Asymmetric SCF coupling coefficients for highly symmetric open-shell molecules

Vector coupling coefficients (VCC), amn and bmn, appearing in the restricted open-shell Hartree-Fock (ROHF) method, are known to be symmetric: amn = anm and bmn = bnm. We present the results of non-empirucal SCF calculations on the states of the methane dication CH42+ (Td, t24), showing the validity of the use of non-symmetric VCC as well. A similar conclusion has been made in calculations on transition metal atoms. Although the SCF results based on the non-symmetric VCC are correct in both the molecular and atomic cases, this conclusion in itself is in contradiction with existing ROHF theory. A brief discussion of this contradiction is presented.