Cycloheptatrienyl trianion: an elusive bridge in the search of exchange coupled dinuclear organolanthanide single-molecule magnets† †Electronic supplementary information (ESI) available: Full synthetic details, crystallography, magnetic properties measurements, and ab initio details. CCDC 1454168–14

Lanthanide inverse sandwich compounds of the cycloheptatrienyl trianion give rise to ferromagnetic exchange and slow relaxation of the magnetisation.


Introduction
The use of h-cyclopentadienyl (h 5 -C 5 R 5 ), h-arene (h 6 -C 6 R 6 ) and h-cyclooctatetraenyl (h 8 -C 8 R 8 ) ligands in the synthesis of organolanthanide complexes is widespread. These complexes have been extensively studied for their unique physical properties arising from their core 4f orbitals. While the cycloheptatrienyl trianion was rst spectroscopically characterised by Bates et al. in 1977; 1 only a single example of a h 7 -C 7 R 7 lanthanide complex is known. 2 There are only four reported examples of the isolation of f-element compounds with h-cycloheptatrienyl, [2][3][4] and only two of those reports describe their use in dinuclear systems. 2,4 The limited exploration of such species resides in the difficulty of the synthetic preparation and isolation of the elusive 10p-electron 7-membered ring with f-elements (Chart 1).
The amplied interest in the isolation of dinuclear lanthanide complexes with different bridging motifs arises from the ability to probe magnetic communication between metal ions, as they represent the most fundamental unit with which to study magnetic exchange interactions. Some of these reported molecules exhibit slow relaxation of magnetisation below their blocking temperature; these molecules are termed Single-Molecule Magnets (SMMs). [5][6][7][8][9][10][11] Since the discovery of the rst organometallic SMMs in 2010, 12 several complexes have been reported to exhibit this nanomagnetic behavior. [13][14][15][16][17] Most of the examples described are mononuclear compounds, however, the study of dinuclear systems is of the utmost importance when we consider the technological requirements of the future. In regard to SMMs, these include increasing the total spin of molecular magnets through expanding the number of paramagnetic centres. While many different bridging systems exist, 14,18,19 few examples have demonstrated the importance of planar aromatic organometallic ligands towards garnering favourable magnetic interactions. [20][21][22] These systems are an appealing design strategy as they may be employed as building blocks to generate higher nuclearity compounds, while they are more notably effective in harnessing the inherent magnetic anisotropy of 4f and 5f ions. 13,[15][16][17]23,24 Our recent reports with cyclooctatetraenyl 20,21 and arene-bridged 22 systems shows that a weak, yet non-negligible, interaction can be observed with coupling constants between Gd III ions of À0.644 cm À1 and À0.488 cm À1 respectively, utilizing the isotropic spin Hamiltonian (H ¼ À2JS a S b , S a ¼ S b ¼ 7/2) for each system respectively. Herein, the role of the 7-membered cycloheptatrienyl ring in the magnetic exchange between lanthanide ions will be examined and compared with its counterparts, the 6-and 8-membered rings (Chart 1). We investigate how subtle structural differences in a family of rare inverse sandwich compounds inuence the overall magnetic properties and clearly demonstrate the signicance of the 7-membered ring on the bridging interactions and magnetic axiality. We report for the rst time Gd III , Dy III , and Er III compounds with the cycloheptatrienyl bridge. The synthesis, structure, and magnetic characterization of three isostructural dinuclear complexes, [KLn 2 (C 7 H 7 )(N(SiMe 3 ) 2 ) 4 ] (Ln ¼ Gd III (1), Dy III (2), Er III (3)) and one structurally analogous complex, [K(THF) 2 Er 2 (C 7 H 7 )(N(SiMe 3 ) 2 ) 4 ] (4) is presented.

Syntheses and structures
Since the rst report of the synthesis of a uranium cycloheptatrienyl sandwich complex in 1995, 3 there has been limited exploration into the isolation of other f-element complexes containing cycloheptatrienyl. However, other areas of chemistry, such as organic chemistry, have made use of the 6pelectron cycloheptatrienyl cation (the tropylium ion), 25 and there have been reports of the 10p-electron derivative in transition metal chemistry. 26 Thus, the preparation of the above mentioned complexes, 1-4, was carefully designed to result in the facile formation of the trianion through employing chemistry that is previously known for lanthanide ions. In particular, this chemistry involves the polarisation of C-H bonds, 27 and is further complemented by highly basic and sterically demanding ancillary ligands.
