Tris-Silanide f-Block Complexes: Insights into Paramagnetic Influence on NMR Chemical Shifts

The paramagnetism of f-block ions has been exploited in chiral shift reagents and magnetic resonance imaging, but these applications tend to focus on 1H NMR shifts as paramagnetic broadening makes less sensitive nuclei more difficult to study. Here we report a solution and solid-state (ss) 29Si NMR study of an isostructural series of locally D3h-symmetric early f-block metal(III) tris-hypersilanide complexes, [M{Si(SiMe3)3}3(THF)2] (1-M; M = La, Ce, Pr, Nd, U); 1-M were also characterized by single crystal and powder X-ray diffraction, EPR, ATR-IR, and UV–vis–NIR spectroscopies, SQUID magnetometry, and elemental analysis. Only one SiMe3 signal was observed in the 29Si ssNMR spectra of 1-M, while two SiMe3 signals were seen in solution 29Si NMR spectra of 1-La and 1-Ce. This is attributed to dynamic averaging of the SiMe3 groups in 1-M in the solid state due to free rotation of the M–Si bonds and dissociation of THF from 1-M in solution to give the locally C3v-symmetric complexes [M{Si(SiMe3)3}3(THF)n] (n = 0 or 1), which show restricted rotation of M–Si bonds on the NMR time scale. Density functional theory and complete active space self-consistent field spin–orbit calculations were performed on 1-M and desolvated solution species to model paramagnetic NMR shifts. We find excellent agreement of experimental 29Si NMR data for diamagnetic 1-La, suggesting n = 1 in solution and reasonable agreement of calculated paramagnetic shifts of SiMe3 groups for 1-M (M = Pr and Nd); the NMR shifts for metal-bound 29Si nuclei could only be reproduced for diamagnetic 1-La, showing the current limitations of pNMR calculations for larger nuclei.


Synthesis
Complexes 1-M were prepared by salt metathesis reactions between solvated trivalent metal iodide precursors, [MI 3 (THF) x ] (M = La, Ce, Pr, U, x = 4; M = Nd, x = 3.5), and three equivalents of potassium hypersilanide, [K{Si-(SiMe 3 ) 3 }], in diethyl ether (Scheme 1).Crystalline samples of 1-M were obtained in ca.40% yields (range = 33−51%) following workup and recrystallization from hexane.Microcrystalline 1-M showed nearly superimposable ATR-IR spectra (see Supporting Information Figures S42−S47), indicating that they have similar solid-state structures.We consistently obtained low carbon values for 1-M in elemental analyses; we attribute this to incomplete combustion due to silicon carbide formation as this has been postulated for f-block silicon complexes previously, and we note that elemental analysis experiments can be capricious. 48,49We therefore interrogated 1-M by powder XRD and found high phase purity in all cases (see Supporting Information Figures S57−S67 and Table S2).

Structural Characterization
The molecular structures of 1-M were confirmed by single crystal XRD (1-U is shown in Figure 1 and key metrical parameters for all 1-M are compiled in Table 1; see Supporting Information Figures S53−S56 for depictions of other 1-M and Table S3 for additional crystallographic data).(3.155(2) Å). 40 Structurally authenticated U−Si bonds are rare 27 45 In all solid-state structures of 1-M, three Si−Si bonds are located in the plane defined by the central MSi 3 motifs, and the remaining six Si−Si bonds are equally arranged above and below this plane in a fan arrangement.

Solution NMR Spectroscopy
Despite the paramagnetism of 1-Ce, 1-Pr, 1-Nd, and 1-U, we were able to assign solution 1 H, 13 C{ 1 H} and 29 Si DEPT90 NMR spectra for all complexes (see Supporting Information Figures S1−S28 for all solution NMR spectra and Table S1 for selected parameters; selected data are compiled in Table 2); these assignments were verified by 1 H COSY, 1 H− 13 C HMBC and HSQC, and 1 H− 29 Si HMBC experiments.Although 1 H → 29 Si polarization transfer using the DEPT90 approach is expected to increase the sensitivity of 29 Si signals, we note that it is not optimal for concomitant 2 J and 3 J scalar coupling; so the metal-bound Si resonances have low intensities.4 were not observed.NMR data were therefore acquired on ca.9:1 C 6 D 6 : C 4 D 8 O (by volume) solutions of 1-M (50 mM) that have decomposition t 1/2 > 2 h, allowing reliable 1 H NMR integrals to be extracted.We found that C 4 D 8 O had to be added before C 6 D 6 to obtain acceptable NMR spectra, which still contained signals consistent with HSi(SiMe 3 ) 3 and silicone grease impurities; other decomposition products that reproducibly formed were not identified (solutions of 1-Pr showed the fastest decomposition, see Supporting Information Section 1.6.and Figures S29−S31 for a systematic study).
A sample of 1-La with an internal standard of 1,3,5-tritertbutylbenzene was dissolved in neat C 4 D 8 O in an effort to reduce sample decomposition prior to collection of NMR spectra and to investigate THF exchange dynamics further.However, this did not provide NMR data that were easier to interpret than those obtained for the 9:1 C 6 D 6 /C 4 D 8 O solution due to the complex exchange behavior, thus we did not extend this study to C 4 D 8 O solutions of paramagnetic 1-M (see Supporting Information Section S1.7. and Figures S32− S34 for an extended discussion).The 1 H and 13 C{ 1 H} NMR spectra of 1-La, 1-Ce, and 1-U exhibit only slightly shifted THF resonances compared to free THF; the THF signals in the 1 H NMR spectra are broadened with unreliable integrals, and THF resonances are not assigned in samples of 1-Pr and 1-Nd.We note that a number of signals are observed in the 1 H and 13 C{ 1 H} NMR spectra of 1-Pr and 1-Nd that may arise from THF, but we do not assign them as their identity is uncertain due to sample decomposition and complex exchange equilibria.The lower gyromagnetic ratio of 13 C nuclei in combination with the generally short relaxation times in these samples precluded the assignment of THF signals via correlation experiments.
Together, these data indicate that THF may dissociate from 1-M in solution to give [M{Si(SiMe 3 ) 3 } 3 (THF) n ] (n = 0 or 1), which hereafter we, respectively, refer to as M(THF) 0 and M(THF) 1 .We posit that the loss of coordinated THF and generation of vacant coordination site(s) is the origin of the relatively facile solution decomposition of 1-M, as previously found for [Ln(Si t Bu 2 R) 2 (THF) 3 ] (Ln = Sm, Eu, Yb, R = Me; Ln = Sm, Eu, R = t Bu). 46The 1 H NMR spectra of 1-M each contain two resonances for the SiMe 3 groups in a 1:2 ratio (herein referred to as group 1 and group 2, respectively), confirming that the time-averaged structures are still 3-fold symmetric; we note that the resonances associated with group 2 are broad (fwhm > 65 Hz) for the most paramagnetic M(III) ions in 1-Nd and 1-U.
