Redox Modulation of Field-Induced Tetrathiafulvalene-Based Single-Molecule Magnets of Dysprosium

: The complexes [Dy 2 (tta) 6 ( H2SQ )] ( Dy-H 2 SQ ) and [Dy 2 (tta) 6 ( Q )] · 2CH 2 Cl 2 ( Dy-Q ) (tta − = 2-thenoyltriﬂuoroacetonate) were obtained from the coordination reaction of the Dy(tta) 3 · 2H 2 O units with the 2,2 (cid:48) -benzene-1,4-diylbis(6-hydroxy-4,7-di-tert-butyl-1,3-benzodithiol-2-ylium-5-olate ligand ( H 2 SQ ) and its oxidized form 2,2 (cid:48) -cyclohexa-2,5-diene-1,4-diylidenebis(4,7-di-tert-butyl-1,3-benzodithiole-5,6-dione ( Q ). The chemical oxidation of H 2 SQ in Q induced an increase in the coordination number from 7 to 8 around the Dy III ions and by consequence a modulation of the ﬁeld-induced Single-Molecule Magnet behavior. Computational results rationalized the magnetic properties of each of the dinuclear complexes.


Introduction
One of the most promising routes of research in molecular magnetism is the design of lanthanide coordination complexes [1][2][3][4]. Such compounds are able to display magnetic bistability even for mononuclear species [5] due to the intrinsic characteristics of the lanthanide ions [6]. Recently, the observation of memory effects at temperatures close to liquid nitrogen [7][8][9][10] led to the revival of the use of such coordination systems for potential applications in high-density data storage [11,12]. Other applications could be targeted such as switches and sensors [13] when the magnetic properties can be modulated by chemical transformations. The modulations of Single-Molecule Magnet (SMM) behavior can be achieved via crystal-to-crystal chemical transformations [14][15][16], solvato-switching [17][18][19], isomerization-switching [20][21][22][23][24] or redox-switching [25][26][27]. Indeed, the magnetic properties of the lanthanide ions can be easily changed by structural transformation since they are very sensitive to the symmetry and electronic distribution of their surroundings [28]. The literature shows that structural changes can be induced by the use of redox active ligands [25][26][27]. Thus, the combination of lanthanide ions and redox-active ligands seems to be a right way to design SMM with modulations of the magnetic behavior.
In the past, some of us already explored this strategy to design redox-active (chiral) SMMs [29,30] and luminescent SMMs [31].
of lanthanide ions and redox-active ligands seems to be a right way to design SMM with modulations of the magnetic behavior.
[Dy2(tta)6(H2SQ)] (Dy-H2SQ). Dy-H2SQ crystallized in the monoclinic space group C2/c ( Figure  1 and Figure S1, Table S1). The asymmetric unit is composed by one half of the [Dy2(tta)6(H2SQ)] dinuclear specie. Each of the two terminal coordination sites are occupied by one Ln(tta)3 unit. The coordination takes place through the C-O − group while the C-OH group remains free. Such monochelating coordination mode was already observed in the formation of the 1D compound {[Dy(hfac)3(H2SQ)]·2C6H14}n [35]. The confirmation of the bis mono-protonated form of the triad is given by the specific C-O7 (1.316 Å ) and C-O8 (1.347 Å ) distances as well as the torsion angle of 30.3(2)° between the 6-hydroxy-4,7-di-tert-butyl-1,3-benzodithiol and p-phenylene moieties that have previously been observed for the free ligand [33]. The non-planarity of the triad is an indication of a possible charge-separated structure (Scheme 1) instead of a bis radical semiquinone structure because it is possible only if the C39-C40 bond has a single character as observed (1.484 Å ) in the experimental X-ray structure of Dy-H2SQ compound. The X-ray structure further confirmed the charge-separated structure. Indeed, the 1,3-dithiole rings are close to being aromatic since the S1-C39 (1.691(9) Å ) and S2-C39 (1.667 (8)  In the present article, we propose to focus our attention on the H 2 SQ ligand and its oxidized form Q in the coordination reactions with the Dy(tta) 3 ·2H 2 O units. The replacement of the hfac − ancillary anions with tta − is known to change the magnetic performances of the target compound [29,[38][39][40]. Indeed, the resulting X-ray structures of the dinuclear complexes [Dy 2 (tta) 6 (H 2 SQ)] (Dy-H 2 SQ) and [Dy 2 (tta) 6 (Q)]·2CH 2 Cl 2 (Dy-Q) highlighted new coordination spheres around the Dy III compared to those observed for their hfac − parents of formula [Dy 2 (hfac) 6 (H 2 SQ)]·CH 2 Cl 2 and [Dy 2 (hfac) 6 (Q)]) [36] leading to the study of new magnetic properties. Then the modulation of the magnetic properties as consequence of the oxidation of the bridging triads was evaluated.