Inspired by the work of Arliguie et al., 4 who had utilized borohydride chemistry towards the isolation of an f-element h 7 -C 7 H 7 complex, we attempted to utilize lanthanide borohydrides to support the inverse sandwich architecture. However, due to the highly reactive/reducing nature of the borohydrides and the non-innocent character of the cycloheptadienide ligand, the isolation of such systems proved to be difficult. In order to combat the aforementioned issue, we employed bis-(trimethylsilyl) amido ancillary ligands and have since prepared a series of dinuclear complexes of Ln ¼ Dy III , Gd III , Er III (Scheme 1). The synthesis of Ln III [N(SiMe 3 ) 2 ] 3 was rst reported by Bradley et al., 28,29 and has since been revisited in order to investigate the SMM properties of the complexes, which arise from their distinctive crystal eld. 30 Conversely, the sevenmembered bridging motif may be prepared from the commercially available 1,4-cycloheptadiene, where upon a one-electron reduction with potassium metal in the presence of Et 3 N, cycloheptadienide (C 7 H 9 À ) (Scheme 1) is afforded. The salt, KC 7 H 9 , remains stable for several days under inert conditions at À35 C. Solutions of lanthanide tris(bis(trimethylsilyl) amido) and potassium cycloheptadienide are combined at À35 C in toluene and warmed to room temperature gradually. Further reduction of the cycloheptadienide to the aromatic trianion, cycloheptatrienyl, is supported by a mechanism previously reported by Miller and Dekock. 27 Initial coordination of the Ln III ion results in polarisation of the methylene C-H bond and subsequent proton abstraction by a strong base. Interestingly, it was rst postulated that the highly basic nature of the C 7 H 9 À may be responsible for this abstraction, resulting in the formation of 1,4-and 1,3-isomers of cycloheptadiene. However, in this case, the loss of an amido ligand from each of the bridging Ln III ions may suggest that abstraction occurs via the amido, thus inducing the generation of soluble HN(SiMe 3 ) 2 species. The presence of such species was observed in the crude 1 H NMR of compound 3 as a singlet at 0.1 ppm in toluene-d 8 at 298 K, further supporting this hypothesis.
Nevertheless, collection of the ltrate followed by treatment with toluene and hexanes yields compounds 1-3. Conversely, the solvated derivative, compound 4, can be obtained from 3 via extraction into THF (Fig. 1), resulting in the coordination of two molecules of THF to the bound potassium ion, and thereby limiting intermolecular interactions. X-ray quality crystals of 4 were isolated from the subsequent treatment with a toluene/hexanes mixture, conrming the nature of the solvated species.
Single-crystal X-ray diffraction (SCXRD) studies reveal that compounds 1-3 are isostructural and crystallize in the monoclinic space group P2 1 /n. On the other hand, the analogous compound 4 crystallizes in the monoclinic space group C2/c. The structure of the Er III analogue, 3, will be the representative structure described herein (Fig. 1, top). The molecular structure of 3 reveals an inverse cycloheptatrienyl sandwich complex. The dinuclear compound is composed of two Er III ions bridged by the 10p-electron cycloheptatrienyl C 7 H 7 3À trianion in a h 7 -bound fashion, with an Er-C bond distance range of 2.484(8)-2.629(9) A. The remaining coordination environment is occupied by two [N(SiMe 3 ) 2 ] À ligands. Interestingly, one K ion is bound to one side of the molecule via N atoms (N3, N4) from the [N(SiMe 3 ) 2 ] À ligands, thus making this dinuclear unit unsymmetrical. Due to this binding conguration, the N3/ Er2/N4 angle of 98.6(2) is much smaller than the N1/Er1/ N2 angle of 105.7 (2) . It is noteworthy that in the case of 4, due to crystal packing effects the symmetry of the molecule is slightly higher than in 3.
