Unrestricted Hartree-Fock spin density calculations on sulphur-containing radicals: Role ofd-orbitals in the π-electron treatment

Spin density distributions in nine sulphur-containing conjugated radicals have been calculated using orthogonalized atomic orbitals in the unrestricted Hartree-Fock (UHF) formalism of Amos and Snyder, considering both p- and d-orbitals of π-symmetry on sulphur and taking into account the necessary rotational invariance requirements. It is found that the inclusion of d-orbitals slightly improves the spin density results obtained in the p-orbital model. For the radical anions of dibenzothiophene and thieno[2, 3-f]benzothiophene, the symmetry of the natural orbital with occupation number unity in the UHF calculations including d-orbitals is found to be different from the symmetry of the orbital containing the odd electron predicted by Hückel theory using Longuet-Higgins' approach. The present UHF spin density results with the inclusion of d-orbitals of proper symmetry are in better agreement with experiment for these radicals. McLachlan-type spin density calculations have also been carried out on the corresponding radical anions employing new Hückel parameters for the d-orbitals derived in this work from a restricted SCF calculation on thiophene. For both radical anions, calculations with these Hückel parameters for the d-orbitals of π-symmetry reproduce the symmetry of the molecular orbital containing the odd electron as predicted by our UHF calculations. Thus the inclusion of d-orbitals worsens the result if one uses Longuet-Higgins' prescription for sulphur orbitals, as observed earlier in dibenzothiophene by Gerdil and Lucken, while inclusion of d-orbitals of π-symmetry with appropriate Hückel parameters does not give rise to such anomalies in these systems.