Structures and EPR spectra of binary sulfur-nitrogen radicals from DFT calculations †

The scattered electron paramagnetic resonance (EPR) spectroscopic data for binary sulfur-nitrogen (S,N) radicals has been compiled and critically assessed. Many of these are inorganic rings or cages. For each species, possible equilibrium structures in the gas phase and the EPR hyperfine coupling (hfc) constants have been calculated with DFT using the B3LYP functional and basis sets of triple- (or better) quality. Good agreement is obtained between calculated and measured values for the well characterized [S 3 N 2 ] +• , a planar π-radical for which the s -component of the orbitals are likely to be reasonably independent of minor geometrical changes between gas-phase and condensed-phase states. The cage compounds [S 4 N 4 ] –• and [S 4 N 5 ] –2• , for which reliable experimental EPR spectra have been reported, show larger variation between calculated and measured hfc, as a consequence of the dependence of the s orbital content of the molecular orbitals on small structural changes. The very large disagreements between the DFT calculated and experimentally claimed hfc constants for [NS] • , [SNS] • and [S 4 N 4 ] –3• in condensed phases lead us to question their assignment. Among binary S,N radicals, 33 S hfc data has only been reported for [S 3 N 2 ] +• (through isotopic enrichment). These values were essential for the correct identification of the EPR spectra of this important radical which previously was missassigned to other species. Our results suggest that 33 S data will be equally important for the correct identification of the EPR spectra of other binary S,N species, many of which are cyclic systems, e.g. [S 3 N 3 ] • , [S 4 N 3 ] • and [S 4 N 5 ] • .


Introduction
The literature on free radicals derived from binary sulfur-nitrogen (S,N) compounds remains scattered and incomplete [1]. There have been multiple reports of strong and persistent EPR spectra whose assignments have been revised, or which have never been conclusively identified. For example, after several incorrect assignments, the "five-line" 14 N spectrum obtained from solutions of both S4N4 and S2N2 in concentrated aqueous acid was eventually identified as belonging to the thermodynamically stable [S3N2] +• radical by means of 33 S labeling [2]. Another example is the nine-line pattern obtained on reduction of S4N4 by elemental potassium in dimethoxyethane [2a], which has not been conclusively identified.
The "blue radical" formed upon dissolution of cyclo-S7NH in various solvents was later shown to be the diamagnetic acyclic anion [S4N] - [3]. In addition, reliable assignments have not been made for the EPR spectra of several S,N species reported as recently as 1990 [4].
In 1990 Preston and Sutcliffe reviewed the state of knowledge in EPR spectroscopy of binary S,N radicals. This comprehensive account included a compilation of the known 33 S hyperfine coupling (hfc) data, mostly derived from their own work, and the extant evidence for other S,N radicals based only on 14 N data (the majority of cases) [5]. The only binary S,N species for which 33 S data was available at that time was the [S3N2] +• cation radical, which is also the only binary radical for which the full g and a tensor components have been determined from measurements of anisotropic spectra [5]. An earlier review by Oakley discusses the redox properties of sulfur-nitrogen compoundsincluding free radicalsin the context of their fundamental chemical and electronic properties [6]. In the intervening sixteen years, much additional progress has been made on the EPR characterization of paramagnetic molecular species, particularly neutral C,N,S π-radicals which gain considerable thermodynamic and kinetic stability from the incorporation of carbon in the ring frameworks [7]. For binary S,N species there has been no recent progress on the experimental front, but the published electrochemical data was comprehensively reviewed in 2000 [8].
The emergence of density functional theory (DFT) methods has in the past ten years revolutionized our ability to calculate the hfc constants for free radicals of the main group elements. Sieiro and co-workers have recently completed a prospective study of seventy five radicals containing fourteen main group elements, comparing a variety of different functionals and basis sets [9a]. The B3LYP functional was found to be the most reliable, and the use of large triple- basis sets TZVP and EPR-III was recommended for systems up to 10 nuclei. For larger systems, these authors were restricted to the medium-sized 6-31G* basis set (molecules up to twenty atoms were investigated) which still produced reasonable agreement with experimental values [9b]. They report that, using their level of theory, DFT methods provide excellent agreement for 1 H hfc constants in many small molecules, but for heavier nuclei the agreement is found to be only sufficiently good to allow the correct assignment of nuclei by their calculated hfc constants in comparison to experimentally determined values. This, they argue, is the most important contribution that theoretical calculations provide for the field of EPR spectroscopy at the current time. More relevant to the present work are the UB3LYP/TZVP results of Gassmann and Fabian from a study of ten S,N and C,N,S radicals, which demonstrated agreement equivalent to correlated UMP2 ab initio methods compared to available experimental evidence [10]. The DFT method provided an average absolute error of 0.05(1) for 14 N (13%), 0.12(1) for 33 S (24%) and 0.04(1) mT for 1 H (44%) for these planar πradicals. In our own work, we have made use of a variety of DFT methods to assist in the assignment of complex EPR spectra for B, N, Al, P, Ga and In containing radicals (Chart 1) [11]. We found that DFT calculations produce semi-quantitative agreement with the experimental values, and that the calculated values are sufficiently accurate that their input as initial values into extant isotropic EPR simulation software leads to rapid convergence of iterative methods even in the case of very complex experimental spectra [11].
Chart 1 Structures of cubic and spirocyclic main group element radicals [11].
In this paper we report on DFT calculations of all known and several speculative binary S,N neutral radicals and radical ions containing from two to nine atoms. For systems with more than three atoms we only consider rings or cages. We discuss the structures of these molecules obtained from full geometry optimizations in the gas phase. The geometries are compared with experimental and, where relevant, previous computational evidence, as well as with the known structural data for closely related diamagnetic species. The computed hfc constants are compared with experimental data and the validity of their assignments is evaluated. Finally, we provide a few signposts for the resolution of the many outstanding issues.

