Design of a Binuclear Ni(II) Complex with Large Ising-type Anisotropy

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Design of a Binuclear Ni(II) Complex with Large Ising-type Anisotropy and Weak Anti-Ferromagnetic Coupling Fatima El-Khatib,†,‡ Benjamin Cahier,† Maurici López-Jordà,† Régis Guillot,† Eric Rivière,† Hala Hafez,‡ Zeinab Saad,‡ Jean-Jacques Girerd,† Nathalie Guihéry,*,§ and Talal Mallah*,† †

Institut de Chimie Moléculaire et des Matériaux d’Orsay, Université Paris Sud, CNRS, Université Paris Saclay, 91405 Orsay Cedex, France ‡ Lebanese University, Inorganic & Environmental Chemistry Laboratory, Faculty of Sciences I, Hadath, Lebanese University, Beirut, Lebanon § Laboratoire de Chimie et Physique Quantiques, Université Toulouse III, 118 route de Narbonne, 31062 Toulouse, France S Supporting Information *

ABSTRACT: The preparation of a binuclear Ni(II) complex with a pentacoordinate environment using a cryptand organic ligand and the imidazolate bridge is reported. The coordination sphere is close to trigonal bipyramidal (tbp) for one Ni(II) and to square pyramidal (spy) for the other. The use of the imidazolate bridge that undergoes π−π stacking with two benzene rings of the chelating ligand induces steric hindrance that stabilizes the pentacoordinate environment. Magnetic measurements together with theoretical studies of the spin states energy levels allow fitting the data and reveal a large Isingtype anisotropy and a weak anti-ferromagnetic exchange coupling between the metal ions. The magnitude and the nature of the magnetic anisotropy and the difference in anisotropy between the two metal ions are rationalized using wave-function-based calculations. We show that a slight distortion of the coordination sphere of Ni(II) from spy to tbp leads to an Ising-type anisotropy. Broken-symmetry density functional calculations rationalize the weak anti-ferromagnetic exchange coupling through the imidazolate bridge.

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INTRODUCTION One of the challenges in coordination chemistry is the design of complexes with targeted chemical and/or physical properties (catalysis, optical, magnetic, etc). It is the case in the field of molecular magnetism if one aims at preparing binuclear complexes that behave as double quantum bits (qbits) useful for quantum information processing. 1,2 In a binuclear transition-metal ions-containing complex, the Ising-type local anisotropy leads to a state of superposition (q-bit), and the anti-ferromagnetic coupling ensures the apparition of entangled states required for building quantum logical gates.1 A state of superposition can be obtained in the case of an Ising-type magnetic anisotropy, that is, negative axial D and zero, or nearly zero, rhombic E values for the zero-field splitting anisotropy spin Hamiltonian (H = DSz2 + E(Sx2 − Sy2)) parameters.3 And entanglement is ensured through anti-ferromagnetic coupling between the metal ions.1 Practically, it is desired to have as large as possible Ising-type anisotropy to produce a robust q-bit and weak anti-ferromagnetic coupling to address the quantum states with accessible energies such as a weak magnetic field or microwaves available with electron paramagnetic resonance (EPR) apparatus. Much progress was lately achieved, theoretically and experimentally, to correlate the magnitude © XXXX American Chemical Society

and the nature (Ising type or planar) of the magnetic anisotropy with the electronic configuration of the metal ions, the symmetry, and the electronic nature of the surrounding organic ligands in mononuclear complexes.4−13 For example, Ni(II)-containing mononuclear complexes in a pentacoordinate coordination sphere and particularly with a trigonal bipyramidal (tbp) symmetry were recently shown to possess very large Ising-type magnetic anisotropy and can thus be considered as possible candidates for robust q-bits.7,10 However, to date, no attempts to use these highly anisotropic species to build binuclear transition-metal-containing complexes were made. Our objective is to design such complexes. They must respond to the following requirements: (i) chemical stability in solution, (ii) large local Ising-type anisotropy, and (iii) weak antiferromagnetic coupling. We report here the preparation, the crystal structure, the study, and the analysis of the magnetic properties of an imidazolate-bridged binuclear Ni(II) complex embedded in the bis chelating cryptand-like organic ligand 6,16,2,5-tribenzena(1,3)-1,4,8,11,14,18,23,27-octaazabicyclo[9.9.9]nonacosaphane Received: June 26, 2017

