On the performance of approximate spin–orbit Hamiltonians in light conjugated molecules: the fine-structure splitting of HC6H+, NC5H+, and NC4N+

Spin–orbit calculations have been performed on the carbon-rich radical cations HC6H+, NC5H+, and NC4N+ using the full one-and two-electron no-pair spin–orbit Hamiltonian and more approximate approaches. It is found that the full operator can be replaced by an effective one-electron mean-field spin–orbit Hamiltonian almost without loss of accuracy. An analysis of the approximations reveals that multi-center integrals are large, but one- and two-electron terms tend to cancel. The one-center spin–orbit mean-field approach yields fine-structure splittings within 5% of the full results and thus appears to be a favorable means to reliably predict rates of spin-forbidden processes in organic molecules at low cost.