Athanassios K Boudalis
email: bountalis@unistra.fr

In one fell sweep: modeling exchange, hyperfine and dipolar interactions from EPR spectra of copper(II) spin triangles

Keywords: EPR spectroscopy, spin triangles, dipolar interactions, hyperfine interactions, spin Hamiltonian

The weak intramolecular magnetic interactions within a series of Cu II 3 complexes based on the trinucleating 2,4,6tris(di-2-pyridylamino)-1,3,5-triazine (dipyatriz) ligand were investigated by EPR spectroscopy. X-and Q-band EPR spectroscopy in powders and frozen solutions were recorded and the Q-band spectra were interpreted by a multispin Hamiltonian model comprising exchange, dipolar and hyperfine interactions. The described methodology is suitable for the elucidation of weak intramolecular interactions which are not amenable to analysis by SQUID magnetometry.

Introduction

Spin triangles constitute a "rediscovered" class of metal complexes, [START_REF] Boudalis | Half-Integer Spin Triangles: Old Dogs, New Tricks[END_REF] whose magnetic properties have rendered them interesting as potential magnetoelectric materials, [START_REF] Boudalis | First Demonstration of Magnetoelectric Coupling in a Polynuclear Molecular Nanomagnet: Single-Crystal EPR Studies of [Fe 3 O(O 2 CPh) 6 (Py) 3 ]ClO 4 ⋅py under Static Electric Fields[END_REF][START_REF] Robert | Polyanisotropic Magnetoelectric Coupling in an Electrically Controlled Molecular Spin Qubit[END_REF][START_REF] Liu | Electric Field Control of Spins in Molecular Magnets[END_REF][START_REF] Kintzel | Spin-Electric Coupling in a Cobalt(II)-Based Spin Triangle Revealed by Electric-Field-Modulated Electron Spin Resonance Spectroscopy[END_REF][START_REF] Lewkowitz | Direct Observation of Electric Field-Induced Magnetism in a Molecular Magnet[END_REF] with a proposed use as electrically controlled and slow-decoherence spin-chirality qubits. [START_REF] Trif | Spin-Electric Coupling in Molecular Magnets[END_REF][START_REF] Trif | Spin Electric Effects in Molecular Antiferromagnets[END_REF][START_REF] Troiani | Hyperfine-Induced Decoherence in Triangular Spin-Cluster Qubits[END_REF][START_REF] Stepanenko | Field-Dependent Superradiant Quantum Phase Transition of Molecular Magnets in Microwave Cavities[END_REF] Our overall ability to design and implement such devices is predicated on our precise understanding of their magnetic structures, down to the finest details. Traditionally, the general strategy implemented to tackle this task is the same as with most other molecular magnetic materials: magnetometric techniques (e.g. SQUID magnetometry) are first used to elucidate the gross magnetic structure governed by isotropic (Heisenberg-Dirac-van Vleck) interactions and eventually antisymmetric (Dzyaloshinskii-Moriya) interactions, both of superexchange orings. Finer terms, such as zero-field splittings (zfs) or anisotropic interactions, are not very reliably assessed by magnetometric techniques, necessitating the use of spectroscopic techniques, the most prominent of which is Electron Paramagnetic Resonance (EPR) spectroscopy.

The use of EPR spectroscopy has its own limitations, e.g. when dealing with non-Kramers systems and very big zfs terms. While these systems are addressable by High-Frequency (W-band frequencies and above) or THz EPR, the availability of such experiments can be a limiting factor to theirt use. Classical EPR, however, i.e. at Qband frequencies and below, can yield very precise information on weaker terms, such as hyperfine interactions. In addition, low-temperature studies can yield very informative data on the ground states of polynuclear complexes, which then can be used to verify the magnetometry-derived conclusions regarding exchange interactions. [START_REF] Bencini | EPR of Exchange Coupled Systems[END_REF] The above strategy works very nicely in cases where J >> k B T, A, i.e. at the strong exchange limit. When, however, exchange interactions are very weak with respect to the thermal energy and comparable to eventual hyperfine interactions, errors in magnetometric techniques (weighing, diamagnetic corrections) render their use problematic. The large diamagnetic content of biological magnetic systems, can give rise to such problems even for strong exchange interactions. In such cases, EPR spectroscopy can often yield useful information. However, a careful construction of the model is then required, to include any term that might influence the EPR spectrum. These include not just isotropic interactions, but also the full description of the system symmetry that influences its anisotropic terms. These may include Dzyaloshinskii-Moriya interactions (DMI), dipolar interactions, anisotropic exchange and hyperfine interactions, taking proper care to model the various tensor orientations (e.g. g, A, etc) and vectors connecting the different spins.

In previous work we showed that it is possible to derive very accurate descriptions of the magnetic properties of trinuclar Cu II complexes [START_REF] Mathivathanan | Origin of Ferromagnetism and Magnetic Anisotropy in a Family of Copper(II) Triangles[END_REF] by properly accounting for the dipolar terms which induce a zfs in their quartet states. Such studies are not only applicable on single-crystal data, but also to those from randomly oriented samples (powders or frozen solutions). In those previous cases, hyperfine interactions were not considered, either because they were unresolved, or because they were very weak, respectively. Moreover, it was considered that their inclusion might render the problem computationally intractable; in the case of Cu II 3 , the Hilbert space would reach a dimension of (2S + 1) n ×(2I + 1) m = 512 for S = 1/2 (Cu II ), I = 3/2 (for 63/65 Cu), and for n = m = 3 electron and nuclear spins, further complicated by the need to calculate 2 3 = 8 possible isotopologues for the 63/65 Cu nuclei.

The renewed interest of spin triangles as spin-chirality qubits involves excitation of the "chiral transitions" between, not within, the low-lying spin doublets. Therefore, engineering the interdoublet energy gap Δ becomes a question of interest. For spin triangles with monatomic bridges (e.g. O 2-, OH -, RO -) this can be in the order of ~10 2 cm -1 for Cu II 3 triangles, ~10 1 cm -1 for Fe III 3 triangles and ~10 0 cm -1 for Cr III triangles, i.e. in the THz and FIR regimes. Large trinucleating ligands in place of monatomic ones impose larger interspin separations, allowing us to eventually modulate this energy and lower it within the GHz regime, which is more tractable by EPR instrumentation.

Ligand 2,4,6-tris(di-2-pyridylamino)-1,3,5-triazine (dipyatriz), has in the past been used to construct such molecular architectures. Its attractiveness in copper(II) chemistry lies in the fact that the axial ligands of copper(II) ions can be easily changed by proper choice of synthetic conditions, namely the relative ratios of CuCl 2 ⋅2H 2 O and Cu-ClO 4 ⋅6H 2 O starting materials. Exchanging neutral for anionic ligands can therefore be used to rationally modify the total charge of the molecule. Indeed, previously reported complexes include [Cu 3 (dipyatriz) 2 Cl 3 ](ClO 4 ) 3 (1) [START_REF] Barrios | Coordination Complexes Exhibiting Anion•••π Interactions: Synthesis, Structure, and Theoretical Studies[END_REF], [START_REF] Demeshko | 1,3,5-Triazine-Based Tricopper(Ii) Complexes: Structure and Magnetic Properties of Threefold-Symmetric Building Blocks[END_REF] and [Cu 3 (dipyatriz) 2 Cl 3 ]Cl 3 [START_REF] Kintzel | Spin-Electric Coupling in a Cobalt(II)-Based Spin Triangle Revealed by Electric-Field-Modulated Electron Spin Resonance Spectroscopy[END_REF] [START_REF] Chen | A Trinuclear Copper(II) Complex of 2,4,6-Tris(Di-2-Pyridylamine)-1,3,5-Triazine Shows Prominent DNA Cleavage Activity[END_REF], with electric charges of the molecules rationally modifiable from +3 to +6 without noticeably changing the structure of the metal core (though the +5 complex [Cu 3 (dipyatriz) 2 (H 2 O) 2 Cl](ClO 4 ) [START_REF] Kintzel | Spin-Electric Coupling in a Cobalt(II)-Based Spin Triangle Revealed by Electric-Field-Modulated Electron Spin Resonance Spectroscopy[END_REF] has not yet been reported, its synthesis should in principle be feasible through modification of the molecular ratios of CuCl 2 ⋅2H 2 O and Cu(ClO 4 ) 2 ⋅6H 2 O used for the new synthesis of complex 2 reported here). This feature constitutes a degree of freedom for the control of solubilities in desired solvents.

[Cu 3 (dipyatriz) 2 (H 2 O)Cl 2 ](ClO 4 ) 4 (2) [13], [Cu 3 (dipyatriz) 2 (H 2 O) 3 ](ClO 4 ) 6 (3) [14], [Cu 3 (dipyatriz) 2 Cl 3 ][CuCl 4 ]Cl (4)
This was therefore deemed a suitable system to construct spin triangles characterized by moderate to weak interactions, and use EPR spectroscopy to assess their magnetic structures far more accurately than it is possible with magnetometric techniques.

This work describes the modeling of the spin Hamiltonian parameters of a series of Cu II 3 spin triangles of similar structures (Figure 1) using continuous-wave (CW) EPR data at the X-and Q-bands. From a general perspective, these results outline a methodology to fully account for features of EPR spectra arising from exchange and dipolar interactions, by accurately describing the spatial arrangement of the tensorial and vectorial terms of the multispin Hamiltonian. Moreover, the specific results provide precise estimates of exchange interactions mediated by an extended organic superexchange pathway. Such precise estimates, quite difficult to come by via magnetometric methods, are valuable for the calibration of theoretical methods attempting to derive such exchange terms from first principles.

