Key Role of Size and Electronic Configuration on the Sign and Strength of the Magnetic Coupling in a Series of Cu 2 Ln Trimers ( Ln = Ce , Gd , Tb , Dy and Er )

Five new trinuclear complexes with formula [(CuLα ́Me)2Ce(NO3)3] (1) and [(CuLα ́Me)2Ln(H2O)(NO3)2](NO3) ̈ 2(CH3OH) (Ln = Gd(2), Tb(3), Dy(4) and Er(5)) have been synthesized using the bidentate N2O2 donor metalloligand [CuLα ́Me] (H2Lα ́Me = N,N1-bis(α-methylsalicylidene)-1,3-propanediamine) and structurally characterized. In the case of compound 1, the larger ionic radius of Ce(III) leads to a neutral trinuclear complex with an asymmetric CeO10 tetradecahedron coordination geometry formed by four oxygen atoms from two (CuLα ́Me) units and three bidentate NO3 ́ ligands. In contrast, the isomorphic complexes 2–5, with smaller Ln(III) ions, give rise to monocationic trinuclear complexes with a non-coordinated nitrate as a counter ion. In these complexes, the Ln(III) ions show a LnO9 tricapped trigonal prismatic coordination geometry with C2 symmetry formed by four oxygen atoms from two (CuLα ́Me) units, two bidentate NO3 ́ ligands and a water molecule. The magnetic properties show the presence of weak antiferromagnetic interactions in 1 and weak ferromagnetic interactions in 2–5. The fit of the magnetic properties of compounds 2–5 to a simple isotropic-exchange symmetric trimer model, including the anisotropy of the Ln(III) ions, shows that in all cases the Cu-Ln magnetic coupling is weak (JCu-Ln = 1.81, 1.27, 0.88 and 0.31 cm ́1 for 2–5, respectively) and linearly decreases as the number of unpaired f electrons of the Ln(III) decreases. The value found in compound 2 nicely fits with the previously established correlation between the dihedral Cu–O–O–Gd angle and the J value.


Introduction
Lanthanide ions have attracted enormous interest in molecular magnetism during the last few years [1][2][3][4].They are often combined with 3d metal ions or other magnetic centers [5][6][7] to create a large ground spin state (S) and uniaxial anisotropy (D) that play an essential role in creating magnetic bi-stability and related memory effects in single-molecule magnets (SMMs) and single-chain magnets (SCMs) [8][9][10][11].An advantage of 3d-4f coordination clusters is the possibility of obtaining high coercitivity in SMMs, since the exchange interaction serves as an internal bias field that suppresses quantum tunnelling of the magnetization [12][13][14][15][16][17].Thus, notable SMM behaviours have been recently observed without any applied bias field for 3d-4f complexes with relatively high energy barriers for the reversal of the magnetization (U eff ) [15][16][17].Therefore, the exchange coupling between 3d and 4f centres has become a matter of potential relevance in the design of lanthanide-based SMMs or SCMs.The determination of the coupling constant of 3d-4f magnetic exchange from the theoretical fitting of susceptibility measurements is usually done with Gd(III) due to its isotropic nature [18][19][20][21][22]. On the other hand, the presence of large first order spin-orbit coupling of the f-shell electrons in other lanthanides makes it very hard to explain their susceptibility data theoretically [23][24][25].Hence, the determination of magnetic coupling constants of 3d-4f (other than Gd(III)) from susceptibility data is rather challenging unless other techniques are used [16,[26][27][28][29].
The coupling constants between 3d and 4f metal ions were determined first for a bis(diphenoxido) bridged Cu 2 Gd trinuclear family of complexes about three decades ago [18].The complexes were obtained by reacting a bidantate [CuL] metalloligand derived from a salen type N 2 O 2 Schiff base ligand (H 2 L) with various Gd(III)-salts [30][31][32][33][34].This study raised an enormous interest in the field of 3d-4f coordination complexes and subsequently various types of 3d-4f complexes were prepared and studied [2,[35][36][37].However, since then, only a few reports on this particular trinuclear family of complexes have been published [30][31][32][33][34]. Literature shows that only four [CuL] metalloligands ([CuL 1 ], [CuL 2 ], [CuL 3 ] and [CuL 4 ] of Scheme 1) along with the lanthanides Ce(III), Eu(III), Gd(III) and Dy(III) were used for the synthesis of such trinuclear species.Very recently, we determined the structure and evaluated the SMM properties of the Tb III complexes of this long known but less investigated family of complexes [(CuL) 2 Ln(X) n ] (X = uninegative anion) [38].Also, these complexes have been proven to be very flexible and can take on either cisoid or transoid orientations, controlled by reaction conditions [38,39].In this present endeavour, the α-methylated N 2 O 2 metalloligand [CuL α´Me ] (H 2 L α´Me = N,N 1 -bis(α-methylsalicylidene)-1,3-propanediamine, Scheme 1) has been used for the first time to synthesize a series of [(CuL α´Me ) 2 Ln(X) n ] complexes (Ln = Ce(III), Gd(III), Tb(III), Dy(III) and Er(III)).Structural characterization reveals that unlike their non-α-methylated analogous metalloligands (which form both cisoid and transoid complexes) they only form transoid coordination complexes under similar crystallization conditions [38,39].The nature and magnitude of the coupling constants of the magnetic exchange between the Cu(II) and Ln(III) centers of these complexes are determined from the fits of variable temperature magnetic susceptibility and isothermal magnetisation measurements, and a magneto-structural correlation is drawn.This is only the second instance where the fitting of the magnetic susceptibility of trimeric Cu 2 Ln complexes (Ln = Tb, Dy and Er) has been performed.

