Pawan Kumar

Sourav Biswas

Abinash Swain

Joydev Acharya

Vierandra Kumar

Pankaj Kalita

Jessica Flores Gonzalez

Olivier Cador

Fabrice Pointillart
email: fabrice.pointillart@univ-rennes1.fr

Gopalan Rajaraman
email: rajaraman@chem.iitb.ac.in

Vadapalli Chandrasekhar

Azide-Coordination in Homometallic Dinuclear Lanthanide(III) Complexes Containing Nonequivalent Lanthanide Metal Ions: Zero-Field SMM Behavior in the Dysprosium Analogue

Keywords: lanthanide complexes, magnetic anisotropy, Schiff base, single molecule magnets, magnetic measurement, azide

come

Introduction

Single-molecule magnets (SMMs) are discrete molecular complexes comprising 3d/4d/5d/4f/5f metal ions or a combination thereof such as 3d/4f heterometallic complexes which can be magnetized upon application of a magnetic field and which retain their magnetization below a certain temperature known as the blocking temperature (TB). [START_REF] Sessoli | Strategies towards single molecule magnets based on lanthanide ions[END_REF] These systems show slow relaxation of magnetization which depends on an energy barrier (Ueff) for the magnetization reversal. [START_REF] Sessoli | Magnetic bistability in a metal-ion cluster[END_REF] For molecules to display SMM behavior, there is a requirement of a large ground spin state (S) and an Ising type anisotropy. Among the various types of complexes investigated, complexes containing lanthanide metal ions are most promising owing to these having a large ground state single ion magnetic anisotropy which results from a very high spin-orbit coupling. In addition many lanthanide ions such as Dy III and Tb III have a reasonable ground state spin because of the presence of sufficient number of unpaired electrons. [START_REF] Dey | Lanthanide(III)-Based Single-Ion Magnets[END_REF] The investigations on lanthanide complexes as SMMs began with Isikawa's seminal discovery of slow relaxation of magnetization in the sandwich complex [Bu4N][TbPc2]. [START_REF] Ishikawa | Lanthanide Double-Decker Complexes Functioning as Magnets at the Single-Molecular Level[END_REF] It was quickly realized that lanthanide ions with their intrinsic unquenched orbital angular momenta could contribute to magnetic anisotropy. In recent years, a large number of lanthanide-based SMMs with very high effective energy barriers of magnetization above 1000 K [START_REF] Ding | On Approaching the Limit of Molecular Magnetic Anisotropy: A Near-Perfect Pentagonal Bipyramidal Dysprosium(III) Single-Molecule Magnet[END_REF] and blocking temperatures up to 80 K 6 have been reported. While the mononuclear Dy III complexes yielded very attractive blocking temperatures in recent years, the axial limit set by the ligand field has already been breached for mononuclear complexes. Therefore, expanding the structural motif beyond monomers is of importance. [START_REF] Lu | Recent Developments in Lanthanide Single-Molecule Magnets[END_REF] Among these systems dinuclear complexes are of interest because these allow an understanding of the interactions between the two lanthanide ions. [START_REF] Guo | Strong Axiality and Ising Exchange Interaction Suppress Zero-ACCEPTED MANUSCRIPT Field Tunneling of Magnetization of an Asymmetric Dy2 Single-Molecule Magnet[END_REF] The magnetic coupling between the lanthanide ions can generate an exchange ACCEPTED MANUSCRIPT bias field that could minimize the quantum tunneling of the magnetization. [START_REF] Wernsdorfer | Exchange-biased quantum tunnelling in a supramolecular dimer of single-molecule magnets[END_REF] Among such dinuclear complexes those containing non-equivalent lanthanide ions are especially sparse. 8a, 10 We have been involved in the design of polydentate ligands for assembling various types of lanthanide complexes whose nuclearity varied from 1 to 21. [START_REF] Chandrasekhar | Octanuclear {Ln(III)8}(Ln = Gd, Tb, Dy, Ho) Macrocyclic Complexes in a Cyclooctadiene-like Conformation: Manifestation of Slow Relaxation of Magnetization in the Dy(III) Derivative[END_REF] In these efforts we found, similar to some other groups, that aroylhydrazone-based Schiff base ligands are particularly efficient in the construction of lanthanide complexes. [START_REF] Guo | Two-Step Relaxation in a Linear Tetranuclear Dysprosium(III) Aggregate Showing Single-Molecule Magnet Behavior[END_REF] We have synthesized a pyridine-based Schiff base ligand (LH4) and utilized it for preparing lanthanide complexes. Further, we were also interested in incorporating the azide ligand in the assembly of these complexes in view of its demonstrated coordination motif versatility in transition metal complexes. [START_REF] Hong | Unusual Ferromagnetic Couplings in Single End-to-End Azide-Bridged Cobalt(II) and Nickel(II) Chain Systems[END_REF] Although, we anticipated a bridging coordination action from the azide ligand, as discussed below, we observe that this ligand binds in a monodentate fashion as a terminal ligand. Accordingly, herein, we report the synthesis, structural characterization and magnetic studies of [Ln2(LH2)(LH)(CH3OH)(N3)] . xMeOH•yH2O

[ 1, Ln = Dy III , x = 0, y = 2; 2, Ln = Tb III , x = 1, y = 1]. Although we have prepared the Gd(III) analogue (3) , we were unable to establish the bulk purity of this compound. However, we were able to get single crystals in some quantity. We could perform the structural study which are presented in the Supporting Information. Among these complexes, the Dy III analogue is a zerofield SMM. Also, while the Dy III analogue has been shown to have antiferromagnetic interaction between the two Dy III centres, the Tb III analogue has been shown to possess ferromagnetic interactions. These conclusions were possible by a theoretical study of the Gd(III) analogue. The differences between the Dy(III) and Tb(III) derivatives could be correlated to small structural changes in these complexes. All of these aspects are discussed herein through combined experimental and ab initio theoretical calculations.

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Experimental Section

Solvents and other general reagents used in this work were purified according to standard procedures. [START_REF] Vogel | s textbook of practical organic chemistry[END_REF] Pyridine-2,6-dicarboxylic acid, sodium borohydride, sodium azide, DyCl3•6H2O, TbCl3•6H2O and GdCl3•6H2O were obtained from Sigma Aldrich Chemical Co. and were used as received. Diethanolamine, hydrazine hydrate (80%), PBr3, and sodium sulphate (anhydrous) were obtained from S.D. Fine Chemicals, Mumbai, India. Methyl-6-(hydroxymethyl) picolinate, 15 methyl 6-(bromomethyl)picolinate, 15 methyl-6-((bis(2-hydroxyethyl)amine)methyl)picolinate, 11d and 6-((bis(2-hydroxyethyl)amino)methyl)picolinohydrazide (A5), 11d were prepared according to literature procedure.

