Experimental and theoretical interpretation of the magnetic behavior of two Dy(iii) single-ion magnets constructed through β-diketonate ligands with different substituent groups (–Cl/–OCH3)

Two Dy(iii) single-ion magnets, formulated as [Dy(Phen)(Cl-tcpb)3] (Cl-1) and [Dy(Phen)(CH3O-tmpd)3] (CH3O-2) were obtained through β-diketonate ligands (Cl-tcpb = 1-(4-chlorophenyl)-4,4,4-trifluoro-1,3-butanedione and CH3O-tmpd = 4,4,4-trifluoro-1-(4-methoxyphenyl)-1,3-butanedione) with different substituent groups (–Cl/–OCH3) and auxiliary ligand, 1,10-phenanthroline (Phen). The Dy(iii) ions in Cl-1 and CH3O-2 are eight-coordinate, with an approximately square antiprismatic (SAP, D4d) and trigonal dodecahedron (D2d) N2O6 coordination environment, respectively, in the first coordination sphere. Under zero direct-current (dc) field, magnetic investigations demonstrate that both Cl-1 and CH3O-2 display dynamic magnetic relaxation of single-molecule magnet (SMM) behavior with different effective barriers (Ueff) of 105.4 cm−1 (151.1 K) for Cl-1 and 132.5 cm−1 (190.7 K) for CH3O-2, respectively. As noted, compound CH3O-2 possesses a higher effective barrier than Cl-1. From ab initio calculations, the energies of the first excited state (KD1) are indeed close to the experimental Ueff as 126.7 cm−1vs. 105.4 cm−1 for Cl-1 and 152.8 cm−1vs. 132.5 cm−1 for CH3O-2. The order of the calculated energies of KD1 is same as that of the experimental Ueff. The superior SIM properties of CH3O-2 could have originated from the larger axial electrostatic potential (ESP(ax)) felt by the central Dy(iii) ion when compared with Cl-1. The larger ESP(ax) of CH3O-2 arises from synergic effects of the more negative charge and shorter Dy–O distances of the axial O atoms of the first sphere. These charges and distances could be influenced by functional groups outside the first sphere, e.g., –Cl and –OCH3.


Introduction
Since the rst single-molecule magnet (SMM), Mn 12 Ac, was discovered in the 1990s, 1 the search for improved properties, in particular the enhanced relaxation barrier (U eff ) and blocking temperature (T B ), has advanced the development of new compounds with magnetic properties customized by the coordination environment. 2 The relevant explorations focus on mononuclear lanthanide compounds, especially single Dy-center systems, owing to the intrinsic strong spin-orbit coupling and large magnetic anisotropy of lanthanide ions. 3 Furthermore, the relatively simple structure is convenient for chemists to improve the understanding of the magnetostructural correlation by combining with ab initio calculations. 4 The number of mononuclear lanthanide SMMs or singleion magnets (SIMs) derived from the above approach, following signicantly slow relaxations of the magnetization, has grown signicantly. An equatorially coordinated triangular geometry for C 3 , 5 square antiprismatic systems for D 4d , 6 sandwich-type systems for D 8d or D 8h , 7 the pentagonal bipyramidal local geometry for D 5h , 4a,4b,8 linear 2-coordinated systems for D Nh 9 and some systems possessing high charge distribution symmetry, 10 are given different priorities in lanthanide SIM construction. The research reveals that the single-ion magnetic anisotropy of lanthanide ions is extremely sensitive to the subtle changes in the ligand and the local geometrical symmetry. The electrostatic potential distribution around the magnetic center can be regulated by the amount of solvent, 11 the anion ligands, 12 the lattice/coordinated solvents, 13 the pH values of the solution systems, 14 or the counter ions, 15 on the basis of weakening or strengthening the electron density. 16 Interestingly, other functional groups from ligands outside the rst sphere could also effectively inuence the electron density of the rst-sphere atoms and thus affect the SIM properties, which should also be considered in the rational design of promising molecular magnets. 4d Finding a feasible strategy to regulate and control the electrostatic environment around the metal centers and the singleion magnetic anisotropy in SIMs would provide an active direction for understanding the magneto-structural correlation in depth and developing magnetic materials with high U eff and blocking temperature (T B ). Herein, two b-diketonate ligands with different functional groups were chosen for the following reasons: the classical b-diketonate ligands with different functional groups usually coordinate with metal ions in bidentate chelating modes in SIMs, which is benecial for discussing the inuence of the electron density. 