Chalcogen

The electronic structures and molecular properties of S 2 N 2 as well as the currently unknown chalcogen nitrides Se 2 N 2 and SeSN 2 have been studied using various ab initio and density functional methods. All molecules share a qualitatively similar electronic structure and can be primarily described as 2π-electron aromatics having minor singlet diradical character of 6  8% that can be attributed solely to the nitrogen atoms. This diradical character is manifested in the prediction of their molecular properties, in which coupled cluster and multiconfigurational approaches, as well as density functional methods show the best performance. The conventional ab initio methods RHF and MP2 completely fail to describe these systems. Predictions for the vibrational frequencies, IR intensities, Raman activities, 14 N, 15 N, and 77 Se chemical shifts, as well as singlet excitation energies of Se 2 N 2 and SeSN 2 have been made. The computed high-level spectroscopic data will be of considerable value in future efforts aimed at the preparation of the conducting polymers (SeN) x and (SeNSN) x .


Introduction
Poly(sulfur nitride), (SN)x, is an inorganic polymer in which alternating nitrogen and sulfur atoms form planar quasi-one-dimensional chains. 1 One of the many exceptional physical properties it exhibits is good electrical conductivity along the chains. 1 In addition, the material becomes superconducting below liquid helium temperatures i.e. near 0.3 K. 2 In principle, the conductivity of (SN)x can be increased by either full or partial replacement of sulfur atoms with one of the heavier congeners of group 16, selenium or tellurium. However, the preparation and characterization of heavier chalcogen-bearing analogues of (SN)x has not been reported.
Although there are several synthetic strategies leading to (SN)x, 1 the classical route involving the thermal decomposition of S4N4 in the presence of silver wool is the method of choice for the formation of good quality crystals of (SN)x. 3 The same method cannot, however, be readily applied to the synthesis of (SeN)x because of the explosive and nonvolatile nature of the obvious precursor Se4N4. Therefore, the preparation of heavier chalcogen-bearing analogues of (SN)x requires the development of new synthetic methods or precursors. 4 Kelly et al. have outlined a synthetic approach to the preparation of (SeN)x polymer which utilizes metal complexes of Se2N2 8 e.g. the tetrabutylammonium salt of (-N,N'diselenium dinitride)bis[tribromopalladate(II)] 9 from which free Se2N2 could be released via ligand exchange reactions. A similar pathway has been utilized to generate free S2N2 from the adduct with AlCl3. 10  The recent preparation of 1,5-Se2S2N4 11,12 might provide a route to the mixed chalcogen-nitrogen polymer (SeNSN)x. Although this compound is explosive under the influence of heat and mechanical stress, it is sufficiently volatile to undergo thermolysis in the presence of silver wool. The formation of the four-membered ring SeSN2 as a TiCl4 adduct has previously been reported by Haas et al.. 13 Free SeSN2 has also been proposed to be an intermediate in the production of 1,5-Se2S2N4 from Se(NSO)2 13,14 and in reactions of (Me3SiNSN)2E with ECl2 (E = S, Se). 12 However, neither the crystal structure nor molecular properties of a discrete SeSN2 ring have been determined.
Since all proposed routes to (SeN)x and (SeNSN)x polymers involve Se2N2 and SeSN2 ring systems as reaction intermediates, molecular characterization methods capable of confirming the formation of the four-membered rings will play a crucial role in determining whether the synthetic approaches are viable. High-level theoretical calculations can play an important role in providing accurate data regarding the molecular properties of Se2N2 and SeSN2 to which the experimental results can then be compared.
Currently such data are nonexistent. 15 A prerequisite for obtaining accurate molecular properties using computational methods is that the chosen theoretical approach is able to give a balanced description of all factors affecting the electronic structure. When considering the four-membered chalcogen-nitrogen rings, this becomes a non-trivial task. Several theoretical studies have attempted to elucidate the uncertainties associated with the electronic structure of S2N2 and related species. However, total consensus has yet to be reached.