[Dy 2 (tta) 6 (H 2 SQ)] (Dy-H 2 SQ). Dy-H 2 SQ crystallized in the monoclinic space group C2/c (Figure 1 and Figure S1, Table S1). The asymmetric unit is composed by one half of the [Dy 2 (tta) 6 (H 2 SQ)] dinuclear specie. Each of the two terminal coordination sites are occupied by one Ln(tta) 3 unit. The coordination takes place through the C-O − group while the C-OH group remains free. Such mono-chelating coordination mode was already observed in the formation of the 1D compound {[Dy(hfac) 3 (H 2 SQ)]·2C 6 H 14 } n [35]. The confirmation of the bis mono-protonated form of the triad is given by the specific C-O7 (1.316 Å) and C-O8 (1.347 Å) distances as well as the torsion angle of 30.3(2) • between the 6-hydroxy-4,7-di-tert-butyl-1,3-benzodithiol and p-phenylene moieties that have previously been observed for the free ligand [33]. The non-planarity of the triad is an indication of a possible charge-separated structure (Scheme 1) instead of a bis radical semiquinone structure because it is possible only if the C39-C40 bond has a single character as observed (1.484 Å) in the experimental X-ray structure of Dy-H 2 SQ compound. The X-ray structure further confirmed the charge-separated structure. Indeed, the 1,3-dithiole rings are close to being aromatic since the S1-C39 (1.691(9) Å) and S2-C39 (1.667(8) Å) are similar with those for tetrathiafulvanene (TTF) dications (1.670-1.690 Å). In comparison, such chemical bonds are longer in neutral TTF (1.730-1.760 Å) [41][42][43]. The typical o-quinone bond lengths are different compared to those in the terminal six-membered rings in bridging ligand in Dy-H 2 SQ. Thus, each Dy III ion is surrounded by seven oxygen atoms coming from the three tta − anions and the monochelating H 2 SQ ligand, which is a quite unusual coordination polyhedron for trivalent lanthanide. The increase in steric hindrance replacing the hfac − anions with tta − ones led to an unusual decrease in the coordination number from 8 to 7.
ligand in Dy-H2SQ. Thus, each Dy III ion is surrounded by seven oxygen atoms coming from the three tta − anions and the monochelating H2SQ ligand, which is a quite unusual coordination polyhedron for trivalent lanthanide. The increase in steric hindrance replacing the hfac − anions with tta − ones led to an unusual decrease in the coordination number from 8 to 7. The average Dy-O bond length is 2.295 Å but there is a significant difference between the Dy-Otta (2.309 Å ) and Dy-O7 (2.208 Å ) distances.
The crystal packing reveals the formation of an organic sub-network of H2SQ triads along the c axis ( Figure 2). The stabilization of such a sub-network is possible thanks to π-π interactions between the 1,3-benzodithiol and S2⋯S4 contacts (3.788 Å ) between the 1,3-benzodithiol and tta − anions ( Figure  2). The Dy-Dy intramolecular distance is 22.233 Å while the shortest Dy-Dy intermolecular distance is 10.217 Å . [Dy2(tta)6(Q)]·2CH2Cl2 (Dy-Q). Dy-Q crystallized in the monoclinic space group P21/c ( Figure 1 and Figure S2, Table S1). The asymmetric unit is composed by one half of the [Dy2(tta)6(Q)] dinuclear species and one dichloromethane molecule of crystallization. The two quinone coordination sites are occupied by a Ln(tta)3 unit with a bischelating mode. The oxidation of the triad in Q is confirmed by the double character of the C=O7 (1.246 Å ) and C=O8 (1.243 Å ) chemical bonds, which are shorter than the ones in the H2SQ triad. It is also worth noting the decreasing of the torsion angle (9.4(1)°) between the central six-membered ring and bicyclic planes because of the increasing of the aromaticity character of the ligand after oxidation. It was established previously that such an oxidized form cannot be isolated in solid-state due to its instability [33]. Thus, one could conclude that the coordination of both electron withdrawing Dy(tta)3 units led to an energy stabilization of the Q triad. The two Dy III ions are surrounded by eight oxygen atoms coming from the three tta − anions and the bischelating Q ligand. The average Dy-Otta and Dy-OQ are, respectively, equal to 2.327 Å and 2.413 Å , making the average Dy-O bond length (2.349 Å ) longer than for Dy-H2SQ. Such observations can be explained by two reasons: (i) the difference of electronic effect between H2SQ vs. Q i.e., the charge The average Dy-O bond length is 2.295 Å but there is a significant difference between the Dy-O tta (2.309 Å) and Dy-O7 (2.208 Å) distances.
