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

LnII(C5H4SiMe3)1– have been characterized by XANES and DFT.


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 dened 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 À2.7 to À3.9 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 LnX 2 (Ln ¼ La, Ce, Pr, Gd, and Y; X ¼ 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 1À ) 2 (e 1À ). 5 The new Ln(C 5 H 4 SiMe 3 ) 3 1À compounds, containing the putative +2 ions, were synthesized by potassium reduction of Scheme 1 A general reaction scheme for generating Ln II (C 5 H 4 -SiMe 3 ) 3 1À containing salts. Accessing these compounds in crystalline form requires complexation of the potassium cation by 18-crown-6 or 2.2.2-cryptand. 1 trimethylsilylcylopentadienyl lanthanide(III) complexes, Ln(C 5 -H 4 SiMe 3 ) 3 (Scheme 1). More detailed synthetic descriptions for these Ln(C 5 H 4 SiMe 3 ) 3 1À anions, as well as related Ln[C 5 H 3 (SiMe 3 ) 2 ] 3 1À complexes prepared by Lappert and coworkers, have been previously discussed. 6 The new Ln(C 5 H 4 SiMe) 3 1À complexes were unusual in that their Ln-C centroid distances were only 1% (0.020-0.032Å) longer than their Ln III precursors, Ln(C 5 H 4 SiMe 3 ) 3 . Larger variations, by an order of magnitude (0.1 to 0.2Å), 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(C 5 H 4 SiMe 3 ) 3 1À bond lengths for Ln ¼ Eu, Yb, Sm, and Tm were 0.10-0.20Å ($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(C 5 H 4 SiMe 3 ) 3 1À series, suggesting that the salts might contain +3 metals with an electron delocalized into ligand-based orbitals. This scenario wasin a sense reminiscent of the LnX 2 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 4f n 5d 1 electronic conguration, rather than the traditionally expected 4f n+1 5d 0 conguration 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 4f n 5d 1 congurations, 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(C 5 H 4 SiMe 3 ) 3 1À 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 (C 5 H 4 SiMe 3 ) 3 1À (Ln ¼ 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 edgejump 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 4f n 5d 1 ions in Ln(C 5 H 4 SiMe 3 ) 3 1À (Ln ¼ 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 inuence of 4f n+1 5d 0 versus 4f n 5d 1 electronic congurations on the lanthanide L 3 -edge XANES spectra to be determined for the rst time.  Fig. 1. Each spectrum contains large edge features near 6715 eV (L 3 ) and 7310 eV (L 2 ) 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 rst derivatives of the data equaled zero (Table 1). Given the sharp characteristics of these peaks, we nd that the peak maximum provides a more useful metric than the inection point, which is commonly used to evaluate actinide absorption edges. The L 3,2 -edge peak maxima for Sm II 3 , also exhibit a Sm L 3 -edge energy difference of 7-8 eV ( Fig. 2 and Table 1). These results demonstrate that samarium 4f-orbital occupancy (4f 6 5d 0 versus 4f 5 5d 0 ) inuences the peak position more substantially than the ligand identity, as changing cyclopentadienide in Sm III (C 5 H 4 SiMe 3 ) 3 to amido ligands in Sm III [N(SiMe 3 ) 2 ] 3 only shis the L 3 -edge peak maximum to lower energy by 0.4 eV.
