Slow Magnetic Relaxation in Chiral Helicene-Based Coordination Complex of Dysprosium

The complex [Dy(L)(tta)3] with L the chiral 3-(2-pyridyl)-4-aza[6]-helicene ligand (tta− = 2-thenoyltrifluoroaacetonate) has been synthesized in its racemic form and structurally and magnetically characterized. [Dy(L)(tta)3] behaves as a single molecule magnet in its crystalline phase with the opening of a hysteresis loop at 0.50 K. These magnetic properties were interpreted with ab initio calculations.


Introduction
The design of single molecule magnet (SMM), with the aim of enhancing its peculiar magnetic properties, has been a prolific field in the scientific community for decades [1][2][3].Indeed, SMMs can pave the way towards a new generation of materials as, for example, molecular qubits for quantum computing [4], memory storage devices [5] or spin valves [6].In this framework, lanthanide ions are commonly exploited in the effort of reaching slower relaxation rates for the reversal of the magnetization.Indeed, lanthanides are well classified by looking at their electron density distribution, ranging from oblate (planar) to prolate (axial) distribution [7].This is mainly due to their strong spin-orbit coupling, which leads to ground states with large angular momentum J and strong magnetic anisotropy.The crystal field, induced by the donor atoms of the ligands, acts only as a perturbation on the electron density distribution, leading to a fine-tuning of the electronic properties and so of the molecular magnetism.As a consequence, the careful choice of the lanthanide ion and of the ligands (and the induced symmetry) can be used to engineer novel SMMs.However, a complete elucidation of these magneto-structural correlations for these complexes is still missing, even if progresses have been done recently [8][9][10][11].
For all the applications mentioned above, it is crucial to study the correlation between the SMM behavior and other physical properties such as luminescence or redox activity [12].The versatility of ligand chemistry can be exploited in this sense and may offer the possibility to have in a single compound, for instance, a magnetic emitting nanodevice [13][14][15].Indeed, lanthanides have been intensively studied for their peculiar luminescence that covers a broad range of frequencies (from visible to near IR) with sharp line shape emission bands and long lifetime of the excited states [16][17][18][19][20][21][22].However, they show very low absorption coefficients, since the f-f transitions are indeed prohibited (Laporte rule) [23].This results in ineffective direct excitation processes, especially in dilute solution.
To tackle this problem, indirect sensitization, using for example MLCT (Metal-Ligand Charge Transfer) transitions, has been developed by means of ligands functionalization with organic chromophores acting as antennae [24].In the case where the antenna is chiral, the solid-state properties might change between the enantiopure and the racemic crystals.Besides, the magnetic properties of these atoms can be used to modify the light absorption in chiral compounds, an effect known as magneto-chiral dichroism [25,26].
In the case of the [Dy(L)(hfac) 3 ] SMM [27], the chirality of the ligand results in two possible crystal structures (racemic and enantiopure) with similar molecular arrangement but different packings.Interestingly, racemic and enantiopure crystals show notable different magnetic behavior, with the opening of a magnetic hysteresis only in the case of the enantiopure.Moreover, the calculated different nature (antiferromagnetic and ferromagnetic) of the dipolar couplings between first-neighbors allows explaining the magnetic measurements (e.g., temperature dependence of χ M T).
With the aim to enhance the magnetic properties in this series of compounds, we present herein a novel derivative in which the hfac − ligands have been replaced by tta − (2-thenoyltrifluoroaacetonate) ligands.Indeed, it is well known that the swapping of these two ligands in such specific N 2 O 6 environment enhances the magnetic properties [36][37][38], even if in other coordination environments the opposite effect has been recently observed [39].Therefore, we report the synthesis, the single crystal X-ray structural analysis and the magnetic characterization along with extensive ab initio calculations of the novel compound [Dy(L)(tta) 3 ] (1).
1 crystallizes in the triclinic centrosymmetric space group P-1 (Figure 1 and Figure S1, Table S1).The Dy III ion is surrounded by two nitrogen atoms and six oxygen atoms coming from the three 2-thenoyltrifluoroacetonate (tta − ) anions and the L ligand.The N 2 O 6 coordination polyhedron can be described as a distorted square antiprism environment (D 4d symmetry on the basis of SHAPE analysis, Table S2) [41].Thus, the replacement of the 1,1,1,5,5,5-hexafluoroacetylacetonate anions with tta − ones confers an higher symmetry for the coordination environment [27].As already noted, such observation was already done for another complex stemming from this group and a significant positive impact on the magnetic properties was observed [37,38]. 1 crystallizes in the triclinic centrosymmetric space group P-1 (Figures 1 and S1, Table S1).The Dy III ion is surrounded by two nitrogen atoms and six oxygen atoms coming from the three 2thenoyltrifluoroacetonate (tta − ) anions and the L ligand.The N2O6 coordination polyhedron can be described as a distorted square antiprism environment (D4d symmetry on the basis of SHAPE analysis, Table S2) [41].Thus, the replacement of the 1,1,1,5,5,5-hexafluoroacetylacetonate anions with tta − ones confers an higher symmetry for the coordination environment [27].As already noted, such observation was already done for another complex stemming from this group and a significant positive impact on the magnetic properties was observed [37,38].Starting from the racemic mixture of L, both enantiomers are present in the cell (P-1 space group symmetry).The crystal packing reveals that heterochiral dimers are formed with the presence of ππ interactions between the 2,2′-bipyridyl moieties (Figure 2) while an organic network runs along the a-axis thank to π-π interactions between the helicenic parts.The Dy-Dy shortest intermolecular distance was measured equal to 8.935 Å which is similar to the distance measured in the complex involving the Dy(hfac)3 metallo-precursor.Starting from the racemic mixture of L, both enantiomers are present in the cell (P-1 space group symmetry).The crystal packing reveals that heterochiral dimers are formed with the presence of π-π interactions between the 2,2 -bipyridyl moieties (Figure 2) while an organic network runs along the a-axis thank to π-π interactions between the helicenic parts.The Dy-Dy shortest intermolecular distance was measured equal to 8.935 Å which is similar to the distance measured in the complex involving the Dy(hfac) 3 metallo-precursor.