The crystal packing reveals the formation of an organic sub-network of H 2 SQ triads along the c axis ( Figure 2). The stabilization of such a sub-network is possible thanks to π-π interactions between the 1,3-benzodithiol and S2· · · S4 contacts (3.788 Å) between the 1,3-benzodithiol and tta − anions ( Figure 2). The Dy-Dy intramolecular distance is 22.233 Å while the shortest Dy-Dy intermolecular distance is 10.217 Å.
ligand in Dy-H2SQ. Thus, each Dy III ion is surrounded by seven oxygen atoms coming from the three tta − anions and the monochelating H2SQ ligand, which is a quite unusual coordination polyhedron for trivalent lanthanide. The increase in steric hindrance replacing the hfac − anions with tta − ones led to an unusual decrease in the coordination number from 8 to 7. The average Dy-O bond length is 2.295 Å but there is a significant difference between the Dy-Otta (2.309 Å ) and Dy-O7 (2.208 Å ) distances.
The crystal packing reveals the formation of an organic sub-network of H2SQ triads along the c axis ( Figure 2). The stabilization of such a sub-network is possible thanks to π-π interactions between the 1,3-benzodithiol and S2⋯S4 contacts (3.788 Å ) between the 1,3-benzodithiol and tta − anions ( Figure  2). The Dy-Dy intramolecular distance is 22.233 Å while the shortest Dy-Dy intermolecular distance is 10.217 Å . [Dy2(tta)6(Q)]·2CH2Cl2 (Dy-Q). Dy-Q crystallized in the monoclinic space group P21/c ( Figure 1 and Figure S2, Table S1). The asymmetric unit is composed by one half of the [Dy2(tta)6(Q)] dinuclear species and one dichloromethane molecule of crystallization. The two quinone coordination sites are occupied by a Ln(tta)3 unit with a bischelating mode. The oxidation of the triad in Q is confirmed by the double character of the C=O7 (1.246 Å ) and C=O8 (1.243 Å ) chemical bonds, which are shorter than the ones in the H2SQ triad. It is also worth noting the decreasing of the torsion angle (9.4(1)°) between the central six-membered ring and bicyclic planes because of the increasing of the aromaticity character of the ligand after oxidation. It was established previously that such an oxidized form cannot be isolated in solid-state due to its instability [33]. Thus, one could conclude that the coordination of both electron withdrawing Dy(tta)3 units led to an energy stabilization of the Q triad. The two Dy III ions are surrounded by eight oxygen atoms coming from the three tta − anions and the bischelating Q ligand. The average Dy-Otta and Dy-OQ are, respectively, equal to 2.327 Å and 2.413 Å , making the average Dy-O bond length (2.349 Å ) longer than for Dy-H2SQ. Such observations can be explained by two reasons: (i) the difference of electronic effect between H2SQ vs. Q i.e., the charge [Dy 2 (tta) 6 (Q)]·2CH 2 Cl 2 (Dy-Q). Dy-Q crystallized in the monoclinic space group P2 1 /c ( Figure 1 and Figure S2, Table S1). The asymmetric unit is composed by one half of the [Dy 2 (tta) 6 (Q)] dinuclear species and one dichloromethane molecule of crystallization. The two quinone coordination sites are occupied by a Ln(tta) 3 unit with a bischelating mode. The oxidation of the triad in Q is confirmed by the double character of the C=O7 (1.246 Å) and C=O8 (1.243 Å) chemical bonds, which are shorter than the ones in the H 2 SQ triad. It is also worth noting the decreasing of the torsion angle (9.4(1) • ) between the central six-membered ring and bicyclic planes because of the increasing of the aromaticity character of the ligand after oxidation. It was established previously that such an oxidized form cannot be isolated in solid-state due to its instability [33]. Thus, one could conclude that the coordination of both electron withdrawing Dy(tta) 3 units led to an energy stabilization of the Q triad. The two Dy III ions are surrounded by eight oxygen atoms coming from the three tta − anions and the bischelating Q ligand. The average Dy-O tta and Dy-O Q are, respectively, equal to 2.327 Å and 2.413 Å, making the average Dy-O bond length (2.349 Å) longer than for Dy-H 2 SQ. Such observations can be explained by two reasons: (i) the difference of electronic effect between H 2 SQ vs. Q i.e., the charge carried by the coordination sites of H 2 SQ is more negative than those for Q and (ii) the seven-coordination in Dy-H 2 SQ vs. eight-coordination in Dy-Q. Once more, the replacement of hfac − with tta − anions decreased the coordination number from 9 to 8.
