Evaluating the electronic structure of formal Ln^II ions in Ln^II(C₅H₄SiMe₃)₃ ^1– using XANES spectroscopy and DFT calculations

Ln^II(C₅H₄SiMe₃)^1– have been characterized by XANES and DFT.

Abstract

The isolation of [K(2.2.2-cryptand)][Ln(C₅H₄SiMe₃)₃], formally containing Ln^II, for all lanthanides (excluding Pm) was surprising given that +2 oxidation states are typically regarded as inaccessible for most 4f-elements. Herein, X-ray absorption near-edge spectroscopy (XANES), ground-state density functional theory (DFT), and transition dipole moment calculations are used to investigate the possibility that Ln(C₅H₄SiMe₃)₃ ^1– (Ln = Pr, Nd, Sm, Gd, Tb, Dy, Y, Ho, Er, Tm, Yb and Lu) compounds represented molecular Ln^II complexes. Results from the ground-state DFT calculations were supported by additional calculations that utilized complete-active-space multi-configuration approach with second-order perturbation theoretical correction (CASPT2). Through comparisons with standards, Ln(C₅H₄SiMe₃)₃ ^1– (Ln = Sm, Tm, Yb, Lu, Y) are determined to contain 4f⁶ 5d⁰ (Sm^II), 4f¹³ 5d⁰ (Tm^II), 4f¹⁴ 5d⁰ (Yb^II), 4f¹⁴ 5d¹ (Lu^II), and 4d¹ (Y^II) electronic configurations. Additionally, our results suggest that Ln(C₅H₄SiMe₃)₃ ^1– (Ln = Pr, Nd, Gd, Tb, Dy, Ho, and Er) also contain Ln^II ions, but with 4fⁿ 5d¹ configurations (not 4fⁿ⁺¹ 5d⁰). In these 4fⁿ 5d¹ complexes, the C _3h-symmetric ligand environment provides a highly shielded 5d-orbital of a′ symmetry that made the 4fⁿ 5d¹ electronic configurations lower in energy than the more typical 4fⁿ⁺¹ 5d⁰ configuration.

Introduction

Recent advances in rare-earth metal reduction chemistry have revealed a surprisingly new series of molecular complexes that contained all the rare earth metals in the formal oxidation state of +2,¹ as defined by Parkin and Karen, (Scheme 1).^2,3 These results were unexpected given that the +2 oxidation state had only been observed with six rare earth metals in molecules (Eu, Yb, Sm, Tm, Dy, and Nd). Observing this +2 oxidation state for the other lanthanides was unexpected because the –2.7 to –3.9 V versus standard hydrogen electrode (SHE) Ln^III/Ln^II reduction potentials seemed too negative to allow Ln^II ions to exist in solution.⁴ In the solid state, only the six lanthanides listed above were known to form +2 salts. For the other metals, compounds like LnX₂ (Ln = La, Ce, Pr, Gd, and Y; X = halide) with formal +2 oxidation states had been observed, but subsequent analyses revealed that they contain +3 ions and a delocalized electron in a conduction band, i.e. Ln^III(X^1–)₂(e^1–).⁵

Scheme 1. A general reaction scheme for generating Ln^II(C₅H₄SiMe₃)₃ ^1– containing salts. Accessing these compounds in crystalline form requires complexation of the potassium cation by 18-crown-6 or 2.2.2-cryptand.¹ .

The new Ln(C₅H₄SiMe₃)₃ ^1– compounds, containing the putative +2 ions, were synthesized by potassium reduction of trimethylsilylcylopentadienyl lanthanide(iii) complexes, Ln(C₅H₄SiMe₃)₃ (Scheme 1). More detailed synthetic descriptions for these Ln(C₅H₄SiMe₃)₃ ^1– anions, as well as related Ln[C₅H₃(SiMe₃)₂]₃ ^1– complexes prepared by Lappert and coworkers, have been previously discussed.⁶ The new Ln(C₅H₄SiMe)₃ ^1– complexes were unusual in that their Ln–C_centroid distances were only 1% (0.020–0.032 Å) longer than their Ln^III precursors, Ln(C₅H₄SiMe₃)₃. Larger variations, by an order of magnitude (0.1 to 0.2 Å), were expected based on previous comparisons between conventional Ln^II versus Ln^III structures, which historically provided a diagnostic for the +2 oxidation state. Consistent with this traditional expectation, Ln(C₅H₄SiMe₃)₃ ^1– bond lengths for Ln = Eu, Yb, Sm, and Tm were 0.10–0.20 Å (∼6%) longer than their +3 analogs.⁷ The unusually short bond lengths in the La, Ce, Pr, Nd, Gd, Tb, Dy, Y, Ho, Er, and Lu complexes led to skepticism about the presence of the +2 oxidation state across the Ln(C₅H₄SiMe₃)₃ ^1– series, suggesting that the salts might contain +3 metals with an electron delocalized into ligand-based orbitals. This scenario was – in a sense – reminiscent of the LnX₂ compounds (discussed above).⁵ An alternative description, based on subsequent theoretical analyses, proposed that the small differences in bond distances for La, Ce, Pr, Nd, Gd, Tb, Dy, Y, Ho, Er, and Lu complexes were a direct result of the metal ions having an unusual 4fⁿ 5d¹ electronic configuration, rather than the traditionally expected 4fⁿ⁺¹ 5d⁰ configuration known for Eu^II, Yb^II, Sm^II, and Tm^II.

Attempts have been made to validate the theoretical conclusions using electronic absorption spectroscopy and magnetic susceptibility.⁸ Although the UV-vis analyses showed intense bands that were consistent with the 4fⁿ 5d¹ configurations, forbidden 4f → 4f transitions typically used as diagnostics for lanthanide oxidations states were not experimentally resolved.^1,5,9 Similarly, the magnetic studies showed complicated magnetic behavior that could not be ubiquitously rationalized for all the lanthanides using simple models.^8d For these reasons, it was of great interest to evaluate the electronic structure of the Ln(C₅H₄SiMe₃)₃ ^1– complexes using a combination of X-ray absorption near-edge spectroscopy (XANES) and transition dipole moment density functional theory (DFT). There is an emerging body of literature demonstrating the power of cooperative XANES and DFT analyses in evaluating bonding and electronic structure in inorganic compounds.¹⁰ As such, we have recently used this approach to uniquely characterize the electronic structures of a wide variety of f-element species.¹¹

Herein, we describe the use of a combination of XANES and transition dipole moment DFT calculations to evaluate the possibility that the Ln^II(C₅H₄SiMe₃)₃ ^1– (Ln = Pr, Nd, Sm, Gd, Tb, Dy, Y, Ho, Er, Tm, Yb and Lu) compounds represent molecular Ln^II complexes. In the XANES experiment, an analyte is exposed to high-energy X-rays that excite core electrons to higher, unoccupied states. At the Ln L_3,2-edges, there is an edge-jump consisting of electric-dipole allowed transitions from Ln 2p-orbitals to unoccupied states that contain metal d-character. Moving to higher energies, core electrons are excited into the continuum (Scheme 2). Given that Ln L_3,2-edge XANES probes transitions to Ln 5d-orbitals, this spectroscopic approach provides a particularly sensitive and accurate method for directly characterizing 5d-orbital occupancies for the alleged 4fⁿ 5d¹ ions in Ln(C₅H₄SiMe₃)₃ ^1– (Ln = La, Ce, Pr, Nd, Gd, Tb, Dy, Ho, Er, and Lu) anions. To guide interpretations of these XANES spectra, appropriate ground-state DFT models were developed that formed a basis for extracting probability amplitudes from the transition dipole moments between the calculated excited-states and the ground-state. Combined, these computational and experimental efforts allow the influence of 4fⁿ⁺¹ 5d⁰ versus 4fⁿ 5d¹ electronic configurations on the lanthanide L₃-edge XANES spectra to be determined for the first time.

Scheme 2. Cartoon depicting the origin of L₃-edge XANES transitions.

To best characterize the electronic structure of the [K(2.2.2-cryptand)][Ln(C₅H₄SiMe₃)₃] salts containing new Ln^II ions, XANES and DFT studies are also reported with the compounds containing traditional +2 ions (i.e. Sm^II, Tm^II, and Yb^II) whose electronic configurations were well defined as 4f⁶, 4f¹³, and 4f¹⁴, respectively. These results provide a foundation for analyses of the other Ln(C₅H₄SiMe₃)₃ ^1– anions. For comparison, studies of the neutral 4fⁿ 5d⁰ Ln^III complexes, Ln(C₅H₄SiMe₃)₃, are also reported because the metal oxidation state in these compounds is unambiguously +3. These combined efforts lead to a definitive description of the electronic structure and bonding in the Ln(C₅H₄SiMe₃)₃ ^1– complexes. For the convenience of the reader in the rest of the paper, we refer to compounds with formal +3 oxidation states as Ln^III(C₅H₄SiMe₃)₃ and formal +2 oxidation states as Ln^II(C₅H₄SiMe₃)^1–. When discussing both, the Roman numerals are omitted and Ln(C₅H₄SiMe₃)₃ ^x– (x = 0, 1) is used.