While two resonances were seen for SiMe 3 groups in both the 13 C{ 1 H} and 29 Si DEPT90 NMR spectra of 1-La and 1-Ce, only resonances associated with group 1 were observed in the corresponding spectra of 1-Pr, 1-Nd, and 1-U; this is likely due to the increased anisotropic paramagnetic broadening associated with these ions. 1 Resonances between δ Si values of −65.5 and −82.3 ppm in the 29 Si DEPT90 NMR spectra of 1-M were assigned to the metal-bound silicon atoms (Figure 2); the 29 Si DEPT NMR spectral windows were +175 to −225 ppm.The 29 Si shifts observed fall within a relatively narrow range, considering the differences in both paramagnetism and size of the metal ions across the 1-M series, as the exchange dynamics will vary with metal−ligand distances.The consistent observation of metal-bound silicon resonances for the most paramagnetic 1-M when some SiMe 3 resonances were not seen is in accord with increased line-broadening for the latter signals from dynamic THF exchange outweighing the relative effects of paramagnetic broadening.In the 1 H− 29 Si HMBC NMR spectra of 1-M, correlations were seen between δ Si (MSi) and the δ H (Si(CH 3 ) 3 ) signals corresponding to group 1, but no cross-peaks were observed between δ Si (MSi) and the group 2 SiMe 3 groups.For 1-La and 1-Ce, cross-peaks were seen between δ H (Si(CH 3 ) 3 ) and δ Si (Si(CH 3 ) 3 ) for both the group 1 and group 2 SiMe 3 groups, whereas for 1-Pr, 1-Nd and 1-U correlations were only observed for the group 1 SiMe 3 groups, as the group 2 SiMe 3 resonances were not observed by 13 C{ 1 H} and 29 Si DEPT90 NMR spectroscopy (see above).

Solid-State NMR Spectroscopy
As solution NMR spectroscopy indicated that THF readily dissociates from 1-M in solution to give [M{Si-(SiMe 3 ) 3 } 3 (THF) n ] (n = 0 or 1), we turned to ssNMR spectroscopy to characterize trigonal bipyramidal 1-M with a known geometry (see Table 3 and Supporting Information Table S2 for selected parameters, Figure 3 for the 29 Si ssNMR spectra, and Supporting Information Figures S35−S41 for all other spectra).Magic angle spinning (MAS) conditions were employed with spinning frequencies between 5 and 12 kHz; frequencies were selected depending on the sample to give adequate resolution and signal-to-noise ratios, while shifting the spinning side bands from the spectral regions of interest and limiting excessive spinning rates to avoid rotor crashes.The resolution (fwhm) of the 29 Si ssNMR resonances did not change with MAS frequency [slow (5 kHz) vs moderate (12 kHz) spinning], but the 1 H ssNMR spectral resolution varied dramatically as expected (see Supporting Information).
For diamagnetic 1-La, the signal in the 29 Si MAS NMR spectrum at δ iso = −102.6ppm is assigned to the metal-bound Si atoms (Figure 3).The line shape of this signal is consistent   29 Si apparent transverse relaxation time, determined from the peak fwhm.Si MAS NMR spectra of 1-M recorded at ambient temperature using the indicated MAS frequencies.The spectra of 1-La, 1-Ce, and 1-Pr were recorded with { 1 H−} 29 Si crosspolarization, while the spectra of 1-Nd and 1-U were recorded with direct 29 Si excitation.Asterisks (*) denote spinning side bands, whereas daggers ( †) and double daggers ( ‡) denote HSi(SiMe 3 ) 3 and HSi(SiMe 3 ) 3 with an eight-line multiplet owing to the J coupling to 139 La (I = 7/2, 99.9% naturally abundant) where unequal lifetimes of the 139 La Zeeman states, which are on the order of the reciprocal of the J coupling (∼290 Hz), cause variable broadening of the multiplet lines (see Supporting Information Figure S35).The isotropic shift of the metal-bound silicon resonance in the 29 Si MAS NMR spectrum, δ iso-ss , is comparable but not identical to the corresponding signal seen in solution, δ iso-sol (Δ sol-ss = 19.5 ppm), which is indicative of a different Si environment.The 29 Si MAS NMR data of 1-La can be compared with those recently reported for a series of La(III) Cp silanide anions, though for the majority of these complexes the metal-bound Si atom signals were resolved octets and J coupling constants could be extracted straightforwardly: [La(Cp) 3 (SiR 3 )] − (SiR 3 = Si(H)-(C 6 H 2 Me 3 -2,4,6) 2 , δ iso : −36.0 ppm, 1 J LaSi = 335 Hz; Si(Me)-Ph 2 , δ iso : −1.7 ppm, 1 J LaSi = 337 Hz; SiPh 3 , δ iso : 7.0 ppm, 1 J LaSi = 318 Hz; Si{Si(H)Ph 2 }Ph 2 , δ iso : −21.1 ppm, 1 J LaSi not observed). 55Only one signal was observed for the SiMe 3 groups of 1-La at δ iso = −4.6 ppm, which is at a similar chemical shift to the group 2 SiMe 3 groups in the solution 29 Si DEPT90 NMR spectrum (δ iso = −5.3ppm).However, given the good intensity and resolution of this spectrum and the clear absence of a second SiMe 3 signal, we posit that there is dynamic averaging of the SiMe 3 groups in the solid state at ambient temperature, as seen previously for a Cr(II) borylene complex, [Cr{=BSi(SiMe 3 ) 3 }(CO) 5 ]. 56or all paramagnetic 1-M, we do not observe signals that can be reliably assigned to metal-bound Si atoms, with resonances in the expected region attributed to minor diamagnetic impurities in the sample including HSi(SiMe 3 ) 3 53 and another signal at −82 ppm that could not be identified.As the relaxation rate that causes paramagnetic broadening is ∝1/r 6 (where r is the M−Si distance), we assume that the MSi signals are hidden in the baseline due to the degree of magnetic anisotropy of the M(III) ion; this is evidenced by the broad SiMe 3 resonances, e.g., CeSi expected fwhm ∼4 kHz (32 ppm) and USi expected fwhm ∼25 kHz (200 ppm).In solution, these effects are averaged due to molecular tumbling, allowing metal-bound Si resonances to be observed (see above).Only one signal associated with the SiMe 3 groups is seen in the 29 Si MAS NMR spectra of all paramagnetic 1-M, consistent with the spectrum of 1-La (see above); these signals are paramagnetically shifted from 1-La to various extents depending on the identity of the M(III) ion (δ iso { 29 Si} = 7.2 ppm, 1-Ce; 28.8 ppm, 1-Pr; 52.5 ppm, 1-Nd; 1.1 ppm, 1-U), with the smaller magnetic anisotropy of Ce(III) resulting in a relatively sharp signal and the larger magnetic anisotropies of Pr(III), Nd(III), and U(III) giving broader resonances.These shifts essentially arise from a large deshielding of the δ 11 component of the 29 Si chemical shift tensor (see Table 3), as the δ 22 and δ 33 components typically display negligible change (except for 1-Nd and 1-U).This infers a large anisotropy of the 29 Si chemical shielding of the SiMe 3 moieties and thus asymmetry of the electron distribution along the Si−Si bond, which is influenced by the f-block ion.For 1-Ln, the magnitude of the deshielding of the δ 11 component is inversely proportional to the apparent ionic radius (taken from the M−Si bond distance, Table 1) of the f-ion (i.e., δ 11 { 29 SiMe 3 } Nd > Pr > Ce > La).However, this is not the case for 1-U, where a relative shielding of the δ 22 and δ 33 components of the 29 SiMe 3 groups is observed; this could arise from the intrinsic larger covalent effects of 5f vs 4f orbitals, 6d mixing, or a spin−orbit coupling effect.