Method
The binary S,N radicals we have considered in this study are listed along with a compilation of reported EPR data in Table 1. For each species, full geometry optimization was conducted using the UB3LYP/(aug)cc-pVTZ level of theory as implemented in Gaussian 98 [12]. The nature of the stationary points found was ascertained by performing frequency calculations and they all correspond to local minima in the potential energy hypersurface. In The isotropic hfc constants were calculated at the optimized structures using the UB3LYP functional. The basis set used for nitrogen in hfc constant calculations was customized from Partridge's (very large) uncontracted s,p basis set by augmenting it with d and f functions from the cc-pVTZ basis [13]. For sulfur, the plain cc-pVTZ basis set was employed to speed up the calculations.

Results and discussion
The optimized structures, as gas-phase molecules, of the free radicals in this study are depicted in Figures 1 , 5, 7, 9, 11 and 13 and  Geometry-optimized structures of two and three atom binary S,N radicals.

[NS] •
Far less is known about [NS] • than about the lighter congener, nitric oxide, which plays a significant role in many biological functions [14]. The calculated S-N bond length of [NS] • in the 2 Π½ ground state is 1.501 Å (Figure 1), which may be compared to the experimental value of 1.494 Å from gas-phase spectroscopy [15]. A value of 1.5021 Å was obtained by CCSD(T)/cc-pVQZ calculations [16]. About forty crystal structures have now been reported in which [NS] • is coordinated via nitrogen to transition metals in a range of different oxidation states [17]. The S-N bond distances in these complexes are reported to range from 1.591 [18] to 1.383 Å [19]. The bond distance in [NS] + has been established to be 1.440(5) Å by gas-phase photoelectron spectroscopy [20]. The longer bond in the neutral radical is consistent with occupancy of the π* orbital by a single electron, reducing the formal bond order to 2.5 from 3.0 in the cation.
The ground state of [NS]  is diamagnetic because of the opposing spin and orbital angular momentum [5]. The EPR spectrum of the thermally accessible excited 2 3/2 state has, however, been detected in the gas phase and the 14 N nuclear hyperfine constant determined to be 2.  [25]. In this unusual medium two partly-overlapping EPR spectra were obtained even before electrolysis commenced, one of which can probably be assigned to [S3N2] +• , while the other appears to be an I = 1 quintet (a ~ 0.63 mT) of I = 1 triplets (a ~ 0.20 mT), albeit from a spectrum of poor signal-to-noise ratio. A much better spectrum obtained during reactions of various amines with S3N3Cl3 at low temperature, which may be related to this second species, has since been published (a = 0.735 and 0.175 mT) [4]. Obviously, neither of these spectra are attributable to [NS] • . The authors also report that commencement of electrolysis on solutions of [NS][SbF6] did not appreciably alter the EPR spectra, consistent with the highly irreversible behaviour in voltammetry [25]. Finally, EPR parameters of aN = 1.260(5) mT with g = 2.0067 (5) have been attributed to [NS] • [26]. However, these authors erroneously cite reference [27] as the source of these data, the origin of which remains obscure.   [SNS] • has been detected in the gas phase by mass spectrometry through ionrecombination techniques [29], whereas in condensed phases both the linear asymmetric however, to our knowledge, no previous calculations provide hfc constants. Our calculations predict a large coupling to 14 N and a smaller one to the two 33 S nuclei (2.11 mT and 0.56 mT, respectively), the latter reflecting the small sulfur atomic s component to the total spin density as a consequence of the almost pure p contribution by S to the SOMO ( Figure 2a).
