# Geometry and Electronic Structure of Yb(III)[CH(SiMe3)2]3 from EPR and solid-state NMR augmented by Computations

Anton Ashuiev, Florian Allouche, Md. Ashraful Islam, José P Carvalho, Kevin J Sanders, Matthew P Conley, Daniel Klose, Giuseppe Lapadula, Michael Wörle, Dirk Baabe, et al.

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Anton Ashuiev, Florian Allouche, Md. Ashraful Islam, José P Carvalho, Kevin J Sanders, et al. Geometry and Electronic Structure of Yb(III)[CH(SiMe3)2]3 from EPR and solid-state NMR augmented by Computations. Physical Chemistry Chemical Physics, 2024, 26 (11), pp.8734-8747. 10.1039/D4CP00281D. hal-04301807

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Geometry and Electronic Structure of
Yb(III)[CH(SiMe₃)₂]₃ from EPR and
solid-state NMR augmented by Computations

Anton Ashuiev,† Florian Allouche,† Md. Ashraful Islam,‡ José P. Carvalho,¶ Kevin

J. Sanders,‡ Matthew P. Conley,§ Daniel Klose,† Giuseppe Lapadula,† Michael

Wörle,† Dirk Baabe,‖ Marc D. Walter,‖ Andrew J. Pell,*,‡ Christophe Copéret,*,†

Gunnar Jeschke,*,† Guido Pintacuda,*,‡ and Richard A. Andersen⊥

†Department of Chemistry and Applied Biosciences, ETH Zurich, Wolfgang-Pauli-Strasse
1-5, 8093 Zurich, Switzerland

‡Université de Lyon, Centre de RMN à Très Hauts Champs de Lyon (UMR 5082 - CNRS, ENS Lyon, Université Claude Bernard Lyon 1), F-69100 Villeurbanne, France

¶Department of Materials and Environmental Chemistry, Stockholm University, Svänte
Arrhenius väg 16 C 106 91 Stockholm, Sweden

§Department of Chemistry and Chemical Sciences, University of California Riverside, 501
Big Springs Road, Riverside, CA 92521, USA

‖Institut für Anorganische und Analytische Chemie, Technische Universität Braunschweig,
Hagenring 30, 38106 Braunschweig, Germany

⊥Department of Chemistry, University of California, Berkeley, CA 94720, USA

E-mail: andrew.pell@ens-lyon.fr; ccoperet@ethz.ch; gjeschke@ethz.ch;
guido.pintacuda@ens-lyon.fr

Abstract
Characterization of paramagnetic compounds, in particular regarding the detailed conformation and electronic structure, remains a challenge, and - still today it often relies solely on the use of X-ray crystallography, thus limiting the access to electronic structure information. This is particularly true for lanthanide elements that are often associated with peculiar structural and electronic features in relation to their partially filled f-shell. Here, we develop a methodology based on the combined use of state-of-the-art magnetic resonance spectroscopies (EPR and solid-state NMR) and computational approaches as well as magnetic susceptibility measurements to determine the electronic structure and geometry of a paramagnetic Yb(III) alkyl complex, Yb(III)[CH(SiMe₃)₂]₃, a prototypical example, which contains notable structural features according to X-ray crystallography. Each of these techniques revealed specific information about the geometry and electronic structure of the complex. Taken together, both EPR and NMR, augmented by quantum chemical calculations, provide a detailed and complementary understanding of such paramagnetic compounds. In particular, the EPR and NMR signatures point to the presence of three-centre-two-electron Yb-γ-Me-β-Si secondary metal-ligand interactions in this otherwise tri-coordinate metal complex, similarly to its diamagnetic Lu analogues. The electronic structure of Yb(III) can be described as a single 4f¹³ configuration, while an unusually large crystal-field splitting results in a thermally isolated ground Kramers doublet. Furthermore, the computational data indicate that the Yb-carbon bond contains some π-character, reminiscent of the so-called α-H agostic interaction.

Introduction

Organometallic compounds, perhydrocarbyls in particular (MRn with M = metal; R = hydrocarbyl), often adopt unusual geometries or bonding patterns due to their low coordination numbers and the associated electronic consequences in metal-carbon bondings.¹,² These patterns continue to engage the broader community in understanding how preferences in geometric structure relate to the often complex electronic structure and reactivity in these
compounds. As an example, among diamagnetic compounds, carbons with single bonds that exhibit significant π character to metals show specific deshielded nuclear magnetic resonance (NMR) chemical shifts and associated reactivity, indicating that alkyl groups are often better described as both σ- and π-donors to the metal (Figure 1a).³,⁴ Reduced $J_{C-H}$ coupling constants for these carbons, and associated specific structural distortions, provide evidence for agostic interactions.⁵,⁶ Similar bonding peculiarities are also found in compounds with metal-carbon multiple bonds. The prototypical example is Ta(=CH⁴Bu)(CH₂Bu)₃, which contains a highly deshielded ¹³C signal and a very low $J_{C-H}$ coupling constant for the formally sp² hybridized Ta=C carbon. These signatures are consistent with an α-CH interaction, better described as an additional π-donation from the α-carbon to the electron deficient dº metal centre.³,⁴,⁷

Peculiarities in geometric structure from X-ray diffraction analysis are also observed in monomeric lanthanide perhydrocarbyl complexes, Ln[CH(SiMe₃)₂]₃ (Ln = Y,⁸ La,⁹ Ce,⁸ Sm,⁹ Lu¹⁰) that contain three short Ln···Cγ contacts between one Si-CH₃ group of each of the three proximal -SiMe₃ groups (Fig. 1a). The Ln···Cγ contacts result in lengthening of the Si-CH₃ bonds close to the lanthanide by ~0.04 Å with respect to the other Si-CH₃ groups, indicating that these proximal Si-CH₃ groups interact with the lanthanide. This interaction helps to satisfy the high coordination numbers required to isolate these f-block homoleptic complexes; a strategy that also facilitates isolation of Yb[C(SiMe₃)₂]₂,¹¹ Ln(AlMe₄)₃,¹² and Ln[C(SiHMe₂)₃]₂.¹³,¹⁴ Recent studies of Lu[CH(SiMe₃)₂]₃¹⁰ indicated that the Lu···Cγ interactions are not a result of γ-C-H agostic interactions (2-electron donation from a C-H bond to an electron deficient metal centre),⁶ but are rather due to a three-centre-two-electron (3c-2e) interaction between the Si-Me bond and Lu. In other words, the Lu···Cγ interaction is best described as a pseudo bridging Lu-Me-Si group (Fig. 1a), analogous to Al-Me-Al observed in dimeric AlMe₃¹⁵,¹⁶ or Ln(AlMe₄)₃.¹⁷ The critical data in that study¹⁰ were a combination of high quality X-ray diffraction results, variable temperature ¹H and ¹³C NMR spectra in solution, as well as J-resolved ¹H-¹³C and ²⁹Si Magic-Angle Spinning (MAS)
solid-state NMR spectra. The experimental results were reliably reproduced using both wave-function based and density functional theory (DFT) models of Lu[CH(SiMe₃)₂]₃, and natural bond orbital (NBO) analysis showed that the charges on Cα and Cγ are negative, while the charges on Siβ and Hγ are positive. This analysis was consistent with the proposed bridging Lu–Me–Si group to describe the Lu···Cγ interaction.

<figure><img src="image_2.png" /><figcaption>Figure 1: (a) Typically occurred peculiarities in structure of organometallic compounds, in particular, Ln[CH(SiMe₃)₂]₃. (b) Characterization approach, applied to paramagnetic organometallic lanthanide complexes.</figcaption></figure>

Extending this analysis using similar NMR methods to other Ln[CH(SiMe₃)₂]₃ is however challenging, because most lanthanides contain a partially filled f-shell in their +3 oxidation state. The resulting paramagnetism perturbs the magnetic properties of the nearby nuclei, making data acquisition and interpretation complicated at best, and typically impractical in most instances. Similarly, while electron paramagnetic resonance (EPR) could offer a potential alternative for this class of compounds, the signals are typically not detectable at room temperature using routine continuous wave (CW) methods due to the short electronic spin relaxation times and large hyperfine couplings. However, both fields have seen impressive recent progress. In solid-state NMR, fast MAS and broadband adiabatic irradiation sequences allow for measurements on such samples¹⁸ and in EPR, new EPR pulsed tech-
niques¹⁹ were developed for f-block metal complexes.²⁰,²¹ In parallel, the recent advances in quantum chemical/DFT methods and dedicated formalisms²²⁻³⁰ now allow us to interpret NMR and EPR data in terms of the spatial and electronic structure.³¹⁻³⁷

In this study, we showcase a methodology to assess the detailed electronic structure of a prototypical compound, namely Yb[CH(SiMe₃)₂]₃, by combining state-of-the-art EPR, NMR and computation (Figure 1b). We first synthesized and isolated a series of Yb[CH(SiMe₃)₂]₃[O-2,6-tBu₂-C₆H₃]₃-x (x = 0, 1, 2, 3), and determined their structures by single-crystal X-ray diffraction at 100 K along with their basic magnetic properties by variable-temperature measurements of their magnetic susceptibilities. We next investigate the full geometric and electronic structure of Yb[CH(SiMe₃)₂]₃ based on the most advanced EPR and solid-state NMR, supported by quantum chemical calculations. This approach enables a full characterization of the direct metal-carbon bonding as well as the nature of the secondary Yb···Cγ interaction at low and room temperature. We discuss how this interaction influences the structure and ligand dynamics in solution and in the solid state, and how the CH(SiMe₃)₂ ligand leads to an unusual behavior in the crystal field interactions of the Yb(III) ion.