A

DOI: 10.1021/acs.inorgchem.7b01609 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Table S1). It consists of the tricationic complex [Ni(C3H3N2)NiL]3+ and three ClO4− anions. The Ni(II) ions are pentacoordinate (Figure 2) with slightly different coordination

noted L (Figure 1). The cryptand ligand L possesses two tetradentate coordination sites that favor trigonal geometry.

Figure 1. Schematic view of the bis chelating ligand L.

Several binuclear Ni(II) complexes with the same or similar bis chelating ligands were reported, but the Ni(II) ions were hexacoordinate and thus possess weak magnetic anisotropy.14−17 Only in one case when the bridging ligand is MeCO2−,17 the two Ni(II) were pentacoordinate. But the anti-ferromagnetic coupling was reported to be relatively large, and no information on the magnetic anisotropy was given.

Figure 2. View of the structure of the binuclear species; hydrogen atoms are omitted for clarity (left) and spacefill view highlighting the Ni atoms (green) embedded in the cryptand ligand.

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RESULTS AND DISCUSSION Synthetic Approach. Since a large magnetic anisotropy of the Ising type was demonstrated to occur in trigonal Ni(II) complexes,7,8,10 we reasoned that the use of the bis chelating ligand depicted in Figure 1 including a bridge between the Ni(II) ions should stabilize pentacoordination with hopefully a geometry close to tbp. However, several trials with different bridging ligands either led to hexacoordinated complexes with a solvent molecule or a counteranion such as Cl− or NO3− as the sixth coordinating ligand, or to pentacoordinate complexes with a geometry very close to square pyramidal (spy). We have recently shown that, while Co(II) is stable in a tbp or nearly tbp geometry,12,18 Ni(II) generally prefers to be square pyramidal.12 We reasoned that using a bulky bridging ligand, between the Ni(II) ions, may preclude the approach of a sixth ligand and favors the formation of pentacoordinated sphere with a geometry close to tbp. The imidazolate bridge has these properties.19 The synthesis of the cryptand-like ligand noted L was performed using the procedure already reported.20 The preparation of the binuclear complex of general formula [Ni(μ-Im)NiL](ClO4)3 (Caution! Perchlorate salts may have unpredictable behavior and may explode, they must be handled with care under a protected hood and must never be heated.) and its full characterization by elemental analysis and infrared and mass spectroscopies are given in the Supporting Information. The mass spectroscopy study presents, among others, two peaks corresponding to the binuclear complex free of solvent molecules at m/z values equal to 441.1 and 981.2 corresponding to the di- and mono-cation species [Ni(C3H3N2)NiL(ClO4)]2+ and [Ni(C3H3N2)NiL(ClO4)2]+, respectively, confirming the stability of the complex with pentacoordinate geometry in solution. Structural Description. Single crystals suitable for singlecrystal X-ray diffraction studies were obtained by a slow evaporation of a solution containing the compound (see Supporting Information). The compound crystallizes in the monoclinic space group P21/c (see Supporting Information