Close inspection of the packing arrangement of 3 reveals a close contact between the K ion and a carbon atom (C14) from the [N(SiMe 3 ) 2 ] À , which subsequently promotes a linear chainlike arrangement of the molecules (Fig. S4 †). Interestingly, in the case of compound 4 we still observe a head-to-tail packing arrangement generating a chain-like array, however, there are no close contacts that exist beyond H-H interactions (Fig. S5 †). 31 In regard to compound 3, the intramolecular Er-Er distance of 3.9580(7) A is slightly shorter than the distance observed in a COT 00 (1,4-bis(trimethylsilyl)cyclooctatetraenyl dianion) bridged Er 2 dimer (4.1109(5) A) or an arene bridged Er 2 compound (4.067(1) A). 21,22 A similar Sm 2 inverse sandwich analogue was reported with a bridging COT and terminal [N(SiMe 3 ) 2 ] À ligands with a Sm-Sm distance of 4.308(1) A. 32 However, the larger distance in the case of the Sm example is primarily due to the larger ionic radii of the Sm III ion. Finally, it is noteworthy that the Nd III analogue of the reported example exhibits a Nd-Nd distance of 4.213(3) A, this is presumably a result of the electron rich borohydride ancillary ligands, which allow for increased electron donation to the electropositive Nd III ions. 2 The central cycloheptatrienyl ligand adopts a planar geometry, owing to its 10p-electron aromatic conguration, with the largest atom deviation being 0.06 A out of the plane formed by the seven C atoms. The high charge (À3) and planarity of the bridging ligand, along with the close proximity of Er III ions, is expected to lead to non-negligible magnetic interactions via the delocalised p-orbitals of the cycloheptatrienyl ligand. Therefore, this molecule represents an ideal candidate to probe the exchange interactions between metal ions, while also studying the ligand eld effects of the bridging unit in comparison with its COT and arene counterparts.

Static magnetic properties
Direct current (dc) and alternating current (ac) magnetic susceptibility measurements were performed using a SQUID magnetometer on crushed crystalline samples of complexes 1-4, prepared under an inert atmosphere. Variable temperature magnetic susceptibility measurements under a 0.1 T applied eld in the temperature range of 1.9-300 K are shown in  the cT product remains constant down to 50 K, followed by a gradual decrease with temperature to reach a minimum value of 5.84 cm 3 K mol À1 at 1.9 K. This downturn of the cT product can be attributed to the intramolecular antiferromagnetic interactions between the spin carriers (4.0869(7) A). Owing to the isotropic nature of Gd III ions, the strength of interactions between the two lanthanide ions can be quantied. Application of the Van Vleck equation to the Kambe's vector coupling method was completed by using the isotropic spin Hamiltonian H ¼ À2JS a S b , with S a ¼ S b ¼ 7/2, which was used to t the variation of cT vs. T. The best-t yielded a J value of À0.134 cm À1 for compound 1. The obtained J value is rather weak as a consequence of the shielded f-orbitals of Gd III having minimal orbital overlap with the bridging ligand.
In comparison with the 6-and 8-membered rings, the obtained coupling constant for Gd III is slightly smaller, and unfortunately did not lead to a direct trend related to ring size and charge density. When considering both the dipolar and exchange contributions to the coupling, as determined by ab initio methods (vide infra), both components for the 7membered ring remain the smallest of any of the computed parameters. Perhaps an explanation for this lies within the ligand eld contributions from the ancillary ligands. This may be considered from a formal charge perspective, such that the cycloheptatrienyl bridge adopts a formal charge of À3, which, when distributed over seven atoms, is diluted to approximately À0.43 per C atom. Conversely, the charge distribution over the amido N atom remains highly concentrated. Thus the interaction with the amido ligands remains dominant (vide infra) compared to the donating ability of the bridging C 7 -moiety. This was further proven through our computational studies of the main magnetic axis and LoProp charges (vide infra). Lastly, the presence of the potassium ion prevents the Ln III ions from receiving equal electronic donation from the amido ancillary ligands, where the electron density of N3 and N4 would be split between Er2 and K1, thereby making Er2 less electron rich in comparison to Er1.