# Results and discussion

## Synthesis and X-ray diffraction studies of Yb[CH(SiMe₃)₂]₃

The syntheses of Yb[CH(SiMe₃)₂]₃, Yb[CH(SiMe₃)₂]₂[O-2,6-tBu₂-C₆H₃], and Yb[CH(SiMe₃)₂][O-2,6-tBu₂-C₆H₃]₂ are shown in Fig. 2a (see SI Section 1 for detailed synthetic procedures). Similar to the lutetium complexes isolated previously,¹⁰ the alkylation depends on the stoichiometry of the organolithium reagent. Key to successful isolation of these compounds is the use of sufficient volumes of pentane to dissolve the sparingly soluble polymeric Li[CH(SiMe₃)₂].³⁸ Addition of Li[CH(SiMe₃)₂] as a slurry in smaller volumes of pentane results in poor yields and formation of mixtures of these compounds. All organoytterbium compounds shown in Fig. 2a are isolated as crystalline solids from concen-
trated pentane solutions. Yb[CH(SiMe₃)₂]₃ is blue, Yb[CH(SiMe₃)₂]₂[O-2,6-tBu₂-C₆H₃] is brown, and Yb[CH(SiMe₃)₂][O-2,6-tBu₂-C₆H₃]₂ is red. The study below focuses on the structure and spectroscopic features of Yb[CH(SiMe₃)₂]₃. X-ray structures of Yb[CH(SiMe₃)₂]₂[O-2,6-tBu₂-C₆H₃] and Yb[CH(SiMe₃)₂][O-2,6-tBu₂-C₆H₃]₂ are provided in SI Chapter 2.2 (see Figs. S3 - S6), and their NMR spectra are provided in SI Chapter 7 (see Figs. S15 - S20).

A view of the Yb[CH(SiMe₃)₂]₃ complex is shown in Figs. 2b & S2. The relevant bond distances obtained from this structure are shown in Fig. 2c-d (see also Tab. S2). For comparison the previously reported bond distances for Lu[CH(SiMe₃)₂]₃¹⁰ (Fig. 2e) are also shown in Fig. 2f-g (see also Tab. S2). Yb[CH(SiMe₃)₂]₃ crystallizes in the *P*31_c space group and is isostructural with other isolated Ln[CH(SiMe₃)₂]₃. Yb[CH(SiMe₃)₂]₃ adopts a C₃ symmetric structure with the ytterbium displaced from the plane defined by the three Yb-C bonds by 0.783(3) Å. The Yb–C_α (Yb-C₁) distance is 2.324(3) Å, which is nearly the same as the Lu-C_α distance in Lu[CH(SiMe₃)₂]₃ (2.319(3) Å) and the Sm-C_α distance in Sm[CH(SiMe₃)₂]₃ (2.33(2) Å).

Yb[CH(SiMe₃)₂]₃ contains short Yb···C<sub>γ</sub> contacts at 2.963(3) Å, which is slightly longer than Lu···C<sub>γ</sub> (2.936(2) Å) and Sm···C<sub>γ</sub> (2.85(3) Å) distances in Lu[CH(SiMe₃)₂]₃ and Sm[CH(SiMe₃)₂]₃, respectively. The Neumann projection shown in Fig. 2d contains distances and angles for the proximal Si–CH₃ group interacting with Yb. The C–H bond distances and angles are close to those expected for a tetrahedral sp³ hybridized carbon, again similar to results obtained for Lu[CH(SiMe₃)₂]₃. These structural data infer that a similar 3c-2e Yb–Me–Si interaction is present in Yb[CH(SiMe₃)₂]₃ under the conditions of low-temperature X-ray diffraction studies (i.e. 100 K).
<figure><img src="image_3.png" /></figure>

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<figure><img src="image_9.png" /><figcaption>Figure 2: (a) Synthesis scheme of Yb[CH(SiMe₃)₂]₃[x|O-2,6-tBu₂-C₆H₃]₃-x (x = 1, 2, 3). (b) Structure of the Yb[CH(SiMe₃)₂]₃ complex with displacement ellipsoids at 50 % probability level. For clarity the hydrogen atoms and the solvent molecules CH₂(SiMe₃)₂ are omitted. (c) Sketch of relevant bond lengths and angles of Yb[CH(SiMe₃)₂]₃. The bond lengths are reported in Å, and the bond angles (in red) are reported in degrees (see also Tab. S2). (d) Newman projection down the C(2)-Si(2) bond with bond lengths and angles (in red) obtained from the crystal structure of Yb[CH(SiMe₃)₂]₃. (e) Structure of the Lu[CH(SiMe₃)₂]₃ complex with displacement ellipsoids at 50 % probability level. For clarity the hydrogen atoms and the solvent molecules CH₂(SiMe₃)₂ are omitted. (f) Sketch of relevant bond lengths and angles of Lu[CH(SiMe₃)₂]₃. The bond lengths are reported in Å, and the bond angles (in red) are reported in degrees (see also Tab. S2) (f) Newman projection down the C(2)-Si(2) bond with bond lengths and angles (in red) obtained from the crystal structure of Lu[CH(SiMe₃)₂]₃. For comparison panels e)-g) are reproduced from¹⁰ with permission from the American Chemical Society, copyright 2016 Conley et al.¹⁰.</figcaption></figure>
## Magnetic susceptibility studies

We performed magnetic susceptibility studies for Yb[CH(SiMe₃)₂]₃, Yb[CH(SiMe₃)₂]₂[O-2,6-tBu₂-C₆H₃], Yb[CH(SiMe₃)₂][O-2,6-tBu₂-C₆H₃]₂, and

Yb[O-2,6-tBu₂-C₆H₃]₃ (see SI Chapter 6, Figs. S11 - S14 and Tab. S11 for more details).

All four ytterbium complexes exhibit experimental values of the effective magnetic moment at 300 K that are in the range between μ<sub>eff</sub>(300 K) = 4.30 (χT = 2.31 cm³ K mol⁻¹) - 4.53 μ<sub>B</sub> (χT = 2.57 cm³ K mol⁻¹). In particular, the effective magnetic moment of the Yb[CH(SiMe₃)₂]₃ complex is μ<sub>eff</sub>(300 K) = 4.53 μ<sub>B</sub>. These values are in good agreement with the expectation value for the free Yb(III) ion, described by a single ²F<sub>7/2</sub> term (4f¹³), for which μ<sub>eff</sub>(300 K) = 4.54 μ<sub>B</sub> (χT = 2.58 cm³ K mol⁻¹). Hence, these Yb complexes can be described by a single 4f¹³ configuration, similar to those of the free Yb(III) ion.