There are two reports of EPR spectra that may belong to [SNS] • [4,26]. The first is an I = 1 triplet with aN = 1.13 mT obtained from a mixture of radicals produced as decomposition products during the room-temperature cathodic reduction of [S4N5] -(at low temperature the dianion radical [S4N5] -2• is obtained, vide infra) [26]. For comparison: aN ~5 mT in the [ONO] • radical [5], and our calculated value for [SNS] • aN = 2.11 mT. The second published spectrum assigned to this radical has aN = 1.12 mT, but with much narrower lines which also allowed for observation of 33 S coupling of ~0.5 mT at high gain [4]. However, due to the extremely low natural abundance of 33 Figure 3 shows simulations, using hfc values from our calculations, which predict the appearance of the spectra of this radical at natural abundances of the isotopes and with 33 S enrichment. While the former is indistinguishable in appearance from the many reported spectra for radicals containing one 14 N nucleus, the latter has clearly identifiable patterns unique to radicals involving hyperfine coupling to one 14 N and two 33 S nuclei. impact mass spectra [29]. For example, NSN has been proposed as the species eliminated when R2PN5S3 cage compounds thermally decompose to R2PN3S2 rings [34a]. Surprisingly, the same kind of cage decomposition reactions when either one or both R substituents are F atoms are reported to result in weak EPR signals (aN = 0.516 (5)  It was first postulated as the species formed when S2N2 is reduced with metallic potassium in dimethoxyethane [2a]. A very similar spectrum is obtained when [S4N5] -• is reduced in CH2Cl2 solution at room temperature within an EPR electrolysis cell [26]. An analogous EPR spectrum is also obtained when dilute solutions of [PhCN3S2]2 are prepared in CH2Cl2 in air [36]. In all of these measurements, the two equivalent 14 N nuclei display aN ~0.50 -0.52 mT, in reasonable agreement with our calculated value of 0.40 mT (note that for the heterocycle, assignment to the very similar spectra of dithiadiazolyl free radicalsvide infracannot be ruled out). On the other hand, the reported 33 S hfc for the unique sulfur atom of 0.45 mT is in strong disagreement with the significantly larger calculated value of 3.08 mT [4]. As illustrated in Figure 4, the identity of this radical could be confirmed by measurement of the EPR spectrum of a 33 S-enriched sample. reported by Herberhold [37,38], is rendered soluble in organic solvents upon addition of 18-crown-6 [33]. Chivers  The crystal structure of S2N2 is almost square planar with 90.4 and 89.6° bond angles and S-N distances of 1.654 Å [40]. There are also many calculations reported in the literature for neutral S2N2 [41], which has a complex energy surface [31f]. The marginally longer bonds as well as the folded structure of [S2N2] +• are consistent with the loss of an electron from the non-bonding π-symmetric nitrogen-centered orbital in S2N2 ( Figure 6a).