In the case of the anisotropic compounds 2-4, the cT prole differs signicantly from the Gd III analogue. For example, the cT product of compound 2 decreases very slowly from 300 K with temperature, followed by a more rapid decrease below 20 K to reach a minimum value of 23.15 cm 3 K mol À1 at 1.9 K. On the other hand, the cT product of compounds 3 and 4 exhibit a slightly different trend upon decreasing temperature. The cT products for compounds 3 and 4 decrease gradually from 300 K to minimum values below 15 K of 19.64 cm 3 K mol À1 and 20.53 cm 3 K mol À1 , respectively. This decrease in the cT product is followed by a rapid increase below 10 K to reach maximum values of 20.92 cm 3 K mol À1 and 22.58 cm 3 K mol À1 , respectively. The nal increase in the value of the cT product is attributed to intramolecular ferromagnetic interactions between the Er III ions. This will be further conrmed through ab initio calculations (vide infra).
As seen in Fig. S6-S9, † the eld dependence of the magnetisation measurements performed at low temperatures exhibit non-saturation, even at 7 T and 1.8 K, for all compounds. This can be attributed to weak intramolecular antiferromagnetic interactions between the Ln III ions, thereby making the low lying excited states accessible by applying a magnetic eld, even at the lowest measurable temperature of 1.8 K. This nding is further exemplied through our computational study, where the energies of the rst and second excited states are minimally separated from the ground state (vide infra). In the case of compounds 2-4 the presence of magnetic anisotropy is also likely to contribute to this lack of saturation in the magnetisation. Contrary to the COT 00 bridged counterparts, no hysteretic behaviour was observed down to 1.8 K and therefore alternating current (ac) magnetic susceptibility measurements were performed to investigate the potential SMM behaviour of the anisotropic compounds 2-4.

Dynamic magnetic properties
An ac eld of 3.78 Oe was utilized to probe the slow relaxation dynamics of compounds 2-4, however, no ac signal was observed at zero applied dc eld for all compounds. This is common for lanthanide systems with signicant quantum tunnelling of magnetisation (QTM). However this QTM can be minimised upon application of a static dc eld. As such, a frequency dependent signal was observed for all three compounds ( Fig. 3 and S10-S12 †) with the application of an optimised dc eld. With respect to compound 2, the application of an optimal dc eld of 2000 Oe allowed for the observation of a low frequency process below 4 K. The out-of-phase susceptibility of this processes exhibited minimal shiing in peak maxima with regards to frequency upon decreasing temperature. This type of behaviour may be indicative of a dominant QTM regime. This is not surprising due to the potential for low lying exchange coupled states, thereby enabling a shortcut in the energy barrier such that the rst excited exchange state lies only minimally above the ground state with a calculated energy of 1.9 Â 10 À5 cm À1 (vide infra Table 2). However, we cannot rule out the possibility of intermolecular interactions, as application of large static elds has been shown to propagate spin-spin interactions. 33,34 These types of interactions may lead to the formation of magnetic domains, consequently precluding the analysis from a molecular perspective. Due to these phenomena, an effective energy barrier for this process could not be extracted from this data set. Alternatively, a frequencydependent c 00 signal was observed under a static dc eld for 3 (Fig. 3b). The lack of overlapping peak maxima at low temperatures suggests that QTM is minimized with the application of an optimal static eld of 800 Oe.
