# Isolation of a Bent Dysprosium Bis(amide) Single-Molecule Magnet

Jack Emerson-King, Gemma K Gransbury, George F S Whitehead, Iñigo J Vitorica-Yrezabal, Mathieu Rouzières, Rodolphe Clérac, Nicholas F Chilton, David P Mills

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Jack Emerson-King, Gemma K Gransbury, George F S Whitehead, Iñigo J Vitorica-Yrezabal, Mathieu Rouzières, et al.. Isolation of a Bent Dysprosium Bis(amide) Single-Molecule Magnet. Journal of the American Chemical Society, 2024, 146 (5), pp.3331-3342. 10.1021/jacs.3c12427. hal-04445224

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# Isolation of a Bent Dysprosium Bis(amide) Single-Molecule Magnet

Jack Emerson-King, Gemma K. Gransbury, George F. S. Whitehead, Iñigo J. Vitorica-Yrezabal, Mathieu Rouzières, Rodolphe Clérac,* Nicholas F. Chilton,* and David P. Mills*

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Cite This: J. Am. Chem. Soc. 2024, 146, 3331–3342

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## ACCESS

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Supporting Information

**ABSTRACT:** The isolation of formally two-coordinate lanthanide (Ln) complexes is synthetically challenging, due to predominantly ionic Ln bonding regimes favoring high coordination numbers. In 2015, it was predicted that a near-linear dysprosium bis(amide) cation [Dy{N(Si'Pr₃)₂}₂]⁺ could provide a single-molecule magnet (SMM) with an energy barrier to magnetic reversal (Uₐff) of up to 2600 K, a 3-fold increase of the record Uₐff for a Dy SMM at the time; this work showed a potential route to SMMs that can provide high-density data storage at higher temperatures. However, synthetic routes to a Dy complex containing only two monodentate ligands have not previously been realized. Here, we report the synthesis of the target bent dysprosium bis(amide) complex, [Dy{N(Si'Pr₃)₂}₂][Al{OC(CF₃)₃}₄] (1-Dy), together with the diamagnetic yttrium analogue. We find Uₐff = 950 ± 30 K for 1-Dy, which is much lower than the predicted values for idealized linear two-coordinate Dy(III) cations. Ab initio calculations of the static electronic structure disagree with the experimentally determined height of the Uₐff barrier, thus magnetic relaxation is faster than expected based on magnetic anisotropy alone. We propose that this is due to enhanced spin–phonon coupling arising from the flexibility of the Dy coordination sphere, in accord with ligand vibrations being of equal importance to magnetic anisotropy in the design of high-temperature SMMs.

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## INTRODUCTION

Raising the temperatures at which single-molecule magnets (SMMs) exhibit magnetic remanence is key to unlocking their potential applications in high-density data storage, as the liquid helium cooling currently required is expensive and unsustainable for widespread adoption.¹⁻³ For the last two decades, lanthanide (Ln) SMMs have shown the most promise to achieve this goal,⁴⁻⁷ with axial dysprosium (Dy) complexes predicted to show the highest energy barriers to magnetic reversal (Uₐff) as these ligand fields best complement the magnetic anisotropy intrinsic to the Dy(III) ion.⁸⁻¹⁰ As the isolation of an ideal axial two-coordinate linear Dy(III) complex is a major synthetic challenge (see below), pentagonal bipyramidal Dy complexes with strongly donating apical alkoxides and five weak equatorial donor ligands were the first SMMs to achieve Uₐff values > 1000 K.¹¹ Salts with axial dysprosocenium cations [Dy(CpR)₂]⁺ (CpR = substituted cyclopentadienyl) and related derivatives subsequently raised 100 s magnetic blocking temperatures (Tₛₚ) ever closer to the boiling point of liquid nitrogen (77 K);¹²⁻²² this was attributed to the rigidity of the coordinated aromatic ligands expediting magnetic relaxation via Raman pathways.¹²,²³ The current record-holding SMM [Dy₂(C₅'Pr₅)₂(µ-I)₃] has a Uₐff of 2345 ± 36 K and a Tₛₚ of 72 K, with its 1e⁻ Dy–Dy bond providing a significant contribution to these parameters.¹⁹

Prior to the isolation of these high-barrier SMMs, the near-linear Ln(II) complexes [Ln{N(Si'Pr₃)₂}₂] (Ln = Sm, Eu, Tm, and Yb) were prepared by salt metathesis reactions of 2 equiv of [K{N(Si'Pr₃)₂}] with parent LnI₂.²⁴,²⁵ The experimentally determined atomic coordinates of the Sm(II) derivative (N–Ln–N: 175.5(2)°) were used to calculate that an analogous Dy(III) bis(amide) cation [Dy{N(Si'Pr₃)₂}₂]⁺ could show Uₐff ≈ 2600 K;²⁴ this value was over triple that of the magnitude of the record barrier for Dy SMMs at the time (842 K for a polymetallic Dy-doped yttrium alkoxide complex).²⁶ Further calculations revealed that Uₐff values could remain >1300 K even if the N–Dy–N angle was reduced to as low as 120°, provided that no additional ligands were coordinated.²⁷ In the interim, the bent Ln(III) bis(amide) complexes [Ln{N-(Si'Pr₃)₂}₂][B(C₆F₅)₄] for Ln = Sm, Tm, and Yb were synthesized by oxidation of the parent Ln(II) complexes [Ln{N(Si'Pr₃)₂}₂],²⁴,²⁵,²⁸,²⁹ recently, a related bent Yb(III) bis(amide) complex, [Yb{N(SiPh₂Me)₂}₂][Al{OC(CF₃)₃}₄], has been reported.³⁰ However, due to synthetic difficulties

Received: November 7, 2023

Revised: January 9, 2024

Accepted: January 10, 2024

Published: January 29, 2024

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<figure><img src="image_11.png" /><figcaption>Scheme 1. Synthesis of 1-Ln, 2-Ln, 3-Ln, 4-Ln, and 5-Ln (Ln = Y and Dy)</figcaption></figure>

as an inseparable mixture

associated with directly installing bulky silylamides at small, charge-dense Ln(III) centers by salt metathesis protocols where side-reactions may occur (see below), the desired Dy(III) bis(amide) cation $[Dy\{N(Si'Pr₃)₂\}₂]^⁺$ has not previously been isolated. Indeed, the isolation of any Dy complex containing only two monodentate ligands has proved elusive for the wider synthetic chemistry community to date, which is particularly hampered by the predominantly ionic bonding regimes of relatively large Ln cations favoring higher coordination numbers (CNs).³¹⁻³³

Here, we report the isolation and characterization of the bent Dy bis(amide) complex $[Dy\{N(Si'Pr₃)₂\}₂][Al{OC(CF₃)₃}₄]$ (1-Dy), together with the diamagnetic yttrium analogue 1-Y, and other complexes that were prepared as starting materials toward these synthetic targets. Magnetic measurements reveal that the SMM properties of 1-Dy are not as favorable as originally predicted, with magnetization vs field hysteresis loops close at zero field at 2 K. Ab initio calculations show that the bent geometry still imposes very large magnetic anisotropy in 1-Dy, as large as for the first dysprosocenium cation $[Dy(Cp'Ut)₂]⁺$.¹²,¹⁵,¹⁶ As molecular rigidity has been shown to be crucial for controlling spin-phonon relaxation in dysprosocenium cations,¹² we propose that the flexible coordination environment in 1-Dy enables rapid magnetic relaxation; the large magnetic anisotropy generated by crystal-field (CF) splitting will therefore not necessarily result in a high-barrier Ln SMM unless spin-phonon relaxation enabled by molecular vibrations is adequately controlled.

## ■ RESULTS

**Synthesis.** Complexes 1-Ln were prepared by the synthetic route shown in Scheme 1; we note that either fluorobenzene or benzene is used as a reaction solvent and in most steps is interchangeable; see the Experimental Section for full details. Analysis of mass balances and in situ ¹H NMR spectra for the Y congeners indicated that all reactions proceeded with complete consumption of the starting materials to give the products indicated exclusively. The separate salt elimination reactions of $[Ln(BH₄)₃(THF)₃]$ (Ln = Y and Dy)³⁴ with 1 equiv of $[K\{N(Si'Pr₃)₂\}]²⁴$ in fluorobenzene at ambient temperature for 1 h gave the heteroleptic Ln(III) mono-amide bis(borohydride) complexes $[Ln\{N(Si'Pr₃)₂\}-BH₄)₂(THF)]$ (2-Ln) in 79–83% isolated yields following filtration and crystallization from n-hexane at –35 °C. The bound THF was removed from 2-Ln by heating solid samples at 120 °C for 2 h at 0.01 mbar. Recrystallization of the desolvated products from 1,2-difluorobenzene layered with n-

hexane gave, by slow diffusion, crystals of tetranuclear Ln(III) complexes $[Ln\{N(Si'Pr₃)₂\}(BH₄)(µ-BH₄)]₄$ (3-Ln) in 54–67% isolated yields. It is critical to remove all of the KBH₄ evolved during the synthesis of 2-Ln; failure to do so has a deleterious impact on the thermal desolvation step. We also found that samples of 3-Ln recrystallized in the presence of trace amounts of KBH₄ were contaminated with several crystals of the adducts $[{Ln\{N(Si'Pr₃)₂\}(BH₄)(µ-BH₄)}₂\{K(µ-BH₄)\}]∞$ (3-Ln·0.5KBH₄), for which we report the single-crystal XRD structures here for completeness. The optimized experimental procedures described herein provide pure samples of 2-Ln.

The separate salt elimination reactions of 3-Ln with an excess (2 equiv) of $[K\{N(Si'Pr₃)₂\}]$ in benzene at the optimal temperature of 30 °C for 72 h gave full conversion to a mixture of the desired Ln(III) bis(amide) borohydride complexes $[Ln\{N(Si'Pr₃)₂\}(BH₄)]$ (4-Ln), species assigned as Ln(III) cyclometalates $[Ln\{N(Si'Pr₃)₂\}\{N(Si'Pr₃)[Si'(Pr)₂\{CH(Me)-CH₂]\}-κ²-N, C\}]$ (5-Ln) and HN(Si'Pr₃)₂; this product distribution is in accord with deprotonation of a silyl group in situ, likely promoted by a highly Lewis acidic Dy(III) ion.³¹ The physical separation of these three highly alkane-soluble species proved challenging; as such, the mixture of 4-Ln, 5-Ln, and HN(Si'Pr₃)₂ was treated with 0.5 equiv of $[HNEt₃][Al{OC(CF₃)₃}₄]²⁸$ in benzene at 20 °C for 4 h, in order to protonate 5-Ln and generate the target homoleptic Ln(III) bis(amide) complexes 1-Ln. After removal of benzene and NEt₃ under vacuum, the resultant oils were triturated with n-hexane to give a solution containing a mixture of 4-Ln and HN(Si'Pr₃)₂, together with the solid 1-Ln and the contaminant $[HNEt₃][Al{OC(CF₃)₃}₄]$. The suspensions were filtered, the volatiles of the filtrates were removed in vacuo, and the resultant oils were recrystallized from hexamethyldisiloxane at –30 °C to enable the separation of 4-Ln from HN(Si'Pr₃)₂. Unfortunately, we found the solid mixtures of 1-Ln and $[HNEt₃][Al{OC(CF₃)₃}₄]$ challenging to separate; recrystallization from fluorobenzene solutions layered with n-hexane consistently afforded the cocrystallized material of both ionic species. As such, pure samples of 1-Ln were instead prepared in 73–79% crystalline yields by a hydride abstraction strategy via the reaction of isolated 4-Ln with 0.9 equiv of $[CPh₃][Al{OC(CF₃)₃}₄]³⁵$ in fluorobenzene at 20 °C for 18 h, followed by slow diffusion of n-hexane into the resulting solutions. Treating a mixture of 1-Y and $[HNEt₃][Al{OC(CF₃)₃}₄]$ with excess $[K\{N(Si'Pr₃)₂\}]$ gave ¹H, ¹³C{¹H} DEPTQ, ²⁹Si{¹H} DEPT90, and ¹⁹F NMR spectra that are consistent with the concomitant formation of 5-Y, HN-
(Si'Pr₃)₂, and K[Al{OC(CF₃)₃}₄]. We have not yet been able to isolate **5-Ln** in pure form for further characterization, but NMR data for a C₆D₆ solution of a 1:2 mixture of **5-Y** and HN(Si'Pr₃)₂ are in line with the proposed cyclometalate formulation (see below).

**Spectroscopic Characterization.** Bulk samples of crystalline 1-Ln, 2-Ln, 3-Ln, and 4-Ln were characterized by elemental analysis, multinuclear NMR spectroscopy, and ATR-IR spectroscopy (see Supporting Information Figures S1–S48 for annotated NMR spectra of 1-Ln, 2-Ln, 3-Ln, 4-Ln, and 5-Y). The ¹H and ¹³C{¹H} DEPTQ NMR spectra of 1-Y in C₆H₅F solution show the anticipated resonances for the methyl and methine environments of the ¹Pr groups, with no additional Y–C or Y–H coupling observed (⁸⁹Y, *I* = 1/2, 100% abundance). The ²⁹Si{¹H} DEPT90 NMR spectrum of 1-Y shows a single resonance at *δ*<sub>Si</sub> = -4.8 ppm, while no resonance was observed in the corresponding spectrum of 1-Dy. The ¹⁹F NMR spectrum of 1-Dy contains a single broad resonance at *δ*<sub>F</sub> = -97.2 ppm (full-width at half-maximum, fwhm ≈ 280 Hz) for the [Al{OC(CF₃)₃}₄]⁻ anion, that is paramagnetically shifted relative to that seen for 1-Y (*δ*<sub>F</sub> = -75.1 ppm).

The ¹H, ¹¹B, ¹³C{¹H} DEPTQ, and ²⁹Si{¹H} DEPT90 NMR spectra of diamagnetic 2-Y, 3-Y, and 4-Y were fully assigned in C₆D₆ solution. For brevity, we do not provide a full discussion of all resonances in the ¹H and ¹³C{¹H} DEPTQ NMR spectra here as chemical shifts and coupling constants were in line with expected values for the functional groups present. In C₆D₆, the ¹¹B NMR spectra of 2-Y and 4-Y feature a single pentet resonance at *δ*<sub>B</sub> = -22.0 ppm (*J*<sub>BH</sub> = 81 Hz) and *δ*<sub>B</sub> = -21.4 ppm (*J*<sub>BH</sub> = 86 Hz), respectively. By contrast, for 3-Y, two broad resonances were observed at *δ*<sub>B</sub> = -20.7 and -3.6 ppm, which we assign as the terminal and bridging BH₄ groups, respectively, implying that this species remains oligomeric in benzene solution. In 1,2-difluorobenzene, a broad pentet resonance was observed at *δ*<sub>B</sub> = -20.9 ppm (*J*<sub>BH</sub> = 80 Hz) for 3-Y, consistent with a fluxional monomeric species, possessing equivalent time-averaged terminal BH₄ groups. The ²⁹Si{¹H} DEPT90 NMR spectra of 2-Y, 3-Y, and 4-Y in C₆D₆ contain a similarly shielded singlet resonance (*δ*<sub>Si</sub>/ppm = -2.7, 2-Y; -3.7, 3-Y; -3.4, 4-Y); with 3-Y, no significant difference was observed in 1,2-difluorobenzene (*δ*<sub>Si</sub> = -3.6 ppm). Interpretation of the NMR data for 2-Dy, 3-Dy, and 4-Dy was limited due to paramagnetic broadening of signals, though their ¹¹B{¹H} NMR spectra contain a single resonance (*δ*<sub>B</sub>/ppm = -18.1, 2-Dy; -9.9, 3-Dy; -14.1, 4-Dy). Additionally, the solution magnetic susceptibilities of these complexes were determined at 298 K by the Evans method;³⁶ all values obtained (range *χT* = 12.5–14.2 cm³ K mol⁻¹) are in line with that expected for a Dy(III) free ion (*χT* = 14.17 cm³ K mol⁻¹).³⁷

The species assigned as the cyclometalate **5-Y** exhibits three signals in the ²⁹Si{¹H} DEPT90 NMR spectrum at -3.2, -5.8, and -7.6 ppm. Three magnetically inequivalent silyl groups are also seen in the corresponding ¹H and ¹³C{¹H} DEPTQ NMR spectra; the latter spectrum contains a doublet resonance at *δ*<sub>C</sub> = 55.3 ppm, *J*<sub>YC</sub> = 47.4 Hz with the correct phase for a methylene group, which was assigned to the Y-bound carbon atom. Due to the presence of multiple coincident resonances in ¹H–¹³C HSQC and ¹H–¹³C HMBC NMR spectra, we were unable to assign the associated ¹H resonance. The resonances assigned to **5-Y** in the ¹H, ¹³C{¹H} DEPTQ, and ²⁹Si{¹H} DEPT90 NMR spectra of **5-Y** are comparable to those

previously reported for the Y(III) silylamide cyclometalate [Y{N(SiMe₃)₂}₂{N(SiMe₃)[Si(Me)₂CH₂]-k²-N,C}K], which has *δ*<sub>Si</sub> = -26.1, -13.5, and -12.0 ppm, and also shows resonances for the bound methylene group at *δ*<sub>H</sub> = -1.27 ppm (*J*<sub>YH</sub> = 2.6 Hz) and *δ*<sub>C</sub> = 23.6 ppm (*J*<sub>YC</sub> = 22.9 Hz).³⁸

The ATR-IR spectra of each Dy/Y pair in 1-Ln, 2-Ln, 3-Ln, and 4-Ln overlap with each other and show a number of redshifted C–H stretching bands that are diagnostic of some methine and methyl groups being in close proximity to and interacting with the Ln centers (see Supporting Information Figures S49–S56). These spectroscopic markers were corroborated by a qualitative analysis of the density-functional theory (DFT)-calculated IR spectra for 1-Y, 2-Y, 3-Y, and 4-Y (see Supporting Information Figures S57–S60) and are in accord with their crystallographically determined solid-state structures (see below and Supporting Information Figures S61–S70). For 1-Ln, these features extended down to 2560 cm⁻¹, with the lowest energy modes computationally assigned to the methine C–H group that is closest to the Ln center; the corresponding resonance for 3-Ln was observed at 2745 cm⁻¹, and for 4-Ln there are two bands at 2756 and 2729 cm⁻¹. Characteristic borohydride vibrations were also observed for 2-Ln, 3-Ln, and 4-Ln.³⁹ The apical B–H stretch of the terminal borohydrides corresponded to sharp features at 2486, 2519, and 2495 cm⁻¹ for 2-Ln, 3-Ln, and 4-Ln, respectively, while the stretching modes of the B–H bonds that are proximal to the metal gave broad, convoluted bands between 2360 and 2060 cm⁻¹ for all complexes.

**Solid-State Structural Characterization.** The solid-state structures of 1-Ln, 2-Ln, 3-Ln, 4-Ln, and 3-Ln·0.5KBH₄ were characterized by single-crystal X-ray diffraction (XRD). All bond distances and angles are in line with expected values, and these only vary to a small extent for each Dy/Y pair in accord with the difference in six-coordinate ionic radii of Dy(III) (0.912 Å) and Y(III) (0.900 Å),⁴⁰ thus we focus our discussion herein on the target axial Dy(III) bis(amide) cation in 1-Dy (Figure 1). We note that the diffraction data for 1-Dy are weak (maximum diffraction angle, 55°); see the Experimental Section for further details. The remaining structures and all crystallographic parameters are collated in the Supporting Information (see Figures S61–S71 and Tables S1–S3).

The [Dy{N(Si'Pr₃)₂}₂]⁺ cation exhibits a bent geometry, with a N–Dy–N angle that deviates significantly from linearity (128.7(2)°), with the NSi₂ fragments in a staggered conformation (twist angle: 63.12(6)°) and at a mean Dy–N distance of 2.206(7) Å. The structure of this cation is similar to the previously reported Sm, Tm, and Yb congeners,²⁸ with deviations in metrical parameters expected on the basis of variation of Ln(III) cation size and Lewis acidity.³¹ In common with the previously reported heavy [Ln{N(Si'Pr₃)₂}₂]⁺ cations, the Dy coordination sphere of 1-Dy is completed by three short Dy···Si (range: 3.207(2)–3.229(2) Å), six short Dy···C (range: 2.845(5)–3.036(7) Å), and six short Dy···H distances (range: 2.293–2.455 Å) for methine and methyl fragments of three different ¹Pr groups. These interactions are presumably driven by the electrostatic stabilization of the coordinatively unsaturated Dy(III) center by the electron density of the Si–C/C–H bonds of the silyl groups, which are proposed to set the bent geometry of the cation, as previously described for Sm, Tm, and Yb congeners.²⁸ The Dy atom is sterically protected by this extremely bulky ligand system, with all visible access channels restricted to <3.4% of the solid angle at Dy (Figure S71).⁴¹ Powder XRD was performed on a sample of
<figure><img src="image_12.png" /><figcaption>**Figure 1.** Solid-state structure of the cation of 1-Dy at 100(2) K. Displacement ellipsoids are set at 50% probability level. Hydrogen atoms and the [Al{OC(CF₃)₃}₄]⁻ counteranion are omitted for clarity. Selected bond distances (Å) and angles (deg): Dy(1)–N(1): 2.209(5); Dy(1)–N(2): 2.202(5); Dy(1)···C(1): 2.845(5); Dy(1)···C(2): 2.987(6); Dy(1)···C(10): 2.883(7); Dy(1)···C(11): 3.036(7); Dy(1)···C(19): 2.863(6); Dy(1)···C(20): 2.929(6); Dy(1)···Si(1): 3.215(2); Dy(1)···Si(2): 3.229(2); Dy(1)···Si(3): 3.207(2); N(1)–Dy(1)–N(2): 128.7(2).</figcaption></figure>

microcrystalline 1-Dy (see Supporting Information Figure S72 and Table S4), confirming that the single-crystal structure obtained is representative of the bulk crystalline material used for magnetic characterization.

