Electrochemical and Electronic Structure Investigations of the [S 3 N 3 ] • Radical and Kinetic Modeling of the [S 4 N 4 ] n /[S 3 N 3 ] n (n = 0, -1) Interconversion

Voltammetric


Introduction
Unsaturated binary sulfur-nitrogen compounds readily undergo redox reactions that are accompanied by remarkable structural changes, which continue to challenge the emerging understanding of mechanistic pathways in main group chemistry. 1 Despite being formally electron-rich they are often capable of being either oxidized or reduced. 2 Tetrasulfur tetranitride, S4N4 (1), is the best known member of this class and has been extensively investigated by electrochemistry, EPR spectroscopy and DFT calculations. 3 Its versatility stems from multifaceted chemical behavior whereby it is the source of many other binary sulfur-nitrogen (S,N) compounds, including the cyclic trisulfur trinitride anion [S3N3] - (2). 4

Chart 1. Chemical Structures for Compounds 1-4.
The redox chemistry of S4N4 has been the subject of numerous studies. 1 Chemical oxidation with reagents such as AsF5 or HSO3F produces the cyclic [S3N2] +• radical cation 5 or, in the presence of an excess of the oxidizing agents SbCl5, AsF5 or S2O6F2, the cyclic dication [S4N4] 2+ . 6 The radical cation [S4N4] +• has not been convincingly characterized. The EPR spectrum of the radical formed on γ-irradiation of S4N4 in CFCl3 at 77 K was attributed to [S4N4] •+ , but no 14 N hyperfine splitting (hfs) was observed. 7a A minor product from the reaction of (NSCl)3 with FeCl3 in CH2Cl2 was identified as [S4N4] +• [FeCl4]on the basis of the X-ray structure; 7 however, the perturbation of the S-N bond lengths in the eight-membered ring is consistent with the formation of the protonated species [S4N4H] + . 8 Ring-size changes also radical upon electrolytic oxidation of [PPN] [S3N3] in CH2Cl2 by EPR spectroscopy were unsuccessful. 10 Very recently the photochemistry of S4N4 was investigated in Ar matrices, demonstrating the facile interconversion of S4N4 to different isomers. 11 Three intermediates were identified with the aid of DFT calculations, two of which are novel S3N3 rings carrying exocyclic (N)-S≡N or (S)-N=S groups. These two bear a strong resemblance to species postulated in this work for the decay of [S4N4] -• and may be directly involved in the coupling of neutral [NS] • with [S3N3] • .
We recently reported 12 the first identification of the radical anions of unsaturated C2N4S2 (3) and P2N4S2 (4) rings by using an in situ electrochemical cell capable of Simultaneous Electrochemical Electron Paramagnetic Resonance (SEEPR) 13 spectroscopy, as well as an investigation of the mechanism of their decomposition by a kinetic analysis employing modern digital simulation of CVs. In connection with our interest in the characterization of short-lived, binary S,N radicals, 14 we now report the application of these methods to detailed investigations of (a) the reduction of S4N4 and (b) the oxidation of [S3N3] -. In part (a) we have used the SEEPR technique to acquire high quality EPR spectra of the anion radical [S4N4] -• using natural abundance, 15 N and 33 S-enriched S4N4 at low temperature. We have also employed digital simulations of CVs to provide insights into the nature of the S4N4 ↔ [S3N3]interconversion.