Figure 1. POV-Ray plot of the cation of 1 superposed to the molecular reference frame RM used in the analysis of its magnetic properties. This is a right-handed reference frame with its origin O at the center of an idealised equilateral triangle, with x || r12, and z normal to the triangle plane.

Results

In the original work [START_REF] Barrios | Coordination Complexes Exhibiting Anion•••π Interactions: Synthesis, Structure, and Theoretical Studies[END_REF] no magnetic studies were reported for 1. For the structurally related complex 4, SQUID magnetometry yielded antiferromagnetic interactions (J = +0.42 cm -1 ) with g iso = 2.04; these results, however, needed to also account for the Curie contribution of the [CuCl 4 ] 2-counteranion putting the derived values into question due to possible correlations. [START_REF] Demeshko | 1,3,5-Triazine-Based Tricopper(Ii) Complexes: Structure and Magnetic Properties of Threefold-Symmetric Building Blocks[END_REF] In related work, SQUID magnetometry of 3 also yielded AF interactions, though much weaker, i.e. J = 0.08 cm -1 (g iso = 2.07). [START_REF] Yuste | Low-Dimensional Copper(II) Complexes with the Trinucleating Ligand 2,4,6-Tris(Di-2-Pyridylamine)-1,3,5-Triazine: Synthesis, Crystal Structures, and Magnetic Properties †[END_REF] Preliminary EPR studies at the X-and Q-bands in the solid state (Figure 2) revealed largely unresolved spectra for 1 and 2. These exhibit clear low-field features which disappear upon dissolution. Thus, these might tentatively be attributed to half-field and third-field transitions due to intermolecular dipolar interactions. However, the complexity of simulating EPR spectral features stemming from intermolecular interactions precludes their confident assignment.

On the other hand, a fine and hyperfine structure are observed in the spectra of 3 both in the X-and the Qbands. At the same time, the low-field region (not shown) is completely devoid of any features. The factors influ-encing EPR spectra in the solid state are more complicated due to the extended intermolecular interactions, but a plausible explanation for the above observations is that the larger intermolecular distances between the hexacations of 3, must play a role in reducing dipolar broadenings in the solid state. Indeed, the shortest intermolecular Cu⋅⋅⋅Cu distances are 7.262, 8.829 and 9.686 Å for 1, 2 and 3, respectively. To better understand the magnetic properties of the three complexes, frozen solution studies were also carried out. In the X-band spectra (Figure 3, left), the hyperfine interactions of the A i|| component were partially resolved for 1 and 3, but not for 2. The g-anisotropy was predictably much less resolved for all three. Q-band spectra were then collected at 5 K in the hopes of better resolving the various contributions. Indeed, at that frequency, not only was the g-anisotropy resolved, but further details emerged (Figure 3, right). First, the perpendicular component of the anisotropy A i⊥ , was also resolved, whereas lateral weak absorptions appeared, which were assigned to intermultiplet (ΔS T = ±1) transitions.

These additional features of the Q-band spectra permitted their thorough analysis based on a more elaborate model. Although all three spectra demonstrated the same overall features, the most detailed analysis was carried out on the spectrum of 1 which exhibited the best S/N ratio. The selected model comprised an isosceles magnetic symmetry of the isotropic (Heisenberg-Dirac-van Vleck) interactions, dipolar interactions and hyperfine interactions. The full multispin Hamiltonian was:

( )

3 3 3 1 2 1 3 2 3 , 1 1 1 ˆˆˆˆˆˆˆˆˆT dip T T i ij j i i B i i i j i i H J J µ = = = ′ = ⋅ + ⋅ + ⋅ + + + ∑ ∑ ∑

S S S S S S S D S I AS B g S   

For the calculations, the fitted quantities were the average of the J and J' values and their difference, defined, respectively, as: J av = (2J + J')/3 and ΔJ = J -J' (whence it can be derived that J = (3J av + ΔJ)/3 and J' = (3J av -2ΔJ)/3). To avoid overparametrization, the g-and A-tensor elements for the three ions were taken as identical, as were the interspin distances. The g-tensor reference frames were fixed to idealized positions based on the crystal structure, characterized by Euler angles E g1 = [90°, 90°, -45°], E g2 = [30°, -90°, 135°] and E g3 = [-30°, 90°, -45°] with respect to the molecular frame (E RM = [0, 0, 0]). The A-tensors were initialized collinear to their respective gtensors (E Ai(0) = E gi ) and allowed to vary slightly around that position during the fitting process. To avoid overparametrization, this variation, Δ A , was common for all three hyperfine tensors (E Ai = E Ai(0) + Δ A ).

Preliminary fits were carried out with a model assuming two 63 Cu and one 65 Cu nucleus, which is very close to the natural abundances of the two nuclei (i.e. 69.17% and 30.83%, respectively). Simulations revealed that these were largely superimposable with the spectrum calculated assuming natural abundances on each site (Figure S1). Since, however, the simulation time rose by a factor of 8 in the latter case due to the calculation of the 2 3 possible isotopologues, this calculation was reserved for only the final fits and statistical analyses of the fitted variables (reported below).

The best-fit parameters to this model, along with their 95% confidence intervals thus determined, are: g i|| = 2.25707±0.00036, g i⊥ = 2.05853±0.00021, σ G = 2.31±0.80 mT pp , σ L = 2.85±0.22 mT pp , r ij = 8.22±0.11 Å, J av = 0.11217±0.00050 cm -1 , ΔJ = 0.0114±0.0018 cm -1 , A i|| = 502.94±8.42 MHz, A i⊥ = 52.0±13.2 MHz, Δ A = [-6.4±2.5°, 3.4±7.4°, 28.8486±0.0005°]. The fit is shown inFigure 4, along with the resonances calculated in the z-and xmolecular orientations of the magnetic field. The fitted tensor elements are shown in Figure 5.

The fitted transitions involve several intermultiplet ones, whose assignment is facilitated by the consideration of the low-field part of the Zeeman diagram (Figure (S2). Briefly, in spin triangles, the spin-spin couplings create magnetic levels whose description can be based on the intermediate spin quantum number S 23 (where Ŝ 23 = Ŝ 2 + Ŝ 3 ), the total spin quantum number S (where Ŝ = Ŝ 1 + Ŝ 23 ) and the quantum number M S of the projection of the total spin (= +S, +S -1,… , -S). In that scheme, S 23 allows us to distinguish between the two spin doublets (e.g., for S i = 1/2 systems, S 23 = 0 or 1). However, in the present case the two doublets are too closely packed and the resonances too numerous for a clear labeling of the states to be possible with the |S 23 , S, M S 〉 scheme. Instead the simplified scheme |S, M S 〉 is used in Figure 4.

Unsurprisingly, the confidence intervals indicate that the g-tensor elements are very well determined. Moreover, we also derive quite small confidence intervals for the average J value, whose magnitude closely tracks the positions of the lateral absorptions. The calculated distance is remarkably close to the crystallographically-determined distance average of 8.29 Å (from 8.28, 8.46 and 8.12 Å distances), thus validating the hypothesis of the point-dipole model. The values of the hyperfine interactions are also quite well determined, and yield reasonable values.

One remark is in order concerning the Euler angles of the local hyperfine tensors. The first two rotation angles which, respectively, define the angular deviations from the triangle dissector and the triangle plane, are predictably small and ill-defined. However, we derive a remarkably narrow confidence interval for the third angle, which defines rotations around the local z-axes. This is interpreted more as an artifact of the covariance matrix calculation rather than as a highly certain determination of that angle. While the fits did coherently converge to a significant rotation around the local z-axes, and while these are considered as bearing true physical meaning, the narrowness of the associated confidence interval is not considered to be quantitatively reliable.

A feature that was consistently difficult to reproduce was the line width of the lateral absorptions, with calculated spectra always yielding much sharper line shapes. Inclusion of antisymmetric (Dzyaloshinskii-Moriya) interactions did not improve the agreement with the experiments. A tentative interpretation is that this line shape is associated with distributions of the exchange terms. Indeed, given the relative flexibility of the molecular scaffold, it is plausible to assume the presence of several slightly different conformations of the molecules in solution. These should be associated with slightly distributed J av and ΔJ values which should contribute to this line broadening. A detailed analysis of magnetic exchange parameter distributions, would require the calculation of a series of EPR spectra, and would therefore be prohibitively time consuming due to the large Hilbert space of this problem. To validate the model used, and justify the number of terms employed, the effect of each of these terms was demonstrated by simulations shown in Figure 6. The most salient observation is the remarkable effect of the exchange terms on the spectral appearance, both in the central and on the lateral absorptions. Simulations considering only the dipolar contributions or a simple mononuclear paramagnetic species were far from the observed spectrum.

Moreover, it was shown that the dipolar term is also necessary to reproduce the finer details of the central absorption; indeed, neglecting the dipolar terms leads to simulations of visibly lower quality, presumably from the absence of the dipolar-induced zfs in the quartet state.

The least conspicuous effect is that of the ΔJ term (Heisenberg asymmetry), also reflected on the relatively larger confidence intervals of its fitted value. Indeed, inclusion of this term mainly affects the appearance of the lateral absorptions, particularly the low-field ones. Although small, however, the role of this term is not insignificant and indicates the power of EPR spectroscopy to detect small differences of already weak exchange terms; indeed, the fitted value of 0.0114 cm -1 or 343 MHz, is of the order of magnitude of the hyperfine terms.

