A Chiral Bipyrimidine-Bridged Dy2 SMM: A Comparative Experimental and Theoretical Study of the Correlation Between the Distortion of the DyO6N2 Coordination Sphere and the Anisotropy Barrier

Chiral bipyrimidine-bridged dinuclear LnIII complexes of general formula [(μ-bipym){((+)-tfacam)3Ln}2] and [(μ-bipym){((-)-tfacam)3Ln}2], have been prepared from the assembly of Ln(AcO)3·nH2O (LnIII = Dy, Gd), (+)/(−)-3-(trifluoroacetyl)camphor enantiopure ligands ((+)/(-)-Htfacam) and bipyrimidine (bipym). The structure and chirality of these complexes have been supported by single-crystal X-Ray diffraction and circular dichroism. The study of the magnetic properties of the GdIII complexes revealed a very weak antiferromagnetic interaction between the GdIII ions through the bipyrimidine bridging ligand. Ab initio CASSCF calculations indicated that the ground Kramers doublet (KD) of both DyIII centers is almost purely axial with the anisotropy axis located close to the two tfacam−ligands at opposite sides of each DyIIIatom, which create an axial crystal field. In keeping with this, ac dynamic measurements indicated slow relaxation of the magnetization at zero field with Ueff = 55.1 K, a pre-exponential factor of τo = 2.17·10−6 s and τQTM = 8 μs. When an optimal dc field of 0.1 T is applied, QTM is quenched and Ueff increases to 75.9 K with τo = 6.16 × 10−7 s. The DyN2O8 coordination spheres and SMM properties of [(μ-bipym){((+)-tfacam)3Ln}2] and their achiral [(Dy(β-diketonate)3)2(μ-bpym)]analogous have been compared and a magneto-structural correlation has been established, which has been supported by theoretical calculations. In contrast to the GdIII compounds, the magnetic exchange interaction between the DyIII ions has been calculated to be very weak and, generally, ferromagnetic in nature. Relaxation mechanisms for [(μ-bipym){((+)-tfacam)3Ln}2] and previously reported analogous have been proposed from ab initio calculations. As the magnetic exchange interaction found to be very weak, the observed magnetization blockade in these systems are primarily dictated by the single ion anisotropy of DyIII ions.


Chiral bipyrimidine-bridged dinuclear Ln III complexes of general formula [(µ-bipym){((+)-tfacam) 3 Ln} 2 ] and [(µ-bipym){((-)-tfacam)
Ln} 2 ], have been prepared from the assembly of Ln(AcO) 3 ·nH 2 O (Ln III = Dy, Gd), (+)/(−)-3-(trifluoroacetyl)camphor enantiopure ligands ((+)/(-)-Htfacam) and bipyrimidine (bipym). The structure and chirality of these complexes have been supported by single-crystal X-Ray diffraction and circular dichroism. The study of the magnetic properties of the Gd III complexes revealed a very weak antiferromagnetic interaction between the Gd III ions through the bipyrimidine bridging ligand. Ab initio CASSCF calculations indicated that the ground Kramers doublet (KD) of both Dy III centers is almost purely axial with the anisotropy axis located close to the two tfacam − ligands at opposite sides of each Dy III atom, which create an axial crystal field. In keeping with this, ac dynamic measurements indicated slow relaxation of the magnetization at zero field with U eff = 55.1 K, a pre-exponential factor of τ o = 2.17·10 −6 s and τ QTM = 8 µs. When an optimal dc field of 0.1 T is applied, QTM is quenched and U eff increases to 75.9 K with τ o = 6.16 × 10 −7 s. The DyN 2 O 8 coordination spheres and SMM properties of [(µ-bipym){((+)-tfacam) 3 Ln} 2 ] and their achiral [(Dy(β-diketonate) 3 ) 2 (µ-bpym)]analogous have been compared and a magneto-structural correlation has been established, which has been supported by theoretical calculations. In contrast to the Gd III compounds, the magnetic exchange interaction between the Dy III ions has been calculated to be very weak and, generally, ferromagnetic in nature. Relaxation mechanisms for [(µ-bipym){((+)-tfacam) 3 Ln} 2 ] and previously reported analogous have been proposed from ab initio calculations. As the magnetic exchange interaction found to be very weak, the observed magnetization blockade in these systems are primarily dictated by the single ion anisotropy of Dy III ions.