Observation of the shiing of peak maxima to lower frequencies below 7 K demonstrates the presence of slow relaxation of magnetisation in 3, indicating eld-induced slow relaxation. From the c 00 data measured between 7 and 3 K, the Arrhenius law (s ¼ s 0 exp(U eff /kT)) was employed in order to extract an effective energy barrier of 58 K, and a pre-exponential factor of 2.9 Â 10 À8 s (Fig. S13 †). More notably, the frequency dependent behaviour is mostly likely attributed to single-ion properties, as the observation of a second relaxation process at high frequencies becomes evident below 3.75 K. Full analysis of this process could not be completed due to the frequency    limitations (0.1-1500 Hz) of the magnetometer. From a structural perspective, the observed single-ion behaviour of 3 is not surprising given the non-centrosymmetric nature of the molecule. Inequivalent metal ion sites have elicited dual relaxation processes at low temperatures in previous studies. [35][36][37][38][39][40][41] However, with respect to compound 3, this is easily visualized via the lack of an inversion centre within the molecule as a consequence of the coordinated potassium ion. The observed magnetic behaviour of 3 greatly contrasts with the results obtained for the Dy III analogue, 2, suggesting that the cycloheptatrienyl trianion, along with the [N(SiMe 3 ) 2 ] À ancillary ligands, provide a more suitable ligand eld for Er III ions. These ndings strongly correlate with our previous studies on COT 00 bridging ligands, where the zero eld energy barrier was improved upon from 25 K for the Dy III analogue to 306 K for Er III . 20,21 Additionally, we further exemplied that the ligand eld provided by the delocalised p-cloud promoted greater magnetic axiality in Er III ions over Dy III ions in single-ion sandwich complexes of COT. 42 While this remains true of the delocalised p-cloud and Er III ions in the present study, the effects of the amido ligands prove dominant over the cycloheptatrienyl, effectively generating greater magnetic axiality in 2 (vide infra). This is in accordance with previous studies, such that the axial orientation of highly charged negative donor atoms favour the oblate electron density of Dy III ions. [43][44][45][46][47][48] The out-of-phase magnetic susceptibility of 4 reveals two independent relaxation processes below 4 K, similar to compound 3 ( Fig. 3c and S11 †). Once again this is not surprising given the unsymmetrical nature of the complex. [35][36][37][38][39][40] In order to probe each of these processes, an optimal dc eld of 1000 Oe was used to elucidate the nature of the high frequency process, whereas an optimal eld of 2000 Oe was employed in the study of the low frequency process. Unfortunately, the nature of the collected data precluded the extraction of an energy barrier to spin reversal, however, it did prove fruitful in gaining a further understanding of the interactions occurring within this system. Interestingly, the low frequency processes exhibit similar characteristics to 2, where upon decreasing temperature, the resulting out-of-phase signal increases in intensity, but demonstrates little-to-no frequency dependent behaviour. Again, this is most likely a result of the low-lying excited exchange states, which promote QTM. Our computational studies (vide infra) elucidated a rst excited state energy of 7.7 Â 10 À5 cm À1 for compound 4 further supporting the nature of this process. Once more, it is worth noting that at large magnetic elds it becomes difficult to infer whether the observed properties are solely molecular in nature, due to the potential of induced spin-spin intermolecular interactions. 33,34 Nonetheless, the presence of the secondary relaxation process at higher frequencies exhibits a shiing peak maxima towards lower frequency upon decreasing temperature (Fig. 3c). Interestingly, this plot is characterised by decreasing susceptibility intensity for an iso-temperature curve with decreasing temperature. This type of behaviour has been similarly noted in Single-Chain Magnets (SCMs), where inter-chain spin-spin interactions give rise to decreasing susceptibility values. 49,50 Even under the optimal eld of 1000 Oe, there is a decrease in intensity of the peaks for the out-of-phase component (Fig. S11 †). While it is difficult to fully conclude the nature of the high frequency process, the preliminary data would suggest that the fundamental component relies on an intermolecularly driven process/relaxation. This nding may also explain the tails observed in the high frequency region of the out-of-phase susceptibility for compounds 2 and 3. In fact, it is not uncommon in lanthanide-based systems to observe a secondary process as a result of intermolecular interactions. 34,51-53 Further investigation into the frequency dependent ac susceptibility measurements as a function of dc eld for 2-4 (Fig. 4), reveal an unusual eld dependence in the second relaxation, such that the high frequency process appears to be augmented by weak static elds, this is likely a result of a direct relaxation process which is promoted by neighbouring spins 40,54 thus supporting the proposed intermolecularly driven relaxation process.