The absolute values of the principal tensor elements of the pairwise dipolar interactions at those distances were 228, 104 and 99 MHz, yielding a total zfs with D dip = 74 MHz (0.0025 cm -1 ), when the local reference frames are taken into account. Given the relatively good quality of the Q-band spectrum of 2, fits were attempted based on the model used for 1, and using that best-fit solution as a point of departure. However, given the relatively poorer spectral quality, a simplification was made by considering collinear g i and A i local tensors. The best-fit parameters to this model, along with their 95% confidence intervals, are: g i|| = 2.25488±0.00061, g i⊥ = 2.06111±0.00025, σ G = 3.3±1.0 mT pp , σ L = 2.41±0.50 mT pp , r ij = 8.35±0.15 Å, J av = 0.11628±0.00073 cm -1 , ΔJ = 0.0150±0.0019 cm -1 , A i|| = 543±14 MHz, A i⊥ = 69.6±6.4 MHz. Δ A was fixed to [0, 0, 0]. The respective calculated spectrum is shown in Figure 7 (left).

Finally, similar fits were attempted for the powder room-temperature spectra of 3 (Figure 7, right)., whose fine structure made such fits feasible. It is suggested that the observation of this fine structure is probably due to the larger intermolecular separations in the solid state, which reduce dipolar broadenings. The previously determined parameters proved to be a suitable starting point for the fits to this spectrum However, the predictably poorer resolution of the hyperfine interactions, as well as some additional features in the lateral (intermultiplet) absorptions, add some uncertainty to these fits. Accordingly, these are treated as simulations and the results are given without a detailed statistical treatment. These are: g i|| = 2.230, g i⊥ = 2.061, σ G = 3.31 mT pp , σ L = 3.85 mT pp , r ij = 8.22 Å, J av = 0.078 cm -1 , ΔJ = 0.011 cm -1 , A i|| = 540.0 MHz, A i⊥ = 48.0 MHz. Δ A was fixed to [0, 0, 0].

Discussion and comparative analyses

This work demonstrates that EPR spectroscopy can be successfully used to address weak spin-spin interactions in relatively complicated polynuclear systems, thus providing an important complement to magnetometric studies. Indeed, the detailed EPR study of 1-3 allowed the estimation of very weak exchange interactions as well as dipolar couplings, to a level of confidence practically unattainable with magnetic susceptometry experiments. Notably, a single EPR experiment for each complex provided sufficient information for the determination of those interactions in parallel to hyperfine ones.

As far as the specific complexes of this study are concerned, these were shown to exhibit a close agreement in their magnetic properties (Table 1), in accordance to their very similar molecular structures. Regarding the exchange and hyperfine interactions, the rationalization of their precise magnitudes requires the use of theoretical models, which is beyond the scope of this work. However, regarding the larger line widths of 3, these may plausibly be attributed to remaining intermolecular dipolar interactions in the solid state which give rise to smaller but nonnegligible dipolar broadenings. [START_REF] Kortz | Structure and Magnetism of the Tetra-Copper(II)-Substituted Heteropolyanion [Cu 4 K 2 (H 2 O) 8 (α-AsW 9 O 33 ) 2 ] 8- †[END_REF] were simulated by a giant spin approach, with the exchange interactions determined independently by variable-temperature magnetic susceptometry. Subsequently, single-crystal studies of the latter complex were complemented by pulsed fieldsweep experiments for the same purpose [START_REF] Choi | Observation of a Half Step Magnetization in the { Cu 3 } -Type Triangular Spin Ring[END_REF][START_REF] Choi | Pulsed-Field Magnetization, Electron Spin Resonance, and Nuclear Spin-Lattice Relaxation in the { Cu 3 } Spin Triangle[END_REF]. Despite the clear presence of intermultiplet resonances in these latter spectra, these resonances were not simulated for the determination of exchange interactions.

Of relevance are also studies of the extensively explored polyoxovanadate system K 6 [V 15 As 6 O 42 (H 2 O)]⋅8H 2 O, or "V 15 ", whose precise determination of the spin-spin interactions has been a contentious issue. The metallic core of the molecule can be considered as three-layered, i.e. {V 6 -V 3 -V 6 }, with the top and bottom "V 6 " layers exhibiting strong antiferromagnetic interactions which quench their magnetizations. Thus the low-temperature magnetic properties of the molecule are usually treated as stemming from the weakly coupled triangular "V 3 " layer. [START_REF] Gatteschi | Layered Magnetic Structure of a Metal Cluster Ion[END_REF] It is of note that while extensive studies have been conducted employing an arsenal of techniques, such as various types of magnetometry [START_REF] Tarantul | High-Field Magnetization of V15 Cluster at Ultra-Low Temperatures: Importance of Antisymmetric Exchange and Its Precise Estimation[END_REF][START_REF] Tarantul | Static Magnetization of V 15 Cluster at Ultra-Low Temperatures: Precise Estimation of Antisymmetric Exchange[END_REF], EPR at various frequencies [START_REF] Vongtragool | High-Frequency Magnetic Spectroscopy on the Molecular Magnetic Cluster V 15[END_REF], inelastic neutron scattering [START_REF] Chaboussant | Mechanism of Ground-State Selection in the Frustrated Molecular Spin Cluster V 15[END_REF], heat capacity [START_REF] Fu | Low-Lying Magnetic Excitations and Magnetocaloric Effect of Molecular Magnet K 6 [V 15 As 6 O 42 (H 2 O)[END_REF] and NMR spectroscopy [START_REF] Furukawa | Local Spin Moment Configuration in the Frustrated s = 1 ∕ 2 Heisenberg Triangular Antiferromagnet V15 Determined by NMR[END_REF], there still remain ambiguities around the precise nature of the spin-spin interactions of this molecule. Application of the models described in this work should complement our understanding of this question.

Conclusions

Overall, the development of detailed models integrating exchange and dipolar interactions, can be very useful for the determination of very weak such interactions, and allow the full unlocking of the information contained in EPR spectra. Indeed, the broad availability of EPR simulation tools, such as Easyspin [START_REF] Stoll | a Comprehensive Software Package for Spectral Simulation and Analysis in EPR[END_REF] or Phi [START_REF] Chilton | A Powerful New Program for the Analysis of Anisotropic Monomeric and Exchange-Coupled Polynuclear d-and f-Block Complexes[END_REF], that consider arbitrary multispin Hamiltonians, makes the development of such models a tractable task, albeit not a routine one. Moreover, the increases in performance of computer processors over the past years have brought the unavoidable computational overhead of such models within the reach of even personal computers.

The combination of the above can allow the detailed description of the magnetic spectra of a large number of weakly interacting molecular or biological polynuclear systems, currently beyond the reach of magnetometric techniques. On the one hand, the new information gleaned from detailed treatment of EPR spectra should be particularly useful in refining first-principles theoretical models attempting to determine such interactions from known molecular structures; accurate determinations of weak exchange, would push these models to their limits and reveal avenues for their improvement. On the other hand this information would be helpful in structure elucidation of biological systems from their EPR signatures; structures of metalloenzyme active sites containing polymetallic weaklycoupled magnetic cores could be deduced in the absence of high-resolution crystal data.

In conclusion, the implementation of such detailed models should complement the understanding of multispin molecular or biological systems, even using powder/frozen solution EPR spectra.

Experimental

Syntheses

Dipyatriz. The synthesis was carried out according to the process described in the literature. [START_REF] Pang | Structures, and Electroluminescence of New Blue Luminescent Star-Shaped Compounds Based on 1,3,5-Triazine and 1,3,5-Trisubstituted Benzene[END_REF] Recrystallization of 4.4 g of the crude product was carried out by dissolving in 120 mL of warm CH 2 Cl 2 and precipitating by the addition of n-hexane. After filtration and drying, the yield was 2.2 g of pure ligand.

Complex 1. This was synthesized according to the process described in the literature using a stoichiometric reaction of the starting materials. [START_REF] Barrios | Coordination Complexes Exhibiting Anion•••π Interactions: Synthesis, Structure, and Theoretical Studies[END_REF] The blue powder that precipitated analyzed as 1⋅4.6H 2 O (0.903 g, 52% on ligand basis or metal basis) and slow evaporation of the filtrate yielded single crystals whose unit cell determination matched the published structure.

Complex 2. This was first reported [START_REF] Barrios | Coordination Complexes Exhibiting Anion•••π Interactions: Synthesis, Structure, and Theoretical Studies[END_REF] as an accidental product and its synthesis has now been rationalized. In particular, solid dipyatriz (0.214 g, 0.360 mmol) was added to a MeOH solution (110 mL) containing CuCl 2 ⋅2H 2 O (0.0460 g, 0.270 mmol) and Cu(ClO 4 ) 2 ⋅6H 2 O (0.100 g, 0.270 mmol). In the absence of full dissolution of the ligand, 35 mL of MeCN were added to the mixture, causing full dissolution in a few minutes and a deep blue solution. In three days, good parallelepiped crystals had formed, whose unit cell determination confirmed their identity. The yield was 37.3 mg (9%).

Complex 3. This was synthesized according to the reported procedure [START_REF] Yuste | Low-Dimensional Copper(II) Complexes with the Trinucleating Ligand 2,4,6-Tris(Di-2-Pyridylamine)-1,3,5-Triazine: Synthesis, Crystal Structures, and Magnetic Properties †[END_REF].