For the majority of paramagnetic 1-M, the corresponding 1 H MAS NMR spectra are relatively uninformative (see Supporting Information Figure S40).However, resonances from metal-bound THF can be observed for 1-Ce (δ iso { 1 H} = 11.3 and 5.9 ppm), which are clearly deshielded compared to those from 1-La (δ iso { 1 H} = 5.2 and 2.6 ppm, see Supporting Information Figure S41), with the CH 2 protons either side of the O atom showing the largest shift.This arises from the proximity of these atoms to the paramagnetic Ce and results in a large deshielding of the δ 11 component of the CSA tensor (see Supporting Information Table S2); it appears that the corresponding δ 22 component becomes more shielded.

Magnetism
The effective magnetic moment (μ eff ) and molar magnetic susceptibility (χ M T) of powdered samples of paramagnetic 1-M suspended in eicosane were examined by variable-temperature DC SQUID magnetometry and CASSCF-SO (see below) calculations (selected parameters compiled in Table 4, see Supporting Information Figures S68−S70 and Table S5 for all magnetic data).There is good agreement between measured and calculated magnetization values and those expected for free M(III) ions Ce(III) (4f 1 2 F 5/2 ), Nd(III) (4f 3 4 I 9/2 ), and U(III) (4f 3 4 I 9/2 ).However, low magnetic susceptibility values were observed for several different batches of 1-Pr; at 300 K, the discrepancy between the experimental data presented and the expected value for a Pr(III) ion (4f 2 3 H 4 ) and the CASSCF-SO predicted value (see below) is ca.0.3 cm 3 mol −1 K, which may warrant future investigation. 1 A gradual decrease in χT with temperature was observed for all 1-M, due to thermal depopulation of excited crystal field states, with a sharper drop in χT < ca.30 K attributed to poor thermal equilibration of the sample at lower temperatures.Magnetic saturation (M sat ) was not reached at 2 K for 1-Ce or 1-Pr in fields up to 7 T, but this was effectively reached for 1-Nd and 1-U under the same conditions, with 2 and 4 K magnetization vs field traces in good agreement with those calculated for 1-Ce, 1-Nd, and 1-U.Both 1-Nd and 1-U exhibit similar waistrestricted hysteresis loops at 2 K (see Supporting Information Figure S70).

EPR Spectroscopy
The electronic structures of the Kramers ion complexes 1-Ce, 1-Nd, and 1-U were probed further by continuous wave Xband (ca.9.4 GHz) EPR spectroscopy, with spectra modeled using EasySpin. 64The easy-axis powder EPR spectrum for 1-Ce at 7 K (Table 5, see Supporting Information Figure S71) is best modeled as an effective S = 1/2 with g 1 = 2.445 and g 2 = 0.786 which are clearly observed, while g 3 ∼ 0.57 is broadened into the baseline.An easy-axis powder EPR spectrum was also observed for 1-Nd at 5 K, where hyperfine coupling to I = 7/2 143 Nd (12.2%) and 145 Nd (8.3%) nuclei could be modeled for the sharp low-field feature (g 1 = 6.26,A 1 = 1860 MHz) and a broad absorption at high field to account for g 2 (0.36), g 3 was not observed (<0.4;Table 5, Figure 5).A frozen solution EPR spectrum of 1-Nd in 2-Me-THF at 7 K reveals a sharp easy-axis component, consistent with the powder EPR spectrum, in addition to a broad rhombic signal spanning 115−850 mT with a peak centered at g 1 ∼ 4.8, a broad derivative-like feature at g 2 ∼ 2.1, and no resolved g 3 feature (broadened into g 2 or <0.4;Table 5, Figure 5).The broad rhombic signal, which deviates significantly from the solid-state data, could arise from Nd(THF) n (n = 0 or 1) and/or a range of intermediate geometries; this assertion is supported by the significant change in the g-values of the ground Kramers doublet when THF ligands are removed; see below (see Supporting Information Table S23).The powder EPR spectrum of 1-U is dominated by a broad feature from 100−600 mT that shows two lower-field features at g ∼ 6.6 and 5.4 and contains a sharp organic radical signal at g = 2.0023 (Table 5, see Supporting Information Figure S72).This spectrum suggests the presence of multiple species from sample decomposition with allowed EPR transitions.

DFT Calculations
We performed restricted spin orbit relativistic DFT calculations on diamagnetic 1-La and [La{Si(SiMe 3 ) 3 } 3 (THF) n ] (n = 0 or 1) using the Amsterdam Density Functional (ADF) suite version 2017 with standard convergence criteria, 65−67 in order to probe their electronic structures (see Experimental Section for details).The model for 1-La used the metrical parameters observed by single crystal XRD with geometryoptimized H atom positions, while in the absence of crystallographic metrical data the atomic positions of models   of La(THF) 1 and La(THF) 0 desolvated analogues were fully geometry-optimized (see Supporting Information Tables S6− S8 for atomic coordinates of geometry-optimized structures).