Ab initio studies
Ab initio calculations for 2-4 were performed in order to gain additional insight into the electronic and magnetic structures of these compounds. All calculations performed were CASSCF/ RASSI/SINGE_ANISO, 55 and employed SCXRD structural data. Electronic and magnetic properties of the individual Ln III sites were obtained through fragment ab initio calculations. The calculated structures have identical structures to those obtained for complexes 2-4, where the neighbouring lanthanide sites are computationally replaced by the diamagnetic Lu III . The CASSCF wavefunction includes all possible electron distributions within the 4f 9 (for Dy III ) and 4f 11 (for Er III ) shells only, while the remaining orbitals were kept doubly occupied. The orbitals and coefficients of the individual congurations were optimized self consistently for all electronic states arising from this denition of the active space. The spin-orbit interaction (described within the AMFI approximation) includes all optimized spin states for Er (3 and 4), while for 2 we could only mix a limited amount of states, namely 21 spin sextet, 128 spin quartet and 130 spin doublet states, which resulted in 898 spin-orbit levels. The obtained low-lying states, arising from the ground J ¼ 15/2 multiplet on individual Ln III sites, are provided in Table 1.
Structural features determining the orientation of local magnetic axes on Ln III sites. As can be observed in Table 1, the g tensors in the ground Kramers doublet states of the individual sites in compounds 2-4 are relatively axial in nature (g X,Y ( g Z ).
The axiality of the ground doublet states are also related to the axiality of the crystal eld acting on the Ln III sites. For the Dy III sites, the main anisotropy axis is oriented in the plane of the N-Dy-N atoms (Table 1) almost parallel to the N-N direction (Fig. 5b). This orientation is related to the much stronger crystal eld effect arising from the N atoms. In particular, the calculated LoProp charges 56 on N atoms (À1.28) are the largest among all neighbouring atoms of the Ln III sites. The covalent ligand eld effect arising from the N atoms is also dominant among all neighbouring atoms. This is revealed by the Dy-N bonds, which are the shortest formed by the lanthanide sites in this environment. In this respect, the role of the central ring in the local axiality of the Dy III sites is diminished, and is in fact rather destructive as compared to the ligand eld imposed by amido groups. In the case where the central ring and the neighbouring Ln III site were absent, the magnetic axiality on one Dy III site would be signicantly stronger. These ndings were not surprising given that recent reports have demonstrated the signicant impact of highly anionic donor ligands in linearlike coordination geometries, with which such compounds should theoretically yield staggering energy barrier values. [44][45][46][47] In stark contrast to the ndings for Dy III , signicantly different orientations for the ground state magnetic anisotropies were observed for the Er III sites in compounds 3 and 4 (Table 1, Fig. 5a). For these compounds, the main magnetic axes are oriented almost perpendicular to the N-Er-N planes. This drastic change in the orientations of the main magnetic axes between Dy III and Er III atoms in a very similar axial ligand eld is due to the opposite signs of the Stevens parameters, a and b, which are related to the second and fourth rank operators of the ground ionic J ¼ 15/2 multiplet for Dy III and Er III . 57 This is seen from the fact that the anisotropy of the highest (8 th ) Kramers doublet of the Dy III sites (which are greatly destabilized due to the crystal eld) is in fact almost parallel to the anisotropy of the ground doublet for the Er III ion in the same crystal eld, thus demonstrating the complementary nature of Dy III and Er III ions. This effect was previously observed in the case of [Er(COT) 2 ] À and [Dy(COT) 2 ] À anions. 42 Similar arrangements of the local magnetic axes were revealed with the previously studied Er 2 C 6 (h 6 -C 6 R 6 ) compounds. 22 Parameters of the ab initio calculated crystal eld for the investigated Ln sites in 2-4 are given in Table S2. † Exchange interaction in 2-4. The above reported ab initio results for separate Ln III sites in 2-4 were further employed in the computation of the exchange spectrum and magnetic properties of the dinuclear complexes using the POLY_ANISO program. 