Singly occupied MOs in mono- and diradical conjugated hydrocarbons: comparison between variational single-reference,...

This work compares three descriptions of the unpaired electrons distribution in conjugated monoradical and diradical hydrocarbons involving one or two methylene groups attached to an aromatic skeleton. The first one is the simple Hückel topological Hamiltonian, the singly occupied molecular orbitals (SOMO) of which may be analytically obtained. The second one is the restricted open-shell self-consistent field (ROHF-SCF) method. The so-obtained distribution of the unpaired electrons on the skeleton appears deeply different from that predicted by the Hückel Hamiltonian, being more strongly localized on the external methylene groups. More elaborate methods treat all π electrons in the π valence molecular orbitals (MOs) through a full valence π complete active space self-consistent field (CASSCF) treatment. The distributions of the unpaired electrons (given by the natural MOs of occupation number close to 1) are surprisingly similar to those predicted by the Hückel model. The spin density distributions, including spin polarization effects, can be improved by further configuration interactions involving one hole-one particle excitations and compared with the experimental hyperfine coupling constant ratios. This comparison confirms the lack of delocalization of the magnetic orbitals defined from the self-consistent single-reference treatment. We show that, provided correct SOMO are used, a single excitation CI performed on top of a single reference gives accurate spin densities. Finally, a rationalization of the role of the dynamic correlation in correcting the excessive localization of the unpaired electron(s) at the ROHF level on the exocyclic methylene group(s) is given, attributing it to the dynamic charge polarization of the charge transfer configurations between methylene and the aromatic frame.