Results

Sm L_3,2-edge XANES

The background-subtracted and normalized Sm L_3,2-edge XANES spectra from [K(2.2.2-cryptand)][Sm^II(C₅H₄SiMe₃)₃] and Sm^II(C₅Me₅)₂(THF)₂ are shown in Fig. 1. Each spectrum contains large edge features near 6715 eV (L₃) and 7310 eV (L₂) and small post-edge shoulders near 6725 and 7320 eV that are superimposed on step-like absorption thresholds. The L_3,2-edge positions were characterized by their peak maxima, where the first derivatives of the data equaled zero (Table 1). Given the sharp characteristics of these peaks, we find that the peak maximum provides a more useful metric than the inflection point, which is commonly used to evaluate actinide absorption edges. The L_3,2-edge peak maxima for Sm^II(C₅H₄SiMe₃)₃ ^1– at 6715.6 and 7311.1 eV are nearly identical to the 6715.2 and 7310.7 eV values determined for Sm^II(C₅Me₅)₂(THF)₂ and similar to the other Sm^II L_3,2-edge XANES spectra reported previously (Table 1).¹²

Fig. 1. The background-subtracted and normalized Sm L_3,2-edge XANES spectra obtained from Sm^III(C₅H₄SiMe₃)₃ (top, black trace), Sm^II(C₅Me₅)₂(THF)₂ (bottom, pink trace), and [K(2.2.2-cryptand)][Sm^II(C₅H₄SiMe₃)₃] (bottom, black dashed trace).

Table 1. Comparison of the peak maxima for Ln^III(C₅H₄SiMe₃)₃, [K(2.2.2-cryptand)][Ln^II(C₅H₄SiMe₃)₃] (Ln = Pr, Nd, Sm, Gd, Tb, Dy, Y, Ho, Er, Tm, Yb and Lu), Sm^II(C₅Me₅)₂(THF)₂, Sm^II[N(SiMe₃)₂](THF)₂, Sm^III[N(SiMe₃)₂]₃, TmI₂(THF)₃, and TmI₃(THF)_3.5. When possible, spectral differences between analogous Ln^II and Ln^III compounds have been included.

Compound	Edge	Peak position (eV) a	Δ(LnIII–LnII) peak position (eV)
PrII(C5H4SiMe3)3 1–	L2	6444.5	0.2
PrIII(C5H4SiMe3)3	L2	6444.7
NdII(C5H4SiMe3)3 1–	L2	6728.5	0.3
NdIII(C5H4SiMe3)3	L2	6728.8
SmII(C5H4SiMe3)3 1–	L3	6715.6	7.6
	L2	7311.1	7.3
SmIII(C5H4SiMe3)3	L3	6723.2
	L2	7318.4
SmII[N(SiMe3)2](THF)2	L3	6715.0	7.8
SmIII[N(SiMe3)2]3	L3	6722.8
SmII(C5Me5)2(THF)2	L3	6715.2	—
	L2	7310.7
GdII(C5H4SiMe3)3 1–	L3	7248.6	0.3
GdIII(C5H4SiMe3)3	L3	7248.9
TbII(C5H4SiMe3)3 1–	L3	7520.3	0.9
	L2	8258.1	1.0
TbIII(C5H4SiMe3)3	L3	7521.2
	L2	8259.1
DyII(C5H4SiMe3)3 1–	L3	7798.1	0.4
DyIII(C5H4SiMe3)3	L3	7798.5
HoII(C5H4SiMe3)3 1–	L3	8075.6	0.5
	L2	8922.3	0.3
HoIII(C5H4SiMe3)3	L3	8076.1
	L2	8922.6
ErII(C5H4SiMe3)3 1–	L3	8364.0	0.5
ErIII(C5H4SiMe3)3	L3	8364.5
TmII(C5H4SiMe3)3 1–	L3	8647.5	7.0
	L2	9617.1	6.6
TmIII(C5H4SiMe3)3	L3	8654.5
	L2	9623.7
TmIII2(THF)3	L3	8646.3	7.7
	L2	9616.0	7.0
TmIIII3(THF)3.5	L3	8653.8
	L2	9623.0
YbII(C5H4SiMe3)3 1–	L3	8942.7	7.3
YbIII(C5H4SiMe3)3	L3	8950.0
LuII(C5H4SiMe3)3 1–	L3	9244.4	1.9
LuIII(C5H4SiMe3)3	L3	9246.3
YII(C5H4SiMe3)3 1–	K	17 052.6, a 17 047.3 b	1.0
YIII(C5H4SiMe3)3	K	17 053.6, a 17 048.7 b

^aThe peak position points were defined as the first point at which the first derivative of the data equaled zero.

^bBecause the yttrium measurements were made at the Y K-edge, inflection points for Y^III(C₅H₄SiMe₃) and [K(2.2.2-cryptand)][Y^II(C₅H₄SiMe₃)] are reported.

The Sm L_3,2-edge XANES spectra obtained from Sm^II(C₅H₄SiMe₃)₃ ^1– and Sm^II(C₅Me₅)₂(THF)₂ are also compared with Sm^III(C₅H₄SiMe₃)₃ in Fig. 1. The Sm^III(C₅H₄SiMe₃)₃ L_3,2-edge spectra differ from the Sm^II spectra in that the edge features are shifted by approximately 7–8 eV to higher energies at 6723.2 and 7318.4 eV, Table 1. The differences in edge-positions for 4f⁶ 5d⁰ (+2) and 4f⁵ 5d⁰ (+3) samarium species are not unique to this suite of samarium cyclopentadienyl compounds.^10,13 For instance, the Sm L₃-edge XANES spectra obtained from Sm^II[N(SiMe₃)₂]₂(THF)₂ and Sm^III[N(SiMe₃)₂]₃, also exhibit a Sm L₃-edge energy difference of 7–8 eV (Fig. 2 and Table 1). These results demonstrate that samarium 4f-orbital occupancy (4f⁶ 5d⁰ versus 4f⁵ 5d⁰) influences the peak position more substantially than the ligand identity, as changing cyclopentadienide in Sm^III(C₅H₄SiMe₃)₃ to amido ligands in Sm^III[N(SiMe₃)₂]₃ only shifts the L₃-edge peak maximum to lower energy by 0.4 eV.

Fig. 2. The background-subtracted and normalized Sm L₃-edge XANES measurements obtained from the Sm^III[N(SiMe₃)₂]₃ (black trace) and Sm^II[N(SiMe₃)₂]₂(THF)₂ (pink dashed trace).

Comparisons between the Sm^II and Sm^III spectra provide insight into the origin of the small post-edge shoulders near 6725 and 7320 eV observed in all of the Sm^II spectra. As shown by the dashed lines in Fig. 1 and 2, this post-edge feature corresponds to the peak maximum of Sm^III. While the magnitude of this feature is invariant with temperature between 8 and 100 K, it shows significant intensity changes during our attempts to reproduce the data, e.g. from sample-to-sample. Hence, we attribute this feature to a small amount of Sm^III contamination, which likely arose from unwanted reactions with small amounts of O₂ or H₂O. Despite our best attempts, we were unsuccessful in obtaining completely pure Sm^II spectra; (1) analytes were shipped to the synchrotron cold and under vacuum, (2) XANES-samples were prepared at low temperature with rigorous exclusion of air and moisture immediately before the experiment, and (3) measurements were obtained rapidly (low temperature, under vacuum) using an unfocused beam. While it is difficult to identify what caused this contamination, the decomposition rate from X-ray radiolysis under our experimental conditions is slow. For example, when samples are cooled under vacuum (8 to 100 K; 10^–7 Torr), the Sm^II spectra are unchanged after 3 hours of exposure to X-rays using an unfocused beam on SSRL's beam line 11-2. These results suggest that the Sm^III species is not being generated during the XANES data acquisition. However, we identified under different experimental conditions – using a focused beam at room temperature under an argon atmosphere on SSRL's beam line 6-2 – that complete conversion of Sm^II(C₅H₄SiMe₃)₃ ^1– to Sm^III occurred in less than 10 seconds.

Tm and Yb L_3,2-edge XANES

The background-subtracted and normalized Tm L_3,2-edge XANES spectra from +2 and +3 thulium compounds are shown in Fig. 3. As observed for the samarium compounds in Fig. 1 and 2, spectra from the [K(2.2.2-cryptand)][Tm^II(C₅H₄SiMe₃)₃] and Tm^III₂(THF)₃ compounds display two main features. There are pronounced peaks near 8645 eV (L₃) and 9615 eV (L₂) and higher energy post-edge shoulders at approximately 8655 eV and 9625 eV. Comparisons with +3 thulium compounds – namely, Tm^III(C₅H₄SiMe₃)₃ and Tm^IIII₃(THF)_3.5 – lead us to interpret the Tm^II spectra in analogy to the Sm^II results described above. For instance, the large edge-features for Tm^II(C₅H₄SiMe₃)₃ ^1– and Tm^III₂(THF)₃ are about 7 eV lower in energy than the edge features from Tm^III(C₅H₄SiMe₃)₃ and Tm^IIII₃(THF)_3.5, Table 1. The spectral shapes and the trend toward lower energy for the Ln^II L₃-edges from Ln(C₅H₄SiMe₃)₃ ^x– (Ln = Tm, Sm; x = 0, 1) are consistent with models of the data generated using quantum chemical ab initio FEFF9.6 code based on the multiple scattering theory (see Fig. S1 and S2†).¹⁴

Fig. 3. The background-subtracted and normalized Tm L_3,2-edge XANES spectra obtained from Tm^III(C₅H₄SiMe₃)₃ (top, pink dashed trace), TmI₃(THF)_3.5 (top, black trace), [K(2.2.2-cryptand)][Tm^II(C₅H₄SiMe₃)₃] (bottom, pink trace), and TmI₂(THF)₃ (bottom, black dashed trace).

As observed in the Sm^II L_3,2-edge XANES experiments, the Tm^II spectra contain post-edge shoulders associated with small amounts of +3 thulium contamination. Variable temperature XANES experiments conducted between 8 and 100 K on these thulium compounds using a small excitation beam (1 × 1 mm) that was rastered across the sample show small variations in peak intensities. However, because the changes are not reversible and not reproducible, we attribute the slight variances to sample decomposition. Nevertheless, the compounds seem quite stable to X-ray radiation damage on the XANES experimental time scale (10 s to 1.5 h) under our experimental conditions; low temperature (8–100 K), under vacuum (10^–7 Torr), and in an unfocused beam on SSRL's beam line 11-2.