Figure 5
Geometry-optimized structures of four and five atom binary S,N radicals. Early claims in the literature for the formation of the [S2N2] +• radical cation from the dissolution of either S2N2 or S4N4 in acidic media [2a,b] have been convincingly reinterpreted in terms of the characteristic I = 1 quintet with aN = 0.32 mT of the thermodynamically stable [S3N2] +• cation radical [2]. Surprisingly, this assignment resurfaced much later when other workers dissolved S2N2 in disulfuric acid, but this claim has never been substantiated [42a]. There is therefore no reliable evidence for the existence of [S2N2] +• in condensed phases, though Preston and Sutcliffe argue that its detection is to be expected based on a calculated heat of formation of -1390 kJ mol -1 [5], and it is a common mass spectral fragment [42b]. To our knowledge, no attempts have been made to generate this radical under mild conditions from solutions of the neutral precursor. There is an unpublished report of electrochemical data for S2N2 in CH3CN/[ n Bu4N][BF4] which is mentioned in reference [43]; oxidation is reported to occur at +0.1 V and reduction at -0.85 vs. SCE, but no details on the reversibility of either process were provided [8]. [S2N2] -• The calculated structure ( Figure 5) of the anion radical [S2N2] -• is found to adopt a D2h geometry quite similar to that of the parent neutral compound. For this species, there is also no experimental evidence for comparison, and only one low-level HF (STO-3G) calculation has been reported [44]. Our calculated bond lengths are longer than in the neutral molecule by 0.064 Å, and intermediate between that of S2N2 (1.654 Å) and a typical N-S single bond length (1.74 Å) as might be expected from the population of an anti-bonding π-MO by a single electron (Figure 6b). It has been suggested that the formation of [S2N2] -• in the presence of neutral S2N2 may induce π*-π* coupling between these species, leading to an adduct (i.e. [S4N4] -• ) which could provide a facile pathway for the conversion of S2N2 to S4N4 [6]. A similar mechanism was proposed to explain the scrambling of sulfur diimides, RN=S=NR', which occurs rapidly in presence of a catalytic amount of reducing agent [45]. and electrochemical generation at low-temperature concomitant with a careful reinvestigation of the voltammetry of S2N2 solutions probably provides the best hope for its detection in solution. For both [S2N2] +• and [S2N2] -• , 33 S isotopic enrichment will greatly increase the reliability of an EPR spectral assignment.

[S3N2] +•
The cation radical [S3N2] +• , a rigorously planar cyclic π-radical, is by far the bestcharacterized binary S,N radical and has been intensively investigated in part because of the false assignment of its EPR spectrum to several other species [2]. Our calculated structure for [S3N2] +• is presented in Figure 5. Several salts in which [S3N2] +• exhibits remarkable thermal stability have been structurally characterized by X-ray crystallography [46]. The calculated and experimental structures are in excellent agreement given that the former is in the gas phase and the latter is in the solid state, and that significant lattice interactions between the cation and associated anions are found in the ionic crystals. A full assignment of the hfc and g tensors was reported by Preston, Sutcliffe and their coworkers from solid-state experiments in which the radical is doped in a diamagnetic crystal host [47]. It is also worth noting that the isoelectronic replacement of the unique S + atom in [S3N2] +• by an RC group generates a whole family of neutral 1,2,3,5-dithiadiazolyl radicals [RCN2S2] • , which have been extensively investigated; this family shares the high thermodynamic stability of [S3N2] +• [7a,b,e-g,k, 8].
The agreement between our calculated and the measured hfc constants is 3% for 14 N and 10-23% for 33 S. The absolute deviations, which are 0.01 mT for nitrogen, and 0.08-0.09 mT for sulfur, are perhaps more instructive than percentage values. Our calculations provide better agreement between theory and experiment than the results of Gassmann and Fabian (Table 1), but qualitatively the two sets of calculations agree very well [10]. Better agreement between calculated and measured hfc constants is to be expected for rigorously planar πradicals such as [S3N2] +• , because minor changes in bond distances and angles are not likely to affect the s character of the total spin density. Conversely, non-planar π radicals such as [S4N4] -• (vide infra) or σ-radicals such as [SNS] • or [NSN] -• will have s contributions to the total spin density that are very sensitive to the smallest geometric perturbations. Indeed, for such species the medium itself is likely to influence the structure and hence any measured hfc constants in comparison to calculated gas-phase values. Another consideration, however, is that the magnitude of the coupling constants to both kinds of nuclei in π-radicals such as [S3N2] +• is small as a consequence of the low atomic s character of the total spin density. This serves to accentuate the relative uncertainty between calculated and experimental hfc values, even when good agreement is found in absolute terms.   [25]. Despite an apparently reversible CV response for the oxidation process, these authors were unable to detect any radicals by EPR spectroscopy upon in situ electrolysis. However, these experiments appear to have been conducted at room temperature, and the lifetime of the neutral radical may simply be too short for observation under their conditions.
Preston and Sutcliffe used gas-phase calculated heats of formation to predict a high likelihood for observation of [S4N2] +• [5]. This radical is predicted to have its spin density delocalized over the planar S-N-S-N-S substructure, with the highest density on the two "terminal" S atoms (Figure 8b). An EPR spectrum from a 33 S-enriched sample will be dominated by two equivalent nitrogen and two equivalent sulfur hfc's, and, thus, should be easily recognizable. To our knowledge, no investigation of the electrochemical oxidation of S4N2 has ever been undertaken.  Figure 8c.) The EPR spectrum of this species would also be more easily identified with 33 S labeling, because the S1 hfc constant is predicted to be considerably smaller than that in [NSN] -• . Chivers and Hojo studied the reduction of neutral S4N2 by polarography and rotating-disk-electrode voltammetry [53] and concluded that "the initial reduction product of 1,3-S4N2, presumably the radical anion [1,3-S4N2] -• , is unstable with respect to disproportionation to other binary sulfur-nitrogen anions." Thus it appears that this will be a challenging species to observe by EPR spectroscopy.

