A comprehensive approach for elucidating the interplay between 4f n+1 and 4f n 5d1 configurations in Ln2+ complexes

Abstract

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 ⁿ⁺¹ or 4f ⁿ 5d¹, depending on the specific metal. Standard reduction potentials and 4f ⁿ⁺¹ to 4f ⁿ 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 ⁿ⁺¹ to 4f ⁿ 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.

Fig. 1. (a) Structures of the complex and (b) the truncated model where the SiMe₃ groups were replaced with hydrogen atoms. See Table S3 for a comparison in the 4fⁿ⁺¹ to 4fⁿ5d¹ promotion energies when using both structures for Tm and Eu systems.

Fig. 2. (a) Correlation between the theoretical 4fⁿ⁺¹ to 4fⁿ5d¹ promotion energy curves and standard reduction potentials calculated from thermodynamic data. (b) Theoretical CASSCF/MC-pDFT 4fⁿ⁺¹ to 4fⁿ5d¹ promotion energies for the Ln²⁺ free ions and the [LnCp₃]⁻ complexes. The black dashed line indicates the crossover between both configurations.

Fig. 3. (a) Comparison between experimental and simulated emission spectra for the [EuCp₃]⁻ system calculated with CASSCF/MC-pDFT/SO (solid green line) and CASSCF/CASPT2/SO (dashed blue line). (b) To better compare the shape of both simulated and experimental spectra, the CASSCF/MC-pDFT/SO spectrum was blue-shifted ∼26 nm whereas the CASSCF/CASPT2/SO was red-shifted ∼33 nm to match the experimental peak.

Fig. 4. Classification of Ln ions based on their charge density distribution when going from the largest M_j state of the Ln³⁺ free ions to the trivalent and divalent complexes. The underlined metals Ce, Eu and Nd were taken as reference to plot the densities. Isovalue = 0.03.

Fig. 5. Qualitative comparison between spherical and pseudo-trigonal symmetries.