Single-molecule magnets (SMMs) are discrete molecules having a bistable magnetic ground state and a sufficient energy barrier to magnetization reversal (U) which can lead to magnetic hysteresis of purely molecular origin. 1 SMMs represent the smallest magnetic units that can be predictively modied with synthetic chemistry. This renders SMMs highly attractive research targets and highlights their potential utility as memory components in future data processing and data storage devices. 2,3 In recent years, SMM design has largely involved exploiting the magnetic anisotropy of a single metal ion with a nely tuned ligand-eld environment. In contrast to the traditional "giant spin" approach in multinuclear metal complexes, designing SMMs with only a single paramagnetic ion offers the inherent advantage of simplied control of the molecular magnetic anisotropy thereby allowing the magnetic anisotropy of a single-ion to be maximized when it resides in an optimal ligand coordination environment. Although signicant progress is being reported for transition metal based mononuclear SMMs, [4][5][6] the majority of mononuclear SMMs aim to exploit the intrinsically large single-ion magnetic anisotropy of lanthanide ions which is due to their unquenched orbital angular momentum and can lead to large magnetic moments, especially in the latter half of the lanthanide series. [7][8][9][10][11] Indeed, lanthanide-based SMMs can be considered the best performing SMMs to-date, especially given the family of biscyclopentadienyl lanthanide based cations, which led most recently to molecules that exhibit magnetic hysteresis at temperatures as high as 80 K. [12][13][14][15][16][17][18] SMM performance is highly dependent on the geometry enforced by the ligands surrounding the central ion. The ligand coordination environment dictates the height of the energy barrier to magnetization reversal (U) as well as inuences the rate of quantum tunneling of the magnetization (QTM). For lanthanide ions, the crystal eld potential acts as a perturbation on the ground spin-orbit coupled, J, term (within the 2S+1 L J coupling scheme) thereby determining the energy spacing between ground and excited m j projections. In the optimal case of spin relaxation occurring by an "over-the-barrier" Orbach mechanism, the value of U will be proportional to the energy gap of the ground and higher excited m j states. 19,20 Molecular symmetry also has direct bearing on the probability of QTM between resonating m j projections. In some ligand eld geometries transverse anisotropy terms will be included in the crystal-eld Hamiltonian, thereby resulting in rapid QTM. 21 With this in mind, understanding how various coordination geometries affect the magnetic anisotropy a Ln 3+ ion is crucial in the continued development of high-performance SMMs. Many of the early examples of Ln-based SMMs featured multidentate oxygen and/or nitrogen-based donor ligands which naturally resulted in SMMs with high coordination numbers. [22][23][24] Of the "classical" Ln-SMM geometries, those featuring axially elongated square antiprismatic (D 4d ), 11,[25][26][27] axially compressed square antiprismatic (D 4d ), 28,29 or compressed pentagonal bipyramidal (D 5h ) 8,10,30,31 geometries have been some of the most thoroughly investigated. More recently, unique and lower coordinate structural motifs for Ln 3+ compounds have been achieved by incorporating organic based ligand scaffolds in SMM design. [32][33][34][35] Modern organometallic lanthanide chemistry has led to structurally and magnetically important molecules such as the C 8 symmetric lanthanide biscyclooctatetraene, [Ln(COT) 2 ] À , [32][33][34][35] and the aforementioned pseudo and strictly linear lanthanide metallocenium, [Ln(Cp R ) 2 ] +1/0 , complexes.
Lanthanide-based SMMs featuring six-coordinate ligand eld geometries have been relatively unexplored in terms of relating molecular geometry to the magnetic behavior of various Ln 3+ ions. 9,[36][37][38][39][40] This is most likely due to the relatively low number of six-coordinate lanthanide complexes reported in the literature as compared to those having higher coordination numbers. Of the cubic and trigonal coordination environments for six-coordinate lanthanide compounds, a trigonal ligand eld is expected to be more suitable for SMM behavior. 41 For a Ln 3+ ion residing in an idealized octahedral (O h ) environment, slow magnetic relaxation is not expected, as the absence of the second-order uniaxial anisotropy parameter, B 0 2 , from the crystal-eld Hamiltonian should exclude the possibility of easyaxis magnetic anisotropy. 37,42,43 In contrast, an ideal trigonal prismatic ligand eld (D 3h ) is predicted to stabilize a highly axial AEm j ground state which could result in dynamic SMM behavior. Indeed, recent reports have shown that a trigonal prismatic geometry can support SMM behavior of Dy 3+ and Tb 3+ ions. 36,37,39,40,44,45 Recently, our group utilized the organometallic chemistry of the 1,1'-diferrocenyl (Fc 2À ) metallo-ligand to synthesize the rst Ln- [1]ferrocenophane molecules, [DyFc 3 (THF) 2 Li 2 ] À and [TbFc 3 (THF) 2 Li 2 ] À , which feature a rare trigonal prismatic arrangement of the six C1 carbons of the three dianionic Fc 2À ligands. 44,45 [DyFc 3 (THF) 2 Li 2 ] À and [TbFc 3 (THF) 2 Li 2 ] À both exhibit zero applied eld SMM behavior, with magnetic anisotropy energy barriers of U ¼ 110 cm À1 and U ¼ 274 cm À1 , respectively. It is important to note that, to the best of our knowledge, [TbFc 3 (THF) 2 Li 2 ] À features the largest zero-eld magnetization energy barrier for a Ln-SMM with trigonal prismatic geometry. We recognized the [LnFc 3 (THF) 2 Li 2 ] À structural motif as an ideal template for investigating the relationship between trigonal prismatic molecular geometry and the magnetic anisotropy of the rest of the late Ln 3+ ions. The homoleptic coordination environment of [LnFc 3 (THF) 2 -Li 2 ] À leads to higher symmetry compared to many of the previously reported trigonal prismatic SMMs which contain hetero-ligand donor atoms.