Static Magnetic Measurements
The temperature dependence of χMT for the sample 1 is represented in Figure 3.The room temperature value is 13.96 cm 3 •K•mol −1 in good agreement with the expected value of 14.17 cm 3 •K•mol −1 for an isolated Dy III ion [42].Upon cooling, χMT decreases monotonically down to 11.20

Static Magnetic Measurements
The temperature dependence of χ M T for the sample 1 is represented in Figure 3.The room temperature value is 13.96 cm 3 •K•mol −1 in good agreement with the expected value of 14.17 cm 3 •K•mol −1 for an isolated Dy III ion [42].Upon cooling, χ M T decreases monotonically down to 11.20 cm 3 •K•mol −1 due to the thermal depopulation of the M J states.Below 5 K, the more rapid decrease could be attributed to the presence of weak dipolar antiferromagnetic interactions as determined by quantum calculations on the analogue complex involving hfac − ancillary ligands [27].The field dependence of the magnetization measured at 2.0 K reaches the value of 5.12 Nβ under a magnetic field of 50 kOe, in agreement with the expected value (5 Nβ) for an Ising ground state (Inset of Figure 3).

Static Magnetic Measurements
The temperature dependence of χMT for the sample 1 is represented in Figure 3.The room temperature value is 13.96 cm 3 •K•mol −1 in good agreement with the expected value of 14.17 cm 3 •K•mol −1 for an isolated Dy III ion [42].Upon cooling, χMT decreases monotonically down to 11.20 cm 3 •K•mol −1 due to the thermal depopulation of the MJ states.Below 5 K, the more rapid decrease could be attributed to the presence of weak dipolar antiferromagnetic interactions as determined by quantum calculations on the analogue complex involving hfac − ancillary ligands [27].The field dependence of the magnetization measured at 2.0 K reaches the value of 5.12 Nβ under a magnetic field of 50 kOe, in agreement with the expected value (5 Nβ) for an Ising ground state (Inset of Figure 3).