## EPR characterization of Yb[CH(SiMe₃)₂]₃

We characterized the Yb(III) alkyl complex Yb[CH(SiMe₃)₂]₃ using pulse EPR spectroscopy¹⁹ that, in combination with computational studies, enables the successful characterization of the spatial and electronic structure of paramagnetic complexes.²⁰,³⁷ The continuous-wave (CW) EPR spectrum of Yb[CH(SiMe₃)₂]₃ (Fig. 3a, blue) was reasonably reproduced by simulation (Fig. 3a, red) by modeling the Yb ion as an electronic spin *S* = 1/2, with *g* tensor principal values of *g*⊥ = 0.7316 and *g*∥ = 7.5698. The spectrum also exhibits a well-resolved satellite structure, due to hyperfine coupling to the two spin-active isotopes ¹⁷¹Yb (spin *I* = 1/2 and natural abundance of 14.31%) and ¹⁷³Yb (spin *I* = 5/2 and natural abundance of 16.13%) of the lanthanide. From spectral simulation (Fig. 3a, red), the ¹⁷¹,¹⁷³Yb hyperfine tensors were determined to be A<sub>⊥</sub>(¹⁷³Yb) = 221 MHz, A<sub>∥</sub>(¹⁷³Yb) = 1650 MHz, and accordingly A<sub>⊥</sub>(¹⁷¹Yb) = 842 MHz, A<sub>∥</sub>(¹⁷¹Yb) = 6285 MHz.
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Figure 3: (a) CW EPR spectrum of Yb[CH(SiMe₃)₂]₃ (blue) and simulation (red), together with an expansion of the low-field region. The black arrow marks the field position of the HYSCORE measurement. (b) Echo-detected EPR spectrum of Yb[CH(SiMe₃)₂]₃. The field position for HYSCORE and EDNMR are marked with a black and red arrow, respectively. (c) HYSCORE spectrum of Yb[CH(SiMe₃)₂]₃ (blue to yellow, see also Fig. S8) and simulation (red) based on a single ¹H hyperfine coupling AᵢₘsO(¹H) = 3.8 ± 0.3 MHz. Anti-diagonal lines indicate the ¹H and ²⁹Si nuclear Zeeman frequencies. Spurious peaks at 21.5/2.0 MHz and 23.5/23.5 MHz are electronic artefacts. (d) ¹H region of EDNMR spectrum of Yb[CH(SiMe₃)₂]₃ (blue), together with simulation (red) of a single effective ¹H coupling with Aₐff(¹H) = 13 ± 1 MHz (gray) and a ¹H matrix peak (gray dashed) at a ¹H nuclear Zeeman frequency of 39.4 MHz.
A higher-resolution picture can be provided by pulsed EPR spectroscopy, which has evolved into a robust tool for the determination of geometry and electronic configuration of organometallic complexes of paramagnetic *d*- and *f*-block metals. In particular, 2D hyperfine sub-level correlation spectroscopy (HYSCORE)³⁹ allows us to detect magnetically active nuclei (e.g. ¹H, ¹³C, ²⁹Si etc.) that are coupled to paramagnetic centres by hyperfine interaction, due to close spatial proximity to these centres. The technique can separate the isotropic (primarily Fermi-contact) and anisotropic (primarily spin-dipolar) parts of the hyperfine interaction tensors that are linked to the electronic properties of the systems (e.g. metal-ligand spin density transfer), and bonding between the nuclei and the paramagnetic centre. The HYSCORE spectrum of Yb[CH(SiMe₃)₂]₃ (Fig. 3c and Fig. S8) reveals the presence of hyperfine coupling to protons in the CH(SiMe₃)₂ alkyl ligands. From the simulation of the HYSCORE spectrum a single ¹H hyperfine tensor was determined to have Aᵢₐₗ(¹H) = 3.8 ± 0.3 MHz, Tᵣₐₗ(¹H) = 4.0 ± 0.5 MHz (Aᵣₐₗ = [-4.0 ± 0.5; -4.0 ± 0.5; 8.0 ± 1.0] MHz), with the tensors principal axes frame (PAF) rotated by 45° ± 15° with respect to the *z* axis of the PAF of the *g* tensor. This interpretation of the HYSCORE data is consistent with the ELDOR-detected NMR (EDNMR)⁴⁰ spectrum shown in Fig. 3d, from which we can extract a single splitting due to an effective hyperfine coupling to ¹H with Aᵣₐₗ(¹H) = 13 ± 1 MHz. Based on previous observations of similar isotropic and dipolar parts of hyperfine coupling tensors for the *S* = 1/2 Ti(III) alkyl complexes,³⁷,⁴¹ the observed ¹H hyperfine couplings could be assigned to the hydrogen atoms that are close in space to the Yb(III) centre, such as α-H atoms of CH(SiMe₃)₂ ligands. The positions of the α-H atoms within the structure of Yb[CH(SiMe₃)₂]₃ were further refined using quantum chemical computations (vide infra). This finding indicates that the transferred spin density is significant only for the closest to the Yb(III) atoms, such as C₁ and H₁, while it is substantially lower for the rest of the ligands. The observed isotropic ¹H hyperfine couplings that are even smaller than those observed for d¹ metal alkyls³⁷,⁴¹ suggest that, in contrast to the case of Cp₃Yb,²⁰ there is no significant charge and spin density transfer to the ligands in Yb[CH(SiMe₃)₂]₃. This is also consistent
with the preferential presence of the unpaired electron in the 4f orbital rather than in the valence 5d orbital, which would result in more significant distribution of the spin density into the ligands of Yb(III). A difficulty of promoting 4f electrons of Yb(III) to the 5d orbital, which effectively prevents the formation of double Yb=C bonds, was previously discussed based on CASSCF calculations.42 Taking into account the results of magnetic susceptibility measurements (vide supra), we propose that the ground state of the Yb[CH(SiMe₃)₂]₃ complex has a single electronic configuration of 4f¹³ (S = 1/2), close to the one of Yb(III) free ion.

## NMR characterization of Yb[CH(SiMe₃)₂]₃

Over the last twenty years, the development of instrumentation and spectroscopic methods in NMR allows us to target paramagnetic lanthanide complexes such as Yb[CH(SiMe₃)₂]₃. Specifically, solid-state NMR with fast MAS and broadband adiabatic irradiation sequences¹⁸ can now be used to obtain data on microcrystalline powders, where the complex dynamics are simplified and only the relevant internal ligand motions are retained. Nonetheless, obtaining high-quality magnetic resonance data on these systems represents only part of the challenge, since the resulting spectra are often very difficult to interpret using standard assignment methods. In this respect, recent progress in wave-function based/DFT methods for the computation of NMR parameters of paramagnetic complexes has also been impressive. For NMR, there have been significant advances both in the development of the formalism of the paramagnetic shifts²²⁻³⁰ and the computational implementation.³¹⁻³⁶ However, applying the developed methods to lanthanides has been a much more difficult matter.

For the Yb[CH(SiMe₃)₂]₃ complex, we are able to draw the conclusions regarding its electronic structure and on the positions of ¹H nuclei closest to the metal centre (α-H atoms of [CH(SiMe₃)₂] ligands, H₁) based on the EPR data and quantum chemistry calculations. However, the weak hyperfine interactions between the unpaired electron and the more distant nuclei prevented us from obtaining any high-resolution information about the rest of the
molecule by EPR. This gap could, however, be filled by paramagnetic NMR.¹⁸ Note that the
signals of H1 nuclei, most likely, cannot be observed by NMR, in particular, due to a severe
reduction of sensitivity because the large paramagnetic relaxation enhancement expected
for these nuclei in close proximity to Yb, or due to the fact that potentially large shifts
push them out of the excitation window. Therefore, EPR and NMR spectroscopies could
be seen as complementary techniques for the characterization of paramagnetic lanthanide
organometallic compounds like Yb[CH(SiMe₃)₂]₃, allowing to obtain the information from
both internal and external coordination environment of the metal center.

The ligands of the complex are expected to exhibit substantial dynamics, which has the effect of averaging the signals. This was observed in the case of the Lu analogue, where variable temperature ¹H solution NMR data were required to partially freeze out these motions and the individual ¹H resonances were obtained by cooling the sample. However, this approach was not successful for the present Yb complex, where no such resolution was obtained over a temperature range between 285 and 182 K, and no detection was possible beyond that because of increased line-broadening (see SI Chapter 3 & Fig. S7).

We therefore proceeded to examine the Yb[CH(SiMe₃)₂]₃ complex via solid-state MAS NMR, which has the advantage of eliminating molecular rotational diffusion, so that only the internal ligand dynamics remain. Such spectra relate to the room-temperature crystal structure, thereby providing a direct bridge to the low-temperature XRD data.

One-dimensional solid-state MAS NMR spectra of ¹H, ¹³C and ²⁹Si are shown in Figure 4a-c. Each of these spectra exhibits poorly resolved patterns, due to hyperfine interactions with the unpaired electron, which induce large shifts and shift anisotropies and extremely large inhomogeneous line-broadenings. We see shift anisotropies that are very large for all three nuclei, of the order of hundreds of ppm, in contrast to the Lu analogue, where the ¹H and ¹³C diamagnetic chemical shift anisotropies (CSAs) were too small to be measured and for ²⁹Si were of the order of tens of ppm. In particular, for the Lu analogue, ²⁹Si CSAs were used to characterize the metal-ligand interaction. That approach is not at first sight
obviously applicable to the paramagnetic Yb complex, since the interpretation of the shift anisotropy is more complex.