EPR spectroscopy CW EPR spectra were collected on an EMXplus spectrometer controlled by the Bruker Xenon software, with the magnetic applied by a Bruker BE25 electromagnet using a Bruker ER082(155/45)Z power supply.

For X-band experiments, the spectrometer was fitted with an EMX microX bridge and a Bruker ER4122SHQE cavity operating in the TE 011 mode. Low-temperature experiments were carried out using an ESR900 dynamic continuous flow cryostat and the temperature was regulated with an Oxford ITC4 servocontrol. For Q-band spectra, the spectrometer was fitted with an EMX premiumQ microwave bridge and an ER5106QTW microwave resonator operating in the TE 012 mode. For low-temperature experiments the resonator was fitted in an Oxford CF935 dynamic continuous flow cryostat and the temperature was regulated with an Oxford ITC503 servocontrol.

Fits to the EPR data and simulations were carried out with Easyspin v. 6.0 using custom-made routines. [START_REF] Stoll | a Comprehensive Software Package for Spectral Simulation and Analysis in EPR[END_REF] The EPR solutions of 1 (0.54 mM in MeOH for the X-band experiments and 1.34 mM in MeOH/MeCN 50:50 for the Q-band experiments), 2 (0.84 mM in MeCN) and 3 (0.40 mM in MeCN) were deoxygenated with freezepump-thaw cycles, flame-sealed under a helium atmosphere in the EPR tubes and stored in liquid nitrogen.

Figure 2 .

 2 Figure 2. Room-temperature powder spectra of 1-3 at the X-band (left) and at the Q-band (right). Only complex 3 shows a partially resolved fine and hyperfine structure.

Figure 3 .

 3 Figure 3. Frozen solution EPR spectra of complexes 1-3. Left: X-band spectra at the indicated temperatures. Right: Q-band spectra at 5 K.

Figure 4 .

 4 Figure 4. Top: CW EPR spectrum of a frozen solution (5 K) at the Q band (black lines) and best fit to the model described in the text. The bottom insets are in scale with respect to the x-axis and expanded only along the y-axis. The top inset is an expansion of the area around the g ~ 2.2 region indicated by the grey rectangle. Bottom: Zeeman diagrams and resonances at the z (green) and x (blue) orientations in the molecular reference frame. The Zeeman diagram was calculated for an isotopologue with three 63 Cu nuclei and assignments were facilitated by the low-field part of the diagram (Figure S2). The low-and high-field signals correspond to intermultiplet ΔMS = 1 transitions. Low-field signals are assigned to |S, MS〉 = |1/2, -1/2〉 → |3/2, +1/2〉 and |1/2, +1/2〉 → |3/2, +3/2〉 transitions, while high-field signals to |3/2, -3/2〉 → |1/2, -1/2〉 and |3/2, -1/2〉 → |1/2, +1/2〉 transitions.

Figure 5 .

 5 Figure 5. Molecular and local reference frames for interactions and tensors used in the spin Hamiltonian. The blue transparent ellipsoids indicate the anisotropy of the g and total anisotropy tensors. This latter derives purely from dipolar interactions.

Figure 6 .

 6 Figure 6. Effect of exchange terms to the calculated spectrum of 1. Neglecting any of the electronelectron interaction terms leads to spectra of visibly worse agreement to the experimental one.

Figure 7 .

 7 Figure 7. Left: Q-band spectrum from a frozen solution of 2 at 5 K and best fits according to the model and parameters described in the text. Right: Q-band spectrum from a powdered sample of 3 at 295 K and simulation according to the model and parameters described in the text.

Table 1 .

 1 Spin-Hamiltonian parameters of 1-3 as determined from fits to frozen solution (1, 2) and powder (3) Q-band EPR spectra.It should be noted that similar systems have been studied in the past, using EPR spectroscopy at even higher fields like in the case of CuII 3 triangles encapsulated in polyoxometallates. In particular, powder W-band EPR spectra of K 9 Na[Cu 3 (H 2 O) 3 (α-TeW 9 O 33 ) 2 ]•16H 2 O [17] and Na 9 [Cu 3 Na 3 (H 2 O) 9 (α-AsW 9 O 33 ) 2 ]⋅26H 2 O

		1	2	3
	g i||	2.25707±0.00036	2.25488±0.00061	2.230
	g i⊥	2.05853±0.00021	2.06111±0.00025	2.061
	σ G / σ L (mT pp )	2.31±0.80 / 2.85±0.22	3.3±1.0 / 2.41±0.50	3.3 / 3.9
	r ij (Å) J av (cm -1 ) ΔJ (cm -1 )	8.22±0.11 0.11217±0.00050 0.0114±0.0018	8.35±0.15 0.11628±0.00073 0.0150±0.0019	8.22 0.078 0.011
	A i|| (MHz)	502.94±8.42	543±14	540
	A i⊥ (MHz)	52.0±13.	69.6±6.4	48
	Δ A (°)	[-6.4±2.5, 3.4±7.4, 28.8486±0.0005]	[0, 0, 0]	[0, 0, 0]

Acknowledgments: This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 746060 (project "CHIRALQUBIT"). I particularly wish to thank Dr. Romain Ruppert for the synthesis of the ligand.


Athanassios K Boudalis
email: bountalis@unistra.fr

Christos P Constantinides

Nicolas Chrysochos

Raanan Carmieli

Gregory Leitus

Andreas Kourtellaris

Daniel B Lawson

Panayiotis A Koutentis

Deciphering the Ground State of a C 3 -Symmetrical Blatter-type Triradical by CW and pulse EPR Spectroscopy

come   L'archive ouverte pluridisciplinaire

Introduction

High-spin organic radicals are of fundamental interest owing to their potential applications in material sciences [1]. Organic radicals are inherently unstable as nature prefers to pair electrons and maximize bonding in a structure. Nevertheless, there are two main design strategies that can help stabilize unpaired spins in organic molecules: i) steric stabilization whereby bulky groups protect sites of high spin density; and, ii) electronic stabilization (resonance) whereby spin density is either highly delocalized or electronegative elements are introduced in the carbon backbone to offer thermodynamic stability [START_REF] Hicks | What's new in stable radical chemistry?[END_REF]. These design strategies have been successful in the preparation of stable S =1/2 organic radicals. For organic polyradicals with high-spin ground states (S = 1, 3/2, etc.) additional design principles must be followed [START_REF] Borden | Effects of electron repulsion in conjugated hydrocarbon diradicals[END_REF][START_REF] Ovchinnikov | Multiplicity of the ground state of large alternant organic molecules with conjugated bonds[END_REF]. Spin-containing units, whether atoms or molecules, are usually connected via ferromagnetic coupling units (FCUs) such as trimethylenemethane (TMM) and m-benzoquinodimethane (m-BQDM) to form high-spin polyradicals [START_REF] Rajca | Organic Diradicals and Polyradicals: From Spin Coupling to Magnetism?[END_REF]. While in closed-shell organic molecules, singlet ground states (S = 0) are separated from low-lying high-spin excited states by tens of kcal mol -1 , inverting this large energy gap in favor of a high-spin state for organic polyradicals remains a challenge to this day [START_REF] Gallagher | High-Spin Organic Molecules[END_REF]. The energy gap of the high-spin ground state from the nearest excited state must be in the same order of magnitude as the thermal energy at room temperature (≈ 0.6 kcal mol -1 ) [7,[START_REF] Lineberger | The synergy between qualitative theory, quantitative calculations, and direct experiments in understanding, calculating, and measuring the energy differences between the lowest singlet and triplet states of organic diradicals[END_REF].

Furthermore, the high-spin state must be stable and sufficiently populated at room temperature.

