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

A successful and commonly used ab initio method for the calculation of crystal field levels and magnetic anisotropy of lanthanide complexes consists of spin-adapted state-averaged CASSCF calculations followed by state interaction with spin-orbit coupling (SI-SO). Based on two observations valid for Ln(III) complexes, namely: (i) CASSCF 4f orbitals are expected to change very little when optimized for different states belonging to the 4f electronic configuration, (ii) due to strong spin-orbit coupling the total spin is not a good quantum number, we show here via a straightforward analysis and direct calculation that the CASSCF/SI-SO method can be simplified to a single configuration-averaged HF calculation and one complete active space CI diagonalization, including spin-orbit coupling, on determinant basis. Besides its conceptual simplicity, this approach has the advantage that all spin states of the 4f$^n$ configuration are automatically included in the SO coupling, thereby overcoming one of the computational limitations of the existing CASSCF/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 that the proposed simplified method yields crystal field levels and magnetic g-tensors that are in very good agreement with those obtained with CASSCF/SI-SO.