Crystal Field in Rare-Earth Complexes: From Electrostatics to Bonding

The flexibility of first-principles (ab initio) calculations with the SO-CASSCF (complete active space self-consistent field theory with a treatment of the spin-orbit (SO) coupling by state interaction) method is used to quantify the electrostatic and covalent contributions to crystal field parameters. Two types of systems are chosen for illustration: 1) The ionic and experimentally well-characterized PrCl₃ crystal; this study permits a revisitation of the partition of contributions proposed in the early days of crystal field theory; and 2) a series of sandwich molecules [Ln(ηⁿ-C_nH_n)₂]^q, with Ln=Dy, Ho, Er, and Tm and n=5, 6, and 8, in which the interaction between Ln^III and the aromatic ligands is more difficult to describe within an electrostatic approach. It is shown that a model with three layers of charges reproduces the electrostatic field generated by the ligands and that the covalency plays a qualitative role. The one-electron character of crystal field theory is discussed and shown to be valuable, although it is not completely quantitative. This permits a reduction of the many-electron problem to a discussion of the energy of the seven 4f orbitals.