Syntheses and Spectroscopic Characterizations of the Complexes
In previous studies, we have synthesized some trinuclear [{(CuL) 2 M 1 }X n ] complexes using [CuL] and [CuL α´Me ] as metalloligands (where, M´are different s-, p-and d-block elements).These studies established that the α-methylation on the N 2 O 2 donor Schiff base ligand has a key role in determining the structures of the resulting compounds [40][41][42][43][44][45][46].However, such studies have not been performed with lanthanide-containing trinuclear coordination clusters for these complexes.Recently, we reported some trinuclear [{(CuL 3 ) 2 Ln}X n ] complexes (H 2 L 3 = N,N 1 -bis(salicylidene)-1,3-propanediamine, Scheme 1, Ln = Tb, Dy) [38,39].In the present endeavour, we have used [CuL α´Me ] as a metalloligand and we have reacted it with a series of lanthanides nitrates (Ce, Gd, Tb, Dy and Er) in a 2:1 ratio following the same procedures already used by us for the [CuL 3 ] metalloligand [38,39].This study will allow us to evaluate any structural change that might occur due to α-methylation.As expected, we have isolated the trinuclear Cu 2 Ln complexes for all the used lanthanides, indicating that these lanthanides can accommodate two [CuL α´Me ] metalloligands around themselves irrespective of their size.Moreover, unlike the previously reported [{(CuL 3 ) 2 Tb}X n ] complex, which is cisoid, in these complexes the relative orientation of the two [CuL α´Me ] around the central Ln(III) ions is always transoid.

Description of the Structures
The molecular structure of complexes 1 and 2 along with the partial atomic numbering scheme is shown in Figures 1 and 2 respectively.The detailed crystallographic and structural parameters are given in Table 1 and Table S1.Complexes 2-5 are isomorphs, differing only in the central Ln atom.Therefore, here we describe only the structure of compound 2. The structures of compounds 3-5 are shown in Figures S1-S3, Supplementary Information respectively.7) distances of 2.709(4) and 2.489(3) Å, respectively.The Addison parameter (τ 5 ) amounts to 0.177 and 0.058 for Cu (1) and Cu(2), respectively, confirming the slightly distorted square-pyramidal geometry for the copper(II) ions (τ 5 is 0 for a perfect square pyramid, whereas it has a value of 1 for a trigonalbipyramid) [50].The r.m.s.deviations of the four basal donor atoms from the mean planes are 0.217 (7) and 0.140(5) Å for Cu (1) and Cu(2), respectively, with the metal atoms located at 0.077(1) and 0.024(1) Å away from the plane, towards the axial O(13) and O(7) atoms, respectively.
It is also to be noted that in presence of the coordinating anion nitrate, the larger lanthanide ions accommodate two [CuL 1 ] (or [CuL 2 ]) metalloligands, whereas the smaller lanthanide ions coordinate only to one metalloligand, presumably to avoid steric hindrance around the smaller Ln(III) ions [32,33].However, in the present study, the flexibility of the [CuL α´Me ] metalloligand allows it to re-orientate around the Ln(III) ion, irrespective of its ionic radius, to form the less sterically hindered trinuclear transoid cluster [30,31,34].On the other hand, in these complexes, the coordination number of the Ln(III) is nine except for the largest Ce(III) ion where it is ten, indicating that from Gd (2) to Er (5) ionic radius of the central lanthanide used in the present study has little influence on the coordination number and the coordination geometry of the trinuclear Cu 2 Ln complexes.