Instrumentation

Melting points were measured using a JSGW melting point apparatus and are uncorrected. IR spectra were recorded as KBr pellets on a Bruker Vector 22 FT IR spectrophotometer operating at 400-4000 cm -1 . Elemental analyses of the compounds were obtained from Thermoquest CE instruments CHNS-O, EA/110 model. ESI-MS spectra were recorded on a MICROMASS QUATTRO II triple quadrupole mass spectrometer. 1 H NMR spectra were recorded in CDCl3 and DMSO-d 6 solutions on a JEOL JNM LAMBDA 400 model spectrometer operating at 500.0 MHz, Chemical shifts are reported in parts per million (ppm) and are referenced with respect to internal tetramethylsilane ( 1 H). A powder X-ray diffraction study was done on 1-2 with Bruker D8 Advance powder X-ray diffractometer. The samples for study were prepared by finely ground the crystals of 1-2 to powder form.

X-ray Crystallography

Single crystal data for the complexes were collected on a Bruker SMART CCD diffractometer (MoKα radiation, λ = 0.71073 Å). The program SMART [START_REF] Smart | SAINT, Software Reference manuals[END_REF] was used for collecting frames of data,

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indexing reflections, and determining lattice parameters, SAINT for integration of the intensity of reflections and scaling, SADABS [START_REF] Sheldrick | SADABS, software for empirical absorption correction[END_REF] for absorption correction, and SHELXTL [START_REF][END_REF] for space group and structure determination and least-squares refinements on F 2 . On the other hand X-ray diffraction data for complex 1Y was collected at low temperature (120 K) by using Rigaku diffractometer with graphite-monochromated molybdenum Kα radiation, λ = 0.71073 Å. Data integration and reduction were processed with CrysAlisPro software. [START_REF]Rigaku Oxford Diffraction[END_REF] .An empirical absorption correction was applied to the collected reflections with SCALE3 ABSPACK integrated with CrysAlisPro.The crystal structures were solved and refined by full-matrix least-squares methods against F 2 by using the program SHELXL-2014 20 using Olex-2 21 software. All the non-hydrogen atoms were refined with anisotropic displacement parameters. Hydrogen positions were fixed at calculated positions and refined isotropically. The crystallographic figures have been generated using Diamond 3.1e software. [START_REF] Bradenburg | Diamond, version 3.1 e. Crystal Impact GbR[END_REF] In addition, some disorderd solvent molecules was present in complex 1-2.We could not assign all the solvent molecules properly due to the disorder and weak residual Q peaks. So the Olex-2 mask program was performed to discard the disordered solvents molecules which give an electron density of around 18 and 26 leading to the presence of two water molecules in 1 and one methanol and one water 2 respectively. The Possible masked electron counts and void volumes has been included in the corresponding CIFs.

The crystal data, the cell parameters and ccdc information for all the complexes are summarized in Table 1 and Table S1.

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The dc magnetic susceptibility measurements were performed on solid polycrystalline samples with a Quantum Design MPMS-XL SQUID magnetometer between 2 and 300 K in applied magnetic field of 200 Oe for temperatures between 2-20 K, 2 kOe between 20 and 80 K and 10 kOe above. The sample was immobilized in a pellet made with Teflon tape. These measurements were all corrected for the diamagnetic contribution as calculated with Pascal's constants. The ac magnetic susceptibility measurements were performed on Quantum Design MPMS-XL SQUID magnetometer in the frequency range of 1 to 1000 Hz.

Computational Details

The ab initio calculations have been performed using MOLCAS 8.2 software package using CASSCF/RASSI-SO/SINGLE_ANISO module. [START_REF] Aquilante | Molcas 8: New capabilities for multiconfigurational quantum chemical calculations across the periodic table[END_REF] For POLY_ANISO simulations, the inputs were taken from the SINGLE_ANISO results. [START_REF] Ungur | Ab initio investigation of the noncollinear magnetic structure and the lowest magnetic excitations in dysprosium triangles[END_REF] In the CASSCF step for Dy III complex, nine electrons in seven 4f active orbitals and for Tb III complex eight electrons in seven 4f orbitals were taken into consideration. For 1 21 sextets and for 2 7 septets, 140 doublets and 195 quartet roots were taken into consideration in RASSI-SO step as established earlier by us and others. [START_REF] Vignesh | Exploring the Influence of Diamagnetic Ions on the Mechanism of Magnetization Relaxation in {CoIII2LnIII2} (Ln = Dy, Tb, Ho) "Butterfly" Complexes[END_REF] The basis sets are of ANO-RCC…8s7p4d3f2g1h TZVP level for the paramagnetic center Ln III and Lu III , ANO-RCC...4s3p2d TZV quality for O and N atoms since they are coordinating to the metal ion and ANO-RCC…3s2p/ ANO-RCC…2s DZV level for the rest of the atoms. The relativistic effect was taken care of by taking DKH Hamiltonian. In order to save disk space, Cholesky decomposition has been incorporated for our calculations. 23a Spin-orbit coupling was taken into account through the RASSI-SO module using the CASSCF functions as input states. From the SINGLE-ANISO computation, the g tensor for the ground state and excited state, magnetic susceptibility, crystal field parameter and orientation of main magnetic axes have been obtained. [START_REF] Singh | Acquiring a record barrier height for magnetization reversal in lanthanide encapsulated fullerene molecules using DFT and ab initio calculations[END_REF]

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Lines model was employed to calculate the exchange interaction between two Ln III sites using POLY-ANISO program. [START_REF] Lines | Orbital Angular Momentum in the Theory of Paramagnetic Clusters[END_REF] The experimentally obtained susceptibility values were simulated with the POLY_ANISO calculated values to get the exchange interaction between the two Ln III centres for both 1 and 2.

The exchange values obtained through this method was further verified by density functional calculations using the Gaussian 09 program employing the DFT broken symmetry approach. [START_REF] Becke | Density-functional thermochemistry. III. The role of exact exchange[END_REF] For this approach, we have used B3LYP hybrid functional, with Cundari-Stevens (CS) relativistic effective core potential for Gd atom and TZV level of basis set for the rest of the atoms. [START_REF] Cundari | Effective core potential methods for the lanthanides[END_REF] Quadratic convergence method was followed to the most stable wave function. Since the Dy III and Tb III ion are highly anisotropic paramagnetic systems, to reduce the complexity in using DFT methods, we have replaced the Dy III and Tb III ion in the corresponding X-ray structure with Gd III ion and computed the Js using the DFT method and rescaled the Js later using appropriate spin to get the exchange values. [START_REF] Rajeshkumar | A computational perspective on magnetic coupling, magneto-structural correlations and magneto-caloric effect of a ferromagnetically coupled {GdIII-GdIII} Pair[END_REF] By this approach, the difference in structural parameters, however small, can be captured in the estimation of J values. Also, this being an independent method offers the possibility to cross-verify results obtained using the Lines model wherein the experimental susceptibility data is fit to the ab initio computed parameters to extract the Js. The exchange values for Dy III /Tb III has been calculated by multiplying 5/7 and 6/7 with the exchange values obtained from DFT using Gd III ion. For the Gd(III) analogue , the exchange values were estimated by the use of broken symmetry calculation using ORCA 4.2 package. For this, TZVP level was used for Gd and for the rest of the atoms def2-SVP has been used.