We previously reported the synthesis and characterization of a C 3 -symmetrical triradical, 3,3',3''-(benzene-1,3,5-triyl)tris(1-phenyl-1H-benzo[e] [1,[START_REF] Hicks | What's new in stable radical chemistry?[END_REF][START_REF] Ovchinnikov | Multiplicity of the ground state of large alternant organic molecules with conjugated bonds[END_REF]triazin-4-yl) (1) (Fig. 1), based on 1,3-diphenyl-1,4-dihydrobenzo[e] [1,[START_REF] Hicks | What's new in stable radical chemistry?[END_REF][START_REF] Ovchinnikov | Multiplicity of the ground state of large alternant organic molecules with conjugated bonds[END_REF]triazin-4-yl (2) (aka Blatter's radical) [START_REF] Zissimou | 3,3′,3′′-(Benzene-1,3,5-triyl)tris(1-phenyl-1H-benzo[e][1,2,4]triazin-4-yl): A C3 symmetrical Blatter-type triradical[END_REF]. Several Blatter-based di-and tri-radicals have since been reported in the literature [START_REF] Gallagher | High-Spin Organic Diradical with Robust Stability[END_REF][START_REF] Gallagher | Thermally and Magnetically Robust Triplet Ground State Diradical[END_REF][START_REF] Shu | Synthesis and Thin Films of Thermally Robust Quartet (S = 3/2) Ground State Triradical[END_REF][START_REF] Zhang | High-Spin (S = 1) Blatter-Based Diradical with Robust Stability and Electrical Conductivity[END_REF][START_REF] Zhang | Temperature Tunable Self-Doping in Stable Diradicaloid Thin-Film Devices[END_REF][START_REF] Hu | Correlation between the strength of conjugation and spin-spin interactions in stable diradicaloids[END_REF][START_REF] Hu | Nitrogen analogues of Chichibabin's and Müller's hydrocarbons with small singlet-triplet energy gaps[END_REF][START_REF] Hu | Nitrogen-coupled blatter diradicals: the fused versus unfused bridges[END_REF]. These include mixed Blatter-nitronyl nitroxide and all Blatter di-and tri-radicals wherein the radical units are connected through strategic locations to promote intramolecular ferromagnetic alignment via the spin polarization mechanism. They possess high-spin ground states with robust stability owing to the excellent air, moisture, and thermal stability of Blatter's radical 2 [START_REF] Blatter | A new stable free radical[END_REF][START_REF] Constantinides | Stable N-and N/S-Rich Heterocyclic Radicals: Synthesis and Applications[END_REF][START_REF] Ji | Recent advances of stable Blatter radicals: synthesis, properties and applications[END_REF][START_REF] Rogers | Recent advances in the chemistry of benzo[e][1,2,4]triazinyl radicals[END_REF][START_REF] Kumar | Recent Advances in Organic Radicals and Their Magnetism[END_REF]. Our extensive synthetic work on this family of radicals has enabled broad access to various derivatives, significantly expanding the structural diversity of the parent radical 2 [START_REF] Constantinides | Characterization and Magnetic Properties of a "Super Stable" Radical 1,3-Diphenyl-7trifluoromethyl-1,4-dihydro-1,2,4-benzotriazin-4-yl[END_REF][START_REF] Koutentis | Catalytic Oxidation N-Phenylamidrazones to 1,3-Diphenyl-1,4-dihydro-1,2,4-benzotriazin-4-yls: An Improved Synthesis of Blatter's Radical[END_REF][START_REF] Berezin | Synthesis and properties of imidazolo-fused benzotriazinyl radicals[END_REF][START_REF] Berezin | Route to Benzo-and Pyrido-Fused 1,2,4-Triazinyl Radicals via N′-(Het)aryl-N′-[2-nitro(het)aryl]hydrazides[END_REF][START_REF] Savva | Preparation of Blatter Radicals via Aza-Wittig Chemistry: The Reaction of N-Aryliminophosphoranes with 1-(Het)aroyl-2-aryldiazenes[END_REF][START_REF] Berezin | From Blatter Radical to 7-Substituted 1,3-Diphenyl-1[END_REF][START_REF] Constantinides | Synthesis of 7-aryl/heteraryl-1,3diphenyl-1,2,4-benzotriazinyls viapalladium catalyzed Stille and Suzuki-Miyaura reactions[END_REF]. This has led to many applications in magnetic materials [START_REF] Constantinides | Antiferromagnetic Interactions in 1D Heisenberg Linear Chains of 7-(4-Fluorophenyl) and 7-Phenyl-Substituted 1,3-Diphenyl-1,2,4-benzotriazin-4-yl Radicals[END_REF][START_REF] Constantinides | Structural, Magnetic, and Computational Correlations of Some Imidazolo-Fused 1,2,4-Benzotriazinyl Radicals[END_REF][START_REF] Constantinides | Ferromagnetic Interactions in a 1D Alternating Linear Chain of π-Stacked 1,3-Diphenyl-7-(thien-2-yl)-1,4-dihydro-1,2,4benzotriazin-4-yl Radicals[END_REF][START_REF] Constantinides | Effective exchange coupling in alternating-chains of a πextended 1,2,4-benzotriazin-4-yl[END_REF][START_REF] Constantinides | A Magnetostructural Investigation of an Abrupt Spin Transition for 1-Phenyl-3-trifluoromethyl-1,4dihydrobenzo[e][1,2,4]triazin-4-yl[END_REF][START_REF] Constantinides | Spin-triplet excitons in 1,3-diphenyl-7-(fur-2-yl)-1,4dihydro-1,2,4-benzotriazin-4-yl[END_REF][START_REF] Constantinides | The Suppression of Columnar π-Stacking in 3-Adamantyl-1-phenyl-1,4dihydrobenzo[e][1,2,4]triazin-4-yl[END_REF][START_REF] Constantinides | Ferromagnetic interactions in a 1D Heisenberg linear chain of 1phenyl-3,7-bis(trifluoromethyl)-1,4-dihydro-1,2,4-benzotriazin-4-yls[END_REF][START_REF] Bazzi | 1-(2-Methoxyphenyl)-3-phenyl-1,4-dihydro-1,2,4-benzotriazin-4-yl: a tricky "structure-to-magnetism" correlation aided by DFT calculations[END_REF][START_REF] Constantinides | Polymorphism in a π stacked Blatter radical: structures and magnetic properties of 3-(phenyl)-1-(pyrid-2-yl)-1,4-dihydrobenzo[e][1,2,4]triazin-4-yl[END_REF], photodetection [START_REF] Zhang | Temperature Tunable Self-Doping in Stable Diradicaloid Thin-Film Devices[END_REF][START_REF] Zheng | A Solid-State Effect Responsible for an Organic Quintet State at Room Temperature and Ambient Pressure[END_REF], liquid crystalline photoconduction [START_REF] Jasinski | Stability of a columnar liquid crystalline phase in isomeric derivatives of the 1,4-dihydrobenzo[e][1,2,4]triazin-4-yl: Conformational effects in the core[END_REF][START_REF] Jasinski | Tuning the Magnetic Properties of Columnar Benzo[e][1,2,4]triazin-4-yls with the Molecular Shape[END_REF][START_REF] Kapuscinski | Magnetic behaviour of bent-core mesogens derived from the 1,4dihydrobenzo[e][1,2,4]triazin-4-yl[END_REF][START_REF] Jasinski | Substituent-Dependent Magnetic Behavior of Discotic Benzo[END_REF], electroactive building blocks for purely all-organic batteries [START_REF] Häupler | Verwendung benzotriazinyl-haltiger Polymere als Ladungsspeicher[END_REF][START_REF] Saal | Blatter radical as a polymeric active material in organic batteries[END_REF][START_REF] Steen | Blatter Radicals as Bipolar Materials for Symmetrical Redox-Flow Batteries[END_REF], ligands for metal complexes [49][START_REF] Morgan | Coordination Complexes of a Neutral 1,2,4-Benzotriazinyl Radical Ligand: Synthesis, Molecular and Electronic Structures, and Magnetic Properties[END_REF][START_REF] Morgan | Coexistence of long-range antiferromagnetic order and slow relaxation of the magnetization in the first lanthanide complex of a 1,2,4-benzotriazinyl radical[END_REF] and metal-organic frameworks [START_REF] Poryvaev | Radical-Doped Metal-Organic Framework: Route to Nanoscale Defects and Magnetostructural Functionalities[END_REF], initiators in controlled polymerizations [START_REF] Demetriou | Benzotriazinylmediated controlled radical polymerization of styrene[END_REF][START_REF] Areephong | Triazine-mediated controlled radical polymerization: new unimolecular initiators[END_REF][START_REF] Areephong | Triazine mediated living radical controlled polymerization[END_REF][START_REF] Rogers | Computational Evaluation of the Oxidative Cleavage of Triazine Derivatives for Electrosynthesis[END_REF], Overhauser DNP polarizing agents for high-field MAS-DNP [START_REF] Perras | Methyl-Driven Overhauser Dynamic Nuclear Polarization[END_REF] and as pH sensors [START_REF] Zheng | The Pyreno-Triazinyl Radical -Magnetic and Sensor Properties[END_REF]. These radicals have been shown to have excellent ability to form stable thin films [START_REF] Ciccullo | A Derivative of the Blatter Radical as a Potential Metal-Free Magnet for Stable Thin Films and Interfaces[END_REF][START_REF] Casu | Nanoscale Studies of Organic Radicals: Surface, Interface, and Spinterface[END_REF] which has led to applications in spintronic devices [START_REF] Low | The Environment-Dependent Behavior of the Blatter Radical at the Metal-Molecule Interface[END_REF][START_REF] Patera | Resolving the Unpaired-Electron Orbital Distribution in a Stable Organic Radical by Kondo Resonance Mapping[END_REF][START_REF] Ciccullo | Interfacing a Potential Purely Organic Molecular Quantum Bit with a Real-Life Surface[END_REF].

Triradical 1 was designed to connect three Blatter-type radicals onto a 1,3,5-trimethylenebenzene core via their C3 carbons. The latter is a non-disjoint non-Kekulé triradical that acts as a ferromagnetic coupling unit [START_REF] Rajca | Organic Diradicals and Polyradicals: From Spin Coupling to Magnetism?[END_REF]. SOMO orbital calculations for Blatter-type radicals indicate that there is a node on C3 carbons and therefore a question arises as to which is the ground state of triradical 1. If the nodes on C3 carbons disrupt the communication between the three 'arms', then the three S =1/2 radicals are independent of each other and triradical 1 will have near degenerate high-and low-spin states. However, if the spin polarization mechanism is in effect and there is sufficient communication between the three radicals then according to Ovchinnikov's rule [START_REF] Ovchinnikov | Multiplicity of the ground state of large alternant organic molecules with conjugated bonds[END_REF] a high-spin S = 3/2 quartet will be the ground state due to the intramolecular ferromagnetic alignment. Following our reported the synthesis of triradical 1, Rajca and co-workers [START_REF] Shu | Synthesis and Thin Films of Thermally Robust Quartet (S = 3/2) Ground State Triradical[END_REF] commented that triradical 1 is "composed of three S = 1/2 spins that are magnetically independent" and that "this triradical might turn out to be a low-spin (doublet) ground state, very close in energy to the excited quartet". In light of this, and to provide experimental support of the ground state, herein, we report detailed solid-state XRD, solution EPR and computational studies to decipher the ground state of this triradical.

