Rival valence bond (VB) descriptions are investigated for the π-electron systems of the sulfurnitrogen rings S 2 N 2 and S 4 N 4 2+ near equilibrium geometry. The lowest-energy compact spincoupled generalized VB (SCGVB) descriptions are provided by variational optimization of two configurations that are found to be symmetry related to one another. Optimization instead of symmetry-pure single-configuration SCGVB wave functions introduces three-center SNS or NSN orbitals, which seem to be an unnecessary complication. For neither system is much achieved by mixing competing solutions. Breathing orbital VB (BOVB) calculations for S 2 N 2 confirm NN singlet diradical character to be more important than SS singlet diradical character, but the largest contribution (ca. 60%) comes from the symmetry-determined linear combination of four symmetry-equivalent structures that lack any obvious diradical character. Much the same pattern was consistently found using a simple but robust projection of various SCGVB descriptions for S 2 N 2 onto the basis of BOVB structures (plus an orthogonal complement).
K E Y W O R D Sbreathing orbital valence bond, π-electron rings, generalized multiconfiguration spin-coupled, S 2 N 2 and S 4 N 4
2+, spin-coupled generalized valence bond (SCGVB)
| INTRODUCTIONAlthough various larger (SN) x systems continue to attract considerable experimental and theoretical attention for a wide range of reasons, we should admit from the outset that our own particular interest in the planar S 2 N 2 ring is associated with the somewhat unusual levels of attention that this small molecule has been receiving from theoretical chemists, particularly those specializing in valence bond (VB) theory. A spin-coupled generalized VB (SCGVB, vide infra) description of S 2 N 2 , reported by Gerratt et al., [1] was interpreted at the time as being dominated by SS singlet diradical character but some other studies, [2][3][4][5][6] and especially the very careful breathing orbital VB (BOVB) work of Braïda et al., [2] have seriously questioned the validity of that interpretation. Indeed, Braïda et al. [2] were able to show by partly qualitative arguments that the SCGVB wave function, when stripped to some extent of the delocalization tails on the fully optimized active orbitals, did in fact appear to be consistent with the BOVB viewpoint, in which a structure with NN singlet diradical character was the largest single contributor. We reexamine this issue in the present work, by means of a novel approach utilizing a robust projection of the SCGVB wave function onto the basis of the BOVB structures.While confirming the main gist of the conclusions of Braïda et al., [2] namely that Gerratt et al. [1] may have misinterpreted the results of their SCGVB calculations, we also show that the interpretation of the BOVB description could be interestingly more nuanced than had been supposed.Additionally, as was shown by Thorsteinsson et al., [7] there can exist rival SCGVB-like solutions that are fairly close in energy to the one described by...