The target of part (b) was [S3N3] • in condensed phases; this radical has previously only been detected in the vapors of (SN)x by photoelectron spectroscopy. 15 The [S3N3] • radical has also been invoked as an intermediate in the formation of [S3N3] salts from the ten-membered ring [S5N5]Cl via ring contraction. 16a Interestingly, the compound [PhCN2S2] [S3N3], which can be obtained by the reaction of the dimer (PhCN2S2)2 with the vapors formed from (SN)x at 160 o C, is described as a biradical [PhCN2S2] • [S3N3] • rather than an ionic compound on the basis of ab initio molecular orbital calculations. 16a However, single-crystal EPR studies could detect only ~1% [PhCN2S2] • trapped in a matrix of what seems to be [PhCN2S2] + [S3N3] -. 16b Surprisingly, despite the apparent solubility of this adduct in common solvents, no solution-phase EPR evidence which could corroborate the biradical nature of this compound was reported. In pursuit of the elusive [S3N3] • radical we have carried out a detailed CV and SEEPR

Experimental
Reagents and General Procedures. S4N4, 3k,l as well as the 15 N and 33 S isotope-labeled analogues, 18 [Cp2Co] [S3N3] 17 and [PPN] [S3N3] 4d-e, 19 were obtained by literature methods. The isotopic purity of 99.9 % 33 S4 14 N4 was confirmed using LRMS: 187.9 ( 33 S4 14 N4 + , 2 %); 140.9 ( 33 S3 14 N3 + , 13 %); 93.9 ( 33 S2 14 N2 + , 19 %); 47.0 ( 33 S 14 N + , 100 %). Dichloromethane and acetonitrile (BDH, reagent grade) were purified by distillation (CH3CN: first from P2O5, then CaH2, CH2Cl2: from CaH2). Both solvents were purged with dry nitrogen prior to use. These solutions were purged with dry nitrogen for 10 min directly before use, and were kept under a blanket of nitrogen during all experiments. CVs, bulk electrolysis, and rotating disk electrode (RDE) measurements were performed with a Princeton Applied Research PARSTAT 2273 potentiostat in conjunction with a PINE Model AFMSRXE Modulated Speed Rotator. The voltammetry cell design has been described previously. 12 The cell used for RDE measurements replaced the central size-10 joint with a 60×15 mm cylinder to accommodate the rotating electrode. Initial background scans characterized the size of the accessible electrochemical window and provided an estimate of the likely background current. The CVs were obtained over scan rates of 0.05-20 V s -1 . The potentials for S4N4 and [PPN] [S3N3] [S3N3] are also quoted vs. ferrocene, for which the cobaltocene/cobaltocenium redox couple is known to appear at -1.35 V in dichloromethane. 20 The 3.0 mm BASi glassy carbon (GC) working electrode area (6.6 x 10 -2 cm 2 ) was determined from the peak current value obtained for the reversible one-electron reduction of ferrocene ( where Ip is the peak current (A), n (the number of electrons in the charge-transfer process) is taken to be 1.0, A is the electrode area (cm 2 ), D is the diffusion coefficient (taken to be 2.3 x 10 -5 cm 2 s -1 ), 21 C is the concentration (mol cm -3 ), ν is the scan rate (V s -1 ), and the other symbols have their usual meanings.
where Il is the limiting current,  is the angular frequency of rotation (s -1 ), (υk) is the kinematic viscosity and the other symbols have been described above. Values for kinematic viscosity at 20 °C were taken to be those for the pure solvents: 0.004536 cm 2 s -1 for CH3CN 22 and 0.003318 cm 2 s -1 for CH2Cl2. 22 The almost linear plots of the Ip c1 vs. ν ½ obtained for the first reduction process in S4N4, as well as of Ip a2 vs. ν ½ for the first oxidation process in [S3N3] in CH2Cl2 at a GC working electrode implies that the mass transport process at the peak potential is controlled by diffusion in both cases. From the Randles-Sevcik relationship (Eqn. 1) an estimation of the diffusion coefficients was also obtained from straight line fits to the Ip c1 vs. ν ½ and Ip a2 vs. ν ½ plots, respectively.  28 coupled cluster (CCSD) 29 and complete active space (CAS) methods, 30 36 The anion and solvent are shown in Figure 1, and the asymmetric unit including [PPN] + is provided in the ESI as Figure S1. Selected bond lengths and angles for this compound are listed in Table 2 [S3N3•HOCH3].