**Magnetic Measurements.** The static and dynamic magnetic properties of 1-Dy in the solid state and as a 200 mM frozen solution sample in fluorobenzene were probed by dc (direct current) and ac (alternating current) susceptibility measurements (see Supporting Information Figures S73–S107 and Tables S5–S10). The χT value determined at 300 K under a 0.1 T dc field (14.75 cm³ K mol⁻¹, Figure S73) is slightly higher than that determined at 298 K in fluorobenzene solution (12.97 cm³ K mol⁻¹, Figure S74) and the expected Dy(III) free ion value (14.17 cm³ K mol⁻¹).³⁷ We observe a regular decrease in χT with decreasing temperature as excited CF states are thermally depopulated until ca. 10 K where there is a sharper decrease, reaching χT = 7.71 cm³ K mol⁻¹ at 2 K (Figure S73); zero field-cooled (ZFC) and field-cooled (FC) data collected in a smaller 0.001 or 0.005 T dc field show that this drop is mainly due to Zeeman depopulation effects, dropping only to χT = 11.3 cm³ K mol⁻¹ at 1.85 K (Figures S76 and S77). Magnetization (M) vs field (H) experiments show that the magnetization saturates at M<sub>sat</sub> = 5.42 µ<sub>B</sub> under a 7 T applied dc field (Figure S78), suggesting an m<sub>I</sub> = ± 15/2 ground state (M<sub>sat</sub> = 5.00 µ<sub>B</sub>).⁷ The waist-restricted M vs. H hysteresis loops of 1-Dy (Figure 2) are typical for Ln SMMs;⁵ the presence of rapid quantum tunneling of magnetization (QTM) is evidenced by the closed loop at zero field at 2 K (Figure S80). The nonlinearity of the M vs. H data at low fields

<figure><img src="image_13.png" /><figcaption>**Figure 2.** M vs H hysteresis loops of 1-Dy suspended in eicosane from 2 to 10 K in between −1 and +1 T; the inset shows closing of the loop at zero field at 2 K. Sweep rate is 22 Oe s⁻¹.</figcaption></figure>

is in accord with rapid QTM being quenched in increasing fields.

### Magnetization

Ac susceptibility measurements of polycrystalline 1-Dy were performed up to 10 kHz to study the magnetization dynamics. Temperature- and frequency-dependent behavior were seen for the in-phase (χ') and out-of-phase (χ") components of ac susceptibility in zero dc field, with maxima in χ" due to slow relaxation of the magnetization present between 2 and 108 K (Figures S89–S91, Table S5).⁴² The ac data were fit using the generalized Debye model⁴²,⁴³ to extract relaxation times along with estimated standard deviations (ESDs) as arising from a distribution in the relaxation times;⁴⁴,⁴⁵ note that T<sub>B</sub> is not defined in zero field as τ < 100 s at all temperatures. The temperature dependence of the magnetic relaxation time suggests Orbach relaxation at high temperatures, Raman-I relaxation at intermediate temperatures, and QTM at the lowest temperatures (Figure 3a).² The average temperature-dependent relaxation time was modeled using eq 1, giving initial estimates of U<sub>eff</sub> = 850 K, τ₀ = 6.8 × 10⁻⁹ s, C = 8 × 10⁻⁴ s⁻¹ K⁻ⁿ, n = 3.3, and τ<sub>QTM</sub>⁻¹ = 7.4 s (Figure S104). Ac susceptibility measurements in a 0.08 T dc field (Figures S92–S94, Table S6) indicate that QTM is quenched under these conditions (Figure 3a), and the average relaxation time can be fit with eq 1, with τ<sub>QTM</sub>⁻¹ = 0 to give U<sub>eff</sub> = 915 K, τ₀ = 3.8 × 10⁻⁹ s, C = 4 × 10⁻⁵ s⁻¹ K⁻ⁿ, and n = 4.1 (Figure S105).

$$ \tau^{-1}(T) = CT^n + \tau_0^{-1}\exp\left(-\frac{U_{\text{eff}}}{T}\right) + \tau_{\text{QTM}}^{-1} \quad (1) $$

$$ \tau^{-1}(H) = \frac{\tau_{\text{QTM}}^{-1}}{1 + QH^p} + C_T + DH^m \quad (2) $$

$$ \tau^{-1}(H, T) = \frac{\tau_{\text{QTM}}^{-1}}{1 + QH^p} + CT^n + AH^4T + \tau_0^{-1}\exp\left(-\frac{U_{\text{eff}}}{T}\right) \quad (3) $$

Performing an ac susceptibility experiment at 12 K as a function of magnetic field allows us to investigate field-
<figure><img src="image_14.png" /><figcaption>**Figure 3.** Temperature dependence (a; at 0 and 0.08 T) and field-dependence (b; at 12 and 40 K) of the magnetic relaxation time ($\tau$) for 1-Dy. Open circles are the experimental data and bars denote ESDs from the generalized Debye model and the relaxation time distribution.42,43 Solid lines are the result of the best global simulation (eq 3) as discussed in the text.</figcaption></figure>

dependent relaxation dynamics (Figures S95 and S96, Table S7). The relaxation time increases with increasing field below ca. 0.04 T and then plateaus until ca. 0.4 T, above which it increases again (Figure 3b). This is consistent with the quenching of QTM in low fields,46,47 followed by a plateau defined by the field-independent processes (predominantly the Raman-I mechanism,48 as the Orbach contribution is insignificant at 12 K), and then an increase at higher fields owing to either a field-dependent Raman-II or a Direct single-phonon mechanism.47,48 Fitting the average field-dependent relaxation time with a model accounting for these three terms (eq 2) gives $\tau_{QTM}^{-1} = 10 \text{ s}^{-1}$, $Q = 2 \times 10^7 \text{ T}^{-p}$, $p = 3.8$, $C_{12 \text{K}} = 1.3 \text{ s}^{-1}$, $D = 4.4 \text{ s}^{-1} \text{ T}^{-m}$, and $m = 3.8$ (Figure S106). The field exponent of the Raman-II/Direct term (m) is approaching the value expected for the single-phonon Direct process in the high-temperature limit of m = 4,49 and so we suggest this as the more likely mechanism.

The parameters of these individual models are in reasonable agreement; however, we sought to determine parameters for a unified model that can describe the complete field and temperature dependence of the relaxation time. To do so, we refined a set of global parameters for QTM, Raman-I, Direct, and Orbach processes (eq 3) against the temperature-dependent rates at 0 and 0.08 T dc fields and the field-dependent rates at 12 and 40 K (Figures S97 and S98, Table S8) using the individual model parameters as starting values (Figure 3). To reduce the number of parameters, we assumed a Direct process with $H^4$ field dependence and linear temperature dependence,50 and $\tau_{QTM}^{-1}$ was fixed to the average of the 2–5 K rates in 0 dc field. This function is complex and nonlinear, so errors were determined by independently varying each parameter such that the resultant time lies within one ESD of the experimental distributions. The global model provides good reproduction of all experimental data with the following parameters: $\tau_{QTM}^{-1} = 7.1_{-0.6}^{+0.8} \text{ s}^{-1}$, $Q = 2_{-1}^{+2} \times 10^{10} \text{ T}^{-p}$, $p = 5.7_{-0.2}^{+0.5} \text{ K}^{-n}$, $n = 3.9 \pm 0.1$, $A = 0.4 \pm 0.2 \text{ s}^{-1} \text{ K}^{-1} \text{ T}^{-4} \text{ s}^{-1}$, $U_{\text{eff}} = 950 \pm 30 \text{ K}$, and $\tau_0 = (2.6 \pm 0.4) \times 10^{-9} \text{ s}$. The zero-field QTM rate ($\tau_{QTM}^{-1}$) is rapid, in agreement with the M vs H hysteresis data, and the field-exponent (p) is slightly larger than the axial SMM [Dy(O'Bu)(Cl)(THF)$_5$]-[B(C$_6$F$_5$)$_4$] of 3.8 $\pm$ 0.2.46

It has previously been shown that the linearity of the N-Dy-N angle in bis-amide complexes should correlate with $U_{\text{eff}}$.27 We hypothesized that in solution the N-Dy-N angle in 1-Dy may increase, as has been observed for the Yb congener;28 phase-dependent geometries have previously been shown to be a feature of f-block silylamide chemistry.54 A ca. 200 mM solution of 1-Dy in fluorobenzene was prepared by dissolving a known mass of solid in an appropriate mass of solvent, and this solution was flash-frozen in liquid nitrogen. The ac susceptibility experiments for the frozen solution sample give relatively noisy data (Figure S99); the Cole-Cole profiles are much broader and more asymmetric than the solid-state data and cannot be modeled well by the generalized Debye model. To account for the asymmetric distribution in relaxation times, the low-temperature (2–13 K) data were fit to a phenomenological Havriliak-Negami model (eq 4, Figures S100 and S101, Table S9) which includes parameters for the skew (γ) and the width (α) of the relaxation time distribution. For symmetric distributions (γ = 1), the Havriliak-Negami model becomes equivalent to the generalized Debye model.51

$$ \chi(\omega) = \chi_s + \frac{\chi_T - \chi_s}{[1 + (i\omega\tau)^{1-\alpha}]^{\gamma}} \quad (4) $$

At higher temperatures (31–79 K), a shoulder in the Cole-Cole plot emerges, and the ac data are best fit by a double-generaized Debye model (Figures S102 and S103 and Table S10). Furthermore, magnetic hysteresis loops are more open in frozen solution than in the solid state (but remain waist-restricted, Figures S86–S88). The low-temperature frozen solution relaxation data show a comparable QTM rate to the solid-state sample, whereas the high-temperature fits encompass a major component (65%) that has rates in line with the solid-state data and a minor component (35%) that has considerably slower dynamics (Figure S107); the minor component and the hysteresis data are both in accord with a sample that relaxes measurably slower than the solid-state material. These observations are consistent with the frozen solution sample containing a broader and more asymmetric
distribution of molecular geometries, with some molecules in the distribution having larger N-Dy-N angles and hence larger anisotropy and slower magnetic relaxation rates; we note that the interactions of Si-C/C-H bonds of the silyl groups with the Dy(III) ion seen in the solid state are also likely to be important in the solution phase.

**Ab Initio Calculations.** First-principles complete active space self-consistent field spin-orbit (CASSCF-SO) calculations were performed using OpenMolcas⁵² from the atomic coordinates of the cation in **1-Dy** determined by single-crystal XRD. These calculations show that the ground state is an almost pure $m_J = \pm 15/2$ Kramers doublet, with Ising-like g-values ($g_x = g_y = 0$, $g_z = 19.86$; Table S11). The first two excited Kramers doublets are at 616 K (98% $m_J \pm 13/2$, 0.8° between excited $g_z$ and ground $g_z$) and 1185 K (94% $m_J \pm 11/2$, 1.6°) above the ground state (Figures S108 and S109), with the second excited state being highly mixed.¹²

## ■ DISCUSSION

All previously reported examples of axial Dy SMMs with no equatorial donor ligands contain bulky η⁵-cyclopentadienyl ligands or related derivatives,¹²⁻²² hence there is no literature precedent for refined magnetostructural comparisons with **1-Dy**. The Dy(III) ion in **1-Dy** is bound by two monodentate σ-donor bis(silyl)amides; although some of the charge density is delocalized about the ligand scaffolds due to negative hyperconjugation with the triisopropylsilyl groups,⁵³,⁵⁴ the N atoms can be formally treated as point-charge Lewis bases to a first approximation. This differs from the highest-performing Dy SMMs bound by π-aromatic ligands in the literature,¹²⁻²² which donate the electron density to Dy from delocalized molecular orbitals located about a pentagonal arrangement of atoms. Accordingly, the degree of magnetic anisotropy and the purity of $m_J$ states should be more sensitive to deviations from ideal linearity in complexes like **1-Dy** than for a sandwich-type complex. We previously reported the solid-state structures of the bent Tm(III) complex [Tm{[N(Si⁴Pr₃)₂]₂}][B(C₆F₅)₄] (N-Tm-N: 125.49(9)°),²⁸ and considering that the six-coordinate ionic radii of Dy(III) (0.912 Å) and Tm(III) (0.88 Å) are quite similar,⁴⁰ we anticipated a similar N-Dy-N angle for **1-Dy**. However, previous computational studies on a series of model two-coordinate DyL₂ compounds (L = mono- or dianionic monodentate C- or N-donor ligand) predicted that $U_{eff}$ should decrease regularly with bending (e.g., [Dy{N-(SiH₃)₂}₂]; $U_{eff} = 2072$ cm⁻¹ at 180° N-Dy-N and 919 cm⁻¹ at 120°),²⁷ thus **1-Dy** remained a desirable synthetic target.

The N-Dy-N angle in **1-Dy** (128.7(2)°) is far more bent than the corresponding $C_{\text{centroid}}$·Dy··$C_{\text{centroid}}$ angle of any isolated dysprosocenium cation (smallest known, [(C₅⁴Pr₄H₂)₂]⁺ = 147.2(8)°),¹³ and **1-Dy** has shorter Dy-N bonds (2.206(7) Å mean) than the mean Dy··$C_{\text{centroid}}$ distances in these systems (e.g., [Dy(C₅⁴Pr₄H₂)₂]⁺ = 2.29(1) Å).¹³ Despite substantially different structures, a comparison of the total calculated CF splitting of the ⁶H₁₅/₂ multiplet between **1-Dy** and [Dy(Cp⁴⁴ttt)₂]⁺ (for which we have commensurate CASSCF-SO calculations; $Cp⁴⁴ttt = \{C₅H₂tBu₃-1,2,4\}$, mean Dy··$C_{\text{centroid}}$ = 2.416(2) Å and mean $C_{\text{centroid}}$··Dy··$C_{\text{centroid}}$ = 152.56(7)°)¹² shows that **1-Dy** has a substantially larger overall splitting (2459 K vs 2124 K); however, the energy gap to the first excited state is slightly smaller (616 vs 703 K), and the second excited state of **1-Dy** has large transverse g-values. Although these calculations may not fully capture the full effects of the multiple Dy··Si-C/C-

H interactions present in **1-Dy**, we note that the two close equatorial Dy··H-C contacts seen in the solid-state structure of [Dy(Cp⁴⁴ttt)₂][B(C₆F₅)₄] did not appear to have a significant effect on SMM behavior.¹² However, the $U_{eff}$ for **1-Dy** (950 ± 30 K) is roughly half the value observed for [Dy(Cp⁴⁴ttt)₂]⁺ (1780 ± 40 K).⁴⁴ Conventional usage of the average transition matrix elements of magnetic moment to infer magnetic relaxation probabilities²⁷ suggests that the $U_{eff}$ value for **1-Dy** should be near the top of the CF manifold (Figure S108), while the experimentally determined $U_{eff}$ value lies in between the first and second excited states. This discrepancy highlights that the static electronic structure alone is insufficient to predict relaxation dynamics. While this would be an excellent opportunity to deploy our recent methods to calculate magnetic relaxation dynamics ab initio,⁵⁵,⁵⁶ unfortunately, for **1-Dy**, there are eight formula units in the crystallographic unit cell (1472 atoms), thus this system is currently too large to perform periodic DFT calculations. We propose that the modulation of the CF by phonons (i.e., spin-phonon coupling) has a larger impact on the electronic states in **1-Dy** than for [Dy(Cp⁴⁴)₂]⁺ because in the former complex the CF is almost exclusively dominated by two flexible monatomic donor ligands rather than the more rigid η⁵-Cp⁴ rings in [Dy(Cp⁴⁴)₂]⁺ and related derivatives,¹²⁻²² which have been shown to be crucial for dictating spin dynamics in [Dy(Cp⁴⁴ttt)₂]⁺.⁵⁷

## ■ CONCLUSIONS

In this work, the isolation of compounds containing the [Dy{N(Si⁴Pr₃)₂]⁺ cation has realized a long-standing goal to synthesize a formally two-coordinate Dy(III) complex, allowing the magnetic properties of this new class of SMM to be determined. We have found a larger than predicted effect of the molecular geometry on SMM behavior, with the significantly bent [Dy{N(Si⁴Pr₃)₂]⁺ cation showing relatively low-lying and highly mixed excited $m_J$ states. Frozen solution magnetic data indicate a species with substantially slower relaxation dynamics, suggesting that a more linear N-Dy-N angle can be adopted in this phase, but this could not be unambiguously confirmed. We propose that fast magnetic relaxation in [Dy{N(Si⁴Pr₃)₂]⁺ arises from a combination of its large deviation from linearity and the flexible coordination environment providing multiple close Dy··H-C/C-Si contacts, in accord with the rigidity of coordinated ligands being of equal importance to the control of molecular geometry for SMMs to show high-blocking temperatures.

## ■ EXPERIMENTAL SECTION

**Experimental Materials and Methods.** All manipulations were conducted under argon with the strict exclusion of oxygen and water by using Schlenk line and glovebox techniques. Glassware was flame-dried under vacuum prior to use. Argon was passed through a column of activated 3 Å molecular sieves and Cu catalyst prior to use. Isolated compounds were dried in vacuo on a Schlenk line to the point at which the flask could maintain a constant static pressure of less than 5 × 10⁻³ mbar. C₆H₆ and C₆D₆ were purchased in anhydrous form, degassed, and stored under argon over a K mirror or activated 3 Å molecular sieves, respectively. n-Hexane was refluxed over molten K for 3 days, distilled, and stored under argon over a K mirror. C₆H₅F and 1,2-C₆H₅F₂ were stirred over neutral alumina for 4–6 h, filtered, refluxed over CaH₂ for 3 days, distilled, and stored under argon over activated 3 Å molecular sieves. Hexamethyldisiloxane (HMDSO) was refluxed over CaH₂ for 3 days, distilled, and stored under argon over activated 3 Å molecular sieves. [Ln(BH₄)₃(THF)₃] (Ln = Y, Dy),³⁴
[HNeT₃][Al{OC(CF₃)₃}]₄],¹⁷ and [CPh₃][Al{OC(CF₃)₃}]₄³⁵ were prepared according to literature procedures; [K{N(Si'Pr₃)₂}] was prepared by an adapted literature procedure,²⁴ which is detailed in the Supporting Information.

NMR spectra (see Figures S1–S48) of 1-Ln, 2-Ln, 3-Ln, 4-Ln, 5-Y/HN(Si'Pr₃)₂, HN(Si'Pr₃)₂, and [K{N(Si'Pr₃)₂}] were recorded at 298 K on a Bruker AVIII HD 400 cryoprobe spectrometer operating at 400.07 (¹H) 128.36 (¹¹B), 100.60 (¹³C), 376.40 (¹⁹F), or 79.48 (²⁹Si) MHz. Chemical shifts are reported in ppm and coupling constants in Hz. ¹H and ¹³C{¹H} DEPTQ NMR spectra recorded in C₆D₆ were referenced to the solvent signal.⁵⁸ Spectra recorded in protonated solvents were locked to, and where possible referenced with, an internal sealed capillary of C₆D₆. The solution magnetic susceptibilities of 1-Dy, 2-Dy, 3-Dy, and 4-Dy were determined at 298 K by the Evans method;⁶⁰ ¹H NMR spectra recorded in C₆H₅F or 1,2-C₆H₄F₂ were referenced using the highest intensity peak of the highest frequency fluoroarene multiplet (δH: 6.87 or 6.85 respectively). ¹¹B/¹¹B{¹H} (H₃BO₃/D₂O), ¹⁹F (C₇H₅F₃/CDCl₃), and ²⁹Si{¹H} DEPT90 (SiMe₄) NMR spectra were referenced to external standards. The C(CF₃)₃ carbon resonances of the [Al{OC(CF₃)₃}]₄⁻ anion were not observed in the ¹³C{¹H} NMR spectra of 1-Ln, likely due to quadrupolar broadening by the 100% abundant *I* = 5/2 ²⁷Al nuclei and coupling to multiple 100% abundant *I* = 1/2 ¹⁹F nuclei.

ATR-IR spectra of 1-Ln, 2-Ln, 3-Ln, and 4-Ln were recorded as microcrystalline powders using a Bruker Alpha FT-IR spectrometer with a Platinum-ATR module within a nitrogen-filled glovebox at ambient temperature (see Figures S49–S56). Elemental analysis (C, H, and N) samples were prepared in an argon-filled glovebox, and the analysis 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. Elemental analysis values obtained for 1-Ln, 2-Ln, 3-Ln, and 4-Ln typically gave carbon compositions that were lower than expected values; this phenomenon has commonly been ascribed to incomplete combustion due to carbide formation, and we note that we have previously observed low carbon values reproducible for Ln {N(Si'Pr₃)₂} complexes.²⁴,²⁵,²⁸,²⁹

Single-crystal XRD data were collected on either an Oxford
Diffraction Agilent Supernova diffractometer equipped with a CCD
area detector and a mirror-monochromated Mo Kα source (1-Y, 2-
Dy, 3-Dy, 3-Dy·0.5KBH₄·1,2-C₆H₄F₂, and 4-Y), a Rigaku XtaLAB
Synergy-S diffractometer equipped with a HyPix 6000HE photon
counting pixel array detector with a mirror-monochromated Mo Kα
X-ray source (4-Dy), or a Rigaku FR-X diffractometer equipped with
a HyPix 6000HE photon counting pixel array detector and a mirror-
monochromated X-ray source (1-Dy, 2-Y, 3-Y, and 3-Y·0.5KBH₄·
C₆H₆) (λ = 0.71073 Å for Mo Kα or λ = 1.5418 Å for Cu Kα
radiation, Figures S61–S71, and Tables S1–S3). Intensities were
integrated from data recorded on 0.5° (1-Dy, 2-Y, 3-Y, and 3-Y·
0.5KBH₄·C₆H₆), or 1° (1-Y, 2-Dy, 3-Dy, 3-Dy·0.5KBH₄·1,2-
C₆H₄F₂, 4-Dy, and 4-Y) frames 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.⁵⁹ The structures were solved using
SHELXT;⁶⁰ the data sets were refined by full-matrix least-squares
on all unique *F*² values.⁶⁰ Anisotropic displacement parameters were
used for all non-hydrogen atoms with constrained riding hydrogen
geometries, with the exception of borohydride H atoms, which were
located in the difference map and refined isotropically; 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. CrysAlisPro⁵⁹ was used for
control and integration, and SHELX⁶⁰,⁶¹ was employed through
OLEX²⁶² for structure solution and refinement. ORTEP-³⁶³ and
POV-Ray⁶⁴ were used for molecular graphics. Despite the use of a
highly intense X-ray source (Rigaku FR-X rotating anode), crystals of
1-Dy and 3-Dy only diffracted to 0.94 and 1.06 Å of resolution,
respectively, and thus the data were trimmed accordingly. Complex 3-
Dy was also found to be highly sensitive to X-ray irradiation,

presenting signs of beam damage (reduction of data resolution and
diffracted intensities) with moderate X-ray exposure at 100 K. The
data affected by the beam damage were removed, leading to a low
completeness (91%) at 1.06 Å.

