Ab Initio Crystal Field for Lanthanides

Abstract

An ab initio methodology for the first-principle derivation of crystal-field (CF) parameters for lanthanides is described. The methodology is applied to the analysis of CF parameters in [Tb(Pc)₂ ]^- (Pc=phthalocyanine) and Dy₄ K₂ ([Dy⁴ K² O(OtBu)¹² ]) complexes, and compared with often used approximate and model descriptions. It is found that the application of geometry symmetrization, and the use of electrostatic point-charge and phenomenological CF models, lead to unacceptably large deviations from predictions based on ab initio calculations for experimental geometry. It is shown how the predictions of standard CASSCF (Complete Active Space Self-Consistent Field) calculations (with 4f orbitals in the active space) can be systematically improved by including effects of dynamical electronic correlation (CASPT2 step) and by admixing electronic configurations of the 5d shell. This is exemplified for the well-studied Er-trensal complex (H₃ trensal=2,2',2"-tris(salicylideneimido)trimethylamine). The electrostatic contributions to CF parameters in this complex, calculated with true charge distributions in the ligands, yield less than half of the total CF splitting, thus pointing to the dominant role of covalent effects. This analysis allows the conclusion that ab initio crystal field is an essential tool for the decent description of lanthanides.

Keywords: ab initio calculations; covalent interactions; electrostatic models; lanthanides; single-molecule magnets.