<figure><img src="image_14.png" /><figcaption>Figure 4: NMR spectra of Yb[CH(SiMe₃)₂]₃: (a) ¹H MAS spectra at 30 kHz MAS, (b) ¹³C MAS spectra of at 14.286 kHz MAS and (c) ²⁹Si MAS spectra at 30 kHz MAS, showing two distinct ²⁹Si signals. The spinning sidebands are marked with asterisks (*). 2D aMAT spectrum: (d) ¹H at 30 kHz, (e) ¹³C at 20 kHz and (f) ²⁹Si at 20 kHz. The indirect dimension projections were deconvolved using asymmetric Gaussian functions to extract the isotropic shifts and quantify shift dispersion. (g)-(i) extracted slices with isotropic shift corresponding to the maxima of the deconvolved projections and labelled with Roman numerals. Each slice was subsequently fitted considering a simple CSA model using the Haeberlen convention⁴³ ($\delta_{iso} = \frac{1}{3}(\tilde{\delta}_{xx} + \tilde{\delta}_{yy} + \tilde{\delta}_{zz})$, $\Delta\delta = \tilde{\delta}_{zz} - \tilde{\delta}_{iso}$ and $\eta = (\tilde{\delta}_{yy} - \tilde{\delta}_{xx})/\Delta\delta$, where $\tilde{\delta}_{xx}$, $\tilde{\delta}_{yy}$ and $\tilde{\delta}_{zz}$ are the components of the CSA tensor in the principal axes frame). See SI chapter 1.6 for more details.</figcaption></figure>

The first problem to be addressed is the lack of resolution of the individual signals in each
of the three spectra, due to the overlapping spinning sideband manifolds of neighboring res-
onances. To solve this problem, we employed the 2D adiabatic magic-angle turning (aMAT)
experiment,⁴⁴ which correlates each spinning side-band manifold to its isotropic shift, thus
removing the overlap, as seen in Figure 4d-f for ¹H, ¹³C and ²⁹Si, respectively. In all three
cases, the aMAT spectra are able to resolve two resonances with distinct isotropic shifts. For
²⁹Si, the interpretation is relatively straightforward, with the two signals V and VI being
due to the two inequivalent Si nuclei (specifically, one due to Si₁ and the other to Si₂). By
extension, it is reasonable to tentatively interpret each ¹³C signal (III and IV) as being from
the three methyl groups attached to each of the Si (C₂/₃/₄ and C₅/₆/₇), and each ¹H signal
(I and II) to the corresponding group of protons (H₂/₃/₄ and H₅/₆/₇).

<figure><img src="image_15.png" /></figure>

Figure 5: (a) ¹H-¹³C correlation spectrum achieved by using the TEDOR experiment⁴⁵ at 30 kHz MAS, yielding two distinct correlations of the resonances (III/I) and (IV/II), shown in Fig. 4, which were subsequently used to model the paramagnetic shifts in the following section. The spinning sidebands are marked with asterisks (*). (b) ¹H NMR shift distributions considering solely the contributions arising from the presence of the unpaired electron and neglecting long-range PCS effects stemming from parametric centres in neighboring unit cells (δₚ). The shifts were calculated considering the Moon and Patchkovski,²³ Vaara et al.²⁴,²⁵,²⁸ and van den Heuvel and Soncini²⁶,²⁷ formalism using the *g* tensor obtained using multi-reference perturbation theory (SO-CASPT2) on the DFT optimized geometry (see sections 1.8 and 5.3 of the SI for details) and the experimental ¹H hyperfine tensor. A distribution of relative orientations of the *g* and *A* tensors were considered using Zaremba, Conroy, Wolfsberg orientational averaging scheme with 1154 orientations.⁴⁶⁻⁴⁸ The relative orientation of the *z* axes of the *g* and *A* tensors was kept fixed at 45°, in order to match with the EPR results.
For each of the signals I-VI, a slice extracted from the aMAT spectra was fitted to determine the parameters of the shift tensor (isotropic shift $\delta$, shift anisotropy $\Delta\delta$ and asymmetry parameter $\eta$) (Fig. 4g-i). For each of the three nuclei, within each pair one signal (II, IV and V) possesses a larger isotropic shift and shift anisotropy compared to the second (I, III and VI). We can tentatively assign the former set of three signals to the same $SiMe_3$ group, and the latter set of signals to the other $SiMe_3$ group. This interpretation is supported by a transferred-echo double resonance (TEDOR) experiment$^{45}$ (Fig. 5a), which displays a first unambiguous correlation between I and III, a second unambiguous correlation between II and IV, and no other correlations. These solid-state NMR spectra and our tentative interpretation indicate that each group of $^1$H, $^{13}$C and $^{29}$Si resonances represents a single $SiMe_3$ group in which there are rotations about the C$_1$-Si bond and about the Si-C bonds of each of the three methyls. The rate constants describing each rotation are larger than the spread of the individual chemical shifts of the exchanging sites. Note that the predicted shifts of H$_1$ nuclei (see SI Chapter 5.3 for the details) lie within a range between 230 and 200 ppm (Fig. 5b), and are not observed in any of the 1H NMR spectra (1D, aMAT, TEDOR), as expected.

Therefore, we suggest that the observed signals are consistent with the presence of the two distinct types of $SiMe_3$ groups, associated with $Si_1$ and $Si_2$ nuclei. Note that the span ($\Omega = \delta_{11} - \delta_{33}$) of $Si_1$ is $\Omega(Si_1) = 676$ ppm, and the span of $Si_2$ is $\Omega(Si_2) = 479$ ppm. These values are significantly larger than those previously obtained for $Lu[CH(SiMe_3)_2]_3$ ($\Omega(Si_1) = 46.8$ ppm, $\Omega(Si_2 = 30.2$ ppm),$^{10}$ which is expected because that compound is diamagnetic. The pattern, observed for $Lu[CH(SiMe_3)_2]_3$, was the strongest experimental evidence that, combined with the DFT interpretations, showed that $Si_1$ was interacting with Lu through a Lu-Me-Si 3c-2e interaction.$^{10}$ Although the $\Omega$ values for $Yb[CH(SiMe_3)_2]_3$ are significantly larger, a similar pattern emerges; $Si_1$ has a larger $\Omega(Si)$ than $Si_2$, suggesting that $Si_1$ is also interacting with Yb to form a 2c-2e Yb-Me-Si.
# Computational studies of Yb[CH(SiMe₃)₂]₃

## Ab initio electronic structure

The molecular geometry obtained by XRD was optimized using DFT using the ORCA package⁴⁹ (see Fig. S9, and Tables S7 and S8 for the details of DFT-optimized structure of Yb[CH(SiMe₃)₂]₃). Both the starting and optimized geometries were then used to calculate the electronic energy levels using complete active space (CAS) methods using the MOLCAS package.⁵⁰,⁵¹ The results, reported in Table 1, are similar, and in the following we confined our discussion on the results obtained on the DFT-optimized structure.

<table><caption>Table 1: Ab-initio energy levels (in cm⁻¹) of the ²F (at spin-free level) and ²F₇/₂⁻₅/₂ (at spin-orbit coupling level) manifolds in Yb³⁺(CH(SiMe₃)₂)₃. The spin-orbit energy levels are doubly degenerate.</caption><thead><tr><th></th><th>E<sub>1</sub></th><th>E<sub>2</sub></th><th>E<sub>3</sub></th><th>E<sub>4</sub></th><th>E<sub>5</sub></th><th>E<sub>6</sub></th><th>E<sub>7</sub></th></tr></thead><tbody><tr><td colspan="8" style="text-align: center;">XRD</td></tr><tr><td>SF-CASSCF</td><td>0</td><td>144</td><td>682</td><td>687</td><td>1031</td><td>1123</td><td>1203</td></tr><tr><td>SF-CASPT2</td><td>0</td><td>205</td><td>823</td><td>928</td><td>1181</td><td>1392</td><td>1769</td></tr><tr><td>SO-CASSCF</td><td>0</td><td>525</td><td>889</td><td>1088</td><td>10387</td><td>11007</td><td>11341</td></tr><tr><td>SO-CASPT2</td><td>0</td><td>659</td><td>1043</td><td>1452</td><td>10420</td><td>11166</td><td>11660</td></tr><tr><td colspan="8" style="text-align: center;">Optimized</td></tr><tr><td>SF-CASSCF</td><td>0</td><td>168</td><td>694</td><td>694</td><td>1074</td><td>1083</td><td>1203</td></tr><tr><td>SF-CASPT2</td><td>0</td><td>383</td><td>949</td><td>1002</td><td>1331</td><td>1393</td><td>1729</td></tr><tr><td>SF-CASSCF<sup>a</sup></td><td>0</td><td>172</td><td>746</td><td>748</td><td>1161</td><td>1172</td><td>1297</td></tr><tr><td>SO-CASSCF</td><td>0</td><td>526</td><td>888</td><td>1070</td><td>10387</td><td>11006</td><td>11327</td></tr><tr><td>SO-CASPT2</td><td>0</td><td>689</td><td>1068</td><td>1386</td><td>10428</td><td>11189</td><td>11613</td></tr><tr><td>SO-CASSCF<sup>a</sup></td><td>0</td><td>565</td><td>959</td><td>1154</td><td>9214</td><td>9891</td><td>10241</td></tr></tbody></table>

ᵃ: in ORCA

The seven inner-core active 4f orbitals are shown in Figure 6 along with the three energetically higher bonding type orbitals of the Yb – Cα bonds. Out of the seven active orbitals, the lowest one is non-bonding, followed by two sets of doubly-degenerate orbitals: one undergoes a slight π anti-bonding interaction with the Cα pz orbitals and the other one is non-bonding. The final two orbitals characterize a σ bonding interaction with the Cα sp² hybrid orbitals. The seven 4f orbitals are very little admixed with the ligand orbitals, yet the ligand field splitting at the orbital level, or at the many-electron level, is relatively large
compared to the case of O and N donor ligands (usually 200-300 cm⁻¹). This is similar to the case of YbCp₃, which has also been shown to exhibit a large ligand field splitting.²⁰ The active 4f orbitals are mostly perturbed by electrostatic interactions, while the Yb valence 6s, 6p and 5d orbitals mostly participate in the bonding interactions with the Cα sp² hybrid orbitals. As a result, population analysis of the ground spin-free CASSCF state (see Table 2) leads to significant electron occupations in the Yb(III) atomic valence and Rydberg orbitals.

