Magnetic dynamics and exchange coupling in dinuclear lanthanide complexes bridged by naphthoquinone and anthraquinone radicals

Abstract

The use of the bis(bidentate) quinoid ligands 5,8-dihydroxy-1,4-naphthoquinone (dhnqH₂) and 1,5-dihydroxyanthraquinone (dhaqH₂) in Ln chemistry has afforded four new dinuclear Dy^III complexes, viz., [Dy₂(dhnq)(Tp)₄] (1), [Dy₂(dhaq)(Tp)₄] (2), {K(18-crown-6)}[Dy₂(dhnq)(Tp)₄] (3) and {K(18-crown-6)}[Dy₂(dhaq)(Tp)₄] (4) (Tp = tris(pyrazolyl)borate). In compounds 1 and 2, the Dy^III ions are bridged by the diamagnetic dianionic forms of dhnq²⁻ and dhaq², while complexes 3 and 4 are bridged by the one-electron reduced, radical forms of these ligands. The presence of the ligand-centered radical has been confirmed by X-ray crystallography and SQUID magnetometry. Alternating current (ac) magnetic susceptibility studies revealed that the relaxation dynamics of 1 and 2 are primarily governed by fast quantum tunneling of magnetization (QTM). Conversely, the radical-bridged complexes 3 and 4 behave as single molecule magnets (SMMs) with energy barriers for the magnetization reversal, U_eff, of 24.17 K and 16.70 K, respectively, in the absence of a direct current (dc) applied field. The strong ferromagnetic Dy–radical interactions, computed using ab initio POLY_ANISO calculations, led to coupling constants of J = +5.0 and +1.2 cm⁻¹ for 3 and 4, respectively, which explains the SMM behavior in these complexes.

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Introduction

Single Molecule Magnets (SMMs) are discrete species that exhibit magnetic hysteresis of the pure molecular origin and an effective energy barrier (U_eff) to reversal of the magnetization.^1–4 Apart from their electronic structures, which have been extensively studied over the past several decades, the electron-transport properties of these materials are also of paramount interest for many potential technological applications, including high-density data storage,⁵ molecular electronic devices,⁶ and quantum computation.⁷ The syntheses of these materials often rely on self-assembly reactions between paramagnetic metal ions and organic bridging ligands. Lanthanide ions, in particular Dy^III and Tb^III,^8–11 possess remarkably large single-ion anisotropies compared to other paramagnetic ions of the periodic table, attributes that have been highly successful for the design of new SMMs. Indeed, the first Ln SMM was reported in 2003¹² and since then, a variety of mononuclear^13–20 and polynuclear^11,21,22 4f metal SMMs have been characterized.

Despite the remarkable progress that has been made in the area of lanthanide metal SMMs, some challenges remain, particularly in the case of polynuclear complexes. Typically, the origin of the magnetic relaxation of these systems arises from the presence of dominant single ion effects rather than the result of a unified spin ground state. This situation is due to the poor radial extension of the 4f orbitals, which limits orbital overlap with bridging ligands, the result of which is weak magnetic exchange.⁴ In addition, the majority of bridging ligands that have been used are closed-shell ligands that promote very weak interactions between 4f metal ions and favour fast relaxation processes or quantum tunnelling of the magnetization (QTM). To overcome this limitation, the metal-radical approach²³ has been pursued, which makes use of open-shell bridging ligands with diffuse spin orbitals that can penetrate the core electron density of the lanthanide ions and achieve strong direct coupling.^24–27 Over the last 10 years, considerable effort has been directed at the synthesis of radical-bridged lanthanide complexes with a focus on dinuclear compounds. Indeed, a small but growing number of interesting dinuclear SMMs have been reported,^24,27 including the remarkable compound [K(18-crown-6)(THF)₂][{[(Me₃Si)₂N]₂(THF)Ln}₂(μ–η²:η²-N₂)] which exhibits magnetic hysteresis up to 14 K.²⁸

Following the landmark discovery that the N₂³˙⁻ radical can strongly couple two Ln^III centers, attention has shifted toward identifying organic radicals capable of achieving similarly efficient magnetic exchange. A key determinant in this context is the nature of the radical ligand, specifically, the number of atoms over which the unpaired electron is delocalized and the degree of metal-radical overlap. Numerous N-donor radical ligands have since been explored, including bipyrimidyl (bpym),²⁹ tetrapyridylpyrazine (tppz),³⁰ bisbenzimidazole (Bbim),³¹ hexaazatrinaphthylene (HAN),³² nitronyl nitroxides,²⁷ indigo,³³ triazinyl, and tetrazine.^34,35 In this vein, our group has focused on developing lanthanide complexes featuring the radical form of the tetrazine-based ligand 3,6-bis(pyridyl)-1,2,4,5-tetrazine (bptz). Using this ligand in 4f metal chemistry afforded a dimetallic radical-bridged complex, [Cp₂Co][[Dy(tmhd)₃]₂(bptz˙⁻)] (tmhd = 2,2,6,6-tetramethyl-3,5-heptanedionate),³⁶ and a supramolecular metallacyclic triangle, [Dy₃(hfac)₆(bptz˙⁻)₃] (hfac = 1,1,1,5,5,5-hexafluoro-2,4-pentanedionate).³⁷

While N-donor radicals have dominated the field, O-donor radical ligands remain significantly underexplored. Bis(bidentate) benzoquinoids are a well-known category of organic molecules that undergo redox reactions to generate semiquinoid radicals, which have been successfully employed for the synthesis of many radical-bridged metal complexes. These ligands exhibit rich electronic versatility since they can accommodate a variety of donor atoms, including N, O, and S,^38–40 and non-donor atoms or substituents such as Cl, Br, OMe, NO₂, and SMe₂;^41–43 hence, a wide variety of magnetostructural correlations are rendered possible. Indeed, a number of 3d semiquinoid radical-bridged metal complexes have been reported, ranging from discrete dinuclear compounds^44–49 to extended chains⁵⁰ and multidimensional frameworks.⁵¹ In 4f chemistry, Ln₂ radical-bridged compounds have been reported, bearing the dichloro- and dibromo-2,5-dihydroxy-1,4-benzoquinone radical derivatives.^41,42

Motivated by these insights and building on our previous research in radical bridged complexes,^{36,37,52–55} we decided to extend this work to relatively unexplored bulkier bis(bidentate) quinoid molecules, namely 5,8-dihydroxy-1,4-naphthoquinone (dhnqH₂) and 1,5-dihydroxyanthraquinone (dhaqH₂) (Scheme 1), to ascertain if the addition of extra aromatic rings on the semiquinoid radical scaffold affects the strength of metal-radical coupling and the SMM behaviour of the resulting compounds. Although the bridging capabilities and redox activity of these ligands were explored in complexes with heavier d-block metal ions, there is currently no crystallographic evidence of the radical form of these organic molecules.^56–59

Scheme 1 Redox states of the ligands used in this work.

