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A successful and commonly used ab initio method for the calculation ofcrystal field levels and magnetic anisotropy of lanthanide complexes consistsof spin-adapted state-averaged CASSCF calculations followed by stateinteraction with spin-orbit coupling (SI-SO). Based on two observations validfor Ln(III) complexes, namely: (i) CASSCF 4f orbitals are expected to changevery little when optimized for different states belonging to the 4f electronicconfiguration, (ii) due to strong spin-orbit coupling the total spin is not agood quantum number, we show here via a straightforward analysis and directcalculation that the CASSCF/SI-SO method can be simplified to a singleconfiguration-averaged HF calculation and one complete active space CIdiagonalization, including spin-orbit coupling, on determinant basis. Besidesits conceptual simplicity, this approach has the advantage that all spin statesof the 4f$^n$ configuration are automatically included in the SO coupling,thereby overcoming one of the computational limitations of the existingCASSCF/SI-SO approach. As an example, we consider three isostructural complexes[Ln(acac)$_3$(H$_2$O)$_2$], Ln = Dy$^{3+}$, Ho$^{3+}$, Er$^{3+}$, and find thatthe proposed simplified method yields crystal field levels and magneticg-tensors that are in very good agreement with those obtained withCASSCF/SI-SO.

Configuration-averaged 4f orbitals in ab initio calculations of low-lying crystal field levels in lanthanide(III) complexes