Ten-Coordinate Lanthanide [Ln(HL)(L)] Complexes (Ln = Dy, Ho, Er, Tb) with Pentadentate N3O2-Type Schiff-Base Ligands: Synthesis, Structure and Magnetism

A series of five neutral mononuclear lanthanide complexes [Ln(HL)(L)] (Ln = Dy3+, Ho3+ Er3+ and Tb3+) with rigid pentadentate N3O2-type Schiff base ligands, H2LH (1-Dy, 3-Ho, 4-Er and 6-Tb complexes) or H2LOCH3, (2-Dy complex) has been synthesized by reaction of two equivalents of 1,1′-(pyridine-2,6-diyl)bis(ethan-1-yl-1-ylidene))dibenzohydrazine (H2LH, [H2DAPBH]) or 1,1′-(pyridine-2,6-diyl)bis(ethan-1-yl-1-ylidene))di-4-methoxybenzohydrazine (H2LOCH3, [H2DAPMBH]) with common lanthanide salts. The terbium complex [Tb(LH)(NO3)(H2O)2](DME)2 (5-Tb) with one ligand H2LH was also obtained and characterized. Single crystal X-ray analysis shows that complexes 1–4 have the composition {[Ln3+(HL)−(L)2−] solv} and similar molecular structures. In all the compounds, the central Ln3+ ion is chelated by two interlocked pentadentate ligands resulting in the coordination number of ten. Each lanthanide ion is coordinated by six nitrogen atoms and four oxygen atoms of the two N3O2 chelating groups forming together a distorted bicapped square antiprismatic polyhedron N6O4 with two capping pyridyl N atoms in the apical positions. The ac magnetic measurements reveal field-induced single-molecule magnet (SMM) behavior of the two dysprosium complexes (with barriers of Ueff = 29 K at 800 Oe in 1-Dy and Ueff = 70 K at 300 Oe in 2-Dy) and erbium complex (Ueff = 87 K at 1500 Oe in 4-Er); complex 3-Ho with a non-Kramers Ho3+ ion is SMM-silent. Although 2-Dy differs from 1-Dy only by a distant methoxy-group in the phenyl ring of the ligand, their dynamic magnetic properties are markedly different. This feature can be due to the difference in long-range contributions (beyond the first coordination sphere) to the crystal-field (CF) potential of 4f electrons of Dy3+ ion that affects magnetic characteristics of the ground and excited CF states. Magnetic behavior and the electronic structure of Ln3+ ions of 1–4 complexes are analyzed in terms of CF calculations.

In this paper, we report syntheses, structural characterization and magnetic properties of novel neutral mononuclear lanthanide complexes with the general formula [Ln(HL)(L)](solv) (Ln = Dy, Ho, Er, Tb; solv = CH3OH, C2H5OH, H2O, CHCl3), in which the lanthanide ions are doubly chelated by five-membered rings (N3O2) of two pentadentate ligands, H2DAPBH = 2,6bis(phenylhydrazone)pyridine or H2DAPMBH = 2,6-bis(4-methoxy-benzoylhydrazide)pyridine) resulting in a rather symmetric N6O4 ten-fold coordination. Such a type of coordination is rare for lanthanide complexes with two polydentate planar ligands [55][56][57]. We present results of static and dynamic magnetic measurements of complexes 1-4, which are analyzed in terms of detailed crystalfield (CF) calculations with the aim to relate magnetic relaxation properties of these complexes to the specific electronic structure of Ln 3+ ions and to assess their SMM performance.

Synthetic Aspects
All mononuclear Ln 3+ complexes are obtained in a similar way by mixing hydrated lanthanide nitrate, chloride or formate salts and pentadentate ligand (H2DAPBH or H2DAPMBH) in methyl or ethyl alcohol. In all cases, at the ratio ligand/metal salt = 2 and in the presence of two equivalents of Et3N as a base, the main products are charge-neutral mononuclear complexes of the composition {[Ln(HDAPBH)(DAPBH)]solv}, in which Ln 3+ ion binds two pentadentate ligands. Complexes are readily soluble in hot alcohols. Single crystals of compounds 1-Dy, 2-Dy are obtained by slow evaporation of the filtered mother liquors, while preparation of 3-Ho, 4-Er single crystals requires recrystallization from other solvents.