Herein, we report the synthesis, structural, and magnetic characterization of the late Ln- [1]ferrocenophane complexes, [Li(THF) 4 ][LnFc 3 (THF) 2 Li 2 ] (Ln ¼ Gd (1), Ho (2), Er (3), Tm (4), Yb (5), Lu ( 6)). Of the compounds reported, the Ho- [1] ferrocenophane compound [HoFc 3 (THF) 2 Li 2 ] À exhibits slow magnetic relaxation in the absence of externally applied dc elds which renders it a rare example of a non-Kramers Ho 3+ SMM. Furthermore, we show how small distortions in the trigonal prismatic ligand eld can lead to dramatic differences in magnetization dynamics of the Ho-
The late Ln- [1]ferrocenophane compounds [Li(THF) 4 ][LnFc 3 -Li(THF) 2 ] (Ln ¼ Gd (1), Ho (2), Er (3), Tm (4), Yb (5), or Lu (6)) were prepared using a previously reported protocol via the salt elimination reaction of anhydrous LnCl 3 with excess Li 6 Fc 3 (-TMEDA) 2 (TMEDA ¼ tetramethylethylenediamine) in THF (Fig. 1). 44,45 Crude 1-6 are moderately soluble in Et 2 O which allows for their facile separation from insoluble unreacted starting materials and/or biproducts. Following an Et 2 O extraction, crude 1-6 are recrystallized by slow diffusion of pentane into their concentrated THF solutions, forming highly air and moisture sensitive plate crystals of 1-6 in yields between 21-91% (based on Ln). The relatively high yield of the Tm- [1] ferrocenophane compound 4 (91%), is an outlier and could be a result of the Tm 3+ six-coordinate ionic radii (0.880 Å) being the optimal size for the [LnFc 3 ] 3À coordination environment. Compound 1 can also be synthesized using anhydrous GdI 3 but in lower yields due to difficult separation of (THF) x LiI or [(TMEDA) 2 LiI] 2 salt biproducts. Furthermore, depending on the crystallinity of the LnCl 3 salt, higher yields are obtained for compounds 1-6 by forming the LnCl 3 (THF) x solvate prior to addition to Li 6 Fc 3 (TMEDA) 2 .
The low temperature crystallization of the heaviest Yb-and Lu- [1]ferrocenophane complexes 5 and 6 resulted in a mixture of crystals with two habits: crystals of plate and rod-like shapes could easily be identied. Analysis of both morphologies via single-crystal X-ray diffraction (vide infra) determined the rodshaped crystals to contain structurally unique solvate of the [LnFc 3 (THF) 2 Li 2 ] À anion (hereon denoted as 5 Iso and 6 Iso ) whereas the plate crystals are isostructural to 1-4. The crystalline structure of 5 Iso and 6 Iso differs from 5 and 6 by means of an extra THF solvate molecule located in the crystal lattice. The formation of multiple solvates is unique to the preparation of 5 and 6 and could be a consequence of the ionic radii of Yb 3+ and Lu 3+ being the smallest of the 4f series.
The diamagnetic nature of the 4f 14 electron conguration of the Lu 3+ ion allows for facile analysis of the solution phase structure of 6 and 6 Iso by 1 H-NMR spectroscopy. The 1 H-NMR spectrum of a mixture of 6 and 6 Iso in THF-d 8 shows nearly identical chemical shis as the previously reported [Li(THF) 4 ] [YFc 3 (THF) 2 Li 2 ] compound, with two downeld resonances at 4.05 ppm and 4.09 ppm corresponding to the two sets magnetically inequivalent protons of the diferrocenyl ligands (Fig. 1). The presence of only two resonances corresponding to the Fc 2À ligand protons suggest the solution phase structures of 6 and 6 Iso are similar on the NMR measurement timescale.
Once crystalized, compounds 1-6 are highly insoluble in nonpolar alkanes and ethers such as pentane, diethyl ether, and 1,4-dioxane as well as weakly or non-coordinating polar solvents, such as diuorobenzene. In contrast, 1-6 are highly soluble in polar coordinating solvents such as THF, 2-methyl THF (THF*) and pyridine (py). The solubility properties of 1-6 suggest that dissolution could involve coordination of the polar coordinating solvent to the Li + ions within the lattice of 1-6. Therefore, we hypothesized that various solvent adducts of the general formula [Li(sol) x ][LnFc 3 (sol) 2 Li 2 ], where sol is a polar coordinating solvent, could be synthesized. Indeed, the synthesis of the Ho-
Solid state structures of 1-6, 5 Iso , and 6 Iso . The solid-state structures of compounds 1-6 were determined via singlecrystal X-ray diffraction and are isostructural to the previously reported Tb 3+ and Dy 3+ congeners. All six compounds crystalize in the monoclinic space group P2 1 /c inside a highly anisotropic unit cell (a,c < 15 Å and b > 60 Å). The molecular structure of 1-6 features a single Ln 3+ ion accommodated by three dianionic ferrocenyl ligands (Fc 2À ) that are arranged in a distorted C 3 fashion around the central Ln 3+ ion (Fig. 2). The six-coordinate geometry of each Ln- [1]ferrocenophane molecule is most accurately described as distorted trigonal prismatic with the principal C 3 axis passing through the centroids of the three diferrocenyl C1-carbons, forming a tri-anionic "pocket" above and below the equatorial plane of the molecule. Each charged ligand "pocket" is stabilized by a [Li-THF] + moiety which completes the inner-sphere, [LnFc 3 (THF) 2 Li 2 ] À , monoanionic complex. The molecular charge is balanced by a [Li(THF) 4 ] + unit residing in the outer-sphere.
