Magnetic Anisotropy along a Series of Lanthanide ... - ACS Publications

Jun 24, 2017 - Yi-Quan Zhang,*,† and You Song*,‡. †. Jiangsu Key Laboratory for NSLSCS, School of Physical Science and Technology, Nanjing Norma...
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Magnetic Anisotropy along a Series of Lanthanide Polyoxometalates with Pentagonal Bipyramidal Symmetry Jing Li,†,‡,§ Chen Yuan,†,§ Li Yang,‡ Ming Kong,‡ Jing Zhang,‡ Jing-Yuan Ge,‡ Yi-Quan Zhang,*,† and You Song*,‡ †

Jiangsu Key Laboratory for NSLSCS, School of Physical Science and Technology, Nanjing Normal University, Wenyuan Road 1, Nanjing 210023, P. R. China ‡ State Key Laboratory of Coordination Chemistry, Collaborative Innovation Center of Advanced Mirostructures, School of Chemistry and Chemical Engineering, Nanjing University, Xianlin Road 163, Nanjing 210023, P. R. China S Supporting Information *

ABSTRACT: Magneto-structural correlations in a series of lanthanide polyoxometalates (POMs) with pentagonal bipyramidal symmetry, namely, [Ln 2 (NMP) 12 (PW 12 O 40 )][PW12O40] (NMP is N-methyl pyrrolidone), were studied in detail experimentally combined with theoretical calculations. Furthermore, two types of Dy-based complexes with pentagonal bipyramidal symmetry were built to discuss the dependence of the theoretical energy barriers with the axial Dy−O bond lengths when the magnetic axes in ground Kramers doublet are along the axial orientation or on the equatorial plane. A meaningful conclusion was put forward for designing such Dy-based SIMs with high performance.

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linear two-coordinated,7 D4d for square antiprismatic,5,8 and D5h for pentagonal bipyramidal complexes.9 Recently, Chibotaru et al.10a indicated that the contribution of magnetic anisotropy provided by covalence effects is dominated. Combining both molecule symmetry and covalence effect is a new guidance to design SMMs with high performance.10c Several years ago, Long et al.10b predicted the possible SMM behavior in tripositive lanthanides through the spatial distribution of 4f electron densities with the located ligand field. The shapes of 4f free-ion electron densities can be prolate, oblate, and spherical. Prolate ions with ligand in equatorial minimizing the energy of the mJ = J state are predicted to be in favor of SMM behavior, and in return, the ligand with negative charges in axial position is good for oblate ions, which was proved very well with [Er(COT)2]− (COT = cyclooctatetraene) serial complexes11a−e and a pentagonal bipyramidal (D5h) DyIII single-ion magnets with high performance,9c respectively. Owing to multiple coordinate sites of polyoxometalate (POM) ligand, POM chemistry was a cradle of SMMs.12 Recently, our group synthesized a pentagonal bipyramidal (D5h) DyIII-based complex with polyoxometalates, namely, [Dy2(NMP)12(PW12O40)][PW12O40] (NMP is Nmethyl pyrrolidone). Unfortunately, it only shows poor slow magnetic relaxation behavior even in doping system. To understand the magnetic properties of the pentagonal bipyramidal lanthanide SMMs in detail, we synthesized a series of pentagonal bipyramidal lanthanide SMMs with different

