Ferromagnetically Coupled Copper(II) Clusters Incorporated in Functionalized Boltorn H30 Hyperbranched Polymer Architecture: ESR, Magnetic Susceptibility Measurements, and Quantum-Chemical Calculations.

The unusual temperature behavior of the electron spin resonance (ESR) spectra and magnetic properties are experimentally observed in copper(II) complexes with a dendritic ligand based on the Boltorn H30 polymer (Perstorp Specialty Chemicals AB, Sweden) functionalized with fumaric acid residues in a molar ratio of 1:6. The ESR spectra at low temperatures show signs of transition to higher spin states at temperatures below 8-10 K, and the temperature dependences of the integral ESR signal intensities and magnetic susceptibility show the positive deviation from the Curie-Weiss law, thereby pointing to the presence of ferromagnetic exchange interactions in the system under study. The values of the exchange interaction parameters are calculated by quantum-chemical simulation of the possible structure of the copper(II) complex when assuming the formation of trinuclear coordination sites embedded in the hyperbranched polymer structure. The results of density functional theory calculations indicate the possibility of ferromagnetic exchange through carboxylate bridges in the trinuclear magnetic clusters, and the calculated values of the exchange interaction parameters make it possible to construct theoretical curves of the temperature dependence of the effective magnetic moment, which satisfactorily fit the experimental data, especially considering that polymers are characterized by disperse molecular weights and chemical structures.

Introduction

Hyperbranched polymers and their functionalized forms can serve as a basis for the fabrication of various organic–inorganic hybrid materials combining the properties of both organic and inorganic components.[1] Incorporation of transition metals into dendrimers and highly branched polymer architectures allows one to bring promising electrical, magnetic, optical, sensing, and catalytic properties to this kind of materials. Hyperbranched polymers with “imperfect” structure are more readily available as compared to their “perfect” dendrimer counterparts and exhibit, at the same time, comparable properties despite their random and polydisperse molecular composition. They also can be used as “host” systems (nanocarriers) for encapsulation of “guest” inorganic nanoparticles (metals, metal oxides, etc.)[2,3] and templates for the synthesis of organic–inorganic hybrid nanomaterials.[4] Functionalization of the external groups of hyperbranched macromolecules allows one to incorporate a variety of metal ions in their interior. Metal centers in the dendritic environment can serve as artificial models simulating biological systems such as metalloenzymes, thereby making it possible to study various biochemical reactions in vitro. In particular, commercial hyperbranched polymers produced under the trademark Boltorn (Perstorp Specialty Chemicals AB, Sweden) can be functionalized with fumaric acid residues by the reaction with maleic anhydride.[5] The resulting hyperbranched polymers contain a different number of free carboxyl groups per macromolecule depending on the ratio of reagents and are capable of coordinating transition metals.[6] It was found that the structures and compositions of coordination adducts of the carboxyl-functionalized dendritic oligomer on the basis of third-generation hyperbranched polyester polyol Boltorn H30 are quite sensitive to variation of the degree of functionalization.[7] Depending on the number of monofumaric ester groups per macromolecule, different types of complexes are formed even with the same metal ions. Surprisingly, the electron spin resonance (ESR) spectra of one of the synthesized copper(II) complexes with acid-functionalized Boltorn H30, specifically, the one containing six carboxylic acid groups on average per macromolecule, indicated the formation of a trinuclear ferromagnetically coupled cluster with a ground spin state of S = 3/2 in solid samples.[7] It should be noted that trinuclear copper(II) coordination systems are uncommon, especially considering that carboxylate complexes tend to form antiferromagnetically coupled binuclear structures with the “lantern” geometry as in well-known dimeric copper(II) acetate.[8] At the same time, trinuclear copper clusters play a crucial role in the binding and activation of oxygen in the multicopper oxidases.[9] Hence, the obtained copper(II) triads incorporated in the Boltron H30 dendritic architecture potentially can mimic active centers of oxydase and oxygenase enzymes. Moreover, exchange-coupled systems are of special interest as magnetic materials for newly developing areas of molecular spintronics and quantum information technologies.[10]

Owing to the random molecular structure of the polymer ligand and impossibility to apply well-established diffraction methods for the structural characterization of the coordination sites, the exact structure of the complexes with the functionalized Boltorn H30 ligand was rather difficult to unambiguously determine by the accessible physicochemical methods. Moreover, further clarification of the dendritic structures of the complexes is additionally complicated by the fact that the infrared (IR), ultraviolet, and ESR studies indicate different geometries of coordination sites in solution and powder samples as a result of the coordination of solvent molecules to the metal ions.[7] However, the combination of the quantum-chemical approach and experimental studies of the magnetic properties by the methods of ESR and magnetic susceptibility measurements allowed us to gain insight into the structure of the coordination sites in the synthesized copper(II) complex with the dendritic ligand based on the Boltorn H30 polymer functionalized with fumaric acid residues in a molar ratio of 1:6. It should be noted that the only method to uncover structure–property relationships in this sort of “vague” systems seems to be to simulate their structure using computational techniques and to analyze their magnetic states at a molecular level by using a quantum-chemical approach.

Results and Discussion

The representative structure of the starting hyperbranched polymer ligand for the synthesis of transition complexes is shown in Figure . The copper(II) complex under study was synthesized by the reaction of copper(II) nitrate hydrate with the polymer ligand in aqueous ethanol according to the procedure described in ref (7) and precipitated as a green-blue powder, the IR spectrum of which was consistent with a tetrahedral coordination geometry.

Figure 1

Representative structure of Boltorn H30 and its derivative functionalized with fumaric acid residues in a 1:6 ratio.

ESR Spectra

The room-temperature ESR spectrum of a powder sample of the copper(II) complex with acid-functionalized Boltorn H30 consists of four lines that are denoted as 1, 2, 3, and 4 in ascending order of the magnetic field (Figure ). To establish the origin of these signals, the ESR measurements were performed in the temperature range from 298 to 4.2 K (Figures –4).

Figure 2

Typical powder ESR spectra of the copper(II) complex with functionalized hyperbranched polymer BH30 recorded at (a) room temperature and (b) 30 K.

Figure 4

Behavior of the ESR spectrum of the copper(II) complex with functionalized hyperbranched polymer BH30 in the temperature range of 9–4.5 K.

As is seen from Figure , the visual appearance of the ESR spectra and the line positions remain almost unchanged in the temperature range from 298 to 30 K, whereas the linewidth of the signal preserves its value at about 25 Oe. At higher temperatures, the spectrum consisted of the following four lines: lines 1, 2, and 4 with g-factor values of 2.25, 2.18, and 2.07, respectively; and line 3 with a g-factor value of 2.15 (Figure a). The four-line structure of the ESR spectrum is confirmed in Q-band measurements at room temperature, as shown below. With a decrease in the temperature to 30 K, the amplitudes of the lines gradually increased (Figure b). An increase in the amplitude of line 2 with cooling to temperatures around 15–20 K was proportional to the trend observed in lines 1 and 4, whereas the amplitude of line 3 increases more vigorously—if the ratio between the amplitudes of lines 3 and 4 is about 1.5:1 at room temperature, then it becomes around 3:1 at 9 K (Figure a). When reaching the temperature of around 12 K, line 3 starts to completely dominate over line 2 and the spectrum takes almost a symmetric shape (Figure b). At temperatures below 9 K, all lines broadened and were merged into a single line with a width of around 350 Oe (Figure ).

Figure 3

Behavior of the ESR spectrum of the copper(II) complex with functionalized hyperbranched polymer BH30 (a) at 9 K and (b) in the temperature range of 30–12 K.

An analysis of the temperature dependence of lines 1–4 allowed us to consider the ESR spectrum as a sum of contributions from several types of coordination sites, as it is natural to expect the presence of different coordination types in such undefined structures as functionalized Boltron H30, including the presence of copper(II) ions chemisorbed by the hyperbranched polymer. We assume that the following two types of paramagnetic species mainly contribute to the ESR spectra: the low-symmetric anisotropic paramagnetic centers with nonequivalent g, g, and g values; and trinuclear copper(II) clusters. Presumably, the first type of paramagnetic centers contributes to lines 1, 2, and 4; the second type of paramagnetic centers contributes to line 3 and partly to lines 1 and 4.

To get further insight into the possible structure of copper(II) complexes embedded in the hyperbranched polymer architecture, we have performed additional Q-band ESR measurements at room temperature and temperatures of 20 and 9 K. The room-temperature Q-band ESR spectrum (Figure ) was similar to the ESR spectrum in the X-band range, but resonance lines 1–4 in this case were narrower and well separated from each other. The better-resolved signals made it possible to refine the corresponding g factors as equal to 2.256, 2.179, 2.148, and 2.071. No hyperfine splitting with copper nuclei was observed in the spectra.

Figure 5

Room-temperature Q-band ESR spectrum of the copper(II) complex with functionalized hyperbranched polymer BH30 at a power value of 10 mW.

In addition, saturation of the Q-band ESR signals was investigated. An increase in the saturation power of super high-frequency radiation at room temperature gave rise solely to an increase in the total intensity of ESR signals, whereas the shape of the spectra and the ratio between the line intensities do not change.

The Q-band ESR spectrum at 9 K (Figure ) at a power of 0.1 mW (20 dB) was identical to the X-band ESR spectrum at 9 K and comprised three broad lines with g factors of 2.264, 2.151, and 2.072 (see Figure a). However, an increase in the power of super high-frequency radiation up to 1 mW and above led to drastic changes in the ESR spectra (see Figure a). A clearly resolved triplet of narrow lines with a parameter of 2D ≈ 280–300 Oe emerged instead of the central broad line, which was observed up to a power value of 10 mW and attributed to spin state S = 3/2 of the trinuclear cluster. A computer simulation of the ESR spectrum with use of the EasySpin software package[11] with parameters for the Cu3 complex (S = 3/2, g1 = 2.147, g2 = 2.147, g3 = 2.195, |D| = 0.0151 cm–1) and g values of (2.065, 2.176, 2.257) and (2.074, 2.172, 2.268) for two types of complexes with S = 1/2 gives a good fit to the observed ESR spectrum. Thus, the Q-band ESR measurements clearly showed the presence of two types of paramagnetic centers: a low-symmetric paramagnetic center with spin S = 1/2 and trinuclear sites with spin state S = 3/2 (Figure b).

Figure 6

Q-band ESR spectra of copper(II) complexes embedded in a hyperbranched polymer at 9 K: (a) transformation of the ESR spectrum with an increase in the saturation power; (b) simulated ESR spectrum (1 mW).

At 9 K, the splitting of line 1 into two components was also observed. This fact can be explained by a possible slight difference in the local coordination environment of paramagnetic copper(II) ions, for example, some ions may be coordinated to OH groups of the hyperbranched polymer ligand rather than to COO groups and this gives rise to a slight difference in the g factors. A similar splitting was observed in lines 1 and 2 of the Q-band ESR spectra recorded at 20 K, whereas line 4 was not split, but took an asymmetric shape and apparently consisted of two components.

Conjecturing the model of a polynuclear copper(II) cluster, we proceeded on the basis of the following considerations: (i) the experimentally determined characteristics, such as the temperature dependence of the ESR spectrum [the integral intensity of the EPR spectrum was estimated in the temperature range of 4.5–300 K and its temperature dependence indicated the presence of a weak ferromagnetic (FM) exchange interaction between the copper(II) ions and a positive Curie temperature] and the magnetic susceptibility (see below), the values, and nature of the exchange parameter, and also the external appearance of the ESR spectra are cardinally different from the possible binuclear copper(II) clusters with the lantern structure, which could be expected in copper(II) carboxylates[12−15] that are characterized by antiferromagnetic (AFM) coupling with large exchange interaction parameters of around 200–300 cm–1; (ii) the number of modified branches in the hyperbranched polymer ligand is divisible by 3 (this kind of ESR spectra were not observed in the copper(II) complexes with the analogous hyperbranched ligands that had a larger number of carboxylic groups);[5−7] (iii) the ESR spectrum observed in this study at low temperatures (Figure a) contains the triplet splitting, which is close to the published ESR spectra for the paramagnetic system with S = 3/2;[16−25] (iv) in addition, a forbidden half-field transition (ΔMS = 2) that evidences the formation of a magnetically coupled system is observed in the X-band ESR spectra at the resonance field of about 1560 Oe (the g parameter is about 4.3), the ESR signal intensity of which is 2 orders of magnitude smaller than the intensity of the main signal at g = 2.15 (see Figure A in the Supporting Information); (v) a weak FM coupling between copper(II) ions has earlier been observed in complexes with bridging carboxylate ligands, which showed indirect exchange interaction through the −O=C–O– bridges in the syn–anti coordination.[26−29] All the above considerations lead to the conclusion that the trinuclear copper(II) coordination site with a weak FM interaction is a most probable model that makes it possible to explain the experimentally observed ESR and magnetic properties of the system under study. However, the asymmetry of the ESR lines at higher temperatures and a stronger manifestation of lines 1, 2, and 4 suggests the presence of copper(II) ions with S = 1/2 as well. It should also be noted that this kind of ESR spectra and magnetic behavior is observed only in one complex of copper(II) with a dendritic Boltorn H30 macromolecule functionalized with six fumaric acid residues and cannot be generalized to other Boltorn hyperbranched structures or Boltorn H30 with other degrees of functionalization.

The Cu3 magnetic clusters known to date are characterized either by AFM exchange interactions leading to ground state S = l/2 or FM interactions with ground state S = 3/2. State S = 3/2 is characterized in the ESR spectra by equidistant line splitting into a triplet. However, triplet ESR signals of spin state S = 3/2 have been detected earlier for both types of Cu3 clusters: (i) FM Cu3 clusters with ground state S = 3/2[17−19] and (ii) AFM Cu3 clusters with ground state S = 1/2, but having an excited state S = 3/2 with a close energy level.[16,17,21−25] In particular, such ESR spectra have been recorded by Choi et al. for Cu3 magnetic clusters in the form of an equilateral triangle embedded in polyoxometallates.[23−25] Certainly, polyoxometallates are of special importance among the Cu3 clusters, as AFM triangular spin rings with weak intracluster exchange interactions (|J| < 1–2 cm–1) exhibiting the effects of spin frustration and spin chirality are created based on them. Such a value of the coupling parameter allows one to simultaneously observe both the ground and excited states in the Q-band or W-band ESR spectra and also enables the effect of tunneling between two spin states.

The X-band ESR spectra in our study, specifically, the spectra recorded at a temperature around 10 K, show nearly equidistant splitting of the ESR signal into three lines, which may be manifestation of the spin state with S = 3/2 with a nonzero value of fine structure parameter D. Indeed, it was interesting to compare the results of our study on the copper(II) complex embedded in hyprbranched polyester–polyether polyol modified with fumaric acid residues and the published data on copper(II) complexes with polyoxometallates. In all the above cases, the fine structure is observed. The fine-structure parameters determined in this study (|2D| ≈ 280–300 Oe) (|D| ≈ 0.0140–0.0150 cm–1) are close to that of triangular Cu3 clusters published in refs[21,22] (D ≈ 0.0219–0.0240 cm–1). The small difference between the D values is connected with the fact that the Cu–Cu distance in a triangular cluster in this study is about 5 Å or somewhat greater (4.96–5.41 Å), whereas it approximately equaled 4.69–4.87 Å in the published clusters.[21,22]

On the other hand, the metallodendritic system under study is different from Cu3 clusters embedded in polyoxometallates in the following ways:

The most important difference is that we have observed FM exchange interactions in magnetic clusters embedded in hyperbranched polymer and opposite temperature behavior of the magnetic moment (it increases with a decrease in the temperature) in comparison with AFM Cu3 clusters embedded in polyoxometallates. The exchange interaction parameters in our case are also much larger (at least 7–8 cm–1 vs 1–2 cm–1) and have an opposite sign.

Our results show that the ground spin state of the copper complex in a hyperbranched polymer is a quartet state with S = 3/2, whereas the ground state in polyoxometallates was a doublet state with S = 1/2.

Only ground state S = 3/2 is detected in the ESR spectra of our samples at low temperatures because of relatively large values of the exchange interaction parameters, whereas the signals of both ground state S = l/2 and excited state S = 3/2 are simultaneously recorded in the ESR spectra of polyoxometallates with a relatively small difference in the energy of states.

A step-like magnetization curve is observed in polyoxometallates[25] under conditions of pulse-field magnetization, which is attributable to the transitions from the ground state with S = 1/2 to the excited state with S = 3/2. The magnetization curves of the system we have studied are smooth, as no spin frustrations occur and there are no magnetization jumps.

Magnetic susceptibility data for Cu3 clusters embedded in polyoxometallates are described by a single exchange interaction parameter (J), as the Cu3 cluster is in the shape of an equilateral triangle. We describe the χ(T) dependence of the Cu3 clusters embedded in the hyperbranched polymer structure with three different exchange interaction parameters J1, J2, and J3, as follows from our density functional theory (DFT) calculation results owing to small differences in the Cu–Cu distances within the simulated Cu3 cluster.

Nevertheless, a comparison of the ESR spectra of the system under study with the set of published experimental ESR data for copper clusters, in which the spectra of state S = 3/2 were recorded (either ground or excited),[16,17,21−25] shows that a spectral component typical for spin state S = 3/2 predominantly contributes to the total ESR spectrum in our case. Furthermore, spin state S = 3/2 in the studied system is a ground state.

To further confirm the assumption about the presence of ferromagnetically coupled trinuclear clusters in the studied copper(II) complexes embedded in hyperbranched polymer, the temperature dependence of the total integral intensity of the ESR lines was studied. The integral intensity was assessed by double integration of the ESR spectrum, which actually is the first derivative of the absorption signal. The obtained dependences of the integral intensity, I, of the ESR signals and its inverse value are given in Figure . One can see that the integral intensity of the ESR lines sharply increases at temperatures below 8–9 K, which is consistent with the assumption about the presence of FM exchange interactions in the studied complex. As follows from the temperature dependence of the inverse value of the integral intensity of ESR signals, the interaction between the Cu(II) ions should be weakly FM and the transformation of the complex to the quartet ground state with S = 3/2 takes place at temperatures below 8 K.

Figure 7

Temperature behavior of (a) integral intensity and (b) its inverse value of the ESR spectrum of copper(II) complex with functionalized hyperbranched polymer BH30.

It should be noted that there are a few published ESR spectra recorded at different temperatures (without plotting the IESR–T dependence) for trinuclear copper complexes with a clarified crystal structure. The published data on IESR for an AFM Cu3 cluster (in contrast to FM interactions in this study) with ground state S = 1/2[16,17] simply show that the I3/2/I1/2 ratio between the excited (3/2) and ground (1/2) states decreases with a decrease in the temperature. On the contrary, the intensity of state S = 3/2 in our case increases with a decrease in the temperature (the same trend is observed for μ).

The IESR–T dependences for the AFM Cu3 cluster were also given in ref (25), in particular, for the intensities of two adjacent signals in a central triplet line and a side line. The difference between them was much smaller than in our case for lines 1 and 3 at 9 K, as is seen from Figure a, which evidences the existence of two types of paramagnetic sites/complexes in our study. Moreover, the contribution of FM couplings in our study leads to a substantially sharper increase in the IESR–T curve slope at temperatures below 50 K in comparison with the IESR–T curves for an AFM Cu3 cluster.[25]

Magnetic Susceptibility Measurements

To complement the ESR studies and confirm the conclusions made on the basis of the behavior of ESR spectra at low temperatures, magnetization measurements of the powder copper(II) complex at different temperatures were performed. The temperature dependence of the magnetic susceptibility indicates the deviation from the Curie–Weiss law below 8–10 K and the presence of FM interactions in the studied spin system (Figure ). This agrees well with the results of ESR studies.

Figure 8

Temperature dependence of the magnetic susceptibility and inverse magnetic susceptibility (in the inset and on the right) of the copper(II) complex with functionalized hyperbranched polymer BH30.

It is known that the temperature curves of the magnetic moments for AFM and FM clusters are different: with a decrease in the temperature, the χT and μ values decrease in AFM clusters and increase in FM clusters. In our case, the temperature dependences are similar to those observed for published trinuclear triangular and linear clusters with carboxylate bridges.[29−31] A similar behavior was also observed in trinuclear FM Cu3 clusters with other bridging groups, in particular, CuII3–pyrazolato complexes[19] and complex [(talen)CuII3], in which three Cu(II) ions are bridged through an m-phenylene linkage.[32]

It should be noted that no hysteresis behavior of the field dependence of magnetization of the studied coper(II) complex in the temperature region around 5 K is observed (Figure ). Therefore, the deviation from the Curie–Weiss law at temperatures below 8–10 K cannot be explained by the possible presence of FM impurities. In this connection, the conjecture that the ground spin state of the studied complex with S = 3/2 arises from a ferromagnetically coupled tricopper cluster, which is made on the basis of the ESR data, sounds quite reasonable.

Figure 9

Field dependence of the magnetic moment at different scanning rates for the copper(II) complex with hyperbranched polymer Boltorn H30 functionalized with fumaric acid residues.

Actually, other possible structures, such as chain structures composed of copper complexes with irregular lower-molecular-weight polymer ligands, or chain structures involving separate copper(II) ions and clusters, also may contribute to FM coupling (see Figure ). In an indirect way, we included these additional possibilities for different copper complexes in a positive value of the θ parameter in the theoretical equation of magnetic susceptibility that is given below.

Figure 10

Possible chain structure of copper(II) complexes embedded in low-molecular-weight species of hyperbranched polymer Boltorn H30 functionalized with fumaric acid residues (simulated in Gaussian 09 at the PM6 semi-empirical level; copper atoms are colored in red, carbon atoms in cyan, and oxygen atoms in blue).

In particular, magnetization curves similar to the one shown in Figure were published for FM and AFM Cu3 clusters,[26,29,33−36] with a difference that the curves for the AFM cluster are flatter. The shape of our magnetization curve (Figure ) in steepness is closer to those typical for FM clusters. Apparently, there are two components in this curve: one component is a linear contribution from paramagnetic copper complexes with spin S = 1/2 and another component is a nonlinear contribution from the copper ions involved in the exchange interactions within the polymer system (inside the magnetic clusters, between the clusters, in chain structures, and between separate ions), which are more strongly manifested at low temperatures. This is also evidenced by the ESR spectra. The magnetization curve in Figure is recorded at 5 K, that is, the temperature at which exchange interaction mechanisms are already strongly manifested.

DFT Calculations

To elucidate the structural features that lead to such unusual magnetic behavior of the copper(II) complex of carboxyl-functionalized hyperbranched polymer Boltorn H30, the quantum-chemical simulations were performed using the Gaussian software package.[37] To construct trinuclear copper(II) clusters embedded in the dendritic structure, the preoptimized structure of the acid-functionalized hyperbranched polymer was transformed to bring free carboxylic acid groups close to each other into the orientation favorable for assembling the trigonal coordination sites with carboxyl bridges. The nitrate counter ions were abandoned for the sake of simplicity, and the closest coordination spheres of the copper(II) cations were filled with water molecules. The obtained raw structure of the dendritic complex with two trinuclear coordination sites per macromolecule was optimized to the first stationary point at the semi-empirical UPM6 level (Figure a). To obtain a better starting geometry for higher levels of theory, the full hyperbranched structure was truncated at the central carbon atom of the dendritic core, and the resulting half structure was optimized at the DFT UB3LYP level with the 3-21G basis set until reaching the stationary point with a simplified coarse integration grid and loose convergence criterion (Figure b).

Figure 11

(a) Full structure of the complex of copper(II) with hyperbranched polymer Boltorn H30 functionalized with fumaric acid residues in a molar ratio of 1:6, in which two possible coordination triads are shown by multilayer selection in GaussView; (b) half of the structure cropped out from the full dendritic structure at the central core carbon atom that is shown on the left as a ball atom with two methyl groups added in place of the deleted part of the polymer structure (copper atoms are colored in red, carbon atoms in cyan, hydrogen atoms in gray, and oxygen atoms in blue).

Next, the trinuclear coordination site with the fumaric acid fragments was detached from the rest of the structure and processed at the DFT UB3LYP level with more complex basis sets in a fine integration grid. The coordinates of the fumarate “arms” were fixed at the positions, as if the coordination site still would be attached to a dendritic matrix, by fixing the coordinates of the methyl carbon atoms that have replaced the deleted polymer fragment. An almost equilateral triangle with copper(II) cations at the apexes was obtained after the geometry optimization at higher levels of theory (Figure ). The closest coordination surroundings of the copper(II) ions of two coordination sites in the trinuclear cluster have the configuration of a distorted tetrahedron with the oxygen atoms at the vertices, and one of the coordination sites has an almost planar structure. Generally, the Cu–O bond lengths are different and vary in the range from 1.88 to 2.07 Å for different positions in the coordination sites, and also depending on the level of theory used in the geometry optimization. The described coordination triad hereinafter is referred to as “configuration I”.

Figure 12

Geometry of the simplified trinuclear coordination cluster simulated at the UB3LYP 6-311G++(2d,2p) level for configuration I.

The other half of the preoptimized full structure of the hyperbranched polymer with embedded coordination triads (Figure a) was also treated as above. The coordination triad obtained after performing DFT calculations at higher levels of theory, which is referred to as “configuration II”, was similar to configuration I by the mutual arrangement of the embedded copper(II) cations, but all three coordination sites in this version of a trinuclear cluster had close geometries. The Cu–O bond lengths in configuration II are in the same range as in configuration I.

Table shows the parameters of the coordination triangles (the triangle sides a, b, and c) for configurations I and II, which were obtained after the geometry optimization of the simplified trinuclear coordination clusters by different DFT methods.

Table 1

Triangle Sides a, b, and c in Configurations I and II of the Trinuclear Coordination Clusters Simulated Using Different DFT Methods

	triangle side length in configuration I, Å			triangle side length in configuration II, Å
method	a	b	c	a	b	c
UB3LYP/6-311++G(2d,2p)	4.96	5.28	5.31	5.16	5.32	5.41
USEH1PBE/6-311++G(2d,2p)	4.96	5.14	5.22	5.12	5.29	5.36
UWB97XD/6-311++G(2d,2p)	4.95	5.12	5.20	5.10	5.24	5.35
ULC-wPBE/6-311++G(2d,2p)	4.97	5.12	5.22	5.10	5.25	5.32

The DFT calculation results for two random configurations I and II of the trinuclear coordination site, in which the spin states in separate paramagnetic centers were controlled using the fragmentation procedure, are given in Table . The isotropic exchange interaction parameters are calculated by the broken symmetry (BS) approach using the Ruiz scheme.[38] The exchange interaction parameters obtained with widely used hybrid functional, such as B3LYP and SEH1PBE, give fairly large positive values for each of the coupling pairs in configuration I and confirm the experimentally observed quartet ground state in the studied spin system. It was found earlier that the exchange interaction parameters in the case of transition-metal complexes are best described by the LC-ωPBE exchange correlation functional.[39,40] In addition, the UWB97XD long-range corrected hybrid functional with empirical dispersion corrections has proven to perform well for noncovalent interactions.[41] The obtained exchange coupling constants with the latter two functionals are almost in the same range as in the first two cases. For configuration II, larger discrepancies are observed in the results obtained with different hybrid functionals. However, an overall tendency to form quartet ground state is confirmed, and the results obtained with the more reliable LC-ωPBE and UWB97XD functionals are still comparable.

Table 2

DFT Calculation Results of the Model of Trinuclear Cu(II) Coordination Clusters for Configurations I and IIa

		energy of different spin states, Hartree				square of spin operator, Ŝ2				exchange coupling parameter*, cm–1
configurations and calculation methods		ααα	βαα	αβα	ααβ	ααα	βαα	αβα	ααβ	J12	J23	J13
I	UB3LYP/6-311++G(2d,2p)	–6 863.3836519	–6 863.3835774	–6 863.3835082	–6 863.3835082	3.7564	1.7543	1.7553	1.7553	16.35	46.73	16.35
	USEH1PBE/6-311++G(2d,2p)	–6 860.5432537	–6 860.5431846	–6 860.5431387	–6 860.5431625	3.7567	1.7553	1.7561	1.7556	20.39	30.09	9.95
	UWB97XD/6-311++G(2d,2p)	–6 862.7500638	–6 862.7499588	–6 862.7499924	–6 862.7500003	3.7562	1.7558	1.7555	1.7554	24.77	6.57	21.31
	ULC-wPBE/6-311++G(2d,2p)	–6 861.3803220	–6 861.3802731	–6 861.3802584	–6 861.3802699	3.7554	1.7548	1.7549	1.7550	8.21	14.65	13.27
II	UB3LYP/6-311++G(2d,2p)	–6 863.3821004	–6 863.3819709	–6 863.3820389	–6 863.3820336	3.7565	1.7555	1.7543	1.7541	29.59	–0.27	27.25
	USEH1PBE/6-311++G(2d,2p)	–6 860.5509810	–6 860.5508816	–6 860.5509296	–6 860.5509296	3.7568	1.7563	1.7556	1.7556	21.82	0.74	21.82
	UWB97XD/6-311++G(2d,2p)	–6 862.7579118	–6 862.7578704	–6 862.7578657	–6 862.7578302	3.7562	1.7556	1.7556	1.7559	6.98	16.75	14.67
	ULC-wPBE/6-311++G(2d,2p)	–6 861.3886817	–6 861.3886132	–6 861.3886460	–6 861.3886132	3.7553	1.7550	1.7548	1.7550	7.83	7.83	22.23

Note: *The coupling parameters were calculated in a BS approach without further improvement with an approximate spin projection model.

Indeed, even a larger number of conformational variations are possible in reality for trinuclear coordination sites embedded in the hyperbranched polymer structure, not to mention isolated copper(II) ions and other coordination possibilities, for example, linearly arranged copper(II) clusters connected through carboxylate bridges. But once formed, trinuclear copper(II) clusters contribute to higher spin states at temperatures below 8–10 K and cause the deviation from the Curie–Weiss law.

As was shown for copper(II) formate complexes, two types of mechanisms can be involved in the exchange interaction between copper(II) paramagnetic centers through carboxylate links.[42] It was found that one superexchange path through π orbitals of the C=O groups contributes predominantly to AFM coupling and a superexchange path through σ bonds contributes to FM coupling by a spin-polarization mechanism. In a modification of copper(II) formate complex with syn–anti bonding arrangement of Cu–O–C–O–Cu links, a predominant FM behavior with a positive Curie–Weiss constant of 17 K was observed at low temperatures. Predominance of FM coupling was also found in other copper(II) carboxylate linked complexes with syn–anti coordination.[43−45] A spin-polarization mechanism of superexchange through σ bonds implies a significant negative spin density population on the carbon atoms of carboxylate links and this is confirmed in our calculation results as well (see Figure B in the Supporting Information).

Fitting of the Theoretically Calculated Data to the Experimental Results of Magnetic Susceptibility Measurements

Using different sets of the calculated exchange coupling constants in the tricopper(II) complexes embedded in the hyperbranched polymer structure, theoretical curves for the temperature dependence of the effective magnetic moment, μeff, fitted to the experimental data are obtained (Figure , the curves in the χT–T coordinates are given in Figure C of the Supporting Information and look similar). The theoretical curves were obtained taking into account the contribution of single paramagnetic centers that may be present in the molecule, as followswhere χ is the total value of the magnetic susceptibility of the system, χcl is the magnetic susceptibility related to trinuclear magnetic clusters, χpar is the magnetic susceptibility related to single paramagnetic centers, m is the average number of clusters per molecule, and n is the average number of single paramagnetic centers per molecule. The magnetic susceptibility of trinuclear magnetic clusters as a function of temperature is described by the following formula derived from the van Fleck equation including the energy gaps between the possible spin eigenstates[46,47]where ΔE1 = E1/2+ – E1/2–; ΔE2 = E1/2+ – E3/2

Figure 13

Temperature dependences of the experimental and theoretically calculated effective magnetic moments (B.M.) of the copper(II) complex with the hyperbranched polymer ligand based on Boltorn H30. The theoretical curves are calculated using eqs –4 with the following parameters: m = 2; n = 4; θ = 4.2 K; g1/2+ = 2.1; g1/2– = 2.2; g3/2 = 2.3; gpar = 2.2; and the J12, J23, and J13 parameters are taken from Table (the numbers at the curves correspond to table rows from top to bottom). The experimental curve is obtained using a molecular weight of about 3000 g/mol (a number-averaged molecular weight of 1410 g/mol is adopted for Boltorn H30).

In eq , the parameter θ is the adjustment to the temperature that takes into account possible intermolecular exchange interactions between the clusters and possible presence of interacting chain structures at low temperatures.

The temperature dependence of the magnetic susceptibility related to single paramagnetic centers can be calculated by the well-known formula

In this regard, it should be noted that the processing of the experimental data on magnetic susceptibilities implied using a certain value of the molecular weight for the polymer complex, at the same time as real polymer molecules vary in size. Hence, the molecule shown in Figure does not represent an “average” molecule of the real polymer complex. When processing the experimentally measured magnetic properties, the number-averaged molecular weight, that is, the molecular weight determined as an arithmetic mean of the molecular weights of n polymer molecules, was used. In turn, the available data on the molecular weight distribution of Boltorn polymers differ depending on the used experimental methods. The corrected value of the number-averaged molecular weight of Boltorn H30 (1410 g/mol) is published,[48] which is substantially different from the number-averaged molecular weight of Boltorn H30 provided in the manufacturer’s specification (2333 g/mol). The resulting experimental curves processed using these different values for the molecular weight of the hyperbranched polymer core are shown in Figure . The theoretical curves obtained in the present study are fitted to the experimental curve processed using the number-averaged molecular weight for the copper(II) hyperbranched polymer complex calculated on the basis of the published experimental data for Boltorn H30.[48]

Figure 14

Temperature dependences of the experimental effective magnetic moments (B.M.) processed with different conditional molecular weights of the studied copper(II) dendritic complex (from top to bottom): calculated on the basis of the chemical structure given in Figure , based on the number-averaged molecular weight for Boltorn H30 specified by the manufacturer Perstorp Specialty Chemicals AB, and based on the experimentally corrected molecular weight for Boltorn H30.

As is seen from Figure , the obtained theoretical curves slightly deviate from the experimental data. The character of deviations suggests that the real system has components with larger values of the exchange interaction parameter. It can be explained by the fact that the simulated structure of the coordination site is conformationally flexible and many configurations are possible in the real system under study. Therefore, the exchange interaction parameters between paramagnetic centers in the studied hyperbranched polymer complex must vary in a very wide range. In addition, the possible presence of short linearly arranged exchange-coupled chains is not taken into account in the used model. Notwithstanding that the performed quantum-chemical calculations do not embrace all the diversity of possible chemical configurations of the studied magnetic system, they give the data for building a crude approximate model of the magnetically interacting system, rather satisfactorily explaining the observed experimental data.

Methods

Experimental Measurements

X-band ESR spectra were recorded in Bruker-ESR-300 and Bruker-EMX X-band ESR spectrometers in the range of temperatures 4.2–260 K by using nitrogen and helium flow cryostats (Oxford Instruments). The Q-band spectra were recorded in an Elexsys E580 pulse EPR spectrometer equipped with an ER 5106 QTW standard commercial cavity (Bruker).

Magnetic properties of a powder sample were studied using a vibrating sample magnetometer integrated into a system for the measurement of physical properties (PPMS-9, Quantum Design). The sample was loaded into a gelatin container, which was then attached to a standard copper holder with glue. Temperature-dependent magnetization measurements were performed in a magnetic field of 5 kOe in the temperature range of 5–300 K. Contributions of the sample holder and the container to the magnetization value were subtracted by measuring them separately from the sample. A diamagnetic contribution from the ligand to the measured magnetic susceptibility was taken into account using the Pascal additive scheme.

Calculation Techniques

The chemical structure of the initial Boltorn H30 with fumaric acid functions was first optimized at the semi-empirical PM6 level in a Gaussian 09 software package,[37] and three nearby fumaric acid groups were aligned using the GaussView software package by rotation around appropriate single bonds of the hyperbranched core in such a way that carboxylic acid groups get close to each other and make a triangle. Then, a trigonal tricopper(II) coordination site was assembled using three carboxyl groups as linkers between the metal ions and water molecules for filling the coordination spheres, by taking into account the fact that the studied complex has a tetrahedral structure with a coordination number of 4, as has previously been established from the results of the IR spectroscopy studies.[7] To simplify further calculations, the branches of the dendritic structure that are not involved in coordination with metal ions were truncated at the core central carbon atom and replaced with methyl groups. The assembled structure was optimized in Gaussian 09 at the UPM6 level and the initial geometry of the trinuclear coordination site embedded in the hyperbranched polymer ligand was obtained. It was further optimized at the DFT UB3LYP level with the minimal 3-21G basis set. The coordination site was cropped out from the hyperbranched polymeric part at the binding sites with fumaric acid residues, and methyl groups were attached to the latter. The obtained simplified complex was optimized by the DFT method with fixed coordinates for the methyl carbon atoms that replace the hyperbranched polymer core, using the UB3LYP, UWB97XD, ULC-wPBE, and USEH1PBE hybrid functionals with different basis sets. The different spin states that are obtained by consecutive flipping of spins in each fragment were computed using unrestricted single-point calculations of the fragmented coordination triangle. The corresponding three pairwise coupling constants for the triangular spin system were obtained solving the set of equations derived from the Heisenberg–Dirack–van Vleck spin Hamiltonian in the isotropic Ising configuration

The broken symmetry approach was applied to extract the pairwise exchange interaction constants. This approach developed by Ruiz for polynuclear systems[38] uses the FM and broken symmetry (AFM) DFT solutions to map them into the corresponding Ising energies. In particular, four unique microstates were obtained applying the fragmentation procedure to control the spin states of the individual paramagnetic centers, which made it possible to unequivocally define all three exchange coupling constants from the set of equations describing one ferromagnetically coupled high-spin state and three independent AFM broken-symmetry states.

Conclusions

A copper(II) complex with a commercial hyperbranched polymer Boltorn H30 (Perstorp Specialty Chemicals AB, Sweden) functionalized with six fumaric acid residues is studied by the methods of EPR spectroscopy study and magnetic susceptibility measurements. The EPR spectra of a powder sample of the synthesized copper(II) complex demonstrated four resonance lines with different temperature behavior, suggesting the presence of paramagnetic species with a total spin of 3/2 that can arise from magnetically coupled copper(II) clusters. To confirm the assumption about the ferromagnetically coupled trinuclear copper(II) coordination sites, the temperature dependence of the total integral intensity of the EPR lines was studied. The integrated intensity of the EPR spectrum sharply increases at temperatures below 8–9 K, which is consistent with the assumption about the presence of FM exchange interactions in the studied complex. Magnetic susceptibility measurements of the studied powder copper(II) complex confirm conclusions drawn on the basis of the behavior of the EPR spectra at low temperatures. The temperature dependence of the magnetic susceptibility shows deviation from the Curie–Weiss law below 10 K and indicates the presence of FM exchange interactions in the studied system. Quantum-chemical simulation of the proposed structure for the trinuclear copper(II) coordination sites embedded in the hyperbranched polymer architecture also gives positive values for the exchange interaction parameters. Thus, the combination of the quantum-chemical approach and experimental studies of the magnetic properties by the methods of ESR and magnetic susceptibility measurements allowed us to gain insight into the feasible structure of the coordination sites in the synthesized copper(II) hyperbranched polymer complex despite the impossibility of unambiguous determination of its chemical structure by the accessible physicochemical methods. The theoretical magnetic curves obtained on the basis of the calculated exchange interaction parameters between copper(II) ions in the hyperbranched polymer globule roughly fit the experimental data. The slight deviations are explainable considering the complexity of the real polymer system and the diversity of possible chemical surroundings of paramagnetic sites, which cannot be fully accounted for in quantum-chemical calculations.