The bonding in S2N2 was first described with four localized -bonds and six delocalized -electrons, 1 thus implying some similarity with aromatic structures. 18,19 As 5 opposed to this view, Skrezenek and Harcourt have shown that the primary Lewis-type valence bond (VB) structure for S2N2 resembles the spin-paired singlet diradical structure 2 with a long NN bond across the ring. [20][21][22][23] This opinion, however, has been questioned by Gerratt et al. 24 who used spin-coupled VB theory calculations to show that while the structure is a singlet diradical in nature, the diradical character is solely assigned to the sulfur atoms, 3. More recently Jung et al., 25 using different ab initio and DFT methods, have shown that S2N2 is a closed shell 2π-electron aromatic with an insignificant amount of diradical character. However, large LUMO occupation numbers indicated the presence of a strong antibonding effect which caused a 7% reduction to the aromatic character of S2N2. The conclusions of Jung et al. 25 are for the most part in agreement with our recent high level ab initio analysis of the electronic structure of S2N2, as we also found it to be a primarily aromatic system. 16 Our detailed wave function analysis showed that S2N2 possesses 6% diradical character which could be attributed to the nitrogen atoms. This value is in good agreement with the antibonding effect discussed by Jung et al. 25 However, they do not directly relate the antibonding effect to the diradical character in their conclusions.
The purpose of the current contribution is two-fold. First, before any further theoretical work is done for S2N2 and the related ring systems, it is important to achieve a consensus on the best description of their electronic structures. We consider this to be a 6 realistic objective that can be achieved mainly with a theory-based re-evaluation of the previous work. We show here that the chalcogen-nitrogen ring systems S2N2, Se2N2 and SeSN2 are all mainly aromatic in nature and have only a small amount (68%) singlet diradical character. However, contrary to the conclusions drawn by Jung et al., 25 the diradical character is extremely significant to take into account in theoretical calculations.
Second, once a clear description of the electronic structure has been established, we will use high level ab initio and DFT methods to reproduce the molecular properties of S2N2 and predict those of the currently unknown ring systems SeSN2 and Se2N2. The results for S2N2 enable comparison to experimental data and therefore ascertain the level of accuracy that can be achieved.

Theoretical Methods
Calculations were carried out for S2N2, Se2N2 and SeSN2. Throughout the work, S2N2 and Se2N2 molecules were orientated in the xy-plane: nitrogen atoms were located on the xaxis and chalcogen atoms on the y-axis. SeSN2 was constrained to the yz-plane in such a manner that the chalcogen atoms resided on the z-axis. Full point group symmetries (C2v or D2h) and Dunning's correlation consistent basis sets of triple-zeta quality, cc-pVTZ and aug-cc-pVTZ, were used in all calculations. 26 Geometries of all molecules were fully optimized in their singlet ground states using several different theoretical methods: RHF, MP2, 27 CCSD, CCSD(T), 28

Results and Discussion
The electronic structure of S2N2.
There are two important unanswered questions relating to the electronic structure of S2N2 and its heavier chalcogen analogues: What is the amount of singlet diradical character (if any) and should it be attributed to chalcogen or nitrogen atoms in the molecule? Of all the recent papers published on this topic 16,2025 only Jung et al. 25 report that the diradical 9 character in S2N2 is insignificant. However, their analysis of LUMO occupation numbers shows that the molecule exhibits some strong electron correlations.
The primary evidence by which Jung et al. 25 infer that the diradical character in S2N2 is not significant is the lack of a symmetry-broken UB3LYP solution. However, this lack of symmetry-broken spin-unrestricted DFT solution cannot be held as a definite proof of a non-existent diradical character because DFT solutions are found to be stable even for some of the obvious diradicals such as ozone whose diradical character has been found to be 26% by ab initio methods. 16 In ab initio theory, the instability of the spin- This was shown to be true by Gritsenko and Baerends 39 who used an essentially exact KS potential derived from high level ab initio calculations to describe the dissociation of H2. They found that a single Slater determinant represents the noninteracting KS reference system not only in the equilibrium bond distance, but also when the HH bond is significantly stretched. The performance of current exchange-correlation functionals is not as good, since they are unable to reproduce the non-classical contributions to the energy, which leads to incorrect dissociation curves within the restricted scheme. 40 However, the B3LYP/aug-cc-pVQZ solution first becomes singlet unstable at r(HH) = 2.0·ro which corresponds to 19% diradical character based on the [2,2]-CAS wave function at the same internuclear distance. The corresponding GGA functional BLYP performs even slightly better and displays a singlet instability when r(HH) > 2.1·ro using the same basis set. The poorer performance of the hybrid functional comes from the inclusion of a constant fraction of the RHF exact exchange, which leads to non-physical delocalized exchange-correlation hole upon bond elongation. 40 Consequently, the possible diradical character of S2N2 should be evaluated based on the stability of the spin-restricted Hartree-Fock SCF solution instead of the corresponding DFT solution. We have recently shown that even at the equilibrium geometry, the RHF wave function of S2N2 displays a singlet instability. 16 Because a symmetry-broken UHF solution can be found, it is perfectly valid to state that the strong electron correlations described by Jung et al. 25  Before turning attention to the molecular properties of S2N2 and the related heavier chalcogen containing species SeSN2 and Se2N2, we seek to answer another open question, whether the diradical character in S2N2 should be attributed to nitrogen or to sulfur atoms. Previous VB calculations have come to two different conclusions, [20][21][22][23][24] whereas our recent MO-theory based wave function analyses indicated that the diradical character of S2N2 in its equilibrium geometry can be unquestionably addressed to the nitrogen atoms. 16 In the following we will present further theoretical evidence based on symmetry-broken spin densities of familiar radicals that supports this interpretation.