We calculated the δ Si chemical shifts of both the metal-bound Si atoms and the SiMe 3 groups for 1-La, La(THF) 1 and La(THF) 0 using BP86, PBE0, SAOP and B3LYP functionals, with a range of hybrid density functionals for the latter incorporating between 10 and 50% of the exact exchange energy from Hartree−Fock (HF) theory. 68−81 Here, we report mean values of calculated δ Si chemical shifts for metal-bound Si atoms and weighted averages for those within SiMe 3 groups from all hypersilanide ligands to account for dynamic averaging (Table 6; see Supporting Information Tables S9−S14 for results from other functionals).However, we note that for 1-La, La(THF) 1 , and La(THF) 0 , there are consistently two sets of predicted SiMe 3 29 Si NMR signals in a 1:2 ratio separated by between 6 and 10 ppm, in agreement with the solution 29 Si DEPT90 NMR spectral data (Table 2).
The computed MDC q charges for La and Si Si3 (av.) in 1-La are 1.14 and −0.47, consistent with their formal +3 and −1 charge states, and reflect net donation of electron density from the ligands to La.The mean Nalewajski-Mrozek La−Si bond indices are 0.56, reflecting the polar-covalent nature of those bonds; for comparison, the corresponding mean La−O THF and Si−Si values are 0.19 and 0.95.
The Frontier Kohn−Sham molecular orbitals (KSMOs) of 1-La (Figure S73) are as expected, with the HOMO to HOMO−2 reflecting the symmetric and antisymmetric combinations of the three La−Si bonds.However, these KSMOs are rather delocalized, and so we turned to bond localization methods.The Natural Bond Orbital (NBO) method 82 finds three essentially identical La−Si bonds (Figure S74) of 11 and 89% La and Si character, respectively.The La components are comprised of 25/1/71/3% s/p/d/f character and the Si contributions are 40/60% s/p character; similar orbital breakdowns have previously been calculated for other La silanide complexes. 55These data are very similar to the Natural Localized Molecular Orbital (NLMO) representations of 1-La (Figure S75), which return 11 and 87% La and Si character, respectively.The La and Si components are 35/1/ 62/2% s/p/d/f and 41/59% s/p.Thus, while the NLMO report increased s-character at the expense of d-contributions for La compared to the NBO interpretation, a fairly consistent bonding picture emerges of La binding to sp hybridized Si atoms utilizing sd 3 hybrid orbitals.
We examined the La−Si bond topologies of 1-La using the Quantum Theory of Atoms in Molecules (QTAIM) 83,84 and found three essentially identical La−Si 3,−1-bond critical points.These exhibit ρ, ∇ 2 ρ, H, and ε values of 0.04, 0.02, −0.01, and 0.11.These reflect rather polar and weak La−Si interactions, since covalent bonds tend to have ρ values >0.1 and more negative H terms.The ε term is normally zero, or close to zero, for single and triple bonds, with larger values for double bonds; 85 the modest ε values here reflect that the silanide ligands each bind to the La center in a slightly skewed manner, which is apparent in the NBO and NLMO visualizations of 1-La (Figures S74 and S75), and thus their bond ellipticities are not ideal.

pNMR Calculations
We calculated the pNMR shifts using two methods (see Experimental Section for details): (i) a point-dipole approximation based on the CASSCF-SO-calculated magnetic susceptibility tensor [pseudocontact shift (PCS) approximation, δ PCS para ]; 89 and (ii) a full sum-over-states expression derived from the derivative of the Helmholtz free energy (van den Heuvel and Soncini's method δ vdH-S para ). 47The latter method is calculated directly based on the CASSCF-SO wave function and implicitly includes all through-bond (i.e., contact) and through-space (i.e., pseudocontact) terms, as well as the relativistic paramagnetic spin−orbit (PSO) terms. 90To calculate the experimental paramagnetic shift δ exp para , we subtracted the diamagnetic NMR signals measured for 1-La from the respective signals in the paramagnetic compounds.We report calculated δ para values obtained by averaging the calculated shift for all atoms in the same chemical environment, to approximate conformational averaging in the solution phase.We performed calculations using the XRD structure as well as a gas-phase optimized geometry (which retains the same disposition of ligands as in the XRD structure), and model compounds with one or two THF molecules removed (see Experimental Section for details).Upon dissociation of one THF, the central M(Si) 3 core slightly pyramidalizes and the M−Si bond lengths decrease, which becomes more pronounced when the second THF is displaced (see Supporting Information Tables S19−S21).As suspected, removing THF ligands from 1-M changes the magnetic anisotropy; this is most clearly observed in the effective gvalues of the ground Kramers doublets in 1-Ce and 1-Nd, which change from easy-axis anisotropy when there are two THF ligands coordinated, to rhombic anisotropy with one THF, and finally to easy-plane anisotropy when both THF ligands are removed (see Supporting Information Tables S22  and S23).
For calculation of δ para in the M(THF) 1 and M(THF) 0 structures, there are several models that can be used to account for the solution 1 H NMR spectra of 1-M showing a 2:1 ratio for the SiMe 3 signals.For the M(THF) 1 structures, one can consider one SiMe 3 group of each hypersilanide ligand on the same side of the M(Si M ) 3 plane as the remaining THF ligand ("cis") and the other two SiMe 3 groups on the opposite side ("trans"), as well as the opposite arrangement (two "cis" and one "trans").For the M(THF) 0 structures, one can consider one SiMe 3 group of each hypersilanide ligand closer to the pyramidalized M atom ("proximal"), and the other two further away ("distal"), or vice versa (two "proximal" and one "distal").In some of our model structures, the assignment is not obvious between the three ligands; thus to address this uncertainty, and to account for dynamic rotation of each of the σ-bonds in the hypersilanide framework, we have used three approaches to account for all the possible scenarios.We define the "plane" as the average plane formed by the four M(Si M ) 3 atoms and then determine which nonbound Si atom on each ligand is closest to the plane.In the first approach, these are defined as the group 1 ("in-plane") SiMe 3 groups and the other two as the group 2 ("out-of-plane") groups (see Supporting Information Tables S24−S26).In the second approach, we located the nonbound Si atoms that are farthest from the plane to define group 1, whereas the other two Si atoms that are closer to the plane are defined as group 2 (see Supporting Information Tables S27−S29).In the third approach, we consider the only remaining option for a 2:1 ratio, which is where the SiMe 3 group closest to the plane is averaged with the one that is farthest from the plane to define group 2, and the intermediate SiMe 3 group defines group 1 (see Supporting Information Tables S30−S32).