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 signicant 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 O 2 or H 2 O. 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 À7 Torr), the Sm II spectra are unchanged aer 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 identied under different experimental conditionsusing a focused beam at room temperature under an argon atmosphere on SSRL's beam line 6-2that complete conversion of Sm II (C 5 H 4 SiMe 3 ) 3 1À 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  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 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 Â 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 À7 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 condence 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 (C 5 H 4 SiMe 3 ) 3 compounds to hydrolysis, the highly reducing nature of Sm II and Tm II (which have standard reduction potentials of À1.5 and À2.3 V versus SHE), 4 and of the light sensitivity of Tm III I 3 (THF) 3.5 . As noted previously, 12,15 the consistent 7-8 eV shi between Ln II and Ln III containing compounds highlights the utility of overcoming these sample handling challenges for characterizing Tm II 4f 13 5d 0 versus Tm III 4f 12 5d 0 electronic  congurations 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 shi of $7 eV upon moving from Yb II (4f 14 5d 0 ) to Yb III (4f 13 5d 0 ).  3 . In this gure, 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 risingedge 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 (C 5 H 4 SiMe 3 ) 3 1À anions are quite similar in energy to the neutral Ln III (C 5 H 4 SiMe 3 ) 3 compounds. As shown in Fig. 4 and Table 1 Unfortunately, because of constraints associated with the XANES holder, this transfer was not quantitative and the overall amount of Ho II (C 5 H 4 SiMe 3 ) 3 1À 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 articially 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 (C 5 H 4 SiMe 3 ) 3 was observed before or aer the synchrotron experiment. One cannot rule out the possibility of insoluble Ho III contaminates. complex. However, reduction to form unconventional divalents, Ln ¼ Gd, Tb, Dy, Ho, Er, and Lu, caused the pre-edge features to disappear from the L 3 -edges XANES spectra. This observation is documented by the 2 nd derivative plots shown in Fig. 6 for Ho(C 5 H 4 SiMe 3 ) 3 xÀ (x ¼ 1, 0) (see ESI † for the other L 3 -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 (C 5 -H 4 SiMe 3 ) 3 . If the transition corresponds to a Ln 2p / 5d excitation, 5d-orbital population in Ln II (C 5 H 4 SiMe 3 ) 3 1À would shi 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 analyteswhich have 4f n 5d 0 (for +3 metals) and 4f n+1 5d 0 (for +2 metals) electronic congurations 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 L 3 -edge XANES measurement made on a 1 : 1 mixture of Ho III (C 5 H 4 SiMe 3 ) 3 and Ho II (C 5 H 4 SiMe 3 ) 3 1À , 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 (C 5 H 4 SiMe 3 ) 3 1À L 3 -edge XANES spectra provides a fortuitous alternative ngerprint for the Ln II compounds with 4f n 5d 1 electronic congurations. This is especially valuable when one considers that L 3 /L 2 absorption peak area comparisons and branching ratio analyses were inconclusive ( represent the rst Y K-edge XANES spectrum of a molecule containing Y II . Also consider data from the Lu(C 5 H 4 SiMe 3 ) 3 xÀ (x ¼ 0, 1) pair. Lutetium in the +3 oxidation state has a full 4f-shell. Hence reduction of Lu III (C 5 H 4 SiMe 3 ) 3 , with a 4f 14 5d 0 electron conguration, has to generate a 4f 14 5d 1 conguration in Lu II (C 5 H 4 SiMe 3 ) 3 1À . Consistent with 5d-orbital occupation, the peak maxima difference between Lu III and Lu II in the Lu L 3,2edge XANES was small, measured at 1.9 eV. Taken in the context of these Y(C 5 H 4 SiMe 3 ) 3 xÀ and Lu(C 5 - 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 resultsthe most plausible interpretations of these Ln L 3 -edge XANES data ( Fig. 4) is that reduction of Ln III (C 5 H 4 SiMe 3 ) 3 to form an unconventional Ln II (C 5 H 4 SiMe 3 ) 3 1À compound resulted in addition of an electron into a highly shielded 5d-orbital to generate a 4f n 5d 1 electronic conguration, not 4f n+1 5d 0 . Although we anticipate that the spectra in Fig. 4 contain some Ln III contaminationin analogy to the Sm II and Tm II spectra in Fig. 1 to 3the computational results below provide even more support for the alternative electronic conguration.

Electronic structure calculations
To better understand the origin for the spectroscopic differences between Ln III (C 5 H 4 SiMe 3 ) 3 25 Consistently, our DFT/PBE calculated Ho III (4f 10 5d 0 )-C centroid and Ho II (4f 10 5d 1 )-C centroid distances are in excellent agreement with experimental values (Table 2), while the Ho II (4f 11 5d 0 )-C centroid distances are longer than the experimental results by $0.1Å. 1b,1c These results provide condence in assigning Ho II as having a 4f 10 5d 1 electronic conguration. We refer the interested reader to the experimental section for details of the electronic structure calculation.