A close-to-linear scaling of the Faradaic current was observed with concentration of S4N4 in CH2Cl2 (  [ClO4] at RT but did not report any details on these processes. 3c  [S3N3] in CH2Cl2 clearly show [S3N3] -/0 at En = -0.34 V vs. Fc/Fc + 37 but the absence of any further redox couples up to the solvent limit when the scan is first swept in the cathodic direction. Once the potential is swept anodically over potentials including the [S3N3] -/0 redox couple and the sweep direction is reversed, a new redox couple appears at -1.00 V. CVs of [Cp2Co] [S3N3] in CH2Cl2 also show the  The peak current of a CV wave under Nernstian conditions is given by Eqn.   (1), in good agreement with the literature values (Table 4). 3b,c Spectra obtained at temperatures between -80 to 0 °C are of similar quality with little apparent variation in LW, while those collected above 0 °C suffer from line-broadening similar to that observed at room temperature.   Figure S3(a), along with the highsymmetry spectrum that might result from dynamic exchange with (weighted) average hfs Our attempts to observe this radical in condensed phases began with low temperature SEEPR studies of CH2Cl2 solutions containing either [Cp2Co] [S3N3] or [PPN] [S3N3]. Oxidative electrolysis at a potential of -0.2 V at temperatures between -60 and +20 °C did not generate a spectrum that could be conclusively attributed to [S3N3] • . A persistent five-line pattern was observed (Figure 7), which did not increase in intensity with electrolysis at -0.2 V or decay after stopping electrolysis. The signal did seem to be induced by the presence of the electrodes in solution, and to grow in intensity at lower temperatures. The spectra displayed significant line width variation over the 120 °C temperature range and have a g value of 2.0105. While they could be simulated by using two equivalent nitrogen hfs constants of 0.509 mT, and one (unresolved) nitrogen hfs constant of 0.044 mT, these values do not agree with the calculated hfs as discussed above. Furthermore, the persistent nature of this EPR signal is inconsistent with the estimated lifetime of [S3N3] • (vide infra). We did confirm, however, that [S3N3] is oxidized to  Note that the persistence of the five-line pattern during electrolysis at such negative potentials is also inconsistent with the postulate that it is due to [S3N3] • . Similar five-line spectra have been seen previously and were assigned to the presence of [NSN] -• , a common decomposition product of many unstable S,N species. 3a,43 This species is reported to possess equivalent 14 N nuclei with a(N) ~0.50-0.52 mT and to have g values in the range 2.0105(5) to 2.0103, which fits well with the signal we observe. The line width dependence that we observed for this signal, apparently for the first time, would also seem to be more consistent with a bent σ radical than with a planar S3N3 π-radical. We do not know how the species causing this signal arises but the following observations can be made: (i) this EPR signal is never seen during electrolysis of pure S4N4 solutions; (ii) it does not increase in intensity in response to electrolysis over the potential range 0 to -1.3 V. Though [NSN] -• could arise from disproportionation of S3N3 • (along with the known [SNS] + ion), 14 this cannot be the dominant decomposition pathway in view of observation (ii).
As an alternative route to [S3N3] • , we carried out bulk reductive electrolysis of S4N4 in  (Table S4). Plots that were based on second-order kinetics exhibited a much poorer fit to the data, consistent with a previous report. 3c The accuracy of kf1 values was found to be negatively affected at lower temperatures by a competing factor, the diffusion of the radical anion out of the EPR cavity more rapidly than its actual decay (see ESI, Figures S4, S5). Therefore only rate constants between the temperatures of -22 and +16 °C were used in an Arrhenius activation energy plot ( Figure S6); which yielded a value of 62 ± 2 kJ/mol. This value is slightly higher than the literature value of 47 ± 4 kJ/mol, 3c which may be due to the different solvent used in our study, but also may suggest that the statistical uncertainty in such measurements significantly underestimates the true errors. Values for D (Table 1) for both S4N4 and [S3N3] were obtained from RDE voltammetry experiments, and were assumed to be equivalent for the corresponding oxidized or reduced counterparts.

Simulations of the Cyclic Voltammetric Responses for S4N4 and [S3N3]
where ks and α are, respectively, the standard heterogeneous rate constant and the transfer coefficient associated with the Butler-Volmer formalism 21 for a heterogeneous electron transfer; Keq1 and kf1 are the equilibrium constant and the rate constant for the follow-up chemical reaction. The first-order nature of the decay of [S4N4] -• was previously established in the more polar solvent CH3CN, 3c and values for kf1 at approximately the same temperature obtained in that study were used as a starting point for our own investigations. Several second-order decay mechanisms were also considered, and in all cases these failed to reproduce the experimental CVs over more than one concentration. Many possibilities were also considered for the firstorder decay pathway of the radical anion, which is known to lead ultimately to [S3N3] -. ECC mechanisms 44

which included an intermediate between [S4N4] -• and [S3N3]had parameters for
the second C step that did not affect the overall fit, so ECC was abandoned from consideration for this redox couple.
