Unrestricted Hartree-Fock calculations of spin densities with orthogonalized atomic orbitals: proton and ¹³C hyperfine splittings in some pi hydrocarbon radicals

Abstract

The spin density distribution in a few hydrocarbon radicals has been calculated using orthogonalized atomic orbitals in the Unrestricted Hartree-Fock formalism of Amos and Snyder and including certain more important two-electron hybrid and exchange integrals and all the core-resonance integrals. Our calculated spin densities for the cation and anion radicals of alternant hydrocarbons, which are now different due to the breakdown of the pairing theorem, are, in general, of the right relative order so that even the simple McConnell type of relation can account partly for the observed differences in the proton splittings between cations and anions. The proton splittings for position 2 of naphthalene and anthracene radical ions are correctly predicted, thus clearing up the well-known cation-anion anomaly for this position. Comparative calculations have been made to show that the spin density results are worsened with the neglect of the integrals of the type mentioned before. An empirical analysis correlating the observed ¹³C splittings and the spin density results over a non-orthogonal basis set shows that the available ¹³C splittings in alternant hydrocarbon radical ions can be explained with a set of sigma-pi parameters which are consistent with the theory. It is shown that even though the spin densities in cations and anions may be different, these can lead to similar ¹³C splittings.