Herein, we report the syntheses, crystal structures, magnetic properties, and theoretical studies of two dinuclear Dy^III complexes [Dy₂(dhnq)(Tp)₄]·6CH₂Cl₂ (1·6CH₂Cl₂) and [Dy₂(dhaq)(Tp)₄]·6CH₂Cl₂ (2·6CH₂Cl₂), and their radical-bridged analogues {K(18-crown-6)}[Dy₂(dhnq)(Tp)₄]·2THF (3·2THF) and {K(18-crown-6)}[Dy₂(dhaq)(Tp)₄]·2THF (4·2THF). These results constitute rare examples of O-donor radical-bridged Dy₂ complexes and the first examples of structurally characterized metal complexes bridged by a naphthoquinone or an anthraquinone radical.

Results and discussion

Synthetic comments and description of structures

Complexes 1 and 2 were synthesised by reacting DyCl₃·6H₂O, LH₂ (L = dhnq²⁻ and dhnq²⁻), KTp, and NaOH in a 2 : 1 : 4 : 2 molar ratio in EtOH. The solvent was removed in vacuo, the remaining solid was redissolved in CH₂Cl₂, and the resulting solution was left undisturbed for a day, which afforded crystallographically suitable crystals of [Dy₂(L)(Tp)₄] [L = dhnq²⁻ (1) and dhaq²⁻ (2)] in 75–85% yields.

Compounds 1 and 2 crystallize in the triclinic space group P1̄. Both structures (Fig. 1) feature two crystallographically equivalent [Dy(Tp)₂]⁺ moieties linked together via a doubly deprotonated bridging dhnq²⁻ or dhaq²⁻ ligand for 1 and 2, respectively, with a site of inversion located at the center of the ligand. Each Dy^III ion is 8-coordinate, exhibiting a {N₆O₂} coordination sphere; six coordination sites are occupied by the N atoms of two capping Tp groups, with the remaining two positions being occupied by the O atoms of the bridging ligand. The [Dy(Tp)₂]⁺ moiety exhibits a bent sandwich-type architecture with a B–Dy–B angle of 125.0° in 1 and 128.3° in 2. The bridging dhnq²⁻ and dhaq²⁻ ligands adopt a bis-bidentate binding mode, forming two six-member chelating rings with the metal ions with bite angles of 72.9° and 73.0° and bite distances of the six-member chelate ring of 2.693 Å and 2.698 Å, for 1 and 2, respectively. Within the bridging ligands, the average C–O bond distances are 1.2853 Å and 1.272 Å in 1 and 2, respectively, consistent with reported values for the doubly deprotonated diamagnetic form of dhnq²⁻ and dhaq²⁻ in coordination compounds with 4d metal ions.^56–59 The average Dy–O and Dy–N bond distances are similar in both compounds (2.267 Å and 2.514 Å in 1, and 2.267 Å and 2.508 Å in 2). The coordination geometry of the Dy^III ions was estimated using the SHAPE⁶⁰ program and found to be distorted square antiprismatic in both compounds (CShM = 0.99 and 0.76, respectively; Table S2). The metal ions are almost in the same plane with the bridging ligand (0.033 Å) in 1, while in 2 the Dy^III ions are displaced by 0.123 Å above/below the mean plane of the planar dhaq²⁻ ligand. The intramolecular Dy⋯Dy separation is 9.078 Å in 1 and 9.441 Å in 2. To the best of our knowledge, compounds 1 and 2 are the first examples of lanthanide complexes bearing the dhnq²⁻ and dhaq²⁻ ligands.

Fig. 1 Partially labeled representation of 1 (top) and 2 (bottom). Color Scheme: Dy, yellow; N, blue; C, black; B, magenta; O, red. Hydrogen atoms are omitted for the sake of clarity.

Chemical reduction of compounds 1 and 2 with one equivalent of KC₈ in THF followed by the addition of 18-crown-6 yielded dark green solutions which were layered with Et₂O to afford dark green crystals of the one electron reduced species 3 and 4, {K(18-crown-6)}[Dy₂(L˙)(Tp)₄] [L˙ = dhnq³˙⁻ (3) and dhaq³˙⁻ (4)], in 45–55% yields.

Complex 3 crystallizes in the triclinic space group P1̄, and complex 4 crystallizes in the monoclinic space group C2/c. In each case (Fig. 2), the asymmetric unit consists of a half-molecule of the anionic complex [Dy₂(L˙)(Tp)₄]⁻ [L˙ = dhnq³˙⁻ (3) and dhaq³˙⁻ (4)], one half of the {K(18-crown-6)}⁺ counter cation, and a THF solvent molecule. The anions in 3 and 4 exhibit structures similar to those observed in 1 and 2. The Dy^III ions in 3 and 4 are also 8-coordinate, possessing the same {N₆O₂} coordination environment. In the case of 3, the metal centers exhibit square antiprismatic geometry, while in 4, the coordination geometry of the Dy^III ions is best described as distorted triangular dodecahedral (Table S2). The average Dy–O distances are 2.207 Å and 2.208 Å in 3 and 4, respectively. The average Dy–N bond distance is similar in both compounds (2.557 Å in 3, and 2.539 Å in 4). The [Dy(Tp)₂]⁺ moieties exhibit B–Dy–B angles comparable to those observed for the unreduced analogues (122.3° in 3 and 127.0° in 4). The radical bridging ligands dhnq³˙⁻ and dhaq³˙⁻ adopt the same binding mode as their diamagnetic counterparts, with similar bite angles (74.9° and 75.5° for 3 and 4, respectively) and bite distances of the six-member chelate ring (2.683 Å and 2.703 Å, for 3 and 4, respectively). The metal ions are displaced by 0.115 Å or 0.153 Å above/below the mean plane of the bridging dhnq³˙⁻ or dhaq³˙⁻ ligand for 3 and 4, respectively. The intramolecular Dy⋯Dy separation is 9.008 Å in 3 and 9.316 Å in 4.