To better understand the unusual electronic conguration of Ho II (C 5 H 4 SiMe 3 ) 3 1À , we found it instructive to interpret the DFT calculations using traditional molecular orbital descriptions derived from group theory considerations of M(C 5 H 5 ) 3 in C 3hsymmetry. Hence, a qualitative MO level diagram for the C 3h -Ho II (C 5 H 5 ) 3 1À anion is provided in Fig. 8. As the molecular orbital interactions associated with Ln III (C 5 R 5 ) 3 (R ¼ H or alkyl) have been the subject of numerous theoretical and spectroscopic studies, 26 this discussion is conned 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 (C 5 H 5 ) 3 in D 3h -or C 3v -symmetry, 26b,c,d,g,h,i,j we nd 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 (C 5 H 4 SiMe 3 ) 3 1À .
In the C 3h -point group, symmetry allowed mixing between the metal 5d-and cyclopentadienyl p-orbitalsperpendicular to the ring planesgenerates bonding interactions of a 0 , e 0 , and e 00 symmetries, which were s-pand d-bonding with respect to the metal-cyclopentadienyl centroid axes, Fig. 8. Superimposed on this molecular orbital picture, and at lower energy, are Ln-(C 5 H 5 ) s-, pand d-bonding orbitals of a 0 , a 00 , e 0 , and e 00 symmetries that originate from mixing between the 4f-orbitals   Table 4 Ground-states configurations from Ln(C 5 H 5 ) 3 xÀ (Ln ¼ Sm, Ho; x ¼ 0, 1) complexes from CASPT2/CASSCF calculations. a Geometries relied on the DFT/PBE optimized geometries of Ln(C 5 H 4 SiMe 3 ) 3 xÀ . However, for Ho II (C 5 H 5 ) 3 1À two geometries were investigated that were derived from the calculated Ho II (C 5 H 3 SiMe 3 ) 3 1À structures with either 4f 10 5d 1 or 4f 11 5d 0 electronic configurations
To support the results from the ground-state DFT calculations, CASPT2/CASSCF calculations were performed on the ground-states and low excited-states of simplied Ln(C 5 H 5 ) 3 xÀ (Ln ¼ Sm, Ho; x ¼ 0, 1) complexes. The DFT/PBE optimized geometries of Ln(C 5 H 4 SiMe 3 ) 3 xÀ were used; however, to reduce the computational cost SiMe 3 substituents were replaced with protons having C-H bond lengths of 1.088Å. Two possibilities were investigated for Ho II (C 5 H 5 ) 3

1À
. The rst was associated with the calculated structure of Ho II (C 5 H 4 SiMe 3 ) 3 1À with a 4f 10 5d 1 ground-state electronic conguration. The second investigated Ho II (C 5 H 5 ) 3 1À geometry was based on the calculated 4f 11 5d 0 Ho II (C 5 H 4 SiMe 3 ) 3 1À structure. Although efforts were made to include all the seven 4f and ve 5d orbitals into the active space, the converged CASSCF results for Sm(C 5 H 5 ) 3 xÀ (x ¼ 0, 1) showed that the ve 5d-orbitals were not correlated and removed from the active space. Meanwhile for Ho(C 5 H 5 ) 3 xÀ (x ¼ 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(C 5 H 5 ) 3 xÀ (x ¼ 0, 1) and an additionally 5d z2orbital for Ho(C 5 H 5 ) 3 xÀ (x ¼ 0, 1). The results generated a complete active space of 6-electrons with 7-orbitals for Sm II (C 5 H 5 ) 3

1À
, 5-electrons and 7-orbitals for Sm III (C 5 H 5 ) 3 , 11electrons and 8-orbitals for Ho II (C 5 H 5 ) 3 1À , and 10-electrons with 8-orbitals for Ho III (C 5 H 5 ) 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 "corelike" and nearly degenerated 4f-orbitals resulted in different 4foccupations with nearly the same energies. The CASPT2/ CASSCF results show that Sm III (C 5 H 5 ) 3 has ground sextet state of 4f 5 congurations and that Sm II (C 5 H 5 ) 3 1À has ground septet state of 4f 6 conguration, which are the same as DFT results. In the holmium case, Ho III (C 5 H 5 ) 3 has ground quintet state of 4f 10 5d 0 . For Ho II , both geometries showed a sextet with 4f 10 5d 1 congurations. These Ho II and Ho III results were identical to the DFT calculations. Hence, in terms of evaluating groundstate electronic structures for the Ln(C 5 H 5 ) 3 xÀ (x ¼ 0, 1), the CASPT2/CASSCF results are in excellent agreement with the reported DFT results from Ln(C 5 H 4 SiMe 3 ) 3 xÀ (x ¼ 0, 1).