Synthesis

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Compounds A1 to A5 ( Scheme S1) were prepared according to literature procedures

General Synthetic Procedure for the Preparation of the Complexes 1-2

To a stirred solution of LH4 (0.040g, 0.11 mmol), in methanol (30 mL), LnCl3•6H2O (0.11 mmol)

was added to give a yellow colored solution which was allowed to stir for 10 minutes at room temperature. Then, NaN3 (0.010g, 0.15 mmol) was added followed by the addition of triethylamine (0.046 mL, 0.33 mmol). The reaction mixture was allowed to stir for 6-8 hours at room temperature. The reaction mixture was filtered and stripped off its solvent in vacuo affording a

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semi-solid yellow residue which was dissolved in methanol containing a few drops of chloroform.

Suitable crystals for X-ray diffraction were obtained by slow evaporation of the solvents within a week. A similar synthetic method was employed for the preparation of the yttrium analogue, the diluted analogue of complex 1 (15%). Specific details of each reaction and the characterization data of the complexes are given below.

[Dy2(LH2)(LH)(CH3OH)(N3)] . 2H2O (1)

Quantities: LH4 (0.040g, 0.11 mmol), DyCl3

Results and Discussion

Synthetic Aspects

Polyfunctional ligands have been used with a great deal of efficacy to assemble various complexes containing lanthanide ions. Among such multi-dentate ligands aroylhydrazone-based Schiff base ligands are particularly versatile because of several features including their flexibility involving C-C bond rotation and the potential of utilizing either the enolate or the keto forms of the ligand to bind to the metal ion. 11d, 11f, 31 Harnessing these features, previously we have assembled dinuclear lanthanide complexes (Scheme S2). 11d

Motivated by the above results, we have designed and synthesized 6-((bis(2-hydroxyethyl)amino)-N'-(2-hydroxybenzylidene)picolinohydrazide (LH4). The latter was prepared by following a fivestep synthetic protocol (Scheme S1).

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The ligand LH4 contains seven coordination sites which can be partitioned into two unsymmetrical pockets, a tridentate pocket comprising of a phenolic oxygen, an imine N, and hydrazine O (2O,1N) while the other is pentadentate, consisting of a pyridine N, a common hydrazone oxygen In addition to using the ligand LH4 we have used sodium azide as the co-ligand with the intention of exploring the coordination capability of the azide ion. We anticipated a bridging coordination role for the azide ligand. However, as described below, because of the competing bridging coordination of the enolate form the ligand, the azide takes up a terminal position. Thus, the reaction of LH4, LnCl3 . 6H2O and sodium azide in the presence of triethylamine in a molar ratio of ACCEPTED MANUSCRIPT In order to check the phase purity of the complexes, powder X-ray diffraction measurement for complexes was done and found that the sequence and pattern of the peaks are in reasonable agreement with the simulated data obtained from single-crystal data (Figures S1,S2).

We have carried out ESI-MS studies to check the structural integrity of these complexes in solution. These studies reveal peaks at m/z = 518.5698 and 515.0687 for 1, 2 respectively, corresponding to the species [Dy2(LH2)(LH)H] 2+ , [Tb2(LH2)(LH)H] 2+ .This indicates that these complexes remain partially intact in solution.The ESI-MS spectra of complexes are given in the Supporting Information (Figures S3 andS4).

X-ray Crystallography

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Suitable single crystals of the complexes 1-2 were obtained by slow evaporation of their solutions in methanol/chloroform mixture (1:1) within a week. Single crystal X-ray diffraction study reveals that the complexes 1-2 are isostructural and charge neutral. These crystallize in a monoclinic system (C2/c with Z = 8) Since 1 and 2 are isostructural we describe the molecular structure of 1 as a representative example. A perspective view of 1 is given in Figure 1 and that of complex 2 is given in the Supporting Information (Figures S5 ). Selected bond lengths and bond angles of 1 are given in Table 2 while those of 2 are given in Table S2. 7) Dy( 1)-O( 7)-Dy (2) 114.87 (7) The molecular structure of 1 consists of two Dy III ions, a di anionic ligand [LH2] 2-, a trianionic ligand [LH] 3-, an azide anion and a neutral methanol giving an overall neutral dinuclear assembly.

Interestingly, the two lanthanide ions present in the assembly are non-equivalent as described

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114.87 (7) respectively. Because of the bridging coordination of the enolate form of the ligand, we believe that the azide ligand is forced to function as a terminal ligand to one of the lanthanide centers. On the other lanthanide center the ninth coordination is provided by a neutral methanol.

Overall, the dinuclear assembly contains two types of nine-coordinated Dy III centers; Dy1 (coordination environment, 3N, 6O), Dy2 (coordination environment, 4N, 5O).

In order to ascertain if other mono anions such as chloride would similarly bind in a monodentate fashion, we carried out the reaction using DyCl3.6H2O as the starting material but in the absence of the additional azide ligand. Under these conditions, however, we were not able to isolate any pure crystalline products. S4). The Dy-O bond lengths fall in a range, 2.217-2.557 Å. The Dy-Omethanol (2.492 Å) bond length is slightly longer than those observed previously [START_REF] Biswas | Phosphonate-assisted tetranuclear lanthanide assemblies: observation of the toroidic ground state in the TbIII analogue[END_REF][START_REF] Zou | Phenoxido and alkoxidobridged dinuclear dysprosium complexes showing single-molecule magnet behaviour[END_REF] The deprotonated Dy-Odiethanolamine (O8) (2.312 Å) bond length is slightly longer than that observed in the literature, but smaller than the bond length onvolving the nuetral diethanolamine arm. 11f All the Dy-N bond lengths fall in a very narrow range, 2.487-2.636 Å, consistent with values found in the literature. [START_REF] Biswas | Phosphonate-assisted tetranuclear lanthanide assemblies: observation of the toroidic ground state in the TbIII analogue[END_REF] The bond angles, Dy1-O3-Dy2 and Dy1-O7-Dy2 are 115.80° and 117.86° respectively (Figure 2 and Table 2 ).

The crystal structure of 1 reveals the presence of intra-and intermolecular hydrogen bonds leading to the formation of a 1D polymeric chain(Figure S7-8).

Magnetic Studies

Static magnetic properties: dc magnetic properties of the two complexes 1 and 2 were determined by measuring the thermal dependence of the molar magnetic susceptibility (χM) from 2 to 300 K (Figure 4). The room temperature values of the χMT product are 27.90 cm 3 K mol -1 and 22.42 cm K mol -1 , close to the expected values of 28.34 cm 3 K mol -1 , and 23.64 cm 3 K mol -1 ,respectively for two isolated Dy III ions ( 6 H15/2 and gJ=4/3) and Tb III ( 7 F6 and gJ = 3/2). [START_REF] Kahn | Molecular magnetism[END_REF] On cooling, χMT of monotonously decreases down to 25 K, temperature for which a plateau is almost observed, and then decreases progressively reaching a minimum of 23.60 cm 3 K mol -1 at 2 K. The χMT of remains almost constant down to 75 K then decreases to reach the value of 20.68 cm 3 K mol -1 at K and finally slightly increases at very low temperature (20.88 cm 3 K mol -1 at 2 K). For both compounds 1 and 2, the decrease can be mainly attributed to the depopulation of the ligand-field levels, while the change of slope at a lower temperature than 25 K could be due to the existence of weak magnetic interactions. for two Dy III ions with the presence of a magnetically anisotropic ground state and two Tb III ions (inset of Figure 4). Furthermore, the absence of a superposition in the different M vs. H curves for each system (Figure S9), elucidates the presence of significant magnetic anisotropy for 1 and 2, as well as the possibility of low-lying excites states in the systems.

