Rotaxane CoII Complexes as Field‐Induced Single‐Ion Magnets

Abstract Mechanically chelating ligands have untapped potential for the engineering of metal ion properties. Here we demonstrate this principle in the context of CoII‐based single‐ion magnets. Using multi‐frequency EPR, susceptibility and magnetization measurements we found that these complexes show some of the highest zero field splittings reported for five‐coordinate CoII complexes to date. The predictable coordination behaviour of the interlocked ligands allowed the magnetic properties of their CoII complexes to be evaluated computationally a priori and our combined experimental and theoretical approach enabled us to rationalize the observed trends. The predictable magnetic behaviour of the rotaxane CoII complexes demonstrates that interlocked ligands offer a new strategy to design metal complexes with interesting functionality.

Since their discovery in 1991, [28] single-molecule magnets (SMMs) have received significant attention due to their potential applications in spintronics,d ata storage and quantum computing. [29] Thes low relaxation of the magnetization that defines SMMs is typically dictated by an energy barrier (U)which arises from the magnetic anisotropy,characterized by the zero-field splitting term (D), of anon-zero spin ground state.T ailoring the size and sign of D therefore represents ap romising strategy to design molecules with al arge U. [30] Single-ion magnets (SIMs) containing only one metal center are of particular interest due to the possibility of predicting anisotropy based on ligand field theory. [31,32] However,m ost transition-metal SIMs are discovered serendipitously,n ot least because D relies on subtle geometric effects and accurately predicting the geometry or even stoichiometry of heteroleptic complexes formed from am ixture of ligands remains challenging. [33] Here,f or the first time,w es how that mechanically chelating ligands represent an untapped platform for the design of SIMs.B yf ocusing on rotaxane-based Co II com-plexes,w ea pply computational approaches for the accurate correlation of magnetic anisotropy [34,35] and the electronic structure of Co II ions [31,32,36] to demonstrate that the geometry of the complexes formed can be predicted with sufficient precision to identify interesting magnetic properties ap riori.

Results and Discussion
We compared our previously reported solid-state structure of [Co(1)](ClO 4 ) 2 (see Figure 1A for ligand structures) derived from single crystal X-ray diffraction (SCXRD) analysis ( Figure 1B) [22] with modelled structures generated de novo (Gaussian09, [37] CAM-B3LYP/6-31G*/LAN2DZ-[Co],s ee the Supporting Information for details). It should be noted that the rotaxane framework enforces the formation of ap seudo-heteroleptic complex and prevents binding of additional ligands,t og ive ap redictable,i fr elatively rare,5coordinate all-neutral N-donor distorted square-based pyramidal (sbpy) [38] binding mode,which is not observed with the non-interlocked ligands.
Tw oi ndependent structures with different bond lengths (RMSD = 0.12 ,T able S1) were observed in the asymmetric unit of [Co(1)](ClO 4 ) 2 ,suggesting that high spin (HS) and low spin (LS) configurations co-exist in the solid state.T he coordination spheres of the de novo HS and LS models of [Co(1)] 2+ agree remarkably well, both in terms of geometry and bond lengths (RMSD = 0.05 and 0.04 respectively, Table S10), with one of the structures observed by SCXRD ( Figure 1B for the HS structure), supporting this proposal. Furthermore,arelatively small energetic preference for the HS configuration was predicted computationally for both the de novo structures (5.9 kJ mol À1 )a nd models of [Co(1)] 2+ derived from the corresponding SCXRD geometries (2.7 kJ mol À1 ,s ee the Supporting Information for details), although it should be noted that predicting accurate energy gaps of multiconfigurational complexes is ac hallenge for DFT modelling. Consistent with this,t he EPR spectra of polycrystalline [Co(1)](ClO 4 ) 2 show that the complex exhibits both HS and LS configurations in the solid state (vide infra), in line with the EPR data previously obtained on frozen solutions. [22] Having validated our de novo computational approach in the case of [Co(1)](ClO 4 ) 2 ,wemodelled complexes based on interlocked ligands containing other readily available macrocycle components, [39] one of which (2)i sm ore rigid and the other (3)c ontains ap otentially weakly coordinating ether unit near to the bipyridine ligand ( Figure 1A). [Co(2)] 2+ was predicted to display an all-neutral N, 5-coordinate environment similar to that of [Co(1)](ClO 4 ) 2 but in this case, p-Co and p-p interactions result in distortion of the sbpy geometry and at wisting of the macrocycle relative to the axle (Figure 1B). In the case of [Co(3)] 2+ ,t he weakly coordinating ether Ow as predicted to bind to the metal ion in lowest energy model obtained, resulting in ad istorted-octahedral geometry,a lthough once again the Nd onors are arranged in asbpy geometry ( Figure 1B).