<figure><img src="image_16.png" /><figcaption>Figure 6: Surface plots of the three Yb – Cα bonding orbitals and the seven 4f active orbitals of the Yb<sup>III</sup>(CH(SiMe<sub>3</sub>)<sub>2</sub>)<sub>3</sub> complex (separated by the vertical line). The canonical energies (in cm<sup>-1</sup>) are given in parentheses. The isosurface value is at ± 0.02 a.u. The dominant compositions of the orbitals are also shown.</figcaption></figure>

<table><caption>Table 2: The Mulliken (M) and Löwdin (L) charge populations of the Yb atomic orbitals in Yb<sup>III</sup>(CH(SiMe<sub>3</sub>)<sub>2</sub>)<sub>3</sub> from different calculation methods.</caption><thead><tr><th></th><th>s populations</th><th>p populations</th><th>d populations</th><th>f excess <sup>d</sup></th></tr></thead><tbody><tr><td>SF-CASSCF (M)<sup>a</sup></td><td>0.50(6s+7s)</td><td>1.52(6p+7p)</td><td>1.22(5d+6d)</td><td>0.02</td></tr><tr><td>SF-CASSCF (M)<sup>b</sup></td><td>0.48(6s+7s)</td><td>0.76(6p+7p)</td><td>1.13(5d+6d)</td><td>0.14</td></tr><tr><td>SF-CASSCF (L)<sup>b</sup></td><td>0.19(6s+7s)</td><td>0.60(6p+7p)</td><td>1.87(5d+6d)</td><td>0.52</td></tr><tr><td>ZORA-DFT(PBE0)(M)</td><td>0.72(6s+7s)</td><td>1.06(6p+7p)</td><td>1.84(5d+6d)</td><td>0.18</td></tr><tr><td>ZORA-DFT(PBE0)(L)</td><td>0.32(6s+7s)</td><td>0.77(6p+7p)</td><td>2.28(5d+6d)</td><td>0.60</td></tr></tbody></table>

<sup>a</sup>: basis set: ANO-RCC-TZVP(Yb, Si and Cα) + ANO-RCC-DZP (C,H) in MOLCAS,

<sup>b</sup>:basis set: SARC-DKH-TZVP(Yb) and IGLO-III (rest) in ORCA, <sup>c</sup>: basis set:

SARC-ZORA-TZVP(Yb) and TZVP (rest) in ORCA, <sup>d</sup>: excess of combined 4f+5f orbital occupations than the formal 4f electron number.

At the spin-free (SF) CASSCF level, the <sup>2</sup>F manifold of the central Yb(III) ion splits
into three singlets, of relative energies of 0, 168 and 1203 cm⁻¹, and two orbital doublets at 694 and ~1074 cm⁻¹, following the energy stabilization of the unpaired electron or hole in the trigonal ligand field. Dynamic correlation energy correction at the MS-CASPT2 method further increases the energy splitting by further stabilizing and destabilizing the bonding and anti-bonding type orbitals. At the spin-orbit (SO) level, the four Kramers doublets (KDs) of the ground *J* = 7/2 manifold are split by the axial ligand field in the order *m*<sub>*J*</sub> = ±7/2 < ±5/2 < ±3/2 < ±1/2. The ligand field splitting is around 1400 cm⁻¹, seven times larger than the room temperature thermal energy (200 cm⁻¹). In fact, the first excited KD characterized by *m*<sub>*J*</sub> = ±5/2 is around 690 cm⁻¹ and is not meaningfully populated at room temperature. The irreducible spherical tensor ligand-field parameters extracted from the model spaces of the ground *L* (at SF) and *J* (at SO) manifolds are given in Table 3. The dominant ligand-field parameter is the second-rank axial component *B*<sub>0</sub><sup>2</sup>, but the components of orders three and six are also significant, as expected from the three-fold symmetry axis. The *B*<sub>0</sub><sup>2</sup> component is related to the quadrupole moment of the ligand field and its negative value corresponds to an oblate coordinating sphere. The excited *J* = 5/2 manifold is energetically well separated by more than 10000 cm⁻¹ in accordance with the SO coupling strength (ζ<sub>4f</sub> ≈ 2900 cm⁻¹) of the Yb 4f electrons.<sup>52</sup>

<table><caption>Table 3: The irreducible spherical tensor ligand-field components of rank *k* and order *m* (*B*<sub>*m*</sub><sup>*k*</sup>) and strength parameters (*S*) (in cm⁻¹) of Yb<sup>III</sup>(CH(SiMe<sub>3</sub>)<sub>2</sub>)<sub>3</sub> determined from the ab initio ground *L* (SF) and *J* (SO) manifolds.</caption><thead><tr><th></th><th><i>B</i><sub>0</sub><sup>2</sup></th><th><i>B</i><sub>2</sub><sup>2</sup></th><th><i>B</i><sub>0</sub><sup>4</sup></th><th><i>B</i><sub>2</sub><sup>4</sup></th><th><i>B</i><sub>3</sub><sup>4</sup></th><th><i>B</i><sub>4</sub><sup>4</sup></th><th><i>B</i><sub>0</sub><sup>6</sup></th><th><i>B</i><sub>2</sub><sup>6</sup></th><th><i>B</i><sub>3</sub><sup>6</sup></th><th><i>B</i><sub>4</sub><sup>6</sup></th><th><i>B</i><sub>6</sub><sup>6</sup></th><th><i>S</i></th></tr></thead><tbody><tr><td>SF-CASSCF</td><td>-1839</td><td>11</td><td>-24</td><td>3</td><td>317</td><td>3</td><td>43</td><td>2</td><td>185</td><td>3</td><td>216</td><td>487</td></tr><tr><td>SF-CASPT2</td><td>-2302</td><td>74</td><td>-97</td><td>173</td><td>374</td><td>161</td><td>-465</td><td>58</td><td>331</td><td>62</td><td>550</td><td>630</td></tr><tr><td>SO-CASSCF</td><td>-1854</td><td>11</td><td>-33</td><td>3</td><td>316</td><td>3</td><td>36</td><td>2</td><td>167</td><td>3</td><td>221</td><td>490</td></tr><tr><td>SO-CASPT2</td><td>-2319</td><td>75</td><td>-104</td><td>168</td><td>368</td><td>164</td><td>-454</td><td>51</td><td>296</td><td>55</td><td>580</td><td>634</td></tr></tbody></table>

## Computational interpretation of the EPR data

Based on the DFT-computed structure of Yb(CH(SiMe<sub>3</sub>)<sub>2</sub>)<sub>3</sub> (Fig. S9), we first performed a calculation of hyperfine couplings for the α-H atoms of [CH(SiMe<sub>3</sub>)<sub>2</sub>] ligands (H<sub>1</sub>) with PBE0
functional (see SI Chapter 1.8 for the details). While the precise prediction of isotropic hyper-
fine couplings for H₁ nuclei is unlikely due to the close proximity of H₁ to Yb, which requires
high-level relativistic electronic structure methods for accurate determination of spin den-
sity delocalization, the dipolar (anisotropic) part of the hyperfine coupling tensor could still
be a reliable descriptor for comparison between experimental and computed hyperfine cou-
plings. The computed hyperfine coupling tensors for all three H₁ nuclei of the [CH(SiMe₃)₂]
ligands, similarly to the experimental ones, appeared to be nearly axial: A<sub>iso</sub>(1) = -0.26
MHz, A<sub>dip</sub>(1) = [-4.00 -4.50 8.51] MHz; A<sub>iso</sub>(2) = -0.15 MHz, A<sub>dip</sub>(2) = [-3.80 -3.84 7.64]
MHz; A<sub>iso</sub>(3) = -0.21 MHz, A<sub>dip</sub>(3) = [-4.47 -4.32 8.79] MHz. Furthermore, the calculated
dipolar hyperfine tensor values A<sub>dip</sub> are in a very good agreement with the experimental
values (A<sub>dip</sub> = [-4.0 ± 0.5; -4.0 ± 0.5; 8.0 ± 1.0] MHz). This indicates that the position of
the α-H (H₁) atoms of the [CH(SiMe₃)₂] ligands of Yb(CH(SiMe₃)₂)₃, including the related
Yb-H distances and the unusually short Yb-C-H angles of ca. 93° (see Tables S7 and S8),
are nicely reproduced within the DFT-optimized structure (Fig. S9).