Fig. 2 Partially labeled representation of 3 (top) and 4 (bottom). Color Scheme: Dy, yellow; N, blue; C, black; B, magenta; O, red; K, purple. Hydrogen atoms are omitted for the sake of clarity.

While there are several structural similarities among complexes 1–4, a detailed comparison of the bond distances in 1–4 has revealed significant differences and provided crucial insight into the oxidation state of the dhnq and dhaq bridging ligands. A comparison of 1 with 3 and 2 with 4 reveals a net increase in the average C–O bond order by 1.7% and 2.3% (Table 1), respectively, indicative of the presence of an additional electron in the molecular orbitals of the ligands. Upon reduction, the average C–C bond distances remain unchanged within error, but it is worth noting that these values are influenced by the presence of crystallographic inversion symmetry, which complicates their interpretation.⁶¹ Furthermore, in both 3 and 4, there is a notable 2.6% decrease in the average Dy–O bond distance. This decrease signifies a stronger metal–ligand interaction, in line with the enhanced donating capability of the reduced dhnq³˙⁻ or dhaq³˙⁻ ligands compared to their dianionic counterparts. To the best of our knowledge, compounds 3 and 4 are the first examples of lanthanide radical-bridged complexes bearing the dhnq³˙⁻ and dhaq³˙⁻ ligands.

Table 1 Selected structural parameters: average distances (Å), angles (°), and coordination geometries for the 8-coordinate Dy^III ions in compounds 1·6CH₂Cl₂, 2·6CH₂Cl₂, 3·2THF and 4·2THF

	Diamagnetic ligand		Radical ligand
Complex	l·6CH2Cl2	2·6CH2Cl2	3 BHF	4 BHF
B–Dy–B angle	125.0	128.3	122.3	127.0
Dy–L bite angle	72.9	73.0	74.9	75.5
Dy bite distance	2.639	2.698	2.683	2.703
Dy–O distance	2.267	2.267	2.207	2.208
Dy–N distance	2.514	2.508	2.557	2.539
C–O distance	1.284	1.272	1.306	1.302
Dy–L plane distance	0.033	0.123	0.115	0.153
Dy–Dy intramolecular distance	9.078	9.441	9.008	9.316
Dy coordination geometry	Square antiprismatic	Square antiprismatic	Square antiprismatic	Triangular dodecahedral

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Magnetic studies

Static properties

Direct current (dc) magnetic susceptibility measurements were conducted on powdered polycrystalline samples of 1–4 using a magnetic field of 0.1 T over a temperature range of 2–300 K. The data are displayed as χ_MT versus T plots in Fig. 3. For compounds 1 and 2, the experimental χ_MT values (28.20 and 28.03 cm³ K mol⁻¹, for 1 and 2, respectively) at 300 K are in excellent agreement with the theoretical value (28.34 cm³ K mol⁻¹) expected for two non-interacting Dy^III (⁶H_15/2, S = 5/2, L = 5, g = 4/3) ions.⁶² Upon cooling, the χ_MT product for complexes 1 and 2 decreases smoothly from 300 K to a value of 27.00 cm³ K mol⁻¹ for 1 and 28.25 cm³ K mol⁻¹ for 2 at 100 K. For 1, a more pronounced decrease in the χ_MT product is observed below 100 K, reaching a minimum value of 22.67 cm³ K mol⁻¹ at 2 K. Compound 2 exhibits a similar trend, but only down to 4 K. Below this temperature, there is a slight increase in χ_MT for 2, reaching a value of 26.05 cm³ K mol⁻¹ at 2 K. The decrease observed below 100 K, for 1 and 2, can be attributed to the depopulation of the excited Stark sublevels of the Dy^III ions and/or weak antiferromagnetic interactions between the metal centers, while the slight low-temperature increase observed for 2 may indicate weak ferromagnetic coupling between intramolecular Dy^III ions.⁶³

Fig. 3 Plots of χ_MT versus T for 1–4.

A pronounced disparity in magnetic behavior is observed for the radical-bridged analogues 3 and 4. In both cases, the experimental χ_MT values (29.62 cm³ K mol⁻¹ for 3, and 29.67 cm³ K mol⁻¹ for 4) at 300 K are in agreement with the theoretical value (28.72 cm³ K mol⁻¹) predicted for two non-interacting Dy^III (⁶H_15/2, S = 5/2, L = 5, g = 4/3) ions and an S = 1/2 organic radical. For 3, the χ_MT product exhibits a slight increase as the temperature is decreased, reaching a value of 32.31 cm³ K mol⁻¹ at 28 K. Below this temperature, the χ_MT product increases more sharply, peaking at a value of 51.70 cm³ K mol⁻¹ at 4 K. After reaching this maximum, the χ_MT product falls to a minimum value of 49.17 cm³ K mol⁻¹ as the temperature is lowered to 2 K. The χ_MT product for 4 decreases slightly to a minimum value of 29.53 cm³ K mol⁻¹ at 28 K before increasing to a maximum value of 47.28 cm³ K mol⁻¹ at 2 K. The sudden increase of χ_MT product observed below 28 K, for 3 and 4, can be attributed to the spin alignment of the Dy^III ions induced by the strong magnetic interactions between the dhnq³˙⁻ or dhaq³˙⁻ radicals and the metal centers. These results align with observations made for other radical-bridged lanthanide complexes. The decrease in χ_MT at lower temperatures for 3 can be ascribed to magnetic blocking.^41,42

Field-dependent magnetization measurements were performed on 1–4 at 2, 5, and 7 K temperatures over the range of 0–7 T (Fig. S1–S4). For 1–4, magnetization shows a relatively rapid increase at low fields without reaching saturation at ∼7 T, which indicates significant magnetic anisotropy. Furthermore, the observed magnetization values for the reduced complexes, 3 and 4, at 2 K and 7 T are slightly lower compared to those of compounds 1 and 2. This difference is more likely a consequence of magnetic anisotropy effects, rather than of antiferromagnetic coupling between the metal ions and radical ligands in 3 and 4.