Experimental

Single-crystal and powder XRD

Data were collected on an Oxford-Diffraction Supernova diffractometer, equipped with a CCD area detector utilizing Mo-Kα radiation (λ = 0.71073 Å). A suitable crystal was attached to glass fibers using paratone-N oil and transferred to a goniostat where they were cooled for data collection. Unit cell dimensions were determined and refined by using 1617 (4.67° ≤ θ ≤ 28.65°) reflections. Empirical absorption corrections (multi-scan based on symmetry-related measurements) were applied using CrysAlis RED software [START_REF]CrysAlis CCD and CrysAlis RED[END_REF]. The structures were solved by direct method and refined on F 2 using full-matrix least squares using SHELXL97 [START_REF] Sheldrick | SHELXL-97: A program for the refinement of crystal structure[END_REF]. Software packages used: CrysAlis CCD [START_REF]CrysAlis CCD and CrysAlis RED[END_REF] for data collection, CrysAlis RED [START_REF]CrysAlis CCD and CrysAlis RED[END_REF] for cell refinement and data reduction, WINGX for geometric calculations [START_REF] Farrugia | WinGX suite for small-molecule single-crystal crystallography[END_REF], and DIAMOND [START_REF] Brandenburg | version 3.1d; Crystal Impact GbR[END_REF] for molecular graphics. The non-H atoms were treated anisotropically. The hydrogen atoms were placed in calculated, ideal positions and refined as riding on their respective carbon atoms.

EPR measurements

EPR spectra of frozen glasses of 1 in 2-Methyltetrahydrofuran (1 mM) were recorded on a Bruker Elexsys E580 spectrometer operating at 9.5 GHz and X-band frequencies (9.5 GHz) equipped with an EN4118X-MD4 resonator at temperature range of 5 K-110 K. The temperature was controlled by an Oxford Instruments CF935 continuous flow cryostat using liquid He. Fieldsweep echo-detected (FS-ED) EPR spectra were recorded using the two-pulse echo sequence (π/2-τ-π-τ-echo) where the echo intensity is measured as a function of the magnetic field. The microwave pulse lengths, π/2 and π were 10 and 20 ns, respectively and the time interval between the pulses, τ, was 200 ns. The two-pulse ESEEM sequence, π/2-τ-π-τ-echo, was employed with a two-step phase cycle. The measurements were carried out at a magnetic field where the echo intensity is maximum, and the length of the π/2 and π microwave (MW) pulses were 12 ns and 24 ns, respectively. The pulse interval τ was selected to be 100 ns with a 12 ns increment. For measuring T 1 the inversion recovery sequence, π-T d -π/2-τ-π-τ-echo, was employed with a two-step phase cycle. The measurements were carried out at a magnetic field where the echo intensity is maximum, and the length of the π/2 and π microwave (MW) pulses were 12 ns and 24 ns, respectively. The pulse interval τ was selected to be 200 ns and T d was started from 400 ns and increased with a 1600 ns increment.

The IR trace was fitted to a stretched exponential decay law

1 ( / ) 0 ( ) t T M t M e β - =
. For the echo decay (ED) traces, the presence of three peaks in their FT spectra, characteristic of 1 H, and 2 H and double 2 H modulation frequencies, required the additional consideration of three modulations, at frequencies (f 1-3 ), each decaying with a characteristic time (b 1-3 ). Various tests determined that the exponential decay obeyed to a stretched exponential process. The relaxation law was:

3 2 / ( 2 / ) 0 1 (2 ) 1 cos(4 ) i M b T i i i i M M e k e f β τ τ τ π τ ϕ - - =   = + +     ∑
Fourier transforms were carried out on ED traces after subtraction of the exponential decay background, zero-filling and apodization to a Hamming window function.

Spectra fits to CW spectra were carried out with Easyspin v. 6.0 [START_REF] Stoll | EasySpin, a comprehensive software package for spectral simulation and analysis in EPR[END_REF] using home-written functions.

Computational methodology

Full optimization for the doublet and quartet states of triradical 1 were carried using the UB3LYP method [START_REF] Becke | Density-functional thermochemistry. III. The role of exact exchange[END_REF][START_REF] Lee | Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density[END_REF][START_REF] Vosko | Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis[END_REF][START_REF] Stephens | Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields[END_REF] that performs well for Blatter type radicals [START_REF] Constantinides | Antiferromagnetic Interactions in 1D Heisenberg Linear Chains of 7-(4-Fluorophenyl) and 7-Phenyl-Substituted 1,3-Diphenyl-1,2,4-benzotriazin-4-yl Radicals[END_REF][START_REF] Constantinides | Structural, Magnetic, and Computational Correlations of Some Imidazolo-Fused 1,2,4-Benzotriazinyl Radicals[END_REF][START_REF] Constantinides | Ferromagnetic Interactions in a 1D Alternating Linear Chain of π-Stacked 1,3-Diphenyl-7-(thien-2-yl)-1,4-dihydro-1,2,4benzotriazin-4-yl Radicals[END_REF][START_REF] Constantinides | Effective exchange coupling in alternating-chains of a πextended 1,2,4-benzotriazin-4-yl[END_REF][START_REF] Constantinides | A Magnetostructural Investigation of an Abrupt Spin Transition for 1-Phenyl-3-trifluoromethyl-1,4dihydrobenzo[e][1,2,4]triazin-4-yl[END_REF][START_REF] Constantinides | Spin-triplet excitons in 1,3-diphenyl-7-(fur-2-yl)-1,4dihydro-1,2,4-benzotriazin-4-yl[END_REF][START_REF] Constantinides | The Suppression of Columnar π-Stacking in 3-Adamantyl-1-phenyl-1,4dihydrobenzo[e][1,2,4]triazin-4-yl[END_REF][START_REF] Constantinides | Ferromagnetic interactions in a 1D Heisenberg linear chain of 1phenyl-3,7-bis(trifluoromethyl)-1,4-dihydro-1,2,4-benzotriazin-4-yls[END_REF][START_REF] Bazzi | 1-(2-Methoxyphenyl)-3-phenyl-1,4-dihydro-1,2,4-benzotriazin-4-yl: a tricky "structure-to-magnetism" correlation aided by DFT calculations[END_REF][START_REF] Constantinides | Polymorphism in a π stacked Blatter radical: structures and magnetic properties of 3-(phenyl)-1-(pyrid-2-yl)-1,4-dihydrobenzo[e][1,2,4]triazin-4-yl[END_REF]. Basis sets used in this work included the standard Pople basis sets including the 6-31g(d) and 6-311+G(2d,p) basis sets along with the SVP and TZVP Ahlrichs [START_REF] Weigenda | Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy[END_REF] def2 basis sets. All calculations were performed with Gaussian16 [74] using the University of Michigan's Greatlakes cluster. To estimate the intramolecular exchange-coupling constants (J intra,comp ) we use the magnetic Heisenberg-Dirac-Van Vleck Hamiltonian for three electrons in a symmetric three center triradical molecular system which can be written as

𝐻 � 𝑖𝑛𝑡𝑟𝑎 = -�𝐽 12 • 𝑆 ̂1 • 𝑆 ̂2 + 𝐽 23 • 𝑆 ̂2 • 𝑆 ̂3 + 𝐽 13 • 𝑆 ̂1 • 𝑆 ̂3�
Where 𝐽 𝑖𝑗 is the intramolecular exchange-coupling constants between nearest neighbor spin centers and Ŝ i are the spin operators for the three spin sites. As written 𝐻 � 𝑖𝑛𝑡𝑟𝑎 can be applied to a linear molecular system with spins evenly separated or to a triangular molecular system where the spins are located at the corners of an isosceles triangle [START_REF] Rajca | Organic Diradicals and Polyradicals: From Spin Coupling to Magnetism?[END_REF]. These intramolecular magnetic interactions produce two doublets and one quartet energies [START_REF] Kambe | On the Paramagnetic Susceptibilities of Some Polynuclear Complex Salts[END_REF]. As in this case, the equilateral triangular molecular symmetry reduces the exchange-coupling constants to J intra = J 1 = J 2 = J 3 and the resulting energies of the two degenerate doublet states, E D , and one quartet energies, E Q , can be written as [START_REF] Reta | Magnetic Coupling Constants in Three Electrons Three Centers Problems from Effective Hamiltonian Theory and Validation of Broken Symmetry-Based Approaches[END_REF]:

𝐸 D = + 3 4 � • 𝐽 𝑖𝑛𝑡𝑟𝑎 𝐸 Q = -3 4 � • 𝐽 𝑖𝑛𝑡𝑟𝑎
Computationally, the energy of each magnetic exchange interaction between each spin center is represented as the exchange coupling constant mapped from the energies of the calculated doublet and quartet states. J intra,comp is evaluated from the unprojected formula where

𝐽 𝑖𝑛𝑡𝑟𝑎,𝑐𝑜𝑚𝑝 = + 2 3 �𝐸 Q -𝐸 D �
According to 𝐻 � 𝑖𝑛𝑡𝑟𝑎 , a positive value of the exchange coupling constant J indicates a ferromagnetic interaction between S i and S j whereas a negative exchange coupling constant corresponds to an antiferromagnetic interaction between spin centers.

Results and Discussion

Triradical 1 was previously prepared in a two-step reaction sequence [START_REF] Zissimou | 3,3′,3′′-(Benzene-1,3,5-triyl)tris(1-phenyl-1H-benzo[e][1,2,4]triazin-4-yl): A C3 symmetrical Blatter-type triradical[END_REF]. These data pointed inconclusively to the independence of each triazinyl radical moiety, i.e., their identical behavior attributed to little to no spin-spin coupling between them.