Powder XRD data of a microcrystalline sample of 1-Dy 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 = 1.5418 Å) with a HyPix-6000HE detector and an Oxford Cryosystems nitrogen flow gas system (Figure S72). Data were collected at θ between 2 and 70° with a detector distance of 150 mm and a beam divergence of 1.5 mRad using CrysAlisPro.⁵⁹ For data processing, the instrument was calibrated using silver behenate as standard, then the data were reduced and integrated using CrysAlisPro.⁵⁹ Le Bail profile analysis was performed using JANA2006 software.⁶⁵

Magnetic measurements of 1-Dy (Figures S73–S107 and Tables S5–S10) were performed on a Quantum Design MPMS3 superconducting quantum interference device (SQUID) magnetometer at The University of Manchester or an MPMS XL magnetometer or a PPMS EverCool II susceptometer housed at the Centre de Recherche Paul Pascal at temperatures between 1.8 and 300 K and dc magnetic fields ranging from –7 to +7 T (MPMS3 and MPMS XL) or –9 to +9 T (PPMS EverCool II).

The MPMS3 measurements were collected on a finely ground powder sample of 1-Dy (27.4 mg) restrained in eicosane (22.0 mg) and a 200 mM fluorobenzene (0.102 g) solution of 1-Dy (35.7 mg); these samples were prepared in a glovebox under an atmosphere of argon loaded into borosilicate tubes, which were later flame-sealed under vacuum and loaded into a plastic straw held in place by friction between the diamagnetic tape at the top of the tube and the straw. The solution sample was flash-frozen in liquid nitrogen and rapidly cooled in zero field after loading into the instrument. Measurements were performed in dc scan mode using 40 mm scan length and 6 s scan time. Equilibrium susceptibility measurements were performed on cooling in temperature settle mode 1.8–300 K (solid) or 1.8–180 K (frozen solution) in 0.1 T dc field. Field dependence (H) of the magnetization (M) curves (2 K, 0–7 T) and M vs H hysteresis curves (±5 T for 2–7 K; ±3 T for 8–10 or 12 K) were performed in continuous sweep mode with a sweep rate of 22 Oe s⁻¹. Raw magnetic data were scaled for the shape of the sample using a Quantum Design MPMS3 Geometry Correction Simulator (correction factor: 1.003 for solid and 0.817 for solution), corrected for the diamagnetic contribution of the sample holder (straw + borosilicate tube) and for the mass of eicosane using calibrated blanks or for the mass of fluorobenzene using Pascal’s constants.⁶⁶ The magnetic susceptibility was corrected for the intrinsic diamagnetism of the sample estimated as the molecular weight (g mol⁻¹) multiplied by –0.5 × 10⁻⁶ cm³ K mol⁻¹. Ac magnetic data were recorded for the frozen solution of 1-Dy at 0.1–1000 Hz between 2 and 76 K. Low-temperature (2–13 K) ac data were fit to the Havriliak–Negami model, and high-temperature (31–79 K) data were fit to the double-generalized Debye model in CC-FIT2 5.0.1.⁴⁴,⁴⁵,⁶⁷

The MPMS XL and PPMS EverCool II measurements were
collected on polycrystalline 1-Dy in sealed polypropylene (PP) bags.
For the PPMS VSM dc measurements, the sample was suspended in
mineral oil (MPMS RSO dc: 40.2 mg 1-Dy and 10.9 mg PP; PPMS
VSM dc: 19.5 mg 1-Dy, 18.3 mg PP, and 13.9 mg oil; MPMS ac and
PPMS ACMS ac: 40.2 mg 1-Dy and 10.9 mg PP; MPMS ac: 22.9 mg
1-Dy and 9.46 mg PP); these samples were prepared in a glovebox
under an atmosphere of argon. Data were collected as follows: (i) via
an MPMS XL for dc measurements using the RSO option with fields
up to 7 T and for ac measurements in the 0.001–1500 Hz range and
(ii) via a PPMS EverCool II for dc measurements with the large bore
VSM option with fields up to 9 T and for the ac measurements with
the ACMS-II option in the 10–10,000 Hz range. The FC/ZFC
measurements were performed from 50 K cooling to 1.85 K without
dc field (reset magnet). The field (10 Oe) was set at 1.85 K, and ZFC
measurements were recorded upon heating up to 50 K. FC cooling
measurements were performed by cooling from 50 to 1.85 K, and FC
heating data were collected upon heating from 1.85 to 50 K. During
the MPMS XL and PPMS EverCool II experiments, it is clear that the
amplitude of the magnetization for **1-Dy** decreased slightly over a
period of several weeks and more rapidly during sample transfer/
loading in the experimental setup; we attribute this to a small amount
of sample decomposition as **1-Dy** is relatively air- and moisture-
sensitive and the PP bags are not completely impervious to air and
moisture. However, no modification of the global, qualitative
magnetic behavior was seen, with no shift or shape modification of
the relaxation process. Therefore, the amplitude of the magnetic data
presented herein was normalized to the MPMS3 measurements
collected at Manchester directly after the synthesis and isolation of **1-Dy** in sealed borosilicate tubes. The maximum normalization factor
used in this study was 1.19, which also incorporates errors in the
sample mass, magnetometer calibration, and background corrections.
Ac data for solid **1-Dy** were fitted with the generalized Debye model
with MagSuite software, restraining the frequency window to where
the model fits well.<sup>68</sup>

**Computational Methods.** OpenMolcas⁵⁰ was used to perform CASSCF-SO calculations on **1-Dy** to determine its electronic structure (Figures S108 and S109 and Table S11). The molecular geometry of the single-crystal XRD structure was used with no optimization, taking the largest disorder component only. Integrals were performed in the SEWAD module using basis sets from ANO-RCC library⁶⁹⁻⁷² with VTZP quality for Dy atoms, VDZP quality for the N atoms, and VDZ quality for all remaining 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 optimized in state-averaged CASSCF calculations in the RASSCF module, where the active space was defined by the nine 4f electrons in the seven 4f orbitals of Dy(III). Three such calculations were performed independently for each possible spin state, where 21 roots were included for *S* = 5/2, 224 roots were included for *S* = 3/2, and 490 roots were included for *S* = 1/2. The wave functions obtained from these CASSCF calculations were then mixed by spin-orbit coupling in the RASSI module, where all the 21 *S* = 5/2 states, 128 of the *S* = 3/2 states, and 130 of the *S* = 1/2 states were included. SINGLE_ANISO was used to decompose the resulting spin-orbit wave functions into the CF Hamiltonian formalism.⁷³ Diamond was employed for molecular graphics.⁷⁴

DFT geometry optimizations and vibrational analyses were
performed on the cation of 1-Y and 2-Y, the monomer of 3-Y, and
4-Y, for the purposes of assigning experimental IR spectra (Figures
S57-S60). All calculations were executed by the Orca 5.0 software
package at the PBE0<sup>75,76</sup>-D4<sup>77,78</sup>/def2-TZVP<sup>79</sup> level (including the
default effective core potential for yttrium<sup>80</sup>). The default Orca 5.0
integration grids, convergence method, and convergence thresholds
(for both SCF and geometry iterations) were used throughout. The
SCF energy calculations were expedited by employing the RIJCOSX
approximation<sup>81</sup> (and the associated def2/J auxiliary basis set<sup>82</sup>) and
DIIS convergence acceleration<sup>83</sup> (as is default in Orca 5.0).
Geometry-optimized structures were verified as being minima on
the potential energy surface through the absence of imaginary
vibrational modes. A linear energy scaling was applied to the
computed IR spectra.

**Synthesis.** [Y(N(Si'Pr₃)₂)₂][Al{OC(CF₃)₄}] (1-Y). C₆H₅F (5 mL) was added to a mixture of 4-Y (0.168 g, 0.221 mmol) and [CPh₃][Al{OC(CF₃)₄}] (0.242 g, 0.200 mmol), and the reaction mixture was stirred for 18 h at 20 °C. The resulting suspension was filtered and layered with excess n-hexane (ca. 20 mL), which upon diffusion at ambient temperature afforded the title compound as colorless needles. The crystals were isolated and dried thoroughly in vacuo. Yield: 0.251 g, 0.146 mmol, 73%. This reaction can also be performed in benzene with equivalent success, yielding under the same conditions a biphasic mixture comprising a benzene-clathrated oil of 1-Y beneath a benzene solution of other reaction components. Anal. Calcd for C₅₂H₈₄AlF₃O₄N₂Si₄Y (1713.42 g mol⁻¹) C, 36.45; H, 4.94, N, 1.63. Found: C, 34.38; H, 4.51, N, 1.41. ¹H NMR (400.07 MHz, C₆H₅F): δ 1.15 (d, ³JHH = 7.4 Hz, 72H, CH₃), 0.86 (sept, ³JHH = 7.4 Hz, 12H, CH). ¹³C{¹H} DEPTQ NMR (100.60 MHz, C₆H₅F):

δ 123.28 (q, ¹J<sub>FC</sub> = 294 Hz, CF<sub>3</sub>), 19.57 (s, CH<sub>3</sub>), 18.25 (s, CH). ¹⁹F NMR (376.40 MHz, C₆H₅F): δ -75.05 (s, CF<sub>3</sub>). ²⁹Si{¹H} DEPT90 NMR (79.48 MHz, C₆H₅F): δ -4.79 (s, Si'Pr₃). FTIR (ATR, microcrystalline): ν̃ = 2945 (m), 2867 (m), 1465 (m), 1352 (m), 1296 (m), 1274 (m), 1241 (m), 1208 (s) 1167 (m), 968 (s), 953 (m), 920 (m), 880 (m), 725 (s) cm⁻¹.

[Dy(N(Si'Pr₃)₂)₂][Al{OC(CF₃)₄}] (1-Dy). C₆H₅F (5 mL) was added to a mixture of 4-Dy (0.350 g, 0.418 mmol) and [CPh₃][Al{OC(CF₃)₄}] (0.484 g, 0.400 mmol), and the reaction mixture was stirred for 18 h at 20 °C. The resulting suspension was filtered and layered with excess n-hexane (ca. 20 mL), which upon diffusion at ambient temperature afforded the title compound as colorless needles. The crystals were isolated and dried thoroughly in vacuo. Yield: 0.567 g, 0.317 mmol, 79%. This reaction can also be performed in benzene with equivalent success, yielding under the same conditions a biphasic mixture comprising a benzene-clathrated oil of 1-Dy beneath a benzene solution of the other reaction components. Anal. Calcd for C₅₂H₈₄AlDyF₃O₄N₂Si₄ (1786.91 g mol⁻¹) C, 34.95; H, 4.74, N, 1.57. Found: C, 33.66; H, 4.37, N, 1.41. χT product = 14.2 cm³ mol⁻¹ K, μ<sub>eff</sub> = 10.7 μ<sub>B</sub> mol⁻¹ (Evans method). ¹H NMR (400.07 MHz, C₆D₆): δ 4.76 (br, fwhm ≈ 60 Hz), 4.23 (br, fwhm ≈ 50 Hz), 3.95 (br, fwhm ≈ 160 Hz), 3.67 (br, fwhm ≈ 60 Hz). ¹⁹F NMR (376.40 MHz, C₆H₅F): δ 97.22 (br, fwhm ≈ 280 Hz, CF₃). FTIR (ATR, microcrystalline): ν̃ = 2945 (m), 2867 (m), 1465 (m), 1352 (m), 1296 (m), 1274 (m), 1241 (m), 1208 (s) 1167 (m), 968 (s), 953 (m), 920 (m), 880 (m), 725 (s) cm⁻¹.

[Y(N(Si'Pr₃)₂)(BH₄)₂(THF)] (2-Y). C₆H₅F (10 mL) was added to a mixture of [Y(BH₄)₃(THF)₃] (2.389 g, 5.000 mmol) and [K{N-(Si'Pr₃)₂}] (1.857 g, 5.050 mmol), and the resulting suspension was stirred at 20 °C for 1 h. The volatiles were removed in vacuo, and the residues were extracted into n-hexane (3 × 20 mL) with vigorous agitation and filtered. The solution was concentrated to ca. 10 mL and stored at -25 °C, affording the title complex as colorless needles, which were isolated and thoroughly dried in vacuo. Yield: 2.298 g, 4.424 mmol, 88%. This reaction can also be successfully performed in benzene, following an otherwise identical procedure. Anal. Calcd for C₂₂H₅₈B₂OONSi₂Y (519.35 g mol⁻¹) C, 50.87; H, 11.26, N, 2.70. Found: C, 49.55; H, 11.09, N, 2.45. ¹H NMR (400.07 MHz, C₆D₆: 298 K): δ 3.60 (br s, fwhm ≈ 19 Hz, 4H, CH₂CH₂O), 1.33 (d, ³JHH = 7.3 Hz, 36H, CH₃CH), 1.26 (q, 8H, ¹JBH = 81 Hz, BH₄), 1.15 (sept, ³JHH = 7.3 Hz, 6H, CH₃CH), 1.06 (br s, fwhm ≈ 21 Hz, 4H, CH₃CH₂O). ¹¹B NMR (128.36 MHz, C₆D₆: 298 K): δ 22.0 (p, ¹JBH = 81 Hz, BH₄). ¹³C{¹H} DEPTQ NMR (100.60 MHz, C₆D₆: 298 K): δ 74.6 (CH₂CH₂O), 24.8 (CH₂CH₂O), 20.6 (CH₃CH), 18.4 (CH₃CH). ²⁹Si{¹H} DEPT90 NMR (79.48 MHz, C₆D₆: 298 K): δ -2.7 (Si'Pr₃). FTIR (ATR, microcrystalline): ν̃ = 2951 (m), 2867 (m), 2488 (m), 2178 (b), 1463 (m), 1185 (m), 1095 (w), 999 (m), 923 (s), 873 (s), 719 (s), 653 (s) cm⁻¹.

[Dy(N(Si'Pr₃)₂)(BH₄)₂(THF)] (2-Dy). C₆H₅F (10 mL) (or benzene, see above) was added to a mixture of [Dy(BH₄)₃(THF)₃] (2.757 g, 5.000 mmol) and [K{N(Si'Pr₃)₂}] (1.857 g, 5.050 mmol), and the resulting suspension was stirred at 20 °C for 1 h. The volatiles were removed in vacuo, and the residues were extracted into n-hexane (3 × 20 mL) with vigorous agitation and filtered. The solution was concentrated to ca. 10 mL and stored at -25 °C, affording the title complex as pale-yellow needles, which were isolated and thoroughly dried in vacuo. Yield: 2.470 g, 4.165 mmol, 83%. This reaction can also be successfully performed in benzene, following an otherwise identical procedure. Anal. Calcd for C₂₂H₅₈B₂DyONSi₂ (592.94 g mol⁻¹) C, 44.56; H, 9.86, N, 2.36. Found: C, 43.86; H, 10.22, N, 2.84. χT product = 13.9 cm³ mol⁻¹ K, μ<sub>eff</sub> = 10.5 μ<sub>B</sub> mol⁻¹ (Evans method). ¹H NMR (400.07 MHz, C₆D₆): δ 40.13 (vbr, fwhm ≈ 650 Hz, OCH₃CH₂), 1.55 (br, fwhm ≈ 20 Hz), 1.11 (br, fwhm ≈ 20 Hz, CH₃), 0.78 (br, fwhm ≈ 20 Hz), 0.63 (br, fwhm ≈ 20 Hz), -42.80 (vbr, fwhm ≈ 1610 Hz, OCH₂CH₂). The BH₄ resonance was not located. ¹¹B{¹H} NMR (128.36 MHz, C₆D₆): δ -18.14 (vbr, fwhm ≈ 2490 Hz), BH₄. FTIR (ATR, microcrystalline): ν̃ = 2951 (m), 2867 (m), 2488 (m), 2178 (b), 1463 (m), 1185 (m), 1095 (w), 999 (m), 923 (s), 873 (s), 719 (s), 653 (s) cm⁻¹.
[Y{N(Si'Pr₃)₂}(BH₄)(μ-BH₄)]₄ (3-Y). In a long resealable ampule, 2-Y (4.290 g, 8.259 mmol) was heated to 120 °C in the solid state at ca. 0.01 mbar for 2 h, resulting in partial sublimation of the solid material. After cooling to ambient temperature, the residues were found to have a mass of 3.699 g (8.270 mmol assuming the formula weight of 3-Y), consistent with the removal of 99.2% of the bound THF. The ¹H, ¹¹B, ¹³C, and ²⁹Si NMR spectra of this amorphous material were found to be identical to an authentic crystalline sample of 3-Y, which was prepared as follows. In a long resealable ampule, 2-Y (1.390 g, 2.676 mmol) was heated to 150 °C in the solid state at ca. 0.01 mbar for 2 h, resulting in the partial sublimation of the solid material and minor production of a high-boiling point colorless oil. After cooling to ambient temperature, the residues were extracted into 1,2-C₆H₄F₂ (3 × 5 mL), filtered, and the solution concentrated to ca. 5 mL. Slow diffusion of excess n-hexane (ca. 20 mL) at -25 °C gave the title complex as colorless plates, which were isolated and thoroughly dried in vacuo. An additional crop was obtained upon storage at -25 °C after concentrating the fully diffused supernatant to ca. 5 mL. Yield: 0.641 g, 1.433 mmol, 54%. On one occasion, a sample of 3-Y contaminated with trace KBH₄ was recrystallized by slow evaporation of benzene. Several crystals of 3-Y·0.5KBH₄·C₆H₆ were identified in the crop by single-crystal XRD, though as a homogeneous sample of the impurity was neither obtained nor sought, no further characterization data are reported. Characterization data for 3-Y: Anal. Calcd for C₁₈H₅₀B₂NSi₂Y (447.25 g mol⁻¹) C, 48.33; H, 11.27, N, 3.13. Found: C, 45.67; H, 10.77, N, 2.81. ¹H NMR (400.07 MHz, C₆D₆): δ 1.13–1.07 (m, 50H, CHCH₃, CHCH₃ and BH₄). ¹¹B NMR (128.36 MHz, C₆D₆, 298 K): δ –20.7 (br., fwhm ≈ 480 Hz, BH₄), –3.6 (br., fwhm ≈ 2240 Hz, μ-BH₄). ¹³C{¹H} DEPTQ NMR (100.60 MHz, C₆D₆): δ 19.3 (s, CH₃CH), 14.9 (s, CH₃CH). ²⁹Si{¹H} DEPT90 NMR (79.48 MHz, C₆D₆): δ –3.7 (s, Si'Pr₃). ¹H NMR (400.07 MHz, C₆H₄F₂, C₆D₆): δ 1.13–1.00 (m, 50H, CHCH₃, CHCH₃ and BH₄). ¹¹B NMR (128.36 MHz, C₆H₄F₂, C₆D₆, 298 K): δ –20.9 (br., p, ¹JBH ≈ 80 Hz, fwhm ≈ 120 Hz, BH₄). ¹³C{¹H} DEPTQ NMR (100.60 MHz, C₆H₄F₂, C₆D₆): δ 18.8 (s, CH₃CH), 14.9 (s, CH₃CH). ²⁹Si{¹H} DEPT90 NMR (79.48 MHz, C₆H₄F₂, C₆D₆): δ –3.6 (s, Si'Pr₃). FTIR (ATR, microcrystalline): ν̄ = 2943 (s), 2864 (s), 2756 (w), 2731 (w), 2495 (w), 2229 (br), 1463 (m), 1241 (s), 1216 (s), 941 (s), 879 (s), 698 (s), 658 (s) cm⁻¹.

[Dy{N(Si'Pr₃)₂}(BH₄)(μ-BH₄)]₄ (3-Dy). In a long resealable ampule, 2-Dy (0.3822 g, 0.6446 mmol) was heated to 120 °C in the solid state at ca. 0.01 mbar for 2 h, resulting in the partial sublimation of the solid material. After cooling to ambient temperature, the residues were found to have a mass of 0.3357 g (0.6446 mmol assuming the formula weight of 3-Dy), consistent with the removal of 100% of the bound THF. The ¹H and ¹¹B NMR spectra of this amorphous material were found to be identical to that of an authentic crystalline sample of 3-Dy, which was prepared as follows. In a long resealable ampule, 2-Dy (1.770 g, 2.985 mmol) was heated to 150 °C in the solid state at ca. 0.01 mbar for 2 h, resulting in the partial sublimation of the solid material and minor production of a high-boiling point colorless oil. After cooling to ambient temperature, in a glovebox, the residues were returned to the base of the flask and the above procedure repeated. After cooling to ambient temperature, the residues were extracted into 1,2-C₆H₄F₂ (3 × 5 mL), filtered, and the solution was concentrated to ca. 5 mL. Slow diffusion of excess n-hexane (ca. 20 mL) at -25 °C afforded the title complex as pale-yellow plates, which were isolated and thoroughly dried in vacuo. An additional crop of the title complex was obtained upon storage at -25 °C after concentrating the fully diffused supernatant to ca. 5 mL. Yield: 1.067 g, 2.049 mmol, 67%. As described for 3-Y, trace KBH₄ contamination led to the formation of several crystals of 3-Dy·0.5KBH₄·C₆H₄F₂·1,2 following recrystallization from 1,2-C₆H₄F₂ layered with hexane. This complex was characterized by single-crystal XRD only. Characterization data for 3-Dy: Anal. Calcd for C₁₈H₅₀B₂DyNSi₂ (520.84 g mol⁻¹) C, 41.50; H, 9.67, N, 2.69. Found: C, 39.55; H, 9.81, N, 2.55. χT product = 12.5 cm³ mol⁻¹ K, μeff = 10.0 μB mol⁻¹ (Evans method). ¹H NMR (400.07 MHz, C₆D₆): δ 1.71 (br, fwhm ≈ 20 Hz, CH₃), 1.25 (br, fwhm ≈ 30 Hz), 0.34 (br, fwhm ≈ 30 Hz). ¹¹B{¹H} NMR (128.36 MHz, C₆D₆): δ –9.94 (vbr, fwhm ≈ 2450 Hz, BH₄). FTIR (ATR, microcrystalline):

ν̄ = 2947 (m), 2867 (m), 2751 (w), 2517 (w), 2287 (m), 2166 (w), 2143 (w), 1467 (m), 1208 (s), 1189 (s), 904 (s), 873 (s), 715 (s), 656 (s) cm⁻¹.

