Pseudo-mono-axial ligand fields that support high energy barriers in triangular dodecahedral Dy(iii) single-ion magnets

The synthesis of air-stable, high-performance single-molecule magnets (SMMs) is of great significance for their practical applications. Indeed, Ln complexes with high coordination numbers are satisfactorily air stable. However, such geometries easily produce spherical ligand fields that minimize magnetic anisotropy. Herein, we report the preparation of three air-stable eight-coordinate mononuclear Dy(iii) complexes with triangular dodecahedral geometries, namely, [Dy(BPA-TPA)Cl](BPh4)2 (1) and [Dy(BPA-TPA)(X)](BPh4)2·nCH2Cl2 (X = CH3O− and n = 1 for 2; L = PhO− and n = 2 for 3), using a novel design concept in which the bulky heptadentate [2,6-bis[bis(2-pyridylmethyl)amino]methyl]-pyridine (BPA-TPA) ligand enwraps the Dy(iii) ion through weak coordinate bonds leaving only a small vacancy for a negatively charged (Cl−), methoxy (CH3O−) or phenoxy (PhO−) moiety to occupy. Magnetic measurements reveal that the single-molecule magnet (SMM) property of complex 1 is actually poor, as there is almost no energy barrier. However, complexes 2 and 3 exhibit fascinating SMM behavior with high energy barriers (Ueff = 686 K for 2; 469 K for 3) and magnetic hysteresis temperatures up to 8 K, which is attributed to the pseudolinear ligand field generated by one strong, highly electrostatic Dy–O bond. Ab initio calculations were used to show the apparent difference in the magnetic dynamics of the three complexes, confirming that the pseudo-mono-axial ligand field has an important effect on high-performance SMMs compared with the local symmetry. This study not only presents the highest energy barrier for a triangular dodecahedral SMM but also highlights the enormous potential of the pseudolinear Dy–L ligand field for constructing promising SMMs.

In this respect, our attention was drawn to the bulky heptadentate [2,6- [59][60][61][62][63] Monoanionic O-donor ligands, such as alkoxide, siloxide, and aryloxide, are distributed at axial sites and are particularly effective in high-performance Dy-based SMM complexes. Because most of the coordination sites of the Dy(III) ion are occupied by a single bulky BPA-TPA ligand, we selected a sterically small methoxy (CH 3 O − ) or phenoxy (PhO − ) moiety as a candidate for forming a short, strong Dy-O bond. Herein, we report the synthesis, structural and magnetic characterization, and ab initio calculations of three novel air-stable complexes, [Dy(BPA-TPA)Cl](BPh 4 ) 2 (1) and [Dy(BPA-TPA)(X)](BPh 4 ) 2 -$nCH 2 Cl 2 (X = CH 3 O − and n = 1 for 2; L = PhO − and n = 2 for 3), which possess a triangular dodecahedral coordinate geometry with D 2d symmetry. Dynamic magnetic susceptibility studies reveal that complex 1 only exhibits frequency-dependent out-ofphase (c M ′′ ) signals below 2.4 K under an 800 Oe dc eld, whereas 2 and 3 are zero-eld single-ion magnets with large energy barriers (U eff = 686 K for 2; 469 K for 3); such magnets are unprecedented for the triangular dodecahedral geometry. Furthermore, complete-active-space self-consistent eld (CASSCF) ab initio computational methods were used to provide detailed insight into the magnetic dynamics for these complexes and to understand the role of the axial Dy-O crystal eld in realizing the observed excellent properties. This study provides a unique design approach toward a new class of complexes with the desired pseudolinear Dy-L ligand eld.

Crystal structures
The crystallographic structures of the three above mentioned complexes reveal that complex 1 crystallizes in the monoclinic P2 1 / c space group, while complexes 2 and 3 crystallize in the triclinic P 1 space group (Table S1 in the ESI †). The coordinate structures of the cations of the three complexes are depicted in Fig. 1 and S4, with selected bond lengths given in Tables 1 and S2. † The Dy(III) site in complexes 1-3 is eight-coordinated by one BPA-TPA ligand and one Cl − , CH 3 O − or PhO − anion. The sevennitrogen "pocket" of the BPA-TPA ligand three-dimensionally surrounds the central Dy(III) ion with long Dy-N distances of 2.458(5)-2.619(5)Å for 1, 2.495(5)-2.616(6)Å for 2 and 2.496(3)-2.638(3)Å for 3, indicative of a fully weak crystal eld in each case. The one remaining site is occupied by a CH 3 O − or PhO − anion with a very short Dy-O distance of 2.108(5)Å (for 2) or 2.087(3)Å (for 3), which induces an axially strong ligand eld, whereas a long Dy-Cl axial bond of 2.5835(16)Å is observed for 1, suggesting a nearly spherical and weak ligand eld. This allows us to unambiguously reveal that complexes 2 and 3 bear a pseudolinear Dy-O ligand eld. Continuous shape measures (CShMs) were used to evaluate each conguration, 64-66 the results of which are given in Table S3. † The triangular dodecahedral geometry (D 2d ) provided the lowest CShM value in each case: 2.166 for 1, 2.130 for 2 and 1.820 for 3. In addition, the shortest Dy(III)/Dy(III) distances were determined to be 10.770, 10.095 and 11.798Å for 1-3, respectively, suggesting negligible direct and superexchange magnetic interactions ( Fig.  S8-S10 †).  decreased slightly upon cooling and then suddenly dropped at low temperature to nal values of 6.98 cm 3 K mol −1 for 1, 12.47 cm 3 K mol −1 for 2, and 10.04 cm 3 K mol −1 for 3 ( Fig. 2 and S11 †), which were likely attributed to thermal depopulation of M J sublevels or the presence of large crystal eld (CF) splitting. Field-dependent magnetization (M) curves were also acquired for three complexes at 2 K in the 0-7 T dc eld range, which revealed respective magnetizations of 6.27 Nb for 1, 6.11 Nb for 2 and 5.06 Nb for 3 at 7 T and 2.0 K (Fig. S12-S14 †).

Magnetic properties
Dynamic magnetic relaxation was investigated by measuring the alternating current (ac) magnetic susceptibilities of 1-3 in "tails" were observed below 10 K, consistent with the quantum tunneling of magnetization (QTM) that is commonly observed in lanthanide-based SMMs. [31][32][33][34][35][36][37][38][39][40][41][42][43] The relaxation time (s) extracted using the generalized Debye model 67-69 obeys the Arrhenius law at high temperatures ( Fig. S19 and S20, Tables S4 and S5 †); linear regression provided the following best-tted results: U eff = 686 K and s 0 = 3.1 × 10 −11 s for 2 and U eff = 469 K and s 0 = 9.3 × 10 −11 s for 3 ( Fig. 4). To the best of our knowledge, these are the highest energy barriers for SIMs with triangular dodecahedrons and highlight the potential of the unique pseudolinear Dy-L ligand eld. Prominent QTM was observed below 10 K in each case. Indeed, Raman processes make signicant contributions in most reported SIMs. In addition, direct processes can be neglected for relaxation time products in a zero dc eld. Therefore, the magnetization dynamics of 2 and 3 can be tted using eqn (1), which considers the QTM, Raman, and Orbach mechanisms: To avoid overparameterization, the xed values of U eff and s 0 obtained from the Arrhenius law were applied in the t processes, yielding s QTM = 0.0068 s, C = 0.04 s −1 K −n , n = 2.7, U eff = 686 K (xed) and s 0 = 3.1 × 10 −11 s (xed) for 2, and s QTM = 0.013 s, C = 0.49 s −1 K −n , n = 2.2, U eff = 469 K (xed) and s 0 = 9.3 × 10 −11 s (xed) for 3, as shown in Fig. 4. The values of the Raman parameters C and n are within the ranges observed for Dy-based SMMs.
Upon applying the optimized eld of 1500 Oe, the ac susceptibility data for both complexes show temperature dependence in the whole temperature region (Fig. S21-S24 †) due to the suppression of the QTM at low temperature. The c M ′′ peak is located at 45 K for 2 and 34 K for 3, revealing almost unchanged relaxation at high temperature with respect to the zero-eld data. These frequency-dependent data were also analyzed by the generalized Debye model (Fig. S25-S26 and Tables S6 and S7 †). The Arrhenius t at high temperatures generates U eff = 688 K and s 0 = 3.8 × 10 −11 s for 2 and U eff = 492 K and s 0 = 6.7 × 10 −11 s for 3 ( Fig. S27 and S28 †). These values Table 1 Selected bond lengths (Å) for 2 and 3 2 3 2.507 (5) Dy(1)-N (7) 2.540(3) Fig. 2 Variable-temperature dc susceptibility data for 2 and 3 in a 1000 Oe applied dc field. of the Orbach parameters were employed for the t based on the combination of the Raman and Orbach processes, as shown in Fig. S29 and S30. † The energy barrier values for 2 and 3 under 1500 Oe are in keeping with those for zero dc eld, suggesting the Raman and Orbach processes at the high temperature region are unacted on the application of dc eld.
To investigate the blocking of magnetization, polycrystalline samples of complexes 1-3 were subjected to magnetic hysteresis at a slow average sweep rate of 200 Oe s −1 . It can be expected that no hysteresis loop was found at 2 K for complex 1 (Fig. S31 †). In contrast, clear buttery shaped hysteresis loops that open below 8 K were observed for complexes 2 and 3 (Fig. 5). Magnetization is observed to suddenly drop at low elds that approach H = 0, which reveals the strong contribution from a faster QTM effect, in good agreement with the temperature independence observed below 10 K in the c M ′′ (n) curves and the rapid increase in c M ′′ (T) at low temperatures observed for 2 and 3.

Theoretical analysis
To gain further insight into the magnetic anisotropies and relaxation mechanisms of complexes 1-3, CASSCF calculations on the basis of their X-ray determined geometries were carried out with the OpenMolcas and SINGLE_ANISO programs. [70][71][72][73] For complex 1, a very small energy gap between the ground state and rst excited states of 18.5 cm −1 was predicted. Relatively large g x,y values of 0.428 and 3.426 with the impure ground state of m J = 63%j±15/2 were observed, yielding a large magnetic moment matrix element of 0.64 m B between the ground Kramers doublets (KDs), which indicates that probable magnetic relaxation occurs via the ground state. These computed results explain the weak ac magnetic property even under the applied dc eld for 1.
In contrast to complex 1, a highly anisotropic ground Kramers doublet (KD) with g z z 19.86 was obtained for complexes 2 and 3 together with the rst excited KD assigned to a rather pure m J = ±13/2 state, whereas other KDs show substantial magnetic state mixing (Tables S5 and S6    proceeds through the second excited KD. On the other hand, complex 3 shows a transversal magnetic moment in the rst excited KD of 0.13 m B ; consequently, fast QTM is likely to occur in its rst excited KD. The transversal magnetic moment in the second excited KD of 2 was found to be 1.48 m B ; therefore, fast QTM is expected to occur in its second excited KD. Accordingly, the energy barriers for 2 and 3 calculated according to the schemes in Fig. 6 are 459.6 and 317.5 cm −1 , respectively, which agree well with the experimental values of 476.8 cm −1 (686 K) and 326 cm −1 (469 K).
Aravena et al. reported a new method for predicting effective demagnetization barriers (U eff ) that considers all state energies and their contributions to the tunneling rate. [74][75][76] The entire temperature range for complexes 1-3 can be divided into three regions ( Fig. 7 and S33 †). U eff is always nearly zero in region I, since the contribution from the ground state dominates, while the ground state contribution drops in region II and KD 1 becomes the rst state to function; however, the dominating state changes to other higher excited KDs as the temperature continues to rise. U eff grows to a constant value as the Orbach regime is approached as the temperature increases further in region III. KD 2-4 are the three most important KD contributions to the U eff values of complexes 1-3. We determined the U eff values of complexes 1-3 using eqn (1)-(3); the saturated U eff values for complexes 1-3 were calculated to be 159.3, 508.8 and 425.6 cm −1 , respectively. Only when the relaxation temperatures exceed ca. 55 K for 1, ca. 60 K for 2 and ca. 50 K for 3, these saturations may be achieved. However, in reality, the highest experimental temperatures of the ac susceptibility signals for all complexes are below 50 K, thus leading to the calculated saturation U eff being higher than the experimental values.
CF parameters B (k, q) with high percentages were calculated to further elucidate the mechanism of relaxation, the results of which are shown in Table S7. † The weight of the axial parameters B (2, 0) for 1 is very low, suggesting poor axial CF. However, for 2 and 3, the weights of absolute axial parameters B (2, 0) and B (4, 0) exceed 20% and 10%, respectively, and their values are both negative and larger than transverse B (k, q) (k = 2, 4; q s 0), suggesting strong uniaxial anisotropy. Moreover, the value of the axial parameter B (2, 0) for complex 2 is larger than that of 3, which shows that 2 exhibits a larger CF than 3.
Taken together, the computational results are in complete accordance with the experimental observations. The high performance of SMM for 2 and 3 can be directly related to the strong axial nature of the ligand eld arising from the short axial Dy-O bonds (2.108(5)Å for 2 and 2.087(3)Å for 3). Conversely, the SMM property of 1 is very poor, although the local symmetry of 1 is similar to that of 2 and 3. It is  understandable that the long Dy-Cl bond generates the weak and spherical CF for 1, which may not be able to induce the strong magnetic anisotropy and afford a large m J splitting. It is well known that the magnetic anisotropy and the local symmetry around the spin center seriously affect the properties of SMMs. The magnetic anisotropy determines the upper limit of the total CF splitting energy, while the high symmetry can suppress the QTM, resulting in the relaxation process in which the relaxation process passes through the higher excited KD. Therefore, a strong magnetic anisotropy is an essential precondition for high-performance SMMs. Despite the relatively low local symmetry around the Dy site, fascinating SMM behavior was observed for 2 and 3, which is ascribed to their strong, highly electrostatic Dy-O bond.
In addition, the apparent difference in the energy barrier for 2 and 3 is attributable to differences in the axial ligand. At rst glance, complex 3 has a shorter axial Dy-O bond compared to 2; this should lead to a stronger axial ligand eld acting on Dy(III) for 3. However, this expectation contrasts with the fact that 2 possesses a better SMM property. Actually, the Dy(III) electron density is oblate in shape, which requires the charge to be in the axial direction as much as possible. As reported previously, 35,41,42 the introduction of electron-donating groups in the axial ligand improves the energy barrier. The LoProp charges in the ground KDs of 2 and 3 were calculated using the CASSCF wavefunction (Table S11 †), with the axial oxygen atom in 2 found to be more charged than that in 3, which is ascribable to the superior electron-donating ability of the -CH 3 group compared to the phenyl group. Therefore, the axial CH 3 O − ligand improves SMM properties. Moreover, the charges on the axial oxygen atoms of both complexes are nearly three times larger than those on the neutral nitrogen atoms, which also indicates the axial nature of the total ligand eld felt by the Dy(III) ion in each case.

Conclusion
The bulky heptadentate BPA-TPA ligand was successfully used to synthesize triangular dodecahedral dysprosium(III)-based complexes with mono-axially ligated Cl − (1), CH 3 O − (2) or PhO − (3) moieties. The large axial CF splitting of the J = 15/2 ground state induced by the short axial Dy-O bond results in slow magnetization relaxation through large anisotropic energy barriers (686 K for 2 and 469 K for 3). However, although the local coordination geometry of 1 was similar, only weak frequency-dependent ac signals without the c M ′′ maximum were observed for complex 1, which is caused by the weak and spherical CF generated by the long Dy-Cl bond. Ab initio calculations reveal that 2 and 3 exhibit dominant magnetization reversal barriers that expand to the second and rst Kramers doublets, respectively. According to theoretical predictions, 21 the blocking barrier limit for a SIM is dened by a one-coordinate diatomic complex, such as [DyO] + , to be above 3000 K. 6 However, the synthesis of a model compound with perfect axial symmetry is highly unrealistic and almost impossible to achieve. In the present case, the bulky pentapyridyldiamine ligand prevents additional coordination, and the methoxy or phenoxy oxygen atom provides strong CF splitting and forms a pseudo [DyO] 2+ ligand eld. This nding not only provides a promising blueprint for accessing linear mono-coordinate [DyO] + complexes but also extends the kinds of high-performance SMMs available.

General procedures
All chemicals were commercially available and used without further purication. The [2,6-bis[bis(2-pyridylmethyl)amino] methyl]-pyridine (BPA-TPA) ligand was prepared as described previously. 59-61 C, H and N elemental analyses were performed on an Elementar Vario EL III elemental analyzer. Powder XRD (PXRD) patterns were recorded at room temperature on a Bruker D8 Advance X-ray diffractometer (Fig. S1-S3 †). Experimental PXRD patterns for bulk polycrystalline samples are consistent with those simulated from the single-crystal X-ray data, con-rming the phase purity of complexes 1-3 and their stability in air. Single-crystal XRD data for 1-3 were collected at 296 K on a Bruker APEX II diffractometer equipped with a CCD area detector (Mo Ka radiation, l = 0.71073Å). 77,78 All structures were solved using the SHELXTL-2016 program. Further crystallographic details are provided in Table S1 and Fig. S5-S7. † Complexes 1-3 were subjected to direct-current (dc) magnetic measurements between 2 and 300 K on a Quantum Design SQUID VSM magnetometer at elds up to 7 T. Alternatingcurrent (ac) susceptibility measurements were carried out at ac frequencies in the 1-1000 Hz range in various applied static elds with an oscillating ac eld of 2 Oe. Magnetic susceptibility data were corrected for diamagnetism associated with the constituent atoms, and the sample holder was estimated using Pascal constants.

Synthesis of [Dy(BPA-TPA)Cl](BPh 4 ) 2 (1)
DyCl 3 $6H 2 O (0.188 g, 0.5 mmol), BPA-TPA (0.250 g, 0.5 mmol) and NaBPh 4 (0.513 g, 1.5 mmol) were dissolved in methanol (20 mL), stirred for 30 min and then ltered, affording a white precipitate. White crystals suitable for single-crystal XRD were grown by the slow diffusion of diethyl ether into a CH 3  DyCl 3 $6H 2 O (0.188 g, 0.5 mmol) and BPA-TPA (0.250 g, 0.5 mmol) were dissolved in methanol (15 mL) and reuxed for 2 h. The solvent was removed under reduced pressure, and acetonitrile (10 mL) was added to the light yellow residue, aer which phenol (0.0471 g, 0.5 mmol) and sodium trimethylsilanolate (0.0566 g, 0.5 mmol) were added to the resulting solution. The mixture was reuxed for 2 h and then ltered, and a solution of NaBPh 4 (0.343 g, 1 mmol) in acetonitrile (10 mL) was added to the ltrate. Aer stirring for 30 min, the mixture was ltered, and the solvent was removed under vacuum to give the product as a yellow powder. Yellow crystals suitable for single-crystal XRD were grown by the slow diffusion of hexane into a CH 2 Cl 2 solution of the light yellow product over 2 d. Yield: 59% based on Dy(III); elemental analysis found (%) (

Computational details
CASSCF calculations on mononuclear complexes 1-3 (see Fig. 1 and S3 † for the calculated complete structures of 1-3) based on single-crystal X-ray-determined geometries were performed using the OpenMolcas 70 program package.
Atomic natural orbital basis sets from the MOLCAS ANO-RCC library were used: ANO-RCC-VTZP for Dy III ; VTZ for close N and O; VDZ for distant atoms. The calculations used the second order Douglas-Kroll-Hess Hamiltonian, where scalar relativistic contractions were taken into account in the basis set, and spin-orbit couplings were handled separately in the restricted active space state interaction (RASSI-SO) procedure. For complexes 1-3, active electrons in seven active orbitals include all f electrons (CAS (9 in 7 for Dy III )) in the CASSCF calculation. To exclude all doubt, we calculated all roots in the active space. We mixed the maximum number of spin-free states that are possible using our hardware (all from 21 sextets, 128 from 224 quadruplets, 130 from 490 doublets for Dy III ). The SINGLE_ANISO 71-73 program was used to obtain energy levels, g tensors, magnetic axes (etc.), based on the above CASSCF/RASSI-SO calculations.
The theoretically predicted effective barrier has the following form as a function of temperature: 74,75 U eff ðTÞ ¼ Each Kramers doublet (KD) has a particular demagnetization rate, namely: Z ¼ X i expð ÀE i =k B TÞ (5) k QT;i ¼ g XY ;i 2 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g XY ;i 2 þ g Z;i 2 p where i is the index for each KD, E i represents the doublet energy obtained through CASSCF calculations, Z is the partition function, k B is the Boltzmann constant, and k QT,i is the tunneling relaxation rate for doublet i. The coefficient K i (T)/N that precedes E i in eqn (2) represents the relative contribution of the corresponding KD to relaxation.

Data availability
The datasets supporting this article have been uploaded as part of the ESI material. †

Conflicts of interest
There are no conicts to declare.