DISCUSSION
Calculation of the ssNMR data for 1-La using DFT methods (see Experimental Section) gives mean isotropic 29 Si NMR chemical shifts of δ iso = −102.7 ppm for the metal-bound Si atoms, in excellent agreement with the experimentally observed 29 Si MAS NMR shift of −102.6 ppm.By contrast, the weighted average of the calculated SiMe 3 29   Si shifts for 1-La (δ iso = 4.0 ppm) do not reproduce the experimental ssNMR value of −4.6 ppm, suggesting that ambient temperature dynamics may need to be considered.Though there is little variance in the mean calculated 29 Si δ iso values of SiMe 3 groups between 1-La and desolvated La(THF) 0 and La(THF) 1 (Table 6), the mean of the calculated 29 Si NMR shifts for the metal-bound Si atoms of 1-La and desolvated La(THF) 1 of δ iso = −85.9ppm is similar to the experimentally obtained solution 29 Si DEPT NMR value (δ iso = −82.3ppm); we note that the calculated δ iso = −43.8ppm for the metal-bound Si atoms of the La(THF) 0 derivative, which has poor agreement with experiment.Furthermore, the difference in δ Si values of Group 1 and Group 2 SiMe 3 groups obtained from a 9:1 C 6 D 6 /C 4 D 8 O solution of 1-La at room temperature (ΔSiMe 3 = 7.8 ppm) is close to the mean (ΔSiMe 3 = 8.1 ppm) of equivalent differences calculated for 1-La (ΔSiMe 3 = 9.9 ppm; δ iso = −2.6 and 7.3 ppm) and its M(THF) 1 analogue (ΔSiMe 3 = 6.3 ppm; δ iso = −2.1 and 4.2 ppm).These data are in accord with 1-La forming a dynamic equilibrium with the desolvated La(THF) 1 form and deuterated analogues in the solution NMR experiments.We therefore posit that the presence of two signals for SiMe 3 groups in solutions of 1-M is due to restricted rotation of the M−Si bonds, likely due to the desolvated species showing stronger interactions of coordinatively unsaturated M(III) ions with hypersilanide ligands and the resultant metal coordination spheres being more congested, consistent with the optimized gas-phase geometries.
The solid-state magnetic and EPR data of paramagnetic 1-M are consistent with the CASSCF-SO calculations performed on the solid-state XRD structures, which show easy-axis magnetic ground states in all cases, seemingly dictated by the axial THF ligands (Figure 6).As with the solution NMR data of diamagnetic 1-La (see above), the solution EPR and NMR data of paramagnetic 1-M indicate that THF may be lost in solution, and this scenario can be probed further by analysis of Figure 6.CASSCF-SO-calculated magnetic axes for 1-Ce (blue: g 1 , most magnetic; green: g 2 , intermediate; red: g 3 , least magnetic) for complexes.Metal, silicon, carbon, and hydrogen atoms shown as metallic green, orange, gray, and light gray, respectively.the solution phase pNMR shifts.Although solvent effects were included for the DFT calculations of 1-La by introducing a benzene continuum, they were not for the ab initio calculations of paramagnetic 1-M.The local structure was used for pNMR calculations, as this has the largest effect on the magnetic anisotropy and hence pNMR shifts; the dynamic THF equilibrium will have a far greater influence than "outer sphere" solvent effects.We focus here on pNMR shifts of 1-Ce, 1-Pr, and 1-Nd, which have simpler electronic structures than 1-U (Figure 4). 91omparing the two CASSCF-SO-based theoretical methods for calculation of pNMR shifts to the solution data of paramagnetic 1-Ln (see Supporting Information Tables S24−  S32), we find that the δ PCS para and δ vdH-S para values are in close agreement for all 1 H pNMR signals, which is to be expected as these nuclei are far away from the spin density of the buried 4f orbitals.However, the PCS approximation will be less accurate for nuclei closer to the metal ion where delocalization of spindensity is nonzero, and indeed, this is what we observe for the 29   Si pNMR shifts, even for the noncoordinated 29 Si nuclei.The 29Si NMR resonances of the metal-bound silicon atoms were not well-reproduced as they are hugely sensitive to contact shift.The contact shift contribution to chemical shift is nontrivial, arising from core spin polarization and dynamic electron correlation, intersecting with relativistic core effects, thus we cannot rationalize any trends.
Comparing the experimental solution phase 1 H δ exp para to the calculated δ para results using either XRD or gas-phase optimized structures, we find that the group 1 SiMe 3 shifts have the incorrect sign and the group 2 SiMe 3 shifts are underpredicted in magnitude by several ppm (see Supporting Information Tables S24−S26).As the solution pNMR data show local C 3v point symmetry of the complex (borne out as a 1:2 ratio of the SiMe 3 1 H signals, viz., groups 1 and 2, respectively, with restricted rotation around the M−Si bonds due to steric clashing in the presence of shorter M−Si bonds), the molecules must possess axially symmetric magnetic anisotropy.Furthermore, owing to the good applicability of the PCS approximation for the 1 H nuclei in this case (i.e., the difference between δ PCS para and δ vdH-S para is small), we can therefore write . 89 Because the δ exp para are positive for the group 1 and negative for the group 2 1 H nuclei, and χ z − χ ̅ is a constant common to both sets of 1 H environments, then the structural part must have a different sign for each group of protons.Assuming first that the disposition of the SiMe 3 groups does not change significantly in solution, the group 1 "in-plane" protons would on average be closer to θ = 90°, while the group 2 "out-of-plane" protons would be closer to θ = 0°or θ = 180°.This indicates that the structural part of the term for group 1 is < 0, while for group 2, it is > 0, and thus, χ z − χ ̅ must be < 0 to be consistent with δ exp para .This implies easy-plane anisotropy of the magnetic moment, which would indeed be consistent with Ln(III) ions for Ln = Ce, Pr, and Nd with a trigonal planar ligand field dominated by the three anionic equatorial ligands. 87However, CASSCF-SO calculations using the XRD structure predict easy-axis anisotropy for 1-Ce, 1-Pr, and 1-Nd, dictated by the axial THF ligands (see above; the outcome does not change for the gas-phase optimized structures), which is indeed confirmed by EPR spectroscopy on solid state samples.This apparent disconnect could be resolved if one or both THF molecules dissociate in solution, which is already suggested by missing solution 1 H resonances for some of the THF ligands and 1-La results (see above).Hence, we computationally removed one or both THF ligands(s), optimized the structure in the gas phase, and performed CASSCF-SO pNMR calculations for these structural models to assess if this possibility is consistent with the data.