[Y{N(Si'Pr₃)₂}(BH₄)]₄ (4-Y). A solution of 3-Y (0.447 g, 1.000 mmol) and [K{N(Si'Pr₃)₂}] (0.734 g, 2.000 mmol) in benzene (10 mL) was stirred at 30 °C for 72 h. The volatiles were then removed in vacuo and the residues extracted into n-hexane and filtered. The volatiles were again removed in vacuo, and [HNEt₃][Al{OC(CF₃)₃}]₄ (0.535 g, 0.500 mmol) was added followed by benzene (10 mL). The resulting suspension was vigorously stirred for 4 h at 20 °C, after which the volatiles were removed in vacuo, and the residues were extracted into HMDSO (3 × 1 mL) and filtered. Storage of the solution at -35 °C afforded the title compound as colorless blocks, which were isolated and thoroughly dried in vacuo. Yield: 0.178 g, 0.234 mmol, 23% with respect to 3-Y. Anal. Calcd for C₃₆H₈₈BN₂Si₄Y (761.08 g mol⁻¹) C, 56.81; H, 11.65, N, 3.68. Found: C, 51.98; H, 11.17; N, 2.12. ¹H NMR (400.07 MHz, C₆D₆): δ 1.47 (qd, ¹JBH = 72 Hz, ¹JYH = 14 Hz, 4H, BH₄), 1.35 (d, ³JHH = 7.4 Hz, 72H, CH₃), 1.06 (sept, ³JHH = 7.5 Hz, 12H, CH). ¹¹B NMR (128.36 MHz, C₆D₆): δ –21.41 (p, ¹JBH = 86 Hz, BH₄). ¹³C{¹H} DEPTQ NMR (100.60 MHz, C₆D₆): δ 21.0 (s, CH₃CH), 19.8 (s, CH₃CH). ²⁹Si{¹H} DEPT90 NMR (79.48 MHz, C₆D₆): δ –3.36 (s, Si'Pr₃). FTIR (ATR, microcrystalline): ν̄ = 2943 (s), 2864 (s), 2756 (w), 2731 (w), 2495 (w), 2229 (br), 1463 (m), 1241 (s), 1216 (s), 941 (s), 879 (s), 698 (s), 658 (s) cm⁻¹.

[Dy{N(Si'Pr₃)₂}(BH₄)]₄ (4-Dy). A solution of 3-Dy (0.520 g, 1.000 mmol) and [K{N(Si'Pr₃)₂}] (0.734 g, 2.000 mmol) in benzene (10 mL) was stirred at 30 °C for 72 h. The volatiles were then removed in vacuo and the residues extracted into n-hexane and filtered. The volatiles were again removed in vacuo, and [HNEt₃][Al{OC(CF₃)₃}]₄ (0.535 g, 0.500 mmol) was added followed by benzene (10 mL). The resulting suspension was vigorously stirred for 4 h at 20 °C, after which the volatiles were removed in vacuo and the residues extracted into HMDSO (3 × 1 mL) and filtered. Storage of the solution at -35 °C afforded the title compound as colorless blocks, which were isolated and thoroughly dried in vacuo. Yield: 0.089 g, 0.117 mmol, 12% with respect to 3-Dy. Anal. Calcd for C₃₆H₈₈DyN₂Si₄ (834.67 g mol⁻¹) C, 51.80; H, 10.63, N, 3.36. Found: C, 49.16; H, 10.73; N, 2.97. χT product = 12.6 cm³ mol⁻¹ K, μeff = 10.1 μB mol⁻¹ (Evans method). ¹H NMR (400.07 MHz, C₆D₆): δ 1.35 (br, fwhm ≈ 25 Hz), 0.62 (br, fwhm ≈ 18 Hz). ¹¹B{¹H} NMR (128.36 MHz, C₆D₆): δ –14.1 (vbr, fwhm ≈ 1690 Hz, BH₄). FTIR (ATR, microcrystalline): ν̄ = 2943 (s), 2864 (s), 2753 (w), 2727 (w), 2488 (w), 2240 (br), 1463 (m), 1239 (s), 1212 (s), 939 (s), 879 (s), 698 (s), 659 (s) cm⁻¹.

[Y{N(Si'Pr₃)₂}(Si(Pr)₂{CH(Me)CH₂}]·κ²-N,C)] (5-Y). The HMDSO-insoluble residues (250 mg), obtained from the synthesis of 3-Y similar to that outlined above and found by ¹H NMR spectroscopy to contain 11.3 mol % 1-Y (42.4 mg, 0.0247 mmol) and 88.7 mol % [HNEt₃][Al{OC(CF₃)₃}]₄ (207.6 mg, 0.194 mmol), were combined with [K{N(Si'Pr₃)₂}] (150 mg, 0.408 mmol) and the mixture suspended in benzene (5 mL). After stirring at ambient temperature for 1 h, the volatiles were removed in vacuo and the residues extracted into hexane. The volatiles were again removed in vacuo, and a portion of the resulting colorless oil containing a mixture of the title compound and HN(Si'Pr₃)₂ was analyzed in C₆D₆ solution by NMR spectroscopy. ¹H NMR (400.07 MHz, C₆D₆): 1.67 (d, ³JHH = 6.2 Hz, 3H, Si'Pr₂CH(CH₃)CH₂Y), 1.45 (d, ³JHH = 6.9 Hz, 3H, Si'Pr₂CH(CH₃)CH₂Y), 1.43 (d, ³JHH = 6.5 Hz, 3H, Si'Pr₂CH(CH₃)CH₂Y), 1.38–1.32 (m, 9H, CH₃), 1.30–1.25 (m, 54H, CH₃), 1.12–1.02 (obsc. m, 9H, CH), 1.00–0.90 (m, 3H, CH). ¹³C{¹H} DEPTQ NMR (100.60 MHz, C₆D₆), selected signals: δ 55.34 (d, ¹JYC = 47.4 Hz, Si'Pr₂CH(CH₃)CH₂Y), 24.50 (s, Si'Pr₂CH(CH₃)CH₂Y), 21.79 (s, Si'Pr₂CH(CH₃)CH₂Y), 20.69 (s, Si'Pr₂CH(CH₃)CH₂Y). ²⁹Si{¹H} DEPT90 NMR (79.48 MHz, C₆D₆): δ –3.32 (s, ¹Pr₃SiNSi'Pr₂CH(CH₃)CH₂), –5.75 (s, ¹Pr₃SiNSi'Pr₃), –7.62 (s, ¹Pr₃SiNSi'Pr₂CH(CH₃)CH₂).
■ ASSOCIATED CONTENT

**Data Availability Statement**

Research data files supporting this publication are available from FigShare at https://figshare.com/doi/10.6084/m9. figshare.23807376.

● Supporting Information

The Supporting Information is available free of charge at
https://pubs.acs.org/doi/10.1021/jacs.3c12427.

Additional experimental details, materials, methods, and
associated data (PDF)

**Accession Codes**

CCDC 2284722–2284732 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing data_request@ccdc.cam.ac.uk, or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge, CB2 1EZ, UK; fax: +44 1223 336033.

■ AUTHOR INFORMATION

**Corresponding Authors**

Rodolphe Clérac – Univ. Bordeaux, CNRS, CRPP, 33600 Pessac, France; ● orcid.org/0000-0001-5429-7418; Email: rodolphe.clerac@u-bordeaux.fr

Nicholas F. Chilton – Department of Chemistry, The University of Manchester, Manchester M13 9PL, U.K.; Research School of Chemistry, The Australian National University, Canberra, ACT 2601, Australia; ● orcid.org/0000-0002-8604-0171; Email: nicholas.chilton@anu.edu.au

David P. Mills – Department of Chemistry, The University of Manchester, Manchester M13 9PL, U.K.; ● orcid.org/0000-0003-1575-7754; Email: david.mills@manchester.ac.uk

**Authors**

Jack Emerson-King – Department of Chemistry, The University of Manchester, Manchester M13 9PL, U.K.; ● orcid.org/0000-0002-0309-8344

Gemma K. Gransbury – Department of Chemistry, The University of Manchester, Manchester M13 9PL, U.K.; ● orcid.org/0000-0002-7579-4226

George F. S. Whitehead – Department of Chemistry, The University of Manchester, Manchester M13 9PL, U.K.; ● orcid.org/0000-0003-1949-4250

Iñigo J. Vitorica-Yrezabal – Department of Chemistry, The University of Manchester, Manchester M13 9PL, U.K.

Mathieu Rouzières – Univ. Bordeaux, CNRS, CRPP, 33600 Pessac, France

Complete contact information is available at:
https://pubs.acs.org/10.1021/jacs.3c12427

**Notes**

The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

We thank the University of Manchester for access to the Computational Shared Facility and the European Research Council (StG-851504 and CoG-816268) and the UK EPSRC (EP/R002605X/1, EP/P001386/1, EP/S033181/1 and EP/T011289/1) for funding. We acknowledge the EPSRC UK National Electron Paramagnetic Resonance Service for access to the SQUID magnetometer and the National Nuclear User

Facility at the Center for Radiochemical Research for access to a diffractometer. R.C. and M.R. thank the University of Bordeaux, the CNRS, the Region Nouvelle Aquitaine, and Quantum Matter Bordeaux. N.F.C. thanks the Royal Society for a University Research Fellowship (URF191320).

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Isolation of a bent dysprosium bis(amide) single-molecule magnet

Jack Emerson-King,¹ Gemma K. Gransbury,¹ George F. S. Whitehead,¹ Iñigo J. Vitorica-Yrezabal,¹ Mathieu Rouzières,² Rodolphe Clérac,²,* Nicholas F. Chilton,¹,³,* and David P. Mills¹,*

¹Department of Chemistry, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK.

²Univ. Bordeaux, CNRS, CRPP, UMR 5031, 33600 Pessac, France.

³Research School of Chemistry, The Australian National University, Sullivans Creek Road, Canberra, ACT, 2601, Australia.

Contents

1. Modified synthesis of [KN(Si⁴Pr₃)₂]................................................................................S3

2. NMR spectra ................................................................................................................S5

2.1 HN(Si⁴Pr₃)₂ ................................................................................................................S5

2.2 [KN(Si⁴Pr₃)₂]................................................................................................................S5

2.3 [Y{N(Si⁴Pr₃)₂}₂][Al{OC(CF₃)₃}₄] (1-Y)................................................................................S6

2.4 [Dy{N(Si⁴Pr₃)₂}₂][Al{OC(CF₃)₃}₄] (1-Dy)................................................................................S7

2.5 [Y{N(Si⁴Pr₃)₂}(BH₄)₂(THF)] (2-Y)................................................................................S8

2.6 [Dy{N(Si⁴Pr₃)₂}(BH₄)₂(THF)] (2-Dy)................................................................................S10

2.7 [Y{N(Si⁴Pr₃)₂}(BH₄)(µ-BH₄)]₄ (3-Y) ................................................................................S12
<table>
  <tbody>
    <tr>
      <td>2.8</td>
      <td>[Dy{N(Si<sup>i</sup>Pr<sub>3</sub>)<sub>2</sub>}(BH<sub>4</sub>)(μ-BH<sub>4</sub>)]<sub>4</sub> (3-Dy)</td>
      <td>S16</td>
    </tr>
    <tr>
      <td>2.9</td>
      <td>[Y{N(Si<sup>i</sup>Pr<sub>3</sub>)<sub>2</sub>}<sub>2</sub>(BH<sub>4</sub>)] (4-Y)</td>
      <td>S17</td>
    </tr>
    <tr>
      <td>2.10</td>
      <td>[Dy{N(Si<sup>i</sup>Pr<sub>3</sub>)<sub>2</sub>}<sub>2</sub>(BH<sub>4</sub>)] (4-Dy)</td>
      <td>S19</td>
    </tr>
    <tr>
      <td>2.11</td>
      <td>[Y{N(Si<sup>i</sup>Pr<sub>3</sub>)<sub>2</sub>}{N(Si<sup>i</sup>Pr<sub>3</sub>)[Si(<sup>i</sup>Pr)<sub>2</sub>{CH(Me)CH<sub>2</sub>]}-κ<sup>2</sup>-N,C}] (5-Y)/HN(Si<sup>i</sup>Pr<sub>3</sub>)<sub>2</sub></td>
      <td>S20</td>
    </tr>
    <tr>
      <td>3.</td>
      <td>IR spectra</td>
      <td>S21</td>
    </tr>
    <tr>
      <td>3.1</td>
      <td>[Ln{N(Si<sup>i</sup>Pr<sub>3</sub>)<sub>2</sub>}<sub>2</sub>][Al{OC(CF<sub>3</sub>)<sub>3</sub>}<sub>4</sub>] (1-Ln)</td>
      <td>S21</td>
    </tr>
    <tr>
      <td>3.2</td>
      <td>[Ln{N(Si<sup>i</sup>Pr<sub>3</sub>)<sub>2</sub>}(BH<sub>4</sub>)<sub>2</sub>(THF)] (2-Ln)</td>
      <td>S23</td>
    </tr>
    <tr>
      <td>3.3</td>
      <td>[Ln{N(Si<sup>i</sup>Pr<sub>3</sub>)<sub>2</sub>}(BH<sub>4</sub>)(μ-BH<sub>4</sub>)]<sub>4</sub> (3-Ln)</td>
      <td>S25</td>
    </tr>
    <tr>
      <td>3.4</td>
      <td>[Ln{N(Si<sup>i</sup>Pr<sub>3</sub>)<sub>2</sub>}<sub>2</sub>(BH<sub>4</sub>)] (4-Ln)</td>
      <td>S27</td>
    </tr>
    <tr>
      <td>4.</td>
      <td>DFT calculated IR spectra</td>
      <td>S29</td>
    </tr>
    <tr>
      <td>5.</td>
      <td>Single crystal X-ray diffraction</td>
      <td>S33</td>
    </tr>
    <tr>
      <td>6.</td>
      <td>Powder X-ray diffraction</td>
      <td>S47</td>
    </tr>
    <tr>
      <td>7.</td>
      <td>Magnetic measurements</td>
      <td>S49</td>
    </tr>
    <tr>
      <td>8.</td>
      <td>CASSCF-SO calculations</td>
      <td>S82</td>
    </tr>
    <tr>
      <td>9.</td>
      <td>References</td>
      <td>S85</td>
    </tr>
  </tbody>
</table>
# 1. Modified synthesis of [KN($Si^iPr_3$)$_2$]

**General considerations.** We have previously reported the synthesis of $HN(Si^iPr_3)_2$ and $[KN(Si^iPr_3)_2]$.¹ Here we describe a modified synthesis using $NaNH_2$ as a more operationally convenient starting material in place of condensed $NH_3$, with other synthetic optimizations. The previously reported NMR data are included for completeness. Under dinitrogen, solvents were either refluxed over molten potassium for 4 days (n-hexane), or passed over a column of activated alumina (pentanes, THF, toluene). All solvents were degassed, placed under an argon atmosphere, and stored over either a K mirror (n-hexane, pentanes, toluene) or over activated 3 Å molecular sieves (THF). All subsequent manipulations were performed under argon using standard Schlenk line techniques, with use of a glove box for storage of $NaNH_2$, KH and $[KN(Si^iPr_3)_2]$ under argon. nBuLi (2.5 M in hexanes) and $NaNH_2$ were purchased from Fisher Scientific and were used as received. KH was purchased from Merck as a dispersion in mineral oil, which was removed prior to use through sequential pentane washes. $Si^iPr_3Cl$ was purchased from Fluorochem, degassed, and stirred over Mg turnings prior to use. 3 Å molecular sieves were activated by heating at 310 °C *in vacuo* for > 6 hours.

$HN(Si^iPr_3)_2$. $Si^iPr_3Cl$ (42.1 mL, 200 mmol) was added cautiously to a stirring suspension of $NaNH_2$ (7.80 g, 200 mmol) in THF (200 mL) at ambient temperature, with appropriate external cooling with an ice bath when required to moderate any resulting exotherm. The reaction mixture was stirred at ambient temperature overnight, and the resultant suspension filtered to afford a solution of $H_2NSi^iPr_3$. nBuLi (2.5 M in hexane, 80 mL, 200 mmol) was added to this solution, and the reaction mixture warmed with stirring until butane gas evolution was observed (at ca. 50-60 °C). The reaction was held at this temperature until all gas evolution had subsided, typically 1-2 h, affording a solution of $LiHNSi^iPr_3$. $Si^iPr_3Cl$ (42.1 mL, 200 mmol) was added, and the reaction mixture was heated to 70 °C for 72 hours.
The volatiles were removed *in vacuo* and the residues extracted into pentane (ca. 50 mL) and filtered. Following removal of pentane in vacuo, HN(Si⁴Pr₃)₂ was obtained as a colorless oil by fractional distillation of the crude residues (10⁻² mbar through a Vigreux column, unreacted ⁴Pr₃SiCl removed at ca. 40 °C, HN(Si⁴Pr₃)₂ collected at ca. 100 °C, significant quantities of some non-volatile material remain). Yield: 21.60 g, 65.6 mmol, 33%, formed a white crystalline solid upon standing (melting point ca. 25 °C). ¹H NMR (500 MHz, C₆D₆): δ 1.02–0.87 (complex set of resonances, 42H, CH(CH₃)₂ & (CHCH₃)₂), –0.37 (s, 1H, NH). ²⁹Si{¹H} DEPT90 NMR (79.48 MHz, C₆D₆): δ 6.06.

[KN(Si⁴Pr₃)₂]. A solution of HN(Si⁴Pr₃)₂ (21.6 g, 65.6 mmol) in toluene (100 mL) was added to a stirring suspension of KH (2.62 g, 65.6 mmol) in toluene (100 mL). The reaction mixture was heated until hydrogen evolution was observed (ca. 120 °C). The reaction was held at this temperature until gas evolution had ceased (typically 3 h), allowed to cool, and filtered to remove any insoluble K salts. The solution was concentrated to the point of incipient crystallization and layered with excess hexane, which after slow diffusion afforded the title compound as large colorless crystalline blocks. Occasionally, a brown discoloration is observed when using HN(Si⁴Pr₃)₂ containing trace impurities. Two or three recrystallizations as outlined above are sufficient to afford a product with no detectable protic impurities. Yield: 17.90 g, 48.7 mmol, 74%, colorless crystalline solid. ¹H NMR (400.07 MHz, C₆D₆): δ 1.30 (d, ³JHH = 7.4 Hz, 36H, CHCH₃), 0.90 (sept, ³JHH = 7.5 Hz, 6H, CHCH₃). ²⁹Si{¹H} DEPT90 NMR (79.48 MHz, C₆D₆): δ 16.35.
## 2. NMR spectra

### 2.1 HN(Si$^iPr_3)_2

<figure><img src="image_15.png" /><figcaption>**Figure S1.** ¹H NMR spectrum (400.07 MHz, C₆D₆) of HN(Si⁴Pr₃)₂ at 298 K.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**Figure S2.** ²⁹Si { ¹H} DEPT90 NMR spectrum (79.48 MHz, C₆D₆) of HN(Si⁴Pr₃)₂ at 298 K.</figcaption></figure>

### 2.2 [KN(Si⁴Pr₃)₂]

<figure><img src="image_17.png" /><figcaption>**Figure S3.** ¹H NMR spectrum (400.07 MHz, C₆D₆) of [KN(Si⁴Pr₃)₂] at 298 K.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Figure S4.** $^{29}$Si{$^{1}$H} DEPT90 NMR spectrum (79.48 MHz, C$_{6}$D$_{6}$) of [KN(Si$^{i}$Pr$_{3}$)$_{2}$] at 298 K.</figcaption></figure>

2.3 [Y{N(SiPr$_{3}$)$_{2}$}$_{2}$][Al{OC(CF$_{3}$)$_{3}$}]$_{4}$ (1-Y)

<figure><img src="image_19.png" /><figcaption>**Figure S5.** $^{1}$H NMR spectrum (400.07 MHz, C$_{6}$H$_{5}$F) of 1-Y at 298 K.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Figure S6.** $^{13}$C{$^{1}$H} DEPTQ NMR spectrum (100.60 MHz, C$_{6}$H$_{5}$F) of 1-Y at 298 K.</figcaption></figure>
<figure><img src="image_21.png" /><figcaption>**Figure S7.** <sup>19</sup>F NMR spectrum (376.40 MHz, C<sub>6</sub>H<sub>5</sub>F) of **1-Y** at 298 K.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>**Figure S8.** <sup>29</sup>Si{{<sup>1</sup>H}} DEPT90 NMR spectrum (79.48 MHz, C<sub>6</sub>H<sub>5</sub>F) of **1-Y** at 298 K.</figcaption></figure>

## 2.4 [Dy{N(Si<sup>i</sup>Pr<sub>3</sub>)<sub>2</sub>}<sub>2</sub>][Al{OC(CF<sub>3</sub>)<sub>3</sub>}<sub>4</sub>] (1-Dy)

<figure><img src="image_23.png" /><figcaption>**Figure S9.** <sup>1</sup>H NMR spectrum (400.07 MHz, C<sub>6</sub>H<sub>5</sub>F) of **1-Dy** at 298 K containing an internal sealed capillary of 1 : 1 C<sub>6</sub>D<sub>6</sub> : C<sub>6</sub>H<sub>5</sub>F.</figcaption></figure>
<figure><img src="image_24.png" /></figure>

**Figure S10.** ¹³C{¹H} DEPTQ NMR spectrum (100.60 MHz, C₆H₅F) of 1-Dy at 298 K containing an internal sealed capillary of 1 : 1 C₆D₆ : C₆H₅F.