The unit cells of 1-6 contain two structurally unique Ln-[1] ferrocenophane molecules per asymmetric unit (Ln(1) and Ln(2)), each having similar bonding parameters (Table 1). Across the series the average Ln-C bond distances decrease from 2.572 [8] Å and 2.569 [8] Å for 1 (Gd(1) and Gd(2), respectively) to 2.501 [11] Å and 2.497 [11] Å for compound 6 (Lu(1) and Lu(2), respectively). The observed decrease in Ln-C bond distance with increase in atomic number is most likely due to the increased Lewis acidity and/or the smaller ionic radii of the heaviest Ln 3+ ions. The intramolecular Ln/Fe distances show a more subtle change across the period decreasing from 3.2281 [12] Å and 3.2300 [12] Å for 1 (Gd(1) and Gd(2), respectively) to 3.2108 [16] Å and 3.2068 [16] Å for 6 (Lu(1) and Lu(2), respectively). The average Ln/Fe distances between 3.2300 [12] to 3.2068 [16] Å are some of the closest reported for any heterometallic Ln-Fe species, but lie just outside the sum of the covalent radii of the Fe 2+ and Ln 3+ ions. 46 Despite miniscule differences in the average bonding parameters between the distinct Ln(1) and Ln(2) molecules within each unit cell of 1-6, each molecule shows signicant differences of the average Fc 2À ligand twist angle. Here, the ligand twist angle is dened by the torsion of the two C1 donor atoms of a single diferrocenyl ligand with respect to the centroids (previously described) of the trianionic pockets located above and below equatorial plane of the molecule (see Fig. 3 le inset). A ligand twist angle greater than 0 would indicate distortion of the molecular geometry away from ideal trigonal prismatic geometry. For the Ho(1) and Ho(2) molecules of compound 2, the average ligand twist angles are 10.67 and 12.67 , respectively. It is important to note here that such small differences in the ligand eld geometry can greatly inuence the spectroscopic and magnetic characteristics of a Ln 3+ ion. 47,48 Considering the Ln(2) molecules across the heavy lanthanide series, the average diferrocenyl twist angle has an inversely proportional relationship to the 6-coordinate ionic radius of the Ln 3+ ion, increasing from 9.64 for Gd(2) (r Gd 3+ ¼ 0.938 Å) to 18.56 for Lu(2) (r Lu 3+ ¼ 0.861 Å). The Ln(1) molecules across the period show an identical trend. This inverse relationship between twist angle and ionic radius can be explained by the increased steric hindrance of the [Fc 3 ] 6À ligand eld as the Ln 3+ ionic radius decreases and the needed 'twist' of the Fc 2À ligands to stabilize the smaller Ln 3+ center.
For the trigonal prismatic geometry, comparison of the distance, d, between eclipsed ligand donor atoms or pseudo eclipsed donors (in the case of a ligand twist angle > 0) for a series of similar complexes can indicate the degree of ligand rigidity as well as the axiality trigonal ligand eld of the central Ln 3+ ion. In the case of [LnFc 3 (THF) 2 Li 2 ] À , d would be the distance between the two C1 donors of a single Fc 2À ligand (see Fig. 3 right inset) and is proportional to the C-Ln-C bite angle. For the Ln(2) molecules of 1-6, the largest average d value of the three Fc 2À ligands is 3.336 Å for 1 which features the largest Gd 3+ ion. Upon moving across the row, the average C1/C1 distance of the Fc 2À ligand decreases to a value of 3.249 Å for 6 (Fig. 3 right). The decrease in average Fc 2À C1/C1 distance with decrease in Ln 3+ ionic radii is accompanied by a decrease in the average C1-Fe-C1 angle of the Fc 2À ligand from 104.9 [3] for the Gd(2) in 1 to 102.1 [1] for Lu(2) in 6.
In order to gain a more comprehensive picture of the geometric trends in trigonal prismatic lanthanide compounds, we compared the average ligand twist angle and d values of 1-6 with the same parameters of selected previously reported trigonal prismatic lanthanide complexes 3+ , or Y 3+ ), 39,50 Ln(Bp Me ) 3 ([Bp Me ] À ¼ dihydrobis(methylpyrazole)borate; Ln ¼ Tb 3+ , Dy 3+ , Y 3+ , Ho 3+ , or Er 3+ ), and Ln(Bc Me ) 3 ([Bc Me ] À ¼ dihydrobis(methylimidazolyl) borate; Ln ¼ Tb 3+ , Dy 3+ , Y 3+ , Ho 3+ , or Er 3+ ) 40 (Fig. 3). Of the compared complexes, 1-6, Ln(Bp Me2 ) 3 , Ln(Bp Me ), and Ln(Bc Me ) 3 feature a homo-ligand donor environment around the central Ln 3+ ions. To this end, for the tris-pyrazolyl and tris-imidazolyl borate complexes, the possibility of HB-H/Ln agostic interactions complicate a complete structural comparison with these compounds. Upon inspection of Fig. 3 (Le), it is apparent that the Ln- [1]ferrocenophane complexes, 1-6, feature the greatest susceptibility of ligand twist angle with a change in ionic radius. Furthermore, in contrast to the Ln- [1]ferrocenophane series, [(L CO )Ln(N(SiMe 3 ) 2 ) 2 ], [Ln(L) 3 ], Ln(Bp Me2 ) 3 , Ln(Bp Me ) 3 , and Ln(Bc Me ) 3 feature an increase of the average ligand twist angle with Ln 3+ ionic radius or do not show a signicant correlation at all (in the case of the tris-borate complexes).
In general, all ve sets of compared trigonal prismatic lanthanide complexes exhibit an increase in the average eclipsed/pseudo eclipsed ligand donor distanced, with an increase in Ln 3+ ionic radii (Fig. 3, right). Despite this similar trend, the Ln- [1]ferrocenophane complexes, 1-6, feature the largest average d values of the compared complexes. This distinction is signicant and could suggest the Fc 2À donor ligands of 1-6 might interact more strongly with f-orbitals of z-character, which in turn would have a signicant inuence of the magnetism of these compounds.
