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

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(SiiPr3)2}2]+ could provide a single-molecule magnet (SMM) with an energy barrier to magnetic reversal (Ueff) of up to 2600 K, a 3-fold increase of the record Ueff 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(SiiPr3)2}2][Al{OC(CF3)3}4] (1-Dy), together with the diamagnetic yttrium analogue. We find Ueff = 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 Ueff 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.


■ INTRODUCTION
−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 U eff values > 1000 K. 11 Salts with axial dysprosocenium cations [Dy(Cp R ) 2 ] + (Cp R = substituted cyclopentadienyl) and related derivatives subsequently raised 100 s magnetic blocking temperatures (T B ) 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. 12,23The current record-holding SMM [Dy 2 (C 5 i Pr 5 ) 2 (μ-I) 3 ] has a U eff of 2345 ± 36 K and a T B of 72 K, with its 1e − Dy−Dy bond providing a significant contribution to these parameters. 19ior to the isolation of these high-barrier SMMs, the nearlinear Ln(II) complexes [Ln{N(Si i Pr 3 ) 2 } 2 ] (Ln = Sm, Eu, Tm, and Yb) were prepared by salt metathesis reactions of 2 equiv of [K{N(Si i Pr 3 ) 2 }] with parent LnI 2 . 24,25The 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 i Pr 3 ) 2 } 2 ] + could show U eff ≈ 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). 26Further calculations revealed that U eff 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. 27In the interim, the bent Ln(III) bis(amide) complexes [Ln{N-(Si i Pr 3 ) 2 } 2 ][B(C 6 F 5 ) 4 ] for Ln = Sm, Tm, and Yb were synthesized by oxidation of the parent Ln(II) complexes [Ln{N(Si i Pr 3 ) 2 } 2 ]; 24,25,28,29 recently, a related bent Yb(III) bis(amide) complex, [Yb{N(SiPh 2 Me) 2 } 2 ][Al{OC(CF 3 ) 3 } 4 ], has been reported. 30However, due to synthetic difficulties 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 i Pr 3 ) 2 } 2 ] + has not previously been isolated.−33 Here, we report the isolation and characterization of the bent Dy bis(amide) complex [Dy{N(Si i Pr 3 ) 2 } 2 ][Al{OC-(CF 3 ) 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 ttt ) 2 ] + . 12,15,16As 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 crystalfield (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 1 H 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(BH 4 ) 3 (THF) 3 ] (Ln = Y and Dy) 34 with 1 equiv of [K{N(Si i Pr 3 ) 2 }] 24 in fluorobenzene at ambient temperature for 1 h gave the heteroleptic Ln(III) mono-(amide) bis(borohydride) complexes [Ln{N(Si i Pr 3 ) 2 }-(BH 4 ) 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 i Pr 3 ) 2 }(BH 4 )(μ-BH 4 )] 4 (3-Ln) in 54− 67% isolated yields.It is critical to remove all of the KBH 4 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 KBH 4 were contaminated with several crystals of the adducts [{Ln{N(Si i Pr 3 ) 2 }(BH 4 )(μ-BH 4 )} 2 {K(μ-BH 4 )}] ∞ (3-Ln•0.5KBH 4 ), for which we report the singlecrystal 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 i Pr 3 ) 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 i Pr 3 ) 2 } 2 (BH 4 )] (4-Ln), species assigned as Ln(III) cyclometalates [Ln{N(Si i Pr 3 ) 2 }{N(Si i Pr 3 )[Si( i Pr) 2 {CH(Me)-CH 2 }]-κ 2 -N,C}] (5-Ln) and HN(Si i Pr 3 ) 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 i Pr 3 ) 2 was treated with 0. Additionally, the solution magnetic susceptibilities of these complexes were determined at 298 K by the Evans method; 36 all values obtained (range χT = 12.5−14.2cm 3 K mol −1 ) are in line with that expected for a Dy(III) free ion (χT = 14.17 cm 3 K mol −1 ). 37he species assigned as the cyclometalate 5-Y exhibits three signals in the 29 Si{ 1 H} DEPT90 NMR spectrum at −3.2, −5.8, and −7.6 ppm.Three magnetically inequivalent silyl groups are also seen in the corresponding 1 H and 13 C{ 1 H} DEPTQ NMR spectra; the latter spectrum contains a doublet resonance at δ C = 55.3 ppm, 1 J YC = 47.4Hz 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 1 H− 13 C HSQC and 1 H− 13 C HMBC NMR spectra, we were unable to assign the associated 1 H resonance.The resonances assigned to 5-Y in the 1 H, 13 C{ 1 H} DEPTQ, and 29 Si{ 1 H} DEPT90 NMR spectra of 5-Y are comparable to those previously reported for the Y(III) silylamide cyclometalate [Y{N(SiMe 3 ) 2 } 2 {N(SiMe 3 )[Si(Me) 2 CH 2 ]-κ 2 -N,C}K], which has δ Si = −26.1,−13.5, and −12.0 ppm, and also shows resonances for the bound methylene group at δ H = −1.27ppm ( 2 J YH = 2.6 Hz) and δ C = 23.6 ppm ( 1 J YC = 22.9 Hz). 38he 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. 39The 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•0.5KBH 4 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 i Pr 3 ) 2 } 2 ] + cation exhibits a bent geometry, with a N−Dy−N angle that deviates significantly from linearity (128.7(2)°), with the NSi 2 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. 31In common with the previously reported heavy [Ln{N(Si i Pr 3 ) 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: 2.293−2.455Å) for methine and methyl fragments of three different i Pr 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. 28The 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). 41Powder XRD was performed on a sample of Journal of the American Chemical Society 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 cm 3 K mol −1 , Figure S73) is slightly higher than that determined at 298 K in fluorobenzene solution (12.97 cm 3 K mol −1 , Figure S74) and the expected Dy(III) free ion value (14.17 cm 3 K mol −1 ). 37We 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 cm 3 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 cm 3 K mol −1 at 1.85 K (Figures S76 and S77).Magnetization (M) vs field (H) experiments show that the magnetization saturates at M sat = 5.42 μ B under a 7 T applied dc field (Figure S78), suggesting an m J = ± 15/2 ground state (M sat = 5.00 μ B ). 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 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). 42The ac data were fit using the generalized Debye model 42,43 to extract relaxation times along with estimated standard deviations (ESDs) as arising from a distribution in the relaxation times; 44,45 note that T B 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 temperaturedependent relaxation time was modeled using eq 1, giving initial estimates of U eff = 850 K, τ 0 = 6.8 × 10 −9 s, C = 8 × 10 −4 s −1 K −n , n = 3.3, and τ QTM −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 QTM −1 = 0 to give U eff = 915 K, τ 0 = 3.8 × 10 −9 s, C = 4 × 10 −5 s −1 K −n , and n = 4.1 (Figure S105).