<figure><img src="image_25.png" /></figure>

**Figure S11.** ¹⁹F NMR spectrum (376.40 MHz, C₆H₅F) of 1-Dy at 298 K containing an internal sealed capillary of 1 : 1 C₆D₆ : C₆H₅F.

2.5 [Y{N(Si⁴Pr₃)₂}(BH₄)₂(THF)] (2-Y)

<figure><img src="image_26.png" /></figure>

**Figure S12.** ¹H NMR spectrum (400.07 MHz, C₆D₆) of 2-Y at 298 K.
<figure><img src="image_27.png" /><figcaption>**Figure S13.** ¹H>{¹¹B} NMR spectrum (400.07 MHz, C₆D₆) of **2-Y** at 298 K.</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>**Figure S14.** ¹¹B NMR spectrum (128 MHz, C₆D₆) of **2-Y** at 298 K.</figcaption></figure>

<figure><img src="image_29.png" /><figcaption>**Figure S15.** ¹¹B{¹H} NMR spectrum (128 MHz, C₆D₆) of **2-Y** at 298 K.</figcaption></figure>
<figure><img src="image_30.png" /><figcaption>**Figure S16.** <sup>13</sup>C-{<sup>1</sup>H} DEPTQ NMR spectrum (100.60 MHz, C<sub>6</sub>D<sub>6</sub>) of **2-Y** at 298 K.</figcaption></figure>

<figure><img src="image_31.png" /><figcaption>**Figure S17.** <sup>29</sup>Si-{<sup>1</sup>H} DEPT90 NMR spectrum (79.48 MHz, C<sub>6</sub>D<sub>6</sub>) of **2-Y** at 298 K.</figcaption></figure>

## 2.6 [Dy{N(Si<sup>i</sup>Pr<sub>3</sub>)<sub>2</sub>}(BH<sub>4</sub>)<sub>2</sub>(THF)] (2-Dy)

<figure><img src="image_32.png" /><figcaption>**Figure S18.** <sup>1</sup>H NMR spectrum (400.07 MHz, C<sub>6</sub>D<sub>6</sub>) of **2-Dy** at 298 K.</figcaption></figure>
<figure><img src="image_33.png" /><figcaption>**Figure S19.** ¹H{{¹¹B} NMR spectrum (400.07 MHz, C₆D₆) of **2-Dy** at 298 K.</figcaption></figure>

<figure><img src="image_34.png" /><figcaption>**Figure S20.** ¹¹B NMR spectrum (128 MHz, C₆D₆) of **2-Dy** at 298 K.</figcaption></figure>

<figure><img src="image_35.png" /><figcaption>**Figure S21.** ¹³C{¹H} DEPTQ NMR spectrum (100.60 MHz, C₆H₅F) of **2-Dy** at 298 K containing an internal sealed capillary of 1 : 1 C₆D₆ : C₆H₅F.</figcaption></figure>
2.7 $[Y\{N(Si^iPr_3)_2\}(BH_4)(\mu-BH_4)\}_4$ (3-Y)

<figure><img src="image_36.png" /><figcaption>Figure S22. $^1H$ NMR spectrum (400.07 MHz, C$_6$D$_6$) of 3-Y at 298 K.</figcaption></figure>

<figure><img src="image_37.png" /><figcaption>Figure S23. $^1H\{^{11}B\}$ NMR spectrum (400.07 MHz, C$_6$D$_6$) of 3-Y at 298 K.</figcaption></figure>

<figure><img src="image_38.png" /><figcaption>Figure S24. $^{11}$B NMR spectrum (128 MHz, C$_6$D$_6$) of 3-Y at 298 K.</figcaption></figure>
<figure><img src="image_39.png" /><figcaption>**Figure S25.** <sup>11</sup>B>{<sup>1</sup>H} NMR spectrum (128 MHz, C<sub>6</sub>D<sub>6</sub>) of 3-Y at 298 K.</figcaption></figure>

<figure><img src="image_40.png" /><figcaption>**Figure S26.** <sup>13</sup>C{<sup>1</sup>H} DEPTQ NMR spectrum (100.60 MHz, C<sub>6</sub>D<sub>6</sub>) of 3-Y at 298 K.</figcaption></figure>

<figure><img src="image_41.png" /><figcaption>**Figure S27.** <sup>29</sup>Si{<sup>1</sup>H} DEPT90 NMR spectrum (79.48 MHz, C<sub>6</sub>H<sub>4</sub>F<sub>2</sub>) of 3-Y at 298 K.</figcaption></figure>
<figure><img src="image_42.png" /><figcaption>**Figure S28.** ¹H NMR spectrum (400.07 MHz, C₆H₄F₂) of **3-Y** at 298 K.</figcaption></figure>

<figure><img src="image_43.png" /><figcaption>**Figure S29.** ¹H>{¹¹B} NMR spectrum (400.07 MHz, C₆H₄F₂) of **3-Y** at 298 K.</figcaption></figure>

<figure><img src="image_44.png" /><figcaption>**Figure S30.** ¹¹B NMR spectrum (128 MHz, C₆H₄F₂) of **3-Y** at 298 K. Inset: line fitting of the resonance as a broad pentet, using a generalized-Lorentzian form with no additional constraints, as implemented in MestReNova version 14.3.</figcaption></figure>
<figure><img src="image_45.png" /><figcaption>**Figure S31.** ¹¹B>{¹H} NMR spectrum (128 MHz, C₆H₄F₂) of **3-Y** at 298 K.</figcaption></figure>

<figure><img src="image_46.png" /><figcaption>**Figure S32.** ¹³C>{¹H} DEPTQ NMR spectrum (100.60 MHz, C₆H₄F₂) of **3-Y** at 298 K.</figcaption></figure>

<figure><img src="image_47.png" /><figcaption>**Figure S33.** ²⁹Si>{¹H} DEPT90 NMR spectrum (79.48 MHz, C₆H₄F₂) of **3-Y** at 298 K.</figcaption></figure>
2.8 $[D_y\{N(Si^{i}Pr_3)_2\}(BH_4)(\mu-BH_4)]_4$ (3-Dy)

<figure><img src="image_48.png" /><figcaption>Figure S34. $^{1}$H NMR spectrum (400.07 MHz, C$_{6}$D$_{6}$) of 3-Dy at 298 K.</figcaption></figure>

<figure><img src="image_49.png" /><figcaption>Figure S35. $^{11}$B NMR spectrum (128 MHz, C$_{6}$D$_{6}$) of 3-Dy at 298 K.</figcaption></figure>

<figure><img src="image_50.png" /><figcaption>Figure S36. $^{13}$C${}^{1}$H DEPTQ NMR spectrum (100.60 MHz, C$_{6}$D$_{6}$) of 3-Dy at 298 K.</figcaption></figure>
2.9 [Y{N(Si$^{i}$Pr$_{3}$)$_{2}$}$_{2}$(BH$_{4}$)] (4-Y)

<figure><img src="image_51.png" /><figcaption>Figure S37. $^{1}$H NMR spectrum (400.07 MHz, C$_{6}$D$_{6}$) of 4-Y at 298 K.</figcaption></figure>

<figure><img src="image_52.png" /><figcaption>Figure S38. $^{1}$H{{$^{11}$B}} NMR spectrum (400.07 MHz, C$_{6}$D$_{6}$) of 4-Y at 298 K.</figcaption></figure>

<figure><img src="image_53.png" /><figcaption>Figure S39. $^{11}$B NMR spectrum (128 MHz, C$_{6}$D$_{6}$) of 4-Y at 298 K.</figcaption></figure>
<figure><img src="image_54.png" /><figcaption>**Figure S40.** <sup>11</sup>B>{<sup>1</sup>H} NMR spectrum (128 MHz, C<sub>6</sub>D<sub>6</sub>) of **4-Y** at 298 K.</figcaption></figure>

<figure><img src="image_55.png" /><figcaption>**Figure S41.** <sup>13</sup>C{<sup>1</sup>H} DEPTQ NMR spectrum (100.60 MHz, C<sub>6</sub>D<sub>6</sub>) of **4-Y** at 298 K.</figcaption></figure>

<figure><img src="image_56.png" /><figcaption>**Figure S42.** <sup>29</sup>Si{<sup>1</sup>H} DEPT90 NMR spectrum (79.48 MHz, C<sub>6</sub>D<sub>6</sub>) of **4-Y** at 298 K.</figcaption></figure>
2.10 [Dy{N(Si$^{i}$Pr$_{3}$)$_{2}$}$_{2}$(BH$_{4}$)] (4-Dy)

<figure><img src="image_57.png" /><figcaption>Figure S43. $^{1}$H NMR spectrum (400.07 MHz, C$_{6}$D$_{6}$) of 4-Dy at 298 K.</figcaption></figure>

<figure><img src="image_58.png" /><figcaption>Figure S44. $^{11}$B NMR spectrum (128 MHz, C$_{6}$D$_{6}$) of 4-Dy at 298 K.</figcaption></figure>

<figure><img src="image_59.png" /><figcaption>Figure S45. $^{13}$C{$^{1}$H} DEPTQ NMR spectrum (100.60 MHz, C$_{6}$D$_{6}$) of 4-Dy at 298 K.</figcaption></figure>
2.11 [Y{N(Si$^i$Pr$_3$)$_2$}{N(Si$^i$Pr$_3$)[Si($^i$Pr)$_2${CH(Me)CH$_2$}]-κ$^2$-N,C}] (5-Y)/HN(Si$^i$Pr$_3$)$_2$

<figure><img src="image_60.png" /></figure>

**Figure S46.** $^1$H NMR spectrum (400.07 MHz, C$_6$D$_6$) of 5-Y + HN(Si$^i$Pr$_3$)$_2$ at 298 K, overlaid with a spectrum of isolated HN(Si$^i$Pr$_3$)$_2$ (purple) under the same conditions.

<figure><img src="image_61.png" /></figure>

**Figure S47.** $^{13}$C{$^1$H} DEPTQ NMR spectrum (100.60 MHz, C$_6$D$_6$) of 5-Y + HN(Si$^i$Pr$_3$)$_2$ at 298 K.

<figure><img src="image_62.png" /></figure>

**Figure S48.** $^{29}$Si{$^1$H} DEPT90 NMR spectrum (79.48 MHz, C$_6$D$_6$) of 5-Y + HN(Si$^i$Pr$_3$)$_2$ at 298 K.
### 3. IR spectra

#### 3.1 $[Ln\{N(Si^{i}Pr_{3})_{2}\}_{2}][Al\{OC(CF_{3})_{3}\}_{4}]$ (1-Ln)

<figure><img src="image_63.png" /><figcaption>**Figure S49.** FT-IR (ATR, microcrystalline solid) spectrum of 1-Y at ambient temperature.</figcaption></figure>
<figure><img src="image_64.png" /><figcaption>**Figure S50.** FT-IR (ATR, microcrystalline solid) spectrum of 1-Dy at ambient temperature.</figcaption></figure>
3.2 [Ln{N(Si$^{i}$Pr$_{3}$)$_{2}$}(BH$_{4}$)$_{2}$(THF)] (2-Ln)

<figure><img src="image_65.png" /><figcaption>**Figure S51.** FT-IR (ATR, microcrystalline solid) spectrum of 2-Y at ambient temperature.</figcaption></figure>
<figure><img src="image_66.png" /><figcaption>**Figure S52.** FT-IR (ATR, microcrystalline solid) spectrum of 2-Dy at ambient temperature.</figcaption></figure>
3.3 [Ln{N(Si<sup>i</sup>Pr<sub>3</sub>)<sub>2</sub>}(BH<sub>4</sub>)(μ-BH<sub>4</sub>)]<sub>4</sub> (3-Ln)

<figure><img src="image_67.png" /><figcaption>**Figure S53.** FT-IR (ATR, microcrystalline solid) spectrum of 3-Y at ambient temperature.</figcaption></figure>
<figure><img src="image_68.png" /><figcaption>**Figure S54.** FT-IR (ATR, microcrystalline solid) spectrum of **3-Dy** at ambient temperature.</figcaption></figure>
3.4 [Ln{N(Si<sup>i</sup>Pr<sub>3</sub>)<sub>2</sub>}<sub>2</sub>(BH<sub>4</sub>)] (4-Ln)

<figure><img src="image_69.png" /><figcaption>**Figure S55.** FT-IR (ATR, microcrystalline solid) spectrum of 4-Y at ambient temperature.</figcaption></figure>
<figure><img src="image_70.png" /><figcaption>**Figure S56.** FT-IR (ATR, microcrystalline solid) spectrum of 4-Dy at ambient temperature.</figcaption></figure>
4. DFT calculated IR spectra

<figure><img src="image_71.png" /></figure>

**Figure S57.** Comparison of the DFT-calculated IR spectrum of the cation of 1-Y (top) with the experimentally derived spectra of 1-Y at ambient temperature (bottom). A Lorentzian convolution (full width half maximum = 40 cm⁻¹) is applied to all calculated vibrational modes.
<figure><img src="image_72.png" /><figcaption>**Figure S58.** Comparison of the DFT-calculated IR spectrum of **2-Y** (top) with the experimentally derived spectra of **2-Y** at ambient temperature (bottom). A Lorentzian convolution (full width half maximum = 40 cm⁻¹) is applied to all calculated vibrational modes.</figcaption></figure>
<figure><img src="image_73.png" /><figcaption>**Figure S59.** Comparison of the DFT-calculated IR spectrum of a monomer of **3-Y** (top) with the experimentally derived spectra of **3-Y** at ambient temperature (bottom). A Lorentzian convolution (full width half maximum = 40 cm⁻¹) is applied to all calculated vibrational modes.</figcaption></figure>
<figure><img src="image_74.png" /><figcaption>**Figure S60.** Comparison of the DFT-calculated IR spectrum of 4-Y (top) with the experimentally derived spectra of 4-Y at ambient temperature (bottom). A Lorentzian convolution (full width half maximum = 40 cm⁻¹) is applied to all calculated vibrational modes.</figcaption></figure>
5. Single crystal X-ray diffraction

<table><caption>**Table S1.** Crystallographic data for 1-Ln and 2-Ln.</caption><thead><tr><th></th><th>1-Y</th><th>1-Dy</th><th>2-Y</th><th>2-Dy</th></tr></thead><tbody><tr><td>Formula</td><td>C<sub>52</sub>H<sub>84</sub>AlF<sub>36</sub>N<sub>2</sub>O<sub>4</sub>Si<sub>4</sub>Y</td><td>C<sub>52</sub>H<sub>84</sub>AlDyF<sub>36</sub>N<sub>2</sub>O<sub>4</sub>Si<sub>4</sub></td><td>C<sub>22</sub>H<sub>58</sub>B<sub>2</sub>NOSi<sub>2</sub>Y</td><td>C<sub>22</sub>H<sub>58</sub>B<sub>2</sub>DyNOSi<sub>2</sub></td></tr><tr><td>F<sub>w</sub></td><td>1713.46</td><td>1787.05</td><td>519.40</td><td>592.99</td></tr><tr><td>Crystal size, mm</td><td>0.344 × 0.25 × 0.157</td><td>0.141 × 0.093 × 0.009</td><td>0.37 × 0.079 × 0.03</td><td>0.647 × 0.208 × 0.169</td></tr><tr><td>Crystal system</td><td>orthorhombic</td><td>orthorhombic</td><td>monoclinic</td><td>orthorhombic</td></tr><tr><td>Space group</td><td>Pbca</td><td>Pbca</td><td>P2<sub>1</sub>/c</td><td>P2<sub>1</sub>2<sub>1</sub>2<sub>1</sub></td></tr><tr><td>Collection temperature, K</td><td>100(2)</td><td>100(2)</td><td>100(2)</td><td>100.00(10)</td></tr><tr><td>a, Å</td><td>19.4403(5)</td><td>19.4972(5)</td><td>8.8125(2)</td><td>13.0581(2)</td></tr><tr><td>b, Å</td><td>23.6130(9)</td><td>23.6772(8)</td><td>14.6779(3)</td><td>13.3893(2)</td></tr><tr><td>c, Å</td><td>31.6874(7)</td><td>31.7746(8)</td><td>23.0295(5)</td><td>16.8519(3)</td></tr><tr><td>α, °</td><td>90</td><td>90</td><td>90</td><td>90</td></tr><tr><td>β, °</td><td>90</td><td>90</td><td>92.139(2)</td><td>90</td></tr><tr><td>γ, °</td><td>90</td><td>90</td><td>90</td><td>90</td></tr><tr><td>V, Å<sup>3</sup></td><td>14545.9(8)</td><td>14668.4(7)</td><td>2976.77(11)</td><td>2946.37(8)</td></tr><tr><td>Z</td><td>8</td><td>8</td><td>4</td><td>4</td></tr><tr><td>ρ<sub>calcd</sub>, g cm<sup>-3</sup></td><td>1.565</td><td>1.618</td><td>1.159</td><td>1.337</td></tr><tr><td>μ, mm<sup>-1</sup></td><td>1.014</td><td>7.418</td><td>3.603</td><td>2.630</td></tr><tr><td>No. of reflections made</td><td>76726</td><td>51591</td><td>18752</td><td>23774</td></tr><tr><td>No. of unique reflns, R<sub>int</sub></td><td>17384, 0.0982</td><td>9214, 0.0965</td><td>5985, 0.0323</td><td>6986, 0.0303</td></tr><tr><td>No. of reflns with F<sup>2</sup> > 2σ(F<sup>2</sup>)</td><td>10292</td><td>7179</td><td>5517</td><td>6605</td></tr><tr><td>Transmn coeff range</td><td>0.08940-1.00000</td><td>0.462-1.000</td><td>0.737-1.000</td><td>0.648-1.000</td></tr><tr><td>R, R<sub>w</sub><sup>a</sup> (F<sup>2</sup> > 2σ(F<sup>2</sup>))</td><td>0.0579, 0.1020</td><td>0.0574, 0.1518</td><td>0.0339, 0.0990</td><td>0.0211, 0.0404</td></tr><tr><td>R, R<sub>w</sub><sup>a</sup> (all data)</td><td>0.1281, 0.1243</td><td>0.0743, 0.1647</td><td>0.0363, 0.1004</td><td>0.0239, 0.0417</td></tr><tr><td>S<sup>a</sup></td><td>1.012</td><td>0.985</td><td>1.116</td><td>1.047</td></tr><tr><td>Parameters, Restraints</td><td>1289, 5001</td><td>1043, 1624</td><td>310, 0</td><td>317, 49</td></tr><tr><td>Max., min. diff map, e Å<sup>-3</sup></td><td>0.762, -0.499</td><td>1.143, -1.806</td><td>0.550, -1.365</td><td>0.557, -0.431</td></tr></tbody></table>

<footnote><sup>a</sup> Conventional R = Σ||F<sub>o</sub>| - |F<sub>c</sub>||/Σ|F<sub>o</sub>|; R<sub>w</sub> = [Σw(F<sub>o</sub><sup>2</sup> - F<sub>c</sub><sup>2</sup>)<sup>2</sup>/Σw(F<sub>o</sub><sup>2</sup>)<sup>2</sup>]<sup>1/2</sup>; S = [Σw(F<sub>o</sub><sup>2</sup> - F<sub>c</sub><sup>2</sup>)<sup>2</sup>/no. data - no. params)]<sup>1/2</sup> for all data.</footnote>
<table><caption>**Table S2.** Crystallographic data for 3-Ln and 3-Ln·0.5KBH₄.</caption><thead><tr><th></th><th>3-Y</th><th>3-Dy</th><th>3-Y·0.5KBH₄·C₆H₆</th><th>3-Dy·0.5KBH₄·1,2-C₆H₄F₂</th></tr></thead><tbody><tr><td>Formula</td><td>C<sub>72</sub>H<sub>200</sub>B<sub>8</sub>N<sub>4</sub>Si<sub>8</sub>Y<sub>4</sub></td><td>C<sub>72</sub>H<sub>200</sub>B<sub>8</sub>Dy<sub>4</sub>N<sub>4</sub>Si<sub>8</sub></td><td>C<sub>39</sub>H<sub>107</sub>B<sub>5</sub>KN<sub>2</sub>Si<sub>4</sub>Y<sub>2</sub></td><td>C<sub>39</sub>H<sub>105</sub>B<sub>5</sub>Dy<sub>2</sub>FKN<sub>2</sub>Si<sub>4</sub></td></tr><tr><td>F<sub>w</sub></td><td>1789.19</td><td>2083.55</td><td>987.59</td><td>1151.75</td></tr><tr><td>Crystal size, mm</td><td>0.118 × 0.088 × 0.029</td><td>0.048 × 0.029 × 0.018</td><td>0.195 × 0.087 × 0.041</td><td>0.227 × 0.113 × 0.102</td></tr><tr><td>Crystal system</td><td>monoclinic</td><td>monoclinic</td><td>triclinic</td><td>Triclinic</td></tr><tr><td>Space group</td><td>P2<sub>1</sub>/c</td><td>P2<sub>1</sub>/c</td><td>P-1</td><td>P-1</td></tr><tr><td>Collection temperature, K</td><td>100(2)</td><td>100.01(15)</td><td>100(2)</td><td>100(2)</td></tr><tr><td>a, Å</td><td>18.0513(2)</td><td>17.9951(16)</td><td>8.56937(5)</td><td>8.5475(2)</td></tr><tr><td>b, Å</td><td>28.9661(3)</td><td>28.790(3)</td><td>18.02045(9)</td><td>18.0650(5)</td></tr><tr><td>c, Å</td><td>21.0674(2)</td><td>20.982(3)</td><td>18.50778(7)</td><td>18.4576(7)</td></tr><tr><td>α, °</td><td>90</td><td>90</td><td>89.5896(4)</td><td>91.009(3)</td></tr><tr><td>β, °</td><td>109.8967(13)</td><td>109.999(13)</td><td>82.7373(4)</td><td>98.027(3)</td></tr><tr><td>γ, °</td><td>90</td><td>90</td><td>86.5114(4)</td><td>93.085(2)</td></tr><tr><td>V, Å<sup>3</sup></td><td>10358.1(2)</td><td>10214(2)</td><td>2829.86(2)</td><td>2817.12(15)</td></tr><tr><td>Z</td><td>4</td><td>4</td><td>2</td><td>2</td></tr><tr><td>ρ<sub>calcd</sub>, g cm<sup>-3</sup></td><td>1.147</td><td>1.355</td><td>1.159</td><td>1.358</td></tr><tr><td>μ, mm<sup>-1</sup></td><td>4.039</td><td>16.533</td><td>4.383</td><td>2.820</td></tr><tr><td>No. of reflections made</td><td>136906</td><td>16460</td><td>46757</td><td>24819</td></tr><tr><td>No. of unique reflns, R<sub>int</sub></td><td>21445, 0.0558</td><td>8302, 0.0972</td><td>11540, 0.0251</td><td>12813, 0.0347</td></tr><tr><td>No. of reflns with F<sup>2</sup> > 2σ(F<sup>2</sup>)</td><td>18368</td><td>4715</td><td>10918</td><td>9853</td></tr><tr><td>Transmn coeff range</td><td>0.887-1.000</td><td>0.04783-1.00000</td><td>0.608-1.000</td><td>0.622-1.000</td></tr><tr><td>R, R<sub>w</sub><sup>a</sup> (F<sup>2</sup> > 2σ(F<sup>2</sup>))</td><td>0.0520, 0.1375</td><td>0.0738, 0.1793</td><td>0.0234, 0.0615</td><td>0.0338, 0.0603</td></tr><tr><td>R, R<sub>w</sub><sup>a</sup> (all data)</td><td>0.0590, 0.1419</td><td>0.1453, 0.2084</td><td>0.0248, 0.0622</td><td>0.0557, 0.0674</td></tr><tr><td>S<sup>a</sup></td><td>1.078</td><td>0.898</td><td>1.075</td><td>0.983</td></tr><tr><td>Parameters, Restraints</td><td>1119, 412</td><td>961, 1616</td><td>682, 363</td><td>699, 1049</td></tr><tr><td>Max., min. diff map, e Å<sup>-3</sup></td><td>0.935, -1.908</td><td>1.728, -0.722</td><td>0.403, -0.474</td><td>1.427, -0.954</td></tr></tbody></table>