Thea greement between de novo models of [Co(1-3)] 2+ and their SCXRD-derived structures confirms that the predictable nature of the coordination environment provided by amechanically chelating ligand, combined with the ability of simple computational models to accurately capture weak, geometry distorting interactions,a llows the structure of such complexes to be predicted with reasonable precision. The computationally predicted values of D obtained for the de novo HS models of [Co(1-3)](ClO 4 ) 2 agree remarkably well with models derived from the SCXRD geometries (Table 1) and, excitingly,large negative values of D were predicted for Powders and frozen-solutions of [Co(1-3)](ClO 4 ) 2 were investigated to evaluate their spin configurations and provide an estimate of D. X-band EPR spectra of polycrystalline samples at 10 K( Figure 2A)display features characteristic of both LS (dotted signals at ca. 300 mT) and HS (solid black lines) configurations.T his signal assignment is confirmed by the persistence of the LS signal at 100 K( Figure 2B)atwhich the HS species relaxes too fast to be detectable.T he difference in the LS signal intensities in 1-3 at 100 Ki si n keeping with the calculated HS-LS energy gap and unambiguously points to al igand effect on the spin state population.
TheL Ss pecies exhibit similar g values and hyperfine splitting for all complexes,w here an eight-line hyperfine splitting on g z ,due to the interaction of the unpaired electron with the Co II nucleus (I = 7/2), is visible ( Figure 2B,s ee Table S3 for simulation parameters). The1 0KEPR spectra ( Figure 2A)s pan av ery broad field range,i ndicating significant magnetic anisotropy in the HS state,f or which two distinct sets of signals are visible in all three complexes. Although the transition at low fields occurs at the same effective g value [48,49] (g eff = 7.9) in all complexes,t he highfield signals are dependent on the nature of the ligand. The signal at g eff = 7.9 must arise from atransition within the M s = AE 3/2 doublet, characterized by g z > 2.5, [50] demonstrating that D is negative (see the Supporting Information). EPR spectra of frozen solutions ( Figure S23) were similar to those of polycrystalline samples,s howing that no coupling occurs in the solid state,presumably due to the steric bulk of the ligands preventing close approach of the Co II ions.
To determine the magnitude of D,h igh-field EPR (HFEPR) measurements were carried out on pelletized samples at 4.5 K( Figure 3C for [Co (2) Figure 2A were simulated using D obtained from magnetic data. Foradefinition of the SCXRDderived models see Figure 5and accompanying text.
[e] U eff values (2D) were calculated from experimentally obtained D. respectively.X-band data at 10 K(A) and 100 K(B). In (A) LS species are shown as dashed lines as they are saturated at 10 K. C) High-field EPR spectra and simulated data for [Co (2)](ClO 4 ) 2 at 4.5 K. Simulations for the HS states in (A) and (C) were performed with PHI [51] with parameters listed in Table 1. Simulation parametersf or the LS states (B) are given in Supporting Information ( Table S3). inter-doublet transitions occur up to 375 GHz, setting j D j! 15 cm À1 but preventing accurate determination of D. The large (negative) D value is also responsible for the absence of M s =AE 1/2 intra-doublet signals.T he assignment of the g eff = 7.9 signal to an intra-Kramer transition is confirmed by the linear trend of the peak positions in the entire experimental frequency range ( Figure S24D). TheEPR data show that the ligand environment not only influences the population of the LS state,with [Co(1)](ClO 4 ) 2 @ [Co(3)](ClO 4 ) 2 > [Co (2)](ClO 4 ) 2 ,a spredicted by modelling,b ut that it affects the coordination environment of the HS state,inline with the SCXRD data. Importantly,the EPR data demonstrate experimentally that the HS configuration in complexes [Co(1-3)](ClO 4 ) 2 exhibits al arge negative zerofield splitting (D < À15 cm À1 ), in line with predictions for the de novo models.