[3,5,7-S4N3] •
The calculated structure of this neutral seven-atom ring is shown in Figure 9. It consists of an essentially planar N-S-N-S-N fragment, joined by a puckered -S-Sunit that imparts chirality to the structure. The geometry of the [S4N3] • radical has not previously been investigated, but recent B3LYP/6-311+G** calculations on the cation indicate a totally planar structure with shorter S1-N3 (1.572 Å) and S1-N1 (1.566 Å) bonds [54]. An early crystallographic study of [S4N3][NO3] also showed a planar structure, and yielded average values of 1.522 and 1.557 Å for these same two sets of bonds [55]. The increases in these bond lengths in the calculated structure of [S4N3] • are in accord with population of the π* SOMO in the neutral radical by a single electron (Figure 10a).
The spin density calculated for [S4N3] • is very evenly distributed over the whole ring including the puckered -S-Ssection (except for N3, which is nodal in the SOMO, see the sulfur contributions to the SOMO must be largely confined to p type functions, as is also apparent from Figure 10a.  An EPR spectrum purported to belong to this radical has been reported from γ-irradiation of S7NH powders and crystals [58]. The trace of the hfc tensor measured from these solids gives an estimated isotropic coupling of ~2.6 mT, in reasonable agreement with our calculated value of 1.90 mT. A logical precursor for the generation of [S7N] • is the corresponding anion [S7N]which has been characterized by 14 N and 15 N NMR spectroscopy in liquid ammonia [59]. However, the thermal instability of this anion will make chemical or electrochemical generation of the radical a very challenging proposition.

[S4N4] +•
We next consider three radicals derived from the most important binary S,N compound, the neutral cage compound S4N4. Despite being known since 1835 [1], interest in this compound remains active. The calculated ground-state structure for the 11 -electron system [S4N4] +• is shown in Figure 11. It is a planar species like the corresponding dication [S4N4] 2+ [60], but the monocation radical has D2h symmetry due to Jahn-Teller distortion. The S3-N1 (and symmetry related) set of bonds are shorter than the S1-N1 set, and approach those of an N=S=N unit. In three different salts of [S4N4] 2+ , crystallographic studies provide average (with std. dev.) N-S bond distances of 1.550(7) Å and angles: NSN = 118.5(7)°, SNS = 151(2)° [60]. Although a comparison of X-ray and computed bond lengths is not straightforward, the changes in the radical cation geometry seem to be fully consistent with population of the π* SOMO (Figure 12a), which is antibonding for S1-N1, but essentially  Figure 11 Geometry-optimized structures of eight atom binary S,N radicals derived from S4N4.
The reported EPR spectrum of [S4N4] +• is a ~4.5 mT broad, featureless, signal generated in frozen CFCl3 solutions using γ-irradiation [63]. The average g value of this spectrum is 2.004, and the lack of resolved 14 N hfc was interpreted by the authors to indicate it to be a π*radical (SOMO depicted in Figure 12a), i.e. to have a planar structure, with small hfc to the four equivalent nitrogen nuclei. We question the correctness of this assertion as [S3N2] +• is also a planar π*-radical, but has beautifully resolved and easily detectable (> 0.5 mT) 14 [63]. Attempts to generate the radical cation from chemical oxidation in solution phase have also been tried and have failed [2a]. Similarly, there is no evidence in the literature for an electrochemical oxidation process for S4N4 at accessible potentials [8]. This is consistent with Oakley's assessment that binary S,N compounds are difficult to oxidize, and that the synthesis of salts of [S4N4] 2+ requires very strong oxidizing conditions such as AsF5/SO2 or (FSO3)2/HSOF3 [6]. . It seems unlikely that salts of this unstable radical anion this will ever be isolated to allow for experimental determination of its structure.
To our knowledge, there is only one previous report of a theoretical study of [S4N4] -• which was done at an inadequate HF level (STO-3G) and is omitted from further discussion [44]. Our calculated structure is shown in Figure 11, in which the expected Jahn-Teller distortion of the D2d structure of the neutral S4N4 cage leads to a symmetry-lowered C2v geometry in which all four nitrogen atoms remain equivalent (consistent with the known EPR evidence, vide infra) [64a]. The structure of neutral S4N4 has been determined by gas-phase electron diffraction to have the same D2d symmetry known from X-ray diffraction studies [65]. In the following list, the gas-phase diffraction values are presented in normal text, and that from the recent X-ray structure re-determination are in italics [65]: the S-N distance is 1.623 (4) (20) mT in . The linewidth at -25°C in THF was reported to be 0.046 mT, but was found to broaden to ~0.08 mT in the presence of excess [S4N4],an effect attributed to rapid electron exchange between the radical and the parent species [64a]. The experimental aN values are in reasonable agreement with our calculated value of 0.08 mT, and fit much better than the 0.322(4) mT of the Chapman and Massey spectrum [2a]. Since the flexible nature of this radical anion (as shown by our frequency calculation) implies that vibrational averaging will affect the agreement between solution-phase experiment and gasphase calculation, it is unlikely that better agreement can be expected for this kind of radical.
We are therefore very confident that the Myers/Prater spectrum is correctly attributed to [S4N4]‾ • . We note also that the calculated geometry has two inequivalent pairs of S nuclei, which are predicted to have quite distinct 33 S hfc constants. Hence 33 S substitution may be able to substantiate the predicted structure, so long as the above-mentioned vibrational motion connected to the interchange of the two degenerate conformations is slow on the EPR timescale.
Finally, we briefly consider the origin of the well-resolved nine-line spectrum of an indefinitely stable radical with a( 14 N) = 0.322 (4)