<footnote><sup>a</sup> Conventional R = Σ||F<sub>o</sub>| - |F<sub>c</sub>||/Σ|F<sub>o</sub>|; R<sub>w</sub> = [Σw(F<sub>o</sub><sup>2</sup> - F<sub>c</sub><sup>2</sup>)<sup>2</sup>/Σw(F<sub>o</sub><sup>2</sup>)<sup>2</sup>]<sup>1/2</sup>; S = [Σw(F<sub>o</sub><sup>2</sup> - F<sub>c</sub><sup>2</sup>)<sup>2</sup>/no. data - no. params)]<sup>1/2</sup> for all data.</footnote>
<table><caption>**Table S3.** Crystallographic data for 4-Ln.</caption><thead><tr><th></th><th>4-Y<sup>b</sup></th><th>4-Y<sup>c</sup></th><th>4-Dy</th></tr></thead><tbody><tr><td>Formula</td><td>C<sub>36</sub>H<sub>88</sub>BN<sub>2</sub>Si<sub>4</sub>Y</td><td>C<sub>36</sub>H<sub>88</sub>BN<sub>2</sub>Si<sub>4</sub>Y</td><td>C<sub>36</sub>H<sub>88</sub>BDyN<sub>2</sub>Si<sub>4</sub></td></tr><tr><td>F<sub>w</sub></td><td>761.16</td><td>761.16</td><td>834.75</td></tr><tr><td>Crystal size, mm</td><td>0.205 × 0.184 × 0.103</td><td>0.086 × 0.071 × 0.022</td><td>0.171 × 0.127 × 0.054</td></tr><tr><td>Crystal system</td><td>monoclinic</td><td>orthorhombic</td><td>orthorhombic</td></tr><tr><td>Space group</td><td>P2<sub>1</sub>/c</td><td>Pbca</td><td>Pbca</td></tr><tr><td>Collection temperature, K</td><td>100(2)</td><td>100(2)</td><td>100(2)</td></tr><tr><td>a, Å</td><td>15.9332(13)</td><td>20.3776(3)</td><td>20.3179(5)</td></tr><tr><td>b, Å</td><td>13.1915(8)</td><td>20.0917(4)</td><td>19.9900(5)</td></tr><tr><td>c, Å</td><td>22.5401(14)</td><td>21.6614(4)</td><td>21.7278(4)</td></tr><tr><td>α, °</td><td>90</td><td>90</td><td>90</td></tr><tr><td>β, °</td><td>108.911(8)</td><td>90</td><td>90</td></tr><tr><td>γ, °</td><td>90</td><td>90</td><td>90</td></tr><tr><td>V, Å<sup>3</sup></td><td>4481.8(6)</td><td>8868.6(3)</td><td>8824.9(3)</td></tr><tr><td>Z</td><td>4</td><td>8</td><td>8</td></tr><tr><td>ρ<sub>calcd</sub>, g cm<sup>-3</sup></td><td>1.128</td><td>1.140</td><td>1.257</td></tr><tr><td>μ, mm<sup>-1</sup></td><td>1.433</td><td>3.055</td><td>10.268</td></tr><tr><td>No. of reflections made</td><td>22250</td><td>47249</td><td>51634</td></tr><tr><td>No. of unique reflns, R<sub>int</sub></td><td>9146, 0.0578</td><td>9116, 0.0566</td><td>7995, 0.0790</td></tr><tr><td>No. of reflns with F<sup>2</sup> > 2σ(F<sup>2</sup>)</td><td>6307</td><td>7675</td><td>6169</td></tr><tr><td>Transmn coeff range</td><td>0.719-1.000</td><td>0.912-1.000</td><td>0.69935-1.00000</td></tr><tr><td>R, R<sub>w</sub><sup>a</sup> (F<sup>2</sup> > 2σ(F<sup>2</sup>))</td><td>0.0496, 0.0845</td><td>0.0389, 0.0997</td><td>0.0474, 0.1084</td></tr><tr><td>R, R<sub>w</sub><sup>a</sup> (all data)</td><td>0.0928, 0.0974</td><td>0.0473, 0.1041</td><td>0.0677, 0.1169</td></tr><tr><td>S<sup>a</sup></td><td>1.004</td><td>0.999</td><td>1.031</td></tr><tr><td>Parameters, Restraints</td><td>473, 164</td><td>516, 1314</td><td>492, 329</td></tr><tr><td>Max., min. diff map, e Å<sup>-3</sup></td><td>0.442, -0.434</td><td>0.591, -1.147</td><td>2.149, -1.182</td></tr></tbody></table>

<footnote><sup>a</sup> Conventional R = Σ||F<sub>o</sub>|| - |F<sub>c</sub>||/Σ|F<sub>o</sub>|; R<sub>w</sub> = [Σw(F<sub>o</sub><sup>2</sup> - F<sub>c</sub><sup>2</sup>)<sup>2</sup>/Σw(F<sub>o</sub><sup>2</sup>)<sup>2</sup>]<sup>1/2</sup>; S = [Σw(F<sub>o</sub><sup>2</sup> - F<sub>c</sub><sup>2</sup>)<sup>2</sup>/no. data - no. params)]<sup>1/2</sup> for all data. <sup>b</sup> Polymorph in P2<sub>1</sub>/c. <sup>c</sup> Polymorph in Pbca.</footnote>
<figure><img src="image_75.png" /><figcaption>**Figure S61.** Solid-state crystal structure of the cation of 1-Y at 100(2) K. Displacement ellipsoids set at 50% probability level. Hydrogen atoms and [Al{OC(CF₃)₃}₄]⁻ counter-anion omitted for clarity. Selected bond distances (Å) and angles (°): Y(1)–N(1): 2.194(2); Y(1)–N(2): 2.182(3); Y(1)···C(1): 2.838(3); Y(1)···C(2): 2.962(3); Y(1)···C(10): 2.852(4); Y(1)···C(11): 3.010(4); Y(1)···C(19): 2.826(3); Y(1)···C(20): 2.872(3); Y(1)···Si(1): 3.2023(9); Y(1)···Si(2): 3.2108(11); Y(1)···Si(3): 3.1822(9); N(1)–Y(1)–N(2): 126.70(9).</figcaption></figure>
<figure><img src="image_76.png" /><figcaption>**Figure S62.** Solid-state crystal structure of [Dy{N(Si$^{i}$Pr$_{3}$)$_{2}$}(BH$_{4}$)$_{2}$(THF)] (2-Dy) at 100(2) K. Displacement ellipsoids set at 50% probability level. Non-borohydride hydrogen atoms omitted for clarity. Selected bond distances (Å) and angles (°): Dy(1)–N(1): 2.211(2); Dy(1)···B(1): 2.498(5); Dy(1)···B(2): 2.516(5); Dy(1)–O(1): 2.367(2); Dy(1)···C(1): 3.370(3); Dy(1)···C(10): 3.341(3); Dy(1)···Si(1): 3.3768(8); Dy(1)···Si(2): 3.3404(8); N(1)–Dy(1)···B(1): 112.00(16); N(1)–Dy(1)···B(2): 115.64(16); N(1)–Dy(1)–O(1): 127.22(8); B(1)···Dy(1)···B(2): 113.82(14); B(1)···Dy(1)–O(1): 93.68(15); B(2)···Dy(1)–O(1): 91.85(15).</figcaption></figure>
<figure><img src="image_77.png" /><figcaption>**Figure S63.** Solid-state crystal structure of [Y{N(Si$^{i}$Pr$_{3}$)$_{2}$}(BH$_{4}$)$_{2}$(THF)] (2-Y) at 100(2) K. Displacement ellipsoids set at 50% probability level. Non-borohydride hydrogen atoms and minor disordered THF component omitted for clarity. Selected bond distances (Å) and angles (°): Y(1)–N(1): 2.254(2); Y(1)···B(1): 2.484(3); Y(1)···B(2): 2.484(3); Y(1)–O(1): 2.3449(13); Y(1)···C(1): 3.6506(19); Y(1)···C(10): 3.1241(19); Y(1)···Si(1): 3.4356(5); Y(1)···Si(2): 3.2404(5); N(1)–Y(1)···B(1): 118.95(8); N(1)–Y(1)···B(2): 107.89(7); N(1)–Y(1)–O(1): 128.21(6); B(1)···Y(1)···B(2): 109.13(9); B(1)···Y(1)–O(1): 95.31(8); B(2)···Y(1)–O(1): 94.02(7).</figcaption></figure>
<figure><img src="image_78.png" /><figcaption>**Figure S64.** Solid-state crystal structure of [Dy{N(Si<sup>i</sup>Pr<sub>3</sub>)<sub>2</sub>}(BH<sub>4</sub>)<sub>4</sub>]<sub>4</sub> (**3-Dy**) at 100(2) K. Displacement ellipsoids set at 30% probability level. Non-borohydride hydrogen atoms and <sup>i</sup>Pr CH<sub>3</sub> carbon atoms omitted for clarity. Selected bond distances (Å) and angles (°): Dy(1)–N(1): 2.187(11); Dy(1)···B(1): 2.41(2); Dy(1)···B(2): 2.72(2); Dy(1)···B(8): 2.77(2); N(1)–Dy(1)···B(1): 116.6(6); N(1)–Dy(1)···B(2): 112.0(5); N(1)–Dy(1)···B(8): 126.0(5); B(1)···Dy(1)···B(2): 119.1(7); B(1)···Dy(1)···B(8): 99.1(8); B(2)···Dy(1)···B(8): 79.1(6).</figcaption></figure>
<figure><img src="image_79.png" /><figcaption>**Figure S65.** Solid-state crystal structure of [Y{N(Si<sup>i</sup>Pr<sub>3</sub>)<sub>2</sub>}(BH<sub>4</sub>)<sub>4</sub> (3-Y) at 100(2) K. Displacement ellipsoids set at 50% probability level. Non-borohydride hydrogen atoms and <sup>i</sup>Pr CH<sub>3</sub> carbon atoms omitted for clarity. Selected bond distances (Å) and angles (°): Y(1)–N(1): 2.183(3); Y(1)···B(1): 2.458(6); Y(1)···B(2): 2.785(5); Y(1)···B(8): 2.737(4); N(1)–Y(1)···B(1): 116.1(2); N(1)–Y(1)···B(2): 126.44(11); N(1)–Y(1)···B(8): 112.04(12); B(1)···Y(1)···B(2): 99.3(2); B(1)···Y(1)···B(8): 119.2(2); B(2)···Y(1)···B(8): 79.02(11).</figcaption></figure>
<figure><img src="image_80.png" /><figcaption>**Figure S66.** Solid-state crystal structure of [Dy{N(Si<sup>i</sup>Pr<sub>3</sub>)<sub>2</sub>}<sub>2</sub>(BH<sub>4</sub>)] (4-Dy) at 100(2) K. Displacement ellipsoids set at 50% probability level. Non-borohydride hydrogen atoms and minor <sup>i</sup>Pr disordered components omitted for clarity. Selected bond distances (Å) and angles (°): Dy(1)–N(1): 2.266(4); Dy(1)–N(2): 2.288(4); Dy(1)···B(1): 2.483(6); Dy(1)–C(1): 2.989(4); Dy(1)–C(1): 3.128(4); Dy(1)–Si(1): 3.3152(11); Dy(1)–Si(2): 3.4092(12); Dy(1)–Si(3): 3.4072(13); Dy(1)–Si(4): 3.5734(11); N(1)–Dy(1)–N(2): 130.41(13); N(1)–Dy(1)···B(1): 112.40(15); N(2)–Dy(1)···B(1): 113.93(15).</figcaption></figure>
<figure><img src="image_81.png" /><figcaption>**Figure S67.** Solid-state crystal structure of the P2₁/c polymorph of [Y{N(Si⁴Pr₃)₂}₂(BH₄)] (4-Y) at 100(2) K. Displacement ellipsoids set at 50% probability level. Non-borohydride hydrogen atoms and minor ⁴Pr disordered components omitted for clarity. Selected bond distances (Å) and angles (°): Y(1)–N(1): 2.251(2); Y(1)–N(2): 2.283(2); Y(1)···B(1): 2.483(5); Y(1)–C(1): 2.907(3); Y(1)–C(2): 3.078(3); Y(1)–Si(1): 3.2238(10); Y(1)–Si(2): 3.4025(9); Y(1)–Si(3): 3.4013(10); Y(1)–Si(4): 3.5618(9); N(1)–Y(1)–N(2): 127.36(8); N(1)–Y(1)···B(1): 110.02(11); N(2)–Y(1)···B(1): 116.58(11).</figcaption></figure>
<figure><img src="image_82.png" /><figcaption>**Figure S68.** Solid-state crystal structure of the *Pbca* polymorph of [Y{N(Si<sup>i</sup>Pr<sub>3</sub>)<sub>2</sub>}<sub>2</sub>(BH<sub>4</sub>)] (4-Y) at 100(2) K. Displacement ellipsoids set at 50% probability level. Non-borohydride hydrogen atoms and minor <sup>i</sup>Pr disordered components omitted for clarity. Selected bond distances (Å) and angles (°): Y(1)–N(1): 2.288(2); Y(1)–N(2): 2.268(2); Y(1)···B(1): 2.493(3); Y(1)–C(1): 2.968(2); Y(1)–C(2): 3.104(2); Y(1)–Si(1): 3.3109(7); Y(1)–Si(2): 3.5865(7); Y(1)–Si(3): 3.4046(7); Y(1)–Si(4): 3.4206(6); N(1)–Y(1)–N(2): 128.20(7); N(1)–Y(1)···B(1): 113.15(8); N(2)–Y(1)···B(1): 114.72(8).</figcaption></figure>
<figure><img src="image_83.png" /><figcaption>**Figure S69.** Solid-state crystal structure of a dimeric unit of polymeric [{Dy{N(Si$^{i}$Pr$_{3}$)}$_{2}$}(BH$_{4}$)(μ-BH$_{4}$)}$_{2}${K(μ-BH$_{4}$)}]$_{∞}$·1,2-C$_{6}$H$_{4}$F$_{2}$ (**3-Dy·0.5KBH$_{4}$·1,2-C$_{6}$H$_{4}$F$_{2}$**) at 100(2) K, viewed along the principal axis of the extended 1D coordination polymer. Displacement ellipsoids set at 50% probability level. All hydrogen atoms and co-crystallized 1,2-C$_{6}$H$_{4}$F$_{2}$ omitted for clarity. Selected bond distances (Å): Dy(1)–N(1): 2.185(3); Dy(2)–N(2): 2.185(3); Dy(1)···B(1): 2.656(5); Dy(1)···B(2): 2.739(5); Dy(1)···B(3): 2.516(5); Dy(2)···B(1): 2.842(5); Dy(2)···B(4): 2.509(5); Dy(2)···B(5): 2.558(5); K(1)···B(2): 3.252(5); K(1)···B(4): 3.576(5).</figcaption></figure>
<figure><img src="image_84.png" /><figcaption>**Figure S70.** Solid-state crystal structure of a dimeric unit of polymeric [{Y{N(Si⁴Pr₃)₂}(BH₄)(μ-BH₄)}₂{K(μ-BH₄)}]∞·C₆H₆ (**3-Y·0.5KBH₄·C₆H₆**) at 100(2) K, viewed along the principal axis of the extended 1D coordination polymer. Displacement ellipsoids set at 50% probability level. All hydrogen atoms and co-crystallized C₆H₆ omitted for clarity. Selected bond distances (Å): Y(1)–N(1): 2.1952(13); Y(2)–N(2): 2.2060(13); Y(1)···B(1): 2.650(2); Y(1)···B(2): 2.732(2); Y(1)···B(3): 2.506(2); Y(2)···B(1): 2.824(2); Y(2)···B(4): 2.550(2); Y(2)···B(5): 2.495(2); K(1)···B(2): 3.138(2); K(1)···B(2): 3.617(2).</figcaption></figure>
<figure><img src="image_85.png" /><figcaption>(b)</figcaption></figure>

<figure><img src="image_86.png" /></figure>

**Figure S71.** (a) Space-filling model of the cation of **1-Dy**. Color code: Dy (pink), silicon (gold), nitrogen (violet), carbon (grey) and hydrogen (white). (b) Using the *AtomAccess* program,² the accessibility of the Dy atom in the cation of **1-Dy** is determined by ray-tracing, and the unblocked rays are grouped into adjacent clusters (light blue, green, yellow, magenta). At the Dy atom, a total of 6.5% of the solid angle is exposed, with the largest cluster (light blue) comprising of 3.4% of the solid angle.
6. Powder X-ray diffraction

<figure><img src="image_87.png" /></figure>

**Figure S72.** (a) Le Bail refinement analysis of 1-Dy at 100 K. Experimental powder X-ray diffraction pattern (black), modelled data (red) and difference (blue). (b) Theoretical powder X-ray diffraction pattern simulated from single crystal X-ray diffraction at 100 K (red) compared to experimental pattern at 100 K (black).
<table><caption>**Table S4.** Unit cell values obtained from Le Bail refinement results for 1-Dy.</caption><thead><tr><th>Rwp</th><th>Rwp'</th><th>a</th><th>b</th><th>c</th><th>α</th><th>β</th><th>γ</th></tr></thead><tbody><tr><td>2.222</td><td>11.385</td><td>19.53(3)</td><td>23.74(4)</td><td>31.80(5)</td><td>90</td><td>90</td><td>90</td></tr></tbody></table>
7. Magnetic measurements

<figure><img src="image_88.png" /></figure>

**Figure S73.** Temperature dependence of the molar magnetic susceptibility product ($\chi T$) for 1-Dy suspended in eicosane (black circles) measured under a 0.1 T dc magnetic field and calculated CASSCF susceptibility (red line).

<figure><img src="image_89.png" /></figure>

**Figure S74.** Temperature dependence of the molar magnetic susceptibility product ($\chi T$) for frozen solution of 200 mM 1-Dy in fluorobenzene measured under a 0.1 T dc magnetic field.
<figure><img src="image_90.png" /></figure>

**Figure S75.** Temperature dependence of the molar magnetic susceptibility product ($\chi T$) for 1-Dy suspended in mineral oil in a polypropylene bag measured under a 0.1 T (red) or 1 T (black) applied dc magnetic field, on (a) linear or (b) semi-logarithmic scale.

<figure><img src="image_91.png" /></figure>

**Figure S76.** (a) Magnetic susceptibility ($\chi$) and (b) molar magnetic susceptibility product ($\chi T$) vs. temperature ($T$) for 1-Dy suspended in mineral oil in a polypropylene bag, under an applied dc field of 0.001 T, measured on warming after cooling in zero field (ZFC, black), on cooling in field (FC cool, red) and on warming in field (FC warm, blue).
<figure><img src="image_92.png" /></figure>

**Figure S77.** (a) Magnetic susceptibility ($\chi$) and (b) molar magnetic susceptibility product ($\chi T$) vs. temperature ($T$) for **1-Dy** suspended in mineral oil in a polypropylene bag, under an applied dc field of 0.005 T, measured on warming after cooling in zero field (ZFC, black), on cooling in field (FC cool, red) and on warming in field (FC warm, blue).

<figure><img src="image_93.png" /></figure>

**Figure S78.** Field ($H$) dependence of the magnetization ($M$) (0–7 T) of **1-Dy** suspended in eicosane at 2 K after cooling in zero field. Sweep rate is 22 Oe s$^{-1}$ (0.132 T min$^{-1}$).
<figure><img src="image_94.png" /></figure>

**Figure S79.** *M* vs. *H* hysteresis loops of **1-Dy** suspended in eicosane from 2 to 7 K in between -5 T to +5 T and from 8 to 10 K in between -3 T to +3 T. Sweep rate is 22 Oe s⁻¹ (0.132 T min⁻¹).