For the EC mechanism, 44 the adjustable parameters were the apparent E 0/ (1) as measured vs.
the silver-wire quasi reference electrode (see Table 3 for E 0/ values vs / 0 Fc 0/ E ), kf1, and ks1. For the purposes of simulation the value of α was assumed to be 0.5. Various values for the equilibrium constant Keq1 were investigated, but small values for Keq1 did not lead to optimal fits, so this value was arbitrarily fixed at 10 6 , thus rendering the chemical reaction effectively irreversible over the scan rates investigated. The optimization of simulated CV responses using DigiElch was deemed successful when the simulated and experimental peak heights and positions overlaid each other (see Figure S7). Values for the rate constants were determined from fitting CV's obtained at two different concentrations measured over the scan rate range v = 0.1-0.5 V s -1 (see Table S3) and led to estimates of these values as ks1 = 0.034 ± 0.004 s -1 and kf1 = 1.8 ± 0.2 s -1 .  (6) where ks, α, Keq, and kf have the same meanings as described previously. Exclusion of any coupled homogeneous chemical steps subsequent to the initial electron transfer failed to accurately reproduce the CVs, consistent with previous evidence for the conversion of [S3N3]to S4N4 following oxidative electrolysis. 10 Anomalous deviations in the peak current heights led to complications in simulating the CVs, and could be traced to a hypersensitivity of the anion towards oxygen (see ESI for details on how this was overcome). CVs obtained under a rigorous exclusion of oxygen were simulated to determine values for the electron transfer ks2 and the decay step kf2 rate constants. Both first-and second-order decay mechanisms were considered.
Those which considered the radical to react with itself (dimerization) or with [S3N3] failed to reproduce the CVs. For the EC mechanism described above, the adjustable parameters were the apparent E 0/ (2) (see Table 4 for E 0/ values vs / 0 Fc 0/ E ), kf2, and ks2. The value of α was assumed to be 0.5. Various values for the equilibrium constant Keq2 were investigated, but small values for Keq2 did not lead to optimal fits, and thus this value was again arbitrarily fixed at 10 6 . This resulted in good overlap of the simulated and experimental peak heights and positions ( Figures   S9, S10). Final values for ks2 and kf2 were determined from fitting CV's obtained at two different concentrations measured over the scan rate range v = 0.1-0.5 V s -1 (see Table S6) giving estimates of these values of ks2 = 0.022 ± 0.005 s -1 and kf2 = 0.4 ± 0.1 s -1 . Thus there is also a slow rate of electron transfer for the oxidation of [S3N3] -, followed by an apparent first-order chemical decomposition of the electrogenerated species, which we presume to be the elusive neutral radical [S3N3] • .

[S4N4] -/0 -[S3N3] -/0 interconversion with first-order decay.
Building on the successful simulations of the individual redox couples we set out to characterize the interconversion of the two electroactive species. While the interconversion is necessarily complex because of the 4:3 stoichiometry (as confirmed by bulk electrolysis), our attempts to incorporate this into the kinetic model were not successful. In the end we applied a simplified "square scheme" mechanism, 45 depicted in Scheme 1, which simply combines the parameters developed above for the two redox couples independently. We start by simulating CV's obtained on solutions containing bulk S4N4 over a larger potential window (-0.2 to -1.15 V, Figure 8). In the full-cycle simulations, the adjustable parameters were E o (1), E o (2), kf1, and kf2. The value of α was again assumed to be 0.5.