The nature of byproducts precipitated during the synthesis of the title compounds was deduced by finding the molecular structure of the compound 5-Tb precipitated during the synthesis of the complex [Tb(HL)(L)]•CH3OH. The filtered precipitate was dissolved in dimethoxyethane (DME), from which crystals of 5-Tb separated on slow evaporation. The X-ray single crystal analysis of 5-Tb revealed that it is a nine-coordinate neutral mononuclear complex having a 1:1 ratio of Tb and the dianionic [DAPBH] 2ligand, with a bidentate nitrate anion and two H2O molecules coordinated to the metal ion in axial positions (see Figure 1).
Apparently, similar complexes formed as byproducts in all other cases (in particular, the analysis of solids formed during the synthesis of 1-Dy or 3-Ho complexes showed that they have a composition close to that of 5-Tb with the ratio Ln/ligand = 1). Complexes of similar composition with the H2DAPBH ligand were obtained earlier for several rare earth elements [55][56][57].

X-Ray Crystallography
Single-crystal X-ray diffraction analysis revealed that all the five compounds had a very similar molecular architecture but crystallized in different space groups. The crystallographic data and structure refinements details for complexes 1-Dy, 2-Dy, 3-Ho, 4-Er and 5-Tb are given in Table 1, and the selected bond lengths and angles for ten-coordinate complexes 1-Dy, 2-Dy, 3-Ho and 4-Er are listed in Table 2. The central Ln 3+ ion in all the four compounds was chelated by two interlocked pentadentate ligands (L or L( OCH3 )) with the N3O2 donor set ( Figure 2) resulting in the coordination number of ten (shown schematically in Figure 3a). Each metal ion was coordinating by six nitrogen atoms and four oxygen atoms, which together formed a bicapped square antiprismatic polyhedron capped by the pyridyl N atoms (Figure 3b). In all complexes, one of two pentadentate ligands was dianionic while the other one was monoanionic ( Figure 4). Two ligands in total had the net charge of −3, which provided a charge balance of the Ln(III) complex as a whole. It should be noted that the complexation of two ligands with a rare-earth element led to a strong distortion of the original ligand structure, in contrast to an almost flat conformation in the structure 5-Tb, Figure 1.  and 1-Dy(2), slightly differing in the lengths of bonds and angles. The crystallization water molecules located between 1-Dy(1) and 1-Dy(2) centers were involved in hydrogen bonds with participation of protons of NH groups and O atoms of the solvate water molecules ( Figure S1, Table S1). The shortest intermolecular distances between Dy(III) centers in crystal 1-Dy were 9.7870(12) and 9.8629(12) Å. Complex 2-Dy, [Dy(HL( OCH3 ))(L( OCH3 ))]•C2H5OH•0.5H2O is, in general, close to 1-Dy by structure ( Figure 5), but crystallized in the triclinic structure of the P-1 space group with the two molecules (Z = 2) being symmetry related. Unlike 1-Dy, in which the hydrogen atom of the monoanionic ligand HL − was found in the general position, in this compound it was disordered over two positions with an occupancy of 50% on each possible position (H3 (on N3) and H3′ (on N3A), for details see Figure  5 and the corresponding cif-file). The solvent molecules (H2O and disordered EtOH) were found to form strong hydrogen bonds with the main molecules (Table S2). These interactions formed 1D polymeric chains, packed parallel along the b axis without forming any significant voids. The shortest intermolecular distances between Dy(III) ions in crystal 2-Dy were 9.8713(9) and 10.6176(9) Å. Analogous to 1-Dy, an asymmetric unit of 3-Ho [Ho(HL)(L)]•CH3OH•CH2Cl2 contained two crystallographically independent molecules [Ho(HL)(L)] but, in contrast to 1-Dy, crystallized in the monoclinic space group P21/c. The crystal structure of 3-Ho included two coordinated methanol molecules as intermolecular linkers forming polymeric chains packed along the c axis. Another solvent, methylene chloride, did not interact with complex molecules and filled intermolecular voids. The shortest distances between Ho(III) atoms were 9.7074(11) and 9.8352(11) Å.