Next, the SO-CASPT2 *g* factors, *g*<sub>⊥</sub> = 0.72 and *g*<sub>‖</sub> = 7.77 (see Table 4) are also in
very good agreement with the experimental values and show a substantial improvement
as compared to the SO-CASSCF values (*g*<sub>⊥</sub> = 0.40, *g*<sub>‖</sub> = 7.91, respectively) due to the
better inclusion of the electron dynamical correlation. The anisotropic orbital and spin
contributions to the magnetic moments as a result of the figand field and spin-orbit coupling
admixing of the 4f orbitals are also shown. The magnetic moment of the ground KD is
significantly anisotropic, as characterized by the prolate *m*<sub>J</sub> = ±7/2 state stabilizing the
unpaired electron in the bonding active 4*f*<sub>y</sub>(3*x<sup>2</sup>-*y*<sup>2</sup>) and 4*f*<sub>x</sub>(*x*<sup>2</sup>-3*y*<sup>2</sup>) orbitals, as shown in Figure
6. In addition, the EPR hyperfine coupling parameters to the central <sup>171</sup>Yb (*I* = 1/2) nucleus
were calculated from first principle methods using a finite nuclear model. The SO-CASSCF
calculations are in good agreement with experiments as shown in Table 4. Quantitative
evaluation of the hyperfine coupling value in the strong relativistic limit requires a forefront
level of computational methods and is still in the developing phase. The Fermi contact
$(A_{FC})$, spin-dipolar $(A_{SD})$ and orbital $(A_{orb})$ contributions to the hyperfine tensor in Table 4 indicate a dominant anisotropic nuclear spin - electron orbit coupling which leads to the large Yb(III) hyperfine $A_{\perp}$ and $A_{\parallel}$ components. The good agreement between calculated and experimental *g* tensor values and <sup>171</sup>Yb hyperfine couplings indicates that our computational approach, based on DFT-optimized geometry and CAS methods, describes well the electronic structure of Yb(CH(SiMe<sub>3</sub>)<sub>2</sub>)<sub>3</sub>.

<table><caption>Table 4: The ab initio *g*-factors and hyperfine coupling parameters (in MHz) of the central <sup>171</sup>Yb (<i>I</i> = 1/2) in Yb<sup>III</sup>(CH(SiMe<sub>3</sub>)<sub>2</sub>)<sub>3</sub> . *L* and *S* are the orbital and spin contributions, respectively, to the magnetic moments. The spin-dipolar (SD), orbital (orb) and Fermi-contact (FC) contributions to the calculated hyperfine values are shown.</caption><thead><tr><th></th><th>g<sub>x</sub><sup>L</sup></th><th>g<sub>y</sub><sup>L</sup></th><th>g<sub>z</sub><sup>L</sup></th><th>g<sub>x</sub><sup>S</sup></th><th>g<sub>y</sub><sup>S</sup></th><th>g<sub>z</sub><sup>S</sup></th><th>g<sub>x</sub></th><th>g<sub>y</sub></th><th>g<sub>z</sub></th><th>g<sub>iso</sub></th><th>&Delta;g<sub>ax</sub></th></tr></thead><tbody><tr><td>SO-CASSCF</td><td>0.27</td><td>0.27</td><td>5.92</td><td>0.13</td><td>0.13</td><td>1.99</td><td>0.40</td><td>0.40</td><td>7.91</td><td>2.90</td><td>7.51</td></tr><tr><td>SO-CASPT2</td><td>0.50</td><td>0.45</td><td>5.81</td><td>0.25</td><td>0.24</td><td>1.96</td><td>0.75</td><td>0.69</td><td>7.77</td><td>3.10</td><td>7.05</td></tr><tr><td>SO-CASSCF<sup>a</sup></td><td>0.27</td><td>0.27</td><td>5.92</td><td>0.13</td><td>0.13</td><td>1.99</td><td>0.38</td><td>0.38</td><td>7.90</td><td>2.89</td><td>7.52</td></tr><tr><td></td><td>A<sub>&perp;,SD</sub></td><td>A<sub>&parallel;,SD</sub></td><td>A<sub>&perp;,orb</sub></td><td>A<sub>&parallel;,orb</sub></td><td>A<sub>&perp;,FC</sub></td><td>A<sub>&parallel;,FC</sub></td><td>A<sub>&perp;</sub></td><td>A<sub>&parallel;</sub></td><td></td><td></td><td></td></tr><tr><td>SO-CASSCF<sup>a</sup></td><td>-24</td><td>-748</td><td>287</td><td>6728</td><td>105</td><td>108</td><td>368</td><td>6088</td><td></td><td></td><td></td></tr></tbody></table>

## Computational interpretation of the magnetic susceptibility data

For comparison the first principal calculated molar magnetic susceptibilities of Yb<sup>III</sup>(CH(SiMe<sub>3</sub>)<sub>2</sub>)<sub>3</sub> are provided in Table 5. The main magnetic axis ($\chi_z$) coincides with the $C_3$ axis. The calculated isotropic part of the magnetic susceptibility $\chi T$ at 300 K is 2.30 cm<sup>3</sup> K mol<sup>-1</sup> and is comparable to the experimental result of 2.57 cm<sup>3</sup> K mol<sup>-1</sup>. The axial anisotropy of the molar magnetic susceptibility $\Delta\chi_{ax} = \chi_z - (\chi_x + \chi_y)/2$ is very large in this complex and dominated by the anisotropic contribution from the ground KD (calculated to be $\Delta\chi_{ax}^{KD1} = 23.44*10^{-8}$ m<sup>3</sup> mol<sup>-1</sup>), and is due to the large ligand field splitting and consequent non-homogeneous population in the 4f orbitals.

<footnote><sup>a</sup>: SO-CASSCF in ORCA, Experimental $g_{x,y} = 0.73$, $g_z = 7.57$ and $A_{\perp} = 842$ MHz, $A_{\parallel} = 6285$ MHz</footnote>
<table><caption>Table 5: The molar magnetic susceptibilities of Yb<sup>III</sup>(CH(SiMe<sub>3</sub>)<sub>2</sub>)<sub>3</sub> (in 10<sup>-8</sup> m<sup>3</sup>mol<sup>-1</sup>) at 300 K from ab initio calculations.</caption><thead><tr><th></th><th>χ<sub>x</sub><sup>L</sup></th><th>χ<sub>y</sub><sup>L</sup></th><th>χ<sub>z</sub><sup>L</sup></th><th>χ<sub>x</sub><sup>S</sup></th><th>χ<sub>y</sub><sup>S</sup></th><th>χ<sub>z</sub><sup>S</sup></th><th>χ<sub>x</sub></th><th>χ<sub>y</sub></th><th>χ<sub>z</sub></th><th>χ<sub>iso</sub></th><th>χ<sub>iso</sub>T</th><th>Δχ<sub>ax</sub></th></tr></thead><tbody><tr><td>SO-CASSCF</td><td>2.23</td><td>2.26</td><td>17.56</td><td>0.82</td><td>0.83</td><td>5.87</td><td>3.05</td><td>3.09</td><td>23.43</td><td>9.85</td><td>2.37</td><td>20.36</td></tr><tr><td>SO-CASPT2</td><td>1.63</td><td>1.91</td><td>17.69</td><td>0.63</td><td>0.73</td><td>5.94</td><td>2.26</td><td>2.63</td><td>23.63</td><td>9.50</td><td>2.29<sup>a</sup></td><td>21.19</td></tr></tbody></table>

<sup>a</sup>: SQUID value = 2.57 in CGS unit

## NBO and QTAIM analyses

The DFT optimized structure (Fig. S9) is in particular notable for the unusually short (ca. 93°) Yb-C-H<sub>1</sub> angles for all the [CH(SiMe<sub>3</sub>)<sub>2</sub>]<sub>3</sub> ligands (see Tab. S7). The shortened Yb-C-H angles for the α-H atoms of the [CH(SiMe<sub>3</sub>)<sub>2</sub>]<sub>3</sub> ligands might be explained by a simultaneous electrostatic repulsion from the Yb centre and the two Si atoms of the CH(SiMe<sub>3</sub>)<sub>2</sub> ligand. A similar effect was previously observed for the [CH(SiMe<sub>3</sub>)<sub>2</sub>]<sub>3</sub> ligands of the Lu(III)<sup>10</sup> or Ti(III) analogues.<sup>41</sup> This interaction is essentially described as the donation of electrons from the filled molecular orbital corresponding to the C-H bond to a metal d-orbital of appropriate symmetry, and has been related to a metal-carbon bond acquiring a π (or alkylidene) character, often called α-H agostic interaction in metal alkyls.<sup>3,4,7</sup> In order to investigate the possible presence of the π character within the Yb-C bonds, we conducted a Natural Bond Orbital (NBO) analysis,<sup>53</sup> using the program NBO 7.0<sup>54</sup> (see SI Chapter 5.2 for more details). The molecular orbital set for the NBO analysis was generated with DFT, using the PBE0 functional.

Indeed, the NBO analysis revealed a high degree of deviation of the natural hybrid orbitals (NHO) on α-C atoms from the Yb-C axis ($\theta_{NHO-C-Yb}$ = 17.8° for one [CH(SiMe<sub>3</sub>)<sub>2</sub>]<sub>3</sub> ligand and 17.9° for the other two alkyl ligands). The value of such deviation can be used as a quantitative descriptor of the degree of the π character within the metal-carbon bonds (for a pure σ bond, no deviation would be expected).<sup>4</sup> In fact, the degree of the π character within the Yb-C bonds is higher than the one observed for Ti(III), Ti(IV) and Zr(IV) neutral alkyl complexes, while being somewhat smaller than for the related cationic complexes.<sup>4,37</sup>

Furthermore, the NBO analysis revealed three low-lying natural orbitals, which have
been attributed to the low-lying 5d orbitals, with their occupancies being slightly higher than 5% (see Tab. S11). The spatial distribution of these orbitals (Fig. 7a) includes, in particular, three lobes of p-type on each of the α-C atoms of the $[CH(SiMe_3)_2]_3$ ligands, all being in antiphase with the central d-type lobes (Fig. 7a, marked with arrows). These parts of the orbital can be viewed as π* orbitals of the Yb-C bonds,³⁷ thus confirming the partial alkylidenic character of these bonds.³,⁴

<figure><img src="image_17.png" /><figcaption>Figure 7: (a) Natural spin-α orbital, representing one 5d orbital of Yb[$[CH(SiMe_3)_2]_3$ (red for positive and blue for negative signs of the wavefunction, the same in all panels). The p-type parts of the orbital (two out of three) are marked with arrows. (b) Overlap of the same 5d orbital (wireframe contour) with natural spin-α orbital, corresponding to the bonding orbital of one of Si-Cγ bonds (solid contour).</figcaption></figure>

The obtained significant stabilization energies for these 5d orbitals (see Tab. S9) imply that there are other secondary interactions within the structure of Yb[$[CH(SiMe_3)_2]_3$ that involve these 5d orbitals. One example of such an interaction is the three-centre - two-electron Yb-Me-Si interaction, previously observed for the Lu[$[CH(SiMe_3)_2]_3$ analogue.¹⁰ Indeed, the NBO analysis reveals the constructive overlap between these 5d orbitals and the bonding orbitals of the Si-Cγ bonds (Fig. 7b), thus showing that such interactions are also predicted
for the Yb[CH(SiMe₃)₂]₃ complex.

Next, to further probe the chemical bonding interactions, the DFT computed electron density was analysed by the quantum theory of atoms in molecules (QTAIM) method. The QTAIM approach is based on the topological analysis of the physically observable electron density, and is thus theoretically independent of the computational method. The bonding descriptors, namely the electron density ($ρ_b$), its Laplacian ($∇²ρ_b$), the potential energy density ($V_b$) and the kinetic energy density ($G_b$) at the so-called line critical point (LCP, i.e. the inflection point at the gradient path between two neighboring atoms) are of interest in this kind of analysis. Generally at the LCP, $ρ_b > 0.20$ a.u. with a negative Laplacian indicates a shared electron interaction between two atoms. Accompanied by $|V_b|/G_b > 1$ and $H_b = V_b + G_b < 0$, this typically indicates bound electrons at the LCP, often interpreted as a covalent interaction. For Yb[CH(SiMe₃)₂]₃, the C-H bonds yield typical values of closed shell interactions with $ρ_b > 0.25$ and negative Laplacian, while the Si-C bonds give $ρ_b ≈ 0.11$ with a positive Laplacian, which is characteristic of an ionic interaction. By contrast, the values for both the Yb – Cα and Yb – Cγ ($ρ_b = 0.078$ a.u. and $0.016$ a.u. respectively, with positive Laplacians, see Tab 6) indicate donor-acceptor type bonding interactions.

<table><caption>Table 6: Bonding descriptors at the Yb – Cα and Yb – Cγ (ag) line critical points. The NBO and QTAIM charges are indicated for the atoms concerned by the agostic interactions.</caption><thead><tr><th>Bonds</th><th>ρ<sub>b</sub></th><th>∇<sup>2</sup>ρ<sub>b</sub></th><th>|V<sub>b</sub>|/G<sub>b</sub></th><th>H<sub>b</sub></th></tr></thead><tbody><tr><td>Yb – C<sub>α</sub></td><td>0.078</td><td>0.149</td><td>1.434</td><td>-0.0286</td></tr><tr><td>Yb – C<sub>γ</sub><sup>(ag)</sup></td><td>0.016</td><td>0.058</td><td>0.865</td><td>0.0018</td></tr><tr><td>Charges</td><td>q<sub>Yb</sub></td><td>q<sub>Cα</sub></td><td>q<sub>Siβ</sub></td><td>q<sub>Cγ</sub><sup>(ag)</sup></td></tr><tr><td>NBO<sup>a</sup></td><td>1.32</td><td>-1.38</td><td>1.81</td><td>-1.11</td></tr><tr><td>QTAIM</td><td>3.21</td><td>-2.03</td><td>2.82</td><td>-0.82</td></tr></tbody></table>

<sup>a</sup>: on Lu<sup>III</sup>(CH(SiMe₃)₂)₃ complex.

The NBO and QTAIM charges vary due to their different ways of partitioning the total electron density onto the individual atoms, but both indicate that a Yb – Cγ interaction is caused by the Coulomb attraction between the positively charged Yb and negatively charged Cγ atoms.
Computational interpretation of the NMR data

In order to confirm our tentative interpretation and provide a site-specific assignment, we calculated the NMR shift tensors of all the spin-active nuclei in the complex. The total NMR shift can be expressed as:

$$ \delta = \delta_{\text{orb}} + \delta_{\text{FC}} + \delta_{\text{PSO}} + \delta_{\text{SD}} + \delta_{\text{LR}}, \quad (1) $$

where $\delta_{\text{orb}}$ corresponds to the orbital chemical shift, i.e. the contribution from the orbital motion of the electrons, $\delta_{\text{FC}}$ is the Fermi contact shift due to the through-bond hyperfine interaction, $\delta_{\text{PSO}}$ is the paramagnetic spin-orbital shift due to the interaction between the nuclear spin and the electron orbital angular momentum, $\delta_{\text{SD}}$ and $\delta_{\text{LR}}$ are the short-range intra-molecular and long-range inter-molecular pseudo-contact shifts (PCS) due to the through-space hyperfine interactions, respectively. To account for long-range contributions, we calculated through-space magnetic dipolar contributions using the semi-classical point-dipolar equation (eq. SI-10) and a spherical bath of surrounding paramagnetic ions up to 50 Å distant in the crystal structure. The intramolecular contributions to the NMR shielding tensor of each nucleus were calculated according to the following equation,

$$ \boldsymbol{\sigma} = \boldsymbol{\sigma}^{\text{orb}} - \frac{\chi^s}{N_A \mu_0 \mu_B g_e \gamma \hbar} [A_{\text{FC}} + A_{\text{SD}} + A_{\text{orb}}] \quad (2) $$

where $\boldsymbol{\sigma}^{\text{orb}}$ is the diamagnetic orbital contribution calculated using a scalar relativistic ZORA-DFT method employing the PBE0 functional, $\chi^s$ is the spin-only magnetic susceptibility tensor calculated from the SO-CASPT2 method and the hyperfine tensors are computed either from SO-CASSCF or unrestricted DFT methods. $\mu_B$ is the Bohr magneton and $g_e$ is the free electron g-factor. In accordance with the tentative assignment of the experimental spectra, a three-site fast exchange model was employed to average the shift tensors both within the methyl groups (along the Si-C$_i$ bonds) and the Me$_3$Si groups (along
the C₁-Si bonds). The total computed shift tensors are presented both before (in Table 7) and after (in Table S10) taking into account these rotations.

