We studied the errors affecting the g tensors, and the orientation of the corresponding principal magnetic axes, for the ground Kramers doublets in the Dy(III) complexes, of large interest for the modeling for the magnetic behavior of lanthanide-based SMM complexes. The g tensor values calculated by H BP SO present almost zero transversal g x and g y components, and g z axial component of about 19.4, which is close to the value expected for a pure M J ± 15/2 Kramers doublet (i.e. 20), indicating a strong magnetic anisotropy, see Table .