The SCF-AO's expanded by Löwdin have been used for the calculation of the electron spin dipolar interactions in the riplet-state zero-field splittings of some aromatic molecules. Within a framework of two-center approximation for the spin-spin interaction integrals over atomic orbitals, and adopting the Sklar-type approximation for the exchange-type integrals, excellent agreement with experiments has been obtained for benzene and naphthalene without invoking σ-π interactions. The wavefunctions used were obtained by means of the Pariser-Parr-Pople method, within a full single excitation configuration treatment. This approach has been extended to some aromatic nitrogen heterocycles, but the results, although promising, are poorer, possibly due to the neglect of spin-orbit coupling. Uncertainty in the choice of the C-N resonance integral and the neglect of penetration integrals in the core Hamiltonian may also be factors. Eleven molecules have been treated in all. For comparison, the single-determinant unrestricted Hartree-Fock wavefunctions also have been employed, but these give extremely poor agreement with experiment.