58,59 In this approach, the exchange interaction between magnetic sites is considered within the Lines model, 60 describing the exchange interaction between the localized spins in the absence of the spin-orbit interaction on sites by one parameter for the interacting metal pair. By explicitly considering the spin-orbit interaction on metal sites, the Lines model leads to an exchange matrix, which effectively describes the anisotropic exchange interaction between sites. In particular, the contribution of the intramolecular dipole-dipole magnetic coupling is accounted for exactly, because all of the necessary data are made available through the ab initio calculations. On the basis of the resulting exchange spectrum of the entire system, all macroscopic magnetic properties were computed. The total magnetic interaction (exchange + dipolar) between the lowest Kramers doublets on lanthanide sites can be cast in a good approximation by the non-collinear Ising Hamiltonian: where J exch and J dip are parameters of the exchange and dipolar couplings respectively, whileŝ 1z ¼ 1/2 is the pseudospin of the ground states of the metal sites. Best-t exchange parameters, J exch , and the calculated parameters of the dipolar magnetic coupling, J dip , for the investigated compounds, alongside the resulting exchange spectra are given in Table 2. An alternative approach for the estimation of the exchange coupling parameters in di-and poly-nuclear compounds is given by the broken-symmetry density functional theory approach (BS-DFT). 61 Unfortunately, the BS-DFT approach is not directly applicable for most of the lanthanides given the multicongurational nature of their ground states and their near-degenerate status as a result of weak crystal eld effects. However, an estimation of the exchange in lanthanide-containing compounds is still achievable from the BS-DFT calculations. To this end, the "isotropic" closest metals computationally replace the "anisotropic" metal sites of the investigated compounds, while the ligand framework is kept intact. BS-DFT calculations are performed straightforwardly for the "isotropic" equivalent of the investigated compound. The extracted J iso parameter has to be later rescaled to reect the exchange Hamiltonian between the true spins of the original "anisotropic" metal sites. This method was employed with reasonable success in several previous studies. 63 For the present compounds, the estimated exchange parameters from the BS-DFT studies are ferromagnetic 1.14 cm À1 for 2, 2.45 cm À1 for 3 and 3.16 cm À1 for 4, correlating reasonably with the ferromagnetic exchange values obtained within the Lines model (Table 2). A comparison between the calculated and measured magnetic susceptibilities is depicted in Fig. 2. We notice a clear reduction in the dipolar magnetic coupling values for 2-4 with respect to our previously investigated dinuclear compounds containing a 6-membered bridging moiety. 22 The reduction of J dip is attributed to the different relative orientations of the local magnetic axes of the two Ln III sites, imposed by the different dihedral angles between the N-Ln-N planes. Thus, by controlling this angle through synthetic means we could, in principle, modify the magnetic dipolar interaction (and possibly the exchange) in such compounds. Through this study, we attempted to computationally assess the role of the dihedral angle between N-Ln-N planes in the dinuclear model systems 2-4, as well as the role of the bridging ligand, in the magnetic behaviour as compared to those with 6and 8-membered bridging rings. The results show that the dihedral angle in all three cases is very similar, while the Ln-Ln distance decreases with increasing bridging ring size. We conclude, therefore, that the bulky ancillary ligands (i.e. [N(SiMe 3 ) 2 ] À ligands), and the resulting crystalline packing, are the factors responsible for dening the relative orientations of the local anisotropy axes and dipolar magnetic interaction in this series of compounds.

Conclusions
Compounds 1-4 represent the rst examples of SMMs based on the cycloheptatrienyl trianion ligand. The synthetic route to achieve the aforementioned compounds has been carefully designed to yield the facile formation of the trianion, taking advantage of sterically demanding and highly basic ancillary ligands. When combined with lanthanide ions, this type of bridging motif generates a weak, yet non-negligible, magnetic coupling constant of J ¼ À0.134 cm À1 for the isotropic analogue. Through computational modelling of the anisotropic compounds, we elucidated that exchange coupling is more signicant than dipolar coupling, with the largest J exch being +3.149 cm À1 for compound 4, thereby demonstrating the desirable effects of the 7-membered bridging moiety in generating exchange coupled dinuclear lanthanide systems. This is an area of signicant modern interest in quantum physics, where mediating the interaction of two metal centres via tuning the redox properties of the bridging motif is a method to induce signicant quantum communication. 64,65 Moreover, the incorporation and measurement of these materials in molecular spintronics devices are oen limited to the millikelvin regime, 66 where the surface effects of such materials is only beginning to be better understood. 62 Hence, increasing the energy barrier to spin reversal of SMMs will relax the rigorous experimental requirements for studying these systems. Thus, the current high-energy barriers associated with 4f ions, attributed to single-ion behaviour, will not be sufficient. It is vital that we look for more creative ways to induce signicant interactions between lanthanide ions.