Spin Frustrated Pyrazolato Triangular CuII Complex. Structure and Magnetic Properties, an Overview.

1. Introduction

Triangular Cu^II complexes have been largely studied in the literature, and among them, several systems present a μ₃-X^- (X = Cl^-, Br^-, OH^-, O^2-) bridging unit that, together with other organic auxiliary ligands enables to obtain very stable systems [1,2,3]. Due to their high stability, these triangular fragments can be used as secondary building units (SBU) in constructing several coordination polymers or MOFs systems [4,5,6].

Moreover, triangular complexes are an interesting class of materials since they have been suggested as possible qubits, as they can present spin-electron coupling due to the interplay between three main factors (spin exchange, spin-orbit interaction, and chirality) [7,8,9,10,11,12]. Spin Frustration (SF) has been suggested as the origin of the abovementioned features. This phenomenon originates when an odd number of non-integer spin carriers that are antiferromagnetically coupled cannot be satisfied simultaneously, like in a triangular system [13]. Thus, the energy of the ground state is doubly degenerate, but distortions of the C₃ symmetry of the triangle or by the antisymmetric exchange, which is related to spin-orbit interactions, can break this degeneracy by lowering the symmetry of the system [14,15].

These triangular Cu^II systems have been largely studied since they formed the simplest spin-triangle. This has allowed the possibility of studying in detail the magnetic properties of geometrically spin-frustrated systems [16]. Among these systems, the ones with a hydroxy bridge (μ₃-OH^-) are among the most reported in the literature [17,18]. Systems presenting pyrazolato, triazolato, and other types of auxiliary organic ligands have been magnetically studied in the literature [19,20]. In general, the displacement of the μ₃-OH^- from the Cu₃ plane, together with the type of organic ligands, have been related to the nature of the magnetic exchange interaction between the spin-carrier centers since they affect the overlap of the magnetic orbitals involved in the exchange pathways [21].

Among all the mentioned systems, Cu₃-μ₃OH pyrazolato complexes are among the most reported systems, and they present strong antiferromagnetic properties [22,23]. However, they have not been extensively analyzed in search of magneto-structural features, as has been done for the triazolato complexes [24]. These compounds, depending on the pyrazolato derivative, auxiliary ligand, or counter-anion, may present different nuclearity and/or dimensionality [3,19].

In this work, we present the synthesis and structural characterization of a triangular Cu₃-μ₃OH pyrazolato complex of formula, [Cu₃(μ₃-OH)(pz)₃(Hpz)₃][BF₄]₂ (1-Cu₃), Hpz = pyrazole. Interestingly, this trinuclear complex is isostructural to the hexanuclear QOPJIP structure [Cu₃(μ₃-OH)(pz)₃(Hpz)₃(ClO₄)₂]₂, since the perchlorate anions connect the two triangular units [25]. An extensive structural analysis with other reported triangular Cu₃-μ₃OH pyrazolato complexes has been done. The magnetic properties of 1-Cu₃ are analyzed by experimental data together with DFT calculation, showing that strong antiferromagnetic interactions exist between the Cu^II centers. We present a detailed analysis of the magnetic properties of 1-Cu₃ and compare them with the experimental data of other molecular triangular Cu₃-μ₃OH pyrazolato complexes and with the theoretical magnetic properties of a previously reported Cu₃-μ₃OH complex [21]. Finally, we perform a detailed study of the magnetic properties of 1-Cu₃ and QOPJIP to understand the differences in their magnetic properties.

2. Results and Discussion

ESI-Mass and FTIR Spectra

ES-MS in positive mode (acetonitrile) shows the existence of different fragments of the [Cu₃-μ₃OH]ⁿ⁺ unit, such as: {[Cu₃(μ₃-OH)(pz)₃(Hpz)₃][BF₄]}⁺ (m/Z = 700); {[Cu₃(μ₃-OH)(pz)₃(Hpz)₃]+1e^-}⁺ (m/Z = 613); {[Cu₃(μ₃-OH)(pz)₃(Hpz)₂]+1e^-}⁺ (m/Z = 544); {[Cu₃(μ₃-OH)(pz)₃(Hpz)₁] ]+1e^-}⁺ (m/Z = 476) and {[Cu₃(μ₃-OH)(pz)₃}⁺ (m/Z = 408). See Figure S1. Complementary analyses (EA and FTIR spectroscopy) confirm the purity of the crystalline material (see supporting information, section S2, FTIR).