Despite minor Ln^III contamination in the Sm^II and Tm^II spectra, these results provide confidence and credibility in our abilities to manipulate extremely air and moisture sensitive organometallic complexes at the SSRL synchrotron facility. We remind the reader of the sensitivity of the Ln^III(C₅H₄SiMe₃)₃ compounds to hydrolysis, the highly reducing nature of Sm^II and Tm^II (which have standard reduction potentials of –1.5 and –2.3 V versus SHE),⁴ and of the light sensitivity of Tm^IIII₃(THF)_3.5. As noted previously,^12,15 the consistent 7–8 eV shift between Ln^II and Ln^III containing compounds highlights the utility of overcoming these sample handling challenges for characterizing Tm^II 4f¹³ 5d⁰ versus Tm^III 4f¹² 5d⁰ electronic configurations using L_3,2-edge XANES spectroscopy. Note that while not explicitly described here in detail, Fig. 4 shows that similar results were observed for ytterbium, whose spectrum, also displayed a peak maxima shift of ∼7 eV upon moving from Yb^II (4f¹⁴ 5d⁰) to Yb^III (4f¹³ 5d⁰).

Fig. 4. The background-subtracted and normalized L-edge XANES spectra obtained from Ln^III(C₅H₄SiMe₃)₃ (black traces) and [K(2.2.2-cryptand)][Ln^II(C₅H₄SiMe₃)₃] (pink traces) for Ln = Yb, Sm, Tm, Dy, Nd, Pr, Lu, Ho, Er, Tb and Gd. All spectra were collected at the Ln L₃-edge except Nd and Pr, which were collected at the L₂-edge. Peak maxima are shown in each pane. The spectra have been ordered from top to bottom based on increasing general reduction potentials.^4,16 .

Ln^II(C₅H₄SiMe₃)₃ ^1– Ln L_3,2-edge (Ln = Pr, Nd, Gd, Tb, Dy, Ho, and Er) XANES

The samarium, thulium, and ytterbium L_3,2-edge measurements described above provide an experimental basis for using XANES spectroscopy to evaluate the recently discovered Ln^II(C₅H₄SiMe₃)₃ ^1– (Ln = Pr, Nd, Gd, Tb, Dy, Ho, and Er) compounds.^1a,1b,8 Fig. 4 compares the background-subtracted and normalized Ln L₃- or L₂-edge XANES spectra from [K(2.2.2-cryptand)][Ln^II(C₅H₄SiMe₃)₃] with Ln^III(C₅H₄SiMe₃)₃. In this figure, the spectra are ordered from top to bottom as a function of increasing standard reduction potential, as determined by Morss and Mikheev.^4,16 These data display rising-edge features similar to the samarium and thulium spectra described above. However, in stark contrast to the samarium, thulium, and ytterbium spectra, the L-edge peak maxima from the other Ln^II(C₅H₄SiMe₃)₃ ^1– anions are quite similar in energy to the neutral Ln^III(C₅H₄SiMe₃)₃ compounds. As shown in Fig. 4 and Table 1, small shifts in L₃-edge inflection points are observed for the other Ln(C₅H₄SiMe₃)₃ ^x– (x = 0, 1) compounds, ranging from 0.2 to 1.0 eV.

To evaluate the likelihood that the spectra obtained from Ln^II(C₅H₄SiMe₃)₃ ^1– (Ln = Pr, Nd, Gd, Tb, Dy, Ho, and Er) compounds were indeed correct, a series of control experiments were conducted. Herein we limit the discussion explicitly to the Ho^II/Ho^III case. The first control experiment involved analyzing the Ho^II and Ho^III samples by electronic absorption spectroscopy before and after the Ho L_3,2-edge XANES experiment. Because the Ho^II(C₅H₄SiMe₃)₃ ^1– UV-vis spectrum is distinct from the Ho^III(C₅H₄SiMe₃)₃ precursor, electronic absorption spectroscopy provides a robust method for confirming the presence of Ho^II(C₅H₄SiMe₃)₃ ^1– during the XANES experiment. First, an aliquot of Ho^II(C₅H₄SiMe₃)₃ ^1– was characterized by UV-visible spectroscopy (black trace, Fig. 5; pre-XANES). The spectrum showed the characteristic and broad charge transfer band associated with Ho^II(C₅H₄SiMe₃)₃ ^1–. Moreover, no detectible Ho^III was observed. For comparison, the spectrum from Ho^III(C₅H₄SiMe₃)₃ is shown as a gray trace. A second aliquot of the Ho^II(C₅H₄SiMe₃)₃ ^1– was diluted in BN and the Ho L_3,2-edge XANES experiment was conducted. Subsequently, the sample – Ho^II(C₅H₄SiMe₃)₃ ^1– and BN – was transferred to a Teflon sealable quartz cuvette and the mixture was again characterized by UV-visible spectroscopy (pink trace, post-XANES). Unfortunately, because of constraints associated with the XANES holder, this transfer was not quantitative and the overall amount of Ho^II(C₅H₄SiMe₃)₃ ^1– in the cuvette was unknown. A 20% loss during the transfer is possible. Hence, the intensities in the pre-XANES spectrum cannot be directly compared with those from the post-XANES spectrum. Additionally, the BN in the post-XANES spectrum is insoluble and artificially increases the overall UV-visible baseline due to scattering effects. For data comparison, the post-XANES spectrum was background-subtracted to place overall peak heights on the same approximate absorbance scale. Regardless, this experiment unambiguously demonstrates that no detectable amount of Ho^III(C₅H₄SiMe₃)₃ was observed before or after the synchrotron experiment. One cannot rule out the possibility of insoluble Ho^III contaminates. For example, exposing a Teflon sealable cuvette containing the Ho^II(C₅H₄SiMe₃)₃ ^1– post-XANES samples to air for 2 s caused an immediate loss of Ho^II signal and no ingrowth of Ho^III 4f → 4f transitions. However, when one considers loss of sample during the transfer from the XANES holder to the cuvette, this control experiment suggests that after the Ho L_3,2-edge experiment >80% of the sample was in the form of Ho^II(C₅H₄SiMe₃)₃ ^1–.

Fig. 5. The background-subtracted UV-vis spectra obtained from Ho^III(C₅H₄SiMe₃)₃ (grey trace) and [K(2.2.2-cryptand)][Ho^II(C₅H₄SiMe₃)₃]. Data from Ho^II(C₅H₄SiMe₃)₃ ^1– were collected (1^st) before XANES analysis (black trace), (2^nd) after XANES analysis (pink trace), and (3^rd) after XANES analysis and exposure to air (green trace).

Additional support that the Ho L_3,2-edge XANES spectra obtained from Ho^II(C₅H₄SiMe₃)₃ ^1– was representative of the Ho^II organometallic was gleaned from a series of X-ray absorption decomposition experiments. For example, exposing Ho^II(C₅H₄SiMe₃)₃ ^1–, whose absorption peak is at 8075.6 eV, after XANES analysis to air caused the peak position to shift by 0.5 eV to 8076.0 eV, matching the 8076.1 eV peak in Ho^III(C₅H₄SiMe₃)₃. Analysis of the second derivative of the Ln^II versus Ln^III data additionally revealed a spectral diagnostic for the unconventional Ln^II(C₅H₄SiMe₃)₃ ^1– (Fig. S4†) compounds. For example, all of the +3 Ln^III(C₅H₄SiMe₃)₃ precursors contain a minimum in the second derivative approximately 2 eV lower in energy than the corresponding absorption peak. For Sm, Tm, and Yb, this feature is also persists after reduction to the Ln^II(C₅H₄SiMe₃)₃ ^1– complex. However, reduction to form unconventional divalents, Ln = Gd, Tb, Dy, Ho, Er, and Lu, caused the pre-edge features to disappear from the L₃-edges XANES spectra. This observation is documented by the 2^nd derivative plots shown in Fig. 6 for Ho(C₅H₄SiMe₃)₃ ^{x –} (x = 1, 0) (see ESI† for the other L₃-edge 2^nd derivative spectra). We remind the reader that a minimum in the 2^nd derivative indicates the presence of a peak in the XANES data. Fig. 6 shows the pre-edge peak at 8073.0 eV for Ho^III(C₅H₄SiMe₃)₃. If the transition corresponds to a Ln 2p → 5d excitation, 5d-orbital population in Ln^II(C₅H₄SiMe₃)₃ ^1– would shift this feature higher in energy (owing to electron pairing energy) and make it more difficult to resolve. Consistent with this proposition, for Sm, Tm, and Yb analytes – which have 4fⁿ 5d⁰ (for +3 metals) and 4fⁿ⁺¹ 5d⁰ (for +2 metals) electronic configurations with empty 5d orbitals (for both +3 and +2 metals) – pre-edge features were observed in both the +3 and +2 spectra. Regardless of its identity, this pre-edge feature is unexpectedly sensitive to the amount of Ln^III present in the Ln^II sample, as demonstrated by the Ho L₃-edge XANES measurement made on a 1 : 1 mixture of Ho^III(C₅H₄SiMe₃)₃ and Ho^II(C₅H₄SiMe₃)₃ ^1–, Fig. 6, which showed the pre-edge feature had a lower intensity than the pure Ho^III starting material. The absence of the extra feature in the Ln^II(C₅H₄SiMe₃)₃ ^1– L₃-edge XANES spectra provides a fortuitous alternative fingerprint for the Ln^II compounds with 4fⁿ 5d¹ electronic configurations. This is especially valuable when one considers that L₃/L₂ absorption peak area comparisons and branching ratio analyses were inconclusive (Table S1†), even for the Sm, Tm, and Yb analytes.