CT U T (T) exp
n QTM 1 0 Performing an ac susceptibility experiment at 12 K as a function of magnetic field allows us to investigate field-  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 (predominately 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 singlephonon mechanism. 47,48Fitting the average field-dependent relaxation time with a model accounting for these three terms (eq 2) gives τ QTM −1 = 10 s −1 , Q = 2 × 10 7 T −p , p = 3.8, C 12 K = 1.3 s −1 , D = 4.4 s −1 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 temperaturedependent rates at 0 and 0.08 T dc fields and the fielddependent 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 τ 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: ) 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 t Bu)(Cl)(THF) 5 ]-[B(C 6 F 5 ) 4 ] of 3.8 ± 0.2. 46t has previously been shown that the linearity of the N− Dy−N angle in bis−amide complexes should correlate with U eff . 27We 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 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 solidstate 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) At higher temperatures (31−79 K), a shoulder in the Cole− Cole plot emerges, and the ac data are best fit by a doublegeneralized 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 waistrestricted, 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 OpenMolcas 52 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 = ±15/2 Kramers doublet, with Ising-like gvalues (g x = g y = 0, g z = 19.86;Table S11).The first two excited Kramers doublets are at 616 K (98% m J ± 13/2, 0.8°b etween excited g z and ground g z ) and 1185 K (94% m J ± 11/ 2, 1.6°) above the ground state (Figures S108 and S109), with the second excited state being highly mixed. 12DISCUSSION All previously reported examples of axial Dy SMMs with no equatorial donor ligands contain bulky η 5 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 σdonor 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(Si i Pr 3 ) 2 } 2 ][B(C 6 F 5 ) 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 DyL 2 compounds (L = mono-or dianionic monodentate C-or N-donor ligand) predicted that U eff should decrease regularly with bending (e.g., [Dy{N-(SiH 3 ) 2 } 2 ]; U eff = 2072 cm −1 at 180°N−Dy−N and 919 cm −1 at 120°), 27 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(Cp ttt ) 2 ][B(C 6 F 5 ) 4 ] did not appear to have a significant effect on SMM behavior. 12However, the U eff for 1-Dy (950 ± 30 K) is roughly half the value observed for [Dy(Cp ttt ) 2 ] + (1780 ± 40 K). 44Conventional usage of the average transition matrix elements of magnetic moment to infer magnetic relaxation probabilities 27 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(Cp R ) 2 ] + because in the former complex the CF is almost exclusively dominated by two flexible monatomic donor ligands rather than the more rigid η 5 -Cp R rings in [Dy(Cp R ) 2 ] + and related derivatives, 12−22 which have been shown to be crucial for dictating spin dynamics in [Dy-(Cp ttt ) 2 ] + . 57

