The spin Hamiltonian tensors in the mPV and BB approaches are effectively evaluated from a pseudospin Hamiltonian manifold assuming the ZFS is small such that all the states are homogeneously populated. Therefore, even though the individuals KDs are anisotropic, an effective g-tensor quickly becomes isotropic as the dimension of the manifold increases to augment the thermally populated KDs. In addition, the ZFS D tensor becomes less meaningful unless a high axial symmetry is present . Hence, the anisotropy of χ s and the resulting dipolar shifts are mostly due to the ZFS as shown by . This is the main limitation of both the mPV and BB approaches particularly for a paramagnetic center where the pseudospin S ≥ 3/2. However, when the ZFS of a manifold is comparable to the thermal energy all the KDs are not populated homogeneously. This nonhomogeneity leads to the state-specific Curie and Van Vleck contributions which are correctly evaluated in the VV approach in a sum-over-states fashion both for the magnetic moments and ZFS contributions. Therefore the VV approach is not limited to a model space.