8 Fortunately, with the introduction of a capping ligand, two mononuclear compounds, [Dy(Phen)(Cl-tcpb) 3 ] (Phen ¼ 1,10-phenanthroline, Cl-tcpb ¼ 1-(4-chlorophenyl)-4,4,4-triuoro-1,3-butanedione, Cl-1) and [Dy(Phen)(CH 3 O-tmpd) 3 ] (CH 3 O-tmpd ¼ 4,4,4-triuoro-1-(4methoxyphenyl)-1,3-butanedione, CH 3 O-2), were obtained through solution reaction. The Dy(III) ion in compound Cl-1 has an approximately square antiprismatic (SAP) N 2 O 6 coordination environment, while CH 3 O-2 has a trigonal dodecahedron (D 2d ) conguration. Magnetic characterization indicates that the subtle changes in the different substituent groups from the bdiketonate ligand results in great differences in the coordination environment and dramatically alters the relaxation behaviors of Cl-1 and CH 3 O-2. To further understand the different magnetic behaviors of Cl-1 and CH 3 O-2, ab initio calculations were also performed to explore the magnetic anisotropies of the central Dy(III) ions. A preliminary analysis on the electrostatic potential felt by the Dy(III) ion is utilized to identify the effect of ligands on its magnetic anisotropy. Expectedly, other functional groups outside the rst sphere could also effectively inuence the electron density of the rst sphere atoms and thus affect the SIM properties.

Materials and instruction
All the materials and reagents were obtained commercially without further purication. The FT-IR spectra were recorded in the range of 400-4000 cm À1 using KBr pellets on an EQUINOX55 FT/IR spectrophotometer. Elemental analysis (C, H, N) was implemented on a Perkin-Elmer 2400 CHN elemental analyzer. The phase purity of the bulk or polycrystalline samples were conrmed by powder X-ray diffraction (PXRD) measurements executed on a Rigaku RU200 diffractometer at 60 kV, 300 mA, and Cu Ka radiation (l ¼ 1.5406Å), with a scan speed of 5 min À1 and a step size of 0.02 in 2q. Diffuse reectance spectra were obtained by a U-41000 spectrophotometer applying BaSO 4 powder as a 100% reectance reference. Magnetic measurements were performed in the temperature range of 1.8-300 K with an applied eld of 1000 Oe, using a Quantum Design MPMS-XL-7 SQUID magnetometer on polycrystalline samples.
The diamagnetic corrections for the compounds were estimated using Pascal's constants. Alternating current (ac) susceptibility experiments were performed using an oscillating ac eld of 2.0 Oe at ac frequencies ranging from 1 to 1000 Hz. The magnetization was measured in the eld range 0-7 T.

Synthesis and characterization of the lanthanide compounds
All chemicals were obtained from commercial sources and were used as received without further purication.

X-ray single-crystal diffraction analysis
The single crystal X-ray experiment was performed on an Agilent Xcalibur Eos Gemini diffractometer using graphitemonochromatized Cu Ka radiation (l ¼ 1.5418Å). The data integration and reduction were processed with the CrysAlisPro soware. Absorption correction based on multi-scans was performed using the SADABS program. 17 The structures were solved by the direct method and rened by means of full-matrix least-squares procedures on F 2 with the SHELXL program. 18 All non-hydrogen atoms were rened anisotropically. Other details of crystal data, data collection parameters, and renement statistics are given in Table S1. † The selected bond lengths and angles are listed in Table S2. †

Theoretical methods and computational details
Multicongurational ab initio calculations, including spinorbit coupling (SOC), were performed on the experimental structures of 1 and 2 to explore their magnetic anisotropy. This type of calculation includes two steps: 19 (1) a set of spin eigenstates, were obtained by the state-averaged (SA) CASSCF method; 20 (2) the low-lying SOC states, i.e., Kramers doublets (KD) herein, were obtained by state interaction, which is the diagonalization of the SOC matrix in the space spanned by the spin eigenstates from the rst step. In the CASSCF step, the active space consisted of 9 electrons in 7 orbitals and all the spin eigenstates of 21 sextets were included. Due to the hardware limitations, other highly excited quartets and doublets were not considered. The state interaction step was performed by the RASSI-SO module 21 with the SOC integrals from the AMFI method. 22 The ANO-RCC basis sets, [23][24][25] including VTZP for Dy, VDZ for C and H as well as VDZP for other atoms, were used. All the calculations were carried out with the MOLCAS@UU, a version of MOLCAS 8.0 (ref. 26 and 27) which is freely distributed for academic users. The SIN-GLE_ANISO module, 28,29 developed by Chibotaru et al., was used to obtain the g-tensors, transition magnetic moments and other parameters characterizing the magnetic anisotropy.
