Bond and Antibond Resonances: A Unified Framework for Singlet Biradical Character

While the mathematical description of the electronic structure of biradical(oid)s is nowadays well understood, we feel that the chemical-conceptual understanding of the structure and bonding, especially of singlet biradicaloids, remains underdeveloped. In particular, the degree of "biradical character" of singlet biradicaloids is discussed in the literature using a heterogeneous selection of indices, which are often not directly comparable and therefore hamper the development of a systematic understanding as well as comparison of different biradicaloid species. This paper aims to ameliorate this situation, by taking a holistic approach considering a wide variety of biradical indicators (including e.g. the LUNO occupancy, singlet-triplet (ST) gap, bond order (BO) between the radical centers) and applying established computational methods (DFT, CCSD(T), CASSCF, NEVPT2, MRCI) to attain a unified description across the whole range of biradical character, from closed-shell molecules to "perfect" (open-shell) biradicals. We mainly focus on model systems of inorganic, four-membered ring systems which are formally isolobal to S₂N₂ to discuss our results, but the general conclusions should hold for any structure with biradical character. Most notably, we suggest describing the interaction between the radical electrons in biradicaloids with low to moderate biradical character using bonds and antibonds for an intuitive chemical understanding of these species.