The single-crystal X-ray structures for the Yb 3+ and Lu 3+ solvates, 5 Iso and 6 Iso , were solved in the monoclinic space group I a and Cc, respectively, inside a unit cell with lengths between 20-33 Å. Though solved in different space groups, 5 Iso and 6 Iso are most likely isostructural given the almost identical unit cell volumes of 16 344(3) Å3 (for 5 Iso ) and 16 419(4) Å3 (for 6 Iso ) (see ESI † for details). Both 5 Iso and 6 Iso contain three structurally unique [Li(THF) 4 ][LnFc 3 (THF) 2 Li 2 ] molecules per unit cell along with an uncoordinated THF lattice solvate per Ln- [1]ferrocenophane molecule which is not present in compounds 5 and 6 (Fig. 4). The average Ln-C and Ln/Fe distances for the three independent molecules of 5 Iso and 6 Iso are close to the corresponding distances for the two independent molecules of compound 5 and 6, respectively (Table S12 †). To this end, the average Fc 2À twist angles vary signicantly between corresponding solvates. The most distorted molecules of the THF solvated molecules, 5 Iso and 6 Iso , exhibit a 3.3 and a 2.4 increase in twist angle when compared to the most highly distorted molecules of 5 and 6, respectively. This result is signicant as it highlights how crystal packing effects can greatly inuence the geometry of the inner coordination sphere of the individual molecules in the solid state.
Solid state structures of 2-THF* and 2-py. The single crystal X-ray structures of the Ho- [1]ferrocenophane THF* and pyridine adducts, 2-THF* and 2-py, were solved in the monoclinic and orthorhombic space group P2 1 /n and P2 1 2 1 2 1 , respectively. Both 2-THF* and 2-py feature a [HoFc 3 (sol) 2 Li 2 ] À core similar to that of compound 2 except with displaced THF molecules of the [Li-THF] + units with THF* (for 2-THF*) or pyridine (for 2-py) (Fig. 5). Substitution of inner sphere THF molecules with THF* or pyridine do not signicantly change the Ho-C bond distances which are within error equal to those of compound 2 (Table S13 †). To this end, the Ho/Fe distances decrease from 3.229 [8] and 3.221 [13] for Ho(1) and Ho(2) in 2 to 3.2098 [13] Å Though little variation is observed in the interatomic Ho-C distances between 2, 2-THF*, and 2-py, the average Fc 2À twist angle varies signicantly upon changing the identity of the axial [Li-sol] + moiety. Considering the most highly distorted molecule within each of the unit cells, the average Fc 2À twist angle increases from 12.67 (for 2), to 16.52 (for 2-THF*), to 23.69 (for 2-py) (Fig. 6). The average Fc 2À twist angle for 2-py represents the largest of any of the Ln- [1]ferrocenophane compounds reported herein. As shown previously with the structural variation between the corresponding solvates of the Yb-and Lu- [1] ferrocenophane complexes, crystal packing can greatly inuence the geometry of the [LnFc 3 (THF) 2 Li 2 ] À inner coordination sphere. The variation in the crystal packing for 2, 2-THF*, and 2py is also emphasized by the changes in the closest intermolecular distances between Ho 3+ sites of 10.586 Å (for 2), 11.069 Å (for 2-THF*), and 8.941 Å (for 2-py) (Table S14 †). The varying electronic donor strengths of the solvent molecules likely plays an additional role in the geometric variation between 2, 2-THF*, and 2-py though similar Li-C and Li/Ho interatomic distance between the molecules precludes any further discussion here.
Static magnetic properties of [Li(THF) 4 ][LnFc 3 (THF) 2 Li 2 ] (1-5/5 Iso ). The static magnetic properties of compounds 1-5 were investigated by measuring the temperature dependence of the molar magnetic susceptibility under an external 0.1 T magnetic eld across the 300-2 K temperature range (Fig. 7). The c M T (300 K) values for 2-5 are 14.39 emu K mol À1 (2), 11.71 emu K mol À1 (3), 7.00 emu K mol À1 (4), and 2.50 emu K mol À1 (5) and correspond nicely to the expected values of 14.07 emu K mol À1 , 11.48 emu K mol À1 , 7.15 emu K mol À1 , and 2.57 emu K mol À1 for a single non-interacting Ho 3+ ( 5 I 8 ; S ¼ 2, L ¼ 6; g J ¼ 5/4), Er 3+ ( 4 I 15/2 ; S ¼ 3/2, L ¼ 6; g J ¼ 6/5), Tm 3+ ( 3 H 6 ; S ¼ 1, L ¼ 5; g J ¼ 7/6), and Yb 3+ ( 2 F 7/2 ; S ¼ 1/2, L ¼ 3; g J ¼ 8/7) ions, respectively. The c M T (300 K) value of 1 is 8.84 emu K mol À1 and is slightly higher than the expected value of 7.88 emu K mol À1 for a noninteracting Gd 3+ ion ( 8 S 7/2 ; S ¼ 7/2, L ¼ 0; g J ¼ 2). This discrepancy could be due to small weighing errors or a preferred orientation of the Gd- [1]ferrocenophane plate crystallites aligning with the external eld, resulting in a slight increase of the magnetic moment. Upon cooling, the c M T of 1 remains constant across the entire temperature range suggesting an isolated S ¼ 7/2 ground state and weak intermolecular magnetic interactions between neighboring molecules in the crystal lattice. In contrast, deviation from typical Curie-Weiss behavior is observed for 2-5. For the Ho 3+ and Yb 3+ compounds 2 and 5/ 5 Iso , the c M T value remains nearly constant until ca. 100 K where a gradual decrease is observed to minimum values of 9.77 emu K mol À1 (for 2) and 0.63 emu K mol À1 (for 5) at 2.5 K and 2 K, respectively. A steeper c M T decline at low temperatures is observed for 3, where a drop from 11.08 emu K mol À1 to 5.86 emu K mol À1 occurs between 100-2 K. The most pronounced temperature dependent behavior is observed for the Tm 3+ compound 4 which exhibits a nearly linear decrease of c M T with temperature beginning at 30 K to a minimum value of 0.23 emu K mol À1 at 2 K. The low temperature decline of the c M T value observed for 2-5 is typical for mono-metallic species containing a single anisotropic Ln 3+ ion and is commonly attributed to the depopulation of the crystal eld states, very weak intermolecular antiferromagnetic interactions, and/or blocking of the magnetization. However, the precipitous drop of the c M T value of 4 suggest population of a non-magnetic ground state at the lowest temperatures. This observation is further supported by ab initio calculations which predicts a stabilization of a m j ¼ 0 ground state of the Tm 3+ ion within the crystal eld sublevels (vide infra).