Structure Analysis

The triangular complex (1-Cu₃) crystallizes in the centrosymmetric monoclinic space group P2₁/c (For more information, see CIF file and section S3). The molecular structure consists of a triangular [Cu₃-μ₃OH]ⁿ⁺ core surrounded by three protonated Hpz and three deprotonated pz^- ligands, forming the cationic complex [Cu₃(μ₃-OH)(pz)₃(Hpz)₃]²⁺, which is counterbalanced by two tetrafluoroborate anions. The trinuclear unit is formed by two Cu^II (Cu1 and Cu3) centers with a square pyramid (SqP) geometry and an octahedral Cu2 center (O_h) with a Jahn-Teller distortion. This triangular unit presents pseudo-three-fold symmetry forming an isosceles triangle, with copper-copper distances of 3.3740(8), 3.3574(8), and 3.3702(8) Å for Cu1-Cu2, Cu2-Cu3, and Cu1-Cu3, respectively. As observed for similar systems, the μ₃-OH^- group is not coplanar with the plane formed by the three copper centers, displaced by 0.439 Å. Other displacements reported in the literature for the [Cu₃-μ₃OH]ⁿ⁺ are in the range of 0.363 and 0.759 Å [23,26]. The metal centers present three different types of Cu-O, Cu-N, and Cu-F bonds. The first is around 2.00 Å, the second is between 1.98 and 2.02 Å, and the third is between 2.48 and 2.58 Å (Figure 1).

An original aspect of 1-Cu₃ is the presence of two [BF₄]^- counter-anions (B1 and B2) coordinated to the copper centers of the trinuclear unit. In fact, 1-Cu₃ is the first example of a triangular pyrazolato complex with this type of counter-anion. One of the [BF₄]^- anions (B1) presents a μ₃ coordination mode with three F atoms coordinated to the three Cu^II centers (with F-Cu distances of 2.483(3), 2.530(4), and 2.581(4) Å). The other [BF₄]^- anion (B2) is only coordinated by one F atom to a single Cu^II center (Cu2-F5 = 2.557(4) Å). The structure presents an inversion center (outside the complex) that generates a second triangular [Cu₃(μ₃-OH)(pz)₃(Hpz)₃][BF₄]₂ unit, where the fluorine atom (F7) of the [BF₄]^- anion (B2) is semi-coordinated to Cu1 with a long distance of 2.812(3) Å. Finally, it is worth mentioning that between the triangular units, there are some hydrogen bonds that stabilize the crystal lattice of the complex, with inter-cluster Cu···Cu distances ranging between 7.309(1) and 13.4522(9) Å (Figure 2).

According to the CCDC database, there are at least 96 structures based on pyrazolato (R-pz^-) ligands, forming complexes with the general formula [Cu₃(μ₃-OH)(R-pz)₃(L)₃]^n+/-, where R = -H, -CH₃, -NO₂, among others, and L = pz^0/-, Cl^-, H₂O, NO₃^-,… [2,6,22,23,25,26,27,28,29,30]. The nature of the axial ligand and the type of substitution of the pz^- ligand leads to the formation of either high dimensional systems (usually for R = -COO^-) or discrete complexes. If the axial ligand is monodentate or acts as a chelate or if the pz- ligand's substituent group cannot coordinate with other metal centers, discrete (0D) systems are formed, see Table 1. As a general trend, we observe that when larger ligands are present either as axial or auxiliar ligands, the distance between the Cu₃ plane and the μ₃-OH^- group increases. We also observe that when auxiliary ligands are present, the triangular units can form hexanuclear units by coordinating these auxiliar ligands to the metal centers of the closest triangular units (RUYGEX, RUYGIB, RUYHEY, RETQUD, QOPJIP, DIBXOC, EGIXUQ, EHOLIZ).