Consequently, the oxidation of the triad led to drastic changes in the coordination number and symmetry of the lanthanide surroundings and one could anticipate different magnetic behaviors between the two Dy-H 2 SQ and Dy-Q dinuclear complexes.
Magnetochemistry 2020, 6, x FOR PEER REVIEW 4 of 13 carried by the coordination sites of H2SQ is more negative than those for Q and (ii) the sevencoordination in Dy-H2SQ vs. eight-coordination in Dy-Q. Once more, the replacement of hfac − with tta − anions decreased the coordination number from 9 to 8. Consequently, the oxidation of the triad led to drastic changes in the coordination number and symmetry of the lanthanide surroundings and one could anticipate different magnetic behaviors between the two Dy-H2SQ and Dy-Q dinuclear complexes.

Static Magnetic Measurements
The dc magnetic properties of Dy-H2SQ and Dy-Q were studied measuring the temperature dependence of the magnetic susceptibility. The MT(T) curves are depicted in Figure 4.

Static Magnetic Measurements
The dc magnetic properties of Dy-H 2 SQ and Dy-Q were studied measuring the temperature dependence of the magnetic susceptibility. The M T(T) curves are depicted in Figure 4. carried by the coordination sites of H2SQ is more negative than those for Q and (ii) the sevencoordination in Dy-H2SQ vs. eight-coordination in Dy-Q. Once more, the replacement of hfac − with tta − anions decreased the coordination number from 9 to 8. Consequently, the oxidation of the triad led to drastic changes in the coordination number and symmetry of the lanthanide surroundings and one could anticipate different magnetic behaviors between the two Dy-H2SQ and Dy-Q dinuclear complexes.

Static Magnetic Measurements
The dc magnetic properties of Dy-H2SQ and Dy-Q were studied measuring the temperature dependence of the magnetic susceptibility. The MT(T) curves are depicted in Figure 4.

Dynamic Magnetic Measurements
The dynamic magnetic properties were studied, measuring the molar ac magnetic susceptibility (χ M ) for both compounds Dy-H 2 SQ and Dy-Q. An out-of-phase signal (χ M ") was detected at high frequency in zero magnetic field but the maxima are localized out of the frequency range 1-1000 Hz for both Dy-Q and Dy-H 2 SQ (Figure 5a, Figures S3 and S4).
Magnetochemistry 2020, 6, x FOR PEER REVIEW 5 of 13 The 27.73 cm 3 ·K·mol −1 and 27.81 cm 3 ·K·mol −1 room temperature values for Dy-H2SQ and Dy-Q compounds are close to the expected value considering two isolated Dy III ions ( 6 H15/2 ground state multiplet) (28.34 cm 3 ·K·mol −1 ) [44]. MT products decrease monotonically down to 20.82 cm 3 ·K·mol −1 for Dy-H2SQ and 20.12 cm 3 ·K·mol −1 for Dy-Q when decreasing the temperature. Such behavior is attributed to the thermal depopulation of the MJ states. The expected saturated value of 20 μB for the field dependence of the magnetization measured at 2.0 K for both dinuclear compounds are not reached since at 50 kOe, Dy-H2SQ and Dy-Q exhibited respective experimental values of 10.03 μB and 10.40 μB, highlighting the magnetic anisotropy of the systems [44].