The static magnetic behavior of 1-5 was further investigated by measuring the eld dependence of the magnetization between 2-8 K (Fig. S12 †). For compounds 2-5, the 2 K magnetization values at the 7 T eld limit are 5.11 m B (for 2), 6.16 m B (for 3), 1.28 m B (for 4), and 1.36 m B (for 5), respectively, and are much lower than the expected single ion M s values of 10 m B (for Ho 3+ ), 9 m B (for Er 3+ ), 7 m B (for Tm 3+ ), and 4 m B (for Yb 3+ ). This discrepancy suggests anisotropy of the lowest energy J multiplets of the respective Ln 3+ ion which results in nondegenerate m j microstates. The inherent magnetic anisotropy of 2-5 is further supported by the non-superposition of the M vs. H/T curves between 2-8 K (Fig. S13 †). For compound 1, the 2 K magnetization curve reaches a maximum value of 7.78 m B at 7 T which corresponds nicely to the expected value of 7 m B for a single Gd 3+ ion. This data along with the superposition of the M vs. H/T curves between 2-8 K supports the isotropic nature of an isolated S ¼ 7/2 ground state in 1.
Dynamic magnetic properties of [Li(THF) 4 ][HoFc 3 (THF) 2 Li 2 ] (2). Examples of mononuclear Ho-based molecules that display dynamic magnetic behavior are relatively sparse in the literature. 28,[52][53][54][55][56][57] Even rarer are holmium SMMs which are supported by purely organic based ligand eld environments. 58,59 The rarity of Ho-based SMMs is likely due to Ho 3+ being a non-Kramers ion, which does not necessitate a degenerate magnetic ground state as in Dy 3+ , Er 3+ , or Yb 3+ based molecules. Furthermore, the 100% natural abundance of the I ¼ 7/2 165 Ho nuclei facilitates strong nuclear hyperne interactions which can cause fast QTM. 60 A common characteristic among the few reported Ho-based SMMs is a highly symmetric axial ligand eld environment which stabilizes a suitably anisotropic m j ground state of the oblate Ho 3+ ion. Previous ab initio studies of the Dy-and Tb- [1] ferrocenophane compounds suggest the three diferrocenyl ligands of [LnFc 3 (THF) 2 Li 2 ] À promote a largely axial ligand eld that stabilizes large m j ground states in the oblate Dy 3+ and Tb 3+ ions. Based on these results, we hypothesized that the trigonal prismatic [Fc 3 ] 6À ligand eld could be suitable to promote a highly anisotropic ground state in the oblate Ho 3+ ion resulting in SMM behavior in the [HoFc 3 (THF) 2 Li 2 ] À complex. In order to probe the SMM behavior in 2, the variable temperature alternating current (ac) magnetic susceptibility was measured in the absence of an external magnetic eld. The presence of a broad temperature dependent signal in the molar out-of-phase component ðc 00 M Þ of the ac magnetic susceptibility versus frequency plot indicates 2 is indeed a rare example of zero applied eld Ho 3+ SMM (Fig. 8a). Between 2-5 K, the c 00 M signal maximum is slightly temperature dependent, shiing to higher frequencies upon increasing the temperature. This slight variation of the c 00 M maximum with temperature is signicant as it suggests contributions to the spin relaxation from thermally assisted Raman and/or Orbach mechanisms even at the lowest temperatures. Increasing the temperature above 5 K, the c 00 M maximum becomes increasingly temperature dependent, moving outside the 1000 Hz frequency limit at 11 K.
The exceptionally broad nature of the c 00 M signal of 2 indicates multiple spin relaxation processes are occurring at similar ac frequencies. 61 It is likely that this observation is predominately a result of the two structurally unique Ho(1) and Ho(2) sites in the solid state structure of 2 having slightly different magnetization dynamics. However, the complexity of the spin dynamics of Ln-SMMs has recently been emphasized and the simultaneous contribution from Raman, Orbach, and QTM processes to the spin relaxation of a single Ho 3+ ion cannot be excluded. 62 The molar in-phase ðc
(Cole-Cole parameters dened in ESI †). Eqn (1) represents the sum of two modied Debye functions and describes two magnetic relaxation processes each having a characteristic magnetic relaxation time, s 1 and s 2 , at each temperature.
Using the extracted Cole-Cole parameters at each temperature, a "slow" (SR) and a "fast" (FR) relaxation process could be resolved in the c 00 M versus frequency plot of 2, where the 2 K c 00 M signal maxima of SR and FR appear at 11.6 and 262.5 Hz, respectively (Fig. 8b andc). For FR, the shorter 2 K magnetic relaxation time of s 2 ¼ 0.00058 s (as compared to s 1 ¼ 0.014 s for SR) and the temperature independence of the c 00 M signal maximum suggests signicant contribution of QTM to the spin relaxation. The origin of the increased QTM contribution for FR is most likely due to transverse elds arising from intermolecular interactions between neighboring spin centers or nuclear hyperne interactions.