Dynamic Magnetic Measurements
The out-of-phase component of the ac susceptibility (χM′′) of 1 was measured using immobilized crunched single crystals.It shows frequency dependence in zero external dc field with clear maxima on the χM′′ vs. ν curves (ν the frequency of the ac oscillating field) up to 13 K (Figure 4a).The frequency

Dynamic Magnetic Measurements
The out-of-phase component of the ac susceptibility (χ M ) of 1 was measured using immobilized crunched single crystals.It shows frequency dependence in zero external dc field with clear maxima on the χ M vs. ν curves (ν the frequency of the ac oscillating field) up to 13 K (Figure 4a).The frequency dependence of the ac susceptibility can be analyzed in the framework of the extended Debye model (Figures S2 and S3) [43,44].The temperature dependence of the relaxation time at zero field is extracted between 2.0 and 14.0 K (Table S3).Formally, four different relaxation mechanisms coexist: Direct, Raman, Orbach and QTM [2].The former disappears in the absence of external field while the second and the third are field-independent.The latest is the only temperature independent mechanism.Fitting of the zero-field data with only Raman and QTM is not satisfactory while Raman + Orbach + QTM leads to unrealistic results owing to over-parameterization.The only realistic picture is given by the Orbach + QTM combination.In order to reduce the QTM operating in this system, the optimal magnetic field of 1000 Oe was determined by a scan field (Figure 4b).The application of this moderate external dc field induces a slowing down of the magnetic relaxation with a shift of the maxima of the χ M vs. ν curve at lower frequencies (Figure 4c).It must be mentioned that at moderate fields at least two relaxation processes coexist which merge into one at higher fields than 800 Oe (Figure 4b).Any attempts to fit the thermal behavior of the relaxation time with a combination of the previously mentioned mechanisms fail with a reasonable set of data.The thermal dependence of the relaxation time of the magnetization (Figures S4 and S5 and Table S4) can be fitted considering a combination of two thermally dependent regimes between 3.0 and 14.0 K (Orbach processes) (τ 0 = 2.0(7) × 10 −7 s and ∆ 0 = 68.1(3)cm −1 , τ 1 = 4.9(6) × 10 −4 s and ∆ 1 = 16.0(5)cm −1 ).Relaxation times on the order of few seconds is slow enough to observe the opening of the hysteresis loop at 0.50 K (Figure 5) which remains opened at higher temperatures (Figure S6).One must mention that the hysteresis loop of the racemic form of In order to reduce the QTM operating in this system, the optimal magnetic field of 1000 Oe was determined by a scan field (Figure 4b).The application of this moderate external dc field induces a slowing down of the magnetic relaxation with a shift of the maxima of the χM′′ vs. ν curve at lower frequencies (Figure 4c).It must be mentioned that at moderate fields at least two relaxation processes coexist which merge into one at higher fields than 800 Oe (Figure 4b).Any attempts to fit the thermal behavior of the relaxation time with a combination of the previously mentioned mechanisms fail with a reasonable set of data.The thermal dependence of the relaxation time of the magnetization (Figures S4 and S5 and Table S4) can be fitted considering a combination of two thermally dependent regimes between 3.0 and 14.0 K (Orbach processes) (τ0 = 2.0(7) × 10 −7 s and Δ0 = 68.1(3)cm −1 , τ1 = 4.9(6) × 10 −4 s and Δ1 = 16.0(5)cm −1 ).Relaxation times on the order of few seconds is slow enough to observe the opening of the hysteresis loop at 0.50 K (Figure 5) which remains opened at higher temperatures (Figure S6).One must mention that the hysteresis loop of the racemic form of [Dy(L)(hfac)3] [27] was closed at the same temperature.

