Biradical Paradox Revisited Quantitatively: A Theoretical Model for Self-Associated Biradical Molecules as Antiferromagnetically Exchange Coupled Spin Chains in Solution

An ESR hyperfine splitting pattern of a biradical in solution depends on the magnitude of the intramolecular exchange interaction J_intra compared with the hyperfine coupling constant A. Some biradicals exhibit their hyperfine splitting patterns characteristic of a monoradical, even though their exchange interaction is strong enough, |J_intra| ≫ |A|. The contradiction in ESR spectroscopy is known as “biradical paradox”, puzzling scientists for a long time. In this study, it is shown from ESR spectral simulations underlain by a theoretical model of a series of spin Hamiltonians that noncovalent aggregation of biradical molecules in solution leads to the appearance of paradoxical ESR spectra. Most of the spins in an aggregate of one dimension lose their contribution to the ESR spectra owing to intermolecular antiferromagnetic interactions J_inter, leaving two outermost spins ESR-active in the aggregate of one dimension. Paradoxical ESR spectra appear only when J_intra and J_inter fall within a particular range of the magnitudes which depends on the number of molecules in the aggregate.