Magnetic Properties
The thermal variation of the molar magnetic susceptibility per Cu 2 Ce trimer times the temperature (χ m T) for compound 1 shows, at room temperature, a value of ca.1.6 cm 3 K¨mol ´1, close to the expected one for two isolated Cu(II) S = 1/2 ions (0.75 cm 3 K¨mol ´1 with g = 2) plus one Ce(III) ion (0.80 cm 3 K¨mol ´1 with g J = 6/7) (Figure 3).When the sample is cooled the χ m T value initially exhibits a smooth decrease down to ca. 10 K and a more abrupt decrease at lower temperatures.Unfortunately, all the attempts to fit the magnetic data with a simple model (in order to reduce the number of adjustable parameters) failed, probably due to the larger anisotropy of the Ce(III) ion resulting from the different coordination number and environment of compound 1 when compared with compounds 2-5 (see below).Compound 2 shows, at room temperature, a χ m T value of ca.8.7 cm 3 K¨mol ´1 per Cu 2 Gd trimer, close to the expected one for two Cu(II) ions (0.75 cm 3 K¨mol ´1) plus one Gd(III) ion (7.88 cm 3 K mol ´1; S = 7/2) with g J = 2.When the sample is cooled the χ m T value remains constant down to ca.50 K and then gradually increases to reach a maximum of ca.11.9 cm 3 K¨mol ´1 at ca. 3.5 K. Below this temperature, χ m T shows a sharp decrease and reaches a value of 11.7 cm 3 K¨mol ´1 at 2 K (Figure 4).This behaviour suggests the presence of a predominant ferromagnetic Cu-Gd interaction and, accordingly, we have fitted the magnetic properties to a symmetrical Cu-Gd-Cu trimer model including two equal isotropic interactions and a zero field splitting term to reproduce the decrease at very low temperatures.In order to reduce the number of adjustable parameters, we have fixed g = 2.0 for the Gd(III) ion.This model reproduces very well the magnetic properties of compound 2 (both χ m T, in the whole temperature range, and the isothermal magnetization at 2 K, (Figure 4) with the following set of parameters: g Cu = 2.036, J Cu-Gd = 1.81 cm ´1, D = 0.00 cm ´1 and a tip of 1.0 ˆ10 ´3 cm 3 mol ´1 (Table 2, solid lines in Figure 4).11.82 (J = 6), 14.17 (J = 15/2) and 11.48 (J = 15/2) cm 3 K¨mol ´1, respectively) with g J = 3/2, 4/3 or 6/5 for 3-5, respectively.When the temperature is lowered, the χ m T value shows a progressive increase and reaches maxima of ca.13.8, 17.6 and 16.0 cm 3 K¨mol ´1 at ca. 5, 9 and 3 K for 3-5, respectively.Below these temperatures, χ m T shows a sharp decrease in compounds 3 and 4 reaching values of 12.7 and 14.9 cm 3 K mol ´1 at 2 K, respectively.In compound 5, χ m T remains constant from 3 to 2 K. (Figures 5-7).These behaviours suggest the presence of predominant ferromagnetic Cu-Ln interactions in the three compounds and, accordingly, we have fitted the magnetic properties to a symmetrical Cu-Ln-Cu trimer model (Ln = Tb, Dy or Er), including two equal isotropic interactions and a zero field splitting term to reproduce the decrease at very low temperatures.In order to reduce the number of adjustable parameters, we have fixed g = 3/2, 4/3 or 6/5 for the Tb(III), Dy(III) and Er(III) ions, respectively.This model reproduces very well the magnetic properties of the three compounds in the whole temperature range with the following set of parameters: g Cu = 1.990,J Cu-Tb = 1.27 cm ´1, |D| = 2.0 cm ´1 and a tip of 0.6 ˆ10 ´3cm 3 mol ´1 for 3, (Table 2, solid line in Figure 5), g Cu = 1.991,J Cu-Dy = 0.88 cm ´1 and |D| = 5.1 cm ´1 (Table 2, solid line in Figure 6) for 4 and g Cu = 2.132, J Cu-Er = 0.31 cm ´1 and |D| = 1.4 cm ´1 (Table 2, solid line in Figure 7) for 5.
A confirmation of the weak magnetic couplings found in compounds 1-5 is provided by the isothermal magnetizations at 2 K that show saturation values of ca.2.0, 9.0, 8.5, 9.0 and 7.0 µB for 1-5, respectively (Figure S4, Supplementary Information).
Since compounds 2-5 present ferromagnetic Cu-Ln interactions we have measured these compounds with AC susceptibility in the low temperature range in order to check for the presence of slow relaxation of the magnetization at low temperatures.These measurements show in all cases the absence of an out-of-phase signal at any frequency, indicating the absence of any slow relaxation process above 2 K in these compounds (Figure S5, Supplementary Information).