Dynamic properties

Alternating current (ac) magnetic susceptibility measurements were conducted using a 2 Oe ac field to investigate the magnetic dynamics of 1–4. Compounds 1 and 2, which feature the diamagnetic form of the dhnq²⁻ and dhaq²⁻ ligands, respectively, displayed both in-phase (χ′) and out-of-phase (χ′′) ac susceptibility signals that are frequency and temperature dependent in the absence of an applied dc field (Fig. S5 and S6).

However, within the frequency range of 1–1000 Hz and temperatures spanning from 2 to 25 K, no maxima were detected in the χ′′ signals, suggesting considerable quantum tunnelling of the magnetization (QTM). Additionally, ac susceptibility measurements were performed at various static fields (0–2000 Oe) (Fig. S7 and S8), but they did not improve the SMM properties of 1 and 2. Due to the pronounced QTM, U_eff could not be determined in either case.

In stark contrast, the reduced complexes, 3 and 4, exhibit out-of-phase (χ′′) ac susceptibility peaks that shift to lower frequencies as the temperature decreases, indicative of slow magnetic relaxation (Fig. 4a,b, and Fig. S9–S14). The experimental data between 1.8–4 K and 1.8–3.6 K, for 3 and 4, respectively, were used for the construction of the Cole–Cole plots for complexes 3 and 4 (Fig. S11 and S14). Fitting of the Cole–Cole plots for 3 and 4 using a generalized Debye model^64,65 was performed, allowing for the extraction of the τ and α parameters. The α values are in the range of 0.19–0.08 for 3 and 0.17–0.03 for 4, in accordance with a single temperature-dependent relaxation process. The relaxation times (τ) obtained from the above fitting were plotted vs. 1/T (Fig. 4c) and were analyzed using the following eqn (1):

where τ_QTM⁻¹, CTⁿ, and τ₀⁻¹ exp(−U_eff/k_BT) represent QTM, Raman, and Orbach relaxation processes, respectively. For 3, the best fitting gave U_eff = 24.17 K, τ₀ = 3.00 × 10⁻⁸ s, C = 2.53 × 10⁻² s⁻¹ K^−6.3 and n = 6.3, and for 4 U_eff = 16.70 K, τ₀ = 4.04 × 10⁻⁷ s, C = 1.27 × 10⁻¹ s⁻¹ K^−4.0 and n = 4.0.

Fig. 4 Frequency dependence of the out-of-phase (χ′′) signals of (a) 3 and (b) under 0 Oe; solid lines are guides for the eye. (c) Comparison of the Arrhenius plots of 3 and 4. Solid lines highlight the fits to eqn (1) (see the text for the fit parameters).

These findings indicate that the presence of the radical on the ligand in 3 and 4 effectively suppresses the quantum tunnelling of magnetization prevalent in the unreduced compounds 1 and 2, in accord with other reports for radical-bridged lanthanide complexes. The obtained U_eff values for 3 and 4 are generally lower than those reported for most N-donor radical-bridged Dy₂ complexes. However, as compared to O-donor radical-bridged Dy₂ complexes, the U_eff values for 3 and 4 are slightly higher than the value reported for the bromoanilate radical (U_eff = 10.4 K, H_dc = 0 Oe)³³ and comparable with those reported for the chloroanilate radical (U_eff = 31 K), which were measured in the presence of an external field (H_dc = 1000 Oe).³²

Computational studies

To investigate the observed magnetic behavior and the nature of magnetic anisotropy of each Dy^III center in 1–4, ab initio CASSCF/RASSI/SINGLE_ANISO calculations using the MOLCAS 8.0⁶⁶ (see computational details) were performed. The magnetic anisotropy direction of each Dy^III ion in 1 and 2 is depicted in Fig. 5 (a similar anisotropy direction is observed in 3 and 4). The calculated g_z values for both Dy^III sites in 1–4 have similar values, signifying the same type of single-ion anisotropy behavior for both Dy^III sites (Table 2 and Table S3). Both Dy^III ions in 1–4 exhibit small transverse components (g_x and g_y) and a strong axial component (g_z) in their ground Kramers doublet (KD) states. This suggests a low chance of mixing between the m_J states, which may suppress quantum tunneling of the magnetization (QTM), and supports the presence of optimal Ising-type anisotropy required for slow magnetization relaxation. Thus, at the single-ion level, their capacity to blockade the magnetization is unlikely to happen in the ground KDs, since the m_J = ±15/2 was found to be the ground state, but it could possibly occur in the excited KDs; this implies that the compounds are likely to show SMM behavior at zero dc field. Although reduction of 1 and 2 to the radical-bridged analogues 3 and 4 introduces modest changes in Dy–O distances (and coordination geometry in 4), CASSCF/RASSI/SINGLE_ANISO calculations show that the Dy single ion anisotropy remains essentially the same across the series, indicating that the enhanced SMM behavior of the radical-bridged complexes 3 and 4 arises primarily from Dy–radical exchange, with coordination changes acting only as a secondary tuner.

Fig. 5 Orientations of the local magnetic moments in the ground doublet of each Dy^III center in (top) 1 and (bottom) 2. The blue arrows show the magnetic anisotropy directions of Dy^III ions in the ground states. Similar magnetic anisotropy directions were observed for their respective radical-bridged complexes 3 and 4.

