These results indicate the atomic approximation as the best compromise between computational saving and high accuracy for both the ground and the excited multiplets. On the other hand, surprisingly the simple bare 1e-SOC Hamiltonian well reproduces the gaps within the lowest energy crystal field manifold for the main ions used in the literature for the design of the lanthanidebased SMMs (i.e. Dy, Tb, Er), with errors below 4% with respect to the evaluations made by the use of the complete Breit-Pauli Hamiltonian. Finally, it is noteworthy to mention that the g tensor for the lowest crystal field manifold in Dy(III) complexes are all well reproduced already using the bare 1e-SOC Hamiltonian H ). ). ). ). ).