Thes tatic magnetic properties of [Co(1-3)](ClO 4 ) 2 were assessed by direct current (DC) susceptibility and magnetization measurements on the pelletized samples previously measured by HFEPR (Figure 3a nd Figures S25-27). The measured room temperature cT values of 1.90, 2.45, 2.24 cm 3 Kmol À1 for [Co(1-3)](ClO 4 ) 2 ,respectively,are higher than the value (cT = 1.88 cm 3 Kmol À1 )expected for S = 3/2 systems with g = 2i nt he spin-only approximation, but lie in the typical range for five-coordinated Co II complexes with second-order SOC. [52,53] Themagnitude and thermal dependence of cT ( Figure 3) for [Co(2-3)](ClO 4 ) 2 confirms the HS state as the dominant state of these complexes,a nd the slightly smaller cT measured for 3 compared to 2 is consistent with the higher amount of LS present in this sample (Figure 2B).
For[ Co(1)](ClO 4 ) 2 ,t he cT vs. T data point to an incomplete spin-crossover (SCO) behaviour,with atransition from amixture of states at low Ttoaprogressive conversion to the HS state at T > 100 K, suggesting that the LS configuration is lower in energy.A lthough the modelling suggests that the HS state is favored, it should be noted that the calculated energy gap HS-LS is small (2.7 kJ mol À1 )a nd was obtained in the gas phase and is thus inconclusive.A lthough many 4-and 6-coordinate Co II complexes are known to undergo aS CO transition, including reversible switching between SCO and SIM, [54] 5-coordinate Co II SCO compounds are rare,e specially in conjunction with SIM behaviour, [55] making [Co(1)](ClO 4 ) 2 only the second SCO complex characterized by an eutral CoN 5 coordination. [56] Thes usceptibility decrease at low temperatures was attributed to magnetic anisotropy rather than antiferromagnetic impurities or interactions between the spins (in agreement with EPR analysis), [57] as the field dependent magnetization data collected at 100 Ks how ap erfectly linear trend ( Figure S25). Ther educed magnetization plots ( Figure S26) also indicate magnetic anisotropy due to the absence of asingle master curve. [58,59] To determine the magnetic parameters of [Co(1-3)]-(ClO 4 ) 2 ,the cT vs. T plots (Figure 3) and the magnetization vs. H at multiple temperatures ( Figure S26) were simultaneously fitted with PHI. [51] Thebest fits yielded g average of 2.33, 2.31 and 2.33 and D values of À78, À59 and À95 cm À1 for [Co(1-3)](ClO 4 ) 2 ,r espectively (Table 1, see also Figure S27 for fits with different D values), considerably larger than values obtained for other pentacoordinate mononuclear Co II complexes [60][61][62] (Table S4). Because the spin population varies with temperature for [Co(1)](ClO 4 ) 2 ,o nly the fit of the magnetization was used to estimate the parameters (i.e.t he cT vs.Tp lot was not fitted for [Co(1)](ClO 4 ) 2 in Figure 3), and the best fits were obtained by including acontribution of the LS species at 0.45, 0.05 and 0.1 for [Co(1-3)](ClO 4 ) 2 , respectively ( Table 1). Comparison of solution and solid-state EPR, the magnetization data at 100 Ka nd solution susceptibility values (2.05, 2.56 and 2.29 cm 3 Kmol À1 for [Co(1-3)](ClO 4 ) 2 ,r espectively,s ee the Supporting Information), all indicate that no J coupling needs to be considered. In contrast to EPR, the inclusion of the rhombic zero-field parameter E in the magnetic data did not lead to ab etter fit, (due to the lower sensitivity of SQUID measurements). Thel arge negative D revealed by DC measurements for [Co(1-3)]-(ClO 4 ) 2 (Table 1), which are in good agreement with the values obtained from X-band and HFEPR simulations,a nd the variability of D with the rotaxane framework thus justify their further investigation as potential "tuneable" SIMs.