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Dynamic magnetic properties. ac measurements have been performed for 1 and 2. At zero dc magnetic field 1 displays a frequency dependence of the magnetic susceptibility in the temperature range of 2-15 K in the window 1-1000 Hz frequency of the oscillating field (Figure 5a and S10).

The relaxation time (τ) has been extracted with an extended Debye model [START_REF] Dekker | Activated dynamics in a two-dimensional Ising spin glass: Activated dynamics in a twodimensional Ising spin glass: Rb2Cu1-xCoxF4[END_REF] (see SI, Figure S11, Table S6). The Argand plot confirms that the observed slow magnetic relaxation corresponds to the entire sample (Figure S12). The corresponding thermal variation of the log(τ) is depicted in Figure 5d and clearly shows a linear dependence (Orbach process) in the temperature range of 7-11 K while a deviation from the linearity is observed down to 6 K due to the presence of underbarrier processes such as Raman and Quantum Tunnelling of the Magnetization (QTM). It is well known that the latter can be cancelled by applying a dc magnetic field. 36a, 36b Thus, the field dependence of the magnetic susceptibility at 2 K (Figure S13) shows an optimal behaviour at a

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selected dc magnetic field value of 800 Oe (Figure 5b and Table S7). At 2 K and zero applied dc field, χM" vs.ν curve passes through a maximum at 5 Hz which is shifted to 1 Hz upon applying a 800 Oe magnetic field (Figure 5c and S14) because of the removal of the QTM contribution. The relaxation time (τ) has been extracted with the extended Debye model (Table S7) and the corresponding relaxation time of the magnetization in the temperature range of 2-11 K are given in Figure 5d, corresponding again to a general behavior of the sample as seen in the Argand plot (Figure S15). As for 1 in zero field, the linear region depicted in the temperature dependence of the magnetic relaxation time has deviated at the lower temperatures, which is a sign of a remained contribution of under energy barrier processes. At the optimal field of 800 Oe, the involvement of a significant Direct process or remaining QTM can be discarded. To support this affirmation, the τ vs. H curve was fitted with the equation 1 for the 0-2000 Oe field range (Figure 6b). 36c,36d

τ -= + + + 1 1 3 4 2 2 2 1 m B B H B B H
Eq. 1

With the three terms correspond respectively to the QTM, Direct and field-independent magnetic relaxation processes (Raman and Orbach). The best fit was obtained for B1 = 31.25 s -1 ; B2 = 3.795(10)×10 -5 Oe -2 ; B3 = 1.95(4)×10 -13 s -1 K -1 Oe -4 and B4 = 2.38(4) s -1 leading to τ -1 (QTM) = 1.23 s -1 (blue contribution on Figure 5b), τ -1 (Direct) = 0.16 s -1 (orange contribution on Figure 5b) and τ -1 (Raman+Orbach) = 2.38 s -1 (brown contribution on Figure 5b). Thus, the thermal variation of the magnetic relaxation times could be fitted using a combination of Orbach and Raman processes. Since these two processes are field independent (equation 2), they can be considered constant for both relaxation time at 0 Oe and 800 Oe.

𝜏𝜏 -1 = 𝐶𝐶𝑇𝑇 𝑛𝑛 � 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑛𝑛 + 𝜏𝜏 0 -1 exp �- ∆ 𝐾𝐾𝐾𝐾 � ��������� 𝑂𝑂𝑂𝑂𝑂𝑂𝑅𝑅𝑂𝑂ℎ + 𝜏𝜏 𝐾𝐾𝑇𝑇 -1 � 𝑄𝑄𝐾𝐾𝑄𝑄 Eq. 2

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Indeed, the thermal variation of the relaxation time is simultaneously fitted for 1 in zero and 800

Oe field with Orbach (Δ and τ0) and Raman (C and n) shared parameters while QTM (τTI) appears only at 0 Oe. The best fitted curves are represented on Figure 5d with Δ = 59(3) K, τ0 = 10(4)×10 - 6 s, C=1.2( 2) K -n s -1 , n = 2.3( 1) and τTI = 0.032(2) s. Importantly, τTI fitted from thermal variation matches the zero field limit of Eq. 1 (B1 -1 ) obtained from field variations. The expected n value for Kramers ions should be 9, 37 but it is well known that for molecular systems, [START_REF] Goodwin | Synthesis and Electronic Structures of Heavy Lanthanide Metallocenium Cations[END_REF] the presence of both acoustic and optical phonons could lead to lower values comprised between 2 and 7. [START_REF] Singh | Optical-acoustic two-phonon relaxation in spin systems[END_REF] A search in the literature reveals that Dy-based dimers show a most common coordination number 8 [START_REF] Guo | Strong Axiality and Ising Exchange Interaction Suppress Zero-ACCEPTED MANUSCRIPT Field Tunneling of Magnetization of an Asymmetric Dy2 Single-Molecule Magnet[END_REF][START_REF] Aguilà | Lanthanide Contraction within a Series of Asymmetric Dinuclear [Ln2] Complexes[END_REF] , and more recently the tendency tries to go to low coordination systems 8h . However, very few unsymmetric Dy-based dimers have been reported. 8a, 10d, 110e, 40a-g The properties found in such complexes are consistent with the results found in this work. These results are summarized in Table 3. 8a, 10d, 110e, 40a-g If one considers a similar coordination geometry, viz., the spherical capped square antiprism geometry, examples with field-induced relaxation are known. [START_REF] Antal | Muffin-like lanthanide complexes with an N5O2-donor macrocyclic ligand showing field-induced single-molecule magnet behavior[END_REF] In the present instance, however, we have observed zero field SMM behavior.

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The molecular structure of 1 highlighted two Dy III ions in different coordination sphere i.e. N3O6 and N4O5 respectively for the Dy1 and Dy2 surroundings. One could expect two distinct magnetic behavior while it was observed that both Dy III centers are involved in the magnetic relaxation at the same frequency for a given temperature. The previous published dissymmetrical Dy III dinuclear SMMs displayed either single 40a-40b or multiple 40d-40g relaxation contributions.

