A b i n i t i o calculations of spin-orbit coupling in the Group 13 and 17 atoms

Spin-orbit splitting energies are presented for the lowest doublet states of the atoms in Groups 13 and 17 of the Periodic Table. The splittings are computed in procedures involving the use of spin-orbit operators derived from relativistic effective core potentials (REP) and from separate calculations of the individual states in j–j coupling using REP’s. Comparison with experiment and with results due to all electron numerical Dirac–Fock calculations show that using the spin-orbit operator as a first-order perturbation to calculations carried out in LS coupling leads to an error of up to 7% in comparison to Dirac–Fock results. The indirect effect on the results due to orbital relaxation in the presence of the spin-orbit operator recovers about one-half of this error. The REP-based spin-orbit operator is shown to be quite accurate both for light and for heavy atoms. This is contrasted to the use of the spin-orbit operator comprised of one- and two-electron terms due to the Breit–Pauli approximation and Hartree–Fock wave functions, where the results degrade severely as the atomic mass increases. The nature of the spin-orbit interaction in fluorine is discussed.