INTRODUCTION
During the last few decades, molecular materials in which coexist two or more physical properties (multifunctional molecular materials) have attracted much attention mainly due to their promising potential applications (Coronado et al., 2003a(Coronado et al., ,b, 2008Gómez-Romero and Sánchez, 2004;Fahmi et al., 2009;Rocha et al., 2011;Sanchez et al., 2011;Ouahab, 2012). It is well-known that a molecule without any improper axis of symmetry (S n ) is chiral, that is to say is not superimposable with its mirror image (enantiomer). Interestingly, each enantiomer can interact in a different manner with the environment. Thus, for instance, enantiomers are optically active and rotate the plane of polarized light the same angle but in opposite directions. In multifunctional materials based on coordination compounds, chirality can be spawn by using enantiomerically pure ligands (Amouri and Gruselle, 2008;Pinkowicz et al., 2015). The inherent chirality of the ligand may introduce additional functions to coordination compounds with interesting magnetic properties such as magnetochiral dichroism (MChD) effect Raupach, 1997, 2000;Train et al., 2008Train et al., , 2011, second harmonic generation (SHG) (Bogani et al., 2006;Train et al., 2009), and ferroelectric properties Li et al., 2017). It has been recently shown that mononuclear tris(β-diketonate) Dy III complexes containing a N,N-bidentate chelate aromatic ligand, such as 2,2 ′ -bipyrimidine and 1,10phenanthroline derivatives, as well as Dy 2 dinuclear complexes containing bis(didentate) bridging ligands connecting two tris(βdiketonate) Dy III moieties, such as 2,2'-bipyrimidine and 2,2'bipyrimidine-N-oxide, exhibit Single-Molecule Magnet (SMM) behavior at zero field with significant thermal energy barriers (U eff ) (Chen et al., 2011Wang et al., 2013;Tong et al., 2015;Sun et al., 2016;Yu et al., 2016;Cen et al., 2017;Díaz-Ortega et al., 2018). SMMs are nanomagnets that, in addition to the classical properties of a magnet, such as freezing of magnetization and magnetic hysteresis below the so called blocking temperature (T B ), exhibit interesting quantum properties, such as quantum tunneling of the magnetization (QTM) and quantum phase interference (Aromí and Brechin, 2006;Gatteschi et al., 2006;Andruh et al., 2009;Bagai and Christou, 2009;Sessoli and Powell, 2009;Brechin, 2010;Guo et al., 2011;Rinehart and Long, 2011;Sorace et al., 2011;Clemente-Juan et al., 2012;Luzon and Sessoli, 2012;Wang and Gao, 2012;Habib and Murugesu, 2013;Woodruff et al., 2013;Zhang et al., 2013;Bartolomé et al., 2014;Layfield, 2014;Sharples and Collison, 2014;Craig and Murrie, 2015;Layfield and Murugesu, 2015;Liddle and van Slageren, 2015;Rosado Piquer and Sañudo, 2015;Tang and Zhang, 2015;Frost et al., 2016;Harriman and Murugesu, 2016). SMMs are of current interest not only due to the above indicated outstanding physical properties but also due to their envisaged applications in molecular spintronics (Bogani and Wernsdorfer, 2008;Dediu et al., 2009;Mannini et al., 2010;Vincent et al., 2012;Ganzhorn et al., 2013;Jenkins et al., 2013;Prezioso et al., 2013;Thiele et al., 2014;Lumetti et al., 2016;Cornia and Seneor, 2017), ultra-high density magnetic information storage (Rocha et al., 2005;Affronte, 2009), magneto-optics (Sessoli et al., 2015) and as qubits for quantum computing at molecular level (Leuenberger and Loss, 2001;Ardavan et al., 2007;Stamp and Gaita-Ariño, 2009;Martínez-Pérez et al., 2012;Ghirri et al., 2017). SMM behavior is bound to the existence of an energy barrier (U) that avoid magnetization reversal when the polarizing field is suppressed. In principle, in the absence of QTM and TA-QTM (thermal activated as quantum tunneling of the magnetization), which shortcut the relaxation barrier to an effective value (U eff ), T B increases with the height of the energy barrier. As the height of U primarily depends on the magnetic anisotropy, researchers have focused their attention on complexes containing lanthanide ions (and actinide) Ding et al., 2016;Gregson et al., 2016;Gupta et al., 2016a;Liu et al., 2016;Goodwin et al., 2017;Guo et al., 2017), which exhibit large intrinsic magnetic anisotropy and large magnetic moments in the ground state. The use of lanthanide ions and, particularly the Dy III ion (a Kramers ion for which QTM should be forbidden in the absence of magnetic field) has led to metal complexes with higher energy barriers and improved SMM properties. In polymetallic Ln complexes, Ln···Ln interactions increase quantum tunneling rates, leading to apparently low U eff values. However, it has been shown that weak intramolecular Dy···Dy magnetic interactions in dinuclear Dy 2 complexes do not eliminate the barrier for magnetization reversal when anisotropic axes are parallel (Moreno Pineda et al., 2014). Recently, it has been also shown that the incorporation of a Dy 2 unit with an strong Dy-electron coupling inside a fullerene cage gives rise to a blocking temperature of 18 K. This fact demonstrate that not only the magnetic exchange between the Dy III ions but also the ligand environment is crucial in dictating both the effective energy barrier and eventually the blocking temperature for this structural motif (Singh et al., 2015;Singh and Rajaraman, 2016;Liu F. et al., 2017).
The ligand 2,2'-bipyrimidine (bipym) has been shown to exhibit a great ability to bridge metal ions affording homopolynuclear d and f complexes, as well as heteropolynuclear d/d and d/f complexes. In these complexes, bipym is able to transmit moderate to strong magnetic exchange interactions between the metal ions in d/d complexes and very weak magnetic coupling in f/f systems (De Munno et al., 1996;Znovjyaka et al., 2009;Visinescu et al., 2010). Moreover, bipym is able to sensitize the luminescence of the lanthanide ions in the Vis and near IR regions (Zucchi, 2011).

X-Ray Crystallography
Suitable crystals of complexes d-1, l-1, and d-2 were mounted on a Bruker D8 Venture (Mo Kα radiation, λ = 0.71073 Å, Photon 100 CMOS detector). Details of the crystals, data collection and refinement parameters are given as (Table S1). Once the data were processed (raw data integration, merging of equivalent reflections and empirical correction of the absorption), the structures were solved by either Patterson or Direct methods and refined by full-matrix least-squares on weighted F 2 values using the SHELX suite of programs (Sheldrick, 2007) integrated in Olex2 (Dolomanov et al., 2009). Selected bond lengths and angles can also be found in (Tables S2-S4). Due to the poor quality of the data and crystallographic disorder affecting tfacam ligands the complete resolution of d-2 was not possible. However, the unit cell [triclinic, P1, a = 100356 (6) Å, b = 12.9983 (8) Å, c = 17.4831 (10) Å, α = 101.7875 (19) • , β = 103.1306 (18) • , γ = 106.5972 (18) • , a partial refinement, and comparison between the experimental X-ray powder diffraction diagrams of d-1 and d-2 ( Figure S8) confirm that both complexes are isostructural. To carry out the XRPD experiments, crystals of d-1 and d-2 were ground and deposited in the sample holder of a θ :θ Bruker AXS D8 vertical scan diffractometer. The generator was operated at 40 kV and 40 mA. The scans were performed with 4 • <2θ <30 • with t = 2 s and 2θ = 0.005 • . CCDC-1834837-8 contains the supplementary crystallographic data for this article. These data are provided free of charge by the Cambridge Crystallographic Data Centre.

Physical Measurements
Elemental analyses were carried out at the "Centro de Instrumentación Científica" of the University of Granada on a Fisons-Carlo Erba analyser model EA 1108. FT-IR spectra were recorded with a Bruker Tensor 27 spectrometer using an ATR accessory. Direct (dc) and alternating (ac) current susceptibility measurements were performed with a Quantum Design SQUID MPMS XL-5 device. Ac experiments were performed using an oscillating ac field of 3.5 Oe and frequencies ranging from 1 to 1,500 Hz. Low-temperature magnetization measurements were performed by means of a conventional inductive probe in pulsed-magnetic fields. The temperature was reached as low as 0.4 K using a 3 He cryostat (Nojiri et al., 2007). Polycrystalline specimens were mounted in a capillary tube made of polyimide. Samples of approximately 20 mg were not fixed within the sample tube and then they aligned along the magnetic field direction. Subsequently, a magnetic field was applied several times until orientation effect was saturated and the magnetization curves obtained in further shots were found to be identical. Solid-state CD spectra were performed on a JASCO J-810 spectropolarimeter at room temperature. Crystalline samples were ground to fine powders with potassium chloride and compressed into transparent disks. The concentration of the disks was 1.00 mg per 100 mg (sample/KCl) for CD spectra measurements. The P-E hysteresis loop was recorded with a home-made modified Sawyer-Tower circuit, using a reference capacitor (4.7 nF) and a digital Picoscope 1004 oscilloscope. The circuit was calibrated with monocrystalline BaTiO 3 .

Computational Methodology
MOLCAS 8.0 program package (Karlstrom et al., 2003;Veryazov et al., 2004;Duncan, 2009;Aquilante et al., 2010Aquilante et al., , 2016 has been used to perform post-Hartree-Fockab initio calculations. Diamagnetic substitution method was followed to calculate the magnetic anisotropy on one Dy center while another Dy center was substituted by Lu. Basis set of VTZP quality was used for all the metals and atoms attached in the first coordination sphere of the metal and for rest of the atoms basis set of VDZ quality was used. All the basis set was taken from ANO-RCC (atomic natural orbital type with relativistic core corrections) library implemented in MOLCAS8.0 software (Aquilante et al., 2010). Using DKH Hamiltonian relativistic effects was treated in two steps. For the generation of basis sets scalar terms were included which have been used to determine spin-free wave functions and also energies through the use of the complete active space self-consistent field (CASSCF) method (Chibotaru and Ungur, 2012). Thus, spin-orbit free states were obtained by employing the RASSCF method whereas spin-orbit coupling has been taken into account using RASSI-SO method Langley et al., 2014) which uses CASSCF wave functions as the basis sets and multiconfigurational wave functions as input states. The resulting wave functions and the energies of the molecular multiplets were used for the calculation of the magnetic properties and g tensors of the lowest state using a specially designed routine SINGLE_ANISO (Roos et al., 2008). As a consequence, the magnetic properties of a single magnetic ion are calculated by a fully ab initio approach in which the spin-orbit coupling is considered nonperturbatively. The active space consists all the 4f electrons in seven orbital CAS(9,7) which generates 21 sextet states. The consideration of only these states is sufficient to reproduce the experimental measurements as it has been seen from the previous studies (Upadhyay et al., 2014(Upadhyay et al., , 2017Gupta et al., 2016c;Mukherjee et al., 2016;Vignesh et al., 2017a,b). In order to save disk space, Cholesky decomposition possessing a threshold of 0.2 * 10 −7 has been incorporated for our calculations (Koch et al., 2003). Magnetic exchange interactions, exchange spectrum and all other magnetic properties of Dy 2 dinuclear complex has been deduced using Lines model within the POLY_ANISO (Ungur and Chibotaru, 2007) routine which interfaced with SINGLE_ANISO based on the ab initio results of individual metal fragments (Feltham et al., 2011;Ungur and Chibotaru, 2011;Ungur et al., 2013).
To calculate the magnetic exchange between the Dy ions DFT calculations has been performed with hybrid B3LYP functional using Gaussian 09 programme (Schafer et al., 1992(Schafer et al., , 1994Becke, 1993;Frisch et al., 2016). Since Dy(III) possess first order spin orbit coupling due to weak splitting of 4f orbitals, it cannot be described by single determinant. To get the remedy of these problem Dy atoms was replaced by Gd atoms since it does not contain first order orbital angular momentum and can be described as a single determinant. We have employed Cundari-Stevens (CS) relativistic effective core potential for Gd atom, TZV basis set for the atoms in the first coordination sphere around metal ion (Scuseria and Schaefer, 1989;Schafer et al., 1992Schafer et al., , 1994Cundari and Stevens, 1993). From the second coordination onwards a basis bet of SVP quality was used (Cundari and Stevens, 1993;Hänninen et al., 2018). Quadratic convergence method was followed to the most stable wave function. The energy of the high spin state was obtained from the single determinant approach while the energy of the BS state was obtained by the approach developed by Noodleman (Noodleman, 1981;Hänninen et al., 2018). Exchange is calculated from the energy difference of the BS and HS states. To find the exchange coupling constant between Dy ions resulting exchange was multiplied by a factor of 5/7.
The dinuclear complexes d-1, l-1, and d-2 are, as expected, isostructural and crystallize in the triclinic polar P1 space group. We are going to describe below the structure of d-1 as an example of all of them. The structure consists of well-isolated [(µ-bipym){((+)-tfacam) 3 Dy} 2 ], in which two [Dy(tfacam) 3 ] moieties are connected by the symmetric bis-bidentate 2,2 ′bipyrimidine ligand, with an intramolecular Dy···Dy distance of 6.847 Å (Figure 1). Selected bond distances and angles are gathered on Tables S2, S3. Although both Dy III ions exhibit DyN 2 O 6 coordination environments, which are formed by the coordination of six oxygen atoms from the three tfacam − diketonate ligands and the two nitrogen atoms from the bipym bridging ligand, however, they are crystallographically nonequivalent and show somewhat different bond distances and angles. The analysis of the DyN 2 O 6 coordination spheres of Dy1 and Dy2 by the continuous-shape-measures (CShMs) method and SHAPE software (Llunell et al., 2005) reveals that their geometries are intermediate between several ideal eightcoordinated polyhedra. In the case of Dy1 the lowest CShMs parameters are 0.686 (D 4d square antiprism) and 2.315 (D 2d triangular dodecahedron), whereas for Dy2 the lowest CShMs parameters are 1.083 (D 4d square antiprism) and 1.085 (D 2d triangular dodecahedron), (Table S4). Therefore, for Dy1 the geometry is close to square antiprism, whereas the geometry of Dy2 is the is in between the D 4d ↔D 2d deformation pathway. The Dy-O tfacam bond distances, which are found in the 2.272(4) Å (Dy1-O1)-2.377(4) Å (Dy2-O7) range, are shorter than the Dy-N bipym distances, which fall in the 2.611(5) ((Dy2-N1) Å-2.621(3) Å (Dy1-N4) range. This fact is not unexpected, as the electrostatic interactions between the Dy III ion and oxygen atoms of the tfacam − ligands are larger than those involving the nitrogen atoms of the bipym bridging ligand. Similar bond distances have been observed for the analogous achiral [(µbipym){(β-diketonate) 3 Dy} 2 ] complexes (Sun et al., 2016;Yu et al., 2016). The [(µ-bipym){((+)-tfacam) 3 Dy} 2 ] molecules are well-isolated in the structure because they are neither involved in hydrogen bond interactions nor in close intermolecular contacts. The shortest Dy···Dy distance being of 9.496 Å.
The solid-state CD spectra of complexes d-1 and l-1 support their enantiomeric nature (Figure 2) as they exhibit almost mirror-image CD spectra. Cotton effects were observed for both d-1/l-1 enantiomers between 200 and 350 nm. The spectrum of d-1 shows positive Cotton effects at λmax = 240, 293 y 340 nm, whereas l-1 shows Cotton effects with opposite signs at FIGURE 2 | Solid-state CD spectra of d-1(blue)/l-1(red) based on a pressed KBr pellet of the respective crystals (1% wt) at room temperature. the same wavelengths. These results show that the chirality has been successfully transmitted from the ligand to the coordination environment of the Dy centers.
In spite of belonging to a P1 polar group, polarization measurements as a function of the applied electric field carried out on crystal samples of d-1 and l-1 at room temperature indicate that these compounds do not present P-E hysteresis loop and consequently ferroelectricity, exhibiting typical dielectric behavior. This fact could be due to the lack of enough charge separation between the Dy III cation and the donor atoms of the ligands as to produce large electric dipolar moments.

Magnetic Properties
The magnetic properties are identical for both enantiomer, so we will described only the data obtained from d-enantiomers in this section.
At room temperature, the observed χ M T value for d-1 (27.77 cm 3 ·K·mol −1 ) is close to that expected for two independent Dy III ions in the free-ion approximation (28.34 cm 3 ·K·mol −1 ). Lowering temperature, the χ M T product remains almost constant down to 100 K, when it decreases steadily until approximately 20 K and then more sharply to reach a value of de 21.91 cm 3 ·K·mol −1 at 2 K. This behavior is mainly due to the combined effects of the depopulation of the M J sublevels of the Dy III ions, which arise from the splitting of the ground term by the ligand field, as well as possible dipolar and exchange antiferromagnetic interactions. The magnetization vs. field plots for d-1 at T = 2 K (Figure 3, inset) exhibit a fast increase of the magnetization up to ∼ 1 T and then a slow increase with the field without reaching saturation at 5 T, which is mainly due to the presence of significant magnetic anisotropy and the possible existence of thermally and field accessible excited states. The magnetization value at the highest applied dc magnetic field of 5 T (10.7 N µB ) is about half of that calculated for non-interacting Dy III ions (20 Nµ B ), which can be mainly attributed to crystalfield effects giving rise to significant magnetic anisotropy and to an axial M J = ± 15/2 ground state (Bi et al., 2011;Feltham et al., 2011;Ruiz et al., 2012). With the aim of analyzing the sign and magnitude of the magnetic interaction between the Dy···Dy ions in d-1, we have studied the magnetic properties of the isostructural Gd III complex (d-2). We have followed this strategy because isostructural Gd III and Dy III containing complexes, generally, display the same type of magnetic coupling (Colacio et al., 2010). Nevertheless, this assumption should be taken with caution as some dinuclear Dy III complexes with either oxalate or diphenoxide bridging groups exhibit ferromagnetic interactions between the Dy III (Xu et al., 2010), whereas dinuclear Gd III complexes containing such type of bridging ligands typically exhibit antiferromagnetic interaction between Gd III ions. The room temperature χ M T value for d-2 (16.68 cm 3 ·K·mol −1 ) is close to the calculated value of (15.75 cm 3 ·mol −1 ·K) for two magnetically independent Gd III ions (4f 7 , S = 7/2, g J = 2). On cooling down, the χ M T product remains constant down to 10 K and then decreases to reach a value of 15.73 cm 3 ·K·mol −1 at 2 K. This behavior is more likely due to the combined action of very weak intramolecular exchange interactions between the Gd III ions through the bipym bridging ligand, Zeeman saturation effects and very tiny ZFS of the ground state, which sometimes is observed for this essentially isotropic ion. The field dependence of the magnetization at 2 K (Figure 3, inset) shows a relatively rapid increase of the magnetization up to 2 T and then a linear increase to reach a value of 14.29 Nµ B at 5 T, which is very close to the theoretical saturation value for two Gd III ions with g = 2.0 (14 Nµ B ).
The magnetic susceptibility and magnetization data of d-2 were analyzed with the following Hamiltonian: where the first term takes into account the intramolecular isotropic interaction between the Gd III ions through the bipym ligand and the second term corresponds to the Zeeman effect (the g factor has been considered to be the same for the two Gd III ions), µ B is the Bohr magneton and B the applied magnetic field. The simultaneous best fit of susceptibility and magnetization data with the PHI software (Chilton et al., 2013a) afforded the following set of parameters: J = −0.011 cm −1 , g = 2.056 and R = 4·10 −4 (R = χ M T exp − χ M T calc 2 / χ M T exp 2 ). The extracted J value is of the same order of magnitude, but twice larger than that found in the analogous compound [(Gd(tmh) 3 ) 2 (µ-bpym)] (J = −0.006 cm −1 ) and smaller than those extracted for other bipyrimidine-bridged Gd III complexes containing different ancillary ligands with J values between −0.039 cm −1 and 0.053 cm −1 (Znovjyaka et al., 2009;Visinescu et al., 2010). These results show the non-innocent role played by the coligands in determining the magnitude of the magnetic exchange interactions in bipyrimidine-bridged Gd III complexes. It should be noted that the extracted J value could be considered as the upper limit for the magnetic interaction because it must also comprise the effects of the possible ZFS and Zeeman interaction. In view of these results, it would be reasonable to assume that d-1 also exhibits antiferromagnetic interaction between the Dy III ions.
The ground Kramers doublet of the Dy III ion in d-1 is axial (see below and ab initio calculations) and, in principle, it should exhibit SMM behavior. In good agreement with this, complex d-1 shows frequency and temperature dependence of the outof-phase magnetic susceptibility (χ" M ) at zero field below 20 K (Figure 4) with maxima in the 12.5 K (1,400 Hz)−6.5 K (50 Hz) temperature range.
This behavior is indicative of slow relaxation of the magnetization and confirms its SMM behavior. Moreover, χ" M shows a relatively strong increase (Figures 4A,B) below 4 K, which could be due to fast QTM relaxation. It is worth noting that in spite of the fact that the Dy centers are non-crystallographically equivalent, the temperature, and frequency dependence of the χ" M signals do not show two maxima but instead a broad peak, thus indicating that the relaxation processes for the two Dy centers have very close thermal energy barriers. The temperature dependence of the relaxation times for magnetization reversal (τ ) was extracted from the fit of the frequency dependence of χ" M at different temperatures to the generalized Debye model. Fitting the extracted relaxation times to the Arrhenius equation in the high temperature region (10-15 K), afforded an effective energy barrier for the reversal of the magnetization U eff = 55.1 K and a pre-exponential factor τ o = 2.17·10 −6 s ( Figure 5C). The τ o value is larger than those usually found for Dy III based SMMs, which can be due to the existence of QTM. As it can be observed in the Arrhenius plot, the relaxation times deviate from the linearity below 10 K and became almost temperature independent below 4 K, which allows us to extrapolate a relaxation time for the QTM process τ QTM = 8 µs. The Cole-Cole plots show semicircular shapes with α values in the 0.343 (5.0 K)−0.164 (13.0 K) region, thus confirming the presence of a distribution of relaxation processes ( Figure S9). The α parameter determines the width of the distribution of relaxation times, so that α = 1 corresponds to an infinitely wide distribution of relaxation times, whereas α = 0 represents a process with only a single relaxation time.
It is well-known that QTM in the ground state can be promoted by transverse anisotropy, as well as dipolar and hyperfine interactions. In order to suppress QTM, two strategies are generally used: (i) to apply a small dc field, which removes degeneration in the ground and excited states thus preventing, at least partly, QTM (ii) Magnetic dilution with an isostructural diamagnetic compound for declining dipolar interactions. In view of this, we decided to prepare an isostructural diluted compound of d-1 containing a Dy III /Y III = 1/20 molar ratio (namely d-1') and to measure the temperature dependence of the ac susceptibilitity at zero field and 0.1 T (this is the optimal field inducing a larger relaxation time, Figure S10), as well as that of the undiluted compound at 0.1 T, using a frequency of 1,400 Hz ( Figure S11). From this study the following conclusions can be drawn: (i) Peaks at 0.1 T appear slightly shifted to higher temperatures than those at zero field for the undiluted as well as for the diluted compound. (ii) The low temperature tail due to QTM almost disappears for the diluted complex as well as when a dc field of 0.1 T is applied on the undiluted compound. In view of this, we decided to perform a complete set of ac measurements in the presence of a dc magnetic field of 0.1 T.
As it can be observed in Figures 4C,D, the maxima in the χ M " vs T plot now appear between 13.5 K (1,400 Hz) and 4.0 K (1 Hz). Moreover, the χ M " signal tends to zero after the maxima, thus pointing out that the QMT has been almost completely eliminated. Fitting of the frequency dependence of χ" M at different temperatures to the generalized Debye model, afforded the relaxation times of the magnetization (τ ) at each temperature ( Figure 5A). The effective energy barrier for the reversal of the magnetization (U eff ) and the pre-exponential factor τ 0 extracted from the fit of τ in the high temperature region (15-10 K) to an Arrhenius law were: U eff = 75.9 K and τ o = 6.16 × 10 −7 s ( Figure 5C). As expected, the application of a small dc field of 0.1 T to eliminate, at least partly, the fast relaxation due to QTM, generally induces a slow down of the magnetization relaxation with a concomitant increase of U eff (from 55.1 to 75.9 K) and a decrease in τ 0 .
The deviation of the data from the Arrhenius law below 10 K is a clear indication of the coexistence of several competing relaxation processes. The Cole-Cole plots for these complexes show semicircular shapes in the 6.5-12 K temperature range ( Figure 5B) with α values ranging between 0.211(6.5 K) and 0.158(12 K) which support the existence of several relaxation processes. Since in the studied temperature range (T > 6.5 K and 0.1 T) direct and QTM relaxation processes should be almost negligible, we have fitted the magnetic data to Equation (1), which considers that Raman and Orbach processes contribute simultaneously to the relaxation of the magnetization.  The extracted parameters were: C = 0.31 s −1 K n , n = 3.0, U eff = 90.6 K and τ o = 3.9 × 10 −7 s. Although n = 9 is expected for Kramers ions (Abragam and Bleaney, 1970), this may change depending on the structure of the levels and if both, acoustic and optical phonons, are considered. Thus n values between 1 and 6 are considered as acceptable (Singh and Shrivastava, 1979;   Shirivastava, 1983). As usual, U eff is higher than that obtained at 0. 1 T from the simple Arrhenius law, while the pre-exponential factor τ 0 decreases by half. It should be noted at this point that the value of χ M 'T (χ M ' is the in-phase ac susceptibility, Figure S12) at its low temperature plateau (where all the lines are coincident) of 25.2 cm 3 mol −1 K agrees well with the value expected for randomly oriented crystals with a Mj = ±15/2 Ising ground Kramers doublet (25 cm 3 mol −1 K).
The Dy-O bond distances are shorter than the Dy-N ones in the DyN 2 O 6 coordination spheres of Dy1 and Dy2, and therefore the former have larger electron density than the latter. Taking into account this, the two tfacam − ligands at opposite sides of each Dy atom, create an appropriate axial crystal field with the remaining positions in the equatorial plane occupied by the oxygen atoms of the other tfacam − bidentate ligand and the N,N atoms belonging to the neutral bipym bridging ligand. In this disposition, as qualitatively predicts the simple electrostatic oblate-prolate model (Rinehart and Long, 2011), the oblate electron density of the Dy III ion is forced to be located in the equatorial plane, thus diminishing the electrostatic repulsions with the oxygen atoms of the two β-diketonato ligands defining the axial crystal field (Figure 6A). If so, the anisotropy axis should be located close to the two tfacam − ligands at opposite sides of each Dy III atom. We have calculated the direction of the anisotropy axes of the Dy III ions by using the Chilton's method (Chilton et al., 2013b), which is based on electrostatic arguments, and the results (see Figure 6B) confirm our qualitative prediction using the prolate-oblate model, with an angle between the anisotropy axes of 2.9 • . In order to know how the structural parameters of the DyN 2 O 6 coordination sphere affect the SMM behavior of d-1 and their achiral [(Dy(β-dicetona) 3 ) 2 (µ-bpym)] analogs, the magneto-structural data for these compounds have been compared in Table 1.
As it can be observed in Table 1, it seems that the Dy III ions with a geometry much closer to trigonal dodecahedron D 2d (that having the lowest continuous shape measurement for this geometry) exhibit, in general, higher U eff values. Taking into account this correlation, the U eff for compound d-1 should be similar, or even higher, as that for compound [(Dy(tmh) 3 ) 2 (µbpym)] (4). Surprisingly, the experimental U eff value for the latter compound is higher. Theoretical ab initio calculations have been carried out on 1-4 to justify this discrepancy.

THEORETICAL CALCULATIONS
Ab initio calculations on the d-1 and the previously reported achiral analogous were undertaken using the CASSCF+RASSI-SO method. The aim of this study is two-fold: (i) To support the presence of axial anisotropy and to shed light on the mechanism of the slow magnetic relaxation of these compounds (ii) To confirm the above indicated magneto-structural correlation and to justify the deviation of d-1 from it.
The calculation on d-1 has been performed using the Xray crystal structure where methyl group has been modeled by hydrogen to reduce the computational cost. The eight Kramers doublets (KDs) generated from 6 H 15/2 spin orbit coupled ground term span up to 538 cm −1 for Dy1 (540 cm −1 for Dy2) suggesting moderately axial ligand field generated in the D 4d environment. The computed anisotropy axis of both the centers is shown in Figure 6B. The g zz axes of both centers are collinear with a tilt angle of just 3.8 • , which is very close to that found using the electrostatic model (see above). The energy spectrum, g tensors, angle of the excited state g zz with the ground state of both Dy centers is listed in Tables 2, 3.The g zz axis of both the Dy III centers is found to lie along the β-diketonato ligands parallel to each other to mimic to axial crystal field. The equatorial positions are occupied by the two nitrogen atoms of the of the bipyrimidine ligand and two oxygen atoms of a β-diketonato ligand thus minimizing, as indicated elsewhere (Figure 6A), the electrostatic repulsion between the oblate electron density of Dy III ions with the above mentioned atoms in the equatorial plane. The ground state of both centers is of Ising type as the transverse components of anisotropy in this state are very small and the magnetic moment g z reaches a value close to the value generated from pure m J = 15/2 state (g z = 20). Although the two centre contains significant amount of transverse anisotropy in the KD2, the magnitude is larger for the Dy2 centre. The axiality of both centers started to decrease as it goes to higher KDs while it becomes lowest at 4th excited state, then it started to increase and becomes maximum at KD8. The relaxation mechanisms of both centers are shown in Figure 7. The energy gap between the ground and the first excited state is 141.97 and 129.95 cm −1 for Dy1 and Dy2 center respectively. This implies that the two Dy centers resides in different structural environments. The QTM and TA-QTM of the Dy1 center is estimated to be ten times less compare to Dy2 center. This is reflected by their corresponding wave function analysis of the KDs. The ground state composition of the |15/2> state of the Dy1 center becomes larger compare to Dy2 center. The major contribution of the first excited KDs comes from the |13/2> state where the mixing of this state with other states becomes larger for Dy2 center which increase the TA-QTM for this center. The gzz axis of the ground and first excited state are nearly collinear, thus suggesting that relaxation is likely to proceed further via higher excited states, however very large value of TA-QTM and transverse anisotropy present in the first excited state enforce relaxation via this state. The probability of Orbach (1.81/1.84) and Raman process (0.02/0.07) remain almost same for both the centers while the Raman relaxation is found to be very small. The larger QTM and TA-QTM of the Dy2 center compared to the Dy1 center can be explained by their corresponding distortion from the D 4d (SAPR-8) geometry. The larger deviation of the Dy2 center (1.083) compare to Dy1 center (0.683) in square antiprism geometry facilitate the larger QTM and TA-QTM in the former center.
The ab initio calculated effective energy barrier for Dy1 and Dy2 centers (141.97 and 129.95 cm −1 ) are overestimated compared to the experimental U eff value (55.1 cm −1 ) for magnetization reversal. The discrepancy essentially arise from the (i) QTM which is operative in zero field prompted by dipolar and hyperfine interactions reduces the barrier height. (ii) The limitations computational methodology used (absence of dynamic correlation, modeled structure etc).
The deviation can be explained from the ab initio calculated crystal field parameter. The crystal field parameters are computed (Table S11) using the following equation as implemented in SINGLE_ANISO codeĤ CF = q k=−q B q kÕ q k , WhereÕ q k and B q k are the computed extended Stevens operator and crystal field (CF) parameter, respectively. The probability for the occurrence of QTM is higher when the non-axial B q k terms (q = 0 and k = 2, 4, 6) are larger than the axial (q = 0 and k = 2, 4, 6) terms. The negative value B 0 2 parameter corroborates the stabilization of |15/2> as ground state. The computed non-axial crystal field parameters (B 2 2 , B 1 2 , B −1 2 ) are larger than the axial parameters in d-1 which facilitates the QTM in zero field and explains the overestimation of U cal . In order to gain a deeper insight into the role of magnetic exchange to magnetic relaxation POLY_ANISO program was employed which interfaced with SINGLE_ANISO of individual Dy centers. The calculated g tensors of both the Dy centers strongly anisotropic imply that the resulting interaction is strongly anisotropic. The experimental magnetic susceptibility was fitted by Lines approach (Lines, 1971) to estimate intramolecular and dipolar interactions between Dy III -Dy III . This methodology has been shown to yield good numerical estimate of Js when compared to the experimental values in a variety of dinuclear systems (Oyarzabal et al., 2015;Gupta et al., 2016b;Singh et al., 2017).
The magnetic interactions is modeled by H = -Js 1z1 s 2z2 , where s 1z1 and s 2z2 are the projections of the effective spins = 1/2 of the lowest KDs of the Dy III ions on the principal anisotropy axes. A good fit is obtained by considering J tot = 0.0039 cm −1 (J exch = 0.004 cm −1 and J dipolar = −0.0001 cm −1 ) (Figure 8).
The magnetic anisotropy axis of both Dy III centers are nearly parallel to each other and this is compatible with the ferromagnetic interaction obtained from Lines model. The significant tunnel splitting (0.6 * 10-5) in the third exchange doublets blocks the relaxation via this state (see Table S16 for the spectrum of lowest exchange levels). The observed magnetization blockade of 131 cm −1 is very similar to that forum in the single ion analysis. This is due to the expected weaker exchange coupling between Dy ions. Therefore, the experimentally observed barrier height arises from the contribution of individual Dy III fragments.
We have undertaken a comparative study to elucidate the role of the distortion parameter from the corresponding symmetry to the magnetic anisotropy of the metal center. We have chosen three Dy 2 complexes analogous to d-1 containing bipyrimidine as bridging ligand, six β-diketones as end-cap ligands and a similar DyN 2 O 6 core environment: [(Dy(DBM) 3 ) 2 (µbpym)].2CH 3 Cl(2), [(Dy(DBM) 3 ) 2 (µ-bpym)]MeCN (3), and [(Dy(tmh) 3 ) 2 (µ-bpym)] (4). The first two molecules has been synthesized by Song Gao et. al. (Sun et al., 2016) and the third molecule has been studied by Mario Ruben et al. (Yu et al., 2016). The CShM values of the above three molecules along with those of d-1 are listed in the Table 1. All the three complexes exhibit SMM behavior in zero field with the effective energy barriers indicated in Table 1. The detailed results of the theoretical study carried out on the X-Ray crystal Structures of 2-4 are given in the ESI (Tables S5-S10, S12-S15, S17-S19 and Figures S1-S7).
The calculated blocking barrier as well the angle between the anisotropy axis of each Dy III center with the Dy1-Dy2 axis and the tilt angle between the anisotropy axes of both Dy III centers are given in Tables 1, 4, respectively (the rest of computed parameters, like to those extracted for 1, are given in the ESI).
The results indicate that the ab initio computed barrier heights clearly follow the trend obtained from the distortion parameters. The study of the Dy1 center in complexes 1 and 4 reveals that the computed barrier height decreases from 141.97 cm −1 to 133.70 cm −1 as the CShM parameter in the TDD-8 geometry increases  83→ 133.70). This proportionality between the g zz1 -Dy1-Dy2 and barrier height elucidate that the former angle should be kept as large as possible to get the large barrier height.

PULSE MAGNETIZATION MEASUREMENTS
The magnetization curves in a full cycle pulsed magnetic field at 0.4 K (Saito and Miyashita, 2001), with maximum fields of 0.84, 2.6, 5.2, and 10.4 T, were measured with the aim of confirming the SMM properties of d-1 (Figure 9). The sweep rate depends on the maximum pulsed field, so it is the higher for 10.4 T (4.2 T/ms). Magnetization curves show large hysteresis loops, a sharp reversal at around zero field and saturations at high fields (except for the curve measured at a sweep rate of 0.3 T/s). The hysteresis increases with faster sweeping rate, which is characteristic of SMMs. The saturation moment per Dy III ion is lower than the expected value (20 µβ/f.u.), which can be due to the misalignment between the local magnetization directions of Dy1 and Dy2 ions, as well imperfect alignment with the field. Moreover, the sharp reversal around zero points out that there is an adiabatic magnetization reversal most probably caused by QTM with a small tunneling gap. As indicated elsewhere, the gap may be caused by hyperfine interactions, weak inter-molecular interactions and/or transverse components of the magnetization by the low symmetry around Dy III ion. To analyse the origin of the loop, the differential magnetization dM/dB was plotted (Figure 9 right).
The presence of only one step in the dM/dB vs B plot of the dinuclear complex d-1 at about 1.5 T (at positive as well as negative values of the field) could be due to either: (i) the direct relaxation between the ferromagnetic ground state (↓↑) and the excited antiferromagnetic state (↑↑) originated by magnetic coupling between two Dy ions or (ii) the almost equivalence between Dy1 and Dy2 when magnetic coupling through the bridging ligand is considered to be negligible.

CONCLUSIONS
In summary, the assembly of 2,2 ′ -bypirimidine, Ln(AcO) 3 ·nH 2 O (Ln III = Dy, Gd), and enantiomerically pure (+)/(−)-3-(trifluoroacetylcamphor) is revealed as a good strategy to prepare chiral bipyrimidine-bridged Ln III complexes. The Dy III counterparts possesses and almost pure axial ground Kramers doublet and SMM behavior at zero-field. The experimentally extracted anisotropy barrier for these Dy III complexes is much lower than those obtained for other previously reported analogous complexes [(Dy 2 (β-dicetona) 3 ) 2 (µ-bpym)], which is proposed to be due to the comparatively larger distortion for the former in the DyN 2 O 6 coordination sphere from trigonal dodecahedron geometry. Theoretical ab initio calculations carried out on this [(Dy 2 (β-dicetona) 3 ) 2 (µ-bpym)] complexes indicate that: (i) The calculated blocking barriers follow the above trend of smaller thermal energy barrier for magnetization reversal when the distortion from D 2d geometry of the DyN 2 O 6 coordination sphere is larger. (ii) The relatively low U eff value for the Dy III complexes reported here is due to the existence of a comparatively larger QTM in the ground state. (iii) In contrast to the Gd III complexes, which show weak antiferromagnetic interaction between the Gd III ions, the Dy III complexes, with one exception, exhibit very weak ferromagnetic interactions between the Dy III ions. This fact clearly indicates the difficulty in accurately determining the sign of very weak magnetic exchange interactions. (iii) The experimentally observed barrier height mainly arises from the contribution of individual Dy III fragments due to the weakness of the magnetic exchange interaction. (iv) Relaxation mechanisms for magnetization reversal justify the order of the experimentally extracted U eff values.
Finally, pulse magnetization measurements show only one step in the field dependence of the dM/dB for the Dy III complexes at about 1.5 T, which is due to either the direct relaxation between the ferromagnetic and antiferromagnetic states, originated by magnetic coupling between two Dy ions, or more likely to very weak coupling between equivalent Dy1 and Dy2 centers.
The reported results represent an additional example of how enatiomerically pure ligands can be successfully used to generate bifunctional SMM/chiral materials.

AUTHOR CONTRIBUTIONS
ID-O prepared all the complexes, carried out their spectroscopic characterization, and made supplementary material. JH carried out the magnetic study and the analysis of the results. EC and GR wrote and revised this paper. JG-M and AR carried out ferroelectricity measurements and revised the paper. GR and SD performed theoretical ab initio calculations. HN performed pulse magnetization measurements.

ACKNOWLEDGMENTS
ID-O, JH, and EC are grateful to Ministerio de Economía y Competitividad (MINECO) for Project CTQ2014-56312-P, the Junta de Andalucía (FQM-195 and the Project of excellence P11-FQM-7756) and the University of Granada. A part of this work has been made at HFLSM, IMR, Tohoku University. ID-O also acknowledges support by COLABS. GR would like to thank SERB (EMR/2014/000247) for financial support. SD thanks UGC for Senior Research Fellowship. AC thanks the Marie Curie COFUND Action from the European Commission for co-financing his postdoctoral fellowship.