It is clear from elementary quantum mechanics that the spin density associated with a symmetry-broken singlet UHF wave function is non-physical as it does not equal zero at every point in space. For example, in H2 dissociation the UHF solution breaks the inversion symmetry as the HH distance increases and leads to spin polarization where αspin density concentrates on one nucleus and β-spin density at the other [see Figure 1 showed that the VB structure 2 has only 34% weight in the CAS wave function. Similar conclusion was also obtained by Harcourt et al.. 24 Although 2 is the most significant single Lewis-type VB structure, the combined contribution of the four 2π-electron VB structures 6-9 exceeds its weight. Hence, as it has been pointed out, 24-25 S2N2 is primarily an aromatic system with two bonding π-electrons and strong electron correlation effects.
The present work further confirms that the strong electron correlations are static in nature and arise from the nitrogen-centered diradical character in S2N2.   Table 1 show no distinct anomalies. Therefore, no visible indication of the extraordinary electronic nature of these molecules is evident from the calculated geometrical parameters alone. RHF predicts bond lengths that are 0.05Å too short, whereas MP2 overestimates lengths by nearly the same amount.
As expected, coupled cluster, CASPT2, and DFT show the best performance. As is stronger as the Se2N2 moiety is distorted noticeably from the idealized structure.
The SN bond lengths are calculated to be slightly shorter in SeSN2 than in S2N2, whereas the corresponding SeN bond lengths are predicted to be longer by an equal amount in SeSN2 than in Se2N2. Due to the different size of selenium and sulfur atoms, the geometry of SeSN2 is distorted from the square-planar arrangement in E2N2. The ENE' angles are still close to 90, but the  NSN bond angle is around 97 and the  NSeN angle is approximately 83. Interestingly the  NSeN angle is found to be smaller than the  NSN angle.   [36,14] 626 [76,14] The other methods display a more rational performance. Both PBEPBE and CAS predict too small frequencies for S2N2, which mirrors their tendency to overestimate bond lengths (see Table 1). Again coupled cluster, CASPT2, and PBE0 give results, which are in good quantitative agreement with the experimental values. Thus, PBE0, coupled cluster, and CASPT2 are also expected to give the most accurate data for the vibrational frequencies of SeSN2 and Se2N2. The data given by these methods can be averaged and used to estimate the observable normal modes. The reported values are expected to be accurate to within ±25 cm 1 because the anharmonicity effects are expected to be very small in the current case. The theoretically predicted IR and Raman spectra of SeSN2 are shown in Figure   2(b). All six fundamentals are both IR and Raman allowed. Calculated IR intensities show that the fundamentals ν1ν3 should be considerably weaker than ν4ν6. The three most intense IR transitions are expected to occur at 960 cm 1 , 675 cm 1 and 420 cm 1 .
The two normal modes of SeSN2 displaying the largest Raman activities are ν1 and ν3 with estimated wave numbers of 905 cm 1 and 480 cm 1 , respectively. Two weaker transitions are predicted to occur at 960 cm 1 and 675 cm 1 .   60 offer only qualitative insight as the predicted transition energies are overestimated by several eV. Experimentally, the UV/Vis spectrum of S2N2 shows one broad band with vibrational fine structure in the range 4.5-5.8 eV. 50 The shape of this band clearly suggests the presence of two overlapping bands.

24
The calculated singlet and triplet excitation energies of S2N2, Se2N2 and SeSN2 are presented in Tables 4 and 5, respectively. Only the energies of the lowest eight excited singlet and triplet states are shown. It is only by chance that the lowest eight excited states of S2N2 and Se2N2 all belong to different symmetries. Excitation energies were also calculated using HF (TDHF) and MP2 (second order polarization propagator approximation, SOPPA) methods. The calculated values, however, turned out to be of little practical use and are therefore omitted from tables. For example, TDHF incorrectly predicted the ground state of Se2N2 to be a triplet. Although a SOPPA calculation gave a correct singlet ground state, the triplet excitation energies were still severely underestimated. It is obvious that more elaborate ab initio methods are needed to reach even qualitative accuracy.