Complex 4-Er, [Er(HL)(L)]•4CHCl3•H2O crystallized in the orthorhombic P212121 space group as the solvate with coordinated chloroform and water molecules. Both molecular geometry and coordination environment did not have significant differences from 1-Dy and 3-Ho. Inspection of the hydrogen bonds in the complex revealed that the coordinated water molecule formed two intramolecular and one intermolecular hydrogen bonds with the neighboring molecule of the [Er(HL)(L)] with hydrogen atom H5 ( Figure 2) of the ligand HL − . As well as the other ten-coordinate compounds discussed here, molecules of this complex and water molecules formed linear polymeric chains oriented along the b axis, with interchain cavities filled by chloroform molecules, which in turn also interacted with oxygen atoms via relatively weak C-H•••O interactions; the closest Er-Er distances were 10.5905(8) and 11.5236(10) Å ( Figure S2, Table S4).
Values of the dihedral angle between the planes formed by N(pyridine) and two N atoms, connected with the Ln 3+ ion (Table 2), differed across the complexes over the range of 57.80(10) to 61.6(3)° indicating that distortion of the coordination geometry varied subtly in the complexes described. In order to compare the degree of deviation from the ideal bicapped square antiprismatic coordination of the metal centers in a more unified way, we performed calculations of continuous shape measures by using the SHAPE (2.1) program [59,60]. Results listed in Table S5 indicate substantial deviation from the ideal geometry for all [Ln(HL)(L)] complexes and confirm small but meaningful differences for two symmetry independent molecules in the unit cell of 1-Dy and 3-Ho. Full information about hydrogen bonds in compounds 1-4 are given in Supplementary Information section, Tables S1-S4 and Figures S1 and S2. All ten-coordinate complexes, yet rather similar in coordination fashion for both types (HL − and L 2-) of the ligand, demonstrated variations in the interatomic distances Ln-O (Table 2, Figures 2, 4 and 5), in accordance with the ligand charge. The distances Ln1-O1A and Ln1-O2A (Ln2-O1C and Ln2-O2C) in the case of dianionic ligands were 2.398(9) Å and 2.414(9) Å (2.355(9) Å and 2.503(9) Å) for 1-Dy, 2

.349(3) Å and 2.389(3) Å (2.388(3) Å and 2.389(4) Å) for 3-Ho and 2.358(3) Å and 2.392(3)
Å for 4-Er and tend to be close with some distortions from ideal coordination geometry in most cases. In contrast, the presence of the hydrogen atom of the N-H group in the structure of the monoanionic ligand HL − , which is also involved in the formation of hydrogen bonds leads to slightly stronger distortion from ideal molecular geometry: the interatomic distances Ln1-O1 and Ln1-O2 (Ln2-O1B and Ln2-O2B for the second independent molecule in 1-Dy and 3-Ho were 2.377(8) Å and 2.528 (8)  Additionally, a further noteworthy fact is the difference between 1-Dy and 2-Dy complexes. In contrast to 1-Dy, the unit cell of 2-Dy contains only one crystallographically independent disordered complex molecule, and the disorder exists both in the location of the proton, which with a 50% probability was dispersed over two nitrogen positions, and in the arrangement of the OCH3-phenyl ring ( Figure 5) of two unequal ligand (HL( OCH3 )) −1/2 (the distance Dy1-O1 was slightly larger than Dy1-O1A, 2.496(4) Å and 2.453(4) Å, respectively, but both were longer than Dy1-O2 and Dy1-O2A (2.346(5) Å and 2.360(4) Å (Table 2, Figure 5), and in complexes 1-Dy, 3-Ho and 4-Er). In 2-Dy the interatomic distances (Table 2, Figure 5) Dy1-N2, Dy1-N2A and Dy1-N4 and Dy1-N4A are pairwise close to each other-2.601(5) Å, 2.603(5) Å and 2.561(5) Å and 2.534(5) Å, respectively, that is, in the case of a disordered hydrogen atom, some increase in the bond lengths between the Dy central atom and N atoms of a coordinated ligand (Dy1-N2 and Dy1-N2A) was also observed. In addition, it should be noted that due to this disordering, other additional small and undetectable via X-ray diffraction techniques distortions in the dysprosium local environment in different molecules of the complex 2-Dy in a crystal are still possible.