Spectral simulations
The open-shell Sm and Ho L 3 -edge XANES spectra from Ln(C 5 H 4 SiMe 3 ) 3 xÀ (Ln ¼ Sm, Ho; x ¼ 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 L 3 -edge XANES spectra from Ln(C 5 H 4 SiMe 3 ) 3 xÀ are compared with experimental results in Fig. 9 and 10. In Fig. 9  these gures, the calculated spectra were shied by a constant 241.49 eV (Sm) and 348.17 eV (Ho) to line up the Ln III (C 5 H 4 -SiMe 3 ) 3 L 3 -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 congurations, Ln II 2p 6 .4f n+1 5d 0 / Ln II 2p 5 .4f n+1 5d 1 , and alternatives that involved 5d-orbital occupations, Ln II 2p 6 .4f n 5d 1 / Ln II 2p 5 .4f 1 5d 2 . The resulting near edge energies are summarized in Table 5 alongside analogous values acquired using PBE, BLYP, and B3LYP functionals. The theoretical analyses reveal the primary contributions to the Ln L 3 -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 L 3 -edge energy differences calculated using BHandHLYP were in best agreement with the experiment. For example, in the Sm(C 5 H 4 -SiMe 3 ) 3 xÀ case, where the 4f-and 5d-orbital occupancies are well established, energy differences between the Sm III (4f 5 5d 0 ) and Sm II (4f 6 5d 0 ) L 3 -edge positions are calculated to be 6.5 eV, which is in good agreement with the measured value of 7. 6 (Table 5), e.g. energy differences between the Ho III (4f 10 5d 0 ) and Ho II (4f 10 5d 1 ) L 3edge peak maxima are calculated to be 0.7 eV and measured to be 0.5 eV. The Ho(C 5 H 4 SiMe 3 ) 3 xÀ calculations differ in that they invoke the Ho II low energy 4f 10 5d 1 ground-state electronic conguration. We note that calculations involving the higher energy 4f 11 5d 0 Ho II electronic conguration grossly overestimate the Ho III /Ho II L 3 -edge energy by 6.5 eV.
To better understand the how 4f-versus 5d-orbital occupancy inuence Ln L 3 -XANES spectra, the ground-state 2p-orbital energies are plotted alongside the average 5d-and 6d-orbital energies in Fig. 11 for Ln(C 5 H 4 SiMe 3 ) 3 xÀ (Ln ¼ Sm, Ho; x ¼ 0, 1). We remind the reader that the major contributors to the Ln(C 5 H 4 SiMe 3 ) 3 xÀ L 3 -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 (4f n 5d 0 ) + 1e 1À / Ln II (4f n+1 5d 0 ), 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   3 . Adding the electron into 5dshell, Ln III (4f n 5d 0 ) + 1e 1À / Ln II (4f n 5d 1 ), 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/6daverage orbital energies increase by 4.6 eV and 3.9 eV, respectively. This modest energy shi decreases the L 3 -edge excitation energy for Ho II (C 5 H 4 SiMe 3 ) 3 1À by <1 eV in comparison to Ho III (C 5 H 4 SiMe 3 ) 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.

