Metal–carbon bonding in early lanthanide substituted cyclopentadienyl complexes probed by pulsed EPR spectroscopy

We examine lanthanide (Ln)–ligand bonding in a family of early Ln3+ complexes [Ln(Cptt)3] (1-Ln, Ln = La, Ce, Nd, Sm; Cptt = C5H3tBu2-1,3) by pulsed electron paramagnetic resonance (EPR) methods, and provide the first characterization of 1-La and 1-Nd by single crystal XRD, multinuclear NMR, IR and UV/Vis/NIR spectroscopy. We measure electron spin T1 and Tm relaxation times of 12 and 0.2 μs (1-Nd), 89 and 1 μs (1-Ce) and 150 and 1.7 μs (1-Sm), respectively, at 5 K: the T1 relaxation of 1-Nd is more than 102 times faster than its valence isoelectronic uranium analogue. 13C and 1H hyperfine sublevel correlation (HYSCORE) spectroscopy reveals that the extent of covalency is negligible in these Ln compounds, with much smaller hyperfine interactions than observed for equivalent actinide (Th and U) complexes. This is corroborated by ab initio calculations, confirming the predominant electrostatic nature of the metal–ligand bonding in these complexes.


Synthetic Procedures for 1-Ln
[La(Cp tt )3] (1-La).THF (30 mL) was added to a pre-cooled (−78 °C) ampoule containing LaCl3 (0.491 g, 2 mmol) and KCp tt (1.298 g, 6 mmol).The reaction mixture was allowed to reflux for 16 hours.The solvent was removed in vacuo and toluene (30 mL) was added.The reaction mixture was allowed to reflux for 40 hours.The resultant pale yellow suspension was allowed to settle for 3 hours and filtered.
The solvent was removed in vacuo and toluene (30 mL) was added.The reaction mixture was allowed to reflux for 40 hours.The resultant suspension was allowed to settle for 3 hours and filtered.The green solution was concentrated to 2 mL and stored at 8 °C to give 1-Nd as green crystals (0.460 g, 34%).

Crystallography
The crystal data for complexes 1-La and 1-Nd are compiled in Table S1, and are depicted in Figures S11 and S12, respectively.Crystals of 1-La and 1-Nd were examined using an Oxford Diffraction Supernova diffractometer with a CCD area detector and a mirror-monochromated Mo Kα radiation (λ = 0.71073 Å).Intensities were integrated from data recorded on 1° frames by ω rotation.Cell parameters were refined from the observed positions of all strong reflections in each data set.A Gaussian grid faceindexed (1-Nd) or multi-scan (1-La) absorption correction with a beam profile was applied. 1 The structures were solved using SHELXS; 2 the datasets were refined by full-matrix least-squares on all unique F 2 values, 3 with anisotropic displacement parameters for all non-hydrogen atoms, and with constrained riding hydrogen geometries; Uiso(H) was set at 1.2 (1.5 for methyl groups) times Ueq of the parent atom.The largest features in final difference syntheses were close to heavy atoms and were of no chemical significance.CrysAlisPro 1 was used for control and integration, and SHELX 2,3 was employed through OLEX2 4 for structure solution and refinement.ORTEP-3 5 and POV-Ray 6 were employed for molecular graphics.CCDC 2271676 and 2271677 contain the supplementary crystal data for this article.These data can be obtained free of charge from the Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.
Powder XRD data of microcrystalline samples of 1-Ln mounted with a minimum amount of fomblin were collected at 100(2) K using a Rigaku FR-X rotating anode single crystal X-ray diffractometer using Cu Kα radiation (λ = 1.5418Å) with a Hypix-6000HE detector and an Oxford Cryosystems nitrogen flow gas system (Figures S13-S16).Data were collected between 2-70 °θ with a detector distance of 150 mm and a beam divergence of 1.5 mRad using CrysAlisPro. 1 For data processing, the instrument was calibrated using silver behenate as standard, then the data were reduced and integrated using CrysAlisPro.We observe polycrystallinity effects, previously reported for similar complexes. 8Simulation parameters are given in Table S2.We observe polycrystallinity effects, previously reported for similar complexes. 8Simulation parameters are given in Table S2.S2. were recorded with a two-pulse primary Hahn-echo sequence (/2 - - - -echo), 9 with microwave  pulses of 32 or 64 ns, a fixed delay time  = 300 ns, and with the variation of the static B0 magnetic field.Those measurements at 34 GHz (Q-band; Figure S30) were recorded with microwave  pulses of 40 ns, and a fixed delay time  = 300 ns.Electron spin echo envelope modulation (ESEEM) measurements involved monitoring the echo intensity generated with a primary Hahn-echo sequence as a function of .A similar pulse sequence was used to measure the phase memory time, Tm, with the difference that longer pulse durations (up to 128 ns) were necessary to suppress possible 1 H nuclear modulation effects in the echo decays (Figures S31-S33).Tm was determined by least squares fitting of the experimental echo decay data using a stretched exponential function with a solver based on the Levenberg-Marquardt algorithm.
The fitting function used was: (2) = (0) (−2   ⁄ ) (Equation 1) or, for strongly modulated data, 2) where k is the modulation depth,  is the Larmor angular frequency of a nucleus I coupled to the electron spin,  is the phase correction, X is the stretching parameter, Y(2) is the echo integral for a pulse separation , and Y(0) is the echo intensity extrapolated to  = 0. [10][11][12][13] The extracted Tm times are given in Tables S3-S7.3) where Y1 and YSD are the amplitudes, and TSD is the spectral diffusion time constant, 12 giving the results presented in Tables S3-S7.The presence of two decays is commonly attributed to the occurrence of both spectral diffusion (SD) and spin-lattice relaxation (T1) of which the latter is usually assigned as being the slower process. 13We notice that the magnetization recovery curves do not reach full saturation below 15 K, indicating that the T1 spin-lattice relaxation time is very long.Fitting such curves to an exponential model is likely to introduce some inaccuracy in the determination of the T1 values at these temperatures.Table S7.Extracted spin lattice (T1) and phase memory (Tm) times and the stretching parameter X for 1-Ce at 3 and 5 K (10 mM tol-hex) measured at Q-band.The HYSCORE spectra were recorded at X-band with a four-pulse sequence, /2--/2-t1--t2-/2echo, 9 with pulses /2 and  of 16 and 32 ns, respectively, and fixed  (136, 200 or 400 ns).Times t1 and t2 were varied from 100 to 5200 ns in increments of 20 ns.256 data points were collected in both dimensions.A four-step phase-cycle procedure was used to eliminate unwanted echo contributions.
Fourier transformation of the data in both directions yielded 2D (1, 2) spectra in which the nuclear cross-peaks (i.e.peaks that correlate nuclear frequencies from opposite spin-manifolds) of the 1 H and 13 C nuclei appeared in the (+,+) quadrant of the (1, 2) map, at separations equivalent with the corresponding hyperfine coupling frequencies (weak coupling regime: 2|n|>|A|). 9The contour lineshape of the cross peaks, and their displacement from the anti-diagonal about the nuclear Larmor frequency (n), relate to the magnitude and anisotropy of the hyperfine couplings, and thus analysis of the HYSCORE spectra allows to determine such parameters.
Spectra modelling using EasySpin assumed that the hyperfine coupling matrix (A) for a given 13 C nucleus n is determined by the point dipole (through space) interaction with spin density at the metal ion, given by Equation ( 4): where gn is the scalar isotropic nuclear g-value,  ̿ is the identity matrix,  is the distance of the nucleus from the Ln 3+ ion (in m), n is the Ln-n unit vector expressed in the molecular frame (and ñ is its transpose), βe and βn are the electron and nuclear magnetons, h is Plank's constant, and μ0 is the vacuum permittivity.It is also assumed that gz lies along the pseudo-C3 axis (Figure 6), and that the electron spin density is located at the lanthanide ion.A dip is then calculated for each unique carbon position in the Cp tt ligands, using the crystallographic coordinates of the atoms.Simulations considering only A dip reproduce the experimental data satisfactorily for 1-Nd and 1-Ce (Figure 6).
Modelling of the 1 H HYSCORE data involved a similar approach, including the point dipolar 1 H hyperfine (A dip ) for the protons of the cyclopentadienyl rings (H 2 , H 4 , H 5 ), and all protons of the methyl groups supposed to be close to the Ln(III) ion.with Gaussian 16 Rev.C.01. 16 The Stuttgart effective f-in-core pseudopotentials 17 were used for the lanthanide ions and the cc-pVDZ 18 basis set was used to treat the remaining C and H atoms.
Complete active space self-consistent field with spin-orbit coupling (CASSCF-SO) 19,20 calculations with an active space containing all 4f electrons and seven 4f orbitals were performed to compute the magnetic properties of 1-Ce, 1-Sm, and 1-Nd; for 1-Ce there are two molecules in the unit cell with different metrics so both were calculated.The relativistic atomic natural orbital (ANO-RCC) [21][22][23][24][25] basis sets were used in the CASSCF-SO calculations and the valence orbital treatment was varied based on the distance from the paramagnetic centre: Ln -VTZP; C(Cp), H(Cp), C(tbu1) -VDZP; all other C and H -VDZ.The CASSCF-SO calculations were performed using OpenMolcas version 22.06. 26e 1 H and 13 C HYSCORE simulations of 1-Ce and 1-Nd were obtained by calculating relativistic hyperfine coupling constants using DFT-optimized geometries and the above CASSCF-SO methods, feeding into the Hyperion 27 package.The hyperion2easyspin utility was then used to generate EasySpin 28 input files, and the EPR parameters were used to simulate HYSCORE spectra with saffron. 7re, using five C(Cp) atoms from one ligand and using three H(Cp) atoms (one H2-, H4-and H5-type atom from one Cp ligand), accurately reproduced the experimental 13 C and 1 H spectra, respectively.
Figure S1. 1 H NMR spectrum of complex 1-La in C6D6 zoomed in the region 1 and 7.5 ppm.Solvent residual marked.

Figure S3. 1 H
Figure S3.1 H NMR spectrum of complex 1-Ce in C6D6 zoomed in the region -7 and 28 ppm.Solvent residual marked; minor diamagnetic impurities can be seen between 0 and 4 ppm.

Figure S4. 1 H
Figure S4.1 H NMR spectrum of complex 1-Nd in C6D6 zoomed in the region -20 and 40 ppm.Solvent residual marked; minor diamagnetic impurities can be seen between 0 and 7 ppm.

Figure S5. 1 H
Figure S5.1 H NMR spectrum of complex 1-Sm in C6D6 zoomed in the region -4 and 22. Solvent residual marked; minor diamagnetic impurities can be seen between -1 and 7 ppm.

S13 4 . 2
Figure S13.Simulated X-ray diffraction pattern from single crystal X-ray diffraction at 150 K (red) compared to experimental powder XRD pattern at 100 K (black) for 1-La (arbitrary intensities).

Figure S14 .
Figure S14.Simulated X-ray diffraction pattern from single crystal X-ray diffraction at 150 K (red) compared to experimental powder XRD pattern at 100 K (black) for 1-Ce (arbitrary intensities).

Figure S15 .
Figure S15.Simulated X-ray diffraction pattern from single crystal X-ray diffraction at 150 K (red) compared to experimental powder XRD pattern at 100 K (black) for 1-Nd (arbitrary intensities).

Figure S16 .
Figure S16.Simulated X-ray diffraction pattern from single crystal X-ray diffraction at 130 K (red) compared to experimental powder XRD pattern at 100 K (black) for 1-Sm (arbitrary intensities).

Figure S22 .
Figure S22.Field dependence of the magnetization for 1-Nd at 2 and 4 K. Solid lines from CASSCF-SO calculations using the XRD geometry.

Figure S23 .
Figure S23.Field dependence of the magnetization for 1-Ce at 2 and 4 K. Solid lines from CASSCF-SO calculations on molecule 1 using the XRD geometry (there are two independent molecules with different metrical parameters in the unit cell of 1-Ce, so both were computed; see Section 8 for details).

Figure S24 .
Figure S24.Field dependence of the magnetization for 1-Sm at 2 and 4 K. Solid lines from CASSCF-SO calculations using the XRD geometry.

Figure S28 .
Figure S28.Calculated derivative of the X-band (9.7 GHz) EDFS spectra in Figure 5, for frozen solutions of 1-Nd and 1-Ce at 5 K.

Figure S29 .
Figure S29.(left) X-band (9.7 GHz) EDFS spectrum of a frozen solution (10 mM in 9:1 toluene-hexane at 5 K) of 1-Sm.Arrows indicate the observer field positions where T1 and Tm were measured.(right) Calculated derivative for the same EDFS spectrum.

Figure S33 .
Figure S33.Normalized Hahn echo signal intensities at Q-band of (left) 1-Nd and (right) 1-Ce as a function of the inter-pulse delay 2τ at different magnetic fields at 5 K, measured with π/τ (ns) of 40/400.7.2.3.Spin-lattice Relaxation Time (T1) Spin-lattice relaxation time data (Figures S34-S35) were acquired with a standard magnetization inversion recovery sequence, -t-/2----echo, 9 with t = 32 ns and  = 300 ns for X-band and with t = 40 ns and  = 400 ns for Q-band, and variable t.The spin-lattice relaxation time constant, T1, was determined by fitting the experimental data to the following biexponential decay function:

Table S2 .
Hamiltonian parameters obtained from the CW simulation of 1

Table S6 .
Extracted spin lattice (T1) and phase memory (Tm) times and the stretching parameter X for 1-Nd at 3 K (10 mM tol-hex) measured at Q-band.

Table S8 .
Calculated dipolar interactions of 1-Nd used for HYSCORE simulations.

Table S9 .
Calculated dipolar interactions of 1-Ce used for HYSCORE simulations.

Table S11 .
Crystal field states of 1-Nd.

Table S13 .
Energies, g-values and crystal field states of 1-Sm.

Table S14 .
CASSCF-SO hyperfine couplings of 1-Ce used for HYSCORE simulations, obtained using optimized structure.

Table S15 .
CASSCF-SO hyperfine couplings of 1-Nd used for HYSCORE simulations, obtained using optimized structure.