It is noteworthy that Dy-trensal and Er-trensal show very different behaviours. The first system is accurately reproduced by NOGF3 method both in the low and high energy ranges. Differently, NOGF3 for Er-trensal shows quite large discrepancies with the CAHF/CASCI-SO energies, especially for the levels above 400 cm 1 , with a large underestimation of the gaps by NOGF3 approach versus CAHF/CASCI-SO results.