an 8π-electron (antiaromatic) system isoelectronic with dithiatriazines (RC)S₂N₃. The parent dithiatriazine (R = H) is not known, but aryl derivatives (R = Ph) exist as cofacial dimers in the solid state.^1a Numerous acyclic and cyclic isomers are possible for the putative nitrogen-rich sulfur nitride S₂N₄. Schleyer and co-workers have carried out computational investigations of the thermochemical stability and kinetic persistence of various S₂N₄ isomers at the B3LYP/6-311+G(3df) DFT level.¹³ The results were compared with the corresponding data for the known sulfur nitrides S₂N₂, S₄N₂ and S₄N₄, as well as the nitrogen-rich species SN₄ and S₃N₄. A boat conformation of 1,4-S₂N₄ (11), cf. 1,4-S₂(CH)₄, was predicted to be the most stable of the three possible six-membered rings. The other most thermodynamically stable isomers include two five-membered rings SN₄(=S) (12 and 13) and two acyclic species SNSNNN (14 and 15) (Scheme 5). From a consideration of the kinetic stability (dissociation barriers) of these five isomers it was concluded that the acyclic isomer 14 is the most viable candidate for synthesis. However, its dissociation barrier to give N₂ and cyclo-S₂N₂ is only 21.6 kcal mol⁻¹, cf. 51 kcal mol⁻¹ for cyclo-S₂N₂ (2, E = S). Although this barrier is considerably higher than the value of 7 kcal mol⁻¹ determined for the decomposition of cyclo-SN₄ (section 4.2), the facile formation of S₂N₂ from decomposition of SNSNNN (14) may account for the rapid production of (SN)_x observed in the reaction of [SNS][AsF₆] with CsN₃ in SO₂(l) at −20 °C.⁴⁵

Scheme 5 Structures of the five most stable isomers of S₂N₄. The acyclic isomers 14 and 15 differ only in the conformation; the –NNN fragment in 14 is oriented above the SNSN– plane, whereas 15 is planar.¹³

As a general conclusion, it is important to note that kinetic stability is more important than thermodynamic stability in determining which binary sulfur–nitrogen species can be isolated under ambient conditions. The isomers of the nitrogen-rich cation [S₂N₃]⁺ a 6π-electron system, provide a compelling example of this principle. Despite being less thermodynamically stable than the 1,3-isomer, the 1,2-isomer has been isolated and structurally characterised in the salt [S₂N₃]₂[Hg₂Cl₆].⁴⁶ Although it is the only known monocyclic, nitrogen-rich S,N cation, several salts of the tricyclic cation [S₄N₅]⁺ have been structurally characterised.⁴⁷ The relative stability of 1,2-[S₂N₃]⁺ is attributed to the higher dissociation barriers for its fragmentation compared to the 1,3-isomer for which the dissociation pathway to form [SNS]⁺ + N₂ has a barrier of only 2.6 kcal mol⁻¹.^44a

4.4. Trithiatetrazepine S₃N₄

Planar, cyclic S₃N₄ (16) would be a 10π-electron (aromatic) system (see Scheme 6)⁴⁸ isoelectronic with the known trithiatriazepine (HC)S₃N₃.⁴⁹ However, the isolation of 16 at room temperature is unlikely in view the low energy barrier (14.14 kcal mol⁻¹) for dissociation into SNN and S₂N₂.¹³ The known compound S₃N₃–N=PPh₃ (17) formed from the reaction of S₄N₄ with PPh₃via ring contraction can be considered as the triphenylphosphine adduct of S₃N₄.⁵⁰ It is also noted that the related derivative S₃N₃–N=S has been identified as a short-lived intermediate generated upon flash photolyis of S₄N₄.⁵¹

Scheme 6 S₃N₄ (16) and S₃N₃–NPPh₃ (17).

5. Nitrogen-rich selenium nitrides

As mentioned in section 1, the only binary selenium nitride that has been isolated under ambient conditions and structurally characterised is Se₄N₄ (1, E = Se),^3a although metal complexes of Se₂N₂ (2, E = Se) are also known.^3c,d In that context investigations of the high-pressure phase diagrams of the binary selenium–nitrogen system by Cui and co-workers reported in 2019 are of considerable interest.⁵² These authors identified four stable compounds at high pressures: Cmc2₁-SeN₂, P2₁/m-SeN₃, P1̄-SeN₄ and P1̄-SeN₅. As illustrated in Fig. 9, these novel nitrogen-rich materials are predicted to incorporate a variety of polynitrogen arrangements in the solid state.⁵²

Fig. 9 Crystal structures of the predicted selenium nitrides: (a) Cmc2₁-SeN₂ at 90 GPa (b) P2₁/m-SeN₃ at 80 GPa (c) P1̄-SeN₄ at 140 GPa and (d) P1̄-SeN₅ at 130 GPa. Selenium atoms are depiced in red and nitrogen atoms in blue (redrawn from the structural data in ref. 52).