Thef requency dependence of the in-phase (c')a nd the out-of-phase (c'')m agnetic susceptibility for [Co(1-3)]-(ClO 4 ) 2 was measured in the temperature range 1.8-10 K under an oscillating (1-1500 Hz) field of 1.55 Oe (0.155 mT). In the absence of an external static field, none of the complexes displayed maxima in the out-of-phase susceptibility.A pplication of as tatic field reduces the quantum tunneling of magnetization (QTM) effect by removing the degeneracyb etween microstates and thus out-of-phase maxima for all complexes are observed ( Figure S28-S30). These shift to low frequency with the increase in the magnetic field strength, reaching amaximum shift under an applied field of 100-250 mT,c onsidered to be the optimal field under which to observe the slow magnetic relaxation. Strongly temperature and frequencyd ependent ac susceptibility signals characteristic of single ion magnet (SIM) behaviour were observed in all cases ( Figure S31). This characteristic fieldinduced SIM behaviour,d isplayed by all complexes,i s exemplified for [Co(2)](ClO 4 ) 2 in Figure 4A.  Table S8 for fitting parameters.
Thefitting of the c' and c'' data ( Figure 4A and S31) with the extended Debye model [63] (see the Supporting Information) yielded magnetization relaxation times (t)a nd their distribution (a)a te ach temperature for [Co(1-3)](ClO 4 ) 2 (Tables S5-7). Reliable fits of the AC magnetic data were obtained for the temperature range between 1.8 and 4.8 K.
The a values range between 0.16-0.30, 0.07-0.25 and 0.07-0.25 for [Co(1-3)](ClO 4 ) 2 ,r espectively,s howing an arrow distribution of the relaxation times.The curvature of the plot of ln(t)v s. T À1 ( Figure 4B)p oints to the presence of several relaxation pathways that cannot be fitted with an Orbach process alone.Contributions from additional relaxation pathways were therefore considered and the relaxation times fitted using to Equation (1) (see Table S8 for parameters): where the first term designates the direct process,the second the Raman process and the third the Orbach process;Q TM was set to zero given its dependence on H À2 (H = magnetic field). [64] We fixed the energy barrier to the theoretically expected value of 2D using the experimentally obtained D (224 K (156 cm À1 ), 170 K(118 cm À1 )and 273 K(190 cm À1 )for [Co(1-3)](ClO 4 ) 2 ,r espectively;a ll parameters obtained from the fitting are summarized in Table 1). Fors uch large zero-field splittings,t he D-values derived from dc magnetic measurements are quite reliable,r esulting in reasonable fits of the data, with minimal contribution from the Orbach process ( Figure S32). Thedirect process was considered in the fitting, due to the dependence of the direct coupling between the j+ 3/2i and j À3/2i states to H 4 . [64,65] Theexponent of the Raman mechanism n was set as fit parameter and values in the range from 2.9-4.0 were obtained;even though n = 9ispredicted for Kramers doublets in extended lattices whose dynamics are well described by the Debye model, much lower values have been reported for molecular compounds [57,66,67] due to the importance of optical phonons (essentially molecular vibrations) to the relaxation process. [68] Fixing n = 9did not lead to satisfactory fits of the data.
To understand the origin of the variation in D and hence energy barrier to relaxation in complexes [Co(1-3)](ClO 4 ) 2 , calculations using the experimental geometries from SCXRD data yielded the splitting of the d-orbital energy levels ( Figure 5). Energy levels were determined using state average CASSCF,i mplemented in Orca, [69] taking into account relativistic and SOC effects with an active space considering 7e lectrons and 5r oots in the state averaging (SA-5-CASSCF [7,5]). [70] To probe the role of the rotaxane framework in determining D,w eo ptimized the simplified model of the axle and macrocycle fragment common to the three molecules (Figure 5A). The D term obtained for this moiety is À93.9 cm À1 , al arge negative value close to the experimental value for [Co(1-3)](ClO 4 ) 2 .W ef urther simplified the model to reflect ap urely conformational constraint;t he rotaxane framework was replaced by NH 3 ligands (and one molecule of H 2 Ointhe case of 3), with the ligand-metal distances and related angles constrained to those obtained by SCXRD.U nsurprisingly, given the equivalent symmetry of their primary coordination sphere (Figure 1), all three complexes exhibit similar d-orbital splittings ( Figure 5). Comparable splitting diagrams have been reported for other distorted sbpy and elongated octahedral Co II complexes that display large and negative D values. [32,36,53,71] Thec alculated zero-field splittings for these SCXRD-derived models are in excellent agreement with experiments (Table 1) (Table 1). These calculations show that the rotaxane framework itself is not directly relevant in determining D,b ut rather serves to impose ageometrically constrained environment on the metal ion.
