INTRODUCTION

The derivatives of 2,6-diacetylpyridine are of interest due to the diverse and pronounced biological activity [1, 2] and high complexation ability [3–7]. In particular, 2,6-diacetylpyridine bis(isonicotinoylhydrazone) (H2L1) and 2,6-diacetylpyridine bis(nicotin-oylhydrazone) (H2L2) have nine donor atoms capable of involving in the formation of coordination bonds with metals, seven of them being nitrogen atoms and two of them being oxygen atoms. These ligands can exist in compounds in various tautomeric forms with various degrees of deprotonation (Scheme 1).

Scheme 1.

The syntheses and structural studies of the Co(II), V(II), V(IV), and Fe(III) complexes with the products of condensation of 2,6-diacetylpyridine with hydrazides of iso- and nicotinic acids were presented in our previous works [8–10]. In this work, we present the results of synthesis and spectral (IR) and structural (X-ray diffraction analysis (XRD)) studies of six new Cu(II) complexes (five binuclear and one tetranuclear): [Cu2(H2L1)2](SO4)2 ∙ 4H2O (I), [Cu2(L1)2] · 2MeOH · 0.5EtOH (II), [Cu2(L1)2] · 1.2EtOH · 5.4H2O (III), [Cu2(L2)2] · H2O (IV), [Cu2(L2)2] · 0.1H2O (V), and [Cu4(HL2)4(OH)2](NO3)2 ∙ 6.75H2O (VI), where H2L1 is 2,6-diacetylpyridine bis(isonicotinoylhydrazone) and H2L2 is 2,6-diacetylpyridine bis(nicotinoylhydrazone). Compounds I and VI are ionic, since their organic ligands are coordinated to the metal in the monodeprotonated form, and others are molecular complexes in which the organic ligands are doubly deprotonated.

EXPERIMENTAL

Commercial reagents and solvents (reagent grade) were used as received, and H2L1 and H2L2 were synthesized using known procedures [11, 12].

Synthesis of [Cu2(H2L1)2](SO4)2 ∙ 4H2O (I). Copper sulfate CuSO4 ∙ 5H2O (0.25 g, 1.00 mmol) was dissolved in an ethanol–water (1 : 1.22 vol/vol) mixture (20 mL) to obtain solution 1. 2,6-Diacetylpyridine (0.16 g, 1.00 mmol) was dissolved in methanol (10 mL) to form solution 2. The dissolution of isonicotinic acid hydrazide (0.28 g, 2 mmol) in methanol (12 mL) gave solution 3. Solutions 2 and 3 were simultaneously added with permanent stirring to solution 1. The green-brown reaction mixture was heated at 60°С with a reflux condenser for 4 h, after which the solution was filtered and left to stay at room temperature in air for crystallization. Dark brown crystals of complex I suitable for XRD were formed after 24 h. The crystals were soluble in water, methanol, ethanol, and dimethylformamide (DMF) and insoluble in diethyl ether. The yield was 21.6% (based on copper(II) sulfate pentahydrate)).

For C42H46N14O16S2Cu2

Anal. calcd., %

C, 42.24

H, 3.88

N, 16.42

Cu, 10.64

Found, %

C, 42.11

H, 3.73

N, 16.30

Cu, 10.75

IR (ν, cm–1): 3400 w, 3228 w, 2548 w, 1657 w, 1636 w, 1593 w, 1538 m, 1486 s, 1461 w, 1416 w, 1360 s, 1298 w, 1222 w, 1150 s, 1096 m, 1037 vs, 972 w, 929 w, 901 w, 843 m, 812 m, 753 m, 711 w, 686 m, 646 w, 608 s, 552 w, 519 w, 493 w, 452 w, 426 w.