[S4N5] •
The structure of this neutral radical in the gas phase is shown in Figure 13.  [68]. The average S3-N1 distance is 1.61(2), S1-N1 1.66 (2) and S3-N5 1.66(2) Å, and the transannular S···S distance is 2.71(2) Å [68]. The geometrical parameters are collected together in Table 2 Figure 14a). temperatures, only signals from decomposition products were obtained, vide supra) [26]. The EPR data show the expected large nonet for the four equivalent 14 N nuclei of the cage (aN = 0.175 mT), each line of which is further split into a partly-resolved triplet from the smaller hfc to the unique 14 N nucleus (aN = 0.05 mT). This latter coupling is only slightly larger than the experimental line-width of 0.04 mT. The lifetime of this radical was not investigated and neither has a g factor been reported [26].
Compared to the experimental values, we see relative disagreement of 75% and 50% for the bigger and smaller 14 N hfc constants and the absolute agreement is 0.08 and 0.05 mT, respectively. Here too, the large relative errors reflect the small absolute values of the coupling constants. There is no report of 33 S hfc for this species, which is not surprising given the poor signal-to-noise achieved experimentally [26]. We estimate that ca. 20% enrichment in 33 S would be ideal for measurement of the larger 33 S coupling, and the smaller value could probably be resolved from computer simulation and line-fitting of the spectra.

Conclusions and work in progress
The application of DFT methods has greatly increased the experimentalist's ability to correctly assign the EPR spectra of structurally uncertain free radicals; concomitantly the calculations allow structures to be determined by means of their agreement with EPR spectral data for species which are not sufficiently stable to isolate and characterize by diffraction methods. This powerful approach is now being applied to the intriguing field of binary sulfurnitrogen radicals. In this paper we have confirmed the validity of our approach by the excellent agreement between the calculated and experimental hfc constants of the wellcharacterized [S3N2] +• radical. We can confidently assign the structure of [S4N4]‾ • to the C2v partly-opened cage species shown in Figure 11. Fermi-contact term extracted from a gas-phase EPR experiment (see text for explanation); claims for this radical in condensed phases, such as g-value = 2.0067 (5); aN = 1.260 (5) mT [35] have been questioned [5]. b g-value = 2.0057; a = 1.12 mT [4]. c g-value = 2.0105 (5); a = 0.516 mT [35]; g-value = 2.013; a = 0.55 mT [4]; see also [2a]. i Estimated line-width = 0.04 mT, -40C; g-value not measured [26].
j From the trace of the principle components of the hfc tensor in the solid state [58].