To further investigate the origin of QTM in 2, the magnetically dilute species, [Li(THF) 4 ][Y 0.94 Ho 0.06 Fc 3 (THF) 2 -Li 2 ] (2-dilute), was prepared and magnetically characterized. Similar to 2, the zero-eld ac magnetic susceptibility data of 2dilute provides evidence of multiple spin relaxation processes, with two distinct maxima appearing at 1.2 Hz and 107.8 Hz in the c 00 M vs. Frequency plot at 2 K (Fig. 8d). As previously described, a FR and SR process were resolved by tting the ac magnetic susceptibility of 2-dilute with eqn (1) (Fig. 8e amd f). The 2 K magnetic relaxation times of s 1 ¼ 0.14 s (for SR) and s 2 ¼ 0.0011 s (for FR) are at least half of an order of magnitude longer than the corresponding SR and FR processes for non-dilute 2 at the same temperature. This result is signicant as it suggests that intermolecular magnetic interactions are playing a non-negligible role in the low temperature magnetization dynamics of compound 2. To this end, the c 00 M maximum of the SR processes of 2-dilute at QTM pathways can also be mitigated by creating a eld bias upon the application of an external magnetic eld which breaks the degeneracy of the AEm j crystal eld states thereby lowering the probability of spin relaxation through tunneling mechanisms. The temperature dependence of the ac magnetic susceptibility of compound 2 was measured under an optimal 0.35 T magnetic eld (Fig. S31 †) from 1.8-11 K. In an external eld, the 2 K c 00 M signal of 2@0.35T remains broad but shows a signicant shi of the maximum to lower frequencies suggesting an increase in the magnetic relaxation time (Fig. 9). Heating the sample to 5 K results in a high frequency shi of the c 00 M maximum as well as an increase in the magnitude of the signal. Interestingly, heating past 5 K results in an increase in symmetry of the c 00 M signal and indicates the spin dynamics of 2@0.35T is shiing towards a single relaxation process at higher temperatures. The 2@0.35T magnetic relaxation time for the SR process at 2 K of s 1 ¼ 0.13 s (determined using eqn ( 1)) is close to the corresponding SR process relaxation time for 2-dilute at the same temperature. This observation suggests application of an external eld and magnetic dilution have similar effects on the magnetization dynamics of 2, at least when considering only the SR process.
The magnetic relaxation times extracted using eqn (1) were used to construct Arrhenius plots (ln(s) vs. 1/T) for each of the SR and FR processes of 2, 2-dilute, and 2@0.35T (Fig. 10). Each Arrhenius plot was t using eqn (2), which accounts for spin relaxation through direct, QTM, Raman, and Orbach relaxation processes. 63
In the case of 2 and 2-dilute where H ¼ 0 T, the direct term AH n1 T becomes zero and was therefore disregarded. For 2@0.35T, the direct term A ¼ 114 S À1 T À2 K À1 was determined by tting the eld dependence of the magnetic relaxation time (Fig. S31 †). Due to the complicated nature of the 2@0.35T ac magnetic susceptibility, the low temperature regime (1.8-2.5 K) could not t accurately and only the higher temperature regime (3-11 K) of the SR process was considered in the Arrhenius tting procedure. The best t parameters obtained using this tting procedure for 2, 2-dilute, and 2@0.35T are given in Table 2. It is important to note that the tting parameters for the FR process of 2 and 2-dilute should only be considered as rough estimates, as the c 00 M maximum of the resolved signal lies outside of the measured frequency range at higher temperatures. For all ts, the obtained Raman coefficients (n 2 ) are close to the expected range of n 2 ¼ 5-7 for a non-Kramers ion. 63 For the FR and SR processes of 2, 2-dilute, and 2@0.35T energy barrier values between U ¼ 110-131 cm À1 were obtained.
Dynamic magnetic properties of [HoFc 3 (py) 2 Li 2 ] À (2-py) and [HoFc 3 (THF*) 2 Li 2 ] À (2-THF*). Small perturbations in the crystal-eld environment can greatly inuence the electronic structure and thus the magnetization dynamics of lanthanidebased molecules. In order to explore how small distortions in the trigonal prismatic [Fc 3 ] 6À ligand eld effects the SMM properties of the Ho- [1]ferrocenophane compound, [HoFc 3 (-THF) 2 Li 2 ] À , the static and dynamic magnetic properties of the pyridine solvated complex, [HoFc 3 (py) 2 Li 2 ] À (2-py) were explored.
The static magnetic behavior of 2-py is nearly identical to that of compound 2 (Fig. S11 †). Interestingly, the dynamic magnetic properties of 2-py are markedly different from that of compound 2 (Fig. 11). Compound 2-py features extremely broad signals in the c 00 M vs. frequency plot but does not feature any discernable signal maxima within the measured 1-1000 Hz frequency range. This qualitative observation readily suggests that the magnetic relaxation times for the more geometrically distorted Ho-[1]ferrocenophane molecules in 2-py, are much faster than the magnetic relaxation times observed for the Ho-[1]ferrocenophane molecules in 2, which features a low frequency c 00 M signal maximum at 18.2 Hz at 2 K. Upon increasing the temperature above 2 K, the c 00 M signal of 2-py moves out of the high frequency limit and almost completely disappears at 10 K. Out-of-phase signals at only the highest frequencies without signal maxima within the frequency range could suggest QTM is a major contributor to the spin relaxation in 2-py. Although the magnetic relaxation of 2-py is too fast to allow the extraction of an energy barrier of magnetization reversal, the presented data suggests that the deviation from idealized trigonal prismatic geometry (increase in torsion angle) increases relaxation times. Dynamic magnetic properties of [LnFc 3 (THF) 2 Li 2 ] À (Ln ¼ Er 3+ (3), Tm 3+ (4), and Yb 3+ (5)). For the Er 3+ , Tm 3+ , and Yb 3+ compounds 3, 4, and 5 respectively, no appreciable signal is observed in the c 00 M vs. Frequency plot in the absence of an external magnetic eld. This result is not surprising as the axial [LnFc 3 ] 3À ligand eld likely destabilizes the largest m j ¼ AE15/2, AE6, and AE7/2 projections of the prolate Er 3+ , Tm 3+ , and Yb 3+ ions, respectively. These results are also consistent with dc magnetization data for the Tm 3+ compounds, 4, which suggest the lowest energy m j ¼ 0 ground state for 4.
For the Yb 3+ compound 5/5 Iso , application of an optimal 0.2 T external magnetic eld results in slow magnetic relaxation behavior as evidenced by a narrow temperature dependent signal in c 00 M vs. Frequency plot (Fig. 12a). Between 1.8-2 K, the magnitude of the c 00 M signal increases which could suggest that the spin relaxation is occurring through multiple relaxation mechanisms at the lowest temperatures and subsequently shiing towards a single mechanism upon heating. Heating results in an increased temperature dependence of the c 00 M single maximum which eventually moves outside of the measured frequency range at 3.5 K.