Dynamic Magnetic Measurements
The dynamic magnetic properties were studied, measuring the molar ac magnetic susceptibility (χM) for both compounds Dy-H2SQ and Dy-Q. An out-of-phase signal (χM″) was detected at high frequency in zero magnetic field but the maxima are localized out of the frequency range 1-1000 Hz for both Dy-Q and Dy-H2SQ (Figure 5a, Figures S3 and S4). The most common reason for the fast magnetic relaxation is the existence of quantum tunneling of the magnetization (QTM). The application of a magnetic dc field is a well-known method to cancel the QTM. The magnetic susceptibility was then measured under various applied magnetic fields (Figure 5a, Figures S3 and S4). For both compounds, the application of a small magnetic field led to a shift of the out-of-phase component of the magnetic susceptibility within the experimental windows and the magnetic field value of 1200 Oe was chosen as a good compromise between relaxation time and intensity for Dy-H2SQ ( Figure S4) and the optimal magnetic field for Dy-Q (Figure 5a) as highlighted by the field dependence of the log(τ) (Figures S5 and S6). Under such an applied field, Dy-H2SQ highlighted a frequency dependence of the out-of-phase signal of the susceptibility (Figures S7 and S8). Unfortunately the χ″M signal is very broad, ranging from 100 to 10,000 Hz between 2 and 15 K, and extraction of the relaxation times for this compound using the extended Debye model failed. Under the same applied field of 1200 Oe, Dy-Q highlighted a frequency dependence of the magnetic susceptibility (Figure 5b and Figure S7), which can be analyzed in the framework of the extended Debye model [46,47]. The extended Debye model was applied to fit simultaneously the experimental variations of χM′ and χM″ with the frequency ν of the oscillating field ( 2    ) ( Figure S9). The temperature dependence of the relaxation time is extracted and depicted in Figure 5c (Table S2). A large fraction of the sample shows slow relaxation of the magnetization as depicted by the normalized Argand ( Figure S10). The relaxation time of the magnetization (τ) follows two thermally dependent processes of relaxation: The most common reason for the fast magnetic relaxation is the existence of quantum tunneling of the magnetization (QTM). The application of a magnetic dc field is a well-known method to cancel the QTM. The magnetic susceptibility was then measured under various applied magnetic fields (Figure 5a, Figures S3 and S4). For both compounds, the application of a small magnetic field led to a shift of the out-of-phase component of the magnetic susceptibility within the experimental windows and the magnetic field value of 1200 Oe was chosen as a good compromise between relaxation time and intensity for Dy-H 2 SQ ( Figure S4) and the optimal magnetic field for Dy-Q (Figure 5a) as highlighted by the field dependence of the log(τ) (Figures S5 and S6). Under such an applied field, Dy-H 2 SQ highlighted a frequency dependence of the out-of-phase signal of the susceptibility (Figures S7 and  S8). Unfortunately the χ" M signal is very broad, ranging from 100 to 10,000 Hz between 2 and 15 K, and extraction of the relaxation times for this compound using the extended Debye model failed. Under the same applied field of 1200 Oe, Dy-Q highlighted a frequency dependence of the magnetic susceptibility (Figure 5b and Figure S7), which can be analyzed in the framework of the extended Debye model [46,47]. The extended Debye model was applied to fit simultaneously the experimental variations of χ M and χ M " with the frequency ν of the oscillating field (ω = 2πν) ( Figure  S9). The temperature dependence of the relaxation time is extracted and depicted in Figure 5c (Table  S2). A large fraction of the sample shows slow relaxation of the magnetization as depicted by the normalized Argand ( Figure S10). The relaxation time of the magnetization (τ) follows two thermally dependent processes of relaxation: The best fit was obtained with τ 0 = 1.9(7) × 10 −7 s and ∆ = 18.4(2) cm −1 , and C = 289(93) s −1 K −n and n = 1.88 (39) (Figure 5c). The expected n value for Kramers ions should be 9 [48] but the presence of both acoustic and optical phonons could lead to lower values between 2 and 7 [49][50][51] or even lower for the crystalline phase of Dy III coordination complexes [7][8][9][10]52].