Fig. 6. The background-subtracted and normalized Ho L₃-edge XANES measurements obtained from Ho^III(C₅H₄SiMe₃)₃ (black dashed trace), [K(2.2.2-cryptand)][Ho^II(C₅H₄SiMe₃)₃] (pink dashed trace) complexes, and a mixture of Ho^III and Ho^II samples (green dashed trace). Second derivatives of the data are provides as solid traces. Note the pre-edge features (labeled with a red arrow) that are manifested as a minimum in the 2^nd derivative.

M^II(C₅H₄SiMe₃)₃ ^1– K- and L_3,2-edge XANES (M = Y, Lu)

The subtle rising edge energy shifts between Ln^II(C₅H₄SiMe₃)₃ ^1– and Ln^III(C₅H₄SiMe₃)₃ are reminiscent of those accompanying changes in oxidation state for transition metals (K- and L-edges),^17,18 not lanthanides. For example, changes in d-orbital occupancy only shift the K- and L-edges for transition metals by a few electron volts, which pales in comparison to the 7 eV shifts that accompany oxidation state changes in 4f-element chemistry. For example, the Y K-edge XANES data from Y^II(C₅H₄SiMe₃)₃ ^1– and Y^III(C₅H₄SiMe₃)₃ show a 1.4 eV inflection point shift (Fig. 7, Table 1), which is consistent with the computational results generated using quantum chemical ab initio FEFF9.6 code based on the multiple scattering theory (see Fig. S3†).¹⁴ Hence, both experiment and theory indicate that Y^III(C₅H₄SiMe₃)₃ has a 4d⁰ electronic configuration and Y^II(C₅H₄SiMe₃)₃ ^1– a 4d¹ configuration. These Y K-edge XANES results agree with the previous analyses of Y^II(C₅H₄SiMe₃)₃ ^1– (UV-vis, EPR, structural metrics)^1c and – to the best of our knowledge – represent the first Y K-edge XANES spectrum of a molecule containing Y^II. Also consider data from the Lu(C₅H₄SiMe₃)₃ ^x– (x = 0, 1) pair. Lutetium in the +3 oxidation state has a full 4f-shell. Hence reduction of Lu^III(C₅H₄SiMe₃)₃, with a 4f¹⁴ 5d⁰ electron configuration, has to generate a 4f¹⁴ 5d¹ configuration in Lu^II(C₅H₄SiMe₃)₃ ^1–. Consistent with 5d-orbital occupation, the peak maxima difference between Lu^III and Lu^II in the Lu L_3,2-edge XANES was small, measured at 1.9 eV.

Fig. 7. The background-subtracted and normalized Y K-edge XANES measurements obtained from Y^III(C₅H₄SiMe₃)₃ (black trace) and [K(2.2.2-cryptand)][Y^II(C₅H₄SiMe₃)₃] (pink dashed trace) complexes.

Taken in the context of these Y(C₅H₄SiMe₃)₃ ^x– and Lu(C₅H₄SiMe₃)₃ ^x– (x = 0, 1) XANES measurements – alongside (1^st) the experiments we conducted showing our XANES samples contained only marginal quantities of Ln^III decomposition products, and (2^nd) previously reported UV-vis data, structural metrics, previous computational results – the most plausible interpretations of these Ln L₃-edge XANES data (Fig. 4) is that reduction of Ln^III(C₅H₄SiMe₃)₃ to form an unconventional Ln^II(C₅H₄SiMe₃)₃ ^1– compound resulted in addition of an electron into a highly shielded 5d-orbital to generate a 4fⁿ 5d¹ electronic configuration, not 4fⁿ⁺¹ 5d⁰. Although we anticipate that the spectra in Fig. 4 contain some Ln^III contamination – in analogy to the Sm^II and Tm^II spectra in Fig. 1 to 3 – the computational results below provide even more support for the alternative electronic configuration.

Electronic structure calculations

To better understand the origin for the spectroscopic differences between Ln^III(C₅H₄SiMe₃)₃ versus Ln^II(C₅H₄SiMe₃)₃ ^1–, electronic structure calculations were conducted on a subset of Ln(C₅H₄SiMe₃)₃ ^x– (Ln = Sm, Ho; x = 0, 1) complexes. This analysis compares Sm^II(C₅H₄SiMe₃)₃ ^1–, which is unambiguously +2, with Ho^II(C₅H₄SiMe₃)₃ ^1–, where the electronic configuration is ambiguous. Calculations for the Ln^II(C₅H₄SiMe₃)₃ ^1– compounds were restricted to just Sm and Ho, as a follow-on manuscript will compare theoretical results from the other Ln^II compounds with other +2 lanthanide and actinide species. Initially, DFT/PBE calculations were conducted to optimize the geometric structures of Ln(C₅H₄SiMe₃)₃ ^x– (x = 1, 0), see Table 2 for a comparison of experimental and calculated distances and Table S2 (ESI†) for the coordinates. The computational results reveal a ground-state 4f⁵ 5d⁰ electronic configuration (sextet state) for Sm^III(C₅H₄SiMe₃)₃ and a 4f⁶ 5d⁰ (septet state) configuration for Sm^II(C₅H₄SiMe₃)₃ ^1–. Because of the near-degeneracy of 4f-orbitals and the accompanying marginal participation in metal–ligand covalent bonding,^11e varying 4f-occupations of the ground-state spin multiplicity has little effects on the geometric structures and spectra. The average 2.513 Å Sm^III–C_centroid distance is calculated to be 0.092 Å shorter than the 2.605 Å Sm^II–C_centroid distance. This difference is consistent with the differences in Sm^III versus Sm^II ionic radii¹⁹ and changes in electrostatic interactions between Sm^III versus Sm^II with C₅H₄SiMe₃ ^1– anions. These calculated distances compare well with experimental results^8a and are within the typical error of 2% observed for GGA functionals.

Table 2. The DFT/PBE calculated and experimental Ln–C_centroid (Cnt) distances (Å) from Ln^III(C₅H₄SiMe₃)₃ and Ln^II(C₅H₄SiMe₃)₃ ^1– (Ln = Sm, Ho). Structural metrics from Ho^II(C₅H₄SiMe₃)₃ ^1– with 4f¹⁰ 5d¹ versus 4f¹¹ 5d⁰ electronic configurations were also compared.

Sm(C5H4SiMe3)3 x– (x = 0, 1)
	SmIII, 4f5 5d0		SmII, 4f6 5d0		Δ(SmII–SmIII)
	PBE	Exp8a	PBE	Exp8a	PBE	Exp8a
Sm–Cnt1	2.508	2.459	2.610	2.603	0.102	0.144
Sm–Cnt2	2.512	2.459	2.595	2.607	0.083	0.148
Sm–Cnt3	2.519	2.464	2.609	2.615	0.090	0.151
Avg(Sm–Cnt)	2.513	2.461	2.605	2.608	0.092	0.147

Ho(C5H4SiMe3)3 x– (x = 0, 1)
	HoIII, 4f10 5d0		HoII, 4f10 5d1		HoII, 4f11 5d0	Δ[HoII (4f10 5d1)–HoIII]
	PBE	Exp1b	PBE	Exp1b	PBE	PBE	Exp1b
Ho–Cnt1	2.438	2.391	2.477	2.417	2.536	0.039	0.026
Ho–Cnt2	2.441	2.393	2.461	2.420	2.509	0.020	0.027
Ho–Cnt3	2.448	2.398	2.481	2.432	2.517	0.033	0.034
Avg(Ho–Cnt)	2.442	2.394	2.473	2.423	2.521	0.031	0.029

Consistent with previous hybrid DFT calculations that employed no less than 25% Hartree–Fock (HF) exchange,^1b our calculations show the ground-state electronic structure of Ho^III(C₅H₄SiMe₃)₃ is 4f¹⁰ 5d⁰ (quintet state), whereas Ho^II(C₅H₄SiMe₃)₃ ^1– has a 4f¹⁰ 5d¹ configuration (sextet state). For example, calculations with the BHandHLYP functional show the 4f¹⁰ 5d¹ electronic configuration is 27 kcal mol^–1 more stable than the alternative 4f¹¹ 5d⁰ configuration (quartet state). In contrast, calculations with functionals that included less HF exchange (PBE, BLYP, and B3LYP) incorrectly predict the alternative Ho^II 4f¹¹ 5d⁰ configuration as the ground-state (see details in Tables S2 and S3 of the ESI†).^1b,1c,8a,8d That is to say, GGA and hybrid functionals with lower HF exchange percentages fail to give the correct Ho^II(C₅H₄SiMe₃)₃ ^1– spin state, which is likely attributable to the delocalization error.^20,21 Many reports have described how increasing HF exchange improves the calculated energetics by DFT-based methods such as excitation energy,²² thermochemical kinetics,²³ reaction barriers,²⁴ and electron detachment energy.²⁵ Consistently, our DFT/PBE calculated Ho^III (4f¹⁰ 5d⁰)–C_centroid and Ho^II (4f¹⁰ 5d¹)–C_centroid distances are in excellent agreement with experimental values (Table 2), while the Ho^II (4f¹¹ 5d⁰)–C_centroid distances are longer than the experimental results by ∼0.1 Å.^1b,1c These results provide confidence in assigning Ho^II as having a 4f¹⁰ 5d¹ electronic configuration. We refer the interested reader to the experimental section for details of the electronic structure calculation.