Computational modelling allows the differences observed experimentally between the complexes to be rationalized. Large negative values of D can be obtained due to the presence of significant SOC-induced mixing of low-lying excited states with the ground state.T his is because the D tensor terms (D kl )d epend on the matrix elements of the angular momentum operator,the effective SOCs x ðÞand the energy gap between the first excited state (Q 1 )and the ground state (Q 0 )with D kl / À x 2 EðQ 1 ÞÀEðQ 0 Þ . [60,71] Our calculations show that the transition from Q 0 to Q 1 represents the largest contribution to D for all complexes.W ith relatively similar SOC average matrix elements between Q 1 and Q 0 of 325, 305 and 295 cm À1 and considerably different Q 1 -Q 0 energy gaps (obtained with NEVPT2) of 790, 1169 and 415 cm À1 for [Co(1-3)](ClO 4 ) 2, respectively,i ti se vident that the latter largely determines D. Further analysis illustrates how the geometrical restrictions enforced by the rotaxane scaffold influences the electronic properties of the metal ion and so modulate D.
Forthe three complexes,Q 0 is highly multiconfigurational (see the Supporting Information), the electronic configuration shown in Figure 5 (2)](ClO 4 ) 2 is due to ar elatively large contribution of 20 %f rom the lowest energy configuration to Q 1 for the former in contrast with only 7% for the latter. Forc omplex [Co(3)](ClO 4 ) 2, the N-Co-N angles are closer to 908 8 and the d xy orbital does not significantly overlap with any of the Co À N bonds ( Figure 5). Consequently,the d xy orbital is more stable in [Co(3)](ClO 4 ) 2 resulting in as ignificantly smaller Q 1 -Q 0 gap and amore negative D term.
Our calculations reveal the interplay between the geometry of the frameworks and the electronic structure in tuning the D value.F or rotaxanes with similar SOCs,i mposing geometrical constrains to control the stability of the d xy orbital could be an effective strategy to tune the value of D.

Conclusion
Ther esults presented support the proposal that interlocked molecules can provide al igand platform for the development of SIMs and that computational modelling can be used to direct this process.A lthough hybrid organicinorganic rotaxanes have been proposed as qubits, [72] Table S4) that exhibit SIM behaviour, such as bis(imino)pyridine pincer cobalt complexes [52] (D = À28 cm À1 )a nd [Co(phen)(DMSO)Cl 2 ] [73] (D %À17 cm À1 ). Although [Co(1-3)](ClO 4 ) 2 all exhibited slow relaxation of the magnetization in the presence of am agnetic field, there is clearly room for improvement in tuning the structures to achieve SIM behaviour at higher temperature and in the absence of amagnetic field.
We have shown that the zero-field splittings may be predicted computationally with reasonable accuracy even using de novo models,thanks to the predictable coordination environment provided by the mechanical bond. Magnetostructural correlations with computational methods previously revealed that the size of D may be tuned through structural changes in [Co II (tbta)N 3 ] + complexes by varying the Lewis basicity of the axial ligand on the N 3 À site. [60] Fort he Co II rotaxane-based complexes presented here,o ur calculations suggest anew strategy to tune D,based on the control of the intramolecular angles that determine the stability and population of (in this case) the d xy orbital. We have shown that the HS-LS energy gap may be estimated even using simple DFT de novo models,although it should be noted that higher levels of theory are required to determine D in these complexes exhibiting multiconfigurational ground states.U sing CASSCF,g ood agreement between calculated and experimentally obtained D values could be reached with the SCXRD-derived truncated models,d emonstrating that the enforced coordination geometry is more important than the exact chemical structure of the ligands.A sw eh ave recently demonstrated, [22] the mechanical bond can enforce unusual coordination environments,s uggesting there is scope for further ligand engineering.W ea re now investigating interlocked SIMs with larger total spin values and no nuclear spin to eliminate hyperfine coupling and so improve their efficiency.