Using the ac magnetic susceptibility of compound 5/5 Iso , Cole-Cole curves were constructed and were tted using general Debye equation which considers only one spin relaxation process. The extracted magnetic relaxation times were then used to construct an Arrhenius plot between 1.8-3.5 K (Fig. 12b). Analyzing the Arrhenius plot for compound 5 shows the magnetic relaxation times for 5 are temperature dependent across the full temperature range suggesting low contribution from quantum tunneling processes. Between 2.5-3.5 K, the magnetic relaxation times become increasingly temperature dependent but never become fully linear on the logarithmic scale. This indicates signicant contributions to the spin relaxation from second-order Raman and/or direct processes even at the highest temperature regime. Similar behavior has been observed in the trigonal Yb 3+ SMM, Yb [trensal], where it was reported that considering solely an Orbach relaxation mechanism was insufficient in describing the anisotropy energy barrier of the system. 64 As previously described, the Arrhenius plot for 5/5 Iso was t using eqn (2). The direct exponent, n 1 , was held constant at n 1 ¼ 4 and the direct term, A, was allowed to freely rene along with the other Arrhenius parameters due to the inability in acquiring a reasonable t of the s vs. H plot for compound 5/5 Iso (Fig. S49 †). Using this tting procedure, values of Arrhenius parameters of A ¼ 0.304 S À1 T À2 K À1 , s QTM ¼ 0.00269 s, C ¼ 0.00812 s À1 K À4 , 25 n 2 ¼ 4.25, s o ¼ 9.04 Â 10 À5 s, and U ¼ 6 cm À1 were obtained.
To further investigate the electronic structure of the late lanthanide ions in the trigonal prismatic geometry and the observed magnetic properties of 2-5, multi-congurational ab initio calculations were performed using the Molcas 8.2 package within the CASSCF/SO-RASSI and XMS-CASPT2/SO-RASSI level of theory. 65 For the two independent Ln(1) and Ln(2) molecules of 2-5, there are only small differences of the energies of the spin-orbit states and corresponding g-tensors, therefore only the results obtained for Ln(1) within the XMS-CASPT2 level of theory will be discussed here (Tables S21-S27 †) (Table 3).
The ground state electronic structures for 2-5 are shown in Fig. 13. The axial nature of the trigonal prismatic ligand eld is expected to be least suitable for stabilizing the largest m j projections in the latest prolate lanthanide ions (Er 3+ , Tm 3+ , and Yb 3+ ). The Er- [1]ferrocenophane compound, 3, shows highly mixed ground doublets containing m j ¼ AE1/2 (24%), AE5/2 (23%), and AE7/2 (18.7%) character. The rst and second excited m j states for 3 reside only 28 cm À1 and 52 cm À1 above the ground doublets which contributes to the highly mixed m j composition and large transverse g-tensors (g x and g y ) of 3 (Table 4). These factors contribute to the lack of axial magnetic anisotropy of the ground state and explain the lack of SMM behavior for 3. For compound 4, a non-magnetic, m j ¼ 0, ground state is observed and therefore it does not exhibit any magnetic anisotropy. This corresponds well with the direct current magnetic susceptibility data in which the molar magnetic susceptibility temperature product drops to near zero at 2 K. The composition of the ground doublet of the Yb- [1] ferrocenophane compound, 5, is mostly m j ¼ AE7/2 (51%) and AE3/2 (11%) character and exhibits large transversal g-tensors which leads to a magnetic anisotropy axis which is nearly perpendicular to the principal C 3 axis of the [LnFc 3 (THF) 2 Li 2 ] À motif. Therefore, the lack of SMM behavior of 5 in the absence of an external magnetic eld is not surprising as fast spin relaxation through QTM processes is expected. To this end, the observed slow relaxation under an applied magnetic eld suggests that the ground m j ¼ AE7/2 doublet becomes purer under an applied eld and therefore QTM is at least partially shut down. For 5, the rst excited m j state lies 121 cm À1 above the ground doublet, therefore if the spin relaxation of 5 under an applied eld proceeds via an Orbach mechanism through the rst excited state, and energy barrier $120 cm À1 is likely to be observed under an applied magnetic eld. The experimentally extracted spin reversal barrier of 6 cm À1 is signicantly lower than the energy gap between the ground and rst excited state and suggest that spin relaxation proceeds mainly through a second-order Raman and/or direct mechanism.
For the Ho-[1]ferrocenophane compound, 2, an almost pure m j ¼ AE7 ground state is observed and is well stabilized from the rst and second excited states by 137 cm À1 and 228 cm À1 , respectively. The highly anisotropic ground state leads to an axial magnetic moment vector that resides along the principal {LnFc 3 } C 3 axis explaining the observed SMM behavior of 2. The magnetic blocking barrier of the Ho(2) molecule of 2 was further investigated by following the methodology described in ref. 66 (Fig. 14). The tunneling gaps between the ground doublets are small which suggests ground state QTM is minimal. Spin relaxation is expected to proceed through the rst excited state given the large tunneling gap of 0.77 cm À1 . The energy of the rst excited state (137 cm À1 ) corresponds remarkably well with the experimentally extracted energy barriers of 2, 2-dilute, and 2@0.35T (110-131 cm À1 ).
We present a detailed analysis of trends in structure and magnetic properties of the remaining members of the family of late Ln- [1]ferrocenophane complexes which all feature exclusively carbon-donors coordinated to trigonal prismatic lanthanide ions. The observed trend of increasing Fc 2À twist angle with decreasing ionic radii of the Ln 3+ ions can be rationalized by simple geometric arguments and considering the structural rigidity of the Fc 2À units. The Ho 3+ complex 2 exhibits slow magnetic relaxation in the absence of applied dc elds, rendering it a rare example of a Ho 3+ -based SMM. Structural modication of the approximate trigonal prismatic coordination environment can be achieved remotely via substitution of coordinating solvent molecules to the terminating Li + ions. Specically, an increase in Fc 2À twist angle and deviation from ideal trigonal prismatic geometry is observed in the series 2, 2-THF*, and 2-py which is accompanied by a decrease in magnetic relaxation times at a given temperature for the pyridine solvated molecule 2-py. Taken together our results emphasize the sensitivity of the magnetic structure of Ln 3+ ions in trigonal prismatic coordination environments to the twist angle and provide design guidelines for six-coordinate SMMs.