To better understand the unusual electronic configuration of Ho^II(C₅H₄SiMe₃)₃ ^1–, we found it instructive to interpret the DFT calculations using traditional molecular orbital descriptions derived from group theory considerations of M(C₅H₅)₃ in C _3h-symmetry. Hence, a qualitative MO level diagram for the C _3h–Ho^II(C₅H₅)₃ ^1– anion is provided in Fig. 8. As the molecular orbital interactions associated with Ln^III(C₅R₅)₃ (R = H or alkyl) have been the subject of numerous theoretical and spectroscopic studies,²⁶ this discussion is confined to those orbitals most relevant to the Sm and Ho L_3,2-edge XANES measurements. In contrast to previous theoretical results for M^III(C₅H₅)₃ in D _3h- or C _3v-symmetry,^{26b,c,d,g,h,i,j} we find it more appropriate to describe the MO-interaction using C _3h-symmetry, as this designation more closely mimics data from the crystal structure of Ho^II(C₅H₄SiMe₃)₃ ^1–.

Fig. 8. A qualitative molecular diagram showing molecular orbital interactions in C _3h-symmetry for Ho^II(C₅H₅)₃ ^1–.

In the C _3h-point group, symmetry allowed mixing between the metal 5d- and cyclopentadienyl π-orbitals – perpendicular to the ring planes – generates bonding interactions of a′, e′, and e′′ symmetries, which were σ- π- and δ-bonding with respect to the metal–cyclopentadienyl centroid axes, Fig. 8. Superimposed on this molecular orbital picture, and at lower energy, are Ln–(C₅H₅) σ-, π- and δ-bonding orbitals of a′, a′′, e′, and e′′ symmetries that originate from mixing between the 4f-orbitals and cyclopentadienyl π-orbitals. In general, the Ln(C₅H₄SiMe₃)₃ ^x– (x = 0, 1) compounds exhibit little 4f- and cyclopentadienyl orbital mixing, such that the seven primarily 4f-orbitals span a narrow energy range. In contrast, substantial mixing occurs between the Ln 5d- and cyclopentadienyl π-orbitals, with the exception of the 5d-orbital of 3a′ symmetry (d _z2). Consistent with previous reports,^1b metal–cyclopentadienyl mixing is inhibited in this 3a′ orbital by poor spatial overlap. Hence, the 3a′ orbital is primarily composed of 5d- and 6s-character and best described as a non-bonding 5d-orbital. For Sm^III(C₅H₄SiMe₃)₃ (4f⁵ 5d⁰), Sm^II(C₅H₄SiMe₃)₃ ^1– (4f⁶ 5d⁰), and Ho^III(C₅H₄SiMe₃)₃ (4f¹⁰ 5d⁰), the 3a′ orbital is empty. As testament, the BHandHLYP calculations at PBE optimized ground-state geometries show the Mulliken net spin densities²⁷ to be almost exclusively distributed on 4f-orbitals (Table 3). Meanwhile, for the Ho^II(C₅H₄SiMe₃)₃ ^1– anion (4f¹⁰ 5d¹), significant 6s- and 5d-spin density distribution associated with the highest alpha spin occupied orbital indicates that the 3a′ orbital is singly occupied. A summary of the spin multiplicity results is provided in Table 3. The differences between the 4fⁿ⁺¹ 5d⁰ versus 4fⁿ 5d¹ electronic configurations of the Ln^II ions is observed to influence the metal–cyclopentadienyl bond distances and, as discussed below, is found to significantly impact the Ln L₃-edge XANES spectrum.

Table 3. The spin multiplicity (2S + 1), total S², Mulliken net spin density for lanthanide atomic electron valence orbitals (s, d, f) calculated for Ln(C₅H₄SiMe₃)₃ ^x– (Ln = Sm, Ho; x = 0, 1) using DFT/BHandHLYP.

Compound		2S + 1	S2	Spin	s	d	f
SmIII(C5H4SiMe3)3	4f5 5d0	6	8.77	5.14	0.01	0.09	5.03
SmII(C5H4SiMe3)3 1–	4f6 5d0	7	12.01	6.04	0.01	0.06	5.96
HoIII(C5H4SiMe3)3	4f10 5d0	5	6.00	4.04	0.00	0.04	3.97
HoII(C5H4SiMe3)3 1–	4f10 5d1	6	8.76	4.86	0.22	0.62	3.98
HoII(C5H4SiMe3)3 1–	4f11 5d0	4	3.76	3.02	0.00	0.01	3.01

To support the results from the ground-state DFT calculations, CASPT2/CASSCF calculations were performed on the ground-states and low excited-states of simplified Ln(C₅H₅)₃ ^x– (Ln = Sm, Ho; x = 0, 1) complexes. The DFT/PBE optimized geometries of Ln(C₅H₄SiMe₃)₃ ^x– were used; however, to reduce the computational cost SiMe₃ substituents were replaced with protons having C–H bond lengths of 1.088 Å. Two possibilities were investigated for Ho^II(C₅H₅)₃ ^1–. The first was associated with the calculated structure of Ho^II(C₅H₄SiMe₃)₃ ^1– with a 4f¹⁰ 5d¹ ground-state electronic configuration. The second investigated Ho^II(C₅H₅)₃ ^1– geometry was based on the calculated 4f¹¹ 5d⁰ Ho^II(C₅H₄SiMe₃)₃ ^1– structure. Although efforts were made to include all the seven 4f and five 5d orbitals into the active space, the converged CASSCF results for Sm(C₅H₅)₃ ^x– (x = 0, 1) showed that the five 5d-orbitals were not correlated and removed from the active space. Meanwhile for Ho(C₅H₅)₃ ^x– (x = 0, 1), only the 5d_z2-orbital remained in the active space. Hence, the active space calculations were adjusted to include all seven 4f-orbitals for Sm(C₅H₅)₃ ^x– (x = 0, 1) and an additionally 5d_z2-orbital for Ho(C₅H₅)₃ ^x– (x = 0, 1). The results generated a complete active space of 6-electrons with 7-orbitals for Sm^II(C₅H₅)₃ ^1–, 5-electrons and 7-orbitals for Sm^III(C₅H₅)₃, 11-electrons and 8-orbitals for Ho^II(C₅H₅)₃ ^1–, and 10-electrons with 8-orbitals for Ho^III(C₅H₅)₃.

Although subtle differences were observed, the ground-state electronic structure results from the CASPT2/CASSCF calculations are similar to those obtained by DFT (Table 4). The “core-like” and nearly degenerated 4f-orbitals resulted in different 4f-occupations with nearly the same energies. The CASPT2/CASSCF results show that Sm^III(C₅H₅)₃ has ground sextet state of 4f⁵ configurations and that Sm^II(C₅H₅)₃ ^1– has ground septet state of 4f⁶ configuration, which are the same as DFT results. In the holmium case, Ho^III(C₅H₅)₃ has ground quintet state of 4f¹⁰ 5d⁰. For Ho^II, both geometries showed a sextet with 4f¹⁰ 5d¹ configurations. These Ho^II and Ho^III results were identical to the DFT calculations. Hence, in terms of evaluating ground-state electronic structures for the Ln(C₅H₅)₃ ^x– (x = 0, 1), the CASPT2/CASSCF results are in excellent agreement with the reported DFT results from Ln(C₅H₄SiMe₃)₃ ^x– (x = 0, 1).

Table 4. Ground-states configurations from Ln(C₅H₅)₃ ^x– (Ln = Sm, Ho; x = 0, 1) complexes from CASPT2/CASSCF calculations. ^a Geometries relied on the DFT/PBE optimized geometries of Ln(C₅H₄SiMe₃)₃ ^x–. However, for Ho^II(C₅H₅)₃ ^1– two geometries were investigated that were derived from the calculated Ho^II(C₅H₃SiMe₃)₃ ^1– structures with either 4f¹⁰ 5d¹ or 4f¹¹ 5d⁰ electronic configurations.

Ground-state	Configurations
Sm II (C 5 H 5 ) 3 1–
X7A	100%(1a12a13a14a15a16a17a0)
Sm III (C 5 H 5 ) 3
X6A	58%(1a12a13a14a15a16a07a0) + 41%(1a12a13a14a05a06a17a1)
Ho(C 5 H 5 ) 3 1– ; geometry from Ho II (C 5 H 4 SiMe 3 ) 3 1– (4f 10 5d 1 ) b
X6A	71%(1a22a23a14a25a16a17a18a1) + 21%(1a22a13a24a15a26a17a18a1) + 7%(1a12a23a24a15a16a27a18a1)
Ho(C 5 H 5 ) 3 1– ; geometry from Ho II (C 5 H 4 SiMe 3 ) 3 1– (4f 11 5d 0 ) b
X6A	70%(1a22a23a14a25a16a17a18a1) + 21%(1a22a13a24a15a26a17a18a1) + 7%(1a12a23a24a15a16a27a18a1)
Ho(C 5 H 5 ) 3
X5A	65%(1a22a13a24a15a26a17a18a0) + 20%(1a22a23a14a25a16a17a18a0) + 5%(1a12a23a24a15a16a17a28a0) + 2%(1a22a13a14a15a26a27a18a0) + 1%(1a22a13a14a25a26a17a18a0) + 1%(1a22a13a24a15a16a17a28a0) + 1%(1a22a23a24a15a16a17a18a0)

^a1a-7a are 4f orbitals, and 8a is 5d orbital.

^bRefer to the DFT/PBE calculated ground-state geometrics for Ho^II(4f¹⁰5d¹) and Ho^II(4f¹¹5d⁰), respectively, shown in Table 2.