As expected from the drastic structural changes for the Dy III coordination spheres after oxidation of the bridging ligand, the dynamic magnetic behaviors are also strongly affected. In fact the out-of-phase signal became narrower and the maximum of the χ M " at 2 K was shifted from 1000 Hz to 125 Hz after oxidation. In other words, the oxidation of the bridging triad led to an enhancement of the SMM performances. It is worth noting that a reverse trend was observed for the parent compounds based on the Dy(hfac) 3 units [36]. For the latter analogues, the strong degradation of the magnetic performances after oxidation of the bridging triad was imputed to both change of coordination number from 8 to 9 and the strong variation of intermolecular dipolar magnetic interaction because of the presence of hydrogen bond in the oxidized compound leading to a shortening of the intermolecular Dy-Dy distance from 9.962 Å to 6.071 Å. For Dy-H 2 SQ and Dy-Q, the role of the intermolecular dipolar interactions cannot be put aside but their change of intensity are expected to be much weaker than for their Dy(hfac) 3 based-parents since the intermolecular Dy-Dy distances remain very long (10.217 Å and 10.099 Å). In terms of magnetic performances, the following trend was observed at 2 K under an applied field of 1200 Oe: Dy-H 2 SQ (1000 Hz) < Dy-Q (125 Hz) < [Dy 2 (hfac) 6 (H 2 O) 2 (Q)] (25 Hz) < [Dy 2 (hfac) 6 (H 2 SQ)]·CH 2 Cl 2 (0.04 Hz). One could conclude that the Dy(hfac) 3 analogues displayed better dynamic magnetic properties than the compounds involving the Dy(tta) 3 units and the magnetic modulation is more efficient for [Dy 2 (hfac) 6 (H 2 SQ)]·CH 2 Cl 2 and [Dy 2 (hfac) 6 (H 2 O) 2 (Q)] than for Dy-H 2 SQ and Dy-Q.

Ab Initio Calculations
State-Averaged Complete Active Space Self-Consistent Field approach with restricted-activespace-state-interaction method (SA-CASSCF/RASSI-SO) calculations were carried out for the two dinuclear complexes Dy-H 2 SQ and Dy-Q to rationalize the observed magnetic properties. Since the two dinuclear complexes are centrosymmetric, only half of the complex, i.e., one metal center, was taken into account. The experimental χ M T vs. T and M vs. H curves (Figure 4) are fairly well reproduced by the ab initio calculations. The inconsistence between experimental χ M T product and calculations at low temperature could be due to the presence of antiferromagnetic dipolar interaction, which has not been taken into account in the calculations. The Dy ion in Dy-H 2 SQ presents a strongly mixed ground state (34% M J = | ± 13/2>, 25% M J = | ± 15/2>, 15% M J = | ± 11/2> and 10% M J = | ± 7/2>, Table S3) defined by a g-tensor with a main component g Z = 15.08 and exhibiting non-negligible transversal components with g X = 0.11, g Y = 1.10 confirming the low anisotropy character of the ground state (for a pure M J = | ± 15/2 > ground state, the fully axial, Ising-type, g-tensor expected possess g X = g Y = 0.0 and g Z = 20.0) and the presence of efficient QTM at zero-applied magnetic field. After oxidation of the H 2 SQ triad in the Q one, the change of the seven-coordination sphere into the eight-coordination sphere around the Dy III center induced drastic changes in the electronic properties since an almost Ising ground state was now calculated for the Dy in Dy-Q (90% M J = | ± 15/2>, Table  S4). The transversal components of the magnetic anisotropy tensor are still present (g X = 0.05, g Y = 0.11), justifying the existence of QTM, but they are much weaker than those for Dy-H 2 SQ. At this point, the difference of relaxation time below 4 K can be explained by the difference of magnetic anisotropy generated by the seven and eight coordination sphere.