<figure><img src="image_95.png" /></figure>

**Figure S80.** *M* vs. *H* hysteresis loop of **1-Dy** suspended in eicosane at 2 K, zoomed in between -2 T and 2 T. Sweep rate is 22 Oe s⁻¹ (0.132 T min⁻¹).
<figure><img src="image_96.png" /></figure>

**Figure S81.** Field (*H*) dependence of the magnetization (*M*) (0–9 T) of **1-Dy** suspended in mineral oil in a polypropylene bag at 2–50 K after cooling in zero field. Sweep rate is 20 Oe s⁻¹ (0.12 T min⁻¹).

<figure><img src="image_97.png" /></figure>

**Figure S82.** *M* vs. *H* hysteresis loops of **1-Dy** suspended in mineral oil in a polypropylene bag from 2 to 50 K in between –9 T to +9 T. Inset shows 2 K hysteresis closing at zero field. Sweep rate is 20 Oe s⁻¹ (0.12 T min⁻¹).
<figure><img src="image_98.png" /></figure>

**Figure S83.** *M* vs. *H* hysteresis loops of **1-Dy** suspended in mineral oil in a polypropylene bag from 2 to 50 K, zoomed in to -0.8 T to +0.8 T. Sweep rate is 20 Oe s⁻¹ (0.12 T min⁻¹).

<figure><img src="image_99.png" /></figure>

**Figure S84.** *M* vs. *H* hysteresis loops of **1-Dy** suspended in mineral oil in a polypropylene bag at 2 K, zoomed in to -2 T to +2 T. Sweep rate is 20 Oe s⁻¹ (0.12 T min⁻¹).
<figure><img src="image_100.png" /></figure>

**Figure S85.** Field (*H*) dependence of the magnetization (0–7 T) of a 200 mM frozen solution of **1-Dy** in fluorobenzene at 2 K after cooling in zero field. Sweep rate is 22 Oe s⁻¹ (0.132 T min⁻¹).

<figure><img src="image_101.png" /></figure>

**Figure S86.** *M* vs. *H* hysteresis loops of a 200 mM frozen solution of **1-Dy** in fluorobenzene from 2 to 7 K in between –5 T to +5 T and from 8 to 12 K in between –3 T to +3 T. Inset shows 2 K hysteresis at low field. Sweep rate is 22 Oe s⁻¹ (0.132 T min⁻¹).
<figure><img src="image_102.png" /></figure>

**Figure S87.** *M* vs. *H* hysteresis loops of a 200 mM frozen solution of **1-Dy** in fluorobenzene from 2–12 K, zoomed in to –1 T to +1 T. Sweep rate is 22 Oe s⁻¹ (0.132 T min⁻¹).

<figure><img src="image_103.png" /></figure>

**Figure S88.** *M* vs. *H* hysteresis loop of a 200 mM frozen solution of **1-Dy** in fluorobenzene at 2 K, zoomed in between –2 and +2 T. Sweep rate is 22 Oe s⁻¹ (0.132 T min⁻¹).
<figure><img src="image_104.png" /><figcaption>**Figure S89.** Fitting of the ac frequency dependence of the in-phase component of the ac susceptibility ($\chi'$) for 1-Dy suspended in mineral oil in a polypropylene bag in zero dc field to the generalized Debye model; (a) all data, (b) zoomed in to the high temperature region.</figcaption></figure>
<figure><img src="image_105.png" /><figcaption>**Figure S90.** Fitting of the ac frequency dependence of the out-of-phase component of the ac susceptibility ($\chi''$) for 1-Dy suspended in mineral oil in a polypropylene bag in zero dc field to the generalized Debye model; (a) all data, (b) zoomed in to the high temperature region.</figcaption></figure>
<figure><img src="image_106.png" /><figcaption>**Figure S91.** Cole-Cole plot showing fitting of ac data for 1-Dy suspended in mineral oil in a polypropylene bag in zero dc field to the generalized Debye model; (a) all data, (b) zoomed-in to the high temperature region.</figcaption></figure>
<figure><img src="image_107.png" /><figcaption>**Figure S92.** Fitting of the ac frequency dependence of the in-phase component of the ac susceptibility ($\chi'$) for 1-Dy suspended in mineral oil in a polypropylene bag in a 0.08 T dc field to the generalized Debye model; (a) all data, (b) zoomed in to the high temperature region.</figcaption></figure>
<figure><img src="image_108.png" /><figcaption>**Figure S93.** Fitting of the ac frequency dependence of the out-of-phase component of the ac susceptibility ($\chi''$) for 1-Dy suspended in mineral oil in a polypropylene bag in a 0.08 T dc field to the generalized Debye model; (a) all data, (b) zoomed in to the high temperature region.</figcaption></figure>
<figure><img src="image_109.png" /><figcaption>**Figure S94.** Cole-Cole plot showing fitting of ac data for 1-Dy suspended in mineral oil in a polypropylene bag in a 0.08 T dc field to the generalized Debye model; (a) all data, (b) zoomed in to the high temperature region.</figcaption></figure>
<table><caption>**Table S5.** Best fit parameters to the generalized Debye model for 1-Dy suspended in mineral oil in a polypropylene bag in zero dc field. Note that the α parameter has been fixed at 0.014 for T ≥ 80 K according to its evolution observed at lower temperature.</caption><thead><tr><th>T (K)</th><th>τ (s)</th><th>χ<sub>S</sub> (cm<sup>3</sup> mol<sup>-1</sup>)</th><th>χ<sub>T</sub> (cm<sup>3</sup> mol<sup>-1</sup>)</th><th>α</th></tr></thead><tbody><tr><td>2</td><td>1.47251E-01</td><td>0.9100</td><td>5.9600</td><td>0.2717</td></tr><tr><td>3</td><td>1.43259E-01</td><td>0.7000</td><td>4.0800</td><td>0.2654</td></tr><tr><td>4</td><td>1.37433E-01</td><td>0.5440</td><td>3.1368</td><td>0.2772</td></tr><tr><td>5</td><td>1.35415E-01</td><td>0.4605</td><td>2.5618</td><td>0.2808</td></tr><tr><td>6</td><td>1.34738E-01</td><td>0.4168</td><td>2.1666</td><td>0.2633</td></tr><tr><td>7</td><td>1.30086E-01</td><td>0.3891</td><td>1.8696</td><td>0.2426</td></tr><tr><td>8</td><td>1.22685E-01</td><td>0.3601</td><td>1.6428</td><td>0.2204</td></tr><tr><td>9</td><td>1.13390E-01</td><td>0.3354</td><td>1.4570</td><td>0.1929</td></tr><tr><td>10</td><td>1.04292E-01</td><td>0.3118</td><td>1.3098</td><td>0.1673</td></tr><tr><td>12</td><td>8.55904E-02</td><td>0.2744</td><td>1.0885</td><td>0.1294</td></tr><tr><td>14</td><td>6.83684E-02</td><td>0.2397</td><td>0.9324</td><td>0.1060</td></tr><tr><td>16</td><td>5.43279E-02</td><td>0.2103</td><td>0.8194</td><td>0.1001</td></tr><tr><td>18</td><td>4.37083E-02</td><td>0.1864</td><td>0.7288</td><td>0.0861</td></tr><tr><td>20</td><td>3.53695E-02</td><td>0.1692</td><td>0.6561</td><td>0.0739</td></tr><tr><td>22</td><td>2.87692E-02</td><td>0.1541</td><td>0.5969</td><td>0.0672</td></tr><tr><td>24</td><td>2.34606E-02</td><td>0.1419</td><td>0.5467</td><td>0.0598</td></tr><tr><td>26</td><td>1.93606E-02</td><td>0.1234</td><td>0.5042</td><td>0.0617</td></tr><tr><td>28</td><td>1.60179E-02</td><td>0.1158</td><td>0.4668</td><td>0.0546</td></tr><tr><td>30</td><td>1.33408E-02</td><td>0.1089</td><td>0.4362</td><td>0.0514</td></tr><tr><td>32</td><td>1.10888E-02</td><td>0.1025</td><td>0.4094</td><td>0.0511</td></tr><tr><td>34</td><td>9.38239E-03</td><td>0.0969</td><td>0.3871</td><td>0.0523</td></tr><tr><td>36</td><td>7.88232E-03</td><td>0.0924</td><td>0.3653</td><td>0.0459</td></tr><tr><td>38</td><td>6.73419E-03</td><td>0.0889</td><td>0.3469</td><td>0.0443</td></tr><tr><td>40</td><td>5.75149E-03</td><td>0.0865</td><td>0.3295</td><td>0.0388</td></tr><tr><td>42</td><td>4.91046E-03</td><td>0.0835</td><td>0.3141</td><td>0.0349</td></tr><tr><td>44</td><td>4.21559E-03</td><td>0.0795</td><td>0.3000</td><td>0.0305</td></tr><tr><td>46</td><td>3.55806E-03</td><td>0.0775</td><td>0.2877</td><td>0.0348</td></tr><tr><td>48</td><td>3.04710E-03</td><td>0.0738</td><td>0.2751</td><td>0.0302</td></tr><tr><td>50</td><td>2.56982E-03</td><td>0.0711</td><td>0.2645</td><td>0.0310</td></tr><tr><td>52</td><td>2.18683E-03</td><td>0.0698</td><td>0.2554</td><td>0.0308</td></tr><tr><td>54</td><td>1.84390E-03</td><td>0.0683</td><td>0.2456</td><td>0.0220</td></tr><tr><td>56</td><td>1.54242E-03</td><td>0.0654</td><td>0.2376</td><td>0.0254</td></tr><tr><td>58</td><td>1.30371E-03</td><td>0.0645</td><td>0.2300</td><td>0.0244</td></tr><tr><td>60</td><td>1.08168E-03</td><td>0.0520</td><td>0.2187</td><td>0.0245</td></tr><tr><td>62</td><td>9.04788E-04</td><td>0.0520</td><td>0.2123</td><td>0.0192</td></tr></tbody></table>
<table><tr><td>64</td><td>7.52181E-04</td><td>0.0510</td><td>0.2062</td><td>0.0206</td></tr><tr><td>66</td><td>6.23123E-04</td><td>0.0490</td><td>0.1994</td><td>0.0197</td></tr><tr><td>68</td><td>5.17515E-04</td><td>0.0480</td><td>0.1939</td><td>0.0163</td></tr><tr><td>70</td><td>4.34010E-04</td><td>0.0465</td><td>0.1885</td><td>0.0139</td></tr><tr><td>72</td><td>3.57971E-04</td><td>0.0455</td><td>0.1824</td><td>0.0134</td></tr><tr><td>74</td><td>2.99011E-04</td><td>0.0448</td><td>0.1780</td><td>0.0134</td></tr><tr><td>76</td><td>2.55042E-04</td><td>0.0450</td><td>0.1730</td><td>0.0146</td></tr><tr><td>78</td><td>2.12582E-04</td><td>0.0440</td><td>0.1690</td><td>0.0145</td></tr><tr><td>80</td><td>1.78283E-04</td><td>0.0430</td><td>0.1652</td><td>0.0140</td></tr><tr><td>82</td><td>1.50813E-04</td><td>0.0420</td><td>0.1616</td><td>0.0140</td></tr><tr><td>84</td><td>1.27502E-04</td><td>0.0410</td><td>0.1586</td><td>0.0140</td></tr><tr><td>86</td><td>1.08386E-04</td><td>0.0410</td><td>0.1555</td><td>0.0140</td></tr><tr><td>88</td><td>9.07831E-05</td><td>0.0400</td><td>0.1510</td><td>0.0140</td></tr><tr><td>90</td><td>7.72304E-05</td><td>0.0390</td><td>0.1480</td><td>0.0140</td></tr><tr><td>92</td><td>6.55410E-05</td><td>0.0390</td><td>0.1453</td><td>0.0140</td></tr><tr><td>94</td><td>5.53469E-05</td><td>0.0380</td><td>0.1420</td><td>0.0140</td></tr><tr><td>96</td><td>4.62624E-05</td><td>0.0380</td><td>0.1393</td><td>0.0140</td></tr><tr><td>98</td><td>3.94997E-05</td><td>0.0380</td><td>0.1364</td><td>0.0140</td></tr><tr><td>100</td><td>3.31994E-05</td><td>0.0370</td><td>0.1335</td><td>0.0140</td></tr><tr><td>102</td><td>2.79481E-05</td><td>0.0370</td><td>0.1315</td><td>0.0140</td></tr><tr><td>104</td><td>2.39388E-05</td><td>0.0370</td><td>0.1295</td><td>0.0140</td></tr><tr><td>106</td><td>2.01048E-05</td><td>0.0370</td><td>0.1269</td><td>0.0140</td></tr><tr><td>108</td><td>1.68074E-05</td><td>0.0360</td><td>0.1251</td><td>0.0140</td></tr><tr><td>110</td><td>1.45339E-05</td><td>0.0360</td><td>0.1222</td><td>0.0140</td></tr><tr><td>112</td><td>1.19157E-05</td><td>0.0360</td><td>0.1210</td><td>0.0140</td></tr><tr><td>114</td><td>9.84826E-06</td><td>0.0350</td><td>0.1190</td><td>0.0140</td></tr><tr><td>116</td><td>8.34653E-06</td><td>0.0350</td><td>0.1170</td><td>0.0140</td></tr><tr><td>118</td><td>7.12598E-06</td><td>0.0350</td><td>0.1150</td><td>0.0140</td></tr><tr><td>120</td><td>5.81534E-06</td><td>0.0350</td><td>0.1130</td><td>0.0140</td></tr></table>
<table><caption>**Table S6.** Best fit parameters to the generalized Debye model for 1-Dy suspended in mineral oil in a polypropylene bag in a 0.08 T dc field. Note that the α parameter has been fixed at 0.025 for T ≥ 50 K according to its evolution observed at lower temperature.</caption><thead><tr><th>T (K)</th><th>τ (s)</th><th>χ<sub>S</sub> (cm<sup>3</sup> mol<sup>-1</sup>)</th><th>χ<sub>T</sub> (cm<sup>3</sup> mol<sup>-1</sup>)</th><th>α</th></tr></thead><tbody><tr><td>4</td><td>1.45957E+02</td><td>1.0700</td><td>3.7200</td><td>0.1000</td></tr><tr><td>5</td><td>4.04141E+01</td><td>0.8300</td><td>2.9144</td><td>0.0854</td></tr><tr><td>6</td><td>1.62528E+01</td><td>0.6800</td><td>2.4200</td><td>0.0780</td></tr><tr><td>7</td><td>7.96232E+00</td><td>0.5500</td><td>2.0469</td><td>0.0722</td></tr><tr><td>8</td><td>4.19433E+00</td><td>0.4700</td><td>1.7300</td><td>0.0600</td></tr><tr><td>9</td><td>2.49586E+00</td><td>0.4032</td><td>1.5032</td><td>0.0451</td></tr><tr><td>10</td><td>1.64717E+00</td><td>0.3500</td><td>1.3300</td><td>0.0390</td></tr><tr><td>12</td><td>7.51276E-01</td><td>0.2639</td><td>1.0801</td><td>0.0287</td></tr><tr><td>14</td><td>4.06563E-01</td><td>0.2307</td><td>0.9253</td><td>0.0215</td></tr><tr><td>16</td><td>2.42777E-01</td><td>0.2003</td><td>0.8119</td><td>0.0234</td></tr><tr><td>18</td><td>1.56648E-01</td><td>0.1785</td><td>0.7276</td><td>0.0291</td></tr><tr><td>20</td><td>1.05718E-01</td><td>0.1619</td><td>0.6558</td><td>0.0284</td></tr><tr><td>22</td><td>7.48106E-02</td><td>0.1485</td><td>0.5978</td><td>0.0267</td></tr><tr><td>24</td><td>5.45765E-02</td><td>0.1361</td><td>0.5486</td><td>0.0296</td></tr><tr><td>26</td><td>4.08545E-02</td><td>0.1262</td><td>0.5072</td><td>0.0297</td></tr><tr><td>28</td><td>3.12743E-02</td><td>0.1181</td><td>0.4715</td><td>0.0279</td></tr><tr><td>30</td><td>2.42430E-02</td><td>0.1112</td><td>0.4402</td><td>0.0252</td></tr><tr><td>32</td><td>1.92033E-02</td><td>0.1057</td><td>0.4136</td><td>0.0247</td></tr><tr><td>34</td><td>1.53055E-02</td><td>0.0998</td><td>0.3893</td><td>0.0257</td></tr><tr><td>36</td><td>1.23688E-02</td><td>0.0942</td><td>0.3677</td><td>0.0280</td></tr><tr><td>38</td><td>1.01519E-02</td><td>0.0915</td><td>0.3492</td><td>0.0255</td></tr><tr><td>40</td><td>8.29934E-03</td><td>0.0864</td><td>0.3315</td><td>0.0273</td></tr><tr><td>42</td><td>6.85982E-03</td><td>0.0838</td><td>0.3175</td><td>0.0275</td></tr><tr><td>44</td><td>5.64387E-03</td><td>0.0797</td><td>0.3022</td><td>0.0277</td></tr><tr><td>46</td><td>4.66941E-03</td><td>0.0764</td><td>0.2896</td><td>0.0271</td></tr><tr><td>48</td><td>3.83669E-03</td><td>0.0734</td><td>0.2771</td><td>0.0246</td></tr><tr><td>50</td><td>3.17905E-03</td><td>0.0660</td><td>0.2690</td><td>0.0250</td></tr><tr><td>52</td><td>2.59928E-03</td><td>0.0640</td><td>0.2620</td><td>0.0250</td></tr><tr><td>54</td><td>2.13226E-03</td><td>0.0610</td><td>0.2510</td><td>0.0250</td></tr><tr><td>56</td><td>1.76461E-03</td><td>0.0590</td><td>0.2440</td><td>0.0250</td></tr><tr><td>58</td><td>1.43620E-03</td><td>0.0570</td><td>0.2370</td><td>0.0250</td></tr><tr><td>60</td><td>1.20377E-03</td><td>0.0530</td><td>0.2272</td><td>0.0250</td></tr><tr><td>62</td><td>9.73515E-04</td><td>0.0520</td><td>0.2197</td><td>0.0250</td></tr><tr><td>64</td><td>8.01638E-04</td><td>0.0510</td><td>0.2132</td><td>0.0250</td></tr><tr><td>66</td><td>6.55860E-04</td><td>0.0480</td><td>0.2058</td><td>0.0250</td></tr></tbody></table>
<table><tr><td>68</td><td>5.43950E-04</td><td>0.0480</td><td>0.2017</td><td>0.0250</td></tr><tr><td>70</td><td>4.48051E-04</td><td>0.0460</td><td>0.1953</td><td>0.0250</td></tr><tr><td>72</td><td>3.69712E-04</td><td>0.0455</td><td>0.1901</td><td>0.0250</td></tr><tr><td>74</td><td>3.08685E-04</td><td>0.0455</td><td>0.1855</td><td>0.0250</td></tr><tr><td>76</td><td>2.56518E-04</td><td>0.0450</td><td>0.1810</td><td>0.0250</td></tr><tr><td>78</td><td>2.13719E-04</td><td>0.0430</td><td>0.1762</td><td>0.0250</td></tr><tr><td>80</td><td>1.78518E-04</td><td>0.0420</td><td>0.1710</td><td>0.0250</td></tr><tr><td>82</td><td>1.50733E-04</td><td>0.0420</td><td>0.1680</td><td>0.0250</td></tr><tr><td>84</td><td>1.26104E-04</td><td>0.0410</td><td>0.1640</td><td>0.0250</td></tr><tr><td>86</td><td>1.06245E-04</td><td>0.0400</td><td>0.1600</td><td>0.0250</td></tr><tr><td>88</td><td>8.89631E-05</td><td>0.0400</td><td>0.1570</td><td>0.0250</td></tr><tr><td>90</td><td>7.69043E-05</td><td>0.0390</td><td>0.1530</td><td>0.0250</td></tr><tr><td>92</td><td>6.48354E-05</td><td>0.0380</td><td>0.1500</td><td>0.0250</td></tr><tr><td>94</td><td>5.48439E-05</td><td>0.0380</td><td>0.1470</td><td>0.0250</td></tr><tr><td>96</td><td>4.64501E-05</td><td>0.0380</td><td>0.1440</td><td>0.0250</td></tr><tr><td>98</td><td>3.90646E-05</td><td>0.0370</td><td>0.1420</td><td>0.0250</td></tr><tr><td>100</td><td>3.29244E-05</td><td>0.0370</td><td>0.1392</td><td>0.0250</td></tr><tr><td>102</td><td>2.71707E-05</td><td>0.0360</td><td>0.1365</td><td>0.0250</td></tr><tr><td>104</td><td>2.33151E-05</td><td>0.0360</td><td>0.1350</td><td>0.0250</td></tr><tr><td>106</td><td>1.93660E-05</td><td>0.0355</td><td>0.1320</td><td>0.0250</td></tr><tr><td>108</td><td>1.62626E-05</td><td>0.0345</td><td>0.1290</td><td>0.0250</td></tr><tr><td>110</td><td>1.36940E-05</td><td>0.0343</td><td>0.1274</td><td>0.0250</td></tr><tr><td>112</td><td>1.14634E-05</td><td>0.0342</td><td>0.1248</td><td>0.0250</td></tr><tr><td>114</td><td>9.57551E-06</td><td>0.0343</td><td>0.1223</td><td>0.0250</td></tr><tr><td>116</td><td>8.05873E-06</td><td>0.0343</td><td>0.1205</td><td>0.0250</td></tr><tr><td>118</td><td>6.90180E-06</td><td>0.0343</td><td>0.1185</td><td>0.0250</td></tr><tr><td>120</td><td>5.62728E-06</td><td>0.0343</td><td>0.1167</td><td>0.0250</td></tr></table>
<figure><img src="image_110.png" /><figcaption>**Figure S95.** Fitting the ac frequency dependence of the (a) in-phase ($\chi'$) and (b) out-of-phase ($\chi''$) components of the ac susceptibility for 1-Dy suspended in mineral oil in a polypropylene bag at 12 K and variable dc field to the generalized Debye model.</figcaption></figure>
<figure><img src="image_111.png" /><figcaption>**Figure S96.** Cole-Cole plot showing fitting of ac data for 1-Dy suspended in mineral oil in a polypropylene bag at 12 K and variable dc field to the generalized Debye model.</figcaption></figure>
<figure><img src="image_112.png" /></figure>

<figure><img src="image_113.png" /></figure>

**Figure S97.** Fitting the ac frequency dependence of the (a) in-phase ($\chi'$) and (b) out-of-phase ($\chi''$) components of the ac susceptibility for 1-Dy suspended in mineral oil in a polypropylene bag at 40 K and variable dc field to the generalized Debye model.
<figure><img src="image_114.png" /><figcaption>**Figure S98.** Cole-Cole plot showing fitting of ac data for 1-Dy suspended in mineral oil in a polypropylene bag at 40 K and variable dc field to the generalized Debye model.</figcaption></figure>
<table><caption>**Table S7.** Best fit parameters to the generalized Debye model for 1-Dy suspended in mineral oil in a polypropylene bag in at 12 K and variable dc field.</caption><thead><tr><th>H (Oe)</th><th>τ (s)</th><th>χ<sub>S</sub> (cm<sup>3</sup> mol<sup>-1</sup>)</th><th>χ<sub>T</sub> (cm<sup>3</sup> mol<sup>-1</sup>)</th><th>α</th></tr></thead><tbody><tr><td>0</td><td>8.76416E-02</td><td>0.24000</td><td>1.14100</td><td>0.19054</td></tr><tr><td>50</td><td>8.95203E-02</td><td>0.22571</td><td>1.12571</td><td>0.22815</td></tr><tr><td>100</td><td>1.20253E-01</td><td>0.25000</td><td>1.10218</td><td>0.25000</td></tr><tr><td>200</td><td>3.99786E-01</td><td>0.29856</td><td>1.19057</td><td>0.26000</td></tr><tr><td>300</td><td>6.09480E-01</td><td>0.25899</td><td>1.17527</td><td>0.19746</td></tr><tr><td>400</td><td>7.01920E-01</td><td>0.24639</td><td>1.15543</td><td>0.15000</td></tr><tr><td>500</td><td>7.42237E-01</td><td>0.24205</td><td>1.14030</td><td>0.12577</td></tr><tr><td>600</td><td>7.72583E-01</td><td>0.23816</td><td>1.13025</td><td>0.10270</td></tr><tr><td>700</td><td>7.90682E-01</td><td>0.23855</td><td>1.13002</td><td>0.09000</td></tr><tr><td>800</td><td>7.95703E-01</td><td>0.23602</td><td>1.11806</td><td>0.08159</td></tr><tr><td>900</td><td>7.87238E-01</td><td>0.23509</td><td>1.12188</td><td>0.07900</td></tr><tr><td>1500</td><td>7.81688E-01</td><td>0.23127</td><td>1.10906</td><td>0.07506</td></tr><tr><td>2000</td><td>7.91849E-01</td><td>0.22994</td><td>1.11207</td><td>0.07373</td></tr><tr><td>3000</td><td>7.52655E-01</td><td>0.22690</td><td>1.10312</td><td>0.07378</td></tr><tr><td>4000</td><td>7.01277E-01</td><td>0.22324</td><td>1.07953</td><td>0.06670</td></tr><tr><td>5000</td><td>6.23681E-01</td><td>0.21885</td><td>1.06997</td><td>0.07496</td></tr><tr><td>6000</td><td>5.15704E-01</td><td>0.21561</td><td>1.02939</td><td>0.06724</td></tr><tr><td>7000</td><td>4.21697E-01</td><td>0.20850</td><td>1.00678</td><td>0.08017</td></tr><tr><td>8000</td><td>3.20551E-01</td><td>0.20185</td><td>0.97986</td><td>0.09527</td></tr><tr><td>10000</td><td>1.75568E-01</td><td>0.18550</td><td>0.93379</td><td>0.14775</td></tr></tbody></table>
<table><caption>**Table S8.** Best fit parameters to the generalized Debye model for 1-Dy suspended in mineral oil in a polypropylene bag in at 40 K and variable dc field. Note that the α parameter has been fixed at 0.05, χs has been fixed at 0.072 and for non-zero fields χT has been fixed at the value indicated.</caption><thead><tr><td>H (Oe)</td><td>τ (s)</td><td>χs (cm³ mol⁻¹)</td><td>χT (cm³ mol⁻¹)</td><td>α</td></tr></thead><tbody><tr><td>0</td><td>5.78755E-03</td><td>7.2E-02</td><td>3.2264E-01</td><td>0.05</td></tr><tr><td>200</td><td>6.70644E-03</td><td>7.2E-02</td><td>3.22E-01</td><td>0.05</td></tr><tr><td>400</td><td>7.94366E-03</td><td>7.2E-02</td><td>3.29E-01</td><td>0.05</td></tr><tr><td>600</td><td>8.42191E-03</td><td>7.2E-02</td><td>3.33E-01</td><td>0.05</td></tr><tr><td>800</td><td>8.83600E-03</td><td>7.2E-02</td><td>3.36E-01</td><td>0.05</td></tr><tr><td>1000</td><td>8.82572E-03</td><td>7.2E-02</td><td>3.38E-01</td><td>0.05</td></tr><tr><td>1500</td><td>8.68817E-03</td><td>7.2E-02</td><td>3.38E-01</td><td>0.05</td></tr><tr><td>2000</td><td>8.41760E-03</td><td>7.2E-02</td><td>3.38E-01</td><td>0.05</td></tr><tr><td>2500</td><td>8.13101E-03</td><td>7.2E-02</td><td>3.38E-01</td><td>0.05</td></tr><tr><td>3000</td><td>8.05019E-03</td><td>7.2E-02</td><td>3.38E-01</td><td>0.05</td></tr><tr><td>3500</td><td>7.82158E-03</td><td>7.2E-02</td><td>3.38E-01</td><td>0.05</td></tr><tr><td>4000</td><td>7.55457E-03</td><td>7.2E-02</td><td>3.38E-01</td><td>0.05</td></tr><tr><td>5000</td><td>7.45719E-03</td><td>7.2E-02</td><td>3.38E-01</td><td>0.05</td></tr><tr><td>6000</td><td>7.23738E-03</td><td>7.2E-02</td><td>3.38E-01</td><td>0.05</td></tr><tr><td>7000</td><td>7.08064E-03</td><td>7.2E-02</td><td>3.38E-01</td><td>0.05</td></tr><tr><td>8000</td><td>6.71477E-03</td><td>7.2E-02</td><td>3.38E-01</td><td>0.05</td></tr><tr><td>9000</td><td>6.30572E-03</td><td>7.2E-02</td><td>3.38E-01</td><td>0.05</td></tr><tr><td>10000</td><td>6.04170E-03</td><td>7.2E-02</td><td>3.38E-01</td><td>0.05</td></tr></tbody></table>
<figure><img src="image_115.png" /><figcaption>**Figure S99.** Cole-Cole plot showing ac data (a) 2–13 K, (b) 16–37 K, (c) 40–79 K for 200 mM frozen solution of 1-Dy in fluorobenzene in zero dc field; lines are guides for the eyes.</figcaption></figure>
<figure><img src="image_116.png" /><figcaption>**Figure S100.** Fitting of the ac frequency dependence of the (a) in-phase ($\chi'$) and (b) out-of-phase ($\chi''$) components of the ac susceptibility for a 200 mM frozen solution of 1-Dy in fluorobenzene (2–16 K) in zero dc field to Havriliak-Negami model.</figcaption></figure>
<figure><img src="image_117.png" /><figcaption>**Figure S101.** Cole-Cole plot showing fitting of ac data for 200 mM frozen solution of **1-Dy** in fluorobenzene (2–13 K) in zero dc field to Havriliak-Negami model.</figcaption></figure>

<table><caption>**Table S9.** Best fit parameters to the Havriliak-Negami model for 200 mM frozen solution of **1-Dy** in fluorobenzene in zero dc field.</caption><thead><tr><th>T (K)</th><th>τ (s)</th><th>χ<sub>S</sub> (cm<sup>3</sup> mol<sup>-1</sup>)</th><th>χ<sub>T</sub> (cm<sup>3</sup> mol<sup>-1</sup>)</th><th>α</th><th>γ</th></tr></thead><tbody><tr><td>2</td><td>5.72850E-01</td><td>0.01001</td><td>4.75035</td><td>0.3308</td><td>0.7284</td></tr><tr><td>3</td><td>4.44912E-01</td><td>0.02301</td><td>3.14835</td><td>0.2959</td><td>0.6516</td></tr><tr><td>4</td><td>3.56140E-01</td><td>0.03738</td><td>2.35697</td><td>0.2846</td><td>0.6338</td></tr><tr><td>6</td><td>2.30695E-01</td><td>0.05765</td><td>1.57645</td><td>0.3023</td><td>0.6821</td></tr><tr><td>8</td><td>1.48240E-01</td><td>0.06641</td><td>1.19181</td><td>0.3392</td><td>0.7864</td></tr><tr><td>10</td><td>9.56223E-02</td><td>0.06858</td><td>0.96249</td><td>0.3777</td><td>0.9200</td></tr><tr><td>13</td><td>5.35059E-02</td><td>0.06648</td><td>0.74819</td><td>0.4164</td><td>1.1179</td></tr></tbody></table>
<figure><img src="image_118.png" /><figcaption>**Figure S102.** Fitting of the ac frequency dependence of the (a) in-phase ($\chi'$) and (b) out-of-phase ($\chi''$) components of the ac susceptibility for a 200 mM frozen solution of **1-Dy** in fluorobenzene (31–79 K) in dc zero field to the double generalized Debye model.</figcaption></figure>
<figure><img src="image_119.png" /><figcaption>**Figure S103.** Cole-Cole plot showing fitting of ac data for 200 mM frozen solution of 1-Dy in fluorobenzene (31–79 K) in dc zero field to the double generalized Debye model.</figcaption></figure>
<table><caption>**Table S10.** Best fit parameters to the double generalised Debye model for 200 mM frozen solution of 1-Dy in fluorobenzene in zero dc field.</caption><thead><tr><th>T / K</th><th>τ<sub>1</sub> / s</th><th>τ<sub>2</sub> / s</th><th>Δχ<sub>1</sub> / cm<sup>3</sup> mol<sup>-1</sup></th><th>Δχ<sub>2</sub> / cm<sup>3</sup> mol<sup>-1</sup></th><th>Δχ<sub>total</sub> / cm<sup>3</sup> mol<sup>-1</sup></th><th>α<sub>1</sub></th><th>α<sub>2</sub></th></tr></thead><tbody><tr><td>31</td><td>1.04415E-2</td><td>2.25283E-1</td><td>0.17777</td><td>0.09108</td><td>0.04179</td><td>0.2058</td><td>0.2689</td></tr><tr><td>34</td><td>8.60700E-3</td><td>1.96454E-1</td><td>0.16179</td><td>0.08204</td><td>0.0388</td><td>0.1980</td><td>0.2544</td></tr><tr><td>37</td><td>7.10859E-3</td><td>1.74266E-1</td><td>0.14764</td><td>0.07718</td><td>0.03625</td><td>0.1933</td><td>0.2556</td></tr><tr><td>40</td><td>5.73667E-3</td><td>1.38529E-1</td><td>0.13351</td><td>0.07446</td><td>0.03377</td><td>0.1897</td><td>0.2812</td></tr><tr><td>43</td><td>4.59411E-3</td><td>1.19845E-1</td><td>0.12339</td><td>0.06979</td><td>0.03159</td><td>0.1869</td><td>0.2768</td></tr><tr><td>46</td><td>3.74834E-3</td><td>1.01594E-1</td><td>0.11471</td><td>0.0656</td><td>0.02994</td><td>0.1889</td><td>0.2844</td></tr><tr><td>49</td><td>2.89406E-3</td><td>7.93483E-2</td><td>0.10535</td><td>0.06292</td><td>0.02842</td><td>0.1853</td><td>0.2807</td></tr><tr><td>52</td><td>2.35834E-3</td><td>7.74748E-2</td><td>0.10332</td><td>0.05675</td><td>0.02588</td><td>0.2065</td><td>0.2887</td></tr><tr><td>55</td><td>1.76599E-3</td><td>5.75630E-2</td><td>0.09354</td><td>0.0579</td><td>0.02501</td><td>0.2010</td><td>0.3189</td></tr><tr><td>58</td><td>1.40002E-3</td><td>5.97924E-2</td><td>0.09377</td><td>0.05141</td><td>0.02268</td><td>0.2268</td><td>0.3098</td></tr><tr><td>61</td><td>1.04517E-3</td><td>4.70191E-2</td><td>0.08731</td><td>0.05042</td><td>0.02195</td><td>0.2300</td><td>0.3266</td></tr><tr><td>64</td><td>7.73812E-4</td><td>3.78702E-2</td><td>0.08515</td><td>0.04708</td><td>0.01955</td><td>0.2492</td><td>0.3441</td></tr><tr><td>67</td><td>5.78735E-4</td><td>3.56011E-2</td><td>0.08622</td><td>0.04225</td><td>0.0166</td><td>0.2792</td><td>0.3314</td></tr><tr><td>70</td><td>4.23175E-4</td><td>3.12863E-2</td><td>0.08675</td><td>0.03844</td><td>0.01369</td><td>0.3127</td><td>0.3415</td></tr><tr><td>73</td><td>3.19045E-4</td><td>3.97106E-2</td><td>0.09895</td><td>0.02783</td><td>0.00621</td><td>0.3876</td><td>0.2726</td></tr><tr><td>76</td><td>2.13724E-4</td><td>3.70496E-2</td><td>0.10352</td><td>0.02416</td><td>0.00000</td><td>0.4279</td><td>0.2867</td></tr><tr><td>79</td><td>1.56363E-4</td><td>2.63243E-2</td><td>0.09881</td><td>0.02380</td><td>0.00000</td><td>0.4313</td><td>0.3224</td></tr></tbody></table>
<figure><img src="image_120.png" /><figcaption>**Figure S104.** Temperature dependence of the magnetic relaxation time ($\tau$) of 1-Dy in zero dc field. Bars denote ESDs of distribution of times from the generalized Debye model.³,⁴ Individual fit is of the zero dc field average relaxation times to Eqn 1, without errors.</figcaption></figure>

<figure><img src="image_121.png" /><figcaption>**Figure S105.** Temperature dependence of the magnetic relaxation time ($\tau$) of 1-Dy in 0.08 T dc field. Bars denote ESDs of distribution of times from the generalized Debye model.³,⁴ Individual fit is of the 0.08 T field average relaxation times to Eqn 1 ($\tau_{QTM}^{-1} = 0$), without errors.</figcaption></figure>
<figure><img src="image_122.png" /><figcaption>**Figure S106.** Field dependence of the magnetic relaxation time ($\tau$) of 1-Dy at 12 K. Bars denote ESDs of distribution of times from the generalized Debye model.<sup>3,4</sup> Individual fit is of the 12 K average relaxation times to Eqn 2, without errors.</figcaption></figure>
<figure><img src="image_123.png" /><figcaption>**Figure S107.** Comparison of relaxation times for 1-Dy as a solid suspended in mineral oil in a polypropylene bag using the generalized Debye model (GD, black) and as 200 mM frozen solution in fluorobenzene using the Havriliak-Negami model (HN, red) or the double generalized Debye model (DGD, blue – short time, green – long time) to extract relaxation times. Bars denote ESDs of distribution of rates from the appropriate model.</figcaption></figure>
8. CASSCF-SO calculations

**Table S11.** Electronic structure of **1-Dy** calculated with the crystal field parameters obtained from CASSCF-SO using the solid-state geometry of **1-Dy** in zero-field. Each row corresponds to a Kramers doublet.

<table><thead><tr><th>Energy (cm<sup>-1</sup>)</th><th>Energy (K)</th><th>g<sub>x</sub></th><th>g<sub>y</sub></th><th>g<sub>z</sub></th><th>Angle<sup>a</sup> (deg)</th><th>Wavefunction</th><th>&lt;J<sub>z</sub>&gt;</th></tr></thead><tbody><tr><td>0.00</td><td>0.00</td><td>0.0</td><td>0.0</td><td>19.9</td><td>--</td><td>99.6% |&plusmn; 15/2&rangle;</td><td>&plusmn;7.5</td></tr><tr><td>427.96</td><td>615.74</td><td>0.0</td><td>0.0</td><td>16.9</td><td>0.8</td><td>98% |&plusmn; 13/2&rangle; + 2% |&plusmn; 9/2&rangle;</td><td>&plusmn;6.5</td></tr><tr><td>823.47</td><td>1184.74</td><td>0.1</td><td>0.1</td><td>14.0</td><td>1.6</td><td>94% |&plusmn; 11/2&rangle; + 5% |&plusmn; 7/2&rangle;</td><td>&plusmn;5.4</td></tr><tr><td>1149.15</td><td>1653.38</td><td>0.7</td><td>0.7</td><td>11.1</td><td>5.3</td><td>88% |&plusmn; 9/2&rangle; + 2% |&plusmn; 13/2&rangle; + 9% |&plusmn; 5/2&rangle;</td><td>&plusmn;4.3</td></tr><tr><td>1385.01</td><td>1992.73</td><td>1.3</td><td>2.6</td><td>8.2</td><td>10.6</td><td>76% |&plusmn; 7/2&rangle; + 5% |&plusmn; 11/2&rangle; + 1% |&plusmn; 9/2&rangle; + 1% |&plusmn; 5/2&rangle; + 15% |&plusmn; 3/2&rangle; + 2% |&plusmn; 1/2&rangle; + 1% |&minus; 1/2&rangle;</td><td>&plusmn;3.1</td></tr><tr><td>1531.01</td><td>2202.80</td><td>4.2</td><td>5.2</td><td>8.7</td><td>83.7</td><td>54% |&plusmn; 5/2&rangle; + 7% |&plusmn; 9/2&rangle; + 1% |&plusmn; 7/2&rangle; + 4% |&plusmn; 3/2&rangle; + 23% |&plusmn; 1/2&rangle; + 4% |&minus; 1/2&rangle; + 3% |&minus; 3/2&rangle; + 4% |&minus; 7/2&rangle;</td><td>&plusmn;1.7</td></tr><tr><td>1638.24</td><td>2357.08</td><td>1.2</td><td>2.3</td><td>15.0</td><td>87.5</td><td>46% |&plusmn; 3/2&rangle; + 12% |&plusmn; 7/2&rangle; + 4% |&plusmn; 5/2&rangle; + 1% |&plusmn; 1/2&rangle; + 14% |&minus; 1/2&rangle; + 2% |&minus; 3/2&rangle; + 19% |&minus; 5/2&rangle; + 1% |&minus; 7/2&rangle; + 2% |&minus; 9/2&rangle;</td><td>&plusmn;0.6</td></tr><tr><td>1709.26</td><td>2459.26</td><td>0.2</td><td>0.5</td><td>19.3</td><td>87.9</td><td>39% |&plusmn; 1/2&rangle; + 1% |&plusmn; 7/2&rangle; + 9% |&plusmn; 5/2&rangle; + 16% |&plusmn; 3/2&rangle; + 15% |&minus; 1/2&rangle; + 14% |&minus; 3/2&rangle; + 4% |&minus; 5/2&rangle; + 2% |&minus; 7/2&rangle;</td><td>&plusmn;0.2</td></tr></tbody></table>

<footnote><sup>a</sup> The angle between the g<sub>z</sub> value of the excited Kramers doublet and the ground Kramers doublet.</footnote>
<figure><img src="image_124.png" /><figcaption>**Figure S108.** Energy barrier to magnetic relaxation for a model of 1-Dy. Electronic states from CASSCF-SO calculations, labelled with their dominant $m_J$ composition in the $J = 15/2$ basis. Arrows represent the Orbach relaxation pathway, where the opacity of the arrows is proportional to the transition probability approximated with the average matrix elements of magnetic moment connecting the states, $\gamma_{ij} = (1/3)(|\langle i|\mu_x|j\rangle|^2 + |\langle i|\mu_y|j\rangle|^2 + |\langle i|\mu_z|j\rangle|^2)$, normalized from each departing state and commencing from $|-15/2>$.</figcaption></figure>
<figure><img src="image_125.png" /><figcaption>**Figure S109.** Structure of 1-Dy cation with overlaid $g_z$ vectors for Kramer's doublets (KD1–KD8) calculated with CASSCF-SO. Hydrogen atoms are omitted for clarity.</figcaption></figure>
9. References

(1) Chilton, N. F.; Goodwin, C. A. P.; Mills, D. P.; Winpenny, R. E. P. The First Near-Linear Bis(Amide) f-Block Complex: A Blueprint for a High Temperature Single Molecule Magnet. *Chem. Commun.* **2015**, *51*, 101–103.
https://doi.org/10.1039/C4CC08312A.

(2) Gransbury, G. K.; Corner, S. C.; Kragskow, J. G. C.; Evans, P.; Yeung, H. M.; Blackmore, W. J. A.; Whitehead, G. F. S.; Vitorica-Yrezabal, I. J.; Oakley, M. S.; Chilton, N. F.; Mills, D. P. AtomAccess: A Predictive Tool for Molecular Design and Its Application to the Targeted Synthesis of Dysprosium Single-Molecule Magnets. *J. Am. Chem. Soc.* **2023**, *145* (41), 22814–22825. https://doi.org/10.1021/jacs.3c08841.

(3) Reta, D.; Chilton, N. F. Uncertainty Estimates for Magnetic Relaxation Times and Magnetic Relaxation Parameters. *Phys. Chem. Chem. Phys.* **2019**, *21* (42), 23567–23575. https://doi.org/10.1039/C9CP04301B.

(4) Blackmore, W. J. A.; Gransbury, G. K.; Evans, P.; Kragskow, J. G. C.; Mills, D. P.; Chilton, N. F. Characterisation of Magnetic Relaxation on Extremely Long Timescales. *Phys. Chem. Chem. Phys.* **2023**, *25*, 16735–16744.
https://doi.org/10.1039/D3CP01278F.