From here on, we describe efforts to establish unambiguously the ground state of triradical 1.

We have obtained the structure of triradical 1 (Fig. 2) from single X-ray quality crystals grown Molecules of triradical 1 form one dimensional (1D) chains along the c axis (Fig. 3). There are two symmetry operations in the crystal structure of triradical 1: Two three-fold rotation axis (-y, x-y, x and -x+y, -x, z) with direction [0,0,1] at 0,0,z and two three-fold rotoinversion axis (y, -x+y, -z and x-y, x, -z) with direction [0,0,1] at 0,0,z and inversion at [0,0,0]. Å close contact between the C3 atom of one molecule and the C7 atom of the benzotriazinyl moiety of the opposing molecule (Fig. 3). Each arm of the triradical 1 interacts with a different molecule, which helps establish an extended network of weak interactions.

The polycrystalline sample used in our studies was examined for phase purity. A comparison (Fig. 4) of the powder XRD diffraction pattern of our sample measured at 300K match well the pattern calculated by the single-crystal structure at 100K.

Fig 4.

A comparison of the experimental powder X-ray diffraction pattern at 300 K (red) and the calculated one from the single crystal X-ray structure at 100 K.

To assess the magnetic ground state of the individual molecules, solution studies were preferred to avoid intermolecular interactions that would mask the intramolecular ones, as is often the case in organic radicals [1,[START_REF] Hicks | What's new in stable radical chemistry?[END_REF][START_REF] Rajca | Organic Diradicals and Polyradicals: From Spin Coupling to Magnetism?[END_REF][START_REF] Gallagher | High-Spin Organic Molecules[END_REF].

CW EPR spectra in frozen 2-Methyltetrahydrofuran at 110 K revealed a pattern typical of a zero-field split system (Fig. 4). Preliminary fits were carried out on a spectrum collected at a 0.65 mW microwave power to better highlight all the resonances and allow a determination of the spin Hamiltonian parameters.

Fitting this to a S = 3/2 spin with axial magnetic anisotropy yielded excellent results demonstrating the presence of a thermally populated S = 3/2 state. The line shapes required the introduction of a small strain in g ⊥ . Best-fit parameters were g 3/2|| = 2.0033, g 3/2⊥ = 2.0046, σg 3/2⊥ = 0.0098, D = 0.00286 cm -1 , σ G = 0.020 mT, σ L = 0.48 mT.

To demonstrate the origin of this zfs, we carried out fits to these data using a model considering the dipolar interactions between three S = 1/2 spins. Indeed, dipolar interactions can induce magnetic anisotropy even in systems comprising just S i = 1/2 spins, thus characterized by absence of single-ion zfs [START_REF] Mathivathanan | Origin of Ferromagnetism and Magnetic Anisotropy in a Family of Copper(II) Triangles[END_REF]. Based on such a full multispin Hamiltonian, Easyspin builds the associated matrix and computes the energies of the magnetic levels by diagonalization.

Boltzmann population analysis at the experimental temperature and magnetic fields is taken into account when calculating the intensities of various EPR spectral resonances, allowing a qualitative estimate of the J coupling.

In the absence of hyperfine splittings, and in a spin system with identical g-values [START_REF] Eaton | Continuous wave electron paramagnetic resonance of nitroxide biradicals in fluid solution[END_REF], the presence of exchange interactions is not expected to influence the resonance positions spectra, we therefore carried out such preliminary fits considering J ij = 0. Best-fit parameters were g i|| = 2.0034, g i⊥ = 2.0046, σg i⊥ = 0.0131, r ij = 7.72 Å (i, j = 1-3), σ G = 0.026 mT, σ L = 0.43 mT. The two fits yield very close results, including the g-values. The practically identical values of the main elements of the global and local g-tensors indicates that the two reference frames are collinear, i.e., the local g z axes are parallel to the molecular z-axis; normal to the plane of the central ring. We also note that fits yield g i|| < g i⊥ , in apparent contrast to the previously derived values for the parent monoradical [START_REF] Bazzi | 1-(2-Methoxyphenyl)-3-phenyl-1,4-dihydro-1,2,4-benzotriazin-4-yl: a tricky "structure-to-magnetism" correlation aided by DFT calculations[END_REF]. We are currently unsure of the reasons of this inversion.

That these are frozen solution data may introduce important uncertainties in the derived g-values.

The fitted distances are in close, albeit not perfect, agreement with the interatomic distances between spin-bearing atoms N3 (6.360 Å). The slightly larger fitted distance may indicate a small delocalization of the spin density toward carbon atom C2, and/or the interplay of conformational changes through rotation of the side-groups around bond C3-C4. Another possibility, the presence of anisotropic (or "pseudo-dipolar") exchange interactions, whose effects are added to those of the dipolar interactions, is not considered plausible as its physical origins are the spin-orbit coupling effects, which are typically most pronounced in the case of metal ions.

While information on the exchange couplings could not be obtained by the resonance positions, such information might eventually be obtained by their relative intensities. Indeed, the relative energies of the singlet and quartet states is expected to influence the relative intensities of the central and lateral resonances. Indeed, the central resonance is a sum of the M S = -1/2 → +1/2 transitions, both within the quartet and within the two doublets, whereas the lateral resonances are only due to the M S = -3/2 → -1/2 and +1/2 → +3/2 transitions within the quartet.

Thus, these latter will be relatively enhanced in intensity in the case of a FM coupling, which would make the quartet the ground state.

To assess this, fits were carried out on a spectrum collected at 0.21 μW at 110 K, to minimize any risk of saturation that might distort the spectral intensities. Initial tests demonstrated that fits to such a model were sensitive enough for a qualitative assessment of the sign of J, but not for its quantitative determination. While all fits converged to a FM coupling, the precise J ij value depended on the fitting intervals. In Fig. 6, we present fits with J ij (i, j = 1-3) values fixed to +100 and -100 cm -1 (-J ij S i S j formalism). These show that the strong FM coupling better reproduced the relative intensities of the two resonances. Moreover, the effects of a moderate FM coupling were assessed, by carrying out fits with J values fixed to ±3 cm -1 . These values were selected based on DFT calculations and analysis of the spin-lattice relaxation times (see below), but also to avoid numerical artifacts produced close to perfect frustration (J = 0). These are practically indistinguishable, and both demonstrate a distinctly lower agreement with the experimental spectrum compared to the J = +100 cm -1 fit. While these fits cannot quantitatively determine the J value, on a qualitative level they indicate the presence of FM interactions sufficiently strong to be clearly discerned in the spectra. To further confirm that the quartet is the ground state, we considered variable-temperature EPR spectroscopy studies in solution as the ideal choice. Indeed, SQUID susceptometry in the solid state might be dominated by intermolecular interactions which would mask the intramolecular ones [START_REF] Constantinides | Antiferromagnetic Interactions in 1D Heisenberg Linear Chains of 7-(4-Fluorophenyl) and 7-Phenyl-Substituted 1,3-Diphenyl-1,2,4-benzotriazin-4-yl Radicals[END_REF][START_REF] Constantinides | Structural, Magnetic, and Computational Correlations of Some Imidazolo-Fused 1,2,4-Benzotriazinyl Radicals[END_REF][START_REF] Constantinides | Ferromagnetic Interactions in a 1D Alternating Linear Chain of π-Stacked 1,3-Diphenyl-7-(thien-2-yl)-1,4-dihydro-1,2,4benzotriazin-4-yl Radicals[END_REF][START_REF] Constantinides | Effective exchange coupling in alternating-chains of a πextended 1,2,4-benzotriazin-4-yl[END_REF][START_REF] Constantinides | A Magnetostructural Investigation of an Abrupt Spin Transition for 1-Phenyl-3-trifluoromethyl-1,4dihydrobenzo[e][1,2,4]triazin-4-yl[END_REF][START_REF] Constantinides | Spin-triplet excitons in 1,3-diphenyl-7-(fur-2-yl)-1,4dihydro-1,2,4-benzotriazin-4-yl[END_REF][START_REF] Constantinides | The Suppression of Columnar π-Stacking in 3-Adamantyl-1-phenyl-1,4dihydrobenzo[e][1,2,4]triazin-4-yl[END_REF][START_REF] Constantinides | Ferromagnetic interactions in a 1D Heisenberg linear chain of 1phenyl-3,7-bis(trifluoromethyl)-1,4-dihydro-1,2,4-benzotriazin-4-yls[END_REF][START_REF] Bazzi | 1-(2-Methoxyphenyl)-3-phenyl-1,4-dihydro-1,2,4-benzotriazin-4-yl: a tricky "structure-to-magnetism" correlation aided by DFT calculations[END_REF][START_REF] Constantinides | Polymorphism in a π stacked Blatter radical: structures and magnetic properties of 3-(phenyl)-1-(pyrid-2-yl)-1,4-dihydrobenzo[e][1,2,4]triazin-4-yl[END_REF].

Preliminary attempts to address the question through variable-temperature CW EPR spectroscopy were complicated by the appearance of asymmetric derivative spectra which was attributed to passage effects [START_REF] Weger | Passage Effects in Paramagnetic Resonance Experiments[END_REF][START_REF] Eaton | Electron Paramagnetic Resonance[END_REF]. In fact, these are quite common in molecules with relatively slow spin-lattice relaxation and require particular care to remove (such as low MW powers, small modulation frequencies, slow scans), thus complicating the quantitative comparison of variable-temperature data. In the presence of such effects, double integration is particularly imprecise, since small asymmetries in the derivative spectrum are translated in "absorption" spectra with severely distorted baselines. These require corrections that affect the quantification during the second integration in an unpredictable manner.