spheres. The Ni1 site is closer to tbp (τ = 0.6), while Ni2 is closer to spy (τ = 0.31) according to Addison et al., where τ is equal to 1 and 0 for the pure tbp and spy, respectively.21 The details of the bond distances and angles are given in the Supporting Information (Table S2). The imidazolate bridge is almost parallel to two benzene rings of the cryptand ligand with angles of 5° and 4° between the axes perpendicular to the benzene planes and the imidazolate plane and distances of ∼3.05 Å (see Supporting Information Figure S1); these structural features are compatible with the presence of π−π stacking between the imidazolate and two benzene rings of the cryptand ligand, thus fixing the orientation of the imidazolate in the cavity. The space fill view shows indeed that the Ni(II) ions are protected precluding the coordination of a sixth ligand thus ensuring the stabilization of the pentacoordinated species in solution. Magnetic Properties. When cooled, the χMT product smoothly decreases between T = 300 (2.56 cm3 mol−1 K) and 50 K and then more abruptly to reach a value of 0.24 cm3 mol−1 K at T = 2 K (Figure 3). The value at room temperature corresponds to two non-interacting S = 1 species with an average g value of 2.26. The χMT value at low temperature, close to zero, cannot be only due to zero-field splitting (ZFS) and is compatible with the presence of an anti-ferromagnetic exchange coupling interaction between the two S = 1 Ni(II) ions. The magnetization versus B/T curves at T = 2, 4, 6, and 8 K (Figure 3) are not superimposable, which is the signature of relatively large magnetic anisotropy. We fitted simultaneously the magnetization and the thermal dependence of χMT and χM data, using the PHI package22 and considering the following Hamiltonian: H = β SA •[gA]• B + β SB •[g B]• B + SA •[DA ]• SA + SB •[DB]• SB − J SA • SB

(1)

where β is the Bohr magneton, B is the magnetic field, gA, gB, DA, and DB are the g and ZFS tensors, J is the exchange coupling parameter, and SA and SB are the spin operators of the B


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Inorganic Chemistry

Figure 3. Thermal dependence of χMT (experimental, ○) and χM (experimental, △) (left) and magnetization versus B/T (right) at different T = 2, 4, 6, and 8 K; best fit ().

From the qualitative point of view, this result is not surprising if one assumes that the axial ZFS parameters DA and DB are negative and large and the exchange parameter J is much weaker (in absolute value) than DA and DB. Indeed, for such a case, the mS = ±1 sublevels of each Ni(II) will be the ground levels, and for the binuclear complex all the lowtemperature physics will depend only on the rhombic parameters that split the mS = ±1 sublevels and on J that couples these levels. Theoretical Calculations. This section comprises three parts: (i) the theoretical determination of the energy spectrum of the low-lying magnetic levels, (ii) relativistic wave-function (WF)-based calculations of the local ZFS parameters, and (iii) density functional theory (DFT) calculations to determine the exchange coupling parameter between the Ni(II) ions. WFbased calculations were performed using the Molcas 8.0 package.23 ANO-RCC basis sets were used (details are given in Supporting Information).24,25 Unfortunately, the compound is too large to be fully studied using wave-function-based methods. Only the local anisotropic parameters were therefore extracted. The calculations of these parameters for the two Ni(II) sites in the binuclear complex were performed by replacing each other site by the diamagnetic Zn(II) cation. The ZFS parameters were calculated using a two-step method. Nondynamic correlation is taken into account at the complete active space self-consistent field (CASSCF) level, and the spin− orbit coupling (SOC) is introduced in a second step using the SO-RASSI method.26 Calculations at the CASPT2 level introducing dynamical correlation at the second-order perturbative level were also performed.27,28 The procedure of extraction of the ZFS parameters from the effective Hamiltonian theory29,30 and the computed energies and wave functions has already been successfully used by some of us.4,13,31−35 The broken-symmetry (BS) DFT calculations were performed using the Gaussian package36 to evaluate the exchange coupling J for the binuclear complex.36 The rangeseparated wB97XD functional37 and a TZVP basis set38 were used for all atoms. The BS DFT approach combined with a strategy first proposed by Noodleman is a powerful tool for the calculation of model Hamiltonian parameters.39 While one of its main advantages over WF-based methods lies in its application to larger systems, it is also particularly suited for geometry optimizations,40,41 for the determination of subtle interactions such as double exchange,42 and the biquadratic exchange in systems of spin S = 1.43 Their performances are well-documented in several review papers.44−48 Two brokensymmetry solutions were computed, namely, the MS = mS1 + mS2 = 0 one that has the local mS1 = 1 and mS2 = −1