In our previous works, the b-diketonate ligands with different substituent groups (-F/-CH 3 ) were employed to obtain a series of mononuclear Dy(III) compounds (Scheme 1). For CH 3 -4 (solvent) and CH 3 -3, the latter has a trigonal dodecahedron (D 2d ) conguration of Dy(III) ions, while CH 3 -4 (solvent) shows an approximately square antiprismatic (SAP, D 4d ) N 2 O 6 coordination environment of Dy(III) ions. The uncoordinated 1,4dioxane molecules exist in CH 3 -4 (solvent). Interestingly, the compounds above have weak interactions between the neutral molecules. In CH 3 -3, the neutral molecules are assisted by weak  p/p stacking between the parallel interlayer, and the centroid distance is 3.767 (6)Å, belonging to a slipped stacking and leading to the Dy(III)/Dy(III) distance of 9.193 (5)Å. In CH 3 -4 (solvent), the neutral molecules are connected by weak C(171)-H(117)/O(7) interactions, leading to the Dy(III)/Dy(III) distance of 18.853 (2)Å. F-5 belongs to an approximately SAP conguration. For Cl-1, CH 3 -4 (solvent) and F-5, the CH 3 -4 (solvent) is more inclined toward the SAP conguration, calculated by utilizing the SHAPE 2.1 soware. Cl-1 has the closest distance between the neutral molecules. In CH 3 O-2 and CH 3 -3, the former has the smaller deviation relative to a trigonal dodecahedron (D 2d ) conguration. The longer distance between the neutral molecules can be observed in CH 3 O-2. It is a remarkable fact that the maximum average Dy-N bond length is 2.563Å (2) in CH 3 O-2. F-5 and CH 3 O-2 show similar average Dy-O bond lengths, which are smaller than Cl-1, CH 3 -3 and CH 3 -4 (solvent). The different types of weak interactions between the neutral molecules, congurations and bond lengths would result in different magnetic behaviors.

Magnetic properties
The magnetic experiments of Cl-1 and CH 3 O-2 were performed on polycrystalline samples. PXRD results of Cl-1 and CH 3 O-2 support the pure state of the bulk materials (Fig. S1 †). The values of c M T of Cl-1 and CH 3 O-2 are 13.16 cm 3 mol À1 K and 14.51 cm 3 mol À1 K at room temperature, respectively, which are close to the free-ion value of 14.17 cm 3 mol À1 K for a single Dy(III) ion ( 6 H 15/2 , (Fig. 3). 13 When cooled, the c M T curves for compound Cl-1 decreased slowly in the range from 300 to 100 K. Subsequently, the c M T products decreased sharply below 100 K to the minimum of 9.46 cm 3 mol À1 K for Cl-1 and 11.75 cm 3 mol À1 K for CH 3 O-2 at 1.8 K.
In CH 3 O-2, on lowering the temperature, the c M T product decreased gradually and more rapidly below 50 K. These behaviors could be ascribed to crystal eld splitting, particularly the progressive quenching of excited Dy(III) Stark sublevels and/ or weak intermolecular dipole-dipole effects. 32 The magnetization of the two compounds from zero dc eld to 70 kOe at different temperatures is shown in Fig. 4. The  This journal is © The Royal Society of Chemistry 2018 magnetization of Cl-1 and CH 3 O-2 at 2 K increased upon application of an external eld to a maximum of 4.97 Nb and 5.79 Nb. The maximum values in Cl-1 and CH 3 O-2 at 7 T largely deviate from the expected saturation point of 10 Nb, consisting of the magnetic anisotropy and crystal eld effects at the dysprosium center, which dispel the 16-fold degeneration of the 6 H 15/2 ground state. 33 The M versus H data exhibit obvious buttery-shaped hysteresis loops at 2 K for Cl-1 and CH 3 O-2 (Fig. 5), indicating the fast zero-eld relaxation between the two ground states.
Under the oscillating eld of 3.5 Oe, the zero-eld AC susceptibility experiments were determined in the range of 1.8-20 K and at frequencies of 1, 10, 100, 333, 500, 800 and 1000 Hz in Cl-1. However, for CH 3 O-2, zero-eld AC susceptibilities were measured in the range of 2-18 K and at frequencies of 1, 10, 100, 300, 500, 800, 900 and 1000 Hz. Both in-phase (c 0 ) and out-ofphase (c 00 ) susceptibilities in compound Cl-1 and CH 3 O-2 showed signicant temperature dependence peaks at a relatively high-temperature range (Fig. 6 and 7), which clearly indicates the slow relaxation of magnetization. When cooled, c 0 and c 00 increased again at lower temperatures; such a situation could be due to the emergence of quantum tunneling of magnetization (QTM) without an extra dc eld, which oen occurs in Ln(III)-based SMMs or SIMs (Table 1). 34 Furthermore, the frequency-dependent ac data for compounds Cl-1 and CH 3 O-2 were characterized in the absence of a dc eld at various temperatures; the peaks of the c 00 plots gradually shied with the frequency sequence from middle to high, indicating that the c 00 of compounds Cl-1 and CH 3 O-2 manifested frequency dependence in the selected temperature range (Fig. 8 and 9). The tting of the Cole-Cole plots (c 0 M vs. c 00 ) for Cl-1 and CH 3 O-2 ( Fig. 10 and 11) with the Debye model 13 presented a non-symmetric semicircle, which indicates the presence of a relatively moderate distribution of relaxation time (0.011 < a < 0.181 for Cl-1 and 0.007 < a < 0.161 for CH 3 O-2) (Table 3 and 4). For the relaxation time products under 0 Oe, the direct process can be neglected. The ln(s) versus 1/T plots for compound Cl-1 and CH 3 O-2 presented some curvature (Fig. 12),  indicating that the dynamics cannot be properly modelled by assuming a simple Orbach mechanism. Therefore, the total relaxation rates mainly reect the Orbach process, Raman process and QTM process, using the following equation (eqn (1)): where s is the inverse of the ac frequency, T is the temperature of the maximum in the ac signal, U eff is the effective energy barrier, k is Boltzmann's constant.   Paper coordination environment exhibited more excellent properties than CH 3 -3 with a trigonal dodecahedron (D 2d ) conguration. 35 However, the results in the present cases are in contrast to the explanation above, which veries that the relaxation magnetism    incompletely depends on the coordination symmetry of the Dy(III) centers. Accordingly, the magnetism of dysprosiumbased SMMs might be simultaneously dominated by complicated factors including local symmetry, electrostatics, etc. 10b,36 In our recent work, a similar phenomenon was observed in the two b-diketone mononuclear Dy(III) compounds, formulated as Dy(BTFA) 3 (H 2 O) 2 (D 2d ) and Dy(BTFA) 3 (bpy) (D 4d ) (BTFA ¼ 3benzoyl-1,1,1-triuoroacetone, bpy ¼ 2,2 0 -bipyridine). 10b As noticed, compound Dy(BTFA) 3 (H 2 O) 2 possesses a higher effective barrier than Dy(BTFA) 3 (bpy), despite Dy(BTFA) 3 (H 2 O) 2 exhibiting a lower geometrical symmetry of the Dy(III) ion. This is likely attributable to different charge distributions around the Dy(III) ions in both compounds, which compensate for the discrepancy of the geometrical symmetries and is responsible for the disparities in magnetic anisotropy, as well as energy barrier and slow relaxation behavior between the two compounds. However, the conjecture above urgently needs studies for an in-depth understanding of the signicative magneto-structural correlation.
According to the Dy(III) coordination spheres, the compounds are slightly distorted, with the following order: F-5 > Cl-1 > CH 3 -4 (solvent); CH 3 -3 > CH 3 O-2. The shortest intermolecular distance between Dy(III) ions is 7.911 (6)Å in Cl-1. However, there are no obvious +-+ stacking or hydrogen bonding interactions in Cl-1, probably resulting in the weakening of the QTM relaxation process from the intermolecular interactions. CH 3 O-2 shows shorter bond lengths for Dy-N and Dy-O than CH 3 -3 and a smaller degree of distortion, indicating the strong charge density around the metal ions and further generating enhanced uniaxial magnetic anisotropy. Finally, these different effective energy barriers (DE/k B ) have the following order: CH 3 O-2 > Cl-1 > CH 3 -4 (solvent) > CH 3 -3 > F-5.

Theoretical analysis
The effective energy barrier for the reversal of magnetization, U eff , is a popular parameter that is used to characterize the SMM properties of the compounds. However, only within the Orbach process is U eff clearly dened in principle. In the early stages of the SMM, the compounds were usually polynuclear transition metal structures where the Orbach process dominated the magnetic relaxation; since then, U eff has become popular in the eld of SMM. However, in the case of mononuclear SIMs, several relaxation processes, including both Orbach and others of QTM, direct as well as Raman, exist simultaneously. [37][38][39] Thus, the magnetic relaxation in Ln-based SIMs is not naturally dominated by the Orbach process and the necessary condition for the observation of SMM behavior is the effective suppression of all the fast relaxation process. 38,39 Among all the fast relaxation processes, the quantum tunnelling of magnetization (QTM) within the ground state is the most effective and thus its suppression is the rst target. Irrespective of various sources, the rate of QTM scales as the square of the so-called tunnel splitting D tun . [37][38][39][40] For Kramers ions, e.g., Dy(III), D tun is forced to be zero under the strict absence of a magnetic eld due to timereversal symmetry; however, small internal magnetic elds actually exist with different sources. 38 Therefore D tun in Kramers systems is induced via the Zeeman interaction (eqn (1a)) between the transversal elds (H X and H Y ) and the corresponding components of the magnetic momentsm of the same directions (m X and m Y ). 37-41 Theoretically, each Kramers doublet (KD) could be associated with an effective spin (pseudospin) S ¼ 1/2. 28,37,38 The magnetic moment of such pseudospin is determined by its principal values of the g-tensors as shown in eqn (1b). 37,38 Clearly, small values of the transversal g X and g Y (eqn (1c)) of the ground KD, i.e., KD 0 , will lead to a low magnitude of D tun and  a "-ax" indicates the atoms at the axial positions and "-equ" means the atoms at equatorial positions.
thus zero-eld SIM behavior could exist if the value of g XY for KD 0 is small enough. 42 Besides the principal g values of each KD, ab initio calculations also provide the averaged absolute value of the transversal magnetic moments, m QTM , which could also be used to measure the strength of QTM. As shown in Table  2, the g XY values of KD 0 are 0.1987 Â 10 À1 and 0.5421 Â 10 À02 for Cl-1 and CH 3 O-2, respectively. According to previous results from Ruiz et al., 17 zero-eld SIM behavior could occur if the g XY of KD 0 is smaller than 0.15 Â 10 À01 for mononuclear Dy(III) compounds. Clearly, this criterion is fullled in the case of CH 3 O-2 and, although a little bit larger, the g XY of KD 0 of Cl-1 is also quite close to this value. Therefore our ab initio results do suggest the existence of zero-eld SIM properties in these two compounds, which is consistent with the experimental observation based on ac susceptibility measurements. Due to the smaller value of g XY of KD 0 , the SIM property of CH 3 O-2 is theoretically predicted to be superior to that of Cl-1. This theoretical prediction is also in line with the higher U eff of CH 3 O-2 obtained from the tting of the experimental data. In many cases of Ln-SIMs, the energy of the rst excited KD, i.e., KD 1 , is closely related to the U eff . In the two compounds here, the energies of KD 1 are indeed close to the experimental U eff : 126.7 cm À1 vs. 105.4 cm À1 for Cl-1 and 152.8 cm À1 vs. 132.5 cm À1 for CH 3 O-2. Moreover, the energy of KD 1 for CH 3 O-2 is also higher than that of Cl-1. Thus, the reliability of our ab initio results is veried again in terms of energies of KD 1 .
As shown in our previous results, 14,18,19 the desired electronic structure, which is suitable for the ideal SIM properties of Dy(III) systems, could be approached via an electrostatic route due to the oblate electron density of the Dy(III) ion; i.e., the axial electrostatic potential (ESP) should exceed the equatorial one as much as possible. 6g, 31,40,43 According to the orientation of the magnetic easy axis (Fig. 13), the eight atoms of the rst sphere could be collected into two groups: (1) axial atoms consisting of the four oxygen atoms (O2, O3, O4 and O5 for Cl-1) that lie along the axial direction; (2) equatorial atoms consisting of the two nitrogen atoms and the residual two oxygen atoms (N8, N9, O6 and O7 for Cl-1). With ab initio atomic charge, we could approximate the axial ESP felt by the Dy(III) ion, i.e., ESP (ax) , with the sum of the contribution from the four axial atoms. Similarly, the equatorial ESP, i.e., ESP (equ) , could be approximated as the collection of the contribution from the four equatorial atoms. As shown before, 31,40,43 the lower value of the ratio ESP (equ) / ESP (ax) indicates the higher degree of the excess of the axial ESP over the equatorial, and thus it should lead to the electronic structure, which is more suitable for the ideal SIM properties.
As shown in Table 3, the ESP (equ) /ESP (ax) ratio of CH 3 O-2 is 0.701, clearly lower than that of Cl-1 (0.723). Thus, the superior  SIM property of CH 3 O-2 should originate from the more suitable ESP felt by the central Dy(III) ion when compared with 1. In detail, the difference in ESP (equ) of these two compounds is 0.03 a.u., which is clearly smaller than the corresponding difference in ESP (ax) (0.08 a.u.). In other words, the different amounts of ESP (ax) of these two compounds should play the central role in their differences in terms of SIM properties. When making a further analysis of the charges and distances to the central ion (Table 4), the averaged charges and distances to the central Dy(III) ion are 0.725 |e| and 2.320Å, respectively, for CH 3 O-2. In the case of Cl-1, the averaged charges and distances are 0.688 |e| and 2.345Å, respectively. Therefore the larger amount of ESP (ax) for CH 3 O-2 arises from the synergic effect of the more negative charge and shorter Dy-O distances of the axial O atoms of the rst sphere. Of course, these charges and distances could be inuenced by functional groups outside the rst sphere, e.g., -Cl and -OCH 3 .

Conclusion
Two mononuclear compounds, [Dy(Phen)(Cl-tcpb) 3 ] (Cl-1) and [Dy(Phen)(CH 3 O-tmpd) 3 ] (CH 3 O-2), were synthesized based on b-diketonate ligands (Cl-tcpb ¼ 1-(4-chlorophenyl)-4,4,4-triuoro-1,3-butanedione and CH 3 O-tmpd ¼ 4,4,4-triuoro-1-(4-methoxyphenyl)-1,3-butanedione) with different substituent groups (-Cl/-OCH 3 ) and auxiliary ligand 1,10-phenanthroline (Phen). The Dy(III) ions in Cl-1 have approximately squareantiprismatic (SAP, D 4d ) N 2 O 6 coordination environments. The coordination geometry of Dy(III) ions in CH 3 O-2 can be best described as a trigonal dodecahedron (D 2d ). The dynamic magnetic investigations showed that both compounds exhibited SMM behavior in zero dc eld, while the effective magnetization relaxation barriers increased progressively from 105.4 cm À1 (151.1 K) for Cl-1 to 132.5 cm À1 (190.7 K) for CH 3 O-2. CH 3 O-2 possessed a higher effective barrier than Cl-1, despite Cl-1 exhibiting a higher geometrical symmetry of the Dy(III) ion. Moreover, the energy of KD 1 of CH 3 O-2 was also higher than that of Cl-1. The zero-eld SIM behaviors, as well as the difference in U eff , of these two compounds were reproduced by ab initio calculations. Further studies from the viewpoint of electrostatic potential demonstrated that the larger axial electrostatic potential (ESP) felt by the central Dy(III) ion of CH 3 O-2 is responsible for its better SIM properties when compared with Cl-1. The larger amount of ESP (ax) of CH 3 O-2 arises from the synergic effect of the more negative charge and shorter Dy-O distances of the axial O atoms of the rst sphere. Beyond all doubt, these charges and distances could be affected by functional groups outside the rst sphere, e.g., -Cl and -OCH 3 .

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