In Figures ( )-( ) are represented the crystal field levels within the ground spin-orbit multiplets of 44 different Tb(III)/Dy(III)/Ho(III)/Er(III) complexes estimated by the use of the different methods presented in the previous sections. In the Figures, the energy gaps calculated at FAIMP or NOGF levels are reported on the x axis, while the results obtained from CAHF/CASCI-SO simulations on the integral systems are reported on the y axis for comparison (see also Tables S1-S4 in SI). In FAIMP1 and NOGF1 strategies the metal interacts with the electron densities of the separated molecules included in the environment. For FAIMP1 simulations, the graphs show a general large underestimation of the energy gaps with respect to the CAHF/CASCI-SO results for all the studied ions, with mean percentage errors of about -80%/-90%. This results can be attributed to a poor description of the ligands' density, which, as expected, cannot be described as the simple sum of the densities of the isolated molecules, but the latter must adjust to each others within the complex structure. However, it is noteworthy that general slightly better results are obtained when the densities of the isolated molecules are treated within the NOGF method (see NOGF1 results). This improvement is especially observed for Tb-pc 2 complex, which is formed by two highly p conjugated pc 2 ligands, where NOGF1 methodology reproduces the CAHF/CASCI-SO results with a mean %error smaller than 20% and a small standard deviation of about 4%.