two Ni(II) sites. The rhombic parameter of the D tensors is defined as E = Dxx − Dyy/2, and the axial parameter D is equal to 3Dzz/2, where Dxx, Dyy, and Dzz are the components of the D tensor. We first tried to perform the fit using the axial ZFS parameters DA and DB and the exchange coupling parameter J setting the rhombic parameters EA and EB to zero to avoid overparameterization. It was not possible to obtain a good fit in these conditions. It was particularly not possible to reproduce the increase of the thermal dependence of the susceptibility at low temperature without considering a large amount of paramagnetic mononuclear Ni(II) impurities that could be as large as 40%, which is not possible given that measurements were made several times on pure polycrystalline samples with reproducible experimental results. Introducing rhombicity leads to an excellent fit of the data with the following parameters: DA = −30.7 cm−1, EA = 3.4 cm−1 (|EA/DA| = 0.11), DB = −24.5 cm−1, EB = 7.2 cm−1 (|EB/DB| = 0.29), J = −3.8 cm−1, temperature-independent paramagnetism (TIP) = 3.8 × 10−4 cm3 mol−1, and gA = gB = 2.31 (we assumed here isotropic g tensors). To check the robustness of the fit parameters, we tried different fit procedures by fixing D for the two Ni(II) sites to different values. Different D values for two pentacoordinate Ni(II) sites are expected on the basis of the difference in their local structure. We found that it was possible to fairly reproduce the magnetic data with different sets of parameters; on one hand, we found: DA = −50.0 cm−1, EA = 4.0 cm−1 (|EA/DA| = 0.08), DB = −19.0 cm−1, EB = 6.0 cm−1 (|EB/DB| = 0.31), J = −3.8 cm−1, TIP = 2.0 × 10−4 cm3 mol−1, and gA = gB = 2.25 and, on the other hand, DA = −70.0 cm−1, EA = 9.0 cm−1 (|EA/ DA| = 0.13), DB = −24.0 cm−1, EB = 6.0 cm−1 (|EB/DB| = 0.25), J = −2.4 cm−1, TIP = 0.3 × 10−4 cm3 mol−1, gA = 2.29, and gB = 2.20. However, it is not possible to obtain a good match with the experimental data if the D values are positive, if they are weakly negative, or if |J| is outside the 4−2 cm−1 range. Furthermore, the |E/D| value for one of the Ni(II) ions must be smaller than that of the other, which one is tempted to link to the weaker rhombicity of Ni(II) in the site closer to the tbp geometry. It is, however, important to note that strictly speaking, it is not possible to assign the different sets of parameters to each Ni(II) site. Finally, we assumed that the g tensors isotropic to avoid overparameterization and that the anisotropy tensors of the two Ni(II) sites are collinear. The fact that it is possible to reproduce the experimental data, particularly the low-temperature magnetization ones, with relatively different (but large and negative) sets of the axial ZFS parameters leads to the conclusion that the low-lying states have only weak dependence on the axial ZFS parameters. C


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Inorganic Chemistry components on each Ni(II) ion and the MS = 2 solution. Assimilating the corresponding energies to those of the Ising Hamiltonian (diagonal energies of the Heisenberg Hamiltonian), the magnetic coupling J can be extracted from the energy difference between the two solutions, namely, E(MS = 0) − E(MS = 2) = 2J. Theoretical Determination of the Energy Spectrum of the Magnetic Levels. The detail of the full calculations is given in Supporting Information. In summary, we consider the ZFS and exchange part of the Hamiltonian of eq 1 that can be written in the following form: H0 = DA SAZ 2 + DBSBZ 2 + EA (SAx 2 − SAy 2) → ⎯ → ⎯ + E B(SBx 2 − SBy 2) − J SA SB

magnetic data (see above for the values of the parameters) are given for comparison with those obtained from the best fit (Figure 4). One can see that when one of the Ni sites has a large ZFS axial parameter, the experimental data at a high field and low temperature cannot be perfectly reproduced (see Supporting Information Figure S3). This analysis allows one to define a range of values for the axial ZFS parameters: −70 < DA < −30 and −30 < DB < −20, while for the rhombic parameters one can conclude that |EA/DA| < |EB/DB|. Wave-Function-Based Calculations. To get more insight into the local magnetic anisotropy of the Ni(II) ions and to assign the parameters extracted from the fits to each Ni site of the binuclear complex, we calculated the local ZFS parameters for Ni1 and Ni2. We obtained the following values: D1 = −91.6 cm−1, E1 = −2.8 cm−1 (E1/D1 = 0.03), D2 = −33.8 cm−1, and E2 = −8.3 cm−1 (E2/D2 = 0.27). These results suggest that Ni1 has larger axial anisotropy and less rhombicity than Ni2. They are compatible with recently reported results where the axial magnetic anisotropy was found to be very large (|D| larger than 200 cm−1) for species with a strict trigonal symmetry.7,8,10 One may however be surprised by these lower values of D in comparison to previously reported ones. As explained in ref 7, for a strict trigonal bipyramidal geometry, the xy and x2−y2 orbitals would be degenerate, and a first-order spin−orbit coupling would result in a huge value of D (635 cm−1). The loss of threefold symmetry axis lifts the degnerancy of the orbitals and is responsible for the weaker values of D in the present complex. We calculated the magnetic data with these parameters setting J = −3.8 cm−1 and g1 = g2 = 2.31; the agreement with the experimental is not very good (see Supporting Information Figure S4). The main difference between the calculated parameters and those obtained from fittings of the magnetic data concerns the value of D1. This is because the ground level is coupled with an excited state with an energy difference that depends on D1; increasing this difference reduces the coupling and the composition of its wave function and thus changes its magnetic response. However, the local ZFS parameters obtained from calculations are qualitatively in agreement with those extracted from the analysis of the magnetic data. To get insight into the origin of the difference in magnetic anisotropy between the two Ni sites and the relation between the magnitude of the magnetic anisotropy, its nature (axial/ rhombic), and the local structure of the metal ions as this is necessary for designing complexes with predictable magnetic behavior, we analyzed the ab initio calculated energy spectrum of the states and the nature of their wave functions obtained before considering the effect of the spin−orbit coupling (see Supporting Information Figure S5 and Table S3). The energy difference between the ground (T0) and the first excited (T1) triplet states is weaker for the Ni1 site (geometry close to tbp) than for the Ni2 site (geometry closer to spy; Figure 5), and consequently, the contribution of the first excited state to the overall values of Di is larger for Ni1(−163 cm−1) than for Ni2 (−94 cm−1), because the magnitude of D is inversely proportional to the T0 − T1 energy difference. The other two triplet states (T2 and T3) contribute with positive D values weaker in magnitude than T1 (see Supporting Information, Table S3). There are 6 additional triplet states and 15 singlet states for each Ni(II) ion, but they are all at energies higher than 11 000 cm−1 above the ground state. Even though each state contributes weakly positively (apart from one that contributes negatively) to the overall D values, the sum of

(2)

and we determine its eigenvalues and the eigenfunctions on the nine microstates |mA,mB⟩ (mA = 0, ±1, mB = 0, ±1) basis. Assuming that the main magnetic axes z of the two Ni(II) ions are collinear and that the anisotropic exchange and antisymmetric parameters are negligible, we find that, for negative and large in absolute value DA and DB and a weak and negative exchange parameter J such that |J/(DA + DB)| ≪ 1, the energies of the four low-lying levels (numbered from the lowest) are Λ1 = DA + DB −

J 2 + (EA + E B)2

Λ 2 = DA + DB −

J 2 + (EA − E B)2

Λ3 = DA + DB +

J 2 + (EA − E B)2

Λ4 = DA + DB +

J 2 + (EA + E B)2

(3)

The expressions for Λ2 and Λ3 are exact whatever the values of the parameters are, and their difference is thus independent from the axial ZFS parameters DA and DB. The expressions given for Λ1 and Λ4 are only approximate, because these two levels mix with an excited level (see Supporting Information), the energy of which depends slightly on J and DA + DB. This impacts the magnetization, particularly at large applied magnetic field. Figure 4 depicts the variation of the nine energy levels of the binuclear complex as a function of J considering the parameters obtained from the best fit. The Λ = f(J) plots (see Supporting Information, Figures S2 and S3) with the other sets of parameters that also reproduce well the

Figure 4. Dependence of the energy levels of the binuclear complex with the exchange parameter J for the following spin Hamiltonian (eq 2) values DA = −30.7 cm−1, EA = 3.4 cm−1, DB = −24.5 cm−1, EB = 7.2 cm−1; the dotted line corresponds to the case J = −3.8 cm−1. D


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difference in geometry, because as stated above the coordination spheres of the Ni sites have identical ligands. One may notice that the relative energy of the Ni2 site orbitals is similar to what one expects for a spy geometry considering simple crystal-field arguments. The T1 state is obtained mainly by an electron excitation from orbital3 (O3) to O4 (Figure 5). The energy difference between these two orbitals is larger for Ni2 (1887 cm−1) than for Ni1 (1340 cm−1), and so is the T0− T1 energetic separation, which explains the larger (in absolute value) axial anisotropy parameter of Ni1. The orientation of the local anisotropy tensors’ axes shows that their magnetic z axes are almost collinear; they deviate only slightly from the metal-bridge bonds as depicted in Figure 6. Figure 5. Energy of the first triplet states (left) and of the d orbitals (right) for Ni1 and Ni2 sites. Their decompositions are given in Supporting Information.

their contributions is not negligible but does not counterbalance that of the first excited state. Thus, the axial contribution to the magnetic anisotropy is mainly governed by the first three excited triplet states (T1, T2, and T3, Figure 5). To rationalize the nature of the contribution of each excited state, we analyzed their wave functions. We focus on Ni1; the analysis for Ni2 is similar. The wave function of T0 is multideterminantal mainly formed by the two determinants | xy,z2| and |x2 − y2,z2| with 22% and 73% weights, respectively (we neglected all the determinants that have weights smaller than 5%). The wave function of T1 is formed by the same determinants but with different weights, that is, 62% and 20% for |xy,z2| and |x2 − y2,z2|, respectively. The excitation between T0 and T1 triplet states involves, thus, electron excitation between the xy and x2−y2 orbitals that possess the same ml = ±2 values. As is well-known, the lzsz part of the spin−orbit operator couples these two determinants and leads to the stabilization of the largest mS (±1 here) and thus to a negative D contribution.6 The wave function of T2 is formed by the combination of the |xz,z2| and the |xz,x2 − y2| determinants with 56% and 28% weights, respectively. The coupling between T0 and T2 is achieved via the l+s− + l−s+ part of the spin−orbit operator and not by the lzsz part, because it involves an electron excitation from the xz to the xy (and x2−y2) orbitals that possess ml values differing by ±1. In this case, the mS = 0 level is stabilized, which corresponds to a positive D contribution. Since T2 has higher energy than T1 (5755 cm−1 in comparison to 2252 cm−1, see Figure 5 and Table S3), its contribution to D is weaker in absolute value (+27.4 cm−1 instead of −163.5 cm−1). The T3 state also contributes positively to D1 for the same reason but to a lesser extent than T2, because it is higher in energy. In summary, the overall D1 value for Ni1 is negative, because T1 contributes to a large negative D value, while the other (T2 and T3) triplet states have positive contributions that do not compensate the effect of T1. The same analysis holds for Ni2. The main difference between the two sites is the larger negative contribution of the triplet state T1 in the case of Ni1 than in the case of Ni2 due to its weaker T0−T1energy separation (2252.1 cm−1 in comparison to 4028.4 cm−1, see Supporting Information Figure S5). To get insight into the effect of geometry on the magnitude of magnetic anisotropy, we compared the relative energies the five d orbitals obtained from ab initio calculations (Figure 5), where each orbital is a linear combination of some of the real d orbitals (see Supporting Information Table S4). The difference in the relative energies of the orbitals is mainly due to the

Figure 6. Local anisotropy tensors axes for Ni2 (up) and Ni1 (bottom); x (red), y (green), and z (blue).

The orientation of the axes of the local D tensors is mainly determined by the nature of the first excited state (T1), because this state has the largest contribution to ZFS. We have shown above that the spin−orbit coupling between T0 and T1 involves only the lzsz part of the spin−orbit operator, which fixes the orientation of the easy axis of magnetization of Ni(II) along the pseudo threefold symmetry axis of the pseudo tbp as already found for other Ni(II) complexes with such geometry.7,8,10,11 The presence of a rhombic term (anisotropy between x and y) results from the small deviation from 120° of the angle values in the equatorial plane (Table S2). For Ni2, the geometry of the site is closer to a square pyramid. For a perfect or nearly perfect spy geometry, the complex is expected to have a hard axis of magnetization along the pseudo fourfold axis of the square pyramid (Ni2−N7), as we recently demonstrated.12 However, the calculations show that Ni2 has an easy axis of magnetization along the N5−Ni2− N10(Im) direction that corresponds to the pseudo threefold axis of a distorted tbp and thus perpendicular to the pseudo spy axis. From the magnetic point of view, the Ni2 behaves as if it was in a tbp environment, even though from the structural point of view its geometry is closer to a square pyramid. This leads to the conclusion that a slight distortion of the coordination sphere of a Ni(II) ion from the spy toward tbp changes the orientation of the z axis of the tensor and thus the nature of its magnetic anisotropy from planar to axial. This conclusion must be attenuated by the fact that the rhombicity of the Ni2 site is rather large (E2/D2 = 0.27). E


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and may have an anti-ferromagnetic contribution (JijAF) if the overlap integral between the MOs is also different from zero:

The discrepancy of the theoretical and experimental values of the ZFS parameters can be seen as an indicator of the existence of a large anisotropy of exchange. Indeed, as already shown elsewhere,49,50 while the components of the symmetric Dab tensor of exchange and Dzyaloshinski−Moriya vector are usually quite small,51 the components of the four rank tensors of anisotropy can be very large. In such cases, the spin−orbit state energy expressions of eqs 3 should account for these additional terms, which would lead to different fits of the magnetic data. Broken-Symmetry Density Functional Calculations. The crystal structure and the magnetic properties of two binuclear pentacoordinate Ni(II) complexes with an imidazolate bridge and nearly perfect spy geometry have been reported in the literature.52,53 The exchange coupling parameters were reported to be anti-ferromagnetic and larger than 30 cm−1 in absolute value, and the effect of the ZFS was not taken into account. The exchange parameter in another binuclear complex with benzoimidazole bridging the Ni(II) ions was found equal to −5.8 cm−1 with D = 50 cm−1, but the crystal structure was not reported.54 To rationalize the relatively weak and antiferromagnetic exchange coupling parameter in the present complex, we performed DFT calculations. The computed exchange coupling parameter J was found equal to −3.9 cm−1 in perfect agreement with the value (−3.8 cm−1) obtained from fitting the experimental magnetic data. The molecular orbitals (MOs) were optimized for the MS = 0 broken-symmetry solution. As usual in DFT and contrarily to what is obtained in WF-based methods, the magnetic orbitals (defined as the simply occupied MOs) are strongly delocalized on the ligands. The four singly occupied MOs with α (MO1 and MO2) and β (MO3 and MO4) spin on the Ni2 and Ni1, respectively, are depicted below (Figure 7). The overall exchange interaction (J) between the two Ni ions may be expressed as the sum of four exchange pathways (Jij). Each exchange pathway has a ferromagnetic contribution (JijF)