The only electric dipole-allowed transitions for S2N2 are those to B1u, B2u, and B3u symmetric states. However, the calculated CAS, EOM-CCSD and TDDFT oscillator strengths consistently indicated that transition to the first 1 B1u state is very low in intensity and will therefore not contribute to the spectrum. In addition, the transition to the 1 1 B2u state is found to be considerably more intense than the transition to the 1 1 B3u state as calculated oscillator strengths for these states are 0.13 and 0.03, respectively.
These results are in good agreement with earlier findings. 50,61  It has been noted earlier 50 that the addition of diffuse functions to the basis set leads to changes in the energies of the 1 1 B3u state relative to those of the 1 1 B2u state. As it is possible that some of the excited states might require spatial diffuseness characteristic of Rydberg states, the excitation energies of S2N2 were also calculated with the augmented aug-cc-pVTZ basis set. The results were however virtually indistinguishable from those listed in Table 4 and are not tabulated. The addition of diffuse functions resulted in overall lowering of the excitation energies by 0.04 eV, but the energy ordering of the states remained unchanged. In particular, we find the 1 1 B2u state to be always lower in energy than the 1 1 B3u state. As a result, none of the first eight excited states of S2N2 has much Rydberg character. In addition to the basis set, the reported selective energy lowering effect also depends on the method used and the molecular geometry i.e. the relative energy ordering of the nearly degenerate HOMO and HOMO1 orbitals.
The band maximum in the experimental UV/Vis spectrum of S2N2 is at approximately 5.0 eV (250 nm). 50 It is obvious that the calculated CAS and CCSD singlet excitation energies are overestimated. The same appears to be true also for the TDDFT energies, although the overestimation is not as large. Conversely, the excitation energies are slightly underestimated at the CASPT2 level because calculated 1 1 B3u and 1 1 B2u transition energies are both below the experimental band maximum. Both CAS and PBEPBE results are equally close, but on the different sides of the experimental band maximum.
Identical spectral features are predicted for Se2N2. The calculated oscillator strengths for the three symmetry-allowed transitions 1 1 B1u, 1 1 B2u and 1 1 B3u are 0.00, 0.12 and 0.02, respectively. The band maximum is shifted slightly towards the lower energy end of the spectrum and is expected to occur at ca. 4.3 eV (285 nm). The mixed chalcogen species SeSN2 shows C2v symmetry, which means that the A2 transitions are dipole forbidden. The calculated oscillator strengths predict one strong A1 transition at around 4.5 eV (275 nm) and the possible occurrence of two lower intensity transitions slightly above and below 5.0 eV.
Taken as a whole, the singlet transition energies in Table 4 show that the excitation energies decrease as the selenium content in the ring increases. The same is also true for the triplet energies (see Table 5). In particular, the singlet-triplet energy gap decreases 0.3 eV with every selenium addition and changes from 3.00 eV (S2N2) to 2.35 eV (Se2N2). This might indicate slightly higher reactivity for the selenium-containing rings.
Crystal structures and band gaps. Disulfur dinitride forms monoclinic crystals, space group is P21/c, with two S2N2 molecules per unit cell. 43 The crystal structure shows a and red, respectively. In agreement with the aforementioned results for excitation energies, the band gap energy decreases as the selenium content in the ring increases.

Conclusions
The electronic structures and molecular properties of S2N2 as well as the currently unknown chalcogen nitrides Se2N2 and SeSN2 have been studied using various ab initio and density functional methods. All molecules share a qualitatively similar electronic structure and can be described as 2π-electron aromatic systems. The existence of symmetry-broken spin-unrestricted HF solutions suggests that the strong electron correlation effects exhibited by the S2N2, Se2N2 and SeSN2 ring systems are static in nature and are a direct consequence of their intrinsic minor singlet diradical character.
This effect reduces their aromaticity by 68%. Together with the previous results, the spin-density analyses provided in this work further confirm that the diradical nature can be unquestionably attributed to nitrogen rather than to sulfur atoms. (4) Other attempts to prepare the heavier chalcogen analogues of (SN)x have also been reported. All methods have, however, proven unsuccessful due to the nonexistence of suitable selenium-nitrogen precursors or the different chemistries that the selenium analogues of the known sulfur-nitrogen precursors display.