INTRODUCTION In the field of bistable materials, the studies of single-molecule magnets1 (SMMs) and single-chain magnets2 (SCMs) have a great research value for their theoretical study and potential application. However, the bistable states of SMM (or SCM) only appear under ultralow temperature at present, which seriously limits their application prospect. Magnetic anisotropy arising from the unquenched orbital contribution of metal ions generates a reversal barrier of magnetized molecule, which deeply influences the relaxation temperature.3 Furthermore, high magnetic anisotropy is always counteracted by underbarrier mechanisms, like quantum tunnelling of magnetization (QTM) and Raman process in the relaxation route.4 After the first mononuclear sandwich complex [NBu4]+[Tb(Pc)2]−5 showing SMM behavior was reported, an intense research activity focused on mononuclear 3d and 4f ions for pursuing high magnetic anisotropy and blocking temperature. QTM, which depends mainly on intra-/intermolecular interaction, the crystal-field, and hyperfine interaction, plays an important role in limiting the reversal energy barrier and blocking temperature. The Hamiltonian of crystal field can be described as k Ĥ CF = ∑ Bqk Oq̂ (k = 2, 4, 6; Bkq is the crystal-field parameter; Ô kq is the Stephen operator, which is considered as the source of QTM when q ≠ 0) According to the theoretical prediction,6 in some high symmetry cases, for example, C∞v, D∞h, D4d, D5h, D6d, and I4, the Bkq is vanished when q ≠ 0. In this situation, the QTM can be suppressed in the absence of an external field. On the basis of this theme, a series of high-performance mononuclear SMMs have been discovered, including D∞h for © 2017 American Chemical Society

Received: March 4, 2017 Published: June 24, 2017 7835

DOI: 10.1021/acs.inorgchem.7b00577 Inorg. Chem. 2017, 56, 7835−7841

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Figure 1. (left) Ball, stick, and polyhedral representations of the ionic asymmetric structure of complexes. The complex consists of LnIII, NMP, and polyoxometalate [PW12O40]3−. The code is as follows: Ln (cyan), O (red), N (blue), C (gray). WO6 (red), PO4 (purple). (right) The ligand environment of Ln ions, O1 comes from the polyoxometalate ion, and other coordinated O atoms come from NMP. The Ln−O7 bond is longer than Ln−O6.

Table 1. Selected Bond Lengths (Å) and Angles (deg) in Complexes Tb, Dy, Ho, Er, Tm, Yb O1−Ln O2−Ln O3−Ln O4−Ln O5−Ln O6−Ln O7−Ln O1−Ln−O2 O2−Ln−O3 O3−Ln−O4 O4−Ln−O5 O1−Ln−O5 O1−Ln−O6 O1−Ln−O7 O6−Ln−O7

PW-Tb

PW-Dy

PW-Ho

PW-Yb

PW-Lu

PW-Tm

2.472 2.303 2.309 2.251 2.376 2.221 2.246 68.92 75.72 73.29 72.19 70.46 82.61 93.04 174.50

2.459 2.316 2.298 2.227 2.383 2.222 2.222 70.79 75.56 73.18 72.99 68.67 82.11 93.58 175.53

2.430 2.249 2.262 2.285 2.372 2.186 2.227 72.27 74.52 72.21 73.11 69.13 80.69 91.88 172.19

2.429 2.289 2.217 2.199 2.282 2.141 2.147 69.12 74.48 74.26 71.00 71.99 80.49 92.01 171.75

2.418 2.296 2.251 2.148 2.308 2.156 2.175 69.70 73.40 73.51 74.87 69.21 83.90 93.18 176.69

2.409 2.281 2.272 2.208 2.304 2.193 2.255 68.68 75.48 72.70 72.64 70.74 83.42 92.63 171.79

lanthanide ions and then investigated the magnetic properties combining experiential data with ab initio calculations. Furthermore, we investigated the magneto-structural correlations through changing the bond length of the Dy−O of the model structure from complex Dy with the pentagonal bipyramidal (D5h) ligand field through ab initio calculations. Theory predicted that low coordination lanthanide complexes,13 like [Dy−O]+, are good choices to obtain excellent magnetic performance. However, they are sensitive to air or moisture and hard to synthesize in chemistry due to the large ionic radius of lanthanide ions. Pentagonal bipyramidal (sevencoordinate) DyIII complex is easy to achieve for chemists, and more importantly, it could be stable in air and moisture, which provides great convenience for further fabrication in devices. Hence, the research in this theme is meaningful for chemists to design stable SMMs with high performance.