Static Magnetic Properties
Magnetic susceptibility measurements for complexes 1-4 with the ten-coordinate LnN6O4 core were carried out under the dc applied field of 1000 Oe in the temperature range of 2-300 K, as shown in Figure 6. Magnetic measurements for terbium complexes 5 and 6 were not performed, since they were less relevant to the series of isostructural complexes 1-4 owing to the dissimilar structure of 5-Tb ( Figure 1) and the lack of structural data for 6-Tb. At 300 K, the χMT products of 1-Dy, 2-Dy, 3-Ho and 4-Er complexes were close to the respective free-ion values, 14.17 (Dy 3+ , 6 H15/2), 14.07 (Ho 3+ , 5 I8) and 11.48 (Er 3+ , 4 I15/2) cm 3 K mol −1 ( Figure 6). In all complexes, the χMT product gradually decreased upon cooling to 100 K, below which it fell more rapidly due to progressive thermal depopulation of low-lying excited Stark levels of the Ln 3+ ions. The field dependencies of the magnetization (M/μB vs. H/T) for all complexes were recorded at 2, 3, 4 and 5 K in the field range of 0-4.5 T (insets to Figure  6). The magnetizations reached values of 5.6, 6.25, 5.5 and 4.8 μB, respectively, at 4.5 T and 2 K without saturation. The lack of saturation and the non-superposition on a single master curve for M/μB vs. H/T plots at different temperatures suggest the presence of considerable magnetic anisotropy in the complexes [61][62][63].

Analysis of dc-Magnetic Data
Since dc and ac magnetic properties of lanthanide complexes, and especially their SMM behavior, are highly sensitive to the character of the crystal-field (CF) splitting effect, it is important to establish the energy spectrum of the CF states and specific properties of the ground-state wave functions of Ln 3+ ions in compounds 1-4. To this end, we analyzed dc magnetic properties of our complexes in the framework of the CF theory for Ln 3+ ions, which is based on the conventional CF Hamiltonian: where H0 denotes the free-ion Hamiltonian and HCF is the CF term. The free-ion Hamiltonian H0 describes atomic interactions of 4f-electrons: where fk and F k are the angular and radial Slater parameters, respectively, the second term is the spin orbit operator, and α , β and γ are Trees parameters describing two-electron correlation corrections to the Coulomb repulsion term [64][65][66]. The HCF Hamiltonian incorporates metal-ligand interactions: where Bkq are CF parameters (k = 2, 4, 6; q ≤ k) and Cq k are spherical tensor operators for f-electrons [64][65][66]. Details of CF calculations for Ln 3+ ions were well documented elsewhere [64][65][66][67][68]. The Bkq quantities are phenomenological adjustable CF parameters, which are usually obtained from fitting to the spectroscopic and/or magnetic data for lanthanide compounds. It is noteworthy, however, that in most cases the fitting CF calculations were applied only to metal centers with high enough symmetry in order to keep a reasonable number of variables. For the low-symmetry metal centers (occurring in our [Ln(HL)(L)] complexes) the CF fitting calculations became overparameterized owing to a large number (up to 27) of independent CF Bkq parameters. To avoid these difficulties, we took advantages of the superposition CF model [68,69], which relates the Bkq parameters with the actual geometry of the metal site: where n runs over all metal-ligand pairs involved in the coordination polyhedron (N6O4, Figure 3b) around the Ln 3+ ion, bk(R0) are the three (k = 2, 4, 6) intrinsic, or single ligand CF parameters, (Rn, θn and φn) are polar coordinates of the n-th ligand atom; their radial dependence is approximated by the power-law with tk being the exponent indexes and R0 being the reference distance (i.e., the average metal-ligand distance). The superposition CF model, its foundation and applications were described in the literature [68][69][70][71]. Now we turned to the simulation of magnetic properties of lanthanide complexes with the CF Hamiltonian (2). In most cases, magnetic properties of lanthanide compounds are highly anisotropic.