Table 2 Ab initio computed energies of the lowest Kramers Doublets (KDs) and ground-state g-tensors of each Dy^III centers in all complexes

KDs	1 (dhnq-neutral)		2 (dhaq-neutral)		3 (dhnq-radical)		4 (dhaq-radical)
	Dy1	Dy2	Dy1	Dy2	Dy1	Dy2	Dy1	Dy2
1	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
2	148.1	148.1	149.7	149.7	154.4	154.4	157.8	157.8
3	195.4	195.4	261.9	261.8	241.4	241.4	248.6	248.6
4	226.1	226.1	313.6	313.6	318.9	318.9	326.2	326.3
5	255.7	255.7	329.7	329.7	338.8	338.8	389.9	390.0
6	286.7	286.7	346.4	346.4	383.3	383.3	428.3	428.4
7	330.5	330.5	378.7	378.7	464.8	464.8	493.1	493.2
8	641.6	641.6	697.3	697.3	740.2	740.2	740.7	740.7
gx	0.0473	0.0471	0.0138	0.0138	0.0690	0.0688	0.0367	0.0367
gy	0.0867	0.0868	0.0216	0.0217	0.0441	0.0437	0.0691	0.0691
gz	19.7155	19.7162	19.7806	19.7894	19.4401	19.4396	19.5550	19.5653

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In 1 and 2, the ground state g_zz axis aligns with the O-atoms of the dhnq²⁻ and dhaq²⁻ ligands (see Fig. 5). This is likely owing to the shorter Dy–O (avg.) bond lengths (∼2.27 Å in 1 and ∼2.25 Å in 2) of dhnq²⁻ and dhaq²⁻ ligands compared to the longer Dy–N distances (∼2.5 Å) of Tp ligands. The oblate electron density of the Dy^III ion induces the g_zz axis to preferentially align in the same plane towards the shortest Dy–O bond (O atom of dhnq²⁻ and dhaq²⁻ ligands), avoiding significant electrostatic repulsion with the other coordinated atoms, resulting in a greater ground-first excited state gap in all complexes. Similar magnetic anisotropy directions have been observed for 3 and 4, as shown in Fig. 5.

The computed energies of the eight low-lying KDs (Table 2) for both Dy^III sites have the same energy values, a reflection of the fact that they are symmetrically equivalent⁶⁷ and are found to span an energy gap of 641.6, 697.3, 740.2, and 740.7 cm⁻¹ for 1–4, respectively. To validate the calculated energy barriers, we developed relaxation mechanisms for magnetization blockade for both Dy^III sites in 1–4 (Fig. 6 and Fig. S15). The ground state KDs of both Dy^III sites in 1–4 have small QTM (0.02μ_B for 1, 0.006μ_B for 2, 0.03μ_B for 3, and 0.02μ_B for 4), hence, it allows the magnetization to relax via higher excited states. The Crystal-Field (CF, B_k^q) parameters explain the QTM probability of ground-state KDs. The computed CF parameters for 1–4 are listed in Table S5. In both Dy^III sites in 1–4, significant axial terms (in which q = 0 and k = 2, 4, 6) are computed compared to non-axial terms (in which q ≠ 0 and k = 2, 4, 6), especially the axial terms are dominating in k = 2 terms, suggesting negligible QTM effects.^67–70 A significant TA-QTM (temperature assisted – QTM) in the first excited states was observed (0.83μ_B for 1, 0.1μ_B for 2, 0.34μ_B for 3, and 0.2μ_B for 4), which limits the relaxation of magnetization via these states with energy barriers of 148.1, 149.7, 154.2, and 157.8 cm⁻¹ (Fig. 6) for 1–4, respectively. Single-ion calculation results indicate that the radical-bridged complexes 3 and 4 have relatively large energy barriers compared to their respective neutral counterparts (1 and 2). However, the conclusive relaxation mechanisms in 1–4 are best understood in terms of exchange-coupled systems.

Fig. 6 Ab initio computed magnetization blocking barrier for Dy1 site (same applicable for Dy2 site) in (top) 1, and (bottom) 2. The thick blue line indicates the Kramers doublets (KDs) as a function of computed magnetic moment. The red arrows represent the presence of QTM/TA-QTM between the connecting pairs. The green/purple arrows show the possible pathway via Orbach/Raman relaxation. The numbers provided at each arrow are the mean absolute value for the corresponding matrix element of the transition magnetic moment.

To understand the overall SMM behavior of 1–4 and the effect of Dy–radical coupling on magnetic relaxation, the exchange coupled states relaxation mechanism was developed by considering the magnetic coupling constants (J_exch + J_dip = J_tot) between Dy^III–rad (only in 3 and 4) and Dy^III–Dy^III, as well as an intermolecular coupling constant zJ using the POLY_ANISO program⁷¹ within the Lines model.⁷² The Lines model in POLY_ANISO treats Dy^III ions as isotropic spins with S = 5/2, which is a simplification used for exchange fitting. The full anisotropy is retained from the ab initio CASSCF/RASSI calculations. The computed magnetic coupling constants are tabulated in Table 3. Using the lowest energy states of individual Dy^III ions and the possible exchange interactions, the ab initio calculated magnetic susceptibility data (Fig. 3; solid lines) were computed and are consistent with the experimental data, indicating that the retrieved J values and the U_cal parameters are reliable. These calculations reveal a set of exchange split states (Fig. 7), indicating the formation of coupled spin manifolds due to the bridging radicals in 3 and 4. These states are well isolated from higher excited states and show suppressed QTM in the ground levels for 3 and 4. The observed χ_MT product increase at low temperatures and magnetization values (relative to 1 and 2) is consistent with strong Dy–radical exchange interactions. Thus, the relaxation likely proceeds via thermally activated processes within the exchange-coupled ladder, distinct from the tunneling-dominated mechanisms operative in 1 and 2. The Dy^III–Dy^III interaction is found to be very weakly antiferromagnetic in 1 and 2, whereas it is found to be ferromagnetic in 3 and 4 and larger in magnitude than that of J_Dy–Dy. The presence of ferromagnetic Dy^III–Dy^III and Dy^III–rad interactions in 3 and 4 is attributed to the presence of vacant antibonding orbitals of dhnq and dhaq ligands, which facilitate increased exchange; such an increase in magnitude was previously observed for other Ln^III–rad complexes.^24,47 The J_Dy–rad of 3 is large, with a value of 5.0 cm⁻¹ is among the highest ferromagnetic coupling constants reported for a Ln–rad system.^24,27 Ferromagnetic Ln–rad coupling is uncommon, and to our knowledge, it has been observed primarily in systems containing nitronyl nitroxide radicals.²⁷ We found that the J_tot of the Dy^III–rad interactions in 3 and 4 primarily arises from the J_exch (4.8 cm⁻¹ for 3 and 1.0 cm⁻¹ for 4) with a comparatively small J_dip. In general, the Dy^III–Dy^III exchange interaction is expected to be very weak in dinuclear or polynuclear complexes that significantly reduces the energy of low-lying doublet states of Dy^III ions, resulting in weak or no SMM behavior in a few Dy-based complexes.^11,73 This hypothesis is clearly operative in the cases of 1 and 2 where the presence of large tunneling gaps (see Tables S6, S7 and Fig. S16) between the ground exchange coupled states (non-Kramer doublet states) allow the magnetization to relax in the ground state itself which suggest no SMM behvaiour for 1 and 2. However, the presence of ferromagnetic Dy^III–rad interactions in 3 and 4 produces several low-lying exchange-coupled states and quenches the QTM/TA-QTM in the ground and first excited exchange-coupled states (KDs) to some extent. The TA-QTM becomes larger in the third and fourth exchange-coupled states, which lead to SMM behaviour with an energy barrier of 19.1 cm⁻¹ (27.5 K) and 10.2 cm⁻¹ (14.7 K), respectively (see Tables S8, S9, and Fig. 7). These U_cal parameters are consistent with the experimentally determined barrier of 24.2 K and 16.7 K for 3 and 4, respectively.

