Calculations were carried out on a set of Ln(III) complexes to analyze how the FAIMP and NOGF approximations to the molecular wave function affect the energy gaps within the lowest energy spin-orbit multiplet and the magnetic properties. The results were compared with the energies obtained at the CAHF/CASCI-SO level . In the CAHF/CASCI-SO strategy, the set of molecular orbitals are generated at CAHF level minimizing the average-energy functional represented on the basis of all possible Slater determinants, of any M S quantum number, built up allowing N act active electrons to be distributed in all the possible ways in M act active orbitals. Then, CAHF orbitals are used in the CASCI-SO step to construct the representation of the total Hamiltonian of the system, which includes both the Born-Oppenheimer electrostatic and spin-orbit Hamiltonian, still on the basis of all possible Slater determinants in the CAS space of N act electrons in M act orbitals. Finally, the total Hamiltonian is diagonalized to obtain the energy levels.