To circumvent these complications, we undertook pulsed EPR spectroscopy, which directly yields "absorption" field-swept spectra, while also allowing us to monitor the spin-lattice relaxation time at different temperatures to select shot repetition times (SRTs) of appropriate length to assure full relaxation of the magnetization. Preliminary field-sweep echo-detected (FSED) spectra corresponded perfectly to those derived from CW EPR spectroscopy (Fig. 5). The spin-lattice relaxation time (T 1 ) was characterized by inversion recovery (IR) experiments (Fig. 6 and Table 1) at each temperature to select an appropriate SRT for the subsequent pulse EPR studies (SRT > 5T 1 ). Echo decay experiments (Fig. 7) were also carried out to assess the phase-memory time of the spin system and select an appropriate interpulse delay for FSED experiments. Table 1. Best-fit parameters for T 1 and T M times and their corresponding stretch parameters.

Numbers in parentheses indicate the 95% confidence intervals.

Variable-temperature FSED spectra (Fig. 8) were collected, and integrated to derive their intensity I. The I × T products were plotted as a function of temperature. Unfortunately, after correction for the experimental parameters (number of scans, video gain, shots per point), no clear trend was observed for the data.

We have used DFT calculations to further support the experimental results from the CW EPR and FSED spectroscopy. The ground state of triradical 1 was determined computationally using the energies of the doublet and quartet states (Table 2) calculated from full optimizations at the UB3LYP level and using four basis sets 6-31g(d), 6-311+g(2p,d), def2-SVP and def2-TZVP. All basis sets provide similar doublet-quartet splittings ranging 0.117 -0.124 kcal mol -1 in favor of a quartet ground state (Table 2).

The calculations indicate that there is a ferromagnetic alignment of the three unpaired electrons within the triradical molecule. The intramolecular exchange coupling constant, J intra , was calculated to be 2.73 cm -1 with the smallest basis set of 6-31g(d) and 2.89 cm -1 with the largest basis or the def2-TZVP. The remaining basis sets including the 6-311+g(2d,p) and the def2-SVP give a J of 2.68 cm -1 and 2.85 cm -1 , respectively. The range in the computed J values is 0.16 cm -1 showing very little change with respect to basis.

Table 2. UB3LYP doublet energies, E D (au), quartet energies, E Q (au), the doublet-quartet splitting energy (∆E DQ ) of triradical 1 (kcal mol -1 ), and the computed exchange-coupling constant J intra,comp (cm -1 ).

Conclusions

SOMO orbital calculations for Blatter-type radicals indicate that there is a node on C3 carbons [START_REF] Constantinides | Antiferromagnetic Interactions in 1D Heisenberg Linear Chains of 7-(4-Fluorophenyl) and 7-Phenyl-Substituted 1,3-Diphenyl-1,2,4-benzotriazin-4-yl Radicals[END_REF][START_REF] Constantinides | Structural, Magnetic, and Computational Correlations of Some Imidazolo-Fused 1,2,4-Benzotriazinyl Radicals[END_REF][START_REF] Constantinides | Ferromagnetic Interactions in a 1D Alternating Linear Chain of π-Stacked 1,3-Diphenyl-7-(thien-2-yl)-1,4-dihydro-1,2,4benzotriazin-4-yl Radicals[END_REF][START_REF] Constantinides | Effective exchange coupling in alternating-chains of a πextended 1,2,4-benzotriazin-4-yl[END_REF][START_REF] Constantinides | A Magnetostructural Investigation of an Abrupt Spin Transition for 1-Phenyl-3-trifluoromethyl-1,4dihydrobenzo[e][1,2,4]triazin-4-yl[END_REF][START_REF] Constantinides | Spin-triplet excitons in 1,3-diphenyl-7-(fur-2-yl)-1,4dihydro-1,2,4-benzotriazin-4-yl[END_REF][START_REF] Constantinides | The Suppression of Columnar π-Stacking in 3-Adamantyl-1-phenyl-1,4dihydrobenzo[e][1,2,4]triazin-4-yl[END_REF][START_REF] Constantinides | Ferromagnetic interactions in a 1D Heisenberg linear chain of 1phenyl-3,7-bis(trifluoromethyl)-1,4-dihydro-1,2,4-benzotriazin-4-yls[END_REF][START_REF] Bazzi | 1-(2-Methoxyphenyl)-3-phenyl-1,4-dihydro-1,2,4-benzotriazin-4-yl: a tricky "structure-to-magnetism" correlation aided by DFT calculations[END_REF][START_REF] Constantinides | Polymorphism in a π stacked Blatter radical: structures and magnetic properties of 3-(phenyl)-1-(pyrid-2-yl)-1,4-dihydrobenzo[e][1,2,4]triazin-4-yl[END_REF]. At a first glance the SOMO orbital calculations for triradical 1 (Fig. 9) indicate localization of spin in each 1,2,4-benzo[e]triazin-4-yl moiety and a nodal carbon connecting the arms directly to the 1,3,5-trimethylenebenzene core. However, the spin density distribution (Fig. 10) shows extensive spin delocalization over the central core and effective communication between each radical unit. The spin polarization mechanism is in effect and sufficient communication exists between the three radicals. This is supported by variable-temperature FSED spectroscopy which suggests ferromagnetic exchange within the spin system, leading to a quartet ground state. DFT calculations agree with the experimental EPR data and show that the quartet state is more stable than the doublet state by ca. 0.122 kcal mol -1 . Our data show that despite the anticipation that triradical 1 is "composed of three S = 1/2 spins that are magnetically independent" [START_REF] Shu | Synthesis and Thin Films of Thermally Robust Quartet (S = 3/2) Ground State Triradical[END_REF] the radical units do communicate with each other and align in a ferromagnetic manner.

Fig 1 .

 1 Fig 1. Structure of triradical 1 and Blatter's radical 2.

Crystal refinement data for triradical 1 (

 1 CCDC 1982625) Dark brown cubes. C 45 H 30 N 9 , M = 696.78, Trigonal, space group P3, a = 17.1703(9) Å, b = 17.1703(9) Å, c = 6.8377(4) Å, α = 90°, β = 90°, γ = 120°, V = 1745.81(16) Å 3 , Z = 2, T = 100(2) K, ρ calcd = 1.326 g•cm -3 , 2θ max = 25°. Refinement of 163 parameters on 2044 independent reflections out of 3962 measured reflections (R int = 0.0267) led to R 1 = 0.0491 [I > 2σ(I)], wR 2 = 0.1518 (all data), and S = 1.163 with the largest difference peak and hole of 0.338 e -3 and -0.227 e -3 , respectively.

  by a slow diffusion of n-pentane into a chlorobenzene solution of radical 1. Triradical 1 crystallizes in the trigonal P3 space group with one third of the triradical in the asymmetric unit (i.e. one benzotriazinyl moiety) and two molecules within the cell. Triradical 1 is nonplanar and adopts a shallow concave form with the benzotriazinyl C7 atoms 0.719 Å above the central benzene plane. The benzotriazinyl moieties twist in a propeller-like geometry by 174.1(2)° (torsion angle of N1-C3-C4-C5) and the dihedral angle of the central and triazinyl planes is 7.0(4)°. The N-phenyls twist out of the benzotriazinyl plane by 42.1(3)° (torsion angle of C15-C10-N2-N1) and the dihedral angle of the N-phenyl plane and the triazinyl plane is 47.6(1)°. No intramolecular interactions are observed.

Fig 2 .

 2 Fig 2. Thermal ellipsoid view of triradical 1 (CCDC 1982625). Crystallographic numbering

Fig 3 .

 3 Fig 3. One of the three equivalent supramolecular 1D chains of triradical 1 depicted along the

Fig 5 .

 5 Fig 5. Solution CW EPR spectrum of triradical 1 and fits to two models: a S = 3/2 giant spin

Fig. 6 .

 6 Fig. 6. Zoom of the lateral resonances of 1 at 110 K, showing fits with J ij (i, j = 1-3) values fixed to +100, +3, -3 and -100 cm -1 . The spectra are normalized to the central resonance.

Fig 7 .

 7 Fig 7. CW EPR and FSED spectra of 1 at 100 K. Experimental conditions. FSED: f pEPR =

Fig. 8 .

 8 Fig. 8. IR traces at the spectral maximum of 1 (350 mT) recorded at various temperatures,

Fig. 9 .

 9 Fig. 9. Left: Hahn echo decay traces at the spectral maximum of triradical 1 (350 mT)

Fig 10 .

 10 Fig 10. The three degenerate SOMO molecular orbitals (E SOMO(1-3) = -4.920 eV) of the

Fig 11 .

 11 Fig 11. Spin delocalization of triradical 1 calculated at the UB3LYP/6-31G(2d,p) level of

Acknowledgements C. P. Constantinides thanks the University of Michigan-Dearborn for an UM-Dearborn Scholars award. P. A. Koutentis thanks the A. G. Leventis Foundation for helping to establish the NMR facility at the University of Cyprus, the Cyprus Research Promotion Foundation and the following organizations and companies in Cyprus for generous donations of chemicals and glassware: the State General Laboratory, the Agricultural Research Institute, the Ministry of Agriculture, MedoChemie Ltd., Medisell Ltd., Biotronics Ltd.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.