Including ks1 and ks2 as adjustable parameters resulted in only minor variations in their values (within standard deviation error limits), and therefore these were kept fixed to the average values determined previously (ks1 = 0.03, ks2 = 0.02) in order to limit the number of adjustable parameters. Keq1 was also kept fixed at 10 6 as before, but in the square scheme this makes Keq2 a dependent variable and these parameters are reported among the final fits for completeness (see Table 5). 45 Scheme 1. A simplified "square scheme" mechanism for the interconversion of S4N4 and [S3N3] following first-order decay pathways for both chemical steps. The parameters used here are those defined in Eqn. 3-6.  Table  9 for simulation parameters.  .00 x 10 -6 cm 2 s -1 , as determined by RDE measurements (see Table 1). v = 0.1-0.5 V s -1 . ks1 = 0.03 (s -1 ), ks2 = 0.02 (s -1 ), as determined from the average of the values listed in Tables S5 and S6. b. Invariant parameters determined by original solution composition. c. Ru values were measured on a PARSTAT 2273 potentiostat. d. For the experimental potentials vs. Fc see Table 3. e. K1 was fixed at a high value after considerable testing of alternatives; K2 is a dependent variable.
Values for kf1 and kf2 leading to the best possible overlap of the simulated and experimental peak heights and positions are listed in Table 5; In order to insure the general validity of these parameters, simulations of CV measurements covering a similar extended potential range (-0.15 to -1.1 V) starting from solutions of [PPN] [S3N3] were also undertaken ( Figure 9). The adjustable parameters were again E o (1), E o (2), kf1, and kf2. ks1 and ks2 were again kept fixed at 0.03 and 0.02, respectively, and Keq1 was fixed at 10 6 . Once again the kf2 values are in excellent agreement with those determined previously, but values for kf1 are just outside of the standard deviation from the initial [S4N4] -/0 study. These results are also compiled in Table 5 and from a conservative comparison of the four data sets from two chemically different species, best estimates for the key parameters have been determined as follows: ks1 = 0.034 ± 0.004 s -1 , kf1 = 2.0 ± 0.5 s -1 , ks2 = 0.022 ± 0.005 s -1 and kf2 = 0.4 ± 0.2 s -1 . We note that these values using the higher estimated errors are all, within experimental error, the same as those determined for the individual redox couples. Moreover, kf1 is in qualitative agreement with rates determined from EPR lifetimes (Table S4) Table 10 for simulation parameters. The alternate pathway that was considered was suggested by careful inspection of concentration profiles generated in DigiElch in the simulations starting from bulk S4N4 over an extended potential window to include both redox couples ( Figure 10).  [S3N3] in the presence of a poised electrode surface which could then react with [S3N3] • to regenerate S4N4. This results in a second-order pathway for this step, as described by Scheme 2. Figure 10. Concentration profile generated from a 2.40 mM S4N4 solution and using parameters generated from Scheme 2. The quantity of each species is given subsequent to one complete CV cycle, starting from and ending at -0.7 V, at and beyond the surface of the electrode.

Scheme 2.
An alternative "square scheme" mechanism for the involvement of [NS] • in the interconversion of S4N4 and [S3N3] -. The second chemical step is now second-order with Rate = kf2' [S3N3][NS].
The same experimental data were then fitted to the new mechanism. The adjustable parameters for this study were E o (1), E o (2), kf1 and kf2'. Again, ks1 and ks2 were kept fixed at 0.03 and 0.02, respectively, and again Keq1 was fixed at 10 6 , with Keq2 as the dependent variable. The fits obtained are comparable to those attained using Scheme 1 and the results are listed in Table   6. However, the fits starting from bulk solutions of [PPN] [S3N3], unlike S4N4, required the inclusion of an [NS] • bulk concentration term. These fits resulted in a best estimate for the second-order rate constant kf2' of 1.1 ± 0.3 x 10 3 s -1 M -1 and unchanged values for the other parameters. In this case the rate is proportional to the product of two different concentrations for the second-order reaction (see ESI). Solving for t1/2' results in lifetimes for [S3N3] • in the range of 0.2 to 0.8 s, which are shorter than that those estimated from the first-order decay pathway. This may be significant in terms of our inability to detect an EPR signal for this radical. One of the reviewers suggested that dimerization of the radical might still be a factor despite our inability to detect such a process in the voltammetric modeling. A dimer structure has been detected by gasphase DFT calculations as shown in Figure S11 but the interaction does not appear to be strong.