Spectral simulations

The open-shell Sm and Ho L₃-edge XANES spectra from Ln(C₅H₄SiMe₃)₃ ^x– (Ln = Sm, Ho; x = 0, 1), were calculated using the transition dipole moment approach based on the Kohn–Sham ground-state molecular orbitals. Using this method the core excitation energies were calculated as the energy differences between occupied and virtual orbitals. Previous studies have demonstrated that this approach provides a sound basis for interpreting the experimental XANES spectra.²⁸ BHandHLYP simulated Ln L₃-edge XANES spectra from Ln(C₅H₄SiMe₃)₃ ^x– are compared with experimental results in Fig. 9 and 10. In these figures, the calculated spectra were shifted by a constant 241.49 eV (Sm) and 348.17 eV (Ho) to line up the Ln^III(C₅H₄SiMe₃)₃ L₃-edge peaks, which in turn accounts for omission of the atomic and extra-atomic relaxation associated with the core excitation, relativistic stabilization, and errors associated with the functionals.^29,30 In the Ln^II cases, two options were explored, transitions that involved conventional electronic configurations, Ln^II 2p⁶…4fⁿ⁺¹ 5d⁰ → Ln^II 2p⁵…4fⁿ⁺¹ 5d¹, and alternatives that involved 5d-orbital occupations, Ln^II 2p⁶…4fⁿ 5d¹ → Ln^II 2p⁵…4f¹ 5d². The resulting near edge energies are summarized in Table 5 alongside analogous values acquired using PBE, BLYP, and B3LYP functionals.

Fig. 9. A comparison of the experimental (•) and transition dipole moment calculations (pink traces) for the Sm L₃-edge XANES measurements obtained from Sm^III(C₅H₄SiMe₃)₃ (top) and [K(2.2.2-cryptand)][Sm^II(C₅H₄SiMe₃)₃] (bottom). The calculated spectra were shifted by a constant 241.49 eV, which aligned the Sm^III(C₅H₄SiMe₃)₃ experimental and calculated edge peak.

Fig. 10. A comparison of the experimental (•) and transition dipole moment calculations (pink and green traces) for the Ho L₃-edge XANES obtained from Ho^III(C₅H₄SiMe₃)₃ (top) and [K(2.2.2-cryptand)][Ho^II(C₅H₄SiMe₃)₃] (bottom). The calculated spectra were shifted by a constant 348.17 eV, which aligned the Ho^III(C₅H₄SiMe₃)₃ experimental and calculated edge peak.

Table 5. DFT calculated and experimental peak maximum for the Ln(C₅H₄SiMe₃)₃ ^{x –} (Ln = Sm, Ho; x = 0, 1) XANES spectra.

		PBE	BLYP	B3LYP	BHandHLYP	Exp.
SmIII(C5H4SiMe3)3	4f5 5d0	6873.4	6874.8	6910.7	6964.6	6723.2
SmII(C5H4SiMe3)3 1–	4f6 5d0	6870.8	6872.2	6906.1	6958.1	6715.6
Δ[SmIII–SmII]		2.6	2.6	4.6	6.5	7.6
HoIII(C5H4SiMe3)3	4f10 5d0	8325.6	8327.1	8366.6	8424.5	8076.1
HoII(C5H4SiMe3)3 1–	4f10 5d1	8325.8	8327.3	8366.2	8423.8	8075.6
HoII(C5H4SiMe3)3 1–	4f11 5d0	8322.6	8324.1	8361.1	8418.0	—
Δ[HoIII–HoII (4f10 5d1)]		–0.2	–0.2	0.4	0.7	0.5
Δ[HoIII–HoII (4f11 5d0)]		3.0	3.0	5.5	6.5	—

The theoretical analyses reveal the primary contributions to the Ln L₃-edge XANES spectra are electric dipole allowed excitations from Ln 2p-orbitals to unoccupied states that contain metal d-character. Of the functionals explored, the L₃-edge energy differences calculated using BHandHLYP were in best agreement with the experiment. For example, in the Sm(C₅H₄SiMe₃)₃ ^x– case, where the 4f- and 5d-orbital occupancies are well established, energy differences between the Sm^III (4f⁵ 5d⁰) and Sm^II (4f⁶ 5d⁰) L₃-edge positions are calculated to be 6.5 eV, which is in good agreement with the measured value of 7.6 eV. Results from the B3LYP calculations modestly agree with the experimental data, while larger deviations are observed using BLYP and PBE. The two GGA functionals, BLYP and PBE, without any HF exchange give the same L₃-edge energy difference. This comparison (BHandHLYP, B3LYP, BLYP, and PBE) unambiguously shows the importance of Hartree–Fock (HF) exchange in computationally evaluating L₃-edge XANES spectra. This result highlights the importance of high HF exchange in correctly capturing electron transition energies and is consistent with conclusions from previous theoretical studies.²²

Calculations on Ho(C₅H₄SiMe₃)₃ ^x– are similar to those from Sm(C₅H₄SiMe₃)₃ ^x– in that the BHandHLYP provides the best agreement with the experimental data (Table 5), e.g. energy differences between the Ho^III (4f¹⁰ 5d⁰) and Ho^II (4f¹⁰ 5d¹) L₃-edge peak maxima are calculated to be 0.7 eV and measured to be 0.5 eV. The Ho(C₅H₄SiMe₃)₃ ^x– calculations differ in that they invoke the Ho^II low energy 4f¹⁰ 5d¹ ground-state electronic configuration. We note that calculations involving the higher energy 4f¹¹ 5d⁰ Ho^II electronic configuration grossly overestimate the Ho^III/Ho^II L₃-edge energy by 6.5 eV.

To better understand the how 4f- versus 5d-orbital occupancy influence Ln L₃-XANES spectra, the ground-state 2p-orbital energies are plotted alongside the average 5d- and 6d-orbital energies in Fig. 11 for Ln(C₅H₄SiMe₃)₃ ^x– (Ln = Sm, Ho; x = 0, 1). We remind the reader that the major contributors to the Ln(C₅H₄SiMe₃)₃ ^x– L₃-edge XANES spectra result from dipole allowed transitions between core 2p- and unoccupied d-orbitals. Upon reduction of Ln^III to Ln^II, the 2p-, 5d-, and 6d-orbital energies increase. For both Sm and Ho, adding the electron into the 4f-shell, Ln^III (4fⁿ 5d⁰) + 1e^1– → Ln^II (4fⁿ⁺¹ 5d⁰), raises the Ln 2p- and 5d-/6d-orbital energies by 11.5–12.0 eV and 5.0–5.5 eV, respectively. These changes in orbital energies account for Sm^II(C₅H₄SiMe₃)₃ ^1– L₃-edge excitation energy being ∼7 eV less than that of Sm^III(C₅H₄SiMe₃)₃. Adding the electron into 5d-shell, Ln^III (4fⁿ 5d⁰) + 1e^1– → Ln^II (4fⁿ 5d¹), also increases the Ln 2p- and 5d-/6d-orbital energies; however, to a lesser extent. Most notably for the 2p-orbitals. For example, the Ho 2p- and 5d/6d-average orbital energies increase by 4.6 eV and 3.9 eV, respectively. This modest energy shift decreases the L₃-edge excitation energy for Ho^II(C₅H₄SiMe₃)₃ ^1– by <1 eV in comparison to Ho^III(C₅H₄SiMe₃)₃. Overall, these results demonstrate that Ln 2p-electrons experienced stronger Coulomb repulsion from Ln 4f-electrons than higher lying 5d-electrons. We additionally correlate the magnitude of this repulsion with the radial distribution of the 4f- versus 5d-orbitals. Because the 4f-orbitals are closer to the nucleus,³¹ increased 4f-orbital occupancy destabilizes the core 2p-orbital energies to a large extent. Meanwhile, occupancy of the more diffuse 5d-orbitals has less impact on the 2p-orbital energies.

Fig. 11. Quantitative comparison of ground-state 2p- and average 5d/6d-orbital energies from Ln(C₅H₄SiMe₃)₃ ^x– (Ln = Sm, Ho; x = 0, 1) for a variety of electronic configurations. The solid arrow represents the excitation energy associated with the Ln L₃-edge excitation. To plot both Sm and Ho on the energy scale, the energies associated with the Ln^III 2p-orbitals were set to zero.

Discussion

Herein we describe the use of XANES spectroscopy to characterize the electronic configurations of formally +2 lanthanide compounds of the general formula Ln^II(C₅H₄SiMe₃)₃ ^1–. Through comparisons with a carefully selected series of standards, including Ln^III(C₅H₄SiMe₃)₃, our XANES results from Sm^II(C₅H₄SiMe₃)₃ ^1–, Tm^II(C₅H₄SiMe₃)₃ ^1– and Yb^II(C₅H₄SiMe₃)₃ ^1–demonstrate that these compounds contained Ln^II ions with 4f⁶ 5d⁰ (Sm^II), 4f¹³ 5d⁰ (Tm^II), and 4f¹⁴ 5d⁰ (Yb^II) electronic configurations. These results are in agreement with previously acquired spectroscopic data, i.e. UV-vis, magnetic susceptibility, and the Ln–C_centroid distances (which were ∼0.1 Å longer than the Ln^III analogue). Consistent with previous studies,^8a,8d the measurements highlight the utility of Ln L_3,2-edge XANES spectroscopy in characterizing f-orbital occupancies from Ln^III (4fⁿ 5d⁰) and Ln^II (4fⁿ⁺¹ 5d⁰) ions. For example, changes in 4f-electron occupancy shift the Ln peak maxima in the L_3,2-edges by approximately 7 eV. The magnitude of these shifts is impressive in comparison to transition metal K- and L-edge XANES experiments,^17,18 where changes in d-orbital occupancies are known to shift absorption edges by only a few eV.