1 J = ( )[J1,3 + J1,4 + J2,3 + J2,4 ] with Jij = JijF + Jij AF 4 (4)

where the indexes i and j refer to the singly occupied MOs, 4 is the product of the number of single electrons, JijF > 0, and JijAF < 0. Because of the very large distance between the two magnetic centers and despite the presence of non-negligible coefficients on the atoms of the bridging ligands (that are always overestimated in DFT calculations), the magnetic coupling is obviously expected to be very weak. The ferromagnetic contributions must be negligible, as they are proportional to the differential overlap between the magnetic MOs. Concerning the anti-ferromagnetic contributions that are proportional to the overlap integral between two MOs, they must be considered one by one. The α- and β-spin MO1 and MO3 have very weak and negligible contributions of the imidazole bridge, respectively; the overlap integrals involving these two orbitals are thus negligible, and the corresponding exchange pathways J1,3, J1,4, and J2,3 have thus negligible contributions to the overall exchange coupling. At the contrary, the overlap integral between MO2 and MO4 is relatively large because of the relatively large contribution of the imidazolate bridge to these orbitals; the J2,4 pathway contributes thus mainly to the anti-ferromagnetic coupling. Finally, the MOs have contributions on the benzene rings that may bring anti-ferromagnetic contributions to the overall exchange. The plot of the spin density calculated in the MS = 0 solution shows that the three benzene groups do not carry any spin density (see Figure 8 and Figure S6) and that the only channel of the magnetic coupling goes through the imidazole bridge. In summary, the exchange coupling between the Ni sites is expected to be weak as found experimentally and confirmed by the BS-DFT calculations. It is worth mentioning that, because the shortest intermolecular Ni−Ni distances are larger than 8 Å, intermolecular exchange coupling is negligible.

Figure 7. Singly occupied α on Ni2 (MO1 and MO2) and β on Ni1(MO3 and MO4) singly occupied magnetic orbitals calculated for the MS = 0 broken-symmetry solution.

Figure 8. Plot of the spin density calculated in the MS = 0 solution. F


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Author Contributions

CONCLUDING REMARKS Our objective concerned the design of a binuclear Ni(II) complex with large magnetic anisotropy of the Ising type (easy axis of magnetization) and weak anti-ferromagnetic coupling as potential candidate for a double q-bit system. Since trigonal Ni(II) complexes have huge Ising-type anisotropy,7,8,10 we used a cryptand ligand that possesses two trigonal tetradentate coordination sites that may favor such environment.18 However, despite the geometry imposed by the cryptand, Ni(II) complexes tend to be hexacoordinated with very weak anisotropy. To circumvent this problem, we used imidazolate as the bridging ligand. The imidazolate bridge is sandwiched between two of the benzene rings of the cryptand by π−π stacking, thus fixing its orientation within the cavity that precludes the coordination of a sixth ligand on the Ni(II) ions and stabilizes pentacoordinate environments for the metal ions. The geometry of the metal ions is close to tbp for one Ni(II) and to spy for the other. However, the two metal ions were found to possess easy axis of magnetization that are almost collinear despite their different geometry. This is because a slight distortion of the geometry of a Ni(II) ion from spy to tbp is sufficient to orient its easy axis of magnetization along the pseudo threefold axis of the distorted tbp. We have, thus, achieved most of the requirements, that is, a binuclear complex with a large local magnetic anisotropy, nearly collinear easy axes of magnetization, and weak anti-ferromagnetic coupling. However, the anisotropy is not purely of the Ising type, because the symmetry of the Ni(II) ions is not strictly trigonal. Achieving strict axial symmetry remains one of the most challenging aspects in the quest to engineer magnetic anisotropy. We have already achieved perfect trigonal symmetry in a binuclear Co(II) complex, but the Ising-type anisotropy was not as large as in the present case.18 The design of a binuclear Ni(II) complex with perfect C3 symmetry is still a challenge to be achieved. Using the [Ni(Me6tren)X]+ or the [Ni(MDABCO)2Cl3]+ mononuclear complexes may be a possible route to do so.7,10

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F.E.K. and B.C. contributed equally to this work. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is partially financed by ANR-Project MolQuSpin 13BS10-0001-03. This work is supported by a public grant overseen by the French National Research Agency (ANR) as part of the “Investissements d’Avenir” program “Labex NanoSaclay” (Reference: ANR-10-LABX-0035). We acknowledge the Université Paris-Sud Reǵion Ilede France SESAME program 2012 No. 12018501 and CNRS. F.E.-K. thanks the Lebanese AZM & Saade association (http://www.azmsaade. net) for financial support. T.M. thanks the Institut Universitaire de France for financial support.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b01609. Experimental and magnetic data and theoretical calculations (PDF) Accession Codes

CCDC 1522970 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing data_ [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. (N.G.) *E-mail: [email protected]. (T.M.) ORCID

Talal Mallah: 0000-0002-9311-3463 G


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Design of a Binuclear Ni(II) Complex with Large Ising-type Anisotropy

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