Theoretical analysis of intermolecular covalent π-π bonding and magnetic properties of phenalenyl and spiro-biphenalenyl radical π-dimers

Singlet-triplet splittings ΔE _ST and intermolecular covalent π-π bonding characteristics of the prototypical phenalenyl π-dimer and eight spiro-biphenalenyl radical jr-dimer structures are analyzed with the aid of restricted and unrestricted density functional theory calculations and paramagnetic susceptibility data fitted using the Bleaney-Bowers dimer model and the Curie-Weiss model. Single determinant approximations for ΔE _ST as a function of transfer integrals and on-site Coulomb repulsion energy are presented for the two-electron two-site π-dimers of phenalenyls and the two-electron four-site π-dimers of spiro-biphenalenyl radicals. Within the range of intermolecular separation of 3.12 < D < 3.51 Å, for the shorter separations, restricted theory works quite well and indicates the presence of a relatively strong intermolecular covalent π-π bonding interaction. For the longer separations, the singlet-triplet splittings are small; electron correlation plays a significant role, and only the unrestricted theory provides results that are in qualitative agreement with experiments. The bonding interactions in the π-dimers are gradually weakened with increasing D, showing a transition from low D values with significant intermolecular π-π bonding and electron delocalization to high D values with localized spins and a biradicaloid character.