The magnetization M and applied magnetic field H related by M = χH, where χ is the tensor of magnetic susceptibility: which is represented by a 3 × 3 matrix χαβ (where α, β = x, y, z); its components χαβ can be calculated in terms of the |i> wave functions of Ln 3+ ions using the Gerloch-McMeeking equation [72]: where Na is the Avogadro number, Ei is the energy of the CF state |i>, k is the Boltzmann constant, T is the absolute temperature, and μα, μβ are the components of the magnetic moment operator: where μB is the Bohr magneton and L and S are, respectively, the operators of the total orbital momentum. The eigenvalues of the matrix χαβ (6) correspond to the principal components of the magnetic susceptibility (χx, χy, χz); the powder magnetic susceptibility is written as χ = (χx + χy + χz)/3. In the frame of this technique, we simulated magnetic dc susceptibility of four lanthanide complexes with the aim is to determine the CF splitting pattern of the ground J-multiplets produced by the N6O4 polyhedron (Figure 3b). With this approach, we derived the CF parameters Bkq from the fitting of the χT curves simulated with Equation (6) to the experimental dc magnetic data for [Ln(HL)(L)] complexes ( Figure 6). However, the conventional CF computational scheme with freely variable Bkq parameters cannot directly be applied to complexes 1-4, since it is likely to be unreliable due to overparameterization, which is characteristic of low-symmetry metal sites (C2 or C1 in 1-4). In such systems, CF fitting to the magnetic susceptibility curves typically converges to several least squares minima that are incompatible with each other. For this reason, we used the superposition CF model [68,70], which relates the usual Bkq CF parameters with the specific geometry of the coordination polyhedron around the Ln 3+ ion via three intrinsic CF parameters bk (k = 2, 4, 6) (Equation (4)). Importantly, since the bk parameters describe metal-ligand bonding energy for f-electrons, they are transferable between different Ln 3+ ions in complexes with similar ligand coordination; this allows the approximate prediction of CF parameters for metal sites with known atomic positions. Therefore, for isostructural series of lanthanide compounds, the CF splitting pattern of different lanthanide ions can be reproduced with a single set of intrinsic bk parameters; this fact can be used to check the consistency of the set of CF parameters.
Given these considerations, CF calculations for [Ln(HL)(L)] complexes were carried out in two steps. First, a primary set of bk parameters (b2 = 800, b4 = 380, and b6 = 260 cm -1 at R0 = 2.45 Å, both for O and N atoms) was obtained from simulation of the dc magnetic susceptibility for the Dy, Ho and Er complexes with the same superposition model parameters. Calculations were carried out with fixed power-law indexes t2 = 5, t4 = 8 and t6 = 11 estimated elsewhere [69,70]; atomic parameters of Ln 3+ ions involved in the free-ion Hamiltonian (Equation (3)) are taken from the literature [66,67]. The polar coordinates (Rn, θn and φn) in Equation (5) corresponds to the actual geometry of the N6O4 coordination polyhedra in compounds 1-4 ( Figure 3b). It is also noteworthy that calculations of the χαβ tensor with Equation (6) involves the CF states |i> of both the lowest J-multiplet and several excited multiplets in order to include second-order contributions to the χαβ components resulting from high-lying excited states, which are mixed to the ground state by the magnetic field; this computational scheme is implemented with routines described previously [73][74][75]. Calculations with these parameters provide an approximate general agreement with the experimental χMT curves for the 1-Dy, 2-Dy, 3-Ho and 4-Er complexes.