The binary selenium nitride Cmc2₁-SeN₂ has a layer structure (Fig. 9a), while P2₁/m-SeN₃, P1̄-SeN₄ and P1̄-SeN₅ incorporate N_∞-chains (Fig. 9b), oligomeric N₈-chains (Fig. 9c) or distorted [N₆]³⁻ anionic rings alternating with layers of N_∞-chains (Fig. 9d). The high energy-content of the latter three phases is reflected in the values of their energy densities, which are 3.27, 3.26 and 4.08 kJ g⁻¹, respectively.⁵²

Information on the dissociation barriers for these binary selenium nitrides is not available.

6. Ternary S,N,P molecules

A phosphorus atom P has the same number of electrons as an S⁺ cation, consequently there can be an isoelectronic relationship between certain ternary S,N,P neutral molecules and well-known binary S,N cations. The latter species can be isolated as thermally stable salts, which have been structurally characterised, and the cations have been shown to exhibit a range of chemical reactions.^1a,b The recent identification of the ternary systems SNP^12a and SP₂N₂ ^12b provide cogent examples of this isoelectronic connection.

Francisco, Zeng et al., conducted an initial investigation of the pyrolysis and photolysis of the triazide SP(N₃)₃.^12a The experimental work was presaged by DFT calculations of the three triatomic SNP isomers, viz. linear SNP (18), linear SPN (19) and the three-membered ring cyclo-PSN (thiazaphosphirine) (20) at the B3LYP/6-311+G(3df). As indicated in Fig. 10, the cyclic isomer 20 is separated from the linear isomers 18 and 19 by barriers of 138 and 95 kJ mol⁻¹, respectively; the SNP arrangement 18 was predicted to be the global minimum. In one experimental approach the pyrolysis of SP(N₃)₃ at 1000 °C followed by trapping of the products in an argon matrix at 16 K generated SPN (19) [eqn (1)]. This species was identified with the help of ¹⁵N-labelling by comparison of calculated and experimental IR frequencies, which also revealed the formation of other nitrogen-containing species, PN, SN and SN₂.^12a

SP(N₃)₃ → SPN + 4N₂ (1)

Fig. 10 Calculated reaction coordinate of SPN isomers 18–20; bond lengths are given in Å.^12a (Reproduced with permission from X. Zeng, H. Beckers, H. Willner and J. S. Francisco, Angew. Chem., Int. Ed., 2012, 51, 3334–3339. @ 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

In an alternative procedure the photolysis of SP(N₃)₃ in solid argon resulted in a stepwise dissociation to give the most stable SNP isomer 18 as the final product. In both the pyrolysis and photolysis experiments selective UV irradiation produced the linear SPN (19) and cyclo-PSN (20), which were identified by IR spectroscopy.^12a

The structure of SNP (18) can be represented by the two Lewis structures shown in Fig. 11a. The calculated P–N bond length is 1.502 Å, slightly greater than the sum of the triple bond radii for P and N (1.48 Å), and the calculated P–N stretching frequency of 1314 cm⁻¹ is close to that of diatomic PN (1327 cm⁻¹).^12a The SNP isomer (18) is isoelectronic with the linear sulfur–nitrogen cation [SNS]⁺, which has an extensive cycloaddition chemistry.⁵³ The similarity of the frontier orbitals of SNP (18) (Fig. 11b) with those of [SNS]⁺ suggest that the ephemeral SNP species could be trapped via cycloaddition reactions, e.g. with alkynes or nitriles.

Fig. 11 (a) Lewis resonance structures and (b) HOMO and LUMO of the isomer SNP.¹² (Reproduced with permission from X. Zeng, H. Beckers, H. Willner and J. S. Francisco, Angew. Chem., Int. Ed., 2012, 51, 3334–3339. @ 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

A subsequent IR analysis of the products of the flash pyrolysis of SP(N₃)₃ under conditions used to generate SNP (18) (vide supra) revealed a new species with IR frequencies that increased in intensity with prolonged deposition time.^12b The mid- and far-IR frequencies of this product appeared as quartets when ¹⁵N labelled SP(N₃)₃ was used as a precursor, indicating a molecule with two structurally non-equivalent N atoms.^12b In order to elucidate the identity of this species, theoretical calculations of the dimerisation of SNP were carried out. As illustrated in Fig. 12, the activation energy for head to-tail association of SNP to give cyclo-SNPSNP is low. However, the structural equivalence of the two nitrogen atoms in this six-membered ring rules it out as the source of the new IR bands. Instead, the energetically favourable loss of a sulfur atom from cyclo-SNPSNP, which is formally an 8π-electron system, to give the five-membered ring cyclo-SNPNP (2,4-diphospha-3,5-diaza-thiole), a 6π-electron system, is invoked to explain the observed and calculated IR data (Fig. 12).^12b

Fig. 12 Head-to-tail dimerisation of SNP and subsequent formation of cyclo-SNPNP; relative energies (kJ mol⁻¹) and computed bond lengths (Å) at the B3LYP/6-311+G(3df) level.¹³ (Reproduced with permission from X. Zeng, H. Li, H. Sun, H. Beckers, H. Willner and H. F. Schaefer III, Angew. Chem., Int. Ed., 2015, 54, 1327–1330. @ 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

The aromatic nature of cyclo-SNPNP, which is isoelectronic with the known sulfur–nitrogen dication [S₃N₂]²⁺,^1a may contribute to its stability. However, the 6π-electron cation cyclo-[SNSNP]⁺ is expected to exhibit higher stability owing to the positive charge and possible isolation as a salt. By analogy with the cycloaddition of [NS]⁺ with [SNS]⁺ to give [S₃N₂]²⁺,⁵³ cycloaddition of SNP with an [NS]⁺ salt could generate the putative cation cyclo-[SNSNP]⁺.

A third example of the isoelectronic relationship between ternary S,N,P molecules and binary S,N cations involves the well-known planar, cyclic cation [S₄N₄]²⁺, a fully delocalised 10π-electron system.^1a The replacement of two antipodal S atoms in the supposed planar molecule S₄N₄ by P atoms generates 1,5-P₂N₄S₂, isoelectronic with [S₄N₄]²⁺. According to Gleiter, this ternary S,N,P molecule would incorporate an unpaired 3p electron at each P centre (21).^7a The diradical species 21 would be stabilised by addition of two radicals R˙ at the phosphorus centres to give RP(NSN)₂PR (22) with two 4π-electron –N=S=N– groups bridging the two RP^III centres (Scheme 7). Although the free ligand is not known, metal complexes of 22 (R = ^tBu, NⁱPr₂) in which the P₂N₄S₂ ring is almost planar have been structurally characterized 30 years ago.⁵⁴

Scheme 7 Stabilisation of P₂N₄S₂ (21) by reaction with two R˙ radicals to give RP(NSN)₂PR (22).^7a

The aromatic character of 1,5-P₂N₄S₂ (21) has been compared with that of the isoelectronic 10π-electron heterocycle dithiatetrazocine (HC)₂N₄S₂ using density functional methods.^55,56 It was found that replacement of the two HC groups by the more electronegative P atoms decreases the aromatic character.⁵⁵ However, the ternary ring system was suggested to be a reasonable synthetic target.

In contrast to the planar P(III)-containing heterocycle 22, the corresponding P(V) systems R₂P(NSN)₂PR₂ (1,5-diphosphadithiatetrazocines) form bicyclic structures with a weak transannular S⋯S interaction similar to that discussed for S₄N₄ in section 3.1.1. A recent fragment-based energy analysis by Jacobsen estimates that the cross-ring connection in 1,5-diphosphadithiatetrazocines is about half as strong as a typical S–S bond.⁵⁷ This class of S,N,P heterocycle is considered to be an unusual inorganic example of bishomoaromaticity.^7a,58

7. Summary and outlook

Although the complexities of the electronic structures of the well-known binary sulfur nitrides S₂N₂ and S₄N₄ and their selenium analogues are still under consideration, the focus of recent investigations of this class of inorganic compounds has been on the potential applications of both known and unknown systems. The foremost example is the use of the facile transformation of S₂N₂ into the blue-black polymer (SN)_x for the detection of fingerprints on metal surfaces, which is being considered as an alternative to existing processes for this application in forensic science (section 3.2.4). A more speculative function involves the possible use of S₂N₂ or other sulfur–nitrogen rings as hydrogen-storage materials (section 3.2.5). Although the feasibility of this application is questionable in the case of S₂N₂, sulfur–nitrogen systems with higher chemical and thermal stability, e.g. C,S,N heterocycles, may be worthy of computational and experimental interrogation for this purpose.

In the area of sulfur-rich nitrides, the unknown molecule S₃N₂ is predicted to have quite different properties compared to those of the well-characterised six-membered ring 1,3-S₄N₂, which is a labile, low melting compound. By contrast, computational studies indicate that crystalline S₃N₂ will form a two-dimensional network involving only σ bonds rather than an 8π-electron five-membered ring. Furthermore, it has been proposed that S₃N₂ will exhibit chemical and thermal stability and behave as a wide direct band gap semiconductor with possible optoelectronic applications. As suggested in section 2, this neutral sulfur nitride should be experimentally accessible under ambient conditions so that these predictions can be tested.

Nitrogen-rich sulfur nitrides, e.g. thiatetrazole cyclo-SN₄, have long been considered as potential high energy-density materials (section 4.2). Until recently, this purported 5-membered ring and the acyclic triatomic molecule NSN have only been invoked as fleeting intermediates in the decomposition of sulfur–nitrogen ring systems. In the last few years, however, seminal experimental and computational studies of the combination of a chalcogen (sulfur or selenium) and nitrogen gas (N₂) at very high pressures have yielded unanticipated information about the structures and properties of this new class of chalcogen nitride. In general, the computational work indicates that at high pressures a variety of nitrogen-rich compounds with structures that are quite different from the metastable sulfur nitrides known to exist at ambient temperatures and pressures (Scheme 1) will be formed. Experimental verification of this prediction has been provided by the identification an SN₂ solid at pressures above 64 GPa. This novel material has a CaCl₂ structure comprised of SN₆ octahedra with triply coordinated N atoms, as forecasted by earlier computational work (section 4.1). In the light of these experimental results, the predicted formation of stable binary selenium nitrides SeN_x (x = 2, 3, 4 or 5) at high pressures should provide an incentive for an experimental study of the selenium–N₂ system with the characterisation of the elusive (SeN)_x polymer as one of the target molecules.

Finally, recently characterised acyclic and cyclic neutral S,N,P molecules are considered in the context of the known structures and reactions of binary sulfur–nitrogen cations, which are isolectronic with the ternary S,N,P systems. This comparison is intended to provide some guidance to the future development of the chemistry of these interesting ternary systems.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

The authors thank an anonymous reviewer for the suggestion of computational and experimental investigations of the reaction S₄N₄ with molecular H₂, which they had been considering. They are also grateful to Professor Dennis Salahub (University of Calgary) for helpful discussions of the electronic structure of S₄N₄.

References

1. (a) T. Chivers, A Guide to Chalcogen-Nitrogen Chemistry, World Scientific Publishing Co., Singapore, 2005; (b) T. Chivers and R. S. Laitinen, in Handbook of Chalcogen-Nitrogen Chemistry: New Perspectives in Sulfur, Selenium and Tellurium, ed. F. A. Devillanova and W.-W. du Mont, 2nd edn, 2013, ch. 4, vol. 1; (c) The chemistry of the ephemeral monomeric radical species NE (E = S, Se, Te) is covered comprehensively in a recent book chapter. R. T. Boeré and T. Roemmele, in Comprehensive Inorganic Chemistry II, ed. J. Reedijk and K. Poeppelmeier, Elsevier, Oxford, 2013, ch. 1.14, vol. 1, pp. 375–411.
2. (a) S₄N₄: M. L. Delucia and P. Coppens, Inorg. Chem., 1978, 17, 2336–2338; (b) S₂N₂: C. M. Mikulski, P. J. Russo, M. S. Soran, A. G. MacDiarmid, A. F. Garito and A. J. Heeger, J. Am. Chem. Soc., 1975, 97, 6358–6363; (c) (SN)_x: M. J. Cohen, A. F. Garito, A. J. Heeger, A. G. MacDiarmid, C. M. Mikulski, M. S. Soran and J. Kleppinger, J. Am. Chem. Soc., 1976, 98, 3844–3848; (d) S₄N₂: T. Chivers, P. W. Codding, W. G. Laidlaw, S. W. Liblong, R. T. Oakley and M. Trsic, J. Am. Chem. Soc., 1983, 105, 1186–1192; (e) S₅N₆: T. Chivers and J. Proctor, J. Chem. Soc., Chem. Commun., 1978, 642–643.
3. (a) Se₄N₄: H. Folkerts, B. Neumüller and K. Dehnicke, Z. Anorg. Allg. Chem., 1994, 620, 1011–1015, and references cited therein; (b) Se₂S₂N₄: A. Maaninen, J. Siivari, R. S. Laitinen and T. Chivers, Inorg. Chem., 1999, 38, 3450–3454; (c) Se₂N₂: P. F. Kelly and A. M. Z. Slawin, J. Chem. Soc., Dalton Trans., 1996, 4029–4030; (d) P. F. Kelly and A. M. Z. Slawin, Angew. Chem., Int. Ed. Engl., 1995, 34, 1758–1759.
4. The black powder obtained from the reaction of Se₂Cl₂ with trimethylsilyl azide in dichloromethane was originally claimed to be Se₄N₂, but it was subsequently identified as the selenium–nitrogen chloride Se₃N₂Cl₂. (a) K. Dehnicke, F. Schmock, K. F. Kohler and G. Frenking, Angew. Chem., Int. Ed. Engl., 1991, 30, 577; (b) T. Chivers, J. Siivari and R. S. Laitinen, Angew. Chem., Int. Ed. Engl., 1992, 31, 1518–1519.
5. A. Maaninen, J. Siivari, R. S. Laitinen and T. Chivers, Inorg. Chem., 1997, 36, 2170–2177.
6. For a summary of the literature prior to 2012, see: J. Moilanen, A. J. Karttunen, H. M. Tuononen and T. Chivers, J. Chem. Theory Comput., 2012, 8, 4249–4258.
7. (a) R. Gleiter, G. Haberhauer and S. Woitschetzki, Chem. – Eur. J., 2014, 20, 13801–13810; (b) R. Gleiter and G. Haberhauer, Coord. Chem. Rev., 2017, 344, 263–298.
8. T. T. Takaluoma, K. Laasonen and R. S. Laitinen, Inorg. Chem., 2013, 52, 4648–4657.
9. (a) R. S. P. King, P. F. Kelly, S. E. Dean and R. J. Mortimer, Chem. Commun., 2007, 4812–4814; (b) P. F. Kelly, R. S. P. King and R. J. Mortimer, Chem. Commun., 2008, 6111–6113; (c) S. M. Bleay, P. F. Kelly and R. S. B. King, J. Mater. Chem., 2010, 20, 10100–10102; (d) S. M. Bleay, P. F. Kelly, R. S. P. King and S. G. Thorngate, Sci. Justice, 2019, 59, 606–621 . The identity of the S₂N₂ precursor is not revealed in this paper.
10. (a) H. Xiao, X. Shi, X. Liao, Y. Zhang and X. Chen, Phys. Rev. Mater., 2018, 2, 024002; (b) Y. Chen, X. Liao, X. Shi, H. Xiao, Y. Liu and X. Chen, Phys. Chem. Chem. Phys., 2019, 21, 5916–5924; (c) Auxetic materials become thicker when stretched and thinner in response to compression.