Discussion
Herein we describe the use of XANES spectroscopy to characterize the electronic congurations of formally +2 lanthanide compounds of the general formula Ln II (C 5 H 4 SiMe 3 ) 3
Consistent with previous reports, the ground-state DFT calculations show the electronic congurations for Sm III (C 5 H 4 -SiMe 3 ) 3 , Sm II (C 5 H 4 SiMe 3 ) 3 1À , and Ho III (C 5 H 4 SiMe 3 ) 3 are Sm III 4f 5 5d 0 , Sm II 4f 6 5d 0 , and Ho III 4f 10 5d 0 , respectively. In contrast for Ho II (C 5 H 4 SiMe 3 ) 3 1À , the calculations indicate that the ground-state electronic conguration is 4f 10 5d 1 , with the nonbonding 5d z2 -orbital of a 0 -symmetry being singly occupied. CASPT2/CASSCF calculations on the simplied models, Ln(C 5 -H 5 ) 3 xÀ (Ln ¼ Sm, Ho; x ¼ 0, 1), were completely consistent with the assignments of the DFT calculations. As such the Ln L 3 -edge XANES spectra were simulated using transition dipole moment calculations for a variety of electronic congurations, spanning Ln III 4f n 5d 0 , Ln II 4f n+1 5d 0 , and Ln II 4f n 5d 1 . For both Sm and Ho, the calculations suggest that reducing Ln III (4f n 5d 0 ) by adding an electron in the 4f-manifold to generate Ln II (4f n+1 5d 0 ) appreciably shis the Ln L 3 -edge by approximately 7 eV. In contrast, reducing Ln III (4f n 5d 0 ) by adding an electron into the 5d-manifold to generate Ln II (4f n 5d 1 ) slightly shis the Ln L 3edge to lower energy (on the order of $1 eV).

Concluding remarks
Our results indicate that the differences in Ln(C 5 H 4 SiMe 3 ) 3 xÀ (Ln ¼ Sm, Ho; x ¼ 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 signicantly destabilize the core 2p-orbital energy levels, which decrease the Ln L 3 -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 L 3edge excitation energy (0.2-1.9 eV). One might describe the 4f 10 5d 1 electron conguration in Ho II (C 5 H 4 SiMe 3 ) 3 1À as mimicking the 4f 10 electronic conguration in Ho III (C 5 H 4 SiMe 3 ) 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 shis and Ln II /Ln III -C centroid bond distances in the other Ln(C 5 H 4 -SiMe 3 ) 3 xÀ (Ln ¼ Pr, Nd, Gd, Tb, Dy, Er, and Lu; x ¼ 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 identied that the tris-cyclopentadienyl coordination environment provides a mechanism for stabilizing Ln II 4f n 5d 1 electronic congurations through the accessibility of a low-lying 5d-orbital of a 0 symmetry. The results additionally suggest an electronic structure break between Tm II (C 5 H 4 -SiMe 3 ) 3 1À and Dy II (C 5 H 4 SiMe 3 ) 3 1À . It appears that 4f n+1 5d 0 electronic congurations are most stable when the reduction potentials for the lanthanide ions in Ln II (C 5 H 4 SiMe 3 ) 3 1À are less than or equal to that of Tm II (C 5 H 4 SiMe 3 ) 3 1À . Meanwhile, those with reduction potentials greater than or equal to Dy II (C 5 H 4 -SiMe 3 ) 3 1À are best described as 4f n 5d 1 . While the generality of this interpretation has yet to be determined, we anticipatebased on previous studies on LnX 2 (X ¼ halide)that the electronic structure breaking point is quite dynamic and can shi 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.

