A comprehensive approach for elucidating the interplay between 4f and 4f 5d¹ configurations in Ln²⁺ complexes

Lanthanides (Ln) are typically found in the +3 oxidation state. However, in recent decades, their chemistry has been expanded to include the less stable +2 oxidation state across the entire series except promethium (Pm), facilitated by the coordination of ligands such as trimethylsilylcyclopentadienyl, C₅H₄SiMe₃ (Cp'). The complexes have been the workhorse for the synthesis and theoretical study of the fundamental aspects of divalent lanthanide chemistry, where experimental and computational evidence have suggested the existence of different ground state (GS) configurations, 4f or 4f 5d¹, depending on the specific metal. Standard reduction potentials and 4f to 4f 5d¹ promotion energies have been two factors usually considered to rationalize the occurrence of these variable GS configurations, however the driving force behind this phenomenon is still not clear. In this work we present a comprehensive theoretical approach to shed light on this matter using the [LnCp₃]^- model systems. We begin by calculating 4f to 4f 5d¹ promotion energies and successfully correlate them with existing experimental data. Furthermore, we analyze how changes in the GS charge distribution between the Ln ions, LnCp₃ and the reduced [LnCp₃]^- complexes (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) correlate with experimental trends in redox potentials and the calculated promotion energies. For this purpose, a comprehensive theoretical work that includes relativistic ligand field density functional theory (LFDFT) and relativistic ab initio wavefunction methods was performed. This study will help the rational design of suitable environments to tune the different GS configurations as well as modulating the spectroscopic properties of new Ln²⁺ complexes.