symmetry) environment, determined by Shape 2.1 software (Table S2 in the Supporting Information). The Ln−O bond lengths are within the range from 2.14 to 2.47 Å. The subtle differences of bond lengths and bond angles are summarized in Table S1 in the Supporting Information. The direct-current (dc) magnetic susceptibilities are measured by polycrystalline samples under 1 kOe, revealing the typical behavior of LnIII ions with strong orbital contribution. The χMT values at room temperature are 23.74, 28.50, 28.46, 23.06, 14.37, 4.96 cm3 mol−1 K (Figure 2), which are in agreement with the expected value (from two isolated Ln

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RESULTS AND DISCUSSION Complexes [Ln2(NMP)12(PW12O40)] [PW12O40] (Ln = TbIII, DyIII, HoIII, ErIII, TmIII, YbIII; see Figure 1) were synthesized in one step starting from the LnCl3·6H2O, NMP and H3PW12O40· nH2O in CH3CN/H2O mixture solvent followed by ref 14. Single-crystal structure analyses reveal that all of the six complexes are isostructural. They crystallize in the triclinic space group P1̅ (Table 1). Six complexes consist of the [PW12O40]3− anion and the [Ln2(NMP)12(PW12O40)]3+ cation, where either of the Ln ions is coordinated with six NMP molecules and connected by [PW12O40]3− (Figure 1). The adjacent Ln···Ln distance is ca. 15 Å. The seven-coordination Ln ion is under a distorted pentagonal bipyramidal (pseudo-D5h

Figure 2. Temperature dependence of χMT under 1.0 kOe applied dc field at 1.8−300 K for a polycrystalline sample of Tb, Dy, Ho, Er, Tm, and Yb derivatives by MPMS Squid VSM. The solid lines represent the calculated magnetic susceptibilities using CASSCF/RASSI. 7836

DOI: 10.1021/acs.inorgchem.7b00577 Inorg. Chem. 2017, 56, 7835−7841

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measured. The frequency dependence of χ″ was observed for Dy-doping (Figure S3 in the Supporting Information) and Ybdoping (Figure S13 in the Supporting Information) with external dc field, but interestingly, no appreciable χ″ were tested for Tb, Ho, and Tm, even with external static field. We successfully evidenced the disappearance of slow magnetic relaxation behavior when the single-electron number is even, which is in good agreement with the tunneling mechanisms: in an integer J state, ground doublet is split by transverse anisotropy, and states on opposite sides of the magnetization blocking barriers are strongly mixed.18 The frequency dependence of the ac susceptibility of Dydoping, Er and Yb-doping were analyzed by the generalized Debye model19 for the single relaxation process (Figures S5, S11, and S15 in the Supporting Information). The fitting results are given in Tables S3−S5 in the Supporting Information. The parameter α is 0.35−0.42, 0.04−0.12, and 0−0.09, respectively. The extracted relaxation time (τ) is plotted as a function of temperature (T) in ln(τ) vs T−1 (Figures S6, S12, and S16 in the Supporting Information). Both complexes Dy-doping and Er exhibit linear increase of ln(τ) as temperature cooled, while Yb-doping shows an exponential increase. The linearity of the curve can be fitted by Arrhenius Law τ = τ0 exp(Ueff/kBT) associated with a possible Orbach relaxation process, with the extracted parameters, Ueff = 6.55 K with τ0 = 1.62 × 10−5 s for Dy-doping, Ueff = 11.13 K with τ0 = 1.57 × 10−6 s for Er and Ueff = 11.84 K with τ0 = 1.14 × 10−6 s for Yb-doping. The fitted energy barrier of Er mostly matches the energy gap between the ground state and the first excited state (24 K) from the calculation (Table S7 in the Supporting Information). Assuming that the relaxation rate is given by Orbach process in the high temperature, and plus Raman process in low temperature, the best-fit curves in Figure 4 were obtained with