Magneto-Structural Correlations
The different behaviour found between compound 1 and the other four compounds (2-5) can be easily rationalized from the structural data that show that compound 1 presents a slightly different coordination environment for the Ln ion.Thus, the Ce ion presents a coordination number of ten with three bidentante NO 3 ´anions and two double phenoxido bridges with Cu(II), whereas in the other four compounds (2)(3)(4)(5) the Ln ions contain a water molecule instead of one bidentate NO 3 ´ligand, resulting in a coordination number of nine (see above).This difference has to be attributed to the larger size of Ce(III) (128.3 pm for 8-coordinate) compared with the other four ions (119.3,118.0, 116.7 and 114.4 pm for the 8-coordinate Ln(III) in 2-5, respectively).As a result of this different coordination number, there are important differences in the structural parameters of the double phenoxido bridges between compound 1 and the other four compounds (see Table 3), leading to the observed differences in the sign of the magnetic coupling.As can be observed in Table 3, the structural parameters of the double phenoxido bridges are almost identical in the non-coordinated complexes 2-5.The magnetic behaviour of compound 1 suggests the possible presence of a very weak antiferromagnetic Cu-Ce coupling.Nevertheless, the first-order angular momentum of the Ce(III) ion avoids an easy interpretation of the magnetic properties in this compound since the magnetic properties arise from both the thermal population of the Stark components of the Ce(III) ions and the possible antiferromagnetic Cu-Ce coupling.A search in the CCDC database shows that there are only six reported Cu 2 Ce trimers with double phenoxido bridges, as in compound 1.Among these six examples, only three have been magnetically characterized (although no magnetic fit has been reported to date).In the three cases the magnetic properties are very similar to those displayed by compound 1 [33,53,56].
8. Correlation between the J value and the dihedral CuOOGd angle in different Cu-Gd dimers connected by double phenoxido bridges (data taken from ref. [54]).The solid line is the fit to an exponential law.The red point corresponds to compound 2.
The magnetic behaviour of compound 3 is similar to those observed in the eight structurally characterized reported examples of Cu 2 Tb trimers with double phenoxido bridges.Furthermore, the observed weak ferromagnetic coupling found in compound 3 (J = 1.27 cm ´1) is of the same order of magnitude as that of the only Cu 2 Tb trimer whose magnetic properties have been fit (J = 2.27 cm ´1) [59].
The Cu 2 Dy compound (4) shows a weak ferromagnetic coupling, similar to those observed in the five structurally characterized reported compounds with Cu 2 Dy trimers with double phenoxido bridges.Interestingly, the value found in 4 (J = 0.88 cm ´1) is very similar to the one found in the only example of Cu 2 Dy trimer whose magnetic properties have been fit (J = 0.902 cm ´1) [59].
Finally, the weak ferromagnetic coupling observed in compound 5 is similar to those observed in the two only examples structurally characterized of Cu 2 Er trimers with double phenoxido bridges [53,59].Again, in the only example whose magnetic properties have been fitted, the value found (J = 0.136 cm ´1) [59] is of the same order of magnitude than the one found in compound 5 (J = 0.31 cm ´1).Note that the differences observed between our J values and those found by other authors can be easily explained if we consider that other authors include a weak-to-moderate antiferromagnetic Cu-Cu exchange interaction to reproduce the decrease observed in the χ m T product at very low temperatures.In our model we have included a D term to account for this decrease since the Cu(II) ions are too far apart to show any magnetic coupling.Since the moderate J Cu-Cu affects the magnetic moment at higher temperatures than the D parameter, its inclusion must affect the final J Cu-Ln value.
Compounds 2-5 show ferromagnetic couplings with coupling constants decreasing as we move forward along the lanthanoids series, i.e., as the number of unpaired f electrons decreases (Table 2).Interestingly, Ishida et al. have recently described a similar trend in a series of isomorphous Cu 2 Ln trimers with similar double oxide bridges [59].Even if Ishida et al. use a different model to fit the magnetic properties, our results confirm the idea that the coupling constants decrease as the number of unpaired f electrons decreases (Figure 9).In our case a linear relation can be inferred, although the number of points is still limited, there are other factors that may change J (as the dihedral Cu-O-O-Ln angle) and the relative errors in the J values are quite big, precluding any definitive correlation.9. Variation of the coupling constant in complexes 2-5 with the number of unpaired f electrons along the lanthanoids series.The solid line is the linear fit.