Fig. 7 Low-lying exchange spectra in (top) 3, and (bottom) 4. The exchange-coupled states are placed on the diagram according to their magnetic moments (bold blue lines). The red arrows show the QTM/TA-QTM between the connecting states (KDs), while the green/purple arrows show the possible spin–phonon transitions. The numbers provided at each arrow are the mean absolute value for the corresponding matrix element of the transition magnetic moment.

Table 3 POLY_ANISO fitted magnetic exchange interactions (cm⁻¹, J_exch + J_dip = J_tot) in 1–4

	Jexch	Jdip	Jtot	zJ
JDy–Dy
1 (dhnq-neutral)	−0.01	−0.02	−0.03	−0.001
2 (dhaq-neutral)	0.005	−0.015	−0.01	0.01
3 (dhnq-radical)	0.58	−0.03	0.55	−0.002
4 (dhaq-radical)	0.62	−0.02	0.6	0.008
JDy–rad
3 (dhnq-radical)	4.8	0.2	5.0	−0.002
4 (dhaq-radical)	1.0	0.2	1.2	0.008

---

The majority of radical-bridged SMMs utilize anionic radical bridging ligands that align perpendicularly to the primary anisotropy axis of each metal ion.^29,74 For example, in the [(Cp₂Me₄Tb)₂(μ–η²: η²-N₂)], it is evident that the presence of the radical spin perpendicular to the local magnetic anisotropy axes caused by the Cp* ligands is harmful to the magnetic anisotropy at the Tb^III and Dy^III sites.⁷⁴ Based on these results, it was predicted that it would be advantageous for the spin of the radical bridge to be collinear with the local anisotropy axes, as this arrangement would facilitate ferromagnetic coupling between the metal ions through space and ensure that the anionic radical bridge enhances the existing magnetic anisotropy rather than diminishing it.⁴ This theory has been fulfilled in our study: the dianionic or trianionic napthaquinone and anthraquinone ligands, together with improved delocalization of the radical spin on the ligand surface, facilitate a co-parallel orientation between the radical spin and the g_zz axis, which promotes the observed ferromagnetic exchange. A similar scenario was reported for the {CpⁱPr₅LnI₃LnCpⁱPr₅} complex, where the unpaired electron residing in the σ-type Ln–Ln bond is co-parallel to the local magnetic anisotropy axes determined by the CpⁱPr₅ ligands, increasing the magnetic anisotropy.²⁰

Conclusions

The first dinuclear Dy₂ compounds, 1 and 2, featuring dianions of the quinoid ligands 5,8-dihydroxy-1,4-naphthoquinone (dhnqH₂) and 1,5-dihydroxyanthraquinone (dhaqH₂) as bridges, are reported. These molecules were further reduced to produce the radical-bridged Dy₂ species, 3 and 4, containing the dhnq³˙⁻ and dhaq³˙⁻ radicals, respectively. These are the first, crystallographically characterized, compounds that contain these radical ligands coordinated to a paramagnetic metal ion. Compounds 1–4 represent rare examples of pairs of Dy₂ compounds with both neutral and radical forms of the same organic bridging ligands, allowing the investigation of the influence of the exchange coupling on the magnetic dynamics. Indeed, magnetic and theoretical studies revealed that in 1 and 2, the coupling is negligible, resulting in weak SMM behaviour (tails of χ′′ signals) and fast magnetic relaxation through QTM. In contrast, placing an additional electron on the bridging ligands in 3 and 4 led to a strong ferromagnetic exchange, which mitigates the occurrence of QTM observed in the unreduced species. Compounds 3 and 4 exhibit maxima of the χ′′ signals below 4 K under zero static field, indicative of SMM behaviour. Fitting of the data, considering all possible relaxation pathways, gave energy barriers of 24.17 K and 16.70 K for 3 and 4, respectively, for the thermally-activated relaxation. The presence of ferromagnetic coupling between the Dy^III ions and the radical, with a coupling constant of +5.0 and +1.2 cm⁻¹ for 3 and 4, was confirmed by the Lines model's POLY_ANISO calculations. The computed U_cal parameters are in excellent agreement with the experimentally determined barriers. Current efforts are underway to isolate other anisotropic Ln^III analogues (i.e., Ln^III = Tb^III, Er^III, and Ho^III) as well as to extend this synthetic strategy to the use of other supporting ligands, which are known to promote a strong axial crystal field for oblate Ln^III ions.

Experimental

Synthetic procedures

For compounds 1 and 2, all manipulations were performed under aerobic conditions using reagent-grade materials and solvents as received. For 3 and 4, all manipulations were carried out under an inert atmosphere of N₂ using standard Schlenk and glovebox techniques. Compounds 1 and 2 were dried under vacuum at 100 °C and stored in the glovebox prior to use. Anhydrous THF lacking butylated hydroxytoluene as an inhibitor was purchased from Sigma Aldrich and stored under an inert atmosphere.

[Dy₂(dhnq)(Tp)₄]·6CH₂Cl₂ (1·6CH₂Cl₂). To a stirred, beige/brown suspension of dhnqH₂ (0.19 g, 1.0 mmol), NaOH (0.08 g, 2.0 mmol), and KTp (1.01 g, 4.0 mmol) in EtOH (80 mL) was added solid DyCl₃·6H₂O (0.75 g, 2.0 mmol). The resulting dark blue solution was stirred for a further 2 h, after which time the solvent was removed in vacuo, and the crude material was extracted using 30 mL of CH₂Cl₂. The extract was filtered, and the solution was layered with Et₂O (30 mL). Slow diffusion after 1 day led to blue needles of 1; these were collected by filtration and washed with Et₂O (3 × 5 mL); the yield was 85%. Upon dryness (under vacuum), the crystalline solid was analyzed as 1. Anal. calc. for C₄₆H₄₄N₂₄B₄O₄Dy₂ (1): C, 40.47; H, 3.25; N, 24.62%. Found: C, 40.43; H, 3.21; N, 24.67%. Selected ATR data (Nujol mull, cm⁻¹): 1565 (m), 1500 (w), 1403 (w), 1300 (m), 1269 (m), 1213 (m), 1148 (w), 973 (m), 922 (w), 859 (w), 807 (w), 757 (m), 722 (s), 668 (m), 620 (m), 611 (w).

[Dy₂(dhaq)(Tp)₄]·6CH₂Cl₂ (2·6CH₂Cl₂). To a stirred, beige/brown suspension of dhaqH₂ (0.24 g, 1.0 mmol), NaOH (0.08 g, 2.0 mmol), and KTp (1.01 g, 4.0 mmol) in EtOH (80 mL) was added solid DyCl₃·6H₂O (0.75 g, 2.0 mmol). The resulting dark red solution was stirred for a further 2 h, after which time the solvent was removed in vacuo, and the crude material was extracted using 30 mL of CH₂Cl₂. The extract was filtered, and the solution was layered with Et₂O (30 mL). Slow diffusion after 1 day led to red needles of 2; these were collected by filtration and washed with Et₂O (3 × 5 mL); the yield was 75%. Upon dryness (under vacuum), the crystalline solid was analyzed as 2. Anal. calc. for C₅₀H₄₆N₂₄B₄O₄Dy₂ (2): C, 42.43; H, 3.28; N, 23.75%. Found: C, 42.38; H, 3.31; N, 23.79%. Selected ATR data (Nujol mull, cm⁻¹): 1733 (w), 1603 (s), 1584 (s), 1617 (s), 1502 (s), 1404 (m), 1300 (s), 1257 (s), 1212 (s), 1199 (m), 1167 (m), 1147 (w), 1120 (s), 1093 (w), 1048 (s), 976 (s), 922 (w), 887 (w), 864 (w), 864 (w), 781 (m), 750 (s), 722 (s), 671 (m), 636 (w), 621 (m), 572 (m), 474 (w).

{K(18-crown-6)}[Dy₂(dhnq)(Tp)₄]·2THF (3·2THF). In a nitrogen-filled glovebox, crystals of [Dy₂(dhnq)(Tp)₄] (1) (0.10 g, 0.07 mmol) were dissolved in THF (10 mL) to yield a dark blue solution. Solid KC₈ (0.01 g, 0.07 mmol) was then added, and the color of the solution turned dark green. The mixture was stirred at room temperature for 1 h, after which time solid 18-crown-6 (0.04 g, 0.15 mmol) was added and the solution was filtered. The filtrate was layered with Et₂O (10 mL). Slow mixing after 1 day produced dark green platelets of 3; these were collected by filtration and washed with Et₂O (3 × 5 mL); the yield was 45%. Upon dryness (under vacuum), the crystalline solid was analyzed as 3. Anal. calc. for C₅₈H₆₈N₂₄B₄O₁₀KDy₂ (3): C, 41.75; H, 4.11; N, 20.15%. Found: C, 41.79; H, 3.98; N, 20.11%. Selected ATR data (Nujol mull, cm⁻¹): 1542 (m), 1495 (s), 1398 (m), 1351 (w), 1300 (s), 1266 (s), 1215 (s), 1199 (m), 1114 (m), 1099 (s), 1043 (s), 972 (m), 953 (s), 920 (w), 894 (w), 832 (m), 806 (w), 774 (s), 752 (s), 722 (s), 667 (m), 623 (m), 533 (w), 499 (w).

{K(18-crown-6)}[Dy₂(dhaq)(Tp)₄]·2THF (4·2THF). In a nitrogen-filled glovebox, crystals of [Dy₂(dhaq)(Tp)₄] (2) (0.10 g, 0.07 mmol) were dissolved in THF (10 mL) to yield a dark red solution. Solid KC₈ (0.01 g, 0.07 mmol) was then added, and the color of the solution turned dark green. The mixture was stirred at room temperature for 1 h, after which time solid 18-crown-6 (0.04 g, 0.15 mmol) was added, and the solution was filtered. The filtrate was layered with Et₂O (10 mL). Slow diffusion after 1 day led to isolation of dark green plates of 4; these were collected by filtration and washed with Et₂O (3 × 5 mL); the yield was 55%. Upon dryness (under vacuum), the crystalline solid was analyzed as 4. Anal. calc. for C₇₀H₈₆N₂₄B₄O₁₀KDy₂ (4): C, 43.33; H, 4.10; N, 19.56%. Found: C, 43.29; H, 3.06; N, 19.51%. Selected ATR data (Nujol mull, cm⁻¹): 1563 (w), 1535 (w), 1349 (m), 1300 (s), 1251 (m), 1198 (m), 1187 (m), 1149 (w), 1108 (s), 1080 (m), 1042 (s), 972 (m), 960 (m), 922 (w), 855 (m), 796 (w), 780 (m), 737 (m), 723 (s), 704 (w), 670 (m), 622 (m), 585 (m), 486 (w).

Crystallography

Diffraction data for complexes 1·6CH₂Cl₂, 2·6CH₂Cl₂, 3·2THF, and 4·2THF were collected on a Bruker D8 diffractometer (Mo Kα graphite-monochromated radiation, λ = 0.71073 Å) with the acquisition controlled by the APEX2 software package.⁷⁵ The data collection temperature, 150(2) K, was controlled by an Oxford Cryosystems Series 700. Images were processed with the software SAINT+,⁷⁶ and absorption effects were corrected with the multi-scan method implemented in SADABS.⁷⁷ The structure was solved using SHELXTL incorporated in the Bruker APEX-III software package and refined using the SHELXLE.^78–80 All non-hydrogen atoms were successfully refined using anisotropic displacement parameters. H-atoms bound to carbon atoms were placed at geometrical positions using the suitable HFIX instructions in SHELXL and included in subsequent refinement cycles in riding-motion approximation with isotropic thermal displacement parameters (U_iso) fixed at the carbon atom to which they are attached. H-atoms associated with the coordinated and non-coordinated MeOH molecules were clearly visible in the difference Fourier maps and included in subsequent refinement stages with the O–H distances restrained to 0.85(2) Å and by using a riding-motion approximation with an isotropic thermal displacement parameter (U_iso) fixed at 1.5 × U_eq of the parent O-atom.

Figures of the structures were created using Mercury⁸¹ and Diamond⁸² software packages. The unit cell parameters, structure solution, and refinement details of 1·6CH₂Cl₂, 2·6CH₂Cl₂, 3·2THF, and 4·2THF are summarized in Table S1. Further crystallographic details can be found in the corresponding CIF files provided in the SI.

Physical studies

Infrared spectra were obtained using a Nicolet Nexus 470 FT-IR Spectrometer. Elemental analyses were performed by Atlantic Microlabs, Inc., Norcross, GA. Variable-temperature direct current (dc) and alternating current (ac) magnetic susceptibility data were collected on a Quantum Design MPMS-XL SQUID magnetometer equipped with a 7 T magnet and operating in the 2–300 K range. The diamagnetic contribution of the polypropylene bag used to hold the sample was subtracted from the raw data. Pascal's constants⁸³ were used to estimate the diamagnetic corrections, which were subtracted from the experimental susceptibilities to give the molar paramagnetic susceptibilities (χ_M). Note: All physicochemical characterizations, except X-ray crystallography, were performed on dried samples. Lattice solvents were removed during this process, and elemental analysis confirmed the desolvated forms of the compounds 1–4.

Computational details

Using MOLCAS 8.0,⁸⁴ ab initio calculations were performed on the Dy^III ions using their crystal structures. The anisotropy of a single Dy^III ion in all complexes was computed using the X-ray structure and by substituting a diamagnetic Lu^III ion for the nearby Dy^III ion. The presence of radical spins of dhnq³˙⁻ and dhaq³˙⁻ ligands in 3 and 4 was considered as point charges while performing the calculations. Relativistic effects were taken into account based on the Douglas–Kroll Hamiltonian.⁸⁵ The spin-free eigenstates are achieved by the Complete Active Space Self-Consistent Field (CASSCF) method.⁸⁶ The basis sets were taken from the ANO-RCC library for the calculations. We employed the [ANO-RCC⋯8s7p5d3f2g1h.] basis set⁸⁷ for Dy^III atoms, the [ANO-RCC⋯3s2p.] basis set for B and C atoms, the [ANO-RCC⋯2s.] basis set for H atoms, the [ANO-RCC⋯3s2p1d.] basis set for O and N atoms, and the [ANO-RCC⋯7s6p4d2f.] basis set for the Lu atom. In the first step, we ran a guessorb calculation using a Seward module to create the starting guess orbitals. Here, we included nine electrons across seven 4f orbitals of the Dy^III ion. Then, using these guess orbitals, we chose the active space based on the number of active electrons in the number of active orbitals and carried out the SA-CASSCF calculations. Here, the Configuration Interaction (CI) procedure was computed for Dy^III ions, and we considered twenty-one sextet excited states, two hundred and twenty-four quartet excited states, and four hundred and eighty doublet excited states in the calculations to compute the anisotropy. All the excited states corresponding to each multiplet of ions were computed in the CASSCF module. After computing these excited states, we mixed all the low-lying excited states (<50000 cm⁻¹) using the RASSI-SO⁸⁸ module to calculate the spin–orbit coupled states. Moreover, these computed SO states were considered in the SINGLE_ANISO⁸⁹ program to compute the g-tensors. The g-tensors for the Kramers doublets of Dy^III were computed based on the pseudospin S = ½ formalism.⁸⁹ Crystal-field (CF) parameters have been extracted using the SINGLE_ANISO code, as implemented in MOLCAS 8.0. The CF parameters for all complexes were analyzed for deeper insight into the mechanism of magnetic relaxation. The corresponding crystal field Hamiltonian is given in the equation:where B_k^q is the crystal field parameter and O_k^q is Steven's operator.

The exchange/dipolar interactions for Dy^III–radical and Dy^III–Dy^III were computed by fitting the experimental data using the POLY_ANISO program.⁷¹ The exchange Hamiltonian adapted for all complexes is shown below.

(here J_i = J_i^dipolar + J_i^exch; i.e., J_i is the total magnetic interaction in the combination of calculated J_i^dipolar and fitted J_i^exch parameters; this describes the interaction between all the neighboring metal centers.)

The low-lying exchange spectra were derived for all complexes using these exchange interactions, and by considering six KDs of each Dy(III) ion, and an additional doublet state of radical spin was considered for complexes 3 and 4.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the SI: crystallographic/refinement tables, dc/ac magnetic measurements and analyses, and ab initio computational figures and tables for complexes 1–4) have been included as part of the SI. See DOI: https://doi.org/10.1039/d5qi01477h.

CCDC 2471757–2471760 (1–4) contain the supplementary crystallographic data for this paper.^90a–d

Acknowledgements

We gratefully acknowledge support for this work by the National Science Foundation (CHE-1808779) and the Robert A. Welch Foundation (Grant A-1449). The SQUID magnetometer used was purchased with funds provided by the Texas A&M University Vice President of Research. We are grateful to the HPRC at Texas A&M for the computing resources. D. I. A. acknowledges finance support from the programme “MEDICUS” of the University of Patras. L. C.-S. thanks financial support received from the PT national funds (FCT/MECI, Fundação para a Ciência e Tecnologia/Ministério da Educação, Ciência e Inovação) through the project UID/50006 – Laboratório Associado para a Química Verde – Tecnologias e Processos Limpos.

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