11. For a recent review of the fundamental chemistry of binary S,N and ternary S,N,O anions, see: T. Chivers and R. S. Laitinen, Chem. Soc. Rev., 2017, 46, 5182–5192.
12. (a) X. Zeng, H. Beckers, H. Willner and J. S. Francisco, Angew. Chem., Int. Ed., 2012, 51, 3334–3339; (b) X. Zeng, H. Li, H. Sun, H. Beckers, H. Willner and H. F. Schaefer III, Angew. Chem., Int. Ed., 2015, 54, 1327–1330.
13. G.-H. Zhang, Y.-F. Zhao, J. I. Wu and P. V. R. Schleyer, Inorg. Chem., 2012, 51, 13321.
14. T. Chivers and R. S. Laitinen, Dalton Trans., 2017, 46, 1357–1367.
15. (a) J. Contreras-Garcia, E. R. Johnson, S. Keinan, R. Chaudret, J.-P. Piquemal, D. N. Beratan and W. Yang, J. Chem. Theory Comput., 2011, 7, 625–632; (b) the energies of strong hydrogen bonds falls within the range 15–40 kcal mol⁻¹.
16. R. Mews, J. Fluorine Chem., 1981, 18, 155–158.
17. Y. Xu, T. Xu, D. Jiajun, S. R. Kirk and S. Jenkins, Int. J. Quantum Chem., 2016, 116, 1025–1039.
18. J. Konu, T. Bajorek, R. S. Laitinen, T. Chivers, R. J. Suontamo and M. Ahlgrén, Eur. J. Inorg. Chem., 2006, 2951–2958 , and references cited therein.
19. M. K. Si and B. Ganguly, Chem. Phys. Lett., 2018, 713, 160–165.
20. D. V. Konarev, E. F. Valeev, Y. L. Slovokhotov and R. N. Lyobovskaya, J. Phys. Chem. Solids, 1997, 58, 1865–1867.
21. A. Maaninen, J. Siivari, R. S. Laitinen and T. Chivers, Inorg. Synth., 2002, 33, 196–199.
22. A. Ghosh and S. Berg, Arrow Pushing in Inorganic Chemistry: A Logical Approach to the Chemistry of the Main-Group Elements, John Wiley & Sons, Inc., New Jersey, 2014, pp. 240–243.
23. (a) B. G. Kumar and K. Muralidharan, Eur. J. Inorg. Chem., 2013, 2102–2108; (b) B. G. Kumar and K. Muralidharan, J. Mater. Chem., 2011, 21, 11271–11275; (c) B. G. Kumar and K. Muralidharan, RSC Adv., 2014, 4, 28219–28224; (d) Cyclic sulfur imides of the type (SNR)₄ (R = Me, Et, Bz) have been characterised as colourless crystalline solids, but the corresponding polymers (SNR)_n are unknown. H. G. Heal, The Inorganic Heterocyclic Chemistry of Sulfur, Nitrogen and Phosphorus, Academic Press Inc., London, U.K., 1980, pp. 16–40.
24. T. L. Roemmele, J. Konu, R. T. Boeré and T. Chivers, Inorg. Chem., 2009, 48, 9454–9462.
25. For an authoritative summary of earlier theoretical calculations for S₂N₂ see: P. B. Karadakov, M. A. H. Al-Yassiri and D. L. Cooper, Chem. – Eur. J., 2018, 24, 16791–16803.
26. Y. Jung, T. Heine, P. V. R. Schleyer and M. Head-Gordon, J. Am. Chem. Soc., 2004, 126, 3132–3138.
27. (a) H. M. Tuononen, R. Suontamo, J. Valkonen and R. S. Laitinen, J. Phys. Chem. A, 2004, 108, 5670–5677; (b) H. M. Tuononen, R. Suontamo, J. Valkonen and R. S. Laitinen, J. Phys. Chem. A, 2005, 109, 6309–6317.
28. B. Braida, A. Lo and P. C. Hiberty, ChemPhysChem, 2012, 13, 811–819.
29. R. D. Harcourt, ChemPhysChem, 2013, 14, 2859–2864.
30. R. Evans, A. J. Downs, R. Köppe and S. C. Peake, J. Phys. Chem. A, 2011, 115, 5127–5137 . The IR frequencies of S₂N₂ in the solid, vapour and matrix-isolated states obtained in previous studies are summarized in Table 3 of this paper.
31. A. Perrin, A. F. Antognini, X. Zeng, H. Beckers, H. Willner and G. Rauhut, Chem. – Eur. J., 2014, 20, 10323–10331.
32. W. Zou, D. Izotov and D. Cremer, J. Phys. Chem. A, 2011, 115, 8731–8742.