ions) for J values of 6, 15/2, 8, 15/2, 6, and 7/2 with gJ = 3/2, 4/3, 5/4, 6/5, 7/6, and 8/7, corresponding to TbIII, DyIII, HoIII, ErIII, TmIII, and YbIII, respectively.15 When cooled, χ M T values decrease because of the depopulation of the excited mJ states. The field dependence of the magnetization at different temperatures was measured (Figure S2 in the Supporting Information). M versus H plotted curves revealed that all of the magnetizations are unsaturated even at 7 T, indicating strong magnetic anisotropy, which is common in lanthanide ions. Complete-active-space self-consistent field (CASSCF) calculations on individual Ln fragment (Figure S18 in the Supporting Information) of six complexes were performed with MOLCAS 8.0 program package.16 The calculated temperature dependence χmT values were presented in Figure 2. The fitted weak Ln−Ln interactions and intermolecular interactions were summarized in Table S6, where the Ln−Ln interactions are very small due to the large Ln−Ln distances. The calculated lowest spin−orbit states (ground mJ multiples) and the principal values of the g tensors of complexes are reported in Table S7 in the Supporting Information. The calculated magnetization axes are presented as green arrows in Figure 3, where we notice the easy axes of the former three

Figure 3. Calculated (green) magnetic axes of six complexes. Ln atoms are drawn in light green, N in blue, O in red, and C in gray. H atoms are omitted for clarity.

complexes (Tb, Dy, and Ho, the complex derivatives were abbreviated with the lanthanide atomic symbol in bold) are nearly on the equatorial plane, while they are out of the plane for the other three complexes (Er, Tm, and Yb). Furthermore, a gradual rotation of the easy axis out of the equatorial plane occurs as the number of 4fn electrons increases (n > 10). A similar phenomena was also reported by Sessoli et al. in Na[LnDOTA(H2O)]·4H2O complexes.17 It is proved that this distorted pentagonal bipyramidal can minimize the energy of the mJ = J state. The shapes for the 4f electron densities of Tb, Dy, and Ho with the lowest mJ = J states are similar, and those of the other three complexes are also similar.10a Given the strong magnetic anisotropy of the whole series, we tested the magnetization dynamics at low temperature by alternating current (ac) field Hac = 2 Oe. Unfortunately, in zero external dc field, all of the complexes did not reveal slow magnetization relaxation behavior. Applying a small static magnetic field, a significant signal of out of phase susceptibility (χ″) was detected for Er (Figure S9 in the Supporting Information). To slow the magnetization dynamic, the analogue lutetium complex doped with LnIII with a molar ratio of 9:1 was prepared, and dynamic magnetization was

Figure 4. Temperature dependence of the relaxation time for Dydoping, Er, and Yb-doping derivatives. The solid lines correspond to the best fit.

U = 24 K and n = 3.89 for Er. τ0 is too large for Dy-doping, indicating a faster slow relaxation rather than SMMs; and the data ares not on the line in low-temperature range for Ybdoping. To get a better estimation of the data, more fitting results with multiprocesses were tried (Figure 4 and Figures S7, S8, and S17 in the Supporting Information). The comparison with the calculated splitting given in Table S7 in the Supporting Information. For Dy-doping, the single phonon direct relaxation mechanism (n = 1) in the relaxation process is more reasonable.20 However, for Yb-doping, Raman process is the main component in the relaxation process with best fit 7837

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Figure 5. Orientations of the local main magnetic axes of the ground Kramers doublet on DyIII of complexes Dy−I to Dy−IV with different axial Dy−O bond length (Dy−O bond length on the equatorial plane is 2.302 Å).

parameter C = 9.02 K−7.23 s−1 and n = 7.23, which is also in accordance with the expected values for Kramer ion SMMs where n ≥ 4. From theoretical predictions and those reported examples,9 the pentagonal bipyramidal Dy complex (D5h symmetry) might be a high-performance SMM. Disappointingly, Dy does not show slow magnetic relaxation behavior in low temperature. From observing the structure of Dy, the Dy−O bond coordinated with POM (2.456 Å) on the equatorial plane is much longer than others (ca. 2.3 Å), which destroys the local symmetry of Dy III ion (Table S1 in the Supporting Information). The low local symmetry, which induces strong QTM, might be one of the reasons for their poor behavior. From our ab initio calculation, moreover, the main magnetic axes on Tb, Dy, and Ho are all on the equatorial plane (Figure 3), which are much different from those reported SMMs9 with high performance (their magnetic axes are all along the axial direction). According to Long et al.’s theory,10b it is reasonable that our reported complexes have poor behavior. For the other three complexes, the above reason is also responsible for their poor behavior. To further explore the reason, we changed the length of the Dy−O bond to let the ligand field around DyIII ion being more and more close to D5h symmetry and then investigated the magneto-structural correlations in this special ligand field through ab initio calculations. To obtain a convincing result, we calculated four structures (Figure 5) based on Dy (Dy−I to Dy−IV, the details of structure parameters are displayed in Tables S8 and S9 in the Supporting Information). From the calculated results of Dy, the transition magnetic moment (0.021 μB) for direct QTM is the largest in five structures (Figure S19 in the Supporting Information), which is in line with the experimental results. What is more, the transition magnetic moments for direct QTM process are decreased as the symmetry is improved. It is proved that the local symmetry has a sensitive influence on QTM. In the same symmetry (D5h), the orientation of the main magnetic axes in the ground Kramers doublet of four complexes (Dy−I to Dy− IV) are all on the equatorial plane (Figure 5). Although the length of axial Dy−O has a little influence on the energy gaps between the ground and the first excited states (ca. 250 cm−1, Dy−I to Dy−IV, Table S8 in the Supporting Information), it strongly influences the magnetic anisotropy of the excited states, which further dominates the most probable relaxation route. As a result, the most probable relaxation route for Dy−II is a thermally assisted QTM via the first excited, but via the second excited states for Dy−I, Dy−III, and Dy−IV (Figure S19 in the Supporting Information). In the view of Figure 6, the longer the axial Dy−O bond length is, the higher the reversal energy is. Under this situation, the ligand field along the axial

Figure 6. Dependence of the calculated energy barriers with the axial Dy−O bond lengths when the magnetic axes in ground Kramers doublet are on the equatorial plane. (inset) Calculated model with the magnetic axis in ground Kramers doublet.

orientation impedes the magnetic anisotropy increasing, which successfully explains the poor performance of Dy−II comparing with the other three model complexes in Figure 5. In conclusion, when the main magnetic axis in the ground state is on the equatorial plane, the weak ligand field strength along the axial orientation is helpful to design high-performance SMMs (Dy−IV (462.2 cm−1) > Dy−III (455.1 cm−1) > Dy−I (446.3 cm−1) > Dy−II (250.6 cm−1); Tables S7 and S8 in the Supporting Information and Figure 6). This conclusion has also been confirmed by chemists with similar structures.21 Next, we will discuss the opposite case that the main magnetic axis in the ground state is along the axial orientation. On the basis of the complex reported by Tong,9b we made the model complex Dy−VI by replacing Cy3PO (Cy = cyclohexyl) with (CH3)3SiO− along the axial orientation without changing Dy−O length and related bond angles. The other four model complexes (Dy−V to Dy−IX, except Dy−VI) were obtained through only changing the Dy−O(Si) lengths based on Dy−VI (Figure 7 and Table S10 in the Supporting Information). CASSCF/RASSI/Single_Aniso calculations show that the most probable relaxation process for Dy−V to Dy−VIII is a thermally assisted QTM via the fourth excited state (|−15/2⟩ → |−13/2⟩ → |−11/2⟩ → |−9/2⟩ → |+9/2⟩ → |+11/2⟩ → | +13/2⟩ →|+15/2⟩, Figure S21 in the Supporting Information), and via the third excited state for Dy−IX, with the theoretical energy barrier decreasing as the axial Dy−O length stretches (Figure 8 and Table S11 in the Supporting Information). Interestingly, the theoretical energy barrier is linear to the axial Dy−O length. To date, the lowest reported Dy−O length22 is 1.95 Å, and its theoretical energy barrier might reach 2012 cm−1. The experimental energy barriers of complexes reported in ref 9 are all as large as the theoretical ones, 7838

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for oblate ion-based SMMs is on the equatorial plane, such as our reported SMMs, they may show poor behavior. When the main magnetic axis in the ground state is along the axial orientation, the high axial symmetry of crystal field at the location of the oblate ion and strong ligand field strength along the axial orientation are helpful to design oblate ion-based SMMs with high performance. Moreover, we found that the negative-charge ligand along the axial orientation also has an important contribution to the energy barrier for oblate ionbased SMMs with pentagonal bipyramidal symmetry, although covalence effect is dominated.

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Figure 7. Orientations of the local main magnetic axes of the ground Kramers doublet on DyIII of complexes Dy−V to Dy−IX with different axial Dy−O bond length (Dy−O bond length on the equatorial plane is 2.35 Å).

EXPERIMENTAL SECTION

All the reagents and solvents were purchased from commercial sources without any purification. Preparation of [Tb 2 (NMP) 12 (PW 12 O 40 )][PW 12 O 40 ] (Tb). H3PW12O40·nH2O (1.3 g) and TbCl3·6H2O (0.149 g) were added in 10 mL of acetonitrile/water (2:1 v/v) mixed solution, then 0.5 mL of N-methyl-2-pyrrolidone was added. After that, the mixture was heated to 90 °C for 1 h without stirring, followed by cooling to room temperature in the dark resulted in light yellow single crystals in ca. 61% yield based on Tb element. The light-yellow crystal will turn black under daylight. Anal. Calcd (%) for C30H54N6O46PTbW12: C 9.92, H 1.50, N 2.31; found: C 9.97, H 1.65, N 2.36. IR (KBr, cm−1): 3402(s), 2942(w), 1634(vs), 1515(m), 1405(w), 1312(w), 1260(w), 1257(m), 1078(vs), 985(vs), 895 (vs), 811(vs), 513(m). Preparation of [Ln2(NMP)12(PW12O40)][PW12O40] (Dy, Ho, Er, Tm, Yb, Lu). Ln was prepared according to the procedure described for Tb but with LnCl3·6H2O (0.150 g) instead of TbCl3·6H2O, as the rare earth reagent resulted in single crystals in ca. 55−74% yield based on Ln element. The crystal also turned black under daylight. Anal. Calcd (%) for C30H54N6O46PDyW12: C 9.92, H 1.50, N 2.31; found: C 9.97, H 1.65, N 2.35. IR (KBr, cm−1): 3401(s), 2942(w), 1634(vs), 1517(m), 1405(w), 1310(w), 1260(w), 1253(m), 1078(vs), 980(vs), 894 (vs), 810(vs), 516(m). Anal. Calcd (%) for C30H54N6O46PHoW12: C 9.92, H 1.50, N 2.31; found: C 9.97, H 1.57, N 2.40. IR (KBr, cm−1): 3402(s), 2941(w), 1634(vs), 1513(m), 1406(w), 1310(w), 1263(w), 1256(m), 1078(vs), 981(vs), 893 (vs), 810(vs), 514(m). Anal. Calcd (%) for C30H54N6O46PErW12: C 9.92, H 1.50, N 2.31; found: C 9.95, H 1.54, N 2.33. IR (KBr, cm−1): 3403(s), 2942(w), 1635(vs), 1517(m), 1403(w), 1310(w), 1262(w), 1254(m), 1080(vs), 980(vs), 893 (vs), 810(vs), 513(m). Anal. Calcd (%) for C30H54N6O46PTmW12: C 9.92, H 1.50, N 2.31; found: C 9.92, H 1.49, N 2.34. IR (KBr, cm−1): 3402(s), 2940(w), 1635(vs), 1513(m), 1404(w), 1310(w), 1260(w), 1255(m), 1078(vs), 982(vs), 893 (vs), 812(vs), 515(m). Anal. Calcd (%) for C30H54N6O46PYbW12: C 9.92, H 1.50, N 2.31; found: C 9.99, H 1.60, N 2.45. IR (KBr, cm−1): 3401(s), 2942(w), 1638(vs), 1514(m), 1403(w), 1310(w), 1264(w), 1255(m), 1075(vs), 978(vs), 891 (vs), 808(vs), 513(m). Anal. Calcd (%) for C30H54N6O46PLuW12: C 9.88, H 1.49, N 2.30; found: C 9.99, H 1.50, N 2.35.IR (KBr, cm−1): 3402(s), 2940(w), 1635(vs), 1513(m), 1404(w), 1310(w), 1260(w), 1255(m), 1078(vs), 982(vs), 893 (vs), 812(vs), 515(m). Preparation of Dy-doping and Yb-doping. The diluted sample, complex Dy-doping, was synthesized in the same way, with the starting DyCl3·6H2O/LuCl3·6H2O = 1:9. The dilution ratios were confirmed by inductively coupled plasma atomic emission spectroscopy (ICP-AES) analyses as 10% ± 0.7%. The diluted sample, complex Yb-doping, was synthesized in the same way, with the starting YbCl3· 6H2O/LuCl3·6H2O = 1:9. The dilution ratios were confirmed by ICPAES analyses as 10% ± 0.3%. Physical Measurement. The measurements of IR spectra were performed with a Nexus 870 FT-IR spectrometer using KBr pellets in the range of 400−4000 cm−1. Elemental analyses of C, H, and N were recorded on a PerkinElmer 240C elemental analyzer. ICP-AES analyses were recorded on Optima 5300DV. The ac magnetic data were measured on an MPMS Squid VSM magnetometer with an ac field of 2 Oe and frequencies varying over the range from 1 to 999 Hz.

Figure 8. Dependence of the theoretical energy barriers with the axial Dy−O bond lengths when the magnetic axes in ground Kramers doublet are along the axial orientation. (inset) Calculated model with the magnetic axis in ground Kramers doublet. The red line is fitted with E = 6954 − 2533.97 × L(Dy−O).

indicating the theoretical calculation is reliable to deal with high axial symmetry of crystal field at the location of DyIII ion. Complex in ref 9b presents a much lower energy barrier than Dy−VI (Figure 8), showing that the negative charges concentrated along the magnetic axes are very important to obtain SMMs with high performance. The two isostructural complexes reported in ref 9a have much different energy barriers compared with model complex Dy−V or Dy−VI. Omitting the tiny difference in structures, the negative charges (Br−, Cl−) on the equatorial plane weaken the magnetic anisotropy and decrease the field symmetry, inducing the decrease of the energy barriers compared with model complexes. Furthermore, the experimental or calculated energy barrier with Br− ion (weaker ligand field strength than that of Cl−) on the equatorial plane is larger than that of the one with Cl−. In conclusion, when the main magnetic axis in the ground state is along the axial orientation, the high axial symmetry of crystal field at the location of DyIII ion and strong ligand field strength along the axial orientation are helpful to design highperformance SMMs. Except for the main effect of covalence, however, the negative-charge ligand along the axial orientation is also helpful to enhance the magnetic anisotropy for Dy-based SMMs. This is confirmed by the SMM in ref 9c, which presents a record magnetic performance.

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CONCLUSIONS According to above analysis, pentagonal bipyramidal symmetry DyIII complex is a good choice to achieve high-performance SMMs. However, if the main magnetic axis in the ground state 7839

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The dc magnetic data were measured at temperatures between 1.8 and 300 K, and the magnetization isothermal measurements were made in fields between 0 and 7 T on an MPMS Squid VSM magnetometer. Experimental susceptibilities were corrected for the diamagnetism estimated Pascal’s tables23 and for sample holder by previous calibration. Ab Initio Calculations. CASSCF calculations on individual Ln fragment (see Figure S18 in the Supporting Information) of complexes Tb, Dy, Ho, Er, Tm, and Yb on the basis of X-ray determined geometry were performed with MOLCAS 8.0 program package.16 For the symmetric structures of Tb, Dy, Ho, Er, Tm, and Yb, we only need to calculate one Ln fragment for each of them. For CASSCF calculations, the basis sets for all atoms are atomic natural orbitals from the MOLCAS ANO-RCC library: ANO-RCC-VTZP for Ln (TbIII, DyIII, HoIII, ErIII, TmIII, or YbIII ion); VTZ for close O; VDZ for distant atoms. The influence of neighboring W ion was taken into account by the closed-shell LaIII ab initio embedding model potentials (AIMP; La.ECP.deGraaf.0s.0s.0e-La-(LaMnO3.). The calculations employed the second-order Douglas−Kroll−Hess Hamiltonian, where scalar relativistic contractions were taken into account in the basis set, and the spin−orbit coupling was handled separately in the restricted active space state interaction (RASSI-SO) procedure. The active electrons in seven active spaces include all f electrons (CAS (8 in 7) for Tb; CAS (9 in 7) for Dy; CAS (10 in 7) for Ho; CAS (11 in 7) for Er; CAS (12 in 7) for Tm; CAS (13 in 7) for Yb) in the CASSCF calculation. To exclude all the doubts, we calculated all the roots in the active space. We mixed the maximum number of spin-free state, which was possible with our hardware (all from 7 septets, all from 140 quintets, and 68 from 500 triplets for the Tb fragment; all from 21 sextets, 128 from 224 quadruplets, 130 from 490 doublets for Dy fragment; all from 35 quintets, 150 from 210 triplets, and 120 from 196 singlets for Ho fragment; all from 35 quadruplets, all from 112 doublets for Er fragment; all from 21 triplets, all from 28 singlets for Tm fragment; all from 7 doublets for Yb fragment). To fit the exchange interactions in six complexes, we took two steps to obtain them. First, we calculated the mononuclear fragments using CASSCF to obtain the corresponding magnetic properties (see the first part). And then, the exchange interaction between the magnetic centers is considered within the Lines model,24 while the account of the dipole−dipole magnetic coupling is treated exactly. For complexes 1−6, the exchange Hamiltonian is ∧

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b00577. Structural and magnetic characterization, theoretical calculation (PDF) Accession Codes

CCDC 1526934−1526939 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. (Y.-Q.Z.) *E-mail: [email protected]. (Y.S.) ORCID

Yi-Quan Zhang: 0000-0003-1818-0612 Author Contributions §

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. These authors contributed equally. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Major State Basic Research Development Program (2013CB922102), National Natural Science Foundation of China (91622115 and 21571097), Specialized Research Fund for the Doctoral Program of Higher Education, and Natural Science Foundation of Jiangsu Province of China (BK20151542).

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∧

∼ ∼ H̑exch = − Jlntotal S S − ln ln1 ln2

Article

REFERENCES

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(1)

total The Jtotal = Ln−Ln is parameter of the total magnetic interaction (J ∧ ∼ Jdiploar + Jexchange) between magnetic center ions. The S Ln = ±1/2 is the ground pseudospin on the Ln site. The dipolar magnetic coupling can be calculated exactly, while the exchange coupling constants were fitted through comparison of the computed and measured magnetic susceptibility and molar magnetization using the POLY_ANISO program.25 Crystallographic Data Collection and Refinement. Crystallographic data of complexes [Ln2(NMP)12(PW12O40)] [PW12O40] (Ln = Tb, Dy, Ho, Er, Tm, and Yb) were collected on Bruker Smart CCD area-detector diffractometer with Mo Kα radiation (λ = 0.710 73 Å) by using a ω scan mode at 296 K. The diffraction data were treated using SAINT,26a and all absorption corrections were applied by using SADABS.26b All non-hydrogen atoms were located by Patterson method26c using the SHELXS programs of the SHELXTL package and subsequent difference Fourier syntheses. Hydrogen bonded to carbon were determined theoretically and refined with isotropic thermal parameters riding on their parents. All non-hydrogen atoms were refined by full-matrix least-squares on F2. All calculations were performed by SHELXTL-97.26d Additional crystallographic information is available in the Supporting Information.

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