Electronic Structures and Spectroscopic Properties of 6  -Electron Ring Molecules and Ions E 2 N 2 and E 42+ (E = S, Se, Te)

The electronic structures and molecular properties of square-planar 6  -electron ring molecules and ions E 2 N 2 and E 42+ (E = S, Se, Te) were studied using various ab initio methods and density functionals. All species were found to contain singlet diradical character in their electronic structures. Detailed analysis of the CAS wave function of S 2 N 2 in terms of different valence bond structures gives largest weight for a Lewis-type singlet diradical VB structure in which the two unpaired electrons reside on nitrogen atoms, though the relative importance of the different VB structures is highly dependent on the level of theory. The diradical character in both E 2 N 2 and E 42+ was found to increase in the series S < Se < Te. The diradical nature of the chemical species is manifested in the prediction of molecular properties, in which the coupled cluster and multiconfigurational approaches, as well as the BPW91 functional show consistent performance. 77 Se NMR chemical shifts of chalcogen cations S x Se 4-x2+ (x = 0-3) were calculated with CAS, BPW91 and B3PW91 methods using the GIAO formalism. The hybrid functional B3PW91 shows inferior performance, but both CAS and BPW91 unquestionably confirm the experimental assignment and are able to predict the NMR chemical shifts of these computationally difficult cases with excellent accuracy.


Introduction
Over the last 30 years, a limited number of tetraatomic square-planar 6-electron ring molecules and ions containing atoms of groups 15  The electronic structure and bonding has most often been discussed in the context of S2N2 due to its role in the synthesis of the superconducting polymeric sulfur nitride (SN)x. 1,2 Based on the localized CNDO/2 orbitals, Adkins and Turner first pictured bonding in S2N2 with four localized -bonds and six delocalized -electrons 1 thus implying some similarity with aromatic structures. 8 A similar conclusion was also drawn by Jafri et al. using canonical RHF orbitals. 9 Findlay et al. 10 later refined the scheme by using localized RHF orbitals to analyze bonding in S2N2. They concluded that the structure is best described as a resonance between the two symmetry-broken Lewis structures 2 and 2'. By contrast, Skrezenek and Harcourt have showed that the primary Lewis-type valence bond structure for S2N2 resembles the spin-paired diradical structure 3 with a long NN bond across the ring, and that the singlet diradical structure 4 and the four zwitterionic Lewis structures 5 -8 make smaller contributions to the ground state resonance scheme. 11,12,13 Similar conclusion was also drawn by Fujimoto et al. via INDO calculations. 15 This view was however later questioned by Gerratt et al. 16 who used spincoupled VB theory calculations to show that the structure is a diradical in nature but addressed the diradical character solely to the sulfur atoms, as described in the structure 4. The most recent contribution to the discussion of bonding in S2N2 comes from Thorsteinsson and Cooper who utilized the newly developed CASVB method to analyze the different bonding models. 17 They found the diradical structure 4 to be lowest in energy, but the alternatives 2-2' and 3 were too close to allow any definite conclusions to be made.
Although S2N2 has been the focus of many in-depth theoretical studies, the electronic structures of other valence isoelectronic square planar 6-electron rings have been discussed in lesser detail. In the majority of theoretical studies their electronic structures have been described without making any reference to the suggested singlet diradical character of S2N2. [18][19][20] In many cases ions such as P4 2and S4 2+ have simply been considered as aromatic and the delocalized models similar to the structure 1 have  In this work we report a rigorous ab initio treatment of the electronic structures and molecular properties of E2N2 molecules and E4 2+ cations (E = S, Se, Te). They were chosen due to the wealth of experimental information available. The possible radical nature of the molecules is discussed by using both symmetry-broken Hartree-Fock formalism and true multiconfigurational ab initio methods. The main purpose of the study is to clarify the numerous uncertainties associated with their electronic structures and give a uniform description of their bonding. We also discuss the harmonic vibrational frequencies and 77 Se NMR chemical shifts at various levels of theory.

Computational Details
All calculations were carried out for E2N2 molecules and E4 2+ cations (E = S, Se or Te).
Throughout the calculations, molecules and ions were orientated in the xy-plane in such a way that their principal rotation axis (C2 or C4) coincided with the z-axis. Nitrogen atoms of E2N2 were located on the x-axis and chalcogen atoms on the y-axis. Full point group symmetries (D2h or D4h) were used whenever possible. Dunning's correlation consistent basis set of triple-zeta quality, cc-pVTZ, were used for all atoms except tellurium for which a quasi-relativistic large core effective core potential was used together with a corresponding triple-zeta valence basis set, SDB-cc-pVTZ. All basis sets were used as they are referenced in the EMSL basis set library. 29 Geometries were fully optimized in their singlet ground states using several different theoretical methods: RHF, MP2, 30 CCSD, 31 CCSD(T), 32 CAS, 33 and CASPT2. 34 Two density functionals, BPW91 35

Results and Discussion
Geometries. This extremely good performance of RHF is however purely accidental. The systematic inconsistency between the experimental and high level theoretical bond parameters probably comes from the fact that no theoretical calculations take into account the effects caused by anion-cation interactions and crystallographic packing. These interactions to the molecular geometry should be minimal for the crystal of Se4 2+ in which the cation has a ideal D4h symmetry. The best match between experimental data and post RHF calculations is indeed obtained in the case of Se4 2+ .