Among the compounds of Table 1, QOPJIP: [Cu₃(μ₃-OH)(pz)₃(Hpz)₃][ClO₄]₂) [25] is isostructural to 1-Cu₃ ([Cu₃(μ₃-OH)(pz)₃(Hpz)₃][BF₄]₂), although there are some differences, mainly related to the nature of the counter-anion. The smaller size of the [BF₄]^- unit located between the two triangular units (compared to ClO₄^-) leads to an important shortening of the distances between the Cu₃-planes for 1-Cu₃ (6.789 Å) as compared to QOPJIP (7.044 Å). This shortening allows the formation of a hydrogen bond between F8 and the hydrogen atom of the μ₃-OH group (not observed in QOPJIP), enlarging the O-H bond in 1-Cu₃ (0.991 Å), compared to QOPJIP (0.979 Å). The lower coordination capacity of BF₄^- compared to ClO₄^- is clearly observed in 1-Cu₃, where the Cu₃(μ₃-OH) units are isolated (except for a very long semi-coordinated Cu1-F7 bond of 2.811(3) Å). In contrast, in QOPJIP, the ClO₄^- anion connects two triangular Cu₃ units through four short Cu-O bonds (in the range 2.44-2.66 Å) to form a hexanuclear complex.

Magnetic Properties. dc Magnetic Measurements

The thermal variation of the product of the molar magnetic susceptibility per Cu₃ unit, times the temperature for 1-Cu₃, measured with a DC field of 100 mT, shows a value of around 0.5 cm³ K mol^-1 at 300 K (Figure 3). This value is below the expected one for three uncoupled paramagnetic Cu(II) ions (1.125 cm³ K mol^-1 with g = 2.0), indicating the existence of bulk antiferromagnetic interactions between the Cu^II atoms of the Cu₃(μ₃-OH) core. When the temperature is lowered, χ_mT steadily decreases, reaching a plateau between 130 and 100 K. Below 100 K, χ_mT further decreases and reaches a value of 0.26 cm³ K mol^-1 at 2 K. The χ_mT value in the plateau is 0.38-0.40 cm³ K mol^-1, which is the expected value for a trinuclear unit with an S = 1/2 ground state [24,25]. The field dependence of the magnetization at 2 K for 1-Cu₃ shows at 5 T a value of around 0.7 μ_B, corresponding to ca. 0.7 electrons, although saturation is not fully reached at 5 T (Figure 3). This behavior is typical of systems with a μ₃-hydroxido moiety with a ground state of S = 1/2 (M = 1 μ_B) that present magnetization values below the expected ones and do not reach saturation, even at high fields [17,35]. Comparing the experimental data with those calculated by the PHI program (see below) for 1-Cu₃ shows a good agreement between them. The lower values of the experimental data confirm the presence of antisymmetric exchange.

The magnetic behavior observed at low temperatures for the χT data can be associated with the spin frustration phenomena, which allows the existence of an antisymmetric exchange, as described by Ferrer et al.[24]. This work described in detail the antisymmetric exchange interaction in a triangular Cu₃ system based on triazolato derivatives. Additionally, we cannot discard that geometry distortions on the local coordination environment may influence the overall magnetic properties. In this sense, several discussions have arisen from this point, and according to Niedner-Schatteburg et al., spin frustration leads to geometric distortion [38,39,40].

The fit of the dc experimental data was done using the PHI program [41]. At first, only the isotropic interactions for the triangular arrangement were considered, giving a good fit in the 50-300 K range. The best fit in the whole temperature range was obtained by adding to the model the antisymmetric exchange (ASE; G_ij), which is a non-isotropic interaction [15,24]. Thus, based on the structural arrangement of the Cu^II triangles, we have used a model with two isotropic exchange interactions (J₁ and J₂) for an isosceles triangle and an antisymmetric exchange, using the Hamiltonian shown below:

$$\widehat{H}=-J_1\left(S_1{S}_2+S_2{S}_3\right)-J_2\left(S_1{S}_3\right)-G\left({\widehat{S}}_1\times {\widehat{S}}_2+{\widehat{S}}_2\times {\widehat{S}}_3+{\widehat{S}}_1\times {\widehat{S}}_3\right)+{\mu }_{B}gH{\sum }_{i=1}^3{\widehat{S}}_i$$

(1)

The best-fit parameters obtained for the isotropic exchange interactions are J₁ = -193.5(6) cm^-1 and J₂ = -205.5(3) cm^-1 with an antisymmetric exchange parameter, |G_Z| = 28 cm^-1 (solid line in Figure 3). These values are listed in Table 2, together with the magnetic parameters of selected molecular [Cu₃-μ₃OH]^n+/- pyrazolato complexes. The isotropic interaction values are strongly antiferromagnetic, being similar to those reported for other pyrazolato and triazolato triangular Cu₃OH complexes. The antisymmetric exchange interactions for triangular Cu^II hydroxido pyrazolato complexes have only been reported for two systems, VAZCOR (|G_Z| = -18.2 cm^-1) and YIFGIG (|G_Z| = -31.2 cm^-1) [17,35]. However, for complexes based on the triazolato ligand, there are more examples in the literature, with |G_Z| values between 17.5 and 44 cm^-1 [24]. Thus, the isotropic and antisymmetric exchange interactions obtained for 1-Cu₃ are within the range observed for other triangular Cu^II hydroxy compounds (see Table 2).

Magneto-structural analysis on triangular systems was done using the experimental data of Table 2. According to the literature, two structural parameters have been selected to study their influence on the magnetic properties of these triangular systems. The first is the displacement of the μ₃-OH^- from the Cu₃ plane, where the magnetic interaction becomes more antiferromagnetic when the displacement is smaller [42]. The second corresponds to the Cu-(μ₃-X)-Cu angle, which seems to be sensitive to the magnetic coupling interaction. The magnetic coupling interaction is switched from ferromagnetic to antiferromagnetic when the angle varies from 76° to 120° [43]. The analysis of these structural parameters with the average magnetic exchange interactions shows that a general tendency is observed only with the displacement of the μ₃-OH^- from the Cu₃ plane (Figure 4).

As mentioned in the Structural Analysis section, 1-Cu_3, and QOPJIP are isostructural crystalline systems. According to the literature, the displacement of the μ₃-OH^- group from the Cu₃ plane influences the magnetic properties. This effect shows that a larger displacement causes a weaker antiferromagnetic interaction, which can be related to a weaker overlap of the magnetic orbitals of the Cu^II centers in the triangular system [44]. However, the smaller displacement observed for 1-Cu₃ (0.439 Å) than for QOPJIP (0.466 Å) suggests that 1-Cu₃ should present a stronger antiferromagnetic interaction between the copper centers than QOPJIP. However, the opposite phenomenon is observed (Figure 5).

We have performed DFT calculations to rationalize the magnetic properties observed for 1-Cu₃ (see Materials and Methods section) [18]. The results were compared to a previously reported theoretical study of the magnetic properties of several μ₃-OH^- bridged trinuclear Cu^II complexes [21]. The theoretical calculations for 1-Cu₃ were done under the same level of theory as for the study mentioned above. The geometrical array of the triangular unit for 1-Cu₃ permits to define three exchange pathways, with magnetic exchange interactions of J₁ = -94,9 cm^-1, J₂ = -87,7 cm^-1, and J₃ = -98.6 cm^-1. For QOPJIP, previously reported DFT calculations also describe three exchange constants: J₁ = -118.3 cm^-1, J₂ = -106.0 cm^-1, and J₃ = -120.6 cm^-1. The difference observed in the magnitude of the magnetic exchange interaction between the calculated and the one obtained by the fitting experimental data for both systems may be related to the so-called strong interaction limit, in which the weak interaction limit treatment of Noodleman would result in J-values generally twice as larger [18]. This difference could also be due because the experimental J values are obtained from bulk magnetic data that include other magnetic phenomena in the crystalline lattice. On the other hand, DFT calculations can isolate the magnetic phenomena for the molecular structure.

The DFT calculation of 1-Cu₃ was completely validated since the overlap parameters, together with their calculated magnetic exchange interactions, fit well on the plot of the J values of the seven studied complexes as a function of the square of the overlap depicted in the previous work of reference [21]. A linear relationship can be observed, as expected from the Kahn-Briat overlap model (Figure 6). These results permit us to infer that the μ₃-OH^- bridged contributes to the exchange phenomenon, together with the other bridges. Finally, Mulliken spin density values were determined for four spin configurations. The obtained values for the Cu^II atoms are in 0.60-0.68 e^- range, similar to those obtained for other similar Cu^II systems [18,21]. These results reflect that most of the electron spin density is located on the metal centers, and the rest of the spin density appears over the atoms of the first coordination sphere through a delocalization mechanism of the spin density. Figure S3 presents the spin density surfaces for the ferromagnetic solution S_T = 3/2 and three broken-symmetry solutions S_T = 1/2 for 1-Cu₃. It is possible to observe that no polarization mechanism of the spin density is observed for the corresponding second coordination spheres.

Finally, from all the results discussed above, it is possible to conclude that both compounds, 1-Cu₃ and QOPJIP, have a similar trinuclear structure with a μ₃-OH^- and μ₂-pz^- bridges and both systems show a tetrahedral anion with a μ₃ coordination mode ([BF₄]^- and [ClO₄]^-). The average DFT calculated J values for 1-Cu_3, and QOPJIP are -93.7 and -114.9 cm^-1, respectively. The displacement of the μ₃-OH^- group from the plane of the three copper atoms is smaller for 1-Cu₃ (0.439 Å) than for QOPJIP (0.466 Å); thus, the first system should have stronger antiferromagnetic interactions, in contrast with the experimental values. These results suggest that the μ₃-ClO₄^- anion is not an innocent ligand and favors an antiferromagnetic exchange between the Cu^II centers, resulting in a stronger antiferromagnetic coupling in QOPJIP.

3. Materials and Methods

Synthesis of [Cu₃(μ₃-OH)(pz)₃(Hpz)₃][BF₄]₂ (1-Cu₃)

Cu(BF₄)₂∙H₂O (765.5 mg, 3 mmol) was dissolved in 20 mL of methanol. Then, a solution of pyrazole (204.2 mg, 3 mmol) and dimethylamine (135.2 mg, 3 mmol) in 15 mL of methanol was added to the first solution. After adding the second solution, the color changes from light blue to greenish blue in the final solution. Greenish blue crystals of 1-Cu₃, suitable for X-ray diffraction, were obtained within three days by slow evaporation of the filtered solution at room temperature. Elemental analysis (Found: C, 27.9 %; N, 19.5 %; H, 3.2 %. Calc. for Cu₃C₁₈H₂₂N₁₂OB₂F₈: C, 27.5 %; N, 21.4 %; H, 2.8 %). Elemental ratio estimated by electron probe microanalysis (EPMA): (Exp.) Theo. Cu : F = (2.89)3 : (8.03)8. ES-MS in positive mode (acetonitrile) shows the existence of only [Cu₃(μ₃-OH)]²⁺ unit, confirmed by mass-spectrometry. The experiments show the existence of the {[Cu₃(μ₃-OH)(pz)₃(Hpz)₃][BF₄]}⁺ (m/Z = 700); {[Cu₃(μ₃-OH)(pz)₃(Hpz)₃]+1e^-}⁺ (m/Z = 613); {[Cu₃(μ₃-OH)(pz)₃(Hpz)₂]+1e^-}⁺ (m/Z = 544); {[Cu₃(μ₃-OH)(pz)₃(Hpz)₁] ]+1e^-}⁺ (m/Z = 476); {[Cu₃(μ₃-OH)(pz)₃}⁺ (m/Z = 408). See Figure S1. IR data (KBr, ν_max/cm^-1) 3400m [ν(NH)], 3137w [ν(μ₃-OH^-)], 1650w, and 1200w [ν_as(CN aromatic)]. See Figure S2.

Physical Characterization

Fourier transform infrared spectroscopy (FTIR) was performed using a NICOLET 5700 (Thermofisher Scientific, Waltham, MA, USA) in the range 4000-650 cm^-1. Elemental analysis (C, N, H) was performed by microanalytical procedures using an EA 1108 elemental analyzer (CE Instruments, Wigan, UK). Electrospray ionization mass spectrometry (ESI-MS) studies of 1-Cu₃ were performed with a QTOF Premier instrument with an orthogonal Z-spray-electrospray interface (Waters, Manchester, UK). A capillary voltage of 3.5 kV was used in the positive scan mode, and the cone voltage was set to 10 V to control the extent of fragmentation.

X-ray Diffraction

A single crystal of compound 1-Cu₃ was mounted on a glass fiber, using a hydrocarbon oil to coat the crystal, and then transferred directly to the cold nitrogen stream for data collection. X-ray data were collected at 120 K on a Supernova diffractometer (Rigaku, Austin, TX, USA) equipped with a graphite-monochromated Enhance (Mo) X-ray Source (λ = 0.71073 Å). The program CrysAlisPro, Oxford Diffraction Ltd., was used for unit cell determination and data reduction. Empirical absorption correction was performed using spherical harmonics, implemented in the SCALE3 ABSPACK scaling algorithm. The structure was solved with the ShelXT structure solution program [45] and refined with the SHELXL-2018 program [46] using Olex 2 [47]. Non-hydrogen atoms were refined anisotropically, and hydrogen atoms were placed in calculated positions that were refined using idealized geometries (riding model). A summary of the data collection and structure refinements is provided in Table S1. CCDC-2174487 (1-Cu₃) contains the supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Center via www.ccdc.cam.ac.uk/data_request/cif.

Magnetic Susceptibility Measurements

Variable temperature susceptibility measurements were carried out for 1-Cu₃ in the temperature range of 2-300 K with an applied magnetic field of 100 mT on a ground polycrystalline sample (with a mass of 37.64 mg) with a Quantum Design (San Diego, CA, USA) MPMS XL-5 SQUID magnetometer. The susceptibility data were corrected for the diamagnetic contributions of the sample using Pascal´s constants [48]. Isothermal magnetization measurements were made between 0 and 5 T at 2 K.

DFT Calculations of the Magnetic Properties

Spin-unrestricted calculations under the Density Functional Theory approach were done using the hybrid B3LYP functional [49,50] and a triple-ζ all-electron basis set for all atoms in all the calculations [51]. A guess function was generated using the Jaguar 5.5 code [52]. Total energy calculations were performed with the Gaussian09 code [53], using the quadratic convergence approach with a convergence criterion of 10⁻⁷ a.u. Mulliken spin densities were obtained from the Single Point calculations using Gaussian09.

The Heisenberg-Dirac-van Vleck spin Hamiltonian was used to describe the exchange coupling in the trinuclear complex is$\widehat{\mathrm{H}}=-\sum _{i>j}{\mathrm{J}}_{\mathrm{i}\mathrm{j}}{\mathrm{S}}_{\mathrm{i}}{\mathrm{S}}_{\mathrm{j}}$; where S_i and S_j are the spin operators of the paramagnetic centers of the compound. The J_i parameters are the magnetic coupling constants between neighboring centers with unpaired electrons. Four different spin distributions (three antiferromagnetic and one ferromagnetic) for the system were calculated, and the obtained energies permit to evaluate the magnetic exchange constants of the system.

Utilizing the non-projected energy of the broken symmetry solution as the energy of the low spin state within the DFT methodology gives good results because it avoids the cancellation of the non-dynamic correlation effects, as has been stated in studies carried out by Ruiz et al. Thus, the J value is obtained using the non-projected method [54,55].

4. Conclusions

A new trinuclear cationic [Cu₃-μ₃OH]ⁿ⁺ complex based on the pyrazolato ligand has been obtained, [Cu₃(μ₃-OH)(pz)₃(Hpz)₃][BF₄]₂ (1-Cu₃). The triangular complex presents the [BF₄]^- as counter-anion and is isostructural with the QOPJIP system. Nevertheless, the smaller size of the BF₄^- anion in 1-Cu₃, compared to the ClO₄^- anion in QOPJIP, prevents the connection of the triangular units in 1-Cu₃, in contrast to what is observed for the isostructural complex QOPJIP.

The magnetic data shows that strong antiferromagnetic interactions, together with antisymmetric interactions, exist in the triangular unit. The analysis of the experimental data and theoretical DFT results lead to the conclusion that there is a correlation between the displacement of the μ₃-OH^- from the Cu₃ plane and the magnetic exchange interactions of the triangular Cu₃ pyrazolato systems. However, the presence of other bridging organic ligands also plays a role in the magnetic exchange. These features affect the overlap of the magnetic orbitals according to the Khan-Briat model, suggesting that a strong overlap of magnetic orbitals exists in these systems.

The differences in the magnetic properties between 1-Cu₃ and QOPJIP were analyzed and rationalized, showing that the different structural parameters, such as the displacement of the μ₃-OH^- from the Cu₃ plane, the nature of the bridging organic ligands and also the size of the counter-anion affect the overall magnetic properties of these systems.