■ CONCLUSIONS
In this work, the isolation of compounds containing the [Dy{N(Si i Pr) 3 } 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(Si i Pr) 3 } 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(Si i Pr) 3 } 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 flamedried 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.C 6 H 6 and C 6 D 6 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.C 6 H 5 F and 1,2-C 6 H 5 F 2 were stirred over neutral alumina for 4−6 h, filtered, refluxed over CaH 2 for 3 days, distilled, and stored under argon over activated 3 Å molecular sieves.Hexamethyldisiloxane (HMDSO) was refluxed over CaH 2 for 3 days, distilled, and stored under argon over activated 3 Å molecular sieves.[Ln(BH 4 ) 3 (THF) 3 ] (Ln = Y, Dy), 34 [HNEt 3 ][Al{OC(CF 3 ) 3 } 4 ], 17 and [CPh 3 ][Al{OC(CF 3 ) 3 } 4 ] 35 were prepared according to literature procedures; [K{N(Si i Pr 3 ) 2 }] was prepared by an adapted literature procedure, 24 58 Spectra recorded in protonated solvents were locked to, and where possible referenced with, an internal sealed capillary of C 6 D 6 .The solution magnetic susceptibilities of 1-Dy, 2-Dy, 3-Dy, and 4-Dy were determined at 298 K by the Evans method; 36 1 H NMR spectra recorded in C 6 H 5 F or 1,2-C 6 H 4 F 2 were referenced using the highest intensity peak of the highest frequency fluoroarene multiplet (δ H : 6.87 or 6.85 respectively). 11B/ 11 B{ 1 H} (H 3 BO 3 /D 2 O), 19 F (C 7 H 5 F 3 /CDCl 3 ), and 29 Si{ 1 H} DEPT90 (SiMe 4 ) NMR spectra were referenced to external standards.The C(CF 3 ) 3 carbon resonances of the [Al{OC-(CF 3 ) 3 } 4 ] − anion were not observed in the 13 C{ 1 H} NMR spectra of 1-Ln, likely due to quadrupolar broadening by the 100% abundant I = 5/2 27 Al nuclei and coupling to multiple 100% abundant I = 1/2 19 F 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 i Pr 3 ) 2 } complexes. 24,25,28,29ingle-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•0.5KBH 4 •1,2-C 6 H 4 F 2 , and 4-Y), a Rigaku XtalLAB 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 mirrormonochromated X-ray source  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. 59The structures were solved using SHELXT; 60 the data sets were refined by full-matrix least-squares on all unique F 2 values. 60Anisotropic 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; U iso (H) was set at 1.2 (1.5 for methyl groups) times U eq of the parent atom.The largest features in final difference syntheses were close to heavy atoms and were of no chemical significance.CrysAlisPro 59 was used for control and integration, and SHELX 60,61 was employed through OLEX2 62 for structure solution and refinement.ORTEP-3 63 and POV-Ray 64 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 = 1.5418Å) 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. 59For data processing, the instrument was calibrated using silver behenate as standard, then the data were reduced and integrated using CrysAlisPro. 59Le Bail profile analysis was performed using JANA2006 software. 65agnetic 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. 66The 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 cm 3 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 hightemperature (31−79 K) data were fit to the double-generalized Debye model in CC-FIT2 5.0.1. 44,45,67he 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 moisturesensitive 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. 68omputational Methods.OpenMolcas 50 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 library 69−72 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. 73Diamond was employed for molecular graphics. 74FT 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 75,76 -D4 77,78 /def2-TZVP 79 level (including the default effective core potential for yttrium 80 ).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 81 (and the associated def2/J auxiliary basis set 82 ) and DIIS convergence acceleration 83 (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.

Figure 2 .
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 .

Figure 3 .
Figure 3. Temperature dependence (a; at 0 and 0.08 T) and fielddependence (b; at 12 and 40 K) of the magnetic relaxation time (τ) for 1-Dy.Open circles are the experimental data and bars denote ESDs from the generalized Debye model and the relaxation time distribution.42,43Solid lines are the result of the best global simulation (eq 3) as discussed in the text.