Related sulfur-nitrogen heterocyclic radicals in dilute, cold, solutions are well known to give EPR signals that are easy to detect even though in the solid-state they form dimers. It is certainly the case, however, that dimerization may explain the null results obtained from the frozen solution spectra. Ultimately we still do not have a good explanation for the apparent EPR silence of this free radical.  Table 1). v = 0.1-0.5 V s -1 . ks1 = 0.03 (s -1 ), ks2 = 0.02 (s -1 ), as determined from the average of the values listed in Tables S5 and S6. b. For the concentration of the bulk compound and Ru values, see Table 5. c. As determined from the simulations only. d. For the experimental potentials vs. Fc see Table 3. e. K1 was fixed at a high value after considerable testing of alternatives; K2 is a dependent variable.
Chemical Mechanisms for the Interconversion of S4N4 and [S3N3] -. The possible mechanisms for the interconversion of S4N4 and [S3N3] are discussed in the light of the detailed kinetic data provided by the digital simulations of the CVs. We start by considering the decomposition of [S4N4] -• , which obeys first-order kinetics and is not influenced by the concentration of S4N4. The previously reported 3c activation energy for this decomposition of 47±4 kJ mol -1 , along with our new value in CH2Cl2 of 62±2 kJ mol -1 is consistent with a vibrationally-induced 1,3 nitrogen shift mechanism (Scheme 3) similar to what has been invoked to explain ring contractions for a variety of S,N heterocycles, i.e., dithiatetrazocine radical anions (3) 12 Mawhinney and Goddard determined that in the gas phase the only such product is the linear NS-SN. 49 Thus several paths might well operate simultaneously for the conversion of [S3N3] • to S4N4.
The Electronic Structure of [S3N3] • . The electronic structure of [S3N3] • has most recently been examined by us using density functional theory (DFT). 14 The calculations fully supported a planar ring geometry with a 2 A2 ground state, in excellent agreement with the previous Hartree-Fock and CI calculations employing basis sets of minimal and double-zeta quality. 15 The radical has C2v symmetry but the geometrical distortions are very small when the optimized structure is contrasted with that of the diamagnetic D3h symmetric [S3N3]  anion. 4 The symmetry lowering upon detachment of an electron is readily understood by noting that the highest occupied molecular orbitals of [S3N3]  form an e´´ symmetric degenerate pair. Thus, the radical undergoes a first-order Jahn-Teller distortion to displace the nuclei to new equilibrium positions of lower symmetry, causing a splitting of the e´´ level to two orbitals which transform as b1 and a2 in the C2v point group.
The ground state electronic configuration of [S3N3] • is …(5b1) 2 (3a2) 1 (6b1) 0 … based on the occupation of the orbitals in the Kohn-Sham reference determinant. 14 However, the energy separation of the highest doubly and singly occupied orbitals is found to be only 0.01 Hartrees. This is not entirely unexpected considering that the 5b1 and 3a2 orbitals originate from the initially degenerate pair and that the molecular framework is very close to being of higher D3h symmetry. It is therefore probable that the lowest 2 B1 state with a configuration …(3a2) 2 (5b1) 1 (6b1) 0 … is energetically similar to the 2 A2 state and that the DFT calculation converged to one of the two possibilities by coincidence. Since DFT is in general not the method of choice to examine the properties of wave functions, we decided to conduct a thorough analysis of the ground state of [S3N3] • using a variety of ab initio methods.
The first signs of the peculiarities in the ground state wave function of [S3N3] • are observed in HF single point calculations which, even when started from the DFT optimized geometry, do not converge after 120 iterations (Gaussian) or converge to a highly improbable 2 A1 state (Molpro). Enforcing the symmetry of the wave function to be A2 helps in both cases after which the HF calculations converge to the same solution as found using DFT. However, an analysis of the HF SCF iterations shows that the convergence problem is not initiated by two close-lying electronic states of different symmetry but rather two close-lying configurations belonging to the same A2 representation of the C2v point group. Hence, we conclude that the ground state wave function of [S3N3] • appears to be multideterminantal in character. This was confirmed by conducting CAS calculations; MP2 and CCSD calculations were also performed for comparative purposes.