Molecular Orbital Analysis of Bonding in E2N2 and E4 2+ .
The RHF/cc-pVTZ valence molecular orbitals of optimized S2N2 and S4 2+ are shown in Figure 1. An in-depth description of MOs is done only for S2N2 and S4 2+ since the valence MO diagrams for the corresponding selenium and tellurium compounds are essentially similar to those of the sulfur compounds.
In the MO picture, the valence orbitals of S2N2 (D2h) can be classified as follows.
The -bonding framework in the molecule contains the MOs 5ag, 3b3u, 4b2u and 2b1g.
Orbitals 6ag, 7ag, 4b3u and 5b2u are also  MOs and although some of them show bonding character inside the ring they can all be regarded as primarily nonbonding combinations of s, px and py orbitals of both nitrogen and sulfur. The four pz orbitals of sulfur and nitrogen make one bonding  MO 2b1u, two nonbonding MOs b2g and 2b3g, and one antibonding MO 3b1u. The two nonbonding orbitals are the highest occupied MOs with nearly equal energies and the antibonding MO 3b1u is the lowest unoccupied orbital.
There are four bonding  MOs in total, which qualitatively make four -bonds. In addition, the bonding 2b1u orbital forms one four-center two-electron -bond. The negative eigenvalue in the stability matrix of all E2N2 molecules corresponds to HOMO-1  LUMO transition which implies that they are the MOs most altered in the broken symmetry approach. Their mixing produces four one-electron orbitals whose spatial forms are depicted for S2N2 in Figure 2. Orbitals  and  correspond to the RHF MO b2g and orbitals * and * to the MO 3b1u. As evident from Figure 2, the symmetry-broken UHF wave function has a C2v symmetry and includes spin polarization with one electron localized in each nitrogen atom. Since the symmetry-broken UHF wave function is a single Slater determinant, it cannot contain a solution where the spins of electrons in orbitals  and  are reversed. Therefore the use of broken-symmetry formalism leads to nonzero total atomic spin densities for nitrogen atoms. Although this is somewhat unphysical in nature, the symmetry-broken wave function addresses the diradical character in E2N2 molecules to nitrogen rather than to sulfur atoms. In fact, if the diradical character were addressable to sulfur atoms, the negative eigenvalue in the stability matrix would then correspond to HOMO  LUMO transition. This is clearly not the case, since all eigenvalues in the B2u symmetry remain positive throughout the stability analysis.
In the case of E4 2+ cations the situation is somewhat more complex. Lewis-type VB structure for E2N2 molecules is the structure 3. The relative importance of the different VB structures seems however to be highly dependent on the level of theory as seen by the diverging opinions in chemical literature. 9-17,22 Since different but equally valid theoretical approaches come to dissimilar conclusions, it is perhaps best not to give unjustified significance to any particular model. 58 After all, none of the proposed bonding models is by itself sufficient for a complete description of the system. This is especially true for different molecular geometries for which the relative weights of the three models 2-2', 3 and 4 can vary greatly. Common to all theoretical analyses is that they demonstrate that the simple view of cyclic electron delocalization as described by structure 1 is clearly an oversimplification of bonding in E2N2 and E4 2+ and suffices only to disguise the extraordinary features of these systems. The calculated harmonic vibrational frequencies for E2N2 and E4 2+ are listed in A significantly better agreement between the experimental and B3PW91 chemical shifts can be obtained if one uses the experimental chemical shift of Se4 2+ as a reference (see Table 4). This suggests that a nearly constant error is made when chemical shifts are calculated using the hybrid functional instead of the pure GGA one. The error presumably comes from the use of constant fraction of the RHF exact exchange in the B3PW91 functional, which in the current case leads to unphysical delocalized exchangecorrelation hole functions. 68 More local treatment of the exchange is a much better approximation of the true situation and the pure GGA functional therefore performs better. The better performance of pure DFT functionals over hybrid functionals has also been reported in the theoretical calculation of 17 O chemical shifts of ozone. 69 The agreement between experimental and CAS chemical shifts can also be improved by using Se4 2+ as a reference chemical shift. The main source of error in this case is most likely the lack of dynamic electron correlation in the CAS formalism.
As the values in Table 4 show, either pure density functionals or multiconfigurational ab initio methods are needed in order to calculate the 77 Se chemical shifts of tetraatomic chalcogen rings with sufficient accuracy. In this respect, the recently reported good performance of RHF in the prediction of the 31 P NMR chemical shift of square-planar P4 2anion seems controversial. 7 However, calculations at the [22,16]-CAS level show that for this system the CI coefficient of the RHF wave function is 0.972, which is considerably larger than that in the case of Se4 2+ (0.890). Therefore, even RHF is able to give a qualitatively correct description of the electronic structure of P4 2and predict the NMR chemical shift with good quantitative accuracy. The weight of the RHF wave function in a multiconfigurational description of other cyclic tetrapnictogen dianions has yet not been determined.

Conclusions
The electronic structures of square-planar 6-electron rings E2N2 and E4 2+ (E = S, Se, Te) were studied using various ab initio methods and density functionals.

References and Notes
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