To show how the different methods proposed in this paper perform in simulating the magnetic properties, we reported in Table 1/2 the main values of the g tensor for the ground and first excited pseudo-Kramers/Kramers doubles (KD) for Tb(III)/Dy(III) complexes, estimated by the different approximations. From the Tables, the discrepancies between the NOGF3 and CAHF/CASCI-SO results for the ground KDs never exceed 1.5% for all the Tb(III) and Dy(III) systems. A very good agreement is also found in the orientation of the main magnetic axis, where the angle between the axis estimeted by NOGF3 and CAHF/CASCI-SO methods are in all cases smaller than 8 degrees, see Tables and. Larger discrepances are observed for the first excited KDs, where now the g-tensor calculated at NOGF3 level are affected by errors of about 5%/10%, and the angles of the main magnetic axes are between 5 and 15 degrees, with the exception of acac3-dpq , acac3-dppz , tta3phen (39 ), hfac3glyme (21 ) ligands for Tb(III), and tta3bipy ligand for Dy(III).