For 1-Ce, none of the pNMR shift calculations give a clear agreement with solution experimental data (see Supporting Information Tables S24, S27 and S30); as Ce(III) has the smallest magnetic moment of all Ln(III) ions in the periodic table, it also has the smallest paramagnetic shifts, and hence approximations in our electronic structure method and our gas-phase structural models are insufficient to capture the subtleties of these data.Considering 1-Nd, both 1 H and 29 Si solution pNMR results show discrepancies between the experimental values and the values predicted using the XRD or optimized M(THF) 2 structures.For the 1 H resonances, calculations using the XRD structure (optimized structure) predict shifts of −6.4 and ca.−0.5 ppm (−2.3 and ca.−0.4 ppm) for the "in-plane"/group 1 and "out-of-plane"/group 2 signals, respectively, compared to the experimental values of 4.9 and −5.0 ppm, respectively.Upon removing one THF ligand and maintaining the "in-plane"/"out-of-plane" averaging, the calculations give chemical shifts of ca.5.8 and −4.2 ppm, respectively, or ca.5.8 and −5.6 ppm when both THF ligands are removed (see Supporting Information Table S26).For the 29 Si "in-plane"/group 1 resonances (group 2 not observed; now considering only δ vdH-S para ), the predicted shift using the XRD structure (optimized structure) is −22.3 ppm (−11.7 ppm), which varies from the experimental value of 6.3 ppm.When one THF ligand is removed, the shift increases to 8.7 ppm, and then to 8.0 ppm when the second THF ligand is removed (see Supporting Information Table S26).Hence, both the 1 H and 29 Si pNMR data suggest a formulation of either Nd(THF) 1 or Nd(THF) 0 for 1-Nd in solution.All chemical shifts show pronounced discrepancy compared to the experiment for the second averaging option (see Supporting Information Table S29), while the third averaging option (see Supporting Information Table S32) is also compatible with Nd(THF) 1 ; however, the agreement of calculated values with experiment is not as close as for "in-plane"/"out-of-plane" averaging.
For 1-Pr, both 1 H and 29 Si calculated pNMR results show discrepancies compared to the experimental solution values when employing bis-THF structures (see Supporting Information Table S25).Using the XRD structure (optimized structure) for 1 H gives shifts of ca.−14.5 and ca.−1.9 ppm (ca.−4.4 and ca.−0.5 ppm) for the "in-plane"/group 1 and "out-of-plane"/group 2 signals, respectively, compared to the experimental values of 7.9 and −8.1 ppm, respectively.By removing one THF ligand and maintaining the "in-plane"/ "out-of-plane" averaging, the calculations give chemical shifts of ca.11.0 and ca.−8.0 ppm, or ca.7.6 and ca.−6.2 ppm when removing the second THF ligand (see Supporting Information Table S25).Hence, the models with some THF lost better align with the experimental data.Similarly, for solution 29 Si pNMR "in-plane"/group 1 resonances (group 2 not observed; now considering only δ vdH-S para ), the XRD structure (optimized structure) gives a shift of −40.9 ppm (optimized structure: −15.0 ppm), deviating substantially from the experimental value of 10.2 ppm.The shifts for Pr(THF) 1 and Pr(THF) 0 are 24.0 and 16.0 ppm, respectively; here, the Pr(THF) 0 model is in better agreement with the experimental data (see Supporting Information Table S25).Using the second averaging method, the pNMR shifts are predicted adequately using a Pr(THF) 0 model (see Supporting Information Table S28), or using a Pr(THF) 1 model with the third averaging method (see Supporting Information Table S31), but in both cases, the calculated parameters are not as close to experiment as for the "in-plane"/"out-of-plane" averaging approach.
We note that in none of the cases are the pNMR shifts of the coordinated 29 Si M atoms correctly predicted for paramagnetic 1-Ln and that the choice of structural model has a significant effect on the calculated values (see Supporting Information Tables S24−S26).This indicates substantial influence of the contact spin density based on structural models that we cannot capture with these simplified static models and minimal CASSCF-SO calculations.For paramagnetic 1-Ln, only one nonmetal-bound 29 Si resonance is observed, again likely a result of dynamic averaging.The weighted average paramagnetic shifts are 11.8, 33.4, and 57.1 ppm for 1-Ce, 1-Pr, and 1-Nd, respectively, while the calculated pNMR shifts using the XRD geometries and CASSCF-SO methods (δ vdH-S para , weighted average of nonmetal-bound 29 Si resonances) are −4.8,−23.6, and −13.8 ppm, for 1-Ce, 1-Pr, and 1-Nd, respectively.Clearly, these values are poorly predicted, which shows that nontrivial spin density is transferred from the metal ions beyond the first coordination sphere and that extensive active space methods would be required to approach experimental accuracy in even these simple complexes.
The 29 Si NMR chemical shifts of a number of uranium complexes have previously been compiled, and though there is no 29 Si NMR data of a U(III) hypersilanide complex for comparison, we note that SiMe 3 groups were assigned in the 2 9 S i N M R s p e c t r a o f [ K ( 1 8 -c r o w n -6 ) ] [ U { [ S i -(SiMe 3 ) 2 SiMe 2 ] 2 O}(THF) 2 (I) 2 ] (−50.0 ppm) 45 and trigonal pyramidal [U{N(SiMe 3 ) 2 } 3 ] (−219 ppm). 92The δ Si values of the SiMe 3 groups (−6.0 ppm) and metal-bound silicon atoms (−70.5 ppm) of U(THF) n (n = 0 or 1) are far downfield of most of the previously reported range of δ Si values for U(III) complexes (between −116 and −247 ppm), which tend to exhibit chemical shifts >100 ppm upfield of parent group 1 ligand transfer agents. 92The comparatively small paramagnetic shift of the SiMe 3 groups and the silanides in U(THF) n (n = 0 or 1) from HSi(SiMe 3 ) 3 (δ Si in C 6 D 6 = −11.6 ppm, SiMe 3 ; −115.6 ppm, HSi) 53 correlates with the paramagnetic line broadening being relatively minor in the M(THF) n (n = 0 or 1) series herein, which delivers the first examples of M(III)bound solution 29 Si DEPT90 NMR resonances for all of the paramagnetic M herein to the best of our knowledge (we note that a signal was tentatively assigned for the silanide atom in [La(Cp") 2 {Si(SiMe 3 ) 3 }] at δ Si = −130.25 ppm, but data from correlation experiments were ambiguous). 41

CONCLUSIONS
The rich multinuclear solution and ssNMR spectra of the M(III) tris-hypersilanide complexes [M{Si(SiMe 3 ) 3 } 3 (THF) 2 ] for M = La, Pr, Ce, Nd, and U, coupled with the high local symmetries of their metal sites, has provided a rare opportunity to study paramagnetic shifts in an isostructural series of f-block complexes by 29 Si NMR spectroscopy.We find by a combination of single crystal XRD and EPR spectroscopy that in the solid state, these complexes show trigonal bipyramidal geometries, with local D 3h symmetries of the central MSi 3 O 2 cores and easy-axis magnetic anisotropy.The 29 Si MAS NMR spectra of these complexes each show only one signal for the trimethylsilyl groups; this equivalency indicates that dynamic averaging of these environments occurs at ambient temperature due to free rotation of M−Si bonds.The 29 Si resonance for the metal-bound silicon atoms is only seen for the diamagnetic La(III) analogue in the solid state, due to the magnetic anisotropy of the paramagnetic M(III) ions broadening the signal into the baseline.Using a combination of characterization methods, we find that the coordinated THF molecules in [M{Si(SiMe 3 ) 3 } 3 (THF) 2 ] are readily displaced in solution to give the desolvated species [M{Si-(SiMe 3 ) 3 } 3 (THF) n ] (n = 0 or 1), which show local C 3vsymmetric cores and easy-plane magnetic anisotropy.The solution 1 H NMR spectra of [M{Si(SiMe 3 ) 3 } 3 (THF) 2 ] in 9:1 C 6 D 6 /C 4 D 8 O solutions each show two trimethylsilyl environments in a 1:2 ratio, and for M = La and Ce, we also observe two signals for SiMe 3 groups in both the 13 C{ 1 H} and 29 Si DEPT solution NMR spectra.We attribute this observation to restricted rotation of M−Si bonds on the NMR time scale upon loss of THF from coordination spheres; unusually, metalbound silicon resonances are seen in all solution 29 Si DEPT90 NMR spectra.