All syntheses and magnetic sample preparation were carried out under the rigorous exclusion of air and moisture using an ultrahigh purity Ar lled glovebox (Vigor) in which the O 2 and H 2 O levels were generally held under 2 ppm and 0.1 ppm, respectively. Tetrahydrofuran, diethyl ether, hexanes, and n-pentane were all dried and deoxygenated using a solvent purication system (JC Meyer or Innovative Technologies SPS) and were stored over molecular sieves (3a, 8 to 12 mesh) prior to use. Pyridine was dried by stirring over CaH 2 for 24 hours and deoxygenated using freeze-pump-thaw methods. Prior to use 2methyl tetrahydrofuran (THF*) was passed through a basic alumina column to remove the butylated hydroxytoluene (BHT) stabilizer. Stabilizer free THF* was deoxygenated by purging N 2 gas through the solvent and was dried by reuxing over Na/ benzophenone. Anhydrous THF* and pyridine were stored over molecular sieves (3a, 8 to 12 mesh). Anhydrous GdCl 3 , HoCl 3 , and ErCl 3 were received as a generous gi from Dr Timothy Hughbanks. Anhydrous TmCl 3 (Millipore Sigma), YbCl 3 (Alfa Aesar), and LuCl 3 (Alfa Aesar) were purchased from commercial sources and were used as received. Li 6 (Fe(h 5 -C 5 -H 4 ) 2 ) 3 (TMEDA) 2 (ref. 67) and [Li(THF) 4 ][YFc 3 (THF) 2 Li 2 ] 44 were prepared as previously described. Carbon and hydrogen elemental analysis were performed on compounds 1-6, and 2-py by Midwest Microlab Inc.
Details regarding the structural determination of compounds 1-6, 5 Iso , 6 Iso , 2-THF*, and 2-py can be found in the ESI. †
Samples used for magnetic characterization were prepared by thoroughly crushing the respective paramagnetic species into a microcrystalline powder and subsequently adding between 20-40 mg to the bottom of a high purity glass NMR tube along with solid n-eicosane ($27-65 mg). The NMR tube containing the paramagnetic species/n-eicosane mixture was equipped with a gas line adaptor, removed from the glovebox, and was sealed under vacuum on a Schlenk line. To prevent torqueing of small crystallites under high magnetic elds, the solid n-eicosane in the sealed sample was melted by heating the sealed tube between 40-43 C in a hot water bath, forming a solid matrix upon cooling to room temperature. Magnetic characterization was carried out using a Quantum Design MPMS 3 SQUID magnetometer. The direct current (dc) magnetic susceptibility was measured under a 0.1 T magnetic eld between 2-300 K. A diamagnetic correction (calculated using Pascal's constants) was included in the calculation of the dc molar magnetic susceptibility and considers the diamagnetic response of eicosane and the complex core electrons. 68 The variable temperature magnetization was measured between 2-8 K up to external magnetic eld strengths of 7 T. The alternating current (ac) magnetic susceptibly was measured using a 0.2 mT alternating eld between 1-1000 Hz using external eld strengths of either 0 T, 0.2 T, or 0.35 T.
[Li(THF) 4 ][GdFc 3 (THF) 2 Li 2 ] (1). A 20 mL vial was charged with GdCl 3 (0.1590 g; 0.6032 mmols), THF (2 mL), and a magnetic stir bar. The suspension was heated to 45 C and stirred vigorously for ca. 8 hours. The suspension was then added to a vial containing a suspension of Li 6 (Fe(C 5 H 4 ) 2 ) 3 (-TMEDA) 2 (0.6618 g; 0.8011 mmols) in THF (5-10 mL), stirred with a glass coated stir bar, forming a cloudy red suspension. The suspension was let stir for 16-18 hours upon which the reaction mixture was ltered through Celite. The dark red ltrate was reduced under dynamic vacuum forming a viscid oil which expanded as a sticky solid upon agitation. The red-orange solid was washed with hexanes (4 Â 5 mL) and was subsequently dried under vacuum to yield a light orange powder. The crude product was extracted into several washings of Et 2 O (4 Â 5 mL) which were ltered through Celite. The Et 2 O ltrate was reduced to dryness under dynamic vacuum and the resulting orange material was dissolved in THF (3-5 mL), ltered through Celite, and placed into a pentane vapor diffusion chamber. Pyrophoric plate crystals of 1 formed overnight at À27 C, which were collected by decantation of the mother liquor, washing with pentane (2 Â 2 mL), and allowing the crystals to dry under an Ar atmosphere at ambient temperature and pressure (0.2166 g; yield ¼ 31.96%). *In contrast to compounds 2-6 and 2-py, elemental analysis on crystalline material of 1 using commercial analysis services resulted in low C and H values. This discrepancy could be due to the smaller crystals obtained for 1 and resulting increased propensity for desolvation of THF molecules or product decomposition prior to analysis.
[Li(THF) 4 ][HoFc 3 (THF) 2 Li 2 ] (2). To a 20 mL vial containing Li 6 (Fe(C 5 H 4 ) 2 ) 3 (TMEDA) 2 (0.4559 g; 0.552 mmols) in THF (5-10 mL) was added solid HoCl 3 (0.1117 g; 0.412 mmols) and an additional THF wash (4-5 mL) forming a red suspension. The suspension was let stir for 16-18 hours upon which the reaction mixture was ltered through Celite. The dark red ltrate was reduced under dynamic vacuum forming a viscid oil which expanded as a sticky solid upon agitation. The red-orange solid was washed with hexanes (3 Â 5 mL) and was subsequently dried under vacuum to yield a light orange powder. The crude product was extracted into several washings of Et 2 O (4 Â 5 mL) which were ltered through Celite. The Et 2 O ltrate was
This journal is © The Royal Society of Chemistry 2020
This journal is © The Royal Society of Chemistry 2020 Chem. Sci., 2020, 11, 3936-3951 | 3945
This journal is © The Royal Society of Chemistry 2020 Chem. Sci., 2020, 11, 3936-3951 | 3949