Is the S2N2 ring a singlet diradical? Critical analysis of alternative valence bond descriptions

Rival valence bond (VB) descriptions are investigated for the pi-electron systems of the sulfur-nitrogen rings S2N2 and S4N42+ near equilibrium geometry. The lowest-energy compact spin-coupled 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 S2N2 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 S2N2 onto the basis of BOVB structures (plus an orthogonal complement).