33. A. J. Bridgeman and B. Cunningham, Spectrochim. Acta, Part A, 2004, 60, 471–480.
34. X. Zeng, A. F. Antognini, H. Beckers and H. Willner, Angew. Chem., Int. Ed., 2015, 54, 2758–2761.
35. A. Datta, Phys. Chem. Chem. Phys., 2009, 11, 11054–11059.
36. C. Wentrup and P. Kambouris, Chem. Rev., 1991, 91, 363–373.
37. J.-H. Lin, H. Zhang, X.-L. Cheng and Y. Miyamoto, Phys. Rev. B, 2016, 94, 195404.
38. F. Li, X. Lv, J. Gu, K. Tu, J. Gong, P. Jin and Z. Chen, Nanoscale, 2020, 12, 85–92.
39. D. Li, F. Tian, Y. Z. Lv, S. Wei, D. Duan, B. Liu and T. Cui, J. Phys. Chem. C, 2017, 121, 1515–1520.
40. D. Laniel, M. Bykov, T. Fedotenko, A. V. Ponomareva, I. A. Abrikosov, K. Glazyrin, V. Svitlyk, L. Dubrovinsky and N. Dubrovinskaia, Inorg. Chem., 2019, 58, 9195–9204.
41. T. Klapötke and A. Schulz, Polyhedron, 1996, 15, 4387–4390.
42. (a) M. K. Cyrañski, T. M. Krygowski, A. R. Katrizky and P. V. R. Schleyer, J. Org. Chem., 2002, 67, 1333–1338; (b) M. K. Cyrañski, P. V. R. Schleyer, T. M. Krygowski, H. Jiao and G. Hohlneicher, Tetrahedron, 2003, 59, 1657–1665.
43. (a) L. J. Wang, P. G. Mezey and M. Z. Zgierski, Chem. Phys. Lett., 2003, 369, 386–393; (b) L. J. Wang and P. G. Mezey, Chem. Phys. Lett., 2004, 387, 233–237.
44. (a) G.-H. Zhang, Y.-F. Zhao, J. I. Wu and P. V. R. Schleyer, Inorg. Chem., 2009, 48, 6773–6780; (b) The molecular structure, IR and UV spectra of SN₄ have been calculated by a modification of DFT; a strong absorption at 212 nm is predicted. D. Glossman-Mitnik, Theor. Chem. Acc., 2007, 117, 57–68.
45. F. A. Kennett, G. K. MacLean, J. Passmore and M. N. S. Rao, J. Chem. Soc., Dalton Trans., 1982, 851–857.
46. S. Herler, P. Mayer, H. Nöth, A. Schulz, M. Suter and M. Vogt, Angew. Chem., Int. Ed., 2001, 40, 3173–3175.
47. T. Chivers, L. Fielding, W. G. Laidlaw and M. Trsic, Inorg. Chem., 1979, 18, 3379–3388.
48. P. W. Fowler, C. W. Rees and A. Soncini, J. Am. Chem. Soc., 2004, 126, 11202–11212.
49. P. J. Dunn, J. L. Morris and C. W. Rees, J. Chem. Soc., Perkin Trans. 1, 1988, 1745–1748.
50. J. Bojes, T. Chivers, A. W. Cordes, G. MacLean and R. T. Oakley, Inorg. Chem., 1981, 20, 16–21 , and references cited therein.
51. E. A. Pritchina, D. S. Terpilovskaya, Y. P. Tsentalovich, H. S. Platz and N. P. Gritsan, Inorg. Chem., 2012, 51, 4747–4755.
52. W. Wang, H. Wang, Y. Liu, F. Tian, D. Duan, H. Yu and T. Cui, Inorg. Chem., 2019, 58, 2397–2402.
53. S. Parsons and J. Passmore, Acc. Chem. Res., 1994, 27, 101–108 , and references cited therein.
54. T. Chivers, K. S. Dhathathreyan, C. Lensink, A. Meetsma, J. C. van de Grampel and J. L. de Boer, Inorg. Chem., 1989, 28, 4150–4154.
55. A. G. Papadopoulos, N. D. Charistos and A. Muñoz-Castro, New J. Chem., 2016, 40, 5090–5098.
56. K. H. Moock, K. M. Wong and R. T. Boeré, Dalton Trans., 2011, 40, 11599–11604.
57. H. Jacobsen, Inorg. Chem., 2013, 52, 11843–11849.
58. For a discussion of the nature of the transannular S⋯S interaction in 1,5-diphosphadithiatetrazocines, including the concept of bishomoaromaticity, see: (a) Q. Zhang, S. Yue, X. Lu, Z. Chen, R. Huang, L. Zheng and P. V. R. Schleyer, J. Am. Chem. Soc., 2009, 131, 9789–9799; (b) H. S. Rzepa, Nat. Chem., 2009, 1, 510–512; (c) T. Chivers, R. W. Hilts, P. Jin, Z. Chen and X. Lu, Inorg. Chem., 2010, 49, 3810–3816.

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