Singlet-triplet splittings Delta E-ST and intermolecular covalent pi-pi bonding characteristics of the prototypical phenalenyl pi-dimer and eight spiro-biphenalenyl radical pi-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 Delta E-ST as a function of transfer integrals and on-site Coulomb repulsion energy are presented for the two-electron two-site pi-dimers of phenalenyls and the two-electron four-site pi-dimers of spiro-biphenalenyl radicals. Within the range of intermolecular separation of 3.12 < D < 3.51 angstrom, for the shorter separations, restricted theory works quite well and indicates the presence of a relatively strong intermolecular covalent pi-pi 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 pi-dimers are gradually weakened with increasing D, showing a transition from low D values with significant intermolecular pi-pi bonding and electron delocalization to high D values with localized spins and a biradicaloid character.