<table><caption>Table 7: Calculated and experimental shift parameters for the proximal (denoted by p) and distal (denoted by d) –SiMe₃ group of Yb<sup>III</sup>(CH(SiMe₃)₂)₃ in the Haeberlen convention after a three-site fast exchange averaging of the shielding tensors. The shielding tensor is computed according to 2 where the magnetic susceptibility tensor has been computed with the SO-CASPT2 method and the hyperfine tensors are either from the SO-CASSCF or DFT(PBE0) methods. Long-range contributions has been accounted using the semi-classical point dipolar equation according to eq. SI10.</caption><thead><tr><th rowspan="2">Method</th><th colspan="2"><sup>29</sup>Si</th><th colspan="2"><sup>13</sup>C</th><th colspan="2"><sup>1</sup>H</th></tr><tr><th>p</th><th>d</th><th>p</th><th>d</th><th>p</th><th>d</th></tr></thead><tbody><tr><td></td><td>δ<sup>orb</sup></td><td>-10.7</td><td>-9.2</td><td>2.8</td><td>4.6</td><td>0.2</td><td>0.4</td></tr><tr><td></td><td>δ<sup>LR</sup></td><td>16.9</td><td>16.5</td><td>28.5</td><td>9.5</td><td>15.6</td><td>27.6</td></tr><tr><td rowspan="5">SO-CASPT2/CASSCF</td><td>δ<sup>SD</sup></td><td>-67.4</td><td>-9.6</td><td>-4.4</td><td>0.5</td><td>7.4</td><td>2.1</td></tr><tr><td>δ<sup>PSO</sup></td><td>-201.0</td><td>-29.2</td><td>-15.9</td><td>1.7</td><td>21.4</td><td>6.6</td></tr><tr><td>δ<sup>FC</sup></td><td>3.0</td><td>7.6</td><td>2.4</td><td>0.5</td><td>0.2</td><td>0.0</td></tr><tr><td>δ<sup>total</sup></td><td>-259.2</td><td>-23.9</td><td>13.4</td><td>16.8</td><td>44.8</td><td>36.7</td></tr><tr><td>Δδ</td><td>-493.2</td><td>-19.3</td><td>-41.4</td><td>-28.4</td><td>10.2</td><td>21.8</td></tr><tr><td rowspan="5">SO-CASPT2/PBE0</td><td>δ<sup>SD</sup></td><td>-61.2</td><td>-10.2</td><td>-1.1</td><td>-0.4</td><td>6.3</td><td>1.9</td></tr><tr><td>δ<sup>PSO</sup></td><td>-78.4</td><td>-10.3</td><td>-8.6</td><td>1.0</td><td>7.4</td><td>2.4</td></tr><tr><td>δ<sup>FC</sup></td><td>-24.4</td><td>-77.4</td><td>67.7</td><td>14.7</td><td>3.0</td><td>0.4</td></tr><tr><td>δ<sup>total</sup></td><td>-157.8</td><td>-90.6</td><td>89.3</td><td>29.4</td><td>32.5</td><td>32.7</td></tr><tr><td>Δδ</td><td>-321.8</td><td>-122.0</td><td>-256.6</td><td>-51.0</td><td>25.1</td><td>18.3</td></tr><tr><td rowspan="2">Exp</td><td>δ</td><td>-220±20</td><td>-30±30</td><td>40±20</td><td>-20±20</td><td>30±20</td><td>-20±20</td></tr><tr><td>Δδ</td><td>-542±3</td><td>409±3</td><td>-183±4</td><td>140[+30,-270]</td><td>153±1</td><td>-56±1</td></tr></tbody></table>

On examining the computed shift tensors, we see that each nuclear species gives two distinct signals, with the shift and shift anisotropy of one species being consistently larger than those of the other species. There are clear quantitative discrepancies with the experimental values, but the general trends are reproduced. We can therefore assign the signals from the Me₃Si(₂) group, with the larger shifts and shift anisotropies, to the proximal (p) ligand, and the signals from Me₃Si(₁), with the smaller shifts and shift anisotropies, to the distal (d) ligand.

It is instructive to examine the breakdown of the shifts into the contributions given in
Eq. (1). The FC contribution is negligible in all cases, due to the very limited transfer of the unpaired spin density to these atoms over two, three or four bonds. The intra-molecular PCS is more significant, and is consistently larger for the proximal ligand than for the distal ligand, for all three nuclear species, which is a straightforward consequence of the former being in closer proximity to Yb than the latter. This conclusion is also true in the presence of rotational dynamics, where upon rotation about the C₁-Si bond, the three methyls on Si₂ are on average closer to the Yb ion than those on Si₁. The same trend is seen for the more dominant PSO contribution, which for the same reasons is consistently larger by up to one order of magnitude for the proximal ligand. Finally, the long-range PCS is also dominant, due to the large magnetic anisotropy of Yb(III) in this complex. A comparison between the proximal and distal ligands reveals more comple trends than for the intra-molecular PCS, due to the packing of molecules in the crystal lattice.

Overall, the interpretation of the NMR data provides evidence that the same structural distortions, observed in the low-temperature XRD structure and associated with the presence of 3c-2e Yb-Me-Si interactions, persist at the higher temperature of the solid-state NMR measurements (ca. 300 K). Therefore, the Yb[CH(SiMe₃)₂]₃ complex possesses the Yb···Cγ interaction, described as a pseudo bridging Yb-Me-Si group and previously observed¹⁰ for Lu[CH(SiMe₃)₂]₃ (see Figure 1), at both low- and room-temperature and irrespective of the presence of the incomplete electronic f-shell.

Conclusions

This study establishes that pulsed EPR and paramagnetic solid-state NMR spectroscopies
are highly complementary and able, when coupled with the advanced computational meth-
ods, to provide detailed information about the geometry and electronic structure of param-
agnetic compounds such as Yb[CH(SiMe₃)₂]₃. Besides the specific geometry typically acces-
sible by X-Ray diffraction, this study provides direct spectroscopic evidences for the 3c-2e
Yb-Me-Si interaction and for the presence of π-character in the Yb-C bond in this para-
magnetic compound, paralleling what is observed for the diamagnetic Lu analog10 and so
commonly among the corresponding dº organometallics,³,⁴,⁷ often referred to as an α-H agos-
tic interaction. In fact, the magnetic data for Yb[CH(SiMe₃)₂]₃ indicates a f¹³ ground state
configuration with no evidence for a multiconfigurational ground state that is often observed
in lanthanide compounds,²⁰,⁵⁵⁻⁵⁸ probably further explaining the observed similarities with
the Lu isostructural compound. Yet, while magnetic susceptibility measurements indicate
that the magnetic moment is consistent with that of a free Yb(III) ion, CAS-based calcula-
tions instead reveal an unusually large crystal-field splitting resulting in a ground KD that is
almost completely thermally isolated even at room temperature and which results in a large
magnetic anisotropy.

Acknowledgement

We acknowledge Laurent Maron (Université Paul Sabatier, Toulouse) for discussions at the
early stage of this project. We acknowledge Maciej Korzynski (ETHZ) for a help with prepa-
ration of the manuscript. We acknowledge Elizaveta A. Suturina (University of Bath) and
Aleksander Jaworski (Stockholm University) for the advices concerning quantum chemistry
calculations in lanthanide complexes. We thank Martin Bröring (Institut für Anorganische
und Analytische Chemie) at TU Braunschweig for providing access to the SQUID magne-
tometer.

**Supporting Information Available**

**Supporting Information**

The Supporting Information is available free of charge on the ACS Publications website.
**Author Information**

Richard A. Andersen passed away on June 16, 2019 while the early draft of this manuscript was being written; this manuscript is dedicated to his memory.

**Corresponding Authors**

* andrew.pell@ens-lyon.fr; ccoperet@ethz.ch; gjeschke@ethz.ch; guido.pintacuda@ens-lyon.fr

**Author contribution**

A.A. and D.K. performed EPR measurements. F.A. and M.P.C. developed the synthetic procedures. J.P.C. and K.J.S. conducted NMR measurements. M.A.I., J.P.C. and A.A. performed quantum chemical calculations. M.W. and F.A. performed XRD studies. D.B. and M.D.W. conducted magnetic susceptibility measurements. M.D.W., A.J.P., C.C., G.J., G.P. and R.A.A. supervised the project. All authors participated in writing the manuscript. A.A., F.A., M.A.I., J.P.C., K.J.S. and M.P.C. declare equal contribution.

**Funding Sources**

A.A. was supported by a SNF - ANR grant (Mr. CAT 2-77275-15). J.P.C. was supported by the Swedish Research Council (2016-03441), M.A.I. by the Agence Nationale de la Recherche (ANR-21-CE29-0010-01) and by an installation grant of the ENS Lyon, and K.J.S. by the European Research Council (ERC-2015-CoG P-MEM-NMR). Calculations were performed thanks to an access grant to the Pôle Scientifique de Modélisation Numérique (PSMN) at the ENS Lyon.
Table of Contents Figure

<figure><img src="image_18.png" /></figure>

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