This set of parameters was then used as a reference point for refined CF calculations performed separately for the individual complexes 1-4. At this stage, a modified CF computational scheme was applied, in which the rank two (k = 2) 'global' Bkq parameters were allowed to vary together with the b4 and b6 'intrinsic' CF parameters (which are different for the N and O atoms in the N6O4 polyhedron) to reach the best agreement with the experimental dc magnetic data for the specific lanthanide complex in the whole temperature range (2-300 K, Figure 6). Application of this approach was motivated by the fact that the second rank CF parameters Bkq were sensitive to long-range metalligand interactions extending beyond the first coordination sphere of the lanthanide ion and, therefore, they were poorly described in terms of the superposition CF model. The simulated χMT curves were well consistent with the experimental data ( Figure 6). To take into account some uncertainty in the actual lanthanide concentration in powdered complexes, a scaling factor for the magnetic susceptibility was applied for complexes 1-4 (+4.2% for 1-Dy, +3.1% for 2-Dy, +6.6% for 3-Ho and +2.7% for 4-Er, respectively).
Calculated CF energy levels of Dy 3+ , Ho 3+ and Er 3+ ions in complexes 1-4 are summarized in Table 3, and the sets of Bkq CF parameters are presented in Table S6. These results indicate that Ln 3+ ions centered in the N6O4 polyhedron ( Figure 3b) reveal rather low CF splitting energy, c.a. Table 3. Calculated crystal-field (CF) splitting energies (cm -1 ) of the lowest J-multiplets of Ln 3+ ions and g-tensors of the ground and first excited CF states in 1-Dy, 2-Dy, 3-Ho and 4-Er complexes. The 400 cm -1 or less (Table 3) is also consistent with the CF strength criterion S [76], which is around 500 cm -1 (see Table S6). This fact alone suggests that [Ln(HL)(L)] complexes are unlikely to be high-performance SMMs due to the absence of large CF splitting energy, which is known to be one of the most important prerequisite to have a high spin-reversal barrier Ueff (see below the next section).

Dynamic Magnetic Properties
The alternating current magnetic susceptibility (ac) measurements serve as a probe for the relaxation processes in the magnetic system, revealing in a frequency dependence of in-phase χ′(ν) and a non-zero out-of-phase χ′′(ν) signal. None of the studied compounds shows the slow magnetic relaxation in measured frequency and temperature ranges (10 Hz to 10 kHz and 2-5 K) in a zero dc magnetic field. Both the in-phase χ′ and out-of-phase χ′′ magnetic susceptibility of the mononuclear complexes 1-Dy, 2-Dy and 4-Er exhibited the frequency-dependent signals in the presence of the dc magnetic field ( Figure S3). The observed magnetic field induced SMM behavior in these complexes was likely due to suppression of the ground state tunneling processes by the dc magnetic field. The SMM-silent behavior of the Ho complex (3-Ho) complex is associated with a non-magnetic character of the ground state of non-Kramers ion Ho 3+ , which is represented by two close-spaced singlet states with the energy separation about 0.6 cm -1 (Table 3); this splitting energy is large enough to cause fast magnetic relaxation.