The Ln L-edge XANES studies from Ln(C₅H₄SiMe₃)₃ ^x– (Ln = Pr, Nd, Gd, Tb, Dy, Ho, and Er; x = 0, 1) show much smaller shifts in rising-edge energies than the samarium, thulium, and ytterbium analogues. For example, the peak maxima differences between Ln^III(C₅H₄SiMe₃)₃ and Ln^II(C₅H₄SiMe₃)₃ ^1– range from only 0.2 to 1.0 eV (Table 1). These values are substantially less than the 7–8 eV change expected for an increase in 4f-orbital occupancy, i.e. Ln^III (4fⁿ 5d⁰) + e^1– → Ln^II (4fⁿ⁺¹ 5d⁰). Instead, the 0.2 to 1.0 eV shifts are reminiscent of the those accompanying the reduction of Y^III(C₅H₄SiMe₃)₃ (4d⁰) to Y^II(C₅H₄SiMe₃)₃ ^1– (4d¹) and Lu^III(C₅H₄SiMe₃)₃ (4f¹⁴ 5d⁰) to Lu^II(C₅H₄SiMe₃)₃ ^1– (4f¹⁴ 5d¹). In these yttrium and lutetium scenarios, the increase in d-orbital occupancy shifts the peak maximum by only ~1 eV (inflection point change of 1.4 eV) and 1.9 eV, respectively. These shifts provide strong evidence that the yttrium ion in Y^II(C₅H₄SiMe₃)₃ ^1– is best described as +2 with a 4d¹ electronic configuration and that the lutetium ion in Lu^II(C₅H₄SiMe₃)₃ ^1– is +2 with a 4f¹⁴ 5d¹. Given that shifts from Ln(C₅H₄SiMe₃)₃ ^x– (Ln = Pr, Nd, Gd, Tb, Dy, Ho, and Er; x = 0, 1) were also small, we initially questioned the possibility that reduction of Ln^III(C₅H₄SiMe₃)₃ (4fⁿ 5d⁰) generated a lanthanide ion with a 4fⁿ 5d¹ electronic configuration, instead of the more typical 4fⁿ⁺¹ 5d⁰ configuration.

To better understand the Ln L₃-edge XANES spectra from Ln(C₅H₄SiMe₃)₃ ^x– (x = 0, 1), DFT calculations were conducted on the Sm(C₅H₄SiMe₃)₃ ^x– and Ho(C₅H₄SiMe₃)₃ ^x– analytes. Consistent with previous reports, the ground-state DFT calculations show the electronic configurations for Sm^III(C₅H₄SiMe₃)₃, Sm^II(C₅H₄SiMe₃)₃ ^1–, and Ho^III(C₅H₄SiMe₃)₃ are Sm^III 4f⁵ 5d⁰, Sm^II 4f⁶ 5d⁰, and Ho^III 4f¹⁰ 5d⁰, respectively. In contrast for Ho^II(C₅H₄SiMe₃)₃ ^1–, the calculations indicate that the ground-state electronic configuration is 4f¹⁰ 5d¹, with the non-bonding 5d_z2-orbital of a′-symmetry being singly occupied. CASPT2/CASSCF calculations on the simplified models, Ln(C₅H₅)₃ ^x– (Ln = Sm, Ho; x = 0, 1), were completely consistent with the assignments of the DFT calculations. As such the Ln L₃-edge XANES spectra were simulated using transition dipole moment calculations for a variety of electronic configurations, spanning Ln^III 4fⁿ 5d⁰, Ln^II 4fⁿ⁺¹ 5d⁰, and Ln^II 4fⁿ 5d¹. For both Sm and Ho, the calculations suggest that reducing Ln^III (4fⁿ 5d⁰) by adding an electron in the 4f-manifold to generate Ln^II (4fⁿ⁺¹ 5d⁰) appreciably shifts the Ln L₃-edge by approximately 7 eV. In contrast, reducing Ln^III (4fⁿ 5d⁰) by adding an electron into the 5d-manifold to generate Ln^II (4fⁿ 5d¹) slightly shifts the Ln L₃-edge to lower energy (on the order of ∼1 eV).

Concluding remarks

Our results indicate that the differences in Ln(C₅H₄SiMe₃)₃ ^x– (Ln = Sm, Ho; x = 0, 1) excitation energies stem from electron repulsion between 2p- and either 5d- or 4f-electrons (Fig. 11). For example, increases in Ln 4f-orbital occupation significantly destabilize the core 2p-orbital energy levels, which decrease the Ln L₃-edge excitation energy by ∼7–8 eV. In contrast, increased occupancy for the more diffuse 5d-orbitals has marginal impact on core 2p-energy levels and the Ln L₃-edge excitation energy (0.2–1.9 eV). One might describe the 4f¹⁰ 5d¹ electron configuration in Ho^II(C₅H₄SiMe₃)₃ ^1– as mimicking the 4f¹⁰ electronic configuration in Ho^III(C₅H₄SiMe₃)₃, with the extra electron ‘hidden’ in a highly shielded 5d-orbital. We anticipate that this interpretation is quite general and will be used to explain the similar Ln^II/Ln^III peak maxima shifts and Ln^II/Ln^III–C_centroid bond distances in the other Ln(C₅H₄SiMe₃)₃ ^x– (Ln = Pr, Nd, Gd, Tb, Dy, Er, and Lu; x = 0, 1) compounds. Hence, our current computational and spectroscopic efforts are focused on evaluating recently reported compounds that contain formally lanthanide(ii) and actinide(ii) ions.

Among the numerous examples where ligand environments with C ₃-symmetry have been exploited to advance transition metal and f-element chemistry,³² our results highlight another extraordinary property associated with a C ₃-ligand framework. For example, we identified that the tris-cyclopentadienyl coordination environment provides a mechanism for stabilizing Ln^II 4fⁿ 5d¹ electronic configurations through the accessibility of a low-lying 5d-orbital of a′ symmetry. The results additionally suggest an electronic structure break between Tm^II(C₅H₄SiMe₃)₃ ^1– and Dy^II(C₅H₄SiMe₃)₃ ^1–. It appears that 4fⁿ⁺¹ 5d⁰ electronic configurations are most stable when the reduction potentials for the lanthanide ions in Ln^II(C₅H₄SiMe₃)₃ ^1– are less than or equal to that of Tm^II(C₅H₄SiMe₃)₃ ^1–. Meanwhile, those with reduction potentials greater than or equal to Dy^II(C₅H₄SiMe₃)₃ ^1– are best described as 4fⁿ 5d¹. While the generality of this interpretation has yet to be determined, we anticipate – based on previous studies on LnX₂ (X = halide) – that the electronic structure breaking point is quite dynamic and can shift to higher reduction potentials, i.e. those of Dy^II and Nd^II, depending in the ligand environment. Our current efforts are focused on identifying the implications of these results on lanthanide reactivity.

Experimental

Sample preparation

The analytes were synthesized at the University of California in Irvine CA with rigorous exclusion of air and moisture.^1c,8a The Ln^III(C₅H₄SiMe₃)₃,³³ Ln^II(C₅H₄SiMe₃)₃ ^1–,^1,8a Sm^II(C₅Me₅)₂(THF)₂,³⁴ Sm^III[N(SiMe₃)₂]₃,³⁵ Sm^II[N(SiMe₃)₂]₂(THF)₂,³⁶ Tm^III₂(THF)₂,³⁷ and Tm^IIII₃(THF)_3.5 (ref. 38) were prepared as previously described. Analytes were sealed in ampoules and transported in a cooler filled with dry ice to the Stanford Synchrotron Radiation Lightsource (SSRL) where they were stored at –80 °C. Three hours prior to analysis by XAFS, the lanthanide samples were transferred into an argon filled glovebox. The samples were kept cold by preparing them on an aluminum block, which had been plumbed to accommodate flowing helium gas cooled from a dry ice/ethanol bath. Note, all equipment (including the holder, spatulas, wrenches, boron nitride, etc.) were cooled on the block prior to sample preparation. Samples were diluted with boron nitride, which had been dried at elevated temperature (200 °C) under vacuum (10^–3 Torr) for 48 hours. A mixture of the analyte and BN were weighed out, such that the edge jump for the absorbing atom was calculated to be at ∼1 absorption length in transmission (between 8 to 30 mg of sample and ∼50 mg of BN). Samples were ground using a Wig-L-Bug®, a Teflon bead, and a polycarbonate capsule. The finely ground powders were pressed as a pellet into a slotted aluminum sample holder. These precautions were taken to minimize self-absorption. The holder was equipped with Kapton windows (1 mil), one was fixed with super glue and the other was Kapton tape. For Pr, Nd, Sm, Gd, Tb, Dy, Y, Ho, Er, Tm, Yb and Lu analytes, the holder was brought out of the glovebox, immediately submerged in liquid nitrogen for transportation to the beam line, and loaded into the cryostat. The cryostat was immediately evacuated and attached to the beamline 11-2 XAFS rail and cooled with either liquid nitrogen or liquid helium.

Data acquisition

The cryostat was attached to the beamline 11-2 XAFS rail (SSRL), which was equipped with three ionization chambers through which nitrogen gas was continually flowed. One chamber (10 cm) was positioned before the cryostat to monitor the incident radiation (I ₀). The second chamber (30 cm) was positioned after the cryostat so that sample transmission (I ₁) could be evaluated against I ₀ and so that the absorption coefficient (μ) could be calculated as ln(I ₀/I ₁). The third chamber (I ₂; 30 cm) was positioned downstream from I ₁ so that the XANES of a calibration foil could be measured against I ₁. A potential of 1600 V were applied in series to the ionization chambers.

Samples were calibrated to the energy of the first inflection point of a calibration foil, whose spectrum was measured in situ from the sample using the transmitted portion of the beam. The measurements were calibrated as follows. The Y K-edges were calibrated to the Y K-edge (17 038.4 eV) of an yttrium foil. The Lu L₃-edge to the Cu K-edge of a copper foil at 8979 eV. The Er and Yb L₃-edges to the Ni K-edge of a nickel foil at 8333 eV. The Tm L₃-edges were calibrated to the Ho L₃-edge at 8070.1 eV. The Dy L₃-edge was calibrated to the Dy L₃-edge of a dysprosium foil at 7790.0 eV. The Ho L₃-edges to the Co K-edge of a cobalt foil at 7709 eV. Sm, Gd, and Tb L-edges to the Fe K-edge of an iron foil at 7111 eV. The Pr, and Nd L-edges to the Cr K-edge of a chromium foil at 5989 eV.