Synthesis of [Cu2(L1)2] · 2MeOH · 0.5EtOH (II) and [Cu2(L1)2] · 1.2EtOH · 5.4H2O (III). Copper sulfate CuSO4 · 5H2O (0.05 g, 0.2 mmol) and H2L1 (0.08 g, 0.2 mmol) were suspended in a DMF–methanol–ethanol (1 : 1.5 : 1.5 vol/vol/vol) mixture (8 mL). The syntheses was carried out in autoclaves with Teflon bushes (10 mL) under elevated pressure. The reaction mixture was heated to 80°C and kept for 48 h. A brown precipitate was filtered off and washed with a minor amount of a DMF–methanol–ethanol mixture, and the mother liquor was left to stay for crystallization in air. Dark brown crystals suitable for XRD were formed after 24 h. The crystals were insoluble in methanol, ethanol, DMF, and diethyl ether.

IR (ν, cm–1): 3414 w, 3065 w, 2930 w, 1657 m, 1602 w, 1566 w, 1486 vs, 1457 m, 1412 w, 1370 vs, 1360 vs, 1314 m, 1296 w, 1260 w, 1224 w, 1160 m, 1134 w, 1097 w, 1056 s, 1012 m, 930 w, 914 w, 851 m, 838 w, 817 m, 759 m, 670 s, 668 w, 530 w, 583 w, 491 w, 437 w, 406 w.

Synthesis of [Cu2(L2)2] · H2O (IV) and [Cu2(L2)2] · 0.1H2O (V). Copper sulfate CuSO4 · 5H2O (0.05 g, 0.2 mmol) and H2L2 (0.08 g, 0.2 mmol) were suspended in a DMF–methanol–ethanol (1 : 1.5 : 1.5 vol/vol/vol) mixture (8 mL). The syntheses was carried out in autoclaves with Teflon bushes (10 mL) under elevated pressure. The reaction mixture was heated to 80°C and kept for 48 h. A brown precipitate was filtered off and washed with a minor amount of a DMF–methanol–ethanol mixture, and the filtrate was left for crystallization in air. Dark brown crystals suitable for XRD were formed in the filtrate after 24 h. The crystals were insoluble in methanol, ethanol, DMF, and diethyl ether.

IR (ν, cm–1): 3382 w, 3075 w, 2336 w, 2053 w, 1655 m, 1580 m, 1558 w, 1495 s, 1460 m, 1409 w, 1369 vs, 1316 m, 1260 w, 1193 w, 1162 m, 1094 m, 1052 m, 1031 m, 927 w, 910 w, 814 m, 737 m, 715 w, 699 m, 672 w, 638 m, 618 m, 603 m, 501 w, 486 w, 459 w, 430 w, 405 w.

Synthesis of [Cu4(HL2)4(OH)2](NO3)2 ∙ 6.75H2O (VI). Copper nitrate Cu(NO3)2 ∙ 3H2O (0.06 g, 0.25 mmol) was dissolved in an ethanol–water (1 : 1.25 vol/vol) mixture (20 mL) to form solution 1. 2,6-Diacetylpyridine (0.04 g, 0.25 mmol) was dissolved in methanol (4 mL) (solution 2), and nicotinic acid hydrazide (0.07 g, 0.5 mmol) was dissolved in methanol (10 mL) (solution 3). Solutions 2 and 3 were simultaneously added with permanent stirring to solution 1. The mixture was refluxed with continuous stirring using a reflux condenser for 4 h, after which the solution was filtered and left to stay in air at room temperature for crystallization. Dark brown crystals suitable for XRD precipitated from the solution after 4 days. The crystals were soluble in water, methanol, ethanol, and DMF and insoluble in diethyl ether. The yield was 4% (based on copper(II) nitrate trihydrate).

For C84H87.50N30O22.75Cu4

Anal. calcd., %

C, 47.15

H, 4.14

N, 19.64

Cu, 11.88

Found, %

C, 47.20

H, 4.16

N, 19.20

Cu, 11.75

IR (ν, cm–1): 3380 w, 3248 w, 1751 w, 1667 m, 1629 w, 1610 w, 1596 w, 1560 w, 1534 m, 1507 m, 1474 w, 1369 vs, 1323 vs, 1297 vs, 1260 m, 1201 w, 1164 m, 1147 m, 1130 m, 1164 m, 1032 w, 1007 w, 992 w, 925 w, 909 w, 822 m, 748 w, 732 m, 699 m, 677 w, 620 w, 573 w, 540 w, 509 w, 482 w, 469 w, 452 w, 440 w, 407 w.

X-ray diffraction analysis. Experimental data for complexes I–VI were obtained at room temperature on an Xcalibur E diffractometer (graphite monochromator, MoKα radiation). The unit cell parameters were determined and experimental data were processed using the CrysAlis Oxford Diffraction Ltd. program [13]. The structures of the compounds were determined by direct methods and refined by least squares in the anisotropic full-matrix variant for non-hydrogen atoms using the SHELX-97 program [14]. The positions of the hydrogen atoms of the water molecules were revealed from the difference Fourier syntheses, and positions of other hydrogen atoms were calculated geometrically and refined isotropically in the rigid body model with Ueff = 1.2 Uequiv or 1.5 Uequiv of the corresponding O, N, and C atoms. An attempt to prepare compound IV as single crystals failed, and the experimental data were obtained from the twin, which was not separated and, hence, the R factor was not decreased. The crystallographic data and experimental characteristics for the structures of compounds I–VI are presented in Table 1. Selected interatomic distances and bond angles of the compounds are given in Table 2. The geometric parameters of intra- and intermolecular hydrogen bonds are listed in Table 3.

Table 1. Crystallographic data, experimental characteristics, and structure refinement parameters for compounds I–VI
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Table 2. Interatomic distances and bond angles in the coordination polyhedra of the structures of compounds I–VI
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Table 3. Geometric parameters of hydrogen bonds in compounds I–VI
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The positional and thermal parameters for the structures of complexes I–VI were deposited with the Cambridge Crystallographic Data Centre (CIF files CCDC nos. 1967853 (I), 1967858 (II), 1967854 (III), 1967855 (IV), 1967856 (V), 1967857 (VI); deposit@ ccdc.cam.ac.uk or http://www.ccdc.cam.ac.uk).

RESULTS AND DISCUSSION

The broad absorption bands of medium and weak intensity observed in the ranges 2500–2325 and 2200–1800 cm–1 of the IR spectrum of compound I are possibly related to the migration of protons from N(2) and N(2)* to the heterocyclic nitrogen atoms (N(1) and N(1)*) of the terminal pyridine rings and to the formation of the PyH+ fragments [15, 16]. The shift of the absorption band ν(C=O) + ν(CN) in the spectra of compounds I–V to the long-wavelength range to 1657 and 1636 cm–1 indicates the involvement of the carbonyl group in the coordination to the metal [8] and thus the stabilization of the organic ligands in the ketone form [17]. In the IR spectra of compounds II–V, the absorption bands of medium and high intensity at 1457 and 1360 cm–1 (complexes II and III) and at 1460 and 1369 cm–1 (compounds IV and V) correspond to bending vibrations of the CH3 groups (δasym(CH3) and δsym(CH3), respectively) [16]. The IR spectra of complexes II and III exhibit absorption bands that can be assigned to the out-of-plane vibrations δ(С–Н) of the aromatic rings: the absorption bands at 759 cm–1 for three adjacent hydrogen atoms (substitution type 1,3) and at 817 cm–1 for two adjacent hydrogen atoms (substitution type 1,4) [17, 18]. In the IR spectra of complexes IV and V, the out-of-plane vibrations δ(С–Н) for three adjacent hydrogen atoms appear at 737 cm–1, whereas those for the isolated hydrogen atom are observed at 814 cm–1 [17, 18].

The IR spectrum of complex VI exhibits the following significant absorption bands: at 3380 cm–1 corresponding to stretching vibrations (ν(OH) + ν(NH)), 1667 cm–1 caused by stretching vibrations of the carbonyl group (ν(C=O)), 1629 cm–1 caused by ν(C=Nazometh.) and strong absorption in a range of 1260–1380 cm–1 caused by ν(\({\text{NO}}_{3}^{ - }\)) [16, 19], 1474 cm–1 caused by δasym(CH3), and 1368 cm–1 caused by δsym(CH3) [16]. The IR spectrum of the tetranuclear complex (VI) exhibits absorption bands at 732 and 822 cm–1 attributed to δ(С–Н) of the aromatic rings for the substitution 1,3- and 1,4-types, respectively [17, 18].

Both molecular copper(II) complexes (II–V) and complexes of the ionic type (I and VI) were synthesized using various synthesis methods. The bis(deprotonated) organic ligands (L1)2– or (L2)2– are coordinated to the metal atom in compounds II–V, the neutral organic ligands H2L1 are coordinated to the metal atom in compound I, and the monodeprotonated ligands (НL2)– are coordinated to the metal atom in complex VI. In the ionic compounds (I and VI), the charges of the complex cations are compensated by the outer-sphere inorganic anions \({\text{SO}}_{{\text{4}}}^{{{\text{2}} - }}\) or \({\text{NO}}_{{\text{3}}}^{ - }\), respectively.

Compound I that crystallizes in the orthorhombic space group Ccca was synthesized by the reaction of H2L1 with copper(II) sulfate in an ethanol–water–methanol mixture (Table 1). The structure is ionic and consists of binuclear complex cations [Cu2(H2L1)2]4+ with the D2 symmetry (Fig. 1a), \({\text{SO}}_{{\text{4}}}^{{{\text{2}} - }}\) anions disordered around the binary axis, and H2O molecules of crystallization in the ratio 1 : 2 : 4, respectively. The complex cation has the structure of a double spiral (Fig. 1b) in which the neutral organic ligands H2L1 are coordinated via the hexadentate chelate-bridging mode to two metal atoms, and the central N(4) atom of the ligand is bridging. The symmetrical coordination polyhedron of the metal atoms is a distorted tetragonal bipyramid and is formed by a set of donor atoms N4O2. The interatomic distances Cu(1)–O(1), Cu(1)–N(3), and Cu(1)–N(4) are 2.033(4), 1.930(6), and 2.502(7) Å, respectively (Table 2). The Cu(1)···Cu(1)* distance in the binuclear cation is 3.239(3) Å. Each neutral ligand H2L1 coordinates to both metal atoms to form four five-membered metallocycles of two types (CuOCNN and CuNCCN), two of which coordinate to one metal atom and two others coordinate to the second metal atom. A similar coordination mode of these ligands has previously been found in the binuclear Cu(II) [12, 20], Co(II) [21], Ni(II) [5, 22], and Zn(II) [23] complexes with ligands of this class. It was concluded on the basis of diverse steric concepts and an analysis of the Fourier syntheses that the hydrogen atom, which should be localized at the nitrogen atom of the hydrazine fragment in H2L1, is stabilized at the nitrogen atom of the terminal heterocycle (N(1)). It is known that the CNC angle in the pyridine fragments is sensitive to protonation [24, 25] and, hence, the CNC bond angle at the nitrogen atom in the terminal pyridine cycle in complex I is larger than 120° (∠CNC 122.1(7)°), which also confirms the proton transfer and formation of the PyH+ fragment.

Fig. 1.
figure 1

Structure of the complex cation [Cu2(H2L1)2]4+ with the partial notation of atoms: (a) the second ligand is drawn by thin lines for clarity and (b) the structure of the double spiral for the complex cation [Cu2(H2L1)2]4+.

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An analysis of the crystal structure shows that the complex cations and \({\text{SO}}_{{\text{4}}}^{{{\text{2}} - }}\) anions are linked to each other into layers parallel to the bc plane by both intermolecular hydrogen bonds (IHB) N–H∙∙∙O and weaker С–H∙∙∙O bonds (Table 3, Fig. 2) and the water molecules are linked with the latter and between each other by IHB O(w)–H∙∙∙O, O(w)–H∙∙∙O(w), and C–H∙∙∙O(w).

Fig. 2.
figure 2

Fragment of the crystal structure of complex I.

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When the solvothermal synthesis method was used, the reactions of H2L1 or H2L2 with copper(II) sulfate afforded two solvatomorphs: [Cu2(L1)2] · 2MeOH · 0.5EtOH (II) and [Cu2(L1)2] · 5.4H2O · 1.2EtOH (III) or [Cu2(L2)2] · H2O (IV) and [Cu2(L2)2] · 0.1H2O (V), respectively. Compounds II–IV crystallize in more symmetric space groups of the orthorhombic or monoclinic crystal system, whereas complex V crystallizes in the triclinic space group P\(\bar {1}\) (Table 1). Two crystallographically independent nonsymmetric complexes are stabilized in the unit cell of the latter. The structures of the molecular complexes [Cu2(L1)2] and [Cu2(L2)2] in compounds II–V are similar to that found in complex cation I (Fig. 3). However, in these compounds, the organic ligands (L1/2)2– coordinate to the metal atom in the doubly deprotonated keto form. The coordination polyhedra of the metal atoms in compounds II–V are distorted tetragonal bipyramids and formed by the donor atoms N4O2 belonging to two different ligands. The interatomic distances Cu(1)–O(1)/O(2), Cu(1)–N(3)/N(5), and Cu(1)–N(4)/N4* are equal, on the average, to 2.106, 1.942, and 2.459 Å, respectively (Table 2). The Cu(1)···Cu(1)* distance in molecular complex II is 3.315(1) Å, that in compound III is 3.300(2), that in compound IV is 3.278(3), and the Cu(1)···Cu(2) and Cu(3)···Cu(4) distances in complex V are 3.280(1) and 3.318(1) Å, respectively.

Fig. 3.
figure 3

Structures of the binuclear molecular complexes [Cu2(L1)2] in compounds (a) II and (b) III, (c) [Cu2(L2)2] in compound IV, and (d) one crystallographically independent complex in compound V with the partial notation of atoms.

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An analysis of the crystal structures shows that in compound II the molecular complexes are linked with each other into chains via weak IHB С–H∙∙∙N(1), the methanol molecules are joined with them by the О–H∙∙∙N(7) bonds, whereas the ethanol molecules are arranged in cavities between them (Table 3, Fig. 4a). Both IHB O(w)–H∙∙∙N between the water molecules and complexes and the IHB formed between the water molecules of crystallization and ethanol molecules (Fig. 4b) can be distinguished in compound III. The complexes in compound IV are bound to the water molecules by IHB O(w)–H∙∙∙О and weak С–H∙∙∙O(w) bonds (Fig. 4c). Weak IHB С–H∙∙∙N(7)/N(7) and С–H∙∙∙О(1)/О(2), which join the molecular complexes in the crystal, and weak IHB С–H∙∙∙O(1)/N(6) and С–H∙∙∙О(1w) linking the water residues with the complexes (Fig. 4d) can be distinguished in compound V.

Fig. 4.
figure 4

Fragments of the crystal structures of compounds (a) II, (b) III, (c) IV, and (d) V.

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Compound [Cu4(HL2)4(OH)2](NO3)2 ∙ 6.75H2O (VI), which crystallizes in the monoclinic space group C2/c, was synthesized from a Cu(NO3)2 ∙ 3H2O–2,6-diacetylpyridine–nicotinic acid hydrazide system in a molar ratio of 1 : 1 : 2. The water molecules are localized in nine positions with various populations. The structure of the compound is ionic and consists of tetranuclear complex cations [Cu4(HL2)4(OH)2]2+ with the C2 symmetry (Fig. 5a), anions \({\text{NO}}_{3}^{ - }\), and H2O molecules of crystallization. In the complex cation, four copper(II) ions are linked by four monodeprotonated ligands (HL2)–, and two organic ligands coordinate to each metal atom, one of which coordinates by the donor atoms O(2)N(5)N(4) and another coordinates by the terminal N(1) atom of the pyridine heterocycle. These four atoms are arranged in the base of the square-pyramidal polyhedron of the metal, and the polyhedron is supplemented by the O atom of the bridging anion ОН–. The interatomic distances Cu(1)–O(2), Cu(1)–N(4), Cu(1)–N(5), Cu(1)–N(1), and Cu(1)–O(1)ОН are equal, on the average, to 1.977, 2.069, 1.918, 1.985, and 2.306 Å, respectively (Table 2). As a result, (HL2)– is a tetradentate chelate-bridging ligand, which coordinates via the tridentate mode to one metal atom by the set of donor atoms ONN to form two five-membered metallocycles via the mode found for compounds I–V, whereas the coordination to another metal atom occurs via the monodentate mode by one terminal N(1) atom of the heterocycle. Unlike the localized H atom at the terminal N atom of the heterocycle of the organic ligand found in compound I, another tautomeric form of the latter is stabilized in complex VI and the remained H atom is localized at the N atom of the azomethine group (N(2)) due to deprotonation. The Cu(1)···Cu(2) and Cu(1)···Cu(2)* distances in the cation are 4.298(4) and 9.092(1) Å, respectively.

Fig. 5.
figure 5

Structures of the (a) tetranuclear complex cation [Cu4(HL2)4(OH)2]2+ with the partial notation of atoms and (b) quaternary spiral for the tetranuclear complex cation [Cu4(HL2)4(OH)2]2+.

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An analysis of the complicated system of hydrogen bonds shows that the tetranuclear complex cation is stabilized by intramolecular hydrogen bonds O(1)ОН–H∙∙∙O(1А)/O(1B) (Table 3) and the complex cations and \({\text{NO}}_{{\text{3}}}^{-}\) anions are bound to each other into layers by the IHB O(w)–H∙∙∙O and O(w)–H∙∙∙N (Table 3, Fig. 6) and weaker С–H∙∙∙O bonds both between the cations and between the cations and anions. Other water molecules are mainly joined between each other by IHB O(w)–H∙∙∙O(w) and are linked to the main framework of the structure by O(w)–H∙∙∙O/N and C–H∙∙∙O(w).

Fig. 6.
figure 6

Fragment of the crystal structure of compound VI.

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In the binuclear Cu(II) complexes, the coordinating agents H2L1 and H2L2 act as bridging ligands, and a magnetic interaction between the copper atoms cannot be excluded. The manifestation of the magnetic interaction, namely, antiferromagnetic interaction, was mentioned for the binuclear nickel(II) complex only [22].

The data of measurements of the magnetic susceptibility (χM) for the binuclear coordination compound [Cu2(H2L1)2](SO4)2 ∙ 4H2O were obtained for the polycrystalline product in the magnetic field with an induction of 0.1 T in a range of 300–2 K, whereas the magnetization isotherms were measured at 2 K in the range with an induction of 0–5 T (Fig. 7).

Fig. 7.
figure 7

Temperature dependences of χMT and χM for compound I.

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All data were corrected with allowance for the holder of the sample and Pascal’s constants. The magnetic interaction constants and factors gCu were determined by the examination of the dependences χMT(T) and χM(T). The examination was performed taking into account the temperature-independent paramagnetism (TIP), contribution of paramagnetic impurities (ρ), and intermolecular interactions (zJ) via the equation

$$\begin{gathered} {{\chi }_{M}}\left( T \right) = \frac{{{{\chi }_{d}}\left( T \right)}}{{\left[ {1 - {{2zJ{\kern 1pt} '{{\chi }_{d}}\left( T \right)} \mathord{\left/ {\vphantom {{2zJ{\kern 1pt} '{{\chi }_{d}}\left( T \right)} {N{{g}^{2}}{{\beta }^{2}}}}} \right. \kern-0em} {N{{g}^{2}}{{\beta }^{2}}}}} \right]}}(1 - \rho ) \\ + \,\,\rho \frac{{N{{g}^{2}}{{\beta }^{2}}}}{{3kT}}S(S + 1) + TIP. \\ \end{gathered} $$

The temperature dependence of the magnetic susceptibility for compound I is shown in Fig. 7. At 300 K the product χMT takes the value 0.94 cm3 K mol–1, which is well consistent with the theoretical value for two Cu(II) atoms (d9, S = 1/2) with g = 2.24. As the temperature decreases, χMT increases continuously reaching a maximum value of 1.107 cm3 K mol–1 at 4 K. This behavior indicates the ferromagnetic interaction between two paramagnetic centers. The sharp decrease in χMT after 4 K is explained by the intermolecular interaction between the binuclear complexes in the solid state.

Using the results of the structural study, the magnetic behavior of coordination compound I can be modeled on the basis of the isotropic Hamiltonian, which describes the interaction between two spins, S1 = S2 = 1/2,

$$H = - 2J{{S}_{1}}{{S}_{2}}.$$

The theoretical values of magnetic susceptibility can be determined by the following analytical solution presented by the equation:

$${{\chi }_{d}} = \frac{{2Ng_{{{\text{Cu}}}}^{2}{{\beta }^{2}}}}{{T{{k}_{B}}}}\frac{1}{{3 + {{e}^{{{{ - 2J} \mathord{\left/ {\vphantom {{ - 2J} {{{k}_{B}}T}}} \right. \kern-0em} {{{k}_{B}}T}}}}}}}.$$

The best coincidence of the theoretical and experimental values (R = 1.57 × 10–6) was obtained for the following set of variable parameters: J = 3.38(6) cm–1, g = 2.251(2), zJ' = –0.243(3) cm–1, and TIP = –6.49 × 10–5 cm3 K mol–1, where zJ' is the contribution of the intermolecular interaction calculated from the magnetic susceptibility [26–28].

$$\chi (T) = \frac{{{{\chi }_{d}}(T)}}{{\left[ {1 - \frac{{2zJ{\kern 1pt} '{{\chi }_{d}}(T)}}{{N{{g}^{2}}{{\beta }^{2}}}}} \right]}}.$$

The contribution of paramagnetic impurities is very low and was ignored in order to decrease the number of variable parameters.

The measurements of the magnetic susceptibility with inductions of 0.1 and 1.0 T at various temperatures and the measurements based on the magnetic fields for tetranuclear compound VI indicate the absence of a magnetic interaction (or an insignificant interaction) between the copper(II) ions (Fig. 8). A slight decrease in χMT(Т) is observed after 4 K, which is probably the result of the intermolecular interaction. The indicated experimental value equal to 1.70 cm3 K mol–1 at 300 K corresponds to four Cu(II) ions with g = 2.13. The absence of a magnetic interaction is consistent with long distances between the copper(II) atoms (Cu(1)∙∙∙Cu(2) 4.298 Å) and the presence of the OH– bridge joining two copper(II) ions along the coordinate 5 of the coordination polyhedron (tetragonal pyramid) at a relatively long distance (Fig. 8).

Fig. 8.
figure 8

Temperature dependences of χMT and χM for compound VI.

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According to the temperature dependence of the magnetic susceptibility (2–300 K), the copper(II) ions with S = 1/2 interact weakly with each other (2J = –0.05(1) cm–1, g = 2.15(2)). The weak magnetic interaction for the Сu4 cluster was confirmed by measurements of the magnetic susceptibility in the fields of various inductions (0–5 T), which is explained by longer bonds between the Cu(1) and Cu(2) copper ions and the О(1) oxygen atom of the bridging groups OH–.