To probe the magnetic relaxation in 1-Dy, 2-Dy and 4-Er complexes, the frequency dependence of ac susceptibility was measured in the presence of the dc magnetic field. The magnetic field was set at value corresponding to the peak in field dependence of out-phase magnetic susceptibility, χ′′(H) (Figure S3a-c).
where T is the absolute temperature, Ueff is the effective energy barrier for the reversal of magnetization and k is the Boltzmann constant. The τ −1 QTM term in Equation (11) represents the temperature-independent contribution from the quantum tunneling of magnetization (QTM) effects, the second and third terms are direct relaxation and Raman process correspondingly, the exponential term describes the thermally activated mechanism of magnetic relaxation (Orbach process) [78]. The parameter n = 6 corresponds to the Raman spin-lattice relaxation process for the case of Kramers system [78]. It is noteworthy that the effective energy barrier Ueff = 87 K obtained from fitting with Equation (11) was considerably higher than the energy position of the first excited CF state at 23 cm -1 (33 K) and close to the energy of the next CF state at 75 cm -1 (108 K), as estimated from CF calculations for 4-Er (Table 3). The χ′(ν), χ′′(ν) dependencies and Cole-Cole χ′′(χ′) plots for the 1-Dy compound measured at H = 800 Oe are presented in Figure 9. The χ′′(ν) (Figure 9b) and Cole-Cole (Figure 9c) plots exhibited two distinct maxima at temperature range of 2-2.45 K. The asymmetric unit of the 1-Dy compound constituted two independent molecules, which slightly differed in bond lengths and angles ( Figure 4, Table 2). Based on the presence of two Dy centers in the structure of 1-Dy, the observed two-humped shape of χ′′(ν) and Cole-Cole χ′′(χ′) plots are likely associated with two different relaxation processes corresponding to various magnetic centers [78][79][80][81][82][83][84]. The χ′(ν), χ′′(ν) dependences in the 2-2.45 K temperature range were fitted by a linear combination of two modified Debye models given by Equations (S1)-(S3) [79,[84][85][86]. The fitting parameters and curves are presented in Table S8 and Figure S4, correspondingly. The values of α1 (0.6-0.45) and α2 (0.41-0.56) noticeably differed from zero signifying the multiple relaxation pathways. At a further temperature increase the two-hump shape of the χ′′(ν) dependence evolved into a single broad peak. At a range of 2.6-4.7 K the χ′(ν), χ′′(ν) dependences were not well captured neither by the modified Debye model for a single relaxation process (Equations (8)-(10)) nor by a linear combination of two modified Debye models (Equations (S1)-(S3)). Tentatively, the broad peak signal still represents the two relaxation processes observed at 2-2.45 K, which were not well separated at intermediate temperature range. As shown in Figure S5, the χ′(ν) and χ′′(ν) dependences at temperatures above 4.85 K were well fitted by the modified Debye model for single relaxation process (Equations (8)-(10)), which allowed us to assume that the peak at temperatures 4.4-5 K corresponds to the same single relaxation process and estimates the value of effective energy barrier. The results of fitting the χ′(ν) and χ′′(ν) dependences by Equations (8)- (10) in the temperature range of 4.4-5 K and Cole-Cole plots are presented in Figure S5 and Table S9. The value of the effective energy barrier, Ueff = 29 K, obtained by the analysis of the temperature dependence of relaxation time with Arrhenius law ( Figure 10) correlated with the energy gap to the first excited Kramers doublet in 1-Dy, 23 cm -1 (33 K), Table 3. In the 2-Dy the Dy 3+ ion was coordinated by a slightly modified ligand (L( OCH3 )), as compared to 1-Dy. Specifically, in 1-Dy the hydrogen atom of the monoanionic ligand (HL -) was localized on one of the two nitrogen atoms (Figure 4) while in 2-Dy, a hydrogen atom was disordered over two positions with an occupancy of 50% on each position ( Figure 5), which led to a different crystal symmetry of 1-Dy and 