The main component of the ground state g-tensor of the Dy III centers for each complex is represented in Figure 6. For both systems, the main magnetic component appears perpendicular to the plane containing the reduced protonated form of the coordinating moiety (for Dy-H 2 SQ, left part of the Figure 6) and the quinone moiety (for Dy-Q, right part of the Figure 6) i.e., the most charged direction as expected for an oblate ion [4]. The transversal magnetic moments between the MJ levels for the Kramers ions of each complex have been computed in order to give more insights into the relaxation mechanisms (Figure 7). A major difference between the two compounds is the large quantum-tunneling elements (0.20 μB and 0.26 μB for the ground and first excited states, respectively) for Dy-H2SQ while Dy-Q displays much weaker QTM values. These differences, which are directly related with the transversal components of the anisotropy tensors, are in the trend of the experimental results with a faster relaxation of the magnetization for Dy-H2SQ than for Dy-Q. The difference between the calculated energy barrier (Δ = 80 cm −1 ) and the experimental barrier (Δ = 18.4 cm −1 ) can be explained by operating an under-barrier relaxation mechanism such as the Raman process [53][54][55][56].

Synthesis General Procedures and Materials
The precursor Dy(tta)3·2H2O (tta − = 2-thenoyltrifluoroacetonate anion) [57] and the 2,2′-benzene-1,4-diylbis(6-hydroxy-4,7-di-tert-butyl-1,3-benzodithiol-2-ylium-5-olate ligand [33] (H2SQ) were synthesized following previously reported methods. All other reagents were commercially available The transversal magnetic moments between the M J levels for the Kramers ions of each complex have been computed in order to give more insights into the relaxation mechanisms (Figure 7). A major difference between the two compounds is the large quantum-tunneling elements (0.20 µB and 0.26 µB for the ground and first excited states, respectively) for Dy-H 2 SQ while Dy-Q displays much weaker QTM values. These differences, which are directly related with the transversal components of the anisotropy tensors, are in the trend of the experimental results with a faster relaxation of the magnetization for Dy-H 2 SQ than for Dy-Q. The difference between the calculated energy barrier (∆ = 80 cm −1 ) and the experimental barrier (∆ = 18.4 cm −1 ) can be explained by operating an under-barrier relaxation mechanism such as the Raman process [53][54][55][56]. The transversal magnetic moments between the MJ levels for the Kramers ions of each complex have been computed in order to give more insights into the relaxation mechanisms (Figure 7). A major difference between the two compounds is the large quantum-tunneling elements (0.20 μB and 0.26 μB for the ground and first excited states, respectively) for Dy-H2SQ while Dy-Q displays much weaker QTM values. These differences, which are directly related with the transversal components of the anisotropy tensors, are in the trend of the experimental results with a faster relaxation of the magnetization for Dy-H2SQ than for Dy-Q. The difference between the calculated energy barrier (Δ = 80 cm −1 ) and the experimental barrier (Δ = 18.4 cm −1 ) can be explained by operating an under-barrier relaxation mechanism such as the Raman process [53][54][55][56].

Crystallography
Single crystals of Dy-H 2 SQ and Dy-Q were mounted on a APEXIII D8 VENTURE Bruker-AXS diffractometer for data collection (MoK α radiation source, λ = 0.71073 Å), from the Diffractometric center (CDIFX), University of Rennes 1, France (Table S1). Structures were solved with a direct method using the SHELXT program [58] and refined with a full matrix least-squares method on F 2 using the SHELXL-14/7 program [59]. The SQUEEZE procedure of PLATON [60] was performed for Dy-H 2 SQ because it contains large solvent accessible voids in which residual peaks of diffraction were observed. The CCDC number is 1898867 and 1898866 for compounds Dy-H 2 SQ and Dy-Q, respectively.

Physical Measurements
The elemental analyses of the compounds were performed at the Centre Régional de Mesures Physiques de l'Ouest, Rennes. The static susceptibility measurements were performed on solid polycrystalline samples with a Quantum Design MPMS-XL SQUID magnetometer. Magnetic field values of 0.2 kOe, 2 kOe and 10 kOe were, respectively, applied for the temperature range of 2-20 K, 20-80 K and 80-300 K. These measurements were realized from immobilized selected and crunched single crystals and they were all corrected for the diamagnetic contribution, as calculated with Pascal's constants. The ac magnetic susceptibility measurements were performed on both a Quantum Design MPMS-XL SQUID magnetometer (1-1000 Hz frequency range) and a Quantum Design PPMS (10-10,000 Hz frequency range) system equipped with an ac/dc probe.