Starting Materials
Reagent grade 2-hydroxyacetophenone and 1,3-propanediamine were obtained from Spectrochem, Mumbai, India and used as received.Reagent grade Ln(NO 3 ) 3 ¨nH 2 O were purchased from Aldrich.Other reagents and solvents used were of commercially available reagent quality, unless otherwise stated.
Caution! Perchlorate salts of metal complexes with organic ligands are potentially explosive.Though not encountered throughout the experiment, only a small amount of material should be prepared and it should be handled with care.The di-Schiff base ligand H 2 L α´Me and the metalloligand [CuL α´Me ] were prepared by the reported method described earlier [60].To a solution (10 mL) of the precursor metalloligand [CuL α´Me ] (0.076 g, 0.2 mmol) in methanol, a solution of Ce(NO 3 ) 3 ¨6H 2 O (0.043 g, 0.1 mmol in 2 mL mehanol) was added and stirred for 30 min at room temperature.The mixture was filtered and kept for slow evaporation at room temperature.Within 24 h, block-shaped dark green X-ray quality single crystals appeared at the bottom of the vessel.

Physical Measurements
Elemental analyses (C, H and N) were carried out using a Perkin-Elmer 2400 series II CHN analyzer.IR spectra (4000-500 cm ´1) were recorded by a Perkin-Elmer RXI FT-IR spectrophotometer in KBr pellets.
The magnetic susceptibility measurements were carried out in the temperature range 2-300 K with an applied magnetic field of 0.1 T on polycrystalline samples of compounds 1-5 (with masses of 53.72, 59.37, 30.24, 28.65 and 53.81 mg, respectively) with a Quantum Design MPMS-XL-5 SQUID susceptometer (XL-7 for samples 3 and 4).The samples were mixed with eicosane to avoid the alignment of the crystals with the magnetic field.The isothermal magnetization was performed on the same samples at 2 K with magnetic fields up to 5 T (7 T for compounds 3 and 4).The susceptibility data were corrected for the sample holders previously measured using the same conditions and for the diamagnetic contributions of the salt as deduced by using Pascal's constant tables (χ dia = ´495.1 ˆ10 ´6, ´495.1 ˆ10 ´6, ´494.1 ˆ10 ´6, ´494.1 ˆ10 ´6 and ´493.1 ˆ10 ´6 emu.mol ´1 for 1-5, respectively).