Sample preparation
The analytes were synthesized at the University of California in Irvine CA with rigorous exclusion of air and moisture.  3.5 (ref. 38) were prepared as previously described. Analytes were sealed in ampoules and transported in a cooler lled with dry ice to the Stanford Synchrotron Radiation Lightsource (SSRL) where they were stored at À80 C. Three hours prior to analysis by XAFS, the lanthanide samples were transferred into an argon lled glovebox. The samples were kept cold by preparing them on an aluminum block, which had been plumbed to accommodate owing 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 À3 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 Teon bead, and a polycarbonate capsule. The nely 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 xed 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 owed. One chamber (10 cm) was positioned before the cryostat to monitor the incident radiation (I 0 ). The second chamber (30 cm) was positioned aer the cryostat so that sample transmission (I 1 ) could be evaluated against I 0 and so that the absorption coef-cient (m) 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 rst inection 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 L 3 -edge to the Cu K-edge of a copper foil at 8979 eV. The Er and Yb L 3 -edges to the Ni K-edge of a nickel foil at 8333 eV. The Tm L 3 -edges were calibrated to the Ho L 3 -edge at 8070.1 eV. The Dy L 3 -edge was calibrated to the Dy L 3 -edge of a dysprosium foil at 7790.0 eV. The Ho L 3 -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 26pole, 2.0 tesla wiggler, utilized a liquid nitrogen-cooled doublecrystal Si[220] monochromator and employed collimating and focusing mirrors. A single energy was selected from the white beam with a liquid-N 2 -cooled double-crystal monochromator utilizing Si[220] (4 ¼ 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 rst inection point of the rising edge of the calibration spectrum. Data were analyzed by tting a line to the preedge region, which was subsequently subtracted from the experimental data to eliminate the background of the spectrum. The data were normalized by tting a rst-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 (C 5 H 4 SiMe 3 ) 3 1À samples to the synchrotron, the compound was characterized by UV-vis, as previously reported. 8 The sample was rst prepared for XANES analysis in an argon-lled glovebox by nely grinding Ho II (C 5 -H 4 SiMe 3 ) 3 1À (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 ne powder. The sample was loaded within a slotted aluminum holder, whose slot dimensions were 5 Â 20 Â 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 L 3 -edge spectrum obtained in transition mode at room temperature. Aer data collection the holder was returned to the glovebox and disassembled. The Ho II (C 5 H 4 SiMe 3 ) 3 1À and BN mixture was transferred to a Teon 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.  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 chargetransfer 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 À5 , and frequency calculations were carried out to verify the local minimum on the potential energy surface. In the groundstate electronic structure calculations for Ln(C 5 H 4 SiMe 3 ) 3 xÀ (Ln ¼ Sm, Ho; x ¼ 0, 1), the high-spin multiplicity was used for each electron conguration. Specically, Sm III (4f 5 5d 0 ) had a ground sextet state, and Sm II (4f 6 5d 0 ) had a ground septet state; Ho III (4f 10 5d 0 ) has ground quintet state, and Ho II (4f 10 5d 1 ) had a ground sextet state, and Ho II (4f 11 5d 0 ) had ground quartet state (Table 3).

DFT-simulation of Ln L 3 -edge XANES spectra
The L 3 -edge XANES spectra from Ln(C 5 H 4 SiMe 3 ) 3 xÀ (Ln ¼ Sm, Ho; x ¼ 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 specic 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(C 5 H 4 SiMe 3 ) 3 xÀ (Ln ¼ Sm and Tm; x ¼ 0, 1) Sm and Tm L 3 -edge and Y(C 5 H 4 SiMe 3 ) 3 xÀ (x ¼ 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 ne 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-conguration 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 simplied Ln(C 5 H 5 ) 3 xÀ (Ln ¼ Sm, Ho; x ¼ 0, 1) complexes. The DFT/PBE optimized geometries of Ln(C 5 H 4 SiMe 3 ) 3 xÀ were used in the calculations. Here the original SiMe 3 substituents, ancillary groups, were replaced with protons having C-H bond lengths of 1.088Å. For Ho(C 5 H 5 ) 3 1À , two geometries derived from Ho II (4f 11 5d 0 ) and Ho II (4f 10 5d 1 ) 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 ve 5d-orbitals into active space were made, the converged CASSCF results showed that for Sm(C 5 H 5 ) 3 xÀ (x ¼ 0, 1) the ve 5d-orbitals are not correlated and were removed out of active space. In contrast for Ho(C 5 H 5 ) 3 xÀ (x ¼ 0, 1), only the 5d z2 -orbital remained in the active space. Therefore, the active space was adjusted to include all the 4forbitals for Sm(C 5 H 5 ) 3 xÀ (x ¼ 0, 1) and additionally the 5d z2character orbital for Ho(C 5 H 5 ) 3 xÀ (x ¼ 0, 1). In the CASPT2 calculations, the ionization-potential/electron-affinity corrected zeroth-order Hamiltonian was used with an IPEA shi of 0.25 a.u. 59 The 1s-core orbitals of the C atoms, and 4s-, 4p-, 4dorbitals of the Sm and Ho atoms were kept frozen in the CASPT2 calculations.