Ab Initio Calculations
Various theoretical models, with various pros and cons, are available to predict the magnetic properties of lanthanides, ranging from complete active space ab initio methods (e.g., CASSCF or CASPT2) to semi-empirical methods (e.g., radial effective charge model, REC) [45].To study the electronic structure of the present compound, we choose SA-CASSCF/RASSI-SO calculations as a good compromise between accuracy with respect to the experimental evidence and "first principle" theoretical model.
Calculations were performed for 1 to understand the observed magnetic properties comparing

Ab Initio Calculations
Various theoretical models, with various pros and cons, are available to predict the magnetic properties of lanthanides, ranging from complete active space ab initio methods (e.g., CASSCF or CASPT2) to semi-empirical methods (e.g., radial effective charge model, REC) [45].To study the electronic structure of the present compound, we choose SA-CASSCF/RASSI-SO calculations as a good compromise between accuracy with respect to the experimental evidence and "first principle" theoretical model.
Calculations were performed for 1 to understand the observed magnetic properties comparing with the ab initio calculated electronic structure (see computational details).The calculated χ M T vs. T and M vs. H (Figure 3) curves fairly well reproduce the experimental curves, even if the agreement for the χ M T vs. T data is still semi-quantitative.Calculations confirm the axial character of the magnetic anisotropy tensor of the ground Kramers doublet with large g z values of 19.55 and almost negligible g x and g y values.The g z value for Dy III is close to the expected g z = 20 for a pure M J = |±15/2> ground state.This is confirmed by the calculated composition of M J = 0.94 |±15/2> + 0.06 |±11/2> for the ground doublet state of 1 (see Table for the wavefunction composition).The calculated ground-state easy axis (Figure 6) for the Dy III ion is oriented perpendicular to the plane formed by the 2,2 -bipyridine moieties as expected for an oblate ion with this coordination sphere [31,36].

Ab Initio Calculations
Various theoretical models, with various pros and cons, are available to predict the magnetic properties of lanthanides, ranging from complete active space ab initio methods (e.g., CASSCF or CASPT2) to semi-empirical methods (e.g., radial effective charge model, REC) [45].To study the electronic structure of the present compound, we choose SA-CASSCF/RASSI-SO calculations as a good compromise between accuracy with respect to the experimental evidence and "first principle" theoretical model.
Calculations were performed for 1 to understand the observed magnetic properties comparing with the ab initio calculated electronic structure (see computational details).The calculated χMT vs. T and M vs. H (Figure 3) curves fairly well reproduce the experimental curves, even if the agreement for the χMT vs. T data is still semi-quantitative.Calculations confirm the axial character of the magnetic anisotropy tensor of the ground Kramers doublet with large gz values of 19.S5 for the wavefunction composition).The calculated groundstate easy axis (Figure 6) for the Dy III ion is oriented perpendicular to the plane formed by the 2,2′bipyridine moieties as expected for an oblate ion with this coordination sphere [31,36].Even if the uniaxiality of the anisotropy is not strictly associated to slow relaxation of the magnetization [46], in most of the cases reported in the literature for Dy III this assumption is valid.Indeed, in this case, the magnetic relaxation pathways can also be easily interpreted on the basis of Even if the uniaxiality of the anisotropy is not strictly associated to slow relaxation of the magnetization [46], in most of the cases reported in the literature for Dy III this assumption is valid.Indeed, in this case, the magnetic relaxation pathways can also be easily interpreted on the basis of magnetic transition moments (Figure 7) calculated with the SINGLE_ANISO program [47,48].It has to be pointed out that in the latter not all the contributions are included.Indeed, the coupling of spin-phonon degrees of freedom in the SMM relaxation is not taken into account in the ab initio model whereas it has been recently evidenced of general importance [49,50].However, these discrepancies are common in literature [3,51,52] and the magnetic transition moments calculated in this work still leads to a fairly good qualitative picture.Indeed, no direct transition between the two M J states of the ground doublet or Orbach processes from the ground state are expected whereas relaxation mechanisms involving states from the third M J state are highly probable.A non-negligible Orbach process has been also found between the second and third M J states.The calculations indicate a difference between the calculated energy barrier (∆ = 82 cm −1 ) and the experimental barrier (∆ = 39-68 cm −1 ).However, the discrepancy between these values can be, reasonably, ascribed in the spin-phonon contributions mentioned above.
mechanisms involving states from the third MJ state are highly probable.A non-negligible Orbach process has been also found between the second and third MJ states.The calculations indicate a difference between the calculated energy barrier (Δ = 82 cm −1 ) and the experimental barrier (Δ = 39-68 cm −1 ).However, the discrepancy between these values can be, reasonably, ascribed in the spinphonon contributions mentioned above.