The magnetic properties of the diluted 15% analogue were studied in order to obtain a greater information of the slow relaxation mechanism in such Dy2 SMM, especially to understand the effects of magnetic interactions within the dynamic magnetic properties in the dimer. The field dependence of the magnetization at 2 K (Figure S16) shows a classic behavior with a value of 0.614 Nβ at 5 T, confirming a magnetic dilution of approximately 6%. 15% display an SMM behavior at zero applied field (Figure 6, S17-18), which is shifted to the higher frequencies ( 158Hz) compared to 1 (5 Hz) at 2 K. Such shift is in agreement with a faster magnetic relaxation time when the magnetic interactions are cancelled by magnetic dilution. As previously, the extended Debye model was used in order to extract the temperature dependence of the relaxation mechanism (Tables S8 andS9) corresponding to a general behavior of the sample (Argand in Figure S15). Again, the thermal variation of the relaxation time is simultaneously fitted

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for zero and 800 Oe field with Orbach parameters (Δ and τ0), injected from the linear fit at high temperature region (from 8 to 12 K) of the in-field relaxation curve (Figure 6d), and Raman (C and n) shared parameters while QTM (τTI) appears only at 0 Oe. The best fitted curves are represented on Figure 6d with Δ = 66(1) K, τ0= 7.3(8)× 10 -7 s, C = 9(3) ×10 -4 K -n s -1 , n = 5.9 (2) and τTI = 1.10(6) ×10 -3 s. Full red and black lines are the best-fitted curves (see text) for 1 and 15% respectively. The Figure 7 depicts the four thermal dependence of the relaxation times for 1 and 15%. Indeed, at zero applied field, the suppression of the magnetic interactions between magnetic centers by magnetic dilution lead to an increase of the fast relaxation QTM process. However, under an applied magnetic field, the magnetization of the diluted sample relaxed slower than the ACCEPTED MANUSCRIPT magnetization of 1 (Figure 7) because of the decrease of the Raman contribution (T < 6 K) for 15% compared to 1. Such diminution of the Raman contribution might be attributed to the diamagnetic dilution which reduces the interactions with the matrix. Such trend in the magnetic relaxation time can be reinforced by the behavior of the hysteresis loop of the magnetization of both compounds at 2 K. In which, once an applied magnetic field and the QTM is released, the hysteresis loop for 15% opens, in opposition to 1 which remains closed (Figure 21).

At zero applied magnetic field, 2 was not displaying any out-of-phase component of the susceptibility at 2 K in the window 1-1000 Hz frequency of the oscillating field (Figure S22). Indeed, 2 involves non-Kramers Tb III ion which requires highly axial symmetric ligand field to possess a bistable ground state and prevent efficient QTM. [START_REF] Mandal | Anion-driven structures and SMM behavior of dinuclear terbium and ytterbium complexes[END_REF] In order to cancel the possible QTM, the magnetic susceptibility has been measured under various applied magnetic field (Figure S23).

As soon as a dc field is applied, an out-of-phase contribution appears at 30 Hz which grows with the increase of the applied magnetic field. The 2800 Oe value is selected as the optimal applied magnetic field. At such field, the magnetic susceptibility displays a frequency dependence between 2 and 6 K (Figure S23) which is an indication of the slow magnetic relaxation for 2. The thermal dependence of the relaxation time has been plotted selecting by hand the maxima of the out-ofphase signal at each temperature (Figure S24). Considering the weak thermal dependence of the relaxation time and the 2800 Oe applied magnetic field value, one might suggest that the most probable magnetic relaxation occurs via a direct process (τ -1 = AH 4 T).

Ab initio Calculations

To investigate and quantify the nature of magnetic relaxations occurring at the individual magnetic centre and for the entire complex, detailed multireference ab initio calculation has been performed for complexes 1 and 2. The methodology employed here for the calculation is given in ACCEPTED MANUSCRIPT computational details (see Experimental Section). First, the magnetic properties at the individual magnetic centre have been calculated using the X-ray structures, wherein one of the Tb/Dy centres were replaced by a diamagnetic Lu III ion. The calculations were performed on the entire complexes without further modelling.

Mechanism of Magnetic relaxation by Individual Dy III /Tb III ions

Single ion calculations at the individual Ln III centre shows that the lowest-lying eight Kramer Doublets (KDs) behave differently for both the centres depending on the nature of the terminal coordination environment. For complex 1, the low lying 8 KDs are lying in the range of 176.3 cm -1 to 820.8 cm -1 for Dy1 centre where methanol is coordinated, whereas for Dy2 centre the ground to highest excited state lays in the range of 117.6 to 536.0 cm -1 (Table S12 in SI) where terminal azide coordination is present. Though the splitting of 8 KDs is upto the range of 820.8 and 536.0 cm -1 , the relaxation is occuring at the 1 st excited state, due to the displacement of the anisotropic axis at the excited state compared to the ground state. The large difference for the two Dy centers is due to the difference in the crystal field effect provided by the two different terminal ligands and their influence on the geometry. [START_REF] Tang | Dysprosium Triangles Showing Single-Molecule Magnet Behavior of Thermally Excited Spin States[END_REF] The MeOH terminal coordination provides stronger axial CF compared to azide coordination. The required crystal field Hamiltonian is described as

𝐻𝐻 𝐶𝐶𝐶𝐶 = ∑ 𝐵𝐵 𝑘𝑘 𝑞𝑞 𝑂𝑂 𝑘𝑘 𝑞𝑞 𝑘𝑘,𝑞𝑞
where 𝐵𝐵 𝑘𝑘 𝑞𝑞 is the crystal-field parameter and 𝑂𝑂 𝑘𝑘 𝑞𝑞 is Steven's operator (Table S14). [START_REF] Stevens | Matrix elements and operator equivalents connected with the magnetic properties of rare earth ions[END_REF] The axial parameter 𝐵𝐵 𝑘𝑘 𝑞𝑞 (where k = 0 and q = 2) is comparatively larger for the Dy1 ion (-8.98) compared to the Dy2 site (-2.35). This is in agreement with our computed low lying energy splitting for the lowest eight doublets. To further understand the difference between electronic effects induced by the MeOH vs azide and geometric effects caused by the same, we performed additional calculations on model systems 1a and 1b. Here model 1a represents a structure where

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both Dy1 and Dy2 are coordinated to the methanol while model 1b represents a structure where both the Dy III centres are coordinated to an azide group. The energy splitting obtained for both the models 1a ( for 1a-Dy1 185.4 to 829.8 cm -1 , 1a-Dy2 137.5 to 630.9 cm -1 ) and 1b (for 1b-Dy1 178.5 to 823.5 cm -1 , 1b-Dy2 131.5 to 675 cm -1 ) are similar to the original structures (see SI, Table S12). This unequivocally reveals that the geometric effects due to the substitution play a prominent role in dictating the anisotropy and not the individual MeOH vs azide electronic effects. The analysis of Loprop charges also arrives at the same conclusion. As the differences lie in the geometry, we looked at the SHAPE analysis, and this reveals that Dy1 has a CShM value 1.432 while Dy2 has 0.905 with respect to ideal nine coordinate Muffine (MFF-9) geometry. Thus, stronger deviation from MFF-9 in Dy1 yields larger anisotropy compared to Dy2.

Further, to understand the magnetic relaxation contributed by the single Dy III centre, we have looked into the nature of the ground state for both the Dy III centres. The ground state for Dy1 is of pure mJ = ±15/2 in nature, whereas for Dy2, a strong mixing of mJ = ±15/2 with other excited states is noticed. The Ucal values obtained for both the centres is 176.3 cm -1 and 117.6 cm -1 respectively.