Magnetic Model
The data were fitted considering an exchange-coupled trimer model with a single isotropic exchange interaction between the central lanthanide and each terminal copper(II).Calculations were performed with the magnetism package MAGPACK [61,62].In order to describe the effect of the crystal field (CF) splitting of the central lanthanide, an axial zero-field splitting has been used.Only this parameter has been considered given the limited information provided by a magnetic susceptibility curve, and despite the crucial importance of correctly determination of the crystal field.In order to evaluate the susceptibility curves, the Zeeman term has been added to the Hamiltonian for the three metals.The Hamiltonian used is as follows:

Crystallographic Data Collection and Refinement
Suitable single crystals of compounds 1-5 were mounted on a Bruker-AXS SMART APEX II diffractometer with a graphite monochromator and Mo-Kα (λ = 0.71073 Å) radiation.The crystals were placed at 60 mm from the CCD.360 frames were measured with a counting time of 5 s.The structures were solved using Patterson method by using the SHELXS 97.Subsequent difference Fourier synthesis and least-square refinement revealed the positions of the remaining non-hydrogen atoms that were refined with independent anisotropic displacement parameters.Hydrogen atoms were placed in idealized positions and their displacement parameters were fixed to be 1.2 times larger than those of the attached non-hydrogen atom except the solvent molecules in 2 to 5 which were assigned from Fourier map.Successful convergence was indicated by the maximum shift/error of 0.001 for the last cycle of the least squares refinement.Absorption corrections were carried out using the SADABS program [63].All calculations were carried out using SHELXS 97 [64], SHELXL 97 [65], PLATON 99 [66], ORTEP-32 [67] and WinGX system ver-1.64[68].Data collection with selected structure refinement parameters and selected bond parameters for all the complexes are given in Table 1 and Tables S1-S3, Supplementary Information respectively.CCDC-1439522 (1), CCDC-1439523 (2), CCDC-1439524 (3), CCDC-1439525 (4) and CCDC-1439526 (5) contain the supplementary crystallographic data for this paper.These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.

Conclusions
We have shown that the flexibility of the Schiff base ligand L α´Me and the use of the corresponding [CuL α´Me ] metalloligand with five different lanthanoid ions has resulted in the synthesis of a new series of trimeric transoid complexes of the type [(CuL α´Me ) 2 Ce(NO 3 ) 3 ] (1) and [(CuL α´Me ) 2 Ln(H 2 O)(NO 3 ) 2 ]¨(NO 3 )¨2(CH 3 OH); Ln = Gd (2), Tb (3), Dy (4) and Er (5).The larger size of the Ce(III) ion has led to a larger coordination number (ten) and to a different coordination geometry as compared with the other Ln(III) complexes (2)(3)(4)(5).These complexes show a different magnetic coupling between the Ln(III) ions and the Cu(II) ions: weak antiferromagnetic for compound 1 (in agreement with all the previously prepared Cu 2 Ce complexes) and weak ferromagnetic for compounds 2-5 (also in agreement with all the previously prepared Cu 2 Ln complexes).Compound 2 fits very well with a previous magneto-structural correlation established in Cu-Gd complexes with double phenoxido bridges between the dihedral Cu-O-O-Gd angle and the J value.Furthermore, complexes 3-5 represent the second example of trimeric Cu 2 Ln complexes (Ln = Tb, Dy and Er) whose magnetic properties have been fitted.Finally, the isomorphism of complexes 2-5, with very similar intra-trimer bond distances and angles, has allowed the establishment of a clear relationship between the number of unpaired f electrons and the strength of the magnetic coupling, in agreement with a previous observation in a related series of Cu 2 Ln trimers.

Scheme 1 .
Scheme 1.The metalloligands used earlier and the one used in this study to prepare Cu 2 Ln compounds.

Figure 3 .
Figure 3. Thermal variation of the χ m T product per Cu 2 Ce trimer for compound 1.

Figure 4 .
Figure 4. Magnetic properties of compound 2: (left) Thermal variation of the χ m T product per Cu 2 Gd trimer; (right) Isothermal magnetization at 2 K. Solid lines are the best fit to the model (see text).

Figure 5 .
Figure 5. Thermal variation of the χ m T product per Cu 2 Tb trimer for compound 3.The solid line is the best fit to the model (see text).

Figure 6 .
Figure 6.Thermal variation of the χ m T product per Cu 2 Dy trimer for compound 4. The solid line is the best fit to the model (see text).

Figure 7 .
Figure 7. Thermal variation of the χ m T product per Cu 2 Er trimer for compound 5.The solid line is the best fit to the model (see text).

Table 1 .
Crystal data and structure refinement parameters of complexes

Table 2 .
Magnetic parameters for compounds 2
a This compound has two crystallographically independent Cu ions.