Crystallography
Single crystal of [Dy(tta) 3 (L)]•CH 2 Cl 2 •C 7 H 8 (1) was mounted on a APEXII Bruker-AXS diffractometer for data collection (MoKα radiation source, λ = 0.71073 Å).The structure was solved by direct methods using the SIR-97 program and refined with a full matrix least-squares method on F 2 using the SHELXL-97 program [55,56].Crystallographic data are summarized in Table S1.Complete crystal structure results as a CIF file including bond lengths, angles, and atomic coordinates are deposited as Supporting Information.CCDC number is 1510324 for compound 1.

Physical Measurements
The elementary analyses of the compound were performed at the Centre Régional de Mesures Physiques de l'Ouest, Rennes, France.The dc magnetic susceptibility measurements were performed on solid polycrystalline sample with a Quantum Design MPMS-XL SQUID magnetometer between 2 and 300 K in an applied magnetic field of 0.02 T for temperatures in the range 2-20 K, 0.2 T between 20 and 80 K and 1 T for temperatures between 80 and 300 K.These measurements were all corrected for the diamagnetic contribution as calculated with Pascal's constants.The ultra-low temperature measurements 1.8 K) were performed with the help of a 3 He insert.

Computational Details
Wavefunction-based calculations were carried out on molecular structures of 1 by using the SA-CASSCF/RASSI-SO approach, as implemented in the MOLCAS quantum chemistry package (versions 8.0) [57].In this approach, the relativistic effects are treated in two steps on the basis of the Douglas-Kroll Hamiltonian.First, the scalar terms were included in the basis-set generation and were used to determine the spin-free wavefunctions and energies in the complete active space self-consistent field (CASSCF) method [58].Next, spin-orbit coupling was added within the restricted-active-space-state-interaction (RASSI-SO) method, which uses the spin-free wavefunctions as basis states [59,60].The resulting wavefunctions and energies are used to compute the magnetic properties and g-tensors of the lowest states from the energy spectrum by using the pseudo-spin S = 1/2 formalism in the SINGLE-ANISO routine [47,48].Cholesky decomposition of the bielectronic integrals was employed to save disk space and speed-up the calculations [61].For 1 the active space of the self consistent-field (CASSCF) method consisted of the nine 4f electrons of the Dy III ion spanning the seven 4f orbitals, i.e., 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 (due to hardware limitations) of the Dy III ion.Twenty-one sextets, 128 quadruplets, and 107 doublets were mixed through spin-orbit coupling in RASSI-SO.All atoms were described by ANO-RCC basis sets [62][63][64].The following contractions were used: [8s7p4d3f2g1h] for Dy, [4s3p2d1f] for the O and N atoms, [3s2p1d] for the C and F atoms, [4s3p1d] for the S atoms and [2s1p] for the H atoms.The atomic positions were extracted from the X-ray crystal structures.Only the position of the H and F atoms were optimized on the Y III parent complexes with the Gaussian 09 (revision D.01) package [65] employing the PBE0 hybrid functional [66,67].The "Stuttgart/Dresden" basis sets [68] and effective core potentials were used to describe the yttrium atom, whereas all other atoms were described with the SVP basis sets [69].
[Dy(L)(tta) 3 ] behaves as a single molecule magnet in its crystalline phase.As expected, the substitution of hfac − ligands by tta − moieties enhances the magnetic behavior with the opening of an hysteresis loop at 0.50 K that was only observed for the enantiopure forms in the case of [Dy(L)(hfac) 3 ] [27].The electronic structure of the complex has been elucidated by mean of SA-CASSCF/RASSI-SO calculations, highlighting the nature of the ground state and contributing in the interpretation of experimental evidences.A qualitative picture of the magnetization blocking barrier is also reported.In the near future, we will pursue our investigation of chiral lanthanide-based SMMs that may offer new perspectives in both the domains of molecular magnetism and chirality with the potential access of properties such as circularly polarized luminescence (CPL) activity that remains anecdotic for lanthanide compounds to date.