2-Dy and magnetic properties. To probe the magnetic relaxation processes in the 2-Dy compound we measured the frequency dependence of ac magnetic susceptibility in the presence of external dc magnetic field (H = 300 Oe, Figure 11). At 2 K the χ′′(ν) curve constituted a pronounced peak at around 20 Hz and a clearly seen onset of secondary signal of smaller magnitude in the higher frequency range (Figure 11). The high frequency relaxation process tentatively stemmed from the disorder in the structure of 2-Dy ( Figure 5). The observed low frequency signal (χ′(ν) and χ′′(ν)) was fitted by the generalized Debye model for a single relaxation process (Equations (8)-(10)), as shown in Figure 11 and Table S10. The best fitting of temperature dependence of relaxation time by Equation (4) was achieved with parameters: C = 4.2 s −1 , n = 4.8, Ueff = 70 K and τ0 = 2.2 × 10 −11 s (Figure 12). The greater value of effective energy barrier Ueff in 2-Dy compared to that in 1-Dy could be attributed to a higher value of the first excited CF state, 39 cm -1 (56 K). In addition, the ground and the first excited Kramers doublets in 2-Dy exhibited strong Ising-type magnetic anisotropy (gx = 0.082, gy = 0.581 and gz = 19.000 for the ground state and gx = 0.306, gy = 0.381 and gz = 17.310 for the first excited CF state at 39 cm -1 , Table 3) that suppressed the transverse magnetic anisotropy and favored the higher value of effective energy barrier. The differences in the electronic structure of the 1-Dy and 2-Dy complexes and their magnetization relaxation are mainly specified by the local structure of the complexes, as known its small modification strongly affects the SMM properties of rare earths [9][10][11][12][13][14][15][16][17][18]. Comparative study of the electronic structure and magnetic properties of two cationic ten-coordinate Dy complexes with two neutral ligands H2DAPBH [Dy(H2DAPBH)2](NO3)3 (7) and one neutral and one monoanionic ligands [Dy(H2DAPBH)(HDAPBH) − ](NO3)2 (8), described in the work [61], showed that the localization of a negative charge on one of the two amido nitrogens leads to distortions in the coordination polyhedron of Dy: shortening of two bonds (Dy-N (hydrazone) and Dy-O (carbonyl)) compared with neutral ligand H2DAPBH and, as a consequence, to a decrease of magnetic anisotropy and the magnetization barrier (Ueff) of complex 8 compared to 7 (19 and 32.4 K, respectively). In our neutral ten-coordinate complex 1-Dy, the hydrogen atom of the monoanionic ligand (HL -) was localized on one of the two nitrogens, which led to an increase in two bond lengths compared with dianionic ligand DAPBH ( Table 2), but these distortions in the 1-Dy coordination sphere are noticeably smaller than those in the complex 8. The latter likely leads to the higher value of effective energy barrier obtained for the 1-Dy compared to that for complex 8. In the case of the 2-Dy compound, one hydrogen was disordered over two nitrogen positions and the bond lengths distortion was insignificant compared to those in the 1-Dy (Table 2), the magnetization barrier was higher than that of 1-Dy. Our results clearly show that small variations of the coordination environment of 4f metal center could significantly affect the relaxation dynamics of rare-earth complexes.

Materials and Methods
2,6-diacetylpyridine, benzoylhydrazide, triethylamine, DyCl3•6H2O, Er(HCOO)3•2H2O, HoCl3•6H2O, Tb(NO3)3•6H2O, dimethoxyethane, ethanol, methanol, chloroform, 4-methoxybenzoic acid, thionyl chloride and hydrazine hydrate solution (50-60% N2H4) were purchased from commercial sources and used without further purification. The infrared spectra were measured on solid samples using a Perkin Elmer Spectrum 100 Fourier Transform infrared spectrometer in the range of 4000-500 cm −1 . NMR spectra were recorded on Bruker AVANCE III (500 MHz) spectrometer. Elemental analyses were carried out by the Analytical Department service at the Institute of Problems of Chemical Physics RAS using Vario MICRO cