Cobalt(II) and Nickel(II) Cubane {M₄O₄} Complexes Derived from Di-2-pyridyl Ketone and Benzoate: Syntheses, Structure and Magnetic Properties ^†

Abstract

Two tetranuclear complexes were obtained by a self-assembly process employing di-2-pyridyl ketone ((py)₂CO), benzoate and M(NO₃)₂ (M = Co and Ni). The compounds [M₄{(py)₂C(OH)O}₄(O₂CPh)₄], where {(py)₂C(OH)O}⁻ is the monoanion of the gem-diol form of (py)₂CO, were characterized through single-crystal X-ray diffraction and magnetic measurements. Structural analysis revealed that both complexes possess a [M₄O₄] cubane-like core. A two-J model and magnetic anisotropy were employed to analyze the magnetic properties of both compounds. These studies indicate the presence of dominant ferromagnetic interactions within both tetranuclear cores. DFT and CASSCF/NEVPT2 calculations were also performed to support the fitting of experimental magnetic data.

1. Introduction

Polynuclear metal complexes have attracted interest in the context of molecular magnetism for more than three decades. Early research primarily focused on the study of magnetic interactions in dinuclear complexes; however, the discovery of slow relaxation of magnetization in Mn₁₂ [1] triggered the search for novel coordination clusters with diverse topologies and single-molecule magnet (SMM) behavior [2,3,4]. Serendipity has played a key role as a synthetic strategy that leads to remarkable structural diversity in magnetic systems. This synthetic approach typically involves the use of flexible polydentate organic ligands capable of coordinating two or more metal ions. These ligands often contain hydroxyl groups that can adopt different coordination modes. Since the primary ligand usually does not saturate the coordination sphere of the metal, the solvent molecules or auxiliary organic or inorganic ligands incorporated during synthesis may also coordinate to the metal. Carboxylates are frequently employed as ancillary ligands owing to their ability to act as both terminal and bridging, with a variety of ligation modes. This versatility adds additional flexibility to the mixed-ligand systems. Although this flexibility complicates predictions regarding the possible outcomes of synthesis, serendipitous self-assembly has allowed researchers to obtain a vast number of coordination clusters with a large diversity of spin topologies and nuclearities. These clusters range from trinuclear structures to systems comprising over tens of metal ions, involving first-row transition metals and lanthanide elements [5,6,7,8,9,10,11,12,13,14,15,16]. Among this diverse group of compounds, tetranuclear complexes featuring the M₄O₄ cubane core are one of the most reported structures. All first-row transition metals form this type of isolated cubane complexes, nickel being the most prominent. The CCSD database lists over 270 entries for tetranuclear compounds featuring the Ni₄O₄ core. Cobalt has also enriched the library of oxo cubane complexes, for which around 130 Co₄O₄ compounds can be found in the CCSD database. The observation of SMM behavior in some of these Ni and Co complexes has stimulated the extensive study of magnetic properties in these M₄O₄ families of compounds [17,18,19,20,21,22,23,24,25,26,27,28,29,30]_. The accidental orthogonality of magnetic orbitals in M₄O₄ cubes may lead to high-spin ground states, which contribute to a significant barrier to magnetization reversal (U), since the upper limit of U is given by S²|D| and (S² − 1/4)|D| for integer and half-integer spin, respectively. The molecular spin ground state and the anisotropy of the system are influenced by the nature of the ligand system. Zero-field splitting (zfs) anisotropy associated with the individual M^II sites and the exchange coupling between them are affected by changes in the coordination sphere of the M^II ions and the M−O−M bond angles. For Ni₄O₄ compounds, a clear correlation between the sign and magnitude of the magnetic exchange constant (J) and the M–O–M bond angle has been established [19,31,32]. On the other hand, although several magnetic studies have been conducted on Co₄O₄ compounds, to the best of our knowledge, magnetostructural correlations have not been reported.

Slight variations in the Ni–O–Ni bond angles can induce significant changes in the magnitude and sign of magnetic interactions, potentially altering the spin ground state. Such changes can occur, for example, through the exchange of coordinated solvent molecules [32] or even by more subtle modifications, such as variations in the peripheral halide atoms of the ligands [33]. Also, changes in coordinated solvent molecules or the substitution of a peripheral H atom with a CH₃ group may switch the SMM behavior in cubane complexes [28,32].

Di-2-pyridyl ketone, (py)₂CO, has been proven highly effective in the synthesis of coordination clusters. In the presence of a metal ion, the carbonyl group can undergo addition reactions with different nucleophilic agents such as water or alcohols (ROH), and as a result, the species (py)₂C(OR)(OH) (R = H, alkyl, aryl) are obtained (Scheme 1). Upon the deprotonation of the hydroxyl groups, the resulting dianionic {(py)₂C(O)₂}²⁻ or the monoanionic {(py)₂C(OR)(O)}⁻ species can function as flexible N, N’, O chelating ligands. This flexibility arises from the ability of the negatively charged oxygen atom to bridge two (µ₂) or three (µ₃) metal ions.

Several polynuclear complexes with nuclearities as high as twenty-six metal centers [34] and diverse topologies have been obtained starting with (py)₂CO [35]. For nickel and cobalt, di-2-pyridyl ketone-based complexes with nuclearities of up to eleven and nine, respectively, have been observed, both with acetate as a coligand [36,37]. Particularly, nine different tetranuclear Ni₄O₄ cubane compounds based on (py)₂CO—both neutral and cationic—can be found in the CCSD, with different auxiliary ligands such as hydroxylamine, dicyanamide, nitrate, sulfate, acetate, water and methanol. Magnetic studies have been conducted on five of these complexes, revealing competing ferromagnetic and antiferromagnetic interactions, resulting in S = 0 or S = 2 spin ground states [38,39,40,41,42]. Regarding di-2-pyridyl ketone-based Co₄O₄ cubane compounds, the CCSD shows seven complexes—both neutral and cationic—in which acetate/water, chloride, acetate and nitrate act as auxiliary ligands. Magnetic properties have been measured for only four of them. Although no data fitting was performed, competing ferro- and antiferromagnetic interactions can be inferred for the compounds [Co₄{(py)₂C(OH)O}₄(NO₃)₃(H₂O)]NO₃, [Co₄{(py)₂C(OH)O}₄(O₂CMe)₃(H₂O)](ClO₄)· 1.8H₂O and [Co₄{(py)₂C(OH)O}₄(O₂CMe)₄]·H₂O [37,39,43]. An intermediate S = 3 spin ground state was suggested for the latter, while a second hydrated form, [Co₄{(py)₂C(OH)O}₄(O₂CMe)₄]·7H₂O, shows antiferromagnetic interactions leading to a non-magnetic ground state [44].

Based on the previous discussion about the potential structural diversity and magnetic properties of these systems and taking into account the limited number of studies in which benzoate (PhCO₂⁻) serves as an auxiliary ligand in (py)₂CO-based coordination clusters, we explored the chemistry of M^II/(py)₂CO/PhCO₂⁻ systems, where M = Ni and Co. In this paper, we report the synthesis, crystal structures and both experimental and theoretical studies of magnetic properties of compounds [M₄{(py)₂C(OH)O}₄(O₂CPh)₄], where M = Co (1) and Ni (2). Both compounds present a M₄O₄ cubane core, which exhibits predominant ferromagnetic interactions, leading to high-spin ground states. Broken-symmetry DFT and CASSCF/NEVPT2 calculations support these results.

2. Materials and Methods

2.1. Materials and Characterization

All reagents and solvents were purchased from commercial sources and used without further purification. Infrared spectra were recorded with a Shimadzu IR Prestige-21 FTIR spectrometer using KBr pellets from 4000 to 400 cm⁻¹. Elemental analyses of carbon, hydrogen and nitrogen were performed on a Thermo Flash 2000 analyzer.

Magnetic measurements were carried out on polycrystalline samples of 1 and 2 using a Cryogenics SX600 SQUID magnetometer from 2 to 280 K under an applied magnetic field of 1 and 0.1 kOe for 1 and 2, respectively. The device was calibrated with YFe garnet NIST reference samples. Diamagnetic corrections were estimated from Pascal’s constants, and experimental susceptibilities were also corrected for the magnetization of the sample holder.

2.2. Synthesis of [Co₄{(py)₂C(O)(OH)}₄(O₂CPh)₄] (1) and [Ni₄{(py)₂C(O)(OH)}₄(O₂CPh)₄] (2)

Compound 1 was obtained by adding 73 mg of Co(NO₃)₂∙6H₂O (0.25 mmol) to 10 mL of methanol solution containing NaO₂CPh (0.5 mmol) and 46 mg of (py)₂CO (0.25 mmol). The resulting solution was filtered off and layered with toluene (10 mL). Well-shaped rhombic blue–purple crystals were obtained after 30 days and were filtered off, washed with ethanol and left to dry in air. Yield: 41 mg (34%). Anal. Calc. for [Co₄{(py)₂C(O)(OH)}₄(O₂CPh)₄] (2): C: 56.71; H: 3.69; N: 7.35(%). Found: C: 56.65; H:3.59; N: 7.36 (%). IR (ν/cm⁻¹, KBr): 3494(m), 3416(m), 2800 (m), 1601 (s), 1560 (s), 1387 (s), 1225 (m), 1121 (m), 1071 (m), 1044 (m), 953 (w), 803 (w), 771 (w), 723 (m), 683 (m), 595 (w), 533 (w), 515 (w), 429 (w).

Single crystals of compound 2 were obtained by the same procedure followed for 1 but replacing Co(NO₃)₂∙6H₂O with Ni(NO₃)₂∙6H₂O. Yield: 50 mg (40%). Anal. Calc. for [Ni₄{(py)₂C(O)(OH)}₄(O₂CPh)₄] (1): C: 56.74; H: 3.69; N: 7.35(%). Found: C: 56.50; H:3.61; N: 7.32 (%). IR (ν/cm⁻¹, KBr): 3500 (m), 3419 (m), 2800 (m), 1601 (s), 1560 (s), 1384 (s), 1223 (m), 1125 (m), 1080 (s), 1045 (m), 1022 (m), 951 (m), 803 (m), 769 (m), 728 (s), 684 (m), 589 (w), 533 (w), 515 (w), 429 (w), 417 (w), 400 (w).

2.3. X-Ray Data Collection and Structure Refinement

Single-crystal X-ray diffraction data were collected on an Xcalibur Atlas Gemini Ultra (1) or Bruker KAPPA CCD (2) diffractometer using graphite-monochromated Mo Kα radiation (λ = 0.71073 Å) at room temperature. For 1, CRYSALISPRO software [45] was used to determine the unit cell parameters, the integration of the collected reflections and the absorption correction. The structure solutions and full-matrix least-squares refinements based on F² were performed with the SHELXS and SHELXL programs [46]. For 2, the final unit cell parameters were determined from all reflections obtained with the DIRAX program [47,48], whereas the integration of the collected reflections was performed using the EVALCCD program [49]. Absorption correction using equivalent reflections was performed with the SADABS program [47]. All non-hydrogen atoms were refined anisotropically, while hydrogen atoms were set in calculated positions and refined as riding atoms. Details of the crystal structure, collection and refinement are gathered in

Table 1. Crystal data and structure refinement for compounds 1 and 2.

Compound	1	2
Empirical formula	C72H56Co4N8O16	C72H56N8Ni4O16
Formula weight	1524.97	1524.01
Temperature/K	293(2)	293(2)
Crystal system	Tetragonal	Tetragonal
Space group	I-42d	I-42d
a/Å	14.322(1)	14.172(3)
b/Å	14.322(1)	14.172(3)
c/Å	38.300(1)	37.900(8)
Volume/Å3	7856.1(11)	7612.1(3)
Z	4	4
ρcalc/g cm−3	1.289	1.330
μ/mm−1	0.895	1.041
F(000)	3120.0	3136.0
Radiation	Mo Kα (λ = 0.71073)	Mo Kα (λ = 0.71073)
2θ range for data collection/°	6.45 to 59.15	10.064 to 50.054
Index ranges	−18 ≤ h ≤ 18 −19 ≤ k ≤ 15 −51 ≤ l ≤ 51	−16 ≤ h ≤ 16 −16 ≤ k ≤ 16 −42 ≤ l ≤ 45
Reflections collected	38328	39546
Independent reflections	5178	3340
Rint	0.058	0.081
Data/restraints/parameters	5178/0/215	3340/0/227
Goodness-of-fit on F2	0.998	1.095
Final R indexes [I ≥ 2σ(I)]	R1 = 0.0401, wR2 = 0.1048	R1 = 0.0437 wR2 = 0.1215
Final R indexes [all data]	R1 = 0.0557, wR2 = 0.1085	R1 = 0.0530, wR2 = 0.1290
Largest diff. peak/hole / e Å−3	0.72/−0.32	0.81/−0.34
Flack parameter	−0.011(8)	0.06(4)
CCDC identification	2417038	2417037

. CCDC numbers 2417037-2417038 contain the supplementary crystallographic data for this article. These data are provided free of charge by the Cambridge Crystallographic Data Centre.

2.4. Computational Methodology

All calculations were performed in the ORCA software suite version 5.0.3 [50] using the experimental crystal structure as input. The Def2-tzvp basis set was used for all atoms [51].

Magnetic coupling constants (J) were evaluated by DFT calculations using the Gaussian version of the B3LYP hybrid functional [52,53]. The evaluation of coulomb and exchange two-electron integrals were accelerated using the resolution of identity (RI) and chains of spheres (COSX) [54] approximations with the def2/J auxiliary basis set [55]. A polarizable continuum model (PCM) was introduced in the calculations with parameters corresponding to acetonitrile to reduce the delocalization error typical of DFT methods, mainly in charged systems with close molecular groups and opposite charges [56]. To simplify the calculations, they were carried out on the experimental geometry of M₄, but with the replacement of two paramagnetic M^II ions with diamagnetic Zn^II ions for each magnetic coupling. According to Ruiz et al. [57,58,59,60], magnetic exchange-coupling constants were determined using the broken-symmetry approach (BS-DFT). In all cases, a very tight energy convergence threshold was adopted (ΔE < 1.0 × 10⁻⁹ au). Wavefunction stability was verified at each step through ORCA’s stability test to ensure convergence to the most stable electronic configuration since the particular local electronic configuration of the Co^II ion leads to energetically close excited states [61].

The parameters that determine the axial (D) and rhombic (E) components of the local zero-field splitting (zfs) were estimated from theoretical calculations based on the complete active space self-consistent field method (CASSCF) or through a subsequent second-order N-Electron Valence-State Perturbation Theory (CASSCF/NEVPT2) applied to CASSCF wavefunctions [62,63,64], which often provides accurate values of the energies of nearby excited states and for the zfs tensor of mononuclear first-row transition metal complexes. For this purpose, MZn3 models were built by replacing three M^II ions with diamagnetic Zn^II ones. Simple mononuclear models built from the experimental geometries were also studied (see Discussion). For these calculations, J, C and JK auxiliary basis sets were generated automatically [65]. The contributions to zfs of five triplet and ten doublet and ten quartet and twenty doublet excited states for nickel(II) and cobalt(II) models, respectively, generated from an active space with eight (Ni^II) or seven (Co^II) electrons in five d orbitals, were included through an effective Hamiltonian. The RIJCOSX method was applied by combining the resolution of the identity (RI) and “chain-of-spheres” COSX approximations for the Coulomb and exchange terms [54,66,67].

The magnetic behavior of 1 was analyzed using the XVPMAG package [68], a suite of computational tools designed to efficiently study large and complex systems with varying degrees of precision and methodological approaches. In this study, magnetic susceptibility per tetranuclear M₄ unit (χ_M)-versus-temperature (T) plots were fitted using the Levenberg–Marquardt algorithm [69,70].

For the model incorporating exchange interactions, zero-field splitting (zfs) and the Zeeman effect (Equations (3), (6) and (7), see Section 3.2), the χ_MT product was simulated from the energy matrix. The energy matrix built in the basis of Ms functions and of dimensions 256 × 256 was diagonalized, and the logarithm of the partition function (Z) was computed. Small positive and negative perturbations (ΔH) were applied to derive the second derivative of log(Z) with respect to H (magnetic field), thus obtaining the magnetic susceptibility. Since measurements were conducted on a solid, unoriented sample, the results were averaged over 30 different orientations. Although fewer than 10 orientations can compromise accuracy, some tests have shown that 30 orientations provide sufficient precision compared to simulations performed using 5 × 105 randomly generated orientations. Considering the Thomson problem [71,72], care was taken to ensure that the chosen orientations eliminated any preferential bias by minimizing the electrostatic energy of 30 positive charges positioned on the surface of a sphere.

Additionally, a model incorporating spin-orbit coupling (SOC) for the Co^II ion was applied, as described in Equations (2) and (3) (see Section 3.2). This more precise approach involved the diagonalization of a 20,736 × 20,736 energy matrix. While XVPMAG can handle such a large matrix, a simplified theory approach was employed to optimize computational efficiency, which is particularly suitable when the magnetic coupling is not excessively strong. In this method, the SOC effect was resolved using a reduced 12 × 12 energy matrix associating results with local effective spins (S_eff = 1/2) and then incorporated into the Hamiltonian governing the magnetic interactions (Equation (3)) for these coupled local effective spins. The most efficient implementation of this approach involved constructing and diagonalizing an energy matrix for each total spin (S_T) using S local basis functions and the irreducible tensor operator (ITO) method [73]. The largest matrix in this process had a dimension of only 3 × 3. Nevertheless, this final diagonalization step could be omitted, as the energy levels of the resulting states for this model are already well established.

The experimental magnetic data for 2 were analyzed using the software package PHI v3.1.6 [74].

3. Results

Compounds 1 and 2 were obtained by reaction of M(NO₃)₂·6H₂O, (py)₂CO and NaO₂CPh in methanol. This process can be summarized by Equation (1):

4M(NO₃)₂·6H₂O + 4(py)₂CO + 8NaO₂CPh → [M₄{(py)₂C(OH)O}₄(O₂CPh)₄] + 8NaNO₃ + 4HO₂CPh + 20H₂O

(1)

Both complexes contain the monoanionic gem-diol form derived from di-2-pyridyl ketone. The formation of this species involves a nucleophilic attack by a water molecule on the carbonyl group of py₂CO (see Scheme 1). Hydration water in metal nitrates and even the moisture in the solvent supply the required amount of water in the reaction mixture for the formation of (py)₂C(OH)₂, while the excess of NaO₂Ph facilitates its deprotonation.

The IR spectra of 1 and 2 show medium intense bands in the region of 3500–3400 cm⁻¹ that are assigned to the ν(OH) vibration of coordinated [(py)2C(OH)O]⁻ groups. Other intense bands appear in the region 1600–1380 cm⁻¹, these may be due to contributions from the ν_as(C=O) and ν_s(C=O) of PhCO₂⁻ (1601 cm⁻¹ and 1384/1387 cm⁻¹, respectively) and from the stretching vibrations of pyridyl rings (1560 cm⁻¹).

3.1. Structure Description

Compounds 1 and 2 crystallize in the tetragonal I-42d space group and consist of isomorphous systems. Selected bond lengths and angles are listed in

Table 2. Selected bond lengths (Å), distances (Å) and bond angles (°) for 1 and 2.

(1)		(2)
Co1–O1i	2.111(2)	Ni1–O1i	2.005(4)
Co1–O1	2.032(2)	Ni1–O1	2.079(3)
Co1–O1iii	2.233(3)	Ni1–O1ii	2.166(4)
Co1–O3	2.028(3)	Ni1–O3	2.003(5)
Co1–N1	2.166(3)	Ni1–N1	2.032(6)
Co1–N2iii	2.101(4)	Ni1–N2i	2.088(5)
O1–Co1ii	2.111(2)	O1–Ni1i	2.166(4)
O1–Co1iii	2.233(2)	O1–Ni1ii	2.005(4)
O1–C1	1.395(4)	O1–C1	1.380(7)
C1–O2	1.390(5)	O2–C1	1.389(8)
O4–C12	1.233(6)	O4–C12	1.225(9)
C12–O3	1.258(5)	O3–C12	1.258(9)
Co1···Co1i	3.2175(6)	Ni1···Ni1i	3.089(1)
Co1···Co1ii	3.2337(9)	Ni1···Ni1ii	3.191(1)
Co1···Co1iii	3.2337(9)	Ni1···Ni1iii	3.089(1)
Co1–O1–Co1i	102.61(10)	Ni1–O1–Ni1ii	97.48(16)
Co1i–O1–Co1iii	96.17(9)	Ni1i–O1–Ni1ii	95.47(16)
Co1–O1–Co1iii	97.83(9)	Ni1i–O1–Ni1	102.78(17)

Symmetry operations—for 1: (i) 3/2 − y, −1/2 + x, 3/2 − z; (ii) 1/2 + y, 3/2 − x, 3/2 − z; (iii) 2 − x, 1 − y, +z; for 2: (i) −y, x, 2 − z; (ii) y, −x, 2 − z; (iii) −x, −y, z.

. The asymmetric units are shown in Figure S1 and contain one {(py)₂C(OH)O}⁻ ligand, one benzoate and one M²⁺ cation (M = Co²⁺ (1) and Ni²⁺ (2)).

The structures consist of neutral tetranuclear [M₄{(py)₂C(O)(OH)}₄(O₂CPh)₄] molecules, as can be seen in Figure 1. In both compounds, the metal ions and four oxygen atoms occupy alternated vertices of an S₄ local symmetry [M₄(µ₃-O)₄] cubane-like core. Each {(py)₂C(OH)O}⁻ ligand is coordinated to three different metal ions by one oxygen (O1) and two pyridyl nitrogen atoms (N1 and N2). Furthermore, the coordination sphere is filled with one η¹-monodentate benzoate ligand, leading to distorted octahedral geometry around the metal ions. The M–O1 bond lengths are in the range 2.032(2)–2.233(3) Å and 2.005–2.166(4) Å, whereas the M–O3_benzoate bond distances are 2.028(3) Å and 2.003(5) Å for 1 and 2, respectively. As can be seen, the M–O1 lengths are shorter in 2 than in 1, as expected when comparing nickel(II) and cobalt(II) complexes [75]. These bond lengths fall within the typical values found for similar compounds featuring the cubane-like motif [21,22,23,24,25,26,27]. Moreover, the average M^…M distance in the M₄O₄ moiety is shorter for the nickel derivative [3.123(1) Å for 2 vs. 3.2283(8) Å for 1]. In accordance with the point symmetry exhibited by the M₄O₄ units, the two opposite faces of the cubane that are perpendicular to the S₄ axis are equivalent to each other and distinct from the remaining four side faces. Both sets of faces are characterized by different M^…M distances and M−O1−M bond angles. The four side faces show M−O1−M bond angles of 96.17(9)° and 102.61(10)° for 1 and 97.48(16)° and 102.78(17)° for 2, while bond angles of 97.83(9)° and 95.47(16)° are found for the faces perpendicular to S4 in 1 and 2, respectively.

Intramolecular hydrogen bonds involving the {(py)₂C(OH)O}⁻ alcohol group (O2) and the O4 atom from the benzoate moiety are present in the cubane-like core of both compounds, with the following geometric parameters for 1: O2···O4 = 2.636(4) Å and ∠O2–H2···O4 = 167° and for 2: O2···O4ⁱⁱ = 2.579(7) Å and ∠O2–H2···O4ⁱⁱ = 167° (ii = y, −x, −z + 2). Finally, the crystal packing is further stabilized by a series of weak intermolecular interactions of type Csp2–H···Csp2 and Csp2–H···O in both complexes.

3.2. Magnetic Properties

The static magnetic properties of compounds 1 and 2 under the form χ_MT versus T plots are shown in Figure 2 and Figure 3. Reduced magnetization plots at 2 and 4 K for both compounds were also obtained, with an additional measurement at 8 K for 1. At room temperature, the χ_MT values were approximately 11.7 and 4.6 cm³ K mol⁻¹ for 1 and 2, respectively. These values are slightly higher than the theoretical estimates of 7.5 or 4.4 cm³ K mol⁻¹ expected for four non-interacting Co^II (S = 3/2, g = 2.0) or Ni^II (S = 1, g ≈ 2.1) ions. For the Co^II case, the deviation and the first observed decrease upon cooling are attributed to first-order spin-orbit coupling (SOC), leading to a g-factor exceeding the free-electron value and the depopulation of higher excited J states, respectively [76]. Later, both compounds exhibited a progressive increase in χ_MT upon cooling, reaching maxima of 12.4 and 8.7 cm³ K mol⁻¹ at 5.3 K and 7 K for 1 and 2, respectively. Subsequently, χ_MT decreased to 11.5 (1) and 7.6 (2) cm³ K mol⁻¹ at 2.4 and 2.75 K, respectively. No maximum in magnetic susceptibility was observed within the measured temperature range (Figure S2). This behavior suggests the coexistence of ferromagnetic interactions and zfs, typical for Co^II and Ni^II ions in octahedral ligand fields, or dipolar magnetic couplings between the S = 6 (1) or 4 (2) ground states of neighboring tetranuclear units. The latter explanation is the most plausible in the case of the Co₄ complex with half-integer local spin momenta. Specifically, a positive axial zfs component (D) for the Ni^II ion in 2 could partially explain the low-temperature χ_MT decay, as it would result in a non-magnetic Ms ground state. For 2, the magnetization value at 2 K and 60 kOe (7.4 μB) is lower than the expected saturation value of ≈ 8.4 μ_B for an S = 4 ground state with g = 2.1. Furthermore, the non-superposition of the M-versus-H/T plots (insets in Figure 2 and Figure 3) indicates strong magnetic anisotropy and magnetic couplings. While the reduced magnetization curves of 1 are not expected to superimpose due to the known zfs in octahedral cobalt(II) complexes, the expected effect should be less pronounced due to the large D value typical of such systems. Therefore, the observed magnetic susceptibility behavior of 1 suggests the presence of magnetic interactions on the order of several cm⁻¹ between the Co^II ions. The magnetic behavior of compounds 1 and 2 is intricate, primarily due to the interplay of first-order SOC or zfs with both intra- ferro- and antiferromagnetic interactions and possible additional intermolecular antiferromagnetic interactions. Although the four M^II ions in these compounds are crystallographically equivalent, the molecular symmetry leads to a spin topology that includes multiple magnetic coupling pathways, complicating the analysis.

While simplified models offer some preliminary insights, a comprehensive theoretical study is necessary to quantify these magnetic parameters accurately. The presence of two distinct intramolecular M···M distances in the crystal structure implies the existence of at least two different magnetic coupling constants J_i (Figure 4), which are mediated by two oxygen atoms from the alkoxo groups within the M–O–M exchange pathway, forming a M₂O₂ magnetic unit. As mentioned earlier, previous studies have highlighted the strong dependence of the magnitude and nature of these interactions on the M–O–M angle (α, Figure 5) [19,31,32,59,77,78]. Specifically, α values below a critical “magic angle” favor ferromagnetic coupling, whereas larger angles promote antiferromagnetic interactions. This critical angle is also influenced by the specific metal ion involved, as observed in bis-μ-azido or bis-μ-thiocyanate dinuclear complexes [58]. While well established in copper(II) or nickel(II) dinuclear compounds, the correlation is more nuanced in cobalt(II) systems due to the additional magnetic orbitals involved, including one of t_2g symmetry. Nevertheless, recent studies have indicated a tendency toward stronger ferromagnetic interactions in cobalt(II) complexes for smaller α values, consistent with observations in other transition metal complexes [78,79]. Furthermore, the M₂O₂ coupling units in these systems can be symmetrical or asymmetrical with one or two different α angles, respectively, adding another layer of complexity to the magnetic analysis. Other geometric distortions, such as the butterfly distortion of the M₂O₂ unit described by the δ angle (Figure 5), can affect the magnetic coupling, though in compounds 1 and 2, this distortion is only moderate (

Table 3. Most relevant structural parameters and DFT-calculated exchange-coupling constants (J) for the magnetic exchange pathways in 1 and 2.

	1		2
	J1	J2	J1	J2
dM…M   a	3.217	3.234	3.089	3.191
dM…O   a	2.032; 2.233	2.032; 2.111	2.006; 2.166	2.166; 2.079
α   b	97.8; 97.8	102.6; 96.2	95.5; 95.5	102.8; 97.5
δ   b	14.5	11.0	19.0	8.3
γ   b	39.1; 39.1	57.7; 46.8	35.3; 35.3	48.6; 60.8
JDFT   c	+0.3	+2.6	+14.6	+3.2
JFit   c	+0.12/–0.6	+3.4/+4.8	+14.5/+15.1	+2.3/+2.4

^a In Å. ^b In degrees. ^c In cm⁻¹.

). In dinuclear complexes, α and γ (the angle describing the deviation of the O–R bond from the M₂O plane) are often correlated due to the inherent geometric flexibility of the system [76,77]. However, in M₄O₄ cubane structures, some of the OR bridging groups connect more than two metal ions (μ₃-OR), imposing a specific γ angle and preventing a direct correlation between δ or γ and α [79].

To streamline the computational estimation of magnetic coupling constants in 1 and 2, a strategic simplification was employed: two Ni^II or Co^II ions in the tetranuclear complex were replaced with diamagnetic Zn^II ions, maintaining the experimental geometry of the system. This substitution ensures that only two paramagnetic ions are involved in each magnetic coupling interaction at a time, significantly reducing the complexity of the calculations. Importantly, this approach preserves the electron configuration of the system and avoids electronic artifacts that could arise from geometric truncation or the construction of oversimplified models. The nature and magnitude of J for the two systems were estimated using the broken-symmetry approximation, a well-established method described in prior studies. The results, summarized in Table 3, reveal that the magnetic interactions in both systems are predominantly ferromagnetic. Furthermore, the strength of these interactions is inversely correlated with the α angle for 2, with lower α values corresponding to stronger ferromagnetic coupling, aligning with previously established correlations in the literature, mainly with those results found for similar M₄ cubanes [19,31,32]. It is worth noting that while the magnetic coupling constants (J₁ and J₂) in compound 1 generally agree with the predicted values from a previous correlation in Co₄ truncated dicubanes [79], some discrepancies exist. The observed J₁ value is lower than expected, likely due to one of the M–O bond lengths being significantly longer than usual, which can weaken the magnetic interaction (Table 3). However, it is important to remember that other geometric parameters can also influence the strength and nature of magnetic couplings. The interplay of these factors should be considered for a more in-depth analysis of the magnetic behavior of this compound.

A further contributing factor to the magnetic behavior of compounds 1 and 2 is the zfs tensor. This tensor is characterized by two components: an axial (D) and an equatorial (E) component, with their ratio (E/D) representing the rhombicity. These parameters originate from first-order SOC in Co^II and second-order SOC in Ni^II, which also determine the g-factor components of these ions. To evaluate these parameters for M^II ions, CASSCF calculations were performed on M₄ experimental geometries, wherein diamagnetic Zn^II ions replaced three paramagnetic M^II ions. The results in

Table 4. Calculated zfs parameters, g-factor average (g_avg) and perpendicular (g_⊥) and parallel (g_||) components for MZn₃, M₁ and trimmed M₁ models of 1 and 2 derived from CASSCF and CASSCF/NEVPT2 (in parentheses) calculations.

	CoZn3	Co1	Trimmed Co1	NiZn3	Ni1	Trimmed Ni1
D  a	+44.3	+46.5	+44.8 (+34.1)	+7.6	+9.3	+9.3 (+6.8)
E/D	0.216	0.250	0.255 (0.253)	0.080	0.098	0.089 (0.080)
g||	2.170	2.175	2.178 (2.089)	2.300	2.291	2.290 (2.206)
g⊥	2.666	2.706	2.690 (2.449)	2.358	2.358	2.357 (2.253)
gavg	2.512	2.541	2.531 (2.336)	2.339	2.336	2.335 (2.238)

^a In cm⁻¹.

reveal typical D and g values for cobalt(II) and nickel(II) complexes. The high rhombicity observed is consistent with the significant distortion of the coordination sphere around both metal ions. While CASSCF/NEVPT2 calculations offer a more accurate approach for determining zfs parameters, their computational cost becomes prohibitive when applied to the MZn₃ models. Therefore, a reasonable approximation involves reducing the system to mononuclear M₁ models. The results obtained from these models must be compared with those from the more extensive MZn₃ systems at the same calculation level to evaluate the effect of molecular modeling on the electronic structure and its zfs parameters. Two mononuclear models were employed: one in which the complete coordination sphere ligands were retained (M₁ model), and another in which the peripheral pyridine or phenyl groups were replaced with methyl groups (trimmed M₁ model). Given the consistency of results between the simplified mononuclear models and the more complex MZn₃ system (Table 3), the simplified model is suitable for evaluating zfs parameters, enabling higher-level computational studies. Consequently, CASSCF/NEVPT2 calculations performed on the trimmed M₁ model yielded results comparable to those obtained with simpler, less accurate methodologies, but showing a weaker zfs. This agreement reinforces the reliability of the calculated order of magnitude and sign of D, the magnetic rhombicity (E/D) and the parallel (g_||) and perpendicular (g_⊥) components of the g-factor.

Following the conclusions derived from the theoretical study, a rational analysis of the experimental thermal dependence of χ_MT of 1 was conducted. This analysis initially involved examining the entire temperature range by applying a first-order SOC Hamiltonian (${\widehat{H}}_{SOC}$) through the T-P isomorphism formalism, as described by Equation (2) [76]. This equation characterizes the coupling between orbital (L) and spin (S) angular momenta. The parameters λ, g_e and α represent the SOC parameter, the electron g-factor and the orbital reduction factor (α = Aκ), respectively. Here, the κ parameter accounts for the reduction in orbital momentum due to electron delocalization, while the A parameter reflects the contribution of the upper ⁴T_1g(⁴P) state to the ⁴T_1g(⁴F) ground state, with values ranging from 1.5 to 1.0 under weak and strong crystal-field limits. Under axial distortion of the ideal O_h symmetry in the cobalt coordination sphere, the ground triplet level ⁴T_1g splits into the singlet ⁴A₂ and doublet ⁴E levels. This splitting, driven by second-order SOC, further generates two and four Kramers doublets, separated by an energy gap defined by the ∆ parameter. This model effectively reproduces the magnetic behavior of each Co^II ion when isolated. However, to incorporate magnetic couplings between paramagnetic centers via a spin Hamiltonian, it was assumed that these magnetic interactions were sufficiently weak to act primarily when the ground Kramers doublet of each Co^II ion was predominantly populated. Although this assumption is not strictly true, it is not far from reality, and therefore, it is unnecessary to use other, more sophisticated methods as we have done in the past. Consequently, each paramagnetic center was treated as an effective spin moment (S_eff = 1/2) with a temperature-dependent g_eff, obtained through the application of the ${\widehat{H}}_{SOC}$ Hamiltonian. Under these assumptions, the magnetic interactions were also considered effective (J_eff), related to real interactions by a factor of 25/9 [76]. The exchange-coupling Hamiltonian in Equation (2) is defined based on the spin-interaction topology illustrated in Figure 4. Finally, the dipolar interactions between the ferromagnetic ground states of neighboring Co₄ units were included through θ under a mean-field model via Equation (5). By combining the ${\widehat{H}}_{Exchange}$ and ${\widehat{H}}_{zeem-eff}$ Hamiltonians [Equations (3) and (4)], the best-fit parameters determined using the XVPMag software [68] were A = 1.29, λ = −103.3 cm⁻¹, ∆ = 454 cm⁻¹, J₁ = −0.6 cm⁻¹, J₂ = +4.8 cm⁻¹ and θ = −0.42 K. The agreement between experimental and simulated data was remarkable, as indicated by the agreement factor F = 7.8 × 10⁻⁶, defined as ∑(χ_MT_exp − χ_MT_calcd]²/∑(χ_MT_exp)².

$${\widehat{H}}_{SOC}=-\alpha \lambda \widehat{L}·\widehat{S}+\Delta \left[{\widehat{L}}_z^2-{\displaystyle \frac{1}{3}}L\left(L+1\right)\right]+\beta H\left[g_e\widehat{S}-\alpha \widehat{L}\right]$$

(2)

$${\widehat{H}}_{Exchange}=-J_1\left({\widehat{S}}_{\mathrm{M}1}·{\widehat{S}}_{\mathrm{M}2}+{\widehat{S}}_{\mathrm{M}3}·{\widehat{S}}_{\mathrm{M}4}\right)-J_2\left({\widehat{S}}_{\mathrm{M}1}·{\widehat{S}}_{\mathrm{M}3}+{\widehat{S}}_{\mathrm{M}1}·{\widehat{S}}_{\mathrm{M}4}+{\widehat{S}}_{\mathrm{M}2}·{\widehat{S}}_{\mathrm{M}3}+{\widehat{S}}_{\mathrm{M}2}·{\widehat{S}}_{\mathrm{M}4}\right)$$

(3)

$${\widehat{H}}_{zeem-eff}=g_{eff}\beta H{\displaystyle \sum }_{i=1}^4{\widehat{S}}_{C{o}_i}$$

(4)

$${\chi }_{\mathrm{M}}{T}_{exp}={\chi }_{\mathrm{M}}{T}_{M_4}\times T/\left(T-\theta \right)$$

(5)

Further refinement was undertaken by incorporating second-order SOC, which explicitly accounts for the zfs experienced by the local S = 3/2 ground state of each Co^II ion, as described by Equation (6), where D represents the axial magnetic component of the zfs. A temperature-independent paramagnetism (TIP) term was introduced in the model to address the depopulation of the higher-energy Kramers doublet occurring at elevated temperatures. In order to minimize overparameterization, the zfs rhombic magnetic component (E) was considered null. As before, the dipolar magnetic interaction along the crystal lattice between neighboring Co₄ units was also considered. The combined model, incorporating zfs (Equation 6), exchange (Equation (2)) and Zeeman Hamiltonians (Equation (7)), yielded an excellent fit to the experimental data, as evidenced by the agreement factor F = 6.6 × 10⁻⁵. The best-fit parameters obtained were g = 2.450, D = +58.1 cm⁻¹, J₁ = +0.12 cm⁻¹, J₂ = +3.40 cm⁻¹, TIP = 797.1 × 10⁻⁶ cm³ mol⁻¹ and θ = −1.8 K. The large positive D value obtained is consistent with those reported in the literature for other octahedral high-spin cobalt(II) complexes. However, it is slightly higher than the local D values derived from theoretical calculations (Table 4), even if the local zfs tensors are not aligned (Figure S3). Despite some minor discrepancies, this correspondence further validates the employed model and highlights the accuracy of both the experimental and theoretical approaches in describing the magnetic behavior of the cobalt(II) complex.

$${\widehat{H}}_{zfs}=D{\displaystyle \sum }_{i=1}^4\left[{\widehat{S}}_{z,i}^2-{\displaystyle \frac{1}{3}}{S}_i\left(S_i+1\right)\right]$$

(6)

$${\widehat{H}}_{Zeem}=g\beta H{\displaystyle \sum }_{i=1}^4{\widehat{S}}_{M_i}$$

(7)

The situation is more straightforward for compound 2. In this case, the corresponding Hamiltonian is given by the sum of terms ${\widehat{H}}_{Exchange}+{\widehat{H}}_{zfs}+{\widehat{H}}_{Zeem}$ (Equations (3), (5) and (6)). Typically, the most frequently adopted approach involves assuming that the local z axes are collinear and, consequently, parallel to the S₄ axis in this context [32,33]. In some reported cases, taking into account the distortions in the coordination environment of the nickel atoms, it has been deemed more appropriate to assume that the local anisotropy axes are orthogonal to the S₄ axis [21,25,80,81]. However, in our case, the distortion of the octahedral geometry is significant enough that it precludes a priori confidence in selecting the most suitable canting angle between z and S₄. In fact, CASSCF calculations have revealed a canting angle of 67.7° in this compound. Therefore, we decided to investigate the effect on the quality of the simultaneous magnetization and susceptibility fit when the canting angle (β) is varied between 0 and 90 degrees for positive starting D values. The results, obtained using the PHI package [74], are presented in Figure 6, which shows the optimal outcomes in terms of lower error residuals R (R = [∑(χ_Mexp − χ_Mcalcd)²][∑(M_exp − M_calcd)²]. The best fits to the experimental data are attained with two distinct sets of values, as detailed in

Table 5. Best-fit parameters obtained for complex 2 (see text).

Parameters	Fit
β  a	43	69
J1  b	15.1(2)	14.5(2)
J2  b	2.42(2)	2.34(2)
D  b	11.76(3)	10.44(3)
g	2.050(1)	2.056(1)
R	0.02966	0.01952

^a In degrees. ^b In cm⁻¹.

, corresponding to β angles of 43 and 69°. An excellent fit was achieved without accounting for possible intermolecular interactions. No improvement was observed when an E parameter was included to account for potential rhombic distortion of the Ni^II ions. Remarkably, the values of J₁, J₂, D and β determined through the fitting procedure are in close agreement with those derived from computational calculations.

4. Conclusions

New tetranuclear complexes [M₄{(py)₂C(OH)O}₄(O₂CPh)₄] (M = Co, Ni) were synthesized by reacting M(NO₃)₂·6H₂O, di-2-pyridyl ketone and sodium benzoate in methanol. X-ray crystallography revealed that compounds 1 and 2 feature a cubane-like [M₄O₄] core with S₄ symmetry. Experimental magnetic data analyses for the nickel compound, conducted using simultaneous χ_M(T) and M(H,T) fitting, confirmed ferromagnetic interactions among the four Ni ions in the cubane cluster, resulting in an S = 4 ground state. The obtained exchange-coupling J values correlate well with previously established magnetostructural relationships, where stronger ferromagnetic coupling is associated with a smaller Ni–O–Ni angle. The analysis also indicated significant zfs (D = + 10 − 12 cm⁻¹) and enabled the assessment of local anisotropy axes orientation.

For the cobalt complex, the high magnetic anisotropy was analyzed using two different models for the fitting procedures, considering first-order SOC through T-P isomorphism formalism or local zfs effects. In both approaches, predominant ferromagnetic intracluster interactions were observed, yielding an S = 6 ground state. In contrast to the Ni compound, a low negative J value was observed for the smallest Co–O–Co angle, suggesting that additional structural factors influence Co···Co interactions.

Theoretical calculations, including DFT and CASSCF/NEVPT2 methods, provided valuable insights into the magnetic coupling constants and zfs parameters, aiding in the fitting processes. The remarkable agreement between experimental data and theoretical models highlights the reliability of the methodologies employed. In highly complex systems such as these, computational approaches have once again proven to be essential tools for conducting comprehensive analyses of experimental results.