The calculated energy barrier for magnetic relaxations is overestimated compared to the experimental Ueff value. This suggests that the exchange interaction present between the Dy III ••••Dy III centre/other under-barrier process/QTM effects alters the barrier height for magnetization reversal, hence we looked at the exchange-coupled state of {Dy2} dimer. Though the nature of anisotropy at the ground level is Ising in nature ( Table 4) for both Dy1 and Dy2 centres, the angle of deviation of the ground state axis (Figure 8) significantly deviates at the first excited state for Dy2 ( ~7° vs. ~49° ). The combination angle of deviation of the anisotropic axis and the contribution of higher excited state wave functions lead to different magnetic relaxations offered by Dy2. ACCEPTED MANUSCRIPT For complex 2, the energy spectrum for the lowest Ising doublets is in the range of 0.3 to 535.5 cm -1 and 0.4 to 408.6 cm -1 respectively for Tb1 and Tb2 centres. Despite having significant ground state anisotropy, the non-Kramer nature of the Tb III ion leads to a significant tunnel splitting and lack of zero field SMM behavior for complex 2. The tunnel splitting was found to be 0.19 cm -1 and 0.15 cm -1 for Tb1 and Tb2 centres respectively as a result of different crystal field effects (see Table S13 in SI). The ground state anisotropic axis was plotted for both the complexes 1 and 2 in Figure 9. The anisotropic axis for complex 1 lies parallel to each other in the same plane, which

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agrees well with the earlier reported Dy2 SMMs. 8a, 8h In contrast, for complex 2, a significant tilt between the gzz axis noticed. ACCEPTED MANUSCRIPT

Mechanism of Magnetic Relaxation of Exchange Coupled State of 1 and 2:

For the dinuclear exchanged coupled state, the magnetic relaxation dynamics diagram for complex 1 is plotted in Figure 10 using POLY_ANISO calculations. [START_REF] Chibotaru | The computer programs SINGLE_ANISO and POLY_ANISO[END_REF] For complexes 1 and 2, both the dipolar and exchange interactions were taken into account by using the Lines model using the Hamiltonian given in equation ( 3) below. [START_REF] Boulon | Magnetic Anisotropy and Spin-Parity Effect Along the Series of Lanthanide Complexes with DOTA[END_REF] Following Hamiltonian below is used for calculating the dipolar and exchange interaction between the Ln

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Here Ji=Jidip+Jiexch; that is, Ji are the total magnetic interaction Ln [START_REF] Dey | An approach to estimate the barrier height for magnetisation reversal in {Dy2} SMMs using ab initio calculations[END_REF] The equation is given as follows.

𝑈𝑈 𝑂𝑂𝑅𝑅𝑐𝑐𝑒𝑒𝑐𝑐𝑐𝑐 = � 𝑈𝑈 𝑐𝑐𝑐𝑐𝑐𝑐1

(𝑄𝑄𝐾𝐾𝑄𝑄 𝑜𝑜𝑂𝑂 𝐾𝐾𝑇𝑇-𝑄𝑄𝐾𝐾𝑄𝑄)×10 3 + 𝑈𝑈 𝑐𝑐𝑐𝑐𝑐𝑐1

(𝑄𝑄𝐾𝐾𝑄𝑄 𝑜𝑜𝑂𝑂 𝐾𝐾𝑇𝑇-𝑄𝑄𝐾𝐾𝑄𝑄)×10 3 � + 15𝐽𝐽 …………………(equation 6)

Here Ucal1 and Ucal2 represent the calculated energy barrier for Dy1 and Dy2 center respectively, QTM or TA-QTM represents the value of transition propbabilities between ground states or excited state (one level below where the relaxation is happening). These values are taken from Figure 8 and Table S12 of SI. Using the above formula the Ucaleff is now estimated to be 59 cm -1

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(compare to 41 cm -1 experimental value). This value is improved by 10 cm -1 though a small discrepancy is still there in comparison to the experimental value.

The ferro-antiferro exchange obtained from complexes 1 and 2 is interesting and may be due to subtle structural factors as argued below. It should also be mentioned that the Lines model employed to extract these parameters is semi-empirical and not fully ab initio as generally claimed. The alteration in the Js, however small, could be due to the very small structural distortions present inherently in complexes 1 and 2, and we have earlier established that a small change in bond length or bond angle can lead to the switching of ferromagnetic to antiferromagnetic behavior. [START_REF] Rajeshkumar | A computational perspective on magnetic coupling, magneto-structural correlations and magneto-caloric effect of a ferromagnetically coupled {GdIII-GdIII} Pair[END_REF][START_REF] Dey | An approach to estimate the barrier height for magnetisation reversal in {Dy2} SMMs using ab initio calculations[END_REF] Alternately, it could be purely dictated by the difference in anisotropy between 1 and 2. To ascertain the origin further, DFT calculations were performed on the X-ray structure of 1 and 2 where the anisotropic ions are substituted by the isotropic Gd III ions.

These calculations clearly suggest the J value is antiferromagnetic in 1 and ferromagnetic in 2.

Since the sign is neatly reproduced in the DFT calculations, the nature of switch in the exchange clearly originates from small structural changes.

Further, we have also performed DFT calculations on complex 3, and this yields a ferromagnetic J = +0.1 cm -1 . The exchange values are verified with broken symmetry calculations performed by ORCA as well (+0.07 cm -1 ). The spin density plots are given in Figure 11, and the spin density of

`Scheme 1 .

 1 Scheme 1. LH4 showing unsymmetrical coordination pockets, various conformations based on

1: 1 Scheme 2 .

 12 Scheme 2. Synthesis of Ln2 complexes 1-2.

Figure 1 .

 1 Figure 1. (a) Molecular structure of 1, (b) and (c) side-and top view of 1. Thermal ellipsoids at

  below. The [LH2] 2-and [LH] 3-ligands encapsulate the two Dy III ions in a "head-to-tail" manner utilizing their two coordination pockets, a tridentate P1 (O, 2N) and a pentadentate P2 (3O, 2N) unit to generate the dimeric [Dy2(LH2)(LH)] + motif (Figure1and Scheme 1). Note that in the formation of 1, the ligand has exclusively utilized the enol form to generate the Dy2O2 core. The enolate oxygen atoms (O3 and O7) of the ligand bridge the two metal centers affording a quadrilateral four-membered Dy2O2 core as deduced from the bond distances, Dy1-O3 = 2.359 Å, Dy1-O7 = 2.557 Å, Dy2-O3 = 2.516 Å and Dy2-O7 = 2.341 Å. (Figure2). The Dy••••Dy distance and the two Dy-O-Dy angles in the central Dy2O2 cores are found to be 4.131 Å and 115.80(7),

Figure 2 .

 2 Figure 2. a) Quadrilateral Dy2O2 core of 1; b) core structure of 1. The outer backbone of the ligands

32

 32

Figure 3 .

 3 Figure 3. Spherical capped square antiprism coordination geometry around Dy1 (a) and Dy2 (b).

Figure 4 .

 4 Figure 4. Thermal dependence of the χΜT product for 1 (full black circles), 2 (open triangles).

Figure 5 .

 5 Figure 5. a) Out-of-phase component of the ac magnetic susceptibility data for 1 in zero field in

SMM

  Ueff = 150 K τ0 = 2.3 ×10 -10 ; and Ueff = 198 K [8a] LH2)(LH)(CH3OH)(N3)]•2H2O Capped square antiprismatic geometry SMM Ueff = 59(3) K τ0 = 10(4) ×10 -6 s This work

Figure 6 .

 6 Figure 6. a) Out-of-phase component of the ac magnetic susceptibility data for 15% in zero field in

Figure 7 .

 7 Figure 7. Thermal variation of the relaxation time for 1 at H = 0 Oe (full black spots) and H = 800

Figure 8 .

 8 Figure 8. The SINGLE_ANISO calculated relaxation pathways for Dy1 and Dy2 for complex 1.

Figure 9 .

 9 Figure 9. Arrangement of ground state anisotropy axes for complexes 1 and 2.

Figure 10 :

 10 Figure 10: POLY_ANISO derived magnetic relaxation pathways for complex 1. The red line

Figure 11 .

 11 Figure 11. DFT computed spin density plot for complex 3, the Gd III analogue of complex 1

6 .

 6 95 on Gd III atom indicates spin delocalization. The mechanism of exchange coupling was studied in detail by us previously in {Gd2} dimer bridged by µ-oxo bridges.[START_REF] Rajeshkumar | A computational perspective on magnetic coupling, magneto-structural correlations and magneto-caloric effect of a ferromagnetically coupled {GdIII-GdIII} Pair[END_REF] The nature of magnetic interaction strongly depends on the Gd-O-Gd bond angles. A change of angle even by 1° can lead to a change in the nature of the coupling between the lanthanide ions. For complexes 2 and 3, one ACCEPTED MANUSCRIPT of these angles between Tb-O-Tb and Gd-O-Gd are ~ 114°, and for Dy-O-Dy it is 115°.These angles lie in the borderline area, and may be responsible for the switch in the nature of exchange.ConclusionIn summary we have utilized a multi-dentate aroylhydrazone-based Schiff base ligand, 6-((bis(2hydroxyethyl)amino)-N´-(2-hydroxybenzylidene)picolinohydrazide (LH4) to assemble homometallic dinuclear lanthanide(III) complexes containing non-equivalent lanthanide metal centres [Ln2(LH2)(LH)(CH3OH)(N3)] . xMeOH•yH2O [ 1, Ln = Dy III , x = 0, y = 2; 2, Ln = Tb III , x = 1, y = 1]. The non-equivalence of the lanthanide ions in these complexes arises from the variation of one terminal ligand. Thus, while one of the lanthanides has methanol as the ligand the other has an azide. In all the cases the lanthanide ions are nine-coordinate in a spherical capped square antiprism geometry (as determined by SHAPE analysis). Detailed magnetic studies revealed that 1 is a zero-field SMM with an effective energy barrier (Ueff) 59(3) K of magnetization reversal and a relaxation time of τ0 = 10(4)×10 -6 s while 2 shows a field-induced SMM behavior. Combined ab initio and DFT calculations were performed to understand the observed magnetism. This reveals, that apart from the Kramers vs non-Kramers nature of the lanthanide ion, the individual variations in the coordination geometry around the lanthanide ions seem to play a subtle and important role in dictating the overall magnetic behavior. The change in the behavior of the nature of exchange has also been addressed in relation to the Ln-O-Ln bond angle which agrees with the earlier reported examples. The same magnetic structural correlation of the nature of exchange with metal oxo metal bond angle holds true for the nine coordinated asymmetric dinuclear lanthanide systems as well.

Table 1 .

 1 Crystal data and structure refinement parameters of 1-2

		1	1Y	2
	formula	C37H43Dy2N11O9	C37H43Y2N11O9	C37H43N11O9Tb2
	g/mol	1110.82	963.64	1139.69
	crystal	Monoclinic	Monoclinic	Monoclinic
	system

11d, 15 . 6-((Bis(2-hydroxyethyl)amino)methyl)-N´-(2-hydroxybenzylidene)picolinohydrazide (LH4)

	Salicylaldehyde (A6) (0.19g, 1.6mmol) was added to a solution of 6-((bis(2-
	hydroxyethyl)amino)methyl)picolinohydrazide (A5) (0.406g, 0.0016mol) in ethanol with stirring.
	The reaction mixture was refluxed for 6 hours, cooled and the the solvent reduced in vacuo. The
	concentrated solution was kept in a refrigerator affording a white precipitate which was washed
	with diethyl ether and dried. This was shown to be 6-((bis(2-hydroxyethyl)amino)methyl)-N'-(2-
	hydroxybenzylidene)picolinohydrazide (LH4) (0.305, 76%). Anal. Calcd. For C18H22N4O4
	(358.40): C, 60.32; H, 6.19; N, 15.63 Found: C, 60.58; H, 5.99; N, 15.52. Mp: 164 °C
	1 HNMR (400 MHz,DMSO-d6)	12.12(s,1H,NH), 11.36(s,1H,Ph-OH), 8.86(s,1H,CH),
	8.04(m,2H

,Py-H), δ=7.84

(d,1H

,Py-H), 7.52

(d,1H,Ph-H), 7.32(t,1H,Ph-H), 6.94(m,2H,Ph-H), 4.47(br,2H,OH)

3.95(s,2H,CH2), 3.50(t,4H,CH2), 2.65(t,4H,CH2), IR (KBr) cm -1 : 3498 (br), 3443 (br), 3176 (br), 2955 (s), 2880 (br), 2804 (s), 1675 (s), 1622 (s), 1594 (w), 1536 (s), 1491 (w), 1474 (w), 1449 (s), 1398 (w), 1380 (s), 1371 (w), 1273 (s), 1244 (w), 1222 (w), 1169 (w), 1154 (s), 1045 (s), 971 (s), 898 (s), 780 (w), 737 (s), 698 (w), 678 (s), 566 (w), 518 (s). ESI-MS m/z, ion: 359.1701, (C18H23N4O4) + .

Table 2 .

 2 Selected bond distance (Å) and bond angles (•) of 1

	Bond distances around Dy1	Bond distances around Dy2	Bond angles around Dy
	Dy(1)-O(7)	2.557(17)	Dy(2)-O(7)	2.341(17)	Dy(1)-O(3)-Dy(2)	115.80(
	Dy(1)-O(8)	2.312(17)	Dy(2)-O(3)	2.516(17)
	Dy(1)-O(3)	2.359(17)	Dy(2)-O(5)	2.376(19)
	Dy(1)-O(9)	2.526(19)	Dy(2)-O(4)	2.404(18)
	Dy(1)-O(2)	2.234(17)	Dy(2)-O(6)	2.217(18)
	Dy(1)-O(1)	2.492(19)	Dy(2)-N(6)	2.487(2)
	Dy(1)-N(11)	2.628(2)	Dy(2)-N(8)	2.516(2)
	Dy(1)-N(10)	2.525(2)	Dy(2)-N(7)	2.636(2)
	Dy(1)-N(4)	2.512(2)	Dy(2)-N(1)	2.544(2)

Table 3 .

 3 Some representative examples of dinuclear dysprosium complexes with unsymmertrical

	coordination environment.
	Compound	Local	Magnetic properties	ref.
		geometries
		around Ln III
		centers
	[Dy2ovph2Cl2(MeOH)3]3 MeCN	Hula hoop-like
		geometry(centre
		1) and
		pentagonal

Table 4 .

 4 Ab initio estimated g-values along with the ground state wave function estimated for 1 and their respective models.

	Complex	gx	gy	gz	Wave functions contributions to the ground state
	1-Dy1	0.0106	0.0171	19.9194 0.99|±15/2⟩
	1-Dy2	0.0124	0.0199	19.7092 0.70|±15/2⟩+0.02|±13/2⟩+.20|±11/2⟩+0.04|±9/2⟩
	1a-Dy1	0.0083	0.0132	19.9226 0.99|±15/2⟩
	1a-Dy2	0.0176	0.0280	19.7353 0.96|±15/2⟩⟩+0.03|±11/2⟩
	1b-Dy1	0.0097	0.0162	19.9138 0.99|±15/2⟩
	1b-Dy2	0.0271	0.0476	19.7406 0.96|±15/2⟩⟩+0.03|±11/2⟩

Table 5 :

 5 Ab initio and DFT computed exchange values for complex 1-3.

	Complexes	Ab initio fitted (in cm -1 )		DFT computed (in cm -1 )
		Jex	Jdip	Jtot	J
	1	-0.60	+0.15	-0.45	-0.55
	2	+0.45	+0.13	+0.58	+0.60
	3	-	-	-	+0.10

  III

  ••••Ln III centres.

	𝐻𝐻 � 𝑒𝑒𝑒𝑒 = -∑ 𝐽𝐽 𝑖𝑖 𝑆𝑆 𝑖𝑖 𝑆𝑆 𝑖𝑖+1 𝑖𝑖	…………………………………………………………………...(Eq 3)

  III

  ••••Ln III , this describes the interaction between the neighbouring metal centres.Lines model yields an excellent fit with the experimental data, and the extracted J values are given in Table5. It has been noticed that the exchange interaction between Dy III ••••Dy III is weakly antiferromagnetic in nature, whereas for complex 2, the interaction between Tb

	𝐻𝐻 � = -(-𝐽𝐽 𝑑𝑑𝑖𝑖𝑑𝑑 𝐿𝐿𝑛𝑛 𝑖𝑖 -𝐿𝐿𝑛𝑛 𝑖𝑖+1	+ 𝐽𝐽 𝑒𝑒𝑒𝑒𝑂𝑂ℎ 𝐿𝐿𝑛𝑛 𝑖𝑖 -𝐿𝐿𝑛𝑛 𝑖𝑖+1 )𝑠𝑠̃𝐿𝐿 𝑛𝑛 𝑖𝑖 𝑠𝑠̃𝐿𝐿 𝑛𝑛 𝑖𝑖+1 …………………………………………(Eq 4)
	𝐽𝐽 𝑑𝑑𝑖𝑖𝑑𝑑 𝐿𝐿𝑛𝑛 𝑖𝑖 -𝐿𝐿𝑛𝑛 𝑖𝑖+1	=	𝜇𝜇 𝐵𝐵 2 𝐷𝐷𝐷𝐷 𝑖𝑖 -𝐷𝐷𝐷𝐷 𝑖𝑖+1 𝑅𝑅 3	𝑔𝑔 𝐿𝐿𝑛𝑛 2 ……………………………………………………...……(Eq 5)

  III

  ••••Tb III is found to ferromagnetic in nature. The mechanism of magnetisation relaxation developed for the dinuclear model is shown in Figure 10. The mechanism computing using the POLY_ANISO routine yields a Ucal value of 69 cm -1 and this matches closely with experimental Ueff value (41cm -1 ). It has been observed that there is a discrepancy in the Ueff value obtained by experiment and Ucal value obatained from ab initio calculation for the exchange coupled state. Recently we have reported an alternate equation to estimate the Ucal values for dinuclear Dy III systems.

ACKNOWLEDGMENTS

We thank the Department of Science and Technology (DST), India; the CNRS, Université de Rennes 1, the European Commission through the ERC-CoG 725184 MULTIPROSMM (project no. 725184) for financial support, and also support for the Single Crystal CCD X-ray Diffractometer facility at IIT-Kanpur. V.C. is grateful to the DST for a J. C. Bose fellowship. P.K. and A.S. thanks University Grants Commission (UGC), India for Senior Research Fellowship. G.R. acknowledges DST/SERB for funding (CRG/2018/000430; DST/SJF/CSA-03/2018-10; SB/SJF/2019-20/12).We sincerely thank Mr. Prakash Nayak, NISER, Bhubanswar, Odisha, India for the PXRD measurements.

Supplementary Information (SI): Crystal data information Table S1 for 3, Simulated singlecrystal data and experimental XRD pattern for 1-2, ESI-MS spectrum of complex 2 and 3, Molecular structure and bond length and bond angle of 2 and 3, Continuous Shape measures calculations, Supramolecular interactions, . Field dependence of molar magnetization plot at 2K and Field dependence of molar magnetization plot in complexes and In-phase component of the ac magnetic susceptibility data for 1, Normalized Cole-Cole plot at several temperatures between 2 and 15 K for 1 under 0 Oe and 800 Oe, ac magnetic susceptibility data and Normalized Cole-Cole plot at several temperatures between 2 and 15 K for 15%, In-phase and out-of-phase components of the ac magnetic susceptibility for 2 at 2 K in an applied DC magnetic field from 0 to 3000 Oe, In-phase (χM') and Out-of-phase (χM'') components of the ac magnetic susceptibility data for 2 in 2800 Oe applied magnetic field, CASSCF +RASSI-SO+SINGLE_ANISO computed energies of the eight low-lying KDs and SINGLE_ANISO computed crystal field parameters 1 and 2, DFT computed spin density on Ln centre using Broken symmetry approach for complex 1-

3.

AUTHOR INFORMATION

Corresponding Authors *E-mail: vc@iitk.ac.in. *E-mail: rajaraman@chem.iitb.ac.in. *E-mail: fabrice.pointillart@univ-rennes1.fr. Fabrice Pointillart: 0000-0001-7601-1927 Gopalan Rajaraman: 0000-0001-6133-3026

ORCID

ACCEPTED MANUSCRIPT

Vadapalli Chandrasekhar: 0000-0003-1968-2980

Notes

The authors declare no competing financial interest.

ACCEPTED MANUSCRIPT

48. Rajeshkumar, T.; Rajaraman, G. Is a radical bridge a route to strong exchange interactions in lanthanide complexes? A computational examination. Chem. Commun. 2012, 48, 7856-7858

'For Table of Content Use Only'

The syntheses, structures and combined theoretical and experimental magnetic properties of a family of dinuclear complexes having non-equivalent lanthanide ions have been studied which showed the Dy III analogue as a zero-field single-molecule magnet.