vector coefficients indicate that the ground state wave function is a linear combination of five Slater determinants which form two configurations: the "closed shell doublet" configuration (5b1) 2 (3a2) 1 (6b1) 0  (5b1) 0 (3a2) 1 (6b1) 2 and the "doublet triradical" configuration (5b1) 1 (3a2) 1 (6b1) 1 . The latter configuration is a linear combination of three Slater determinants differing only with respect to the spin state of the electrons (½,-½,½; ½,½,-½ and -½,½,½) thereby ensuring that the wave function is a true eigenstate of both Sz and S 2 operators. The most important configurations in the ground state wave function of [S3N3] • are depicted in Figure 11 along with the pictures of frontier orbitals. The wave function analysis shows that the doublet 2 A2 state of [S3N3] • is considerably more complex than what can be inferred from the DFT result alone: the near degeneracy of the 5b1, 3a2 and 6b1 orbitals allows three electrons to be distributed in three orbitals giving rise to a small triradical component in the wave function. The triradical character in [S3N3] • is sufficiently small to allow its treatment with modern exchange-correlation functionals and, hence, its presence remains unnoticed within the density functional formalism of electronic structure theory.
Triradicals with an open-shell doublet ground state have been of increasing experimental and theoretical interest during recent years 50 and [S3N3] • represents an interesting addition to the growing continuum of such systems. Since the ground state wave function of [S3N3] • is dominated by the closed-shell doublet configuration, it is not a true triradical species but can be best viewed as a triradicaloid. This is also evident from the calculated (adiabatic) doublet-quartet splitting which is as large as 120 kJ mol 1 . The electronic structure of [S3N3] • can therefore be contrasted to that of S2N2 in which the energetic proximity of the highest occupied (HOMO) and the lowest unoccupied molecular orbital (LUMO) induces a small but nevertheless significant singlet diradical character to the wave function. 51 As in the case of S2N2, 51 the failure in Hartree-Fock to describe the electronic structure of [S3N3] • is best seen when calculating molecular properties. For example, the vibrational frequencies of [S3N3] • show differences up to 300 cm 1 when the HF and DFT values are compared. It is interesting to note that MP2 suffices much better and predicts harmonic vibrational frequencies in reasonable qualitative and quantitative agreement with CCSD and DFT. However, the above does not hold for the band intensities since the most intense IRtransition at the MP2 level of theory -the lowest b2 symmetric normal mode-has practically no intensity when the calculations are done using either density functional or coupled cluster methods. The failure of MP2 in describing [S3N3] • is also apparent from the calculated natural orbital occupation numbers (NOONs), which show one value significantly higher than two (2.13) and one much lower than zero (-0.16). The presence of negative NOONs in the MP2 wave function has been found to be highly indicative of the need for a multiconfigurational description of the system. 52 In addition, the [3,3]-CAS NOON for the 6b1 orbital is 0.21 but the MP2 value is significantly lower, 0.04, giving a clear sign of the poor description of the frontier orbitals within the latter method. However, the CAS calculation used a minimum active space which is significantly smaller than the full valence space generally required to obtain essentially converged orbital occupancies. Hence, in view of the minor triradical character in [S3N3] • , the orbital occupation numbers calculated from the CCSD wave function should be considered the most accurate. Rather expectedly, all NOONs are found to be between 0 and 2 at the CCSD level, and the calculated occupations for the 5b1, 3a2 and 6b1 frontier orbitals are 1.88, 0.96 and 0.13, respectively, in good qualitative agreement with the CAS CI-vector coefficients. However, it is not obvious what effect triradicaloid character in the ground state wavefunction of [S3N3] • might have on the EPR behavior of this elusive species (if any).

Conclusions
The SEEPR technique, used in conjunction with isotopic labeling, is shown to be an effective tool for the identification of transient binary S,N radicals. Investigations of the nature of the interconversion between S4N4 and [S3N3] have revealed that the primary electron-transfer product for S4N4 decays with first-order kinetics. The decay of the primary electron-transfer product for [S3N3] is less straightforward and may follow either first or second-order kinetics. In either scenario, a significant role may be played by the EPR-silent [NS] • radical. SEEPR studies on 15 N and 33 S isotope-labeled S4N4 provide compelling confirmation of the identity of [S4N4] -• . However, it was not possible to detect [S3N3] • by applying the SEEPR technique to the oxidation of the corresponding anion [S3N3] -, confirming previous reports for the non-observation of this species by EPR spectroscopy. [3,3]-CAS calculations unequivocally established that the ground state of [S3N3] • has distinct triradicaloid character.