The DFT-calculated 29 Si NMR shifts of [La{Si-(SiMe 3 ) 3 } 3 (THF) 2 ] and desolvated [La{Si(SiMe 3 ) 3 } 3 (THF) n ] (n = 0 or 1) showed excellent agreement with experimentally obtained values and were in accord with a dynamic equilibrium of [La{Si(SiMe 3 ) 3 } 3 (THF) 2 ] and [La{Si(SiMe 3 ) 3 } 3 (THF)] persisting in the presence of a large excess of THF.The CASSCF-SO-calculated pNMR shifts of trimethylsilyl groups in paramagnetic [M{Si(SiMe 3 ) 3 } 3 (THF) 2 ] and desolvated [M{Si(SiMe 3 ) 3 } 3 (THF) n ] (n = 0 or 1) show reasonable agreement for M = Pr and Nd existing as either [M{Si-(SiMe 3 ) 3 } 3 (THF) 1 ] or [M{Si(SiMe 3 ) 3 } 3 ] in 9:1 C 6 D 6 /C 4 D 8 O solutions, but assigning the experimental data to one of these two structures is challenging given the likelihood of dynamic equilibria in solution, cf. the La homologue.We also cannot rule out the limitations inherent to the computational method used; for instance, gas-phase optimization does not consider the effect of explicit solvent interaction which is in a huge excess for experimentally obtained data.Furthermore, the experimental chemical shifts represent an average over large number of molecules that move over a relativity long time scale, as opposed to the chemical shift from single stationary molecule optimized in the gas phase as computed here; the time scales required for examining these equilibria are out of reach for the ab initio molecular dynamics that would be required to model the M-THF dissociation processes.Finally, the structural ambiguity and complex nature of the paramagnetic shifts does not allow us to accurately model metalbound silicon atoms directly for any of the paramagnetic complexes herein.

General Methods and Materials
All manipulations were conducted under argon with the strict exclusion of oxygen and water by using Schlenk line and glovebox techniques.Solvents were dried by refluxing over Na/K alloy (diethyl ether) or potassium (hexane) and stored over a potassium mirror and then degassed before use.To make up solution samples for NMR, EPR, and UV−vis−NIR spectroscopy, hexane, toluene, THF, Me-THF, C 6 D 6 , and C 4 D 8 O were dried by refluxing over K and were vacuum transferred and degassed by three freeze−pump−thaw cycles before use.Elemental analysis (C and H) was carried out either by Mr Martin Jennings and Mrs Anne Davies at the Microanalytical service, Department of Chemistry, the University of Manchester, or the Elemental Analysis Services Team, Science Centre, London Metropolitan University.The starting materials [K{Si(SiMe 3 ) 3 }], 54 [MI 3 (THF) x ] (M = La, Ce, Pr, x = 4; M = Nd, x = 3.5) 93 and [UI 3 (THF) 4 ] 94 were prepared according to literature procedures.ATR-IR spectra were recorded as microcrystalline powders using a Bruker Alpha spectrometer with Platinum-ATR module.UV−vis− NIR spectroscopy was performed on samples in Youngs tap-appended 10 mm path length quartz cuvettes on an Agilent Technologies Cary Series UV−vis−NIR spectrophotometer from 175 to 3300 nm.Caution: Natural abundance uranium is a weak α-emitter; thus, we recommend the use of suitable designated radiochemical laboratories with α-counting equipment available for safe manipulation of compounds containing this element.
Powder XRD data were obtained on small batches of microcrystalline 1-M that were suspended in Fomblin oil to prevent sample decomposition from oxygen and water.These samples were mounted on a Micromount and placed on a goniometer head under a cryostream to cool the sample to 100 K, freezing the Fomblin to suspend the crystallites for the duration of the experiment.The PXRD data were measured on a Rigaku FR-X diffractometer, operating in powder diffraction mode using Cu Kα radiation (λ = 1.5418Å) with a Hypix-6000HE detector and an Oxford Cryosystems nitrogen flow gas system.Data were collected between 3 and 20°θ, with a detector distance of 150 mm and a beam divergence of 1.5 mRad. 95X-ray data were collected using CrysAlisPro. 96For data processing, the instrument was calibrated using silver behenate as standard.Then, X-ray data were reduced and integrated using CrysAlisPro. 96Pawley refinements with the unit cells obtained from the crystal structures were performed using TOPAS. 97,98-ray diffraction data for single crystals of 1-La, 1-Ce, 1-Pr, 1-Nd, and 1-U in Fomblin on a Micromount were examined using a Rigaku FR-X diffractometer, equipped with a HyPix 6000HE photon counting pixel array detector with graphite-monochromated Mo Kα (λ = 0.71073 Å) (1-U) or Cu Kα (λ = 1.5418Å) (1-La, 1-Ce, 1-Pr, 1-Nd) radiation.Intensities were integrated from data recorded on 1°f rames by ω rotation.Cell parameters were refined from the observed positions of all strong reflections in each data set.A Gaussian grid face-indexed with a beam profile was applied for all structures.96 The structures were solved using SHELXT; 99 the data sets were refined by full-matrix least-squares on all unique F 2 values, 100 with anisotropic displacement parameters for all non-hydrogen atoms and with constrained riding hydrogen geometries; U iso (H) was set at 1.2 (1.5 for methyl groups) times U eq of the parent atom.The largest features in final difference syntheses were close to heavy atoms and were of no chemical significance.CrysAlisPro 96 was used for control and integration, and SHELX 99,100 was employed through OLEX2 101 for structure solution and refinement.ORTEP-3 102 and POV-Ray 103 were employed for molecular graphics.
Magnetic measurements were performed on a Quantum Design MPMS3 superconducting quantum interference device (SQUID) magnetometer.Finely ground powder samples (28−36 mg) were restrained in eicosane (14−18 mg) and flame-sealed in a borosilicate tube under vacuum (see Supporting Information Table S5).Sealed samples were loaded into plastic straws and held in place by friction between diamagnetic tape at the top of the tube and the straw.Raw magnetic data were scaled for the shape of the sample using Quantum Design MPMS3 Geometry Correction Simulator, corrected for the diamagnetic contribution of the sample holder (straw and borosilicate tube) and corrected for the mass of eicosane.The molar susceptibility was corrected for the intrinsic diamagnetic contribution of the sample, estimated as the molecular weight (g mol −1 ) multiplied by 0.5 × 10 −6 cm 3 K mol −1 . 105Measurements were performed in DC scan mode with 40 mm scan length, except susceptibility measurements on 1-Ce and 1-Pr which were performed in VSM mode with 5 mm amplitude.Susceptibility measurements were performed on cooling in 5 kOe (1-Ce) or 1 kOe (1-Pr, 1-Nd, 1-U) DC field.Hysteresis measurements were performed at 2 K in continuous sweep mode with sweep rates of 91 Oe s −1 (2 < |H| < 7 T), 54 Oe s −1 (1 < |H| < 2 T) and 22 Oe s −1 (| H| < 1 T).
Continuous wave electron paramagnetic resonance (EPR) spectra were recorded at X-band (ca.9.4 GHz) frequency on a Bruker EMXPlus spectrometer with 1.8 T electromagnet and Stinger closedcycle helium gas cryostat.Powders of 1-Ce, 1-Nd, and 1-U were finely ground in a glovebox, and 1−2 cm of each sample was loaded into to a 4 mm outer diameter (OD) quartz tube and sealed under vacuum.A solution of 1-Nd in 2-Me-THF (15 mM) was prepared in a glovebox.Quartz tubes of OD 4 mm were filled with ∼3 cm of solution, which was immediately frozen and flame-sealed under vacuum, and then rapidly transferred to the spectrometer within ca. 15 min.Spectra were obtained at base temperature (4−7 K), and powder spectra were obtained for two rotations at ∼90°to one another to identify any features due to polycrystallinity.The field was corrected using a strong pitch sample (g = 2.0028).Spectra were simulated in EasySpin 6.0.0dev.51. 64Powder spectra of 1-Ce and 1-Nd were simulated in the EasySpin function pepper as an effective S = 1/2, with rhombic g values, g = [g 1 , g 2 , g 3 ] and gStrains (distribution of g values) to account for all line broadenings effects.For 1-Nd, g 3 was not observed (<0.4) and so was fixed to 0.2.Hyperfine coupling on the g 1 feature (A 1 ) for 1-Nd was included for the most abundant isotope and scaled for other isotopes based on nuclear g-factors.
The H-only structural optimization of diamagnetic 1-La, and full geometry optimization of desolvated La(THF) 1 and La(THF) 0 analogues were performed using ADF 2017; 65−67 structural optimization of paramagnetic 1-M (where performed) and desolvated M(THF) 1 and M(THF) 0 analogues were conducted in the gas phase using DFT with Gaussian 16,106 and electron correlation were described using the PBE functional. 107All central lanthanide atoms were treated with the Stuttgart RSC-ANO ECP basis set, 108−110 and all remaining atoms with cc-pVDZ. 111−67 Spin−orbit relativistic, single-point calculations, using the optimized geometries described above, employed either the BP86, PBE0, SAOP, or B3LYPHFXX (XX = 10, 15, 20, 25, 30, 35, 40, 45, 50) hybrid functionals.−114 The 29 Si NMR chemical shifts are reported relative to TMS.Scalar relativistic approaches (spin−orbit neglected) were used within the ZORA Hamiltonian to include relativistic effects, 112,113,115 and a benzene solvent continuum was added.The local density approximation (LDA) with a correlation potential was used in all calculations. 116Generalized gradient approximation corrections were performed using the functionals of Becke and Perdew. 117,118NBO analysis was carried out using NBO6. 82QTAIM analysis 83,84 was performed within the ADF package; the MOs and NBOs were visualized using ADFView. 66,67ASSCF-SO calculations were performed with OpenMolcas 77 on XRD structures of paramagnetic 1-M.Basis sets from the ANO-RCC library 119−121 were used with VTZP quality on the metal atom, VDZP quality on the coordinating atoms and VDZ quality on all other atoms, employing the second-order DKH transformation.Cholesky decomposition of the two-electron integrals with a threshold of 10 −8 was performed to save disk space and reduce computational demand.The molecular orbitals (MOs) were averaged in state-averaged CASSCF calculations with active spaces of (1,7) (1-Ce), (2,7) (1-Pr), and (3,7) (1-Nd and 1-U) averaging over seven doublets (1-Ce), 21 triplets and 28 singlets (1-Pr), and 35 quartets and 112 doublets (1-Nd and 1-U).The spin-free wave functions obtained from these CASSCF calculations were mixed by spin−orbit coupling in the RASSI module.The g-values, magnetization, and magnetic susceptibility (isotropic value and tensor) were calculated using SINGLE_-ANISO, 122 and the spin−orbit wave functions were decomposed into their crystal field wave functions, with the quantization axis defined by the g 1 direction in the ground doublet.From the magnetic susceptibility tensor, we calculate the pseudocontact shift (δ PCS para for the 29  where χ ̅ = 1/3Tr(χ). 89To calculate δ PCS para , we have implemented the paramagnetic component of the van den Heuvel and Soncini method 47 in our HYPERION code, 123  para , m̂and are the Zeeman and hyperfine operators, respectively, and are levels with degenerate states v, μ, respectively.

Figure 5 .
Figure 5.Comparison of X-band EPR spectra of 1-Nd as a powder at 5 K (black) and as a frozen solution in 2-Me-THF at 7 K (blue).
which uses a full sum-overstates expression derived from the derivative of the Helmholtz free energy

Table 4 .
Powder Magnetic Moment and Variable-Temperature Molar Susceptibility, μ eff (μ B ) and χ M T (cm 3 mol −1 K), of 1-M Measured by SQUID Magnetometry at 1.8 and 300 K a a χ M T at 2 and 300 K determined by CASSCF-SO calculations; free ion calculated μ eff and χ M T values at 300 K.
a δ b Solid-state