Supplementary Materials:
The following are available online at www.mdpi.com/2312-7481/3/1/2/s1, Figure S1: ORTEP view of 1. Thermal ellipsoids are drawn at 30% probability.Hydrogen atoms and solvent molecules of crystallization are omitted for clarity., Figure S2: Frequency dependence of the ac susceptibility components χ M and χ M at 10 K and in zero external dc field for compound 1 with the best fitted curve with extended Debye

Figure 2 .
Figure 2. Crystal packing of 1 along the a-axis."Spacefill" and "ball and sticks" representations are used for L ligands and organometallic moieties, respectively.

Figure 2 .
Figure 2. Crystal packing of 1 along the a-axis."Spacefill" and "ball and sticks" representations are used for L ligands and organometallic moieties, respectively.

Figure 2 .
Figure 2. Crystal packing of 1 along the a-axis."Spacefill" and "ball and sticks" representations are used for L ligands and organometallic moieties, respectively.

Figure 3 .
Figure 3. Temperature dependence of χMT for 1 (black circles).The inset shows the field variations of the magnetization at 2 K. Full red lines correspond to the simulated curves from ab initio calculations.

Figure 3 .
Figure 3. Temperature dependence of χ M T for 1 (black circles).The inset shows the field variations of the magnetization at 2 K. Full red lines correspond to the simulated curves from ab initio calculations.

Figure 4 .
Figure 4. (a) Frequency dependence of χM′′ between 2 and 14 K; (b) scan field of the frequency dependence of χM′′ at 2 K; (c) frequency dependence of χM′′ between 2 and 14 K under an applied magnetic field of 1000 Oe; and (d) temperature variation of the relaxation time measured in zero field (open squares) and in an external field of 1000 Oe (full squares) with the best fitted curve (red lines) in the temperature range of 2-14 K.

Figure 4 . 12 Figure 5 .
Figure 4. (a) Frequency dependence of χ M between 2 and 14 K; (b) scan field of the frequency dependence of χ M at 2 K; (c) frequency dependence of χ M between 2 and 14 K under an applied magnetic field of 1000 Oe; and (d) temperature variation of the relaxation time measured in zero field (open squares) and in an external field of 1000 Oe (full squares) with the best fitted curve (red lines) in the temperature range of 2-14 K. Magnetochemistry 2017, 3, 2 6 of 12

Figure 5 .
Figure 5. Magnetic hysteresis loop of 1 measured at 0.5 K at a sweep rate of 16 Oe•s −1 .

Figure 5 .
Figure 5. Magnetic hysteresis loop of 1 measured at 0.5 K at a sweep rate of 16 Oe•s −1 .
55 and almost negligible gx and gy values.The gz value for Dy III is close to the expected gz = 20 for a pure MJ = |±15/2> ground state.This is confirmed by the calculated composition of MJ = 0.94 |±15/2> + 0.06 |±11/2> for the ground doublet state of 1 (see Table

Figure 6 .
Figure 6.Representation of complex 1 with the theoretical orientation of the easy magnetic axis of the Dy III center.

Figure 6 .
Figure 6.Representation of complex 1 with the theoretical orientation of the easy magnetic axis of the Dy III center.

Figure
Figure Computed magnetization blocking barrier in complex 1 for the Dy III ion.Numbers provided on each arrow are the mean absolute values for the corresponding matrix elements of the magnetic transition dipole moment.

Figure 7 .
Figure 7. Computed magnetization blocking barrier in complex 1 for the Dy III ion.Numbers provided on each arrow are the mean absolute values for the corresponding matrix elements of the magnetic transition dipole moment.