Computational Details
The atomic positions were extracted from the X-ray diffraction crystal structures of the Dy-H 2 SQ and Dy-Q compounds. The two Dy III magnetic centers were equally treated since the dinuclear complexes are centrosymmetric.
The State-Averaged Complete Active Space Self-Consistent Field approach with the restricted-active-space-state-interaction method (SA-CASSCF/RASSI-SO), as implemented in the MOLCAS quantum-chemistry package (version 8.0), was used to perform all ab-initio calculations [61]. The relativistic effects were treated in two steps on the basis of the Douglas-Kroll Hamiltonian. The CASSCF wavefunctions and energies were determined from the inclusion of the scalar terms in the basis-set generation [62]. Spin-orbit coupling was then added within the RASSI-SO method, which mixes the calculated CASSCF wavefunctions [63,64]. The resulting spin-orbit wavefunctions and energies were used to compute the magnetic properties and g-tensors of the ground state multiplet following the pseudospin S = 1/2 formalism, as implemented in the SINGLE-ANISO routine [55,65]. In order to save disk space and to accelerate the calculations, Cholesky decomposition of the bielectronic integrals was employed [66].
The active space considered in the calculations consisted of the nine 4f electrons of the Dy(III) ion, spanning the seven 4f orbitals; that is, CAS(9,7)SCF. State-averaged CASSCF calculations were performed for all of the sextets (21 roots), all of the quadruplets (224 roots) and 300 out of the 490 doublets of the Dy III ion. Twenty-one sextets, 128 quadruplets and 107 doublets were mixed through spin-orbit coupling in RASSI-SO.
Supplementary Materials: The following are available online at http://www.mdpi.com/2312-7481/6/3/34/s1, Figure S1. ORTEP view of Dy-H 2 SQ. Thermal ellipsoids are drawn at 30% probability. Hydrogen atoms are omitted for clarity; Figure S2. ORTEP view of Dy-Q. Thermal ellipsoids are drawn at 30% probability. Hydrogen atoms and solvent molecules of crystallization are omitted for clarity; Figure S3. (left) Frequency dependence of χ M between 0 and 3000 Oe for Dy-H 2 SQ at 2 K, (b) Frequency dependence of χ M between 0 and 1600 Oe for Dy-Q at 2 K.; Figure S4. Frequency dependence of χ M " between 0 and 3000 Oe for Dy-H 2 SQ at 2K; Figure S5. Representation of the field-dependence of the relaxation time of the magnetization for Dy-H 2 SQ at 2 K.; Figure S6. Representation of the field-dependence of the relaxation time of the magnetization for Dy-Q at 2 K.; Figure S7. Frequency dependence of χ M between 2 and 15 K at 1200 Oe for Dy-H 2 SQ (left) and Dy-Q (right); Figure S8. Frequency dependence of χ M " between 2 and 15 K for Dy-H 2 SQ at 1200 Oe; Figure S9. Frequency dependence of the in-phase (χ M ) and out-of-phase (χ M ") components of the ac susceptibility measured on powder at 4 K and 1200 Oe with the best fitted curves (red lines) for Dy-Q; Figure S10. Normalized Argand plot for Dy-Q between 2 and 5 K; Figure S8. Frequency dependence of the in-phase (χ M ) and out-of-phase (χ M ") components of the ac susceptibility measured on powder at 4 K and 1200 Oe with the best fitted curves (red lines) for Dy-Q. Table S1: X-ray crystallographic data of Dy-H 2 SQ and Dy-Q; Table S2: Best fitted parameters (χ T , χ S , τ and α) with the extended Debye model Dy-Q at 1200 Oe in the temperature range 2-5.5 K; Table S3: Computed energies, g-tensor and wavefunction composition of the ground state doublets in the effective spin 1 2 model for Dy-H 2 SQ ; Table S4: Computed energies, g-tensor and wavefunction composition of the ground state doublets in the effective spin  Acknowledgments: B.L.G. and V.M. thank the French GENCI/IDRIS-CINES center for high-performance computing resources. V.K. and V.C. thank the "Analytical Center IOMC RAS". S.T. and L.K. thank the Algerian PNE program for the financial support during the stay in the French ISCR laboratory.

Conflicts of Interest:
The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.

Abbreviations
The following abbreviations are used in this manuscript: