Among the approximations that aim to include part of the SOC two-electron interaction, the spin-orbit mean field approach almost completely reproduces the Breit-Pauli results for the ground multiplets, and remains within an error of ±4% for the energies of the first excited multiplets. For both the ground and the excited multiplets, we showed that the atomic approximation, where only the one-center 2e-SOC integrals are retained throughout, and contracted with the true CAHF molecular density, does not introduce additional errors with respect to the results where all the 2e-SOC integrals are evaluated. The errors are quite stable varying the ligands' environment for all the approximations studied.