SO differ between the different ions. A quite large underestimation of the crystal field levels affects the results for Ho(III) (µ ≈ -11%, σ ≈ 1%), while smaller deviations affect the results for Nd(III) (µ ≈ -6%, σ ≈ 2%), Pr(III) (µ ≈ -5%, σ ≈ 4%), and Dy(III) (µ ≈ -4%, σ ≈ 1%). The energy gaps are well represented for Sm(III), Tb(III), Er(III), Tm(III), Yb(III) (µ within ±1% and σ < 2%). As an indication of the magnitude of these errors, it has been shown in the literature that the discrepancies between the simulated ab initio and the experimental results can be larger than 10% . As an example, the ab initio crystal field levels in Er(III)-trensal reported in Table of ref. are affected by a MAE ≈ 19% for CASSCF/RASSI-SO model A1 simulation, or MAE ≈ 8% for RASSCF/CASPT2/RASSI-SO model C4, and in both models the ab initio gap between the ground and the first excited Kramers doublet, which is experimentally observed at 54 cm -1 , is affected by an error exceeding +13%. H