Supramolecular Assemblies of Trinuclear Copper(II)-Pyrazolato Units: A Structural, Magnetic and EPR Study

Abstract

Two anionic complexes, {[Cu₃(µ₃-OH)(µ-4-Ph-pz)₃Cl₃]₂[Cu(4-Ph-pzH)₄](µ-Cl)₂}²⁻ (1) and [Cu₃(µ₃-OH)(µ-pz)₃(µ_1,1-N₃)₂(N₃)]⁻ (2), crystallize as one-dimensional polymers, held together by weak Cu-(µ-Cl) and Cu-(µ-N₃) interactions, respectively. Variable temperature magnetic susceptibility analyses determined the dominant antiferromagnetic intra-Cu₃ exchange parameters in the solid state for both complexes, whereas the weak ferromagnetic inter-Cu₃ interactions manifested also in the solid state EPR spectra, are absent in the corresponding frozen solution spectra. DFT calculations were employed to support the results of the magnetic susceptibility analyses.

1. Introduction

Herein, we present a structural, magnetic susceptibility and EPR study of two supramolecular assemblies of metallacyclic Cu^II pyrazolates with Cu₃(µ₃-OH) cores. The focus of this work is the elucidation of weak intermolecular interactions manifested in the magnetic properties and EPR spectra of the supramolecular assemblies.

Supramolecular interactions, such as H-bonding, dipolar, metallophilic and π–π interactions, are important not only for the structural organization of molecules in 3D, but because they often play a crucial role in determining the physical and spectroscopic properties of the assemblies. A corollary of the latter statement is that, in the absence of structural data, the detection of such spectroscopic “signatures” reveals the presence of supramolecular interactions—e.g., in biological systems. Magnetic exchange is among the properties that can be modulated by supramolecular interactions, thereby introducing new functionality into a system [1]. For instance, in the layered Ni(H₂O)₂[Ni(CN)₄]∙xH₂O solid, H-bonding in the interlayer regions is shown to mediate weak ferromagnetic interactions, but when the coordinated water molecules were replaced by 3-halopyridine ligands, removing H-bonding, anti-ferromagnetic interactions through π-clouds became dominant [2]. Weak intramolecular antiferromagnetic exchange is active within a molecule containing two isolated Cu^II centers separated by a K⁺ ion, whereas relatively strong ferromagnetic interactions were found between adjacent units, along a supramolecular pathway [3]. In yet another dinuclear Cu^II complex with chelating 2-hydroxy-1,10-phenanthroline and bridging thiocyanate ligands, it was shown that an intermolecular ferromagnetic exchange was facilitated by π–π interactions between phenanthroline ligands [4,5,6].

The antiferromagnetic exchange among the Cu^II centers of the triangular Cu₃(µ₃-O/OH) units has been studied extensively by us and others [7,8,9,10,11,12]. We have recently turned our attention to interactions between weakly-coupled Cu₃(µ₃-O/OH) species and shown that the presence of weak dipolar interactions str evident in the magnetic susceptibility and EPR spectra of H-bonded Cu₃(µ₃-OH) units [13]. Continuing along the same lines, we report here the structure and magnetochemical studies of a heptanuclear Cu^II assembly employing 4-phenyl-pyrazole ligands and of a polymeric structure containing Cu₃N₆ metallacycles with terminal and bridging azido ligands.

2. Materials and Methods

2.1. Materials

4-Phenyl-pyrazole (4-Ph-pzH) was prepared according to a procedure from the literature [14]. All other reagents were purchased from commercial sources and used as received. Solvents were purified using standard techniques [15]. [PPN]₂[Cu₃(µ₃-Cl)₂(µ-pz)₃Cl₃] and [PPN]₂[Cu₃(µ₃-O)(µ-pz)₃Cl₃] were prepared according to published procedures [12]; PPN⁺ = bis(triphenylphosphine)iminium.

2.2. Instruments

2.2.1. X-Ray Crystallography

Single crystal X-ray diffraction data were collected on a Bruker D8 QUEST CMOS system equipped with a TRIUMPH curved-crystal monochromator and a fine-focus X-ray tube with graphite monochromated Mo-Kα radiation (λ = 0.71073 Å) at ambient or low temperature using the APEX3 or APEX2 suite [16]. Crystal data, data collection and structure refinement details are listed in Supplementary Material (Table S1). Frames were integrated with the Bruker SAINT software package using a narrow-frame algorithm. Absorption effects were corrected using the multi-scan method (SADABS) [17]. Structures were solved by intrinsic phasing methods with ShelXT [18] and refined with ShelXL [19] using full-matrix least-squares minimization using Olex2 [20]. All non-hydrogen atoms were refined anisotropically. H atoms were included in calculated positions riding on the C atoms to which they are bonded, with C–H = 0.93 Å and Uiso(H) = 1.2 Ueq(C). Electron densities of poorly ordered lattice solvent molecules could not be modeled satisfactorily, and they were removed by using the SQUEEZE routine in PLATON [21]. In (1), the C47 and C48 atoms were constrained to have equivalent atomic displacement parameters and the relatively large thermal ellipsoids of C atoms of one of the phenyl rings (C46–C51) were restrained with enhanced rigid bond restraint [22].

2.2.2. EPR Spectroscopy

X-band spectra were recorded on a Bruker ESP300 spectrometer using a 4102ST rectangular cavity operating in the TE₁₀₂ mode. For variable-temperature experiments the cavity was fitted in an ESR900 dynamic continuous flow cryostat and the temperature was regulated with an Oxford ITC4 servocontrol. Q-band spectra were recorded on an EMXplus spectrometer fitted with an EMX premiumQ microwave bridge and an ER5106QTW microwave resonator operating in the TE₀₁₂ mode and controlled by the Bruker Xenon software. For variable-temperature experiments the resonator was fitted in an Oxford CF935 dynamic continuous flow cryostat and the temperature was regulated with an Oxford ITC503 servocontrol. The magnetic field was applied by a Bruker BE25 electromagnet using a Bruker ER082(155/45)Z power supply allowing a field sweep between −5 to 16,000 G.

2.2.3. Magnetic Measurements

The temperature dependence of the magnetization at an applied field of B = 1 T was acquired for powder samples of (1) and (2) using PPMS Dynacool magnetometer (Quantum Design Inc., San Diego, CA, USA). The experimental data were corrected for the underlying diamagnetism and signal of the sample holder. The experimental data were fitted with program Polymagnet [23].

2.3. Synthesis of Compounds (1) and (2)

2.3.1. Synthesis of [PPN]₂{[Cu₃(µ₃-OH)(µ-4-Ph-pz)₃Cl₃]₂[Cu (4-Ph-pzH)₄]}Cl₂} (1)

CuCl₂·2H₂O (0.6 mmol, 102.3 mg), 4-Ph-pzH (0.8 mmol, 115.3 mg), NaOH (1 mmol, 40 mg) and PPNCl (0.1 mmol, 57.4 mg) were added to 15 mL CH₃CN and the reaction mixture was stirred overnight. A small amount of a grey solid was filtered off and the solvent volume was reduced to 4 mL under reduced pressure. Suitable crystals for X-ray diffraction were grown by slow evaporation. Yield: 45% (126 mg, 0.039 mmol). Crystal data for (1): Triclinic, P$\overline{1}$, a = 14.161(7) Å, b = 17.814(8) Å, c = 18.173(9) Å, α = 80.66(1)°, β = 68.33(1)°, γ = 85.25(1)°, V = 4202(4) Å3, Z = 1, R₁ = 0.0661, GoF = 1.020, for 985 parameters and 17,116 observed reflections.

2.3.2. Synthesis of (PPN)[Cu₃(µ₃-OH)(µ-pz)₃(µ_1,1-N₃)₂(N₃)] (2)

Caution! Azide complexes of metal ions in the presence of organic ligands are potentially explosive. Only small amounts should be prepared, and they should be handled with care.

A solution of NaN₃ (0.375 mmol, 24.42 mg) in 5 mL of MeCN was added dropwise to a solution of [PPN]₂ [Cu₃(µ₃-O)(µ-pz)₃Cl₃] (0.0628 mmol, 100 mg) suspended in 10 mL MeCN. The mixture was stirred overnight at rt. Well-shaped crystals suitable for X-ray diffraction were obtained upon slow evaporation of the filtrate at room temperature over three weeks. The crystals were isolated, washed three times with methanol and ether and dried in the vacuum. Yield: 65% (44 mg, 0.041 mmol), based on Cu. Anal. calcd/found for C₄₅H₄₀Cu₃N₁₆OP₂:C, 50.36/50.01; H, 3.84/3.62; N, 20.89/20.48. Compound (2) was similarly synthesized in MeOH (instead of MeCN), albeit with a 40% yield. Crystal data for (2): monoclinic, P2₁/c, a = 8.6121(9) Å, b = 17.034(2) Å, c = 32.237(3) Å, β = 96.493(2)°, V = 4698.8(8) Å3, Z = 4, R₁ = 0.0662, GoF = 0.987, for 623 parameters and 5601 observed reflections.

2.4. Theoretical Calculations

The theoretical calculations based on density functional theory (DFT) were done with ORCA 4.1 package [24] using B3LYP hybrid functional [25,26,27] accounting also for relativistic effects with ZORA Hamiltonian and respective ZORA-def2-TZVP basis set for Cu, N, O, Cl atoms and ZORA-def2-SVP basis set for C and H atoms [28]. Additionally, the calculations utilized the chain-of-spheres (RIJCOSX) approximation to exact exchange as implemented in ORCA [29,30] and the auxiliary basis SARC/J [31]. Increased integration grids (Grid7 and Gridx7 in ORCA convention), increased radial grid (IntAcc = 8) for Cu atoms and tight Self Consistent Field (SCF) convergence criteria were used in all calculations. The molecular fragment used in the calculations was extracted from the experimental X-ray structure. The calculated spin density was visualized with VESTA 3 program [32].

3. Results and Discussion

3.1. Synthesis

The reaction of CuCl₂·2H₂O, 4-Ph-pzH, NaOH and PPNCl in 6:9:13:1 ratio and approximately 5 mL of various solvents yielded the trinuclear complex, PPN[Cu₃(µ₃-OH)(µ-4-Ph-pz)₃Cl₃] [33]. Compound (1) was prepared from the same reagents employing a 6:6:13:1 reagent ratio in a more dilute reaction mixture (15 mL MeCN). Pettinari et al. have obtained a similar heptanuclear complex, [{Cu₃(µ₃-OH)(µ-pz)₃(Cl)₂(Hpz)₂(H₂O)}₂{CuCl₂(Hpz)₂}], by acid digestion of the trinuclear [Cu₃(µ₃-OH)(µ-pz)₃(CH₃COO)₂(pzH)] complex [34].

The azide complex (2) was synthesized in a metathesis reaction from (PPN)₂[Cu₃(µ₃-Cl)₂(µ-pz)₃Cl₃] by exchanging the terminal chlorides for azide using a slight excess of NaN₃ dissolved in MeOH.

3.2. Crystal Structure Description of [PPN]₂[{Cu₃(µ₃-OH)(µ-4-Ph-pz)₃Cl₃}₂{Cu(4-Ph-pzH)₄}]Cl₂ (1)

Complex (1) crystallizes in the triclinic space group P$\overline{1}$ with the asymmetric unit containing one complete trinuclear and one-half of the mononuclear complex. Its crystal structure (Figure 1) is formed by repeating heptanuclear assemblies consisting of two trinuclear [Cu₃(µ₃-OH)(µ-4-Ph-pz)₃Cl₃]⁻ anionic metallacycles on either side of a neutral, mononuclear, square planar [Cu(4-Ph-pzH)₄]; the latter is located on the crystallographic inversion center. In the solid state, two Cl ions act as bridges between the central mononuclear complex and the two trinuclear ones [Cl(4)-Cu(1), 2.744(2) Å; Cl(4)-Cu(4), 2.792(2) Å], occupying axial sites and forming a weakly bonded heptanuclear assembly. The two trinuclear anions contain 4-coordinate distorted square planar Cu-centers and a pyramidal µ₃-OH (the O atom is 0.473(4) Å away from the Cu₃-plane), have their Cu₃-planes parallel to each other and are connected via two long Cu(2)…Cl(1) contacts of 3.023(2) Å to the adjacent heptanuclear unit; the µ-Cl atoms occupy one equatorial and one axial position with a Cu(1)–Cl(2)–Cu(2) angle of 101.00(6)°. The one-dimensional chains thereby generated run parallel to the crystallographic a-axis (Figure 2) separated by the PPN⁺ counterions. The long Cu(4)…Cl(4) distances of 2.792(2) Å between the mononuclear [Cu(4-Ph-pzH)₄]²⁺ unit and the µ-Cl atoms are considered as non-bonding here; however, even longer distances of 2.817–2.839 Å have been reported in the corresponding trans-[CuCl₂(pz*H)₄] complexes (pz*H = pzH [35], 3-tBu-pzH [36] and 3-Ph-pzH [37]). A complete list of bond lengths and angles for (1) is provided as Supplementary Material, Table S2.

3.3. Crystal Structure Description of (PPN)[Cu₃(µ₃-OH)(µ-pz)₃(µ,κ^1,1-N₃)₂(N₃)] (2)

The complex crystallizes in the monoclinic P2₁/c space group with the whole molecule in the asymmetric unit. The structure consists of triangular µ₃-OH-capped metallacyclic units (O atoms at 0.345(2) Å from the Cu₃ plane, Figure 3) connected by end-on bridging azides, forming infinite chains along the crystallographic b-axis (Figure 4), separated by the PPN⁺ counterions. One of the three Cu centers is in square planar, whereas the other two are in distorted square pyramidal geometry. One of the three azide ligands is in a terminal monodentate coordination mode with Cu-N = 1.974(7) Å, and the other two are unsymmetrically bridging, in an end-on (μ,κ^1,1) fashion, between two Cu₃ units with Cu(1)–N(13) = 1.980(5), Cu(2′)-N(13) = 2.421(5) and Cu(2)-N(3) = 2.001(5) Å, Cu(1′)-N(3) = 2.322(5) Å at each bridgehead N, respectively. The bridging azides occupy one equatorial (shorter Cu-N bond) and one axial (longer Cu-N bond) at either side. The corresponding Cu–N_azide–Cu angles are 105.9(2) and 115.0(2)°, respectively, holding the Cu atoms at intermolecular distances of 3.386(1) Å and 3.470(1) Å. As expected, in the two tetragonal pyramidal Cu-centers, the axial Cu-N bonds are significantly longer than the equatorial ones. The azide ions are approximately linear with N–N–N angles of 176.7(7)° and 178.3(7)°; contain unequal N–N bond lengths, longer at the end involving the donor atoms, N3–N4 = 1.191(7) Å and longer at the dangling end, N4–N5 = 1.144(7) Å [38]. A complete list of bond lengths and angles for (2) is provided as Supplementary Material, Table S3.

3.4. Infrared Spectra

The coordination mode of azides to a transition metals is usually characterized by an intense IR band due to ν_as(N₃) at 2000–2055 cm⁻¹ for a terminal and >2055 cm⁻¹ for a bridging N₃^—; the larger values correspond to anions with unsymmetrical N–N–N bonding [39]. A broad trifurcated band with peaks at 2034, 2046 and 2060 cm⁻¹ in the solid state spectrum of (2) (Figure S3) is attributed to the presence of both terminal and bridging azides.

3.5. Magnetic Susceptibility of (1)

The temperature dependence of the effective magnetic moment and the molar magnetization data for (1) are shown in Figure 5. The effective magnetic moment at room temperature is 4.3 µ_B and is rapidly decreasing, reaching a plateau of 3.6 µ_B at ca. 100 K, and then further decreasing below 30 K to 3.1 µ_B at 1.9 K. The theoretical spin-only value for seven non-interacting Cu^II ions with g = 2.0 is 4.58 µ_B, but usually the g-factor for this ion is much larger due to the angular orbital momentum contribution, so an even larger theoretical spin-only value is expected. The lower room temperature value of µ_eff together with its sharp decrease on subsequent cooling thus reflect strong antiferromagnetic exchange. Such strong antiferromagnetic exchange within each Cu₃(µ₃-OH) triangle leads to S_Cu1-2-3 = 1/2 ground spin state. Therefore, the value of µ_eff/µ_B ≈ 3.6 in the temperature interval 50–120 K can be explained by considering coexistence of two S_Cu1-2-3 = 1/2 and one S_Cu4 = 1/2 spin levels. A further decrease of µ_eff below 50 K is then ascribed to weak magnetic interactions between two Cu₃(µ₃-OH) triangles and eventually between Cu₃(µ₃-OH) triangles and the central [Cu(4-Ph-pzH)₄] complex units (see Figure 2). Moreover, another important origin of decrease of µ_eff below 50 K can be attributed to the antisymmetric exchange interactions (ASE, also named Dzyaloshinsky–Moriya interactions) within two Cu₃(µ₃-OH) triangles, as this kind of interaction is typical of triangular molecular systems based on Kramers ions coupled with strong antiferromagnetic exchange [40]. Moreover, an ASE has been identified and quantified in similar coordination compounds with individual Cu₃(µ₃-OH) or Cu₃(µ₃-O) motifs, and its effects on magnetic and spectroscopic properties have been demonstrated [7,41]. Additionally, the presence of ASE in (1) was evidenced by low temperature EPR spectroscopy, as discussed in the following section. Therefore, the following spin Hamiltonian has been postulated in order to quantitatively analyze the experimental magnetic data

$$\begin{array}{l}\widehat{H} =-J_{12}\left(S_1\cdot S_2+S_{1\prime }\cdot S_{2\prime }\right)-J_{13}\left(S_1\cdot S_3+S_{1\prime }\cdot S_{3\prime }\right)-J_{23}\left(S_2\cdot S_3+S_{2\prime }\cdot S_{3\prime }\right)-J_{12\prime }\left(S_1\cdot S_{2\prime }+S_{1\prime }\cdot S_2\right)-J_{14}\left(S_1\cdot S_4+S_{1\prime }\cdot S_4\right)\\ +d_{12}\cdot \left(S_1\times S_2+S_{1\prime }\times S_{2\prime }\right)+d_{23}\cdot \left(S_2\times S_3+S_{2\prime }\times S_{3\prime }\right)+d_{31}\cdot \left(S_3\times S_1+S_{3\prime }\times S_{1\prime }\right)+{\mu }_{\mathrm{B}}{\displaystyle \sum _{i=1}^{7}B}\cdot g\cdot S_i\end{array}$$

(1)

where the isotropic exchange, Zeeman terms and ASE expressed by d_ij vectors, (d_x, d_y, d_z)_ij, are included. The application of Moriya symmetry rules [42] for the Cu₃(µ₃-OH) triangles results in only one non-zero component: d_ij = (0, 0, d_z)_ij and it was assumed that (d_z)_ij are equal for all pairs. Next, the molar magnetization in the direction of the magnetic field B_a = B∙(sinθcosφ, sinθsinφ, cosθ) was calculated as

$$M_a=N_{\mathrm{A}}kT\frac{\partial \ln Z}{\partial B_a}$$

(2)

and since the magnetic data were acquired on a polycrystalline sample, the powder average of the molar magnetization was then calculated as

$$M_{\mathrm{mol}}=1/4\pi {\displaystyle {\int }_0^{2\pi }{\displaystyle {\int }_0^{\pi }{M}_a\sin \theta d\theta d\phi }}$$

(3)

In order to reduce the number of free parameters, DFT calculations were employed (vide infra) from which we may assume J₁₂ ≈ J₂₃, |J₁₂|, |J₂₃| > |J₁₃| and J_12′ ≈ J₁₄, and J_12′, J₁₄ > 0. Thus, magnetic data were fitted under the assumption that magnetic coupling through µ-Cl-ligands between two Cu₃(µ₃-OH) triangles and between Cu₃(µ₃-OH) triangles and the central [Cu(4-Ph-pzH)₄] complex unit is weakly ferromagnetic, whereas the strong antiferromagnetic exchange was expected within Cu₃(µ₃-OH) triangles. Such analysis resulted in best-fit values of J₁₂ = J₂₃ = −281 cm⁻¹, J₁₃ = −226 cm⁻¹, J_12′ = J₁₄ = +19.7 cm⁻¹ and |d_z| = 37.1 cm⁻¹ with an isotropic g-factor g = 2.35 (Figure 5). The temperature-independent paramagnetism was also accounted for by adding a constant term χ_TIP = 5.23 × 10⁻⁹ m³ mol⁻¹ for seven copper atoms based on the generally accepted value for one Cu^II ion equal to 60 × 10⁻⁶ cm³ mol⁻¹ in cgs units [43], or 0.754 × 10⁻⁹ m³ mol⁻¹ in SI units. In summary, the strong antiferromagnetic exchange within the Cu₃(µ₃-OH) triangles was confirmed together with the antisymmetric non-Heisenberg interaction, and the overall analysis was impossible without the introduction of a weak inter-triangle magnetic exchange.

The value of the magnetic exchange within the Cu₃(µ₃-OH) triangles is comparable to those reported in the literature for similar Cu^II-pyrazolato/triazolato-bridged complexes containing µ₃-OH group. It seems that in compound (1) reported herein, the antiferromagnetic exchange is one of the strongest (

Table 1. Selected magnetostructural data for various Cu₃(µ₃-O(H/R)) systems.

Compound a	Cu···Cu (Å)	−J, −zJ′/cm−1	Ref.
[Cu3 (OH)(pz)3(Hpz)2(NO3)2]·H2O	3.351	200, 0	[45]
[Cu3(OH)(pz)3(py)2Cl2]·py	3.112–3.321	140, 0	[46]
[Cu3(OH)(aat)3(CF3SO3)(H2O)](CF3SO3)	3.355	197.7, 0	[47]
[Cu3(OH)(aat)3(NO3)(H2O)2](NO3)·(H2O)2	3.341	190.9, 0	[47]
[Cu3(OH)(aat)3(ClO4)(H2O)2](ClO4)	3.371	198.2, 0	[47]
{[Cu3(O)(triazolate)3(OH)(H2O)6]}n	3.388	112.6, 11.6	[48]
[Cu3(triazolate)3(OH)][Cu2Br4]	3.502	180, 68	[49]
[Cu3Br(Hpz)2(pz)3(OCH3)]Br	3.250–3.255	105, 0	[50]
[Cu3(OH)(aaat)3(H2O)3](NO3)2·H2O	3.347–3.393	195, 0	[8]
{[Cu3(OH)(aat)3(SO4)]·6H2O}n	3.337–3.364	185, 0	[8]
[Cu3(admtrz)4(SCN)3(OH)(H2O)](ClO4)2·H2O	3.254–3.318	120, 53	[51]
[{Cu3(OH)(pz)3(Hpz)3}2SO4](NO3)2·MeCN·MeOH·1.5H2O	3.182–3.354	180, 12.7	[44]
[Ag(Hpz)2]2[{Ag2(Hpz)2(NO3)2}{Cu6(OH)2(pz)6(Hpz)6(SO4)}2](NO3)6·4H2O	3.222–3.356	134, 10.5	[44]
[{Ag(H2O)2}{Cu3(OH)(pz)3(Hpz)3(H2O)(ClO4)3}]	3.302–3.372	158, 9.2	[44]
[Et3NH][Cu3(OH)(pz)3(PhCOO)3]	3.244–3.352	178, 57.5	[13]

^a aat = 3-acetylamino-1,2,4-triazolate; Haaat = 3-acetylamino-5-amino-1,2,4-triazolate; admtrz = 4-amino-3,5-dimethyl-1,2,4-triazole.

) [44].

3.6. EPR Spectroscopy of (1)

Solid state X-band EPR spectra of (1) at 4.2 K showed a complex derivative signal centered around 3000 G, with broad linewidths and a broad resonance around 3800 G (g~1.8), all characteristic of an exchange-coupled system (Figure 6). Upon heating, part of the signal decreased in intensity, leaving an axial signal, which persisted unchanged up to 290 K, and was assigned to the central [Cu(4-Ph-pzH)₄]²⁺ complex, which appears not to be exchange-coupled to the two Cu₃ triangles. This is in agreement with the crystal structure, showing that the main coupling pathway between [Cu(4-Ph-pzH)₄] and the trinuclear units—Cl-counterions at axial sites on either side of the Cu₃-units—involves non-magnetic orbitals (d_z²) and consistent with the analysis of magnetic susceptibility data, where J₁₄ was shown to be the weakest interaction (vide supra, Section 3.5). Whereas the relaxation rate of the intradoublet signal of the Cu₃ accelerates rapidly with increasing temperature, the signal intensity of the mononuclear complex follows a Curie dependence, masking the contribution of the exchange-coupled system above 12 K. Attempts to increase the signal of the exchange-coupled system by exploiting the relaxation differences of the two components, in particular by increasing the microwave power at the low-temperature limit of the apparatus, failed; experiments at 4.0 K with microwave power of 20 mW did not selectively increase the signal intensity of that component.

The above assignment is further corroborated by EPR studies in a frozen THF solution (Figure 7) showing significant differences between the signal attributed to the two components: one axial signal exhibited hyperfine features and the other exhibited a very broad g_⊥ < 2 feature. The latter feature is characteristic of half-integer trinuclear clusters and is due to the presence of magnetic asymmetries operating in tandem with antisymmetric exchange [52,53]. These characteristic features allowed simulations assuming two axial subcomponents. For the former, an S = 1/2 spin, described by the $\widehat{H}=\beta H\tilde{g}\widehat{S}+\widehat{I}\tilde{A}\widehat{S}$ Hamiltonian, and for the latter an effective S = 1/2 spin, described by a simple Zeeman Hamiltonian, were assumed. Simulations with parameters g_1⊥ = 2.145, g_1|| = 2.334, A_1|| = 527 (MHz), g_2⊥ = 1.82 (g-strain = 0.37 FWHM) and g_2|| = 2.268 (relative intensities I₂:I₁ = 0.91:1) gave a satisfactory agreement to the experimental spectrum. Due to the large number of variables, the above parameter set is indicative, as far as line widths and g-strain parameters are concerned.

The presence of the hyperfine signals in solution and not in the solid state for the mononuclear component suggests the presence of dipolar interactions that are removed upon dissolution. To test this hypothesis and better understand the solid-state spectra of (1), complementary Q-band studies were carried out. The solid-state Q-band spectra (Figure S4) were by and large similar to the X-band ones, but they revealed additional features of the two subcomponents (Figure 8). In particular, the signal attributed to [Cu(4-Ph-pzH)₄] was found to be rhombic, with a small split in its x and y components, indiscernible in the X-band experiments. The overall behavior observed in the X-band spectra was confirmed, with a composite spectrum at 5 K.

The solid-state structure is characterized by a network of possible dipolar interactions along the chains formed by the trinuclear and mononuclear complexes previously described (Figure S5). Depending on their magnetic symmetry, i.e., |J| > |J′| versus |J| < |J′|, the spin densities of the triangles may be spread out over all three metal sites, or concentrated on one of them, respectively [13]. Our tentative conclusion from DFT calculation points toward the former case, which is also consistent with the magnetic susceptibility analysis, negating the applicability of the point-dipole approximation and hindering a straightforward analysis of dipolar interactions. Moreover, the non-trivial symmetry of the structure, combined with the extended nature of the system, seriously complicated any such analysis. Therefore, a detailed analysis of the dipole–dipole interactions was not pursued in this case.

3.7. Theoretical DFT Calculations of (1)

The complexity of magnetic interactions in (1) demands some theoretical insight guiding the analysis of the experimental magnetic data. Therefore, the isotropic exchange parameters J_i were calculated with the help of broken-symmetry calculations using several molecular fragments derived from experimental X-ray data (Figure 9). First, the triangular moiety was extracted and energies of high-spin state (HS) and broken-symmetry spin states (BS) were calculated with B3LYP to derive J-parameters for spin Hamiltonian

$$\widehat{H} =-J_{12}\left(S_1\cdot S_2+S_{1\prime }\cdot S_{2\prime }\right)-J_{13}\left(S_1\cdot S_3+S_{1\prime }\cdot S_{3\prime }\right)-J_{23}\left(S_2\cdot S_3+S_{2\prime }\cdot S_{3\prime }\right)$$

(4)

As a result, the energies Δ₁ = −245.197 cm⁻¹, Δ₂ = −323.346 cm⁻¹ and Δ₃ = −251.072 cm⁻¹ were calculated, where Δ_i = ε_BS,i − ε_HS. From these energies, J-values were calculated by Ruiz’s approach [54,55], resulting in J₁₂ = −159 cm⁻¹, J₁₃ = −86.5 cm⁻¹ and J₂₃ = −165 cm⁻¹. It must be noted that this approach is based on the so-called strong interaction limit, whereas the weak interaction limit treatment of Noodleman would have resulted in J-values generally twice larger [56]. Next, the hexanuclear molecular fragment was extracted in order to estimate the magnetic exchange mediated by chlorido-ligands between two trimeric units:

$$\widehat{H} =-J_{12}\left(S_1\cdot S_2+S_{1\prime }\cdot S_{2\prime }\right)-J_{13}\left(S_1\cdot S_3+S_{1\prime }\cdot S_{3\prime }\right)-J_{23}\left(S_2\cdot S_3+S_{2\prime }\cdot S_{3\prime }\right)-J_{12\prime }\left(S_1\cdot S_{2\prime }+S_{1\prime }\cdot S_2\right)$$

(5)

Therefore, energies of HS and BS123 states were calculated, leading to Δ₁₂₃ = +5.808 cm⁻¹, from which J_12′ equals +2.90 cm⁻¹. Finally, the heptanuclear molecular fragment was investigated using spin Hamiltonian

$$\widehat{H} =-J_{12}\left(S_1\cdot S_2+S_{1\prime }\cdot S_{2\prime }\right)-J_{13}\left(S_1\cdot S_3+S_{1\prime }\cdot S_{3\prime }\right)-J_{23}\left(S_2\cdot S_3+S_{2\prime }\cdot S_{3\prime }\right)-J_{14}\left(S_1\cdot S_4+S_{1\prime }\cdot S_4\right)$$

(6)

and HS and BS4 spin states were calculated, resulting in Δ₁₂₃ = +1.723 cm⁻¹. Thus, also this interaction is weakly ferromagnetic, J₁₄ = +0.86 cm⁻¹.

3.8. Magnetic Susceptibility Studies of (2)

The temperature dependence of effective magnetic moment data for compound (2) is depicted in Figure 10. The room temperature effective magnetic moment has value 3.1 µ_B, which is relatively close to the theoretical value 3.0 µ_B for three non-interacting spins S₁ = S₂ = S₃ = 1/2 with g = 2.0. Upon lowering the temperature, the effective magnetic moment continually decreases down to a value of 0.1 µ_B at 1.9 K, indicating the presence of strong antiferromagnetic exchange interactions. The observed magnetic behavior of (2) can be rationalized on a qualitative level by assuming dominant antiferromagnetic exchange within each triangle, which leads to S_eff = 1/2 ground spin state similarly to (1) and also supported by DFT (vide infra). These Cu₃-triangles are then coupled within the infinite chain by azido ligands, which also mediate a weak antiferromagnetic exchange. Established magnetostructural correlations [57,58] also suggest that the Cu–N–Cu angles of 115.0(2) and 105.9(2)° should mediate an antiferromagnetic exchange. Thus, from the magnetic point of view, the coordination polymer of (2) can be simplified to 1D chain of the antiferromagnetically coupled S_eff = 1/2 spins with this spin Hamiltonian:

$$\widehat{H}=-J{\displaystyle \sum _{i=1}^{\infty }{S}_i\cdot S_{i+1}}+{\mu }_{\mathrm{B}}{\displaystyle \sum _{i=1}^{\infty }B\cdot g_i\cdot S_i}$$

(7)

where S_i = S_eff = 1/2. Fortunately, the analytical equation of the molar susceptibility for said system has already been derived by Johnston et al. [59] and the fitting procedure applied to the temperature dependence of the molar susceptibility of (2) resulted in J = −53 cm⁻¹ with g = 2.2. The negative value of J confirms the antiferromagnetic exchange among the trinuclear building block within the coordination polymer in contrast to DFT calculations, which suggest ferromagnetic exchange mediated by azido ligands. Moreover, the deviation of calculated values of the effective magnetic moment at temperatures higher than ca 60 K is attributed to fact that at such high temperature, the proposed approximation of S_eff = 1/2 for each Cu₃-triangle loses its validity, because the excited S_eff = 3/2 state is also populated, explaining the higher values of the effective magnetic moment in comparison to the calculated ones. It must be noted that we have tried to employ spin Hamiltonian analogous to Equation1 also for (2), but the agreement with the experimental data was not achieved. Most probably, the case of both intra and inter Cu₃-triangle antiferromagnetic exchange would demand expanding the spin Hamiltonian to contain more spin centers to better simulate the polymeric character of the compound, which is unfortunately prohibited by large dimension of the respective Hilbert space.

3.9. EPR Spectroscopy of (2)

The 4.2 K solid-state X-band EPR spectrum of (2) is characterized by a main derivative signal at g = 2.05, and a secondary half-field transition at g = 4.06; the latter transition was attributed to magnetic interactions with neighboring complexes of the polymeric structure (Figure 11). Due to the magnetic interaction pathway mediated by the bridging azides, which passes through non-magnetic orbitals of the copper(II) ions, this interaction may not be of exchange but of dipolar origins [60].

In frozen CH₂Cl₂ solutions this half-field transition disappears, in line with a disruption of the polymeric network in solution. In turn, the solution spectrum exhibits a downfield shifted feature (g = 1.74), which is a characteristic signature of magnetic anisotropy induced by the combined operation of a moderate magnetic asymmetry (J ≠ J′) and antisymmetric exchange interactions (Figure 10) [13,52,53].

3.10. Theoretical DFT Calculations of (2)

The magnetic interactions in (2) were also analyzed with the broken-symmetry calculations using two molecular fragments derived from experimental X-ray data (Figure 12). First, the triangular moiety was extracted and energies of high-spin state (HS) and broken-symmetry spin states (BS) were calculated with B3LYP to derive J-parameters for spin Hamiltonian

$$\widehat{H} =-J_{12}\left(S_1\cdot S_2+S_{1\prime }\cdot S_{2\prime }\right)-J_{13}\left(S_1\cdot S_3+S_{1\prime }\cdot S_{3\prime }\right)-J_{23}\left(S_2\cdot S_3+S_{2\prime }\cdot S_{3\prime }\right)$$

(8)

As a result, the energies Δ₁ = −337.724 cm⁻¹, Δ₂ = −362.944 cm⁻¹ and Δ₃ = −349.454 cm⁻¹ were computed. Next, J-values were calculated by Ruiz’s approach, as for (1), resulting in J₁₂ = −176 cm⁻¹, J₁₃ = −162 cm⁻¹ and J₂₃ = −187 cm⁻¹. It should also be stressed that in weak interactions, limit J-values would have been two times larger. Afterwards, the hexamer molecular fragment was extracted in order to estimate the magnetic exchange mediated by azido-ligands between two trimeric units:

$$\widehat{H} =-J_{12}\left(S_1\cdot S_2+S_{1\prime }\cdot S_{2\prime }\right)-J_{13}\left(S_1\cdot S_3+S_{1\prime }\cdot S_{3\prime }\right)-J_{23}\left(S_2\cdot S_3+S_{2\prime }\cdot S_{3\prime }\right)-J_{23\prime }\left(S_2\cdot S_{3\prime }+S_{2\prime }\cdot S_3\right)$$

(9)

Thus, energies of HS and BS123 states were calculated, leading to Δ₁₂₃ = +10.644 cm⁻¹, from which J_23′ equals +5.32 cm⁻¹.

4. Conclusions

The one-dimensional solid state structures of (1) and (2) are held together by weak interactions via bridging anions—chlorides and azides, respectively—which are disrupted in solution. Because of the polymeric nature and low symmetry of these materials, the analysis of the magnetic properties has been supported by DFT calculations, suggesting strong antiferromagnetic exchange within Cu₃ units and weak ferromagnetic interactions among these units. The predominant antiferromagnetic exchange within the Cu₃ units has been unequivocally determined in both cases by the analysis of magnetic susceptibility characteristics. In addition, the operation of an antisymmetric exchange in (1) was evident by both magnetometry and EPR spectroscopy. The much weaker inter-Cu₃ exchange, ferromagnetic in (1) and antiferromagnetic in (2), is attributed to the fact that non-magnetic Cu-orbitals are involved at one or both ends. EPR spectroscopy determined the magnitude of dipolar interaction in solid state (1), while the possible dipolar interaction between Cu₃-units of (2) cannot be determined with certainty. The solution EPR spectra of both compounds are clearly distinguished from those in the solid state and are straightforwardly attributed to individual Cu₃(μ₃-OH) species of (2), and to the presence of isolated mononuclear and trinuclear species in the case of (1). Two new reports, describing the magnetic susceptibilities and (in one case) the EPR spectrum of polymeric supramolecular assemblies of copper(II) complexes, appeared in the literature recently [61,62].