The X-ray absorption near edge spectra (XANES) were measured at the SSRL, under dedicated operating conditions (3.0 GeV, 5%, 500 mA using continuous top-off injections) on end station 11-2. This beamline, which was equipped with a 26-pole, 2.0 tesla wiggler, utilized a liquid nitrogen-cooled double-crystal Si[220] monochromator and employed collimating and focusing mirrors. A single energy was selected from the white beam with a liquid-N₂-cooled double-crystal monochromator utilizing Si[220] (φ = 0) crystals. Harmonic rejection was achieved by detuning the second crystal of the monochromator by 50% at ∼600 eV above the absorbing edge. The vertical slit sizes were 1 mm and the beam was unfocused.

Data analysis

Data manipulations and analyses were conducted as previously described.³⁹ Energy calibrations were conducted externally using the first inflection point of the rising edge of the calibration spectrum. Data were analyzed by fitting a line to the pre-edge region, which was subsequently subtracted from the experimental data to eliminate the background of the spectrum. The data were normalized by fitting a first-order polynomial to the post-edge region of the spectrum and setting the edge jump at to an intensity of 1.0.

UV-visible spectroscopy

Prior to transporting the Ho^II(C₅H₄SiMe₃)₃ ^1– samples to the synchrotron, the compound was characterized by UV-vis, as previously reported.⁸ The sample was first prepared for XANES analysis in an argon-filled glovebox by finely grinding Ho^II(C₅H₄SiMe₃)₃ ^1– (19.4 mg) with cold anhydrous boron nitride, BN (60.6 mg) for 2 min in polystyrene canisters with plexiglass pestles using a Wig-L-Bug® grinder to obtain a homogeneous fine powder. The sample was loaded within a slotted aluminum holder, whose slot dimensions were 5 × 20 × 1 mm. The holder was equipped with Kapton tape windows (1 mL). This holder was nested within an additional holder, also equipped with Kapton windows (1 mL) that were sealed with indium wire gaskets. This holder is well established as providing robust exclusion of air and moisture. The sample holder was placed on the rail at SSRL's beam line 11-2 and the Ho L₃-edge spectrum obtained in transition mode at room temperature. After data collection the holder was returned to the glovebox and disassembled. The Ho^II(C₅H₄SiMe₃)₃ ^1– and BN mixture was transferred to a Teflon sealable quartz cuvette with THF (dried over Na/K alloy and benzophenone). The sample was again removed from the glovebox and analyzed using a CARY 50 spectrometer. The UV-vis data were background-subtracted. Owing to the suspended BN, a constant 1.15 absorption value was subsequently subtracted to set the background to zero.

Density functional calculations

Ground-state electronic structure calculations were performed on the Ln(C₅H₄SiMe₃)₃ ^x– (Ln = Sm, Ho; x = 0, 1) using the generalized gradient approximation (GGA) with the PBE exchange–correlation functional⁴⁰ as implemented in the Amsterdam Density Functional (ADF 2014.11).^41–43 For geometry optimization, the Slater basis sets with the quality of triple-ζ plus one polarization functions (TZP)⁴⁴ were used, with the frozen core approximation applied to the inner shells [1s²–4d¹⁰] for Sm and Ho, [1s²] for C, [1s²–2p⁶] for Si. All electron TZ2P basis sets were used for spectroscopic simulation by employing the PBE,⁴⁰ BLYP,^45,46 B3LYP,^45,46 and BHandHLYP^47,48 functionals. The latter three functionals combine the LYP⁴⁶ GGA for correlation with three different approximations for exchange, i.e., Becke's GGA (B)⁴⁵ for exchange, the Becke's three-parameter (B3)⁴⁷ hybrid functional including 20% HF exact exchange, and the half-and-half hybrid containing 50% HF exact exchange.⁴⁸ The B3LYP and BHandHLYP functionals were chosen because they give good performance in excitation energy of charge-transfer states and were commonly used.^22a,49,50 The BLYP was employed together with B3LYP and BHandHLYP to study the impact of the percentage of HF exchange on the excitation energy and spectral shape. The scalar relativistic (SR) effects were taken into account by the zero-order regular approximation (ZORA).⁵¹ Geometries were fully optimized without symmetry at the SR-ZORA level with the gradient convergence of 10^–5, and frequency calculations were carried out to verify the local minimum on the potential energy surface. In the ground-state electronic structure calculations for Ln(C₅H₄SiMe₃)₃ ^x– (Ln = Sm, Ho; x = 0, 1), the high-spin multiplicity was used for each electron configuration. Specifically, Sm^III (4f⁵ 5d⁰) had a ground sextet state, and Sm^II (4f⁶ 5d⁰) had a ground septet state; Ho^III (4f¹⁰ 5d⁰) has ground quintet state, and Ho^II (4f¹⁰ 5d¹) had a ground sextet state, and Ho^II (4f¹¹ 5d⁰) had ground quartet state (Table 3).

DFT-simulation of Ln L₃-edge XANES spectra

The L₃-edge XANES spectra from Ln(C₅H₄SiMe₃)₃ ^x– (Ln = Sm, Ho; x = 0, 1) were simulated as the Kohn–Sham orbital energy differences, i.e., the energy difference between an occupied orbital and a virtual orbital of the ground-state. For a specific core excitation, the oscillator strength was calculated from the transition dipole approximation between this occupied orbital and the virtual orbital. The core electron excitation was calculated originating from Ln 2p dominated MOs to virtual MOs at the DFT/PBE optimized ground-state geometry. All other excitations from orbitals between the Ln 2p and HOMOs were excluded by restricting the energy range of the occupied orbitals involved in the excitations, so that only excitations from Ln 2p core levels to virtual MOs were allowed. The relaxation due to the core hole was assumed constant. All the calculated transition intensities were evenly broadened with a Gaussian function of full-width at half-maximum of 1.7 eV (i.e., peak width) to emulate the experimental spectra.

FEFF spectral simulations

The Ln(C₅H₄SiMe₃)₃ ^x– (Ln = Sm and Tm; x = 0, 1) Sm and Tm L₃-edge and Y(C₅H₄SiMe₃)₃ ^x– (x = 0, 1) Y K-edge XANES spectra and the angular momentum projected density of states were calculated with the FEFF9.6 ab initio quantum chemical code based on the multiple scattering theory (see ESI†).¹⁴ The potentials of free atoms were calculated with a relativistic Dirac–Fock atom code part of FEFF9.6. The scattering potentials were calculated self-consistently by overlapping the free atomic densities in the muffin tin approximation within a cluster of 334 atoms (SCF card; UNFREEZF card was not included). The energy dependent exchange Hedin–Lundquist potential was used for the fine structure and the atomic background (EXCHANGE card). The full multiple scattering XANES spectra were calculated for an atomic cluster of 334 atoms centered on the absorbing Sm/Tm/Y atom (FMS and XANES cards). Best agreement between calculation and experiment was found by applying “COREHOLE FSR” option to screen the 2p_3/2 (Sm/Tm) or 1s (Y) core-holes. The FOLP card (FOLP 1 1.07) was used for calculating the Sm spectra, as the overlap of the muffin tin radii was reported to be too large by the program. This value was chosen as it was found for the calculations of the Tm and Y spectra. We have obtained comparable results (not shown here) for Tm by including the f valence states in the self-consistent calculations of the scattering potentials (UNFREEZF card).

CASPT2/CASSCF calculations

Using the complete-active-space multi-configuration approach with second-order perturbation theoretical correction (CASPT2)^52,53 implemented in Molpro 2015.1 program, ab initio WFT calculations were performed.^54,55 To reduce the computational cost, CASPT2/CASSCF calculations were carried out on the ground-states and low excited-states of the simplified Ln(C₅H₅)₃ ^x– (Ln = Sm, Ho; x = 0, 1) complexes. The DFT/PBE optimized geometries of Ln(C₅H₄SiMe₃)₃ ^x– were used in the calculations. Here the original SiMe₃ substituents, ancillary groups, were replaced with protons having C–H bond lengths of 1.088 Å. For Ho(C₅H₅)₃ ^1–, two geometries derived from Ho^II (4f¹¹ 5d⁰) and Ho^II (4f¹⁰ 5d¹) were used. We applied the cc-pVDZ basis sets for H and C,⁵⁶ Stuttgart energy-consistent relativistic pseudopotentials ECP28MWB,^57,58 and the corresponding ECP28MWB-SEG basis for Sm and Ho. Although attempts to include all the seven 4f- and five 5d-orbitals into active space were made, the converged CASSCF results showed that for Sm(C₅H₅)₃ ^x– (x = 0, 1) the five 5d-orbitals are not correlated and were removed out of active space. In contrast for Ho(C₅H₅)₃ ^x– (x = 0, 1), only the 5d_z2-orbital remained in the active space. Therefore, the active space was adjusted to include all the 4f-orbitals for Sm(C₅H₅)₃ ^x– (x = 0, 1) and additionally the 5d_z2 – character orbital for Ho(C₅H₅)₃ ^x– (x = 0, 1). In the CASPT2 calculations, the ionization-potential/electron-affinity corrected zeroth-order Hamiltonian was used with an IPEA shift of 0.25 a.u.⁵⁹ The 1s-core orbitals of the C atoms, and 4s-, 4p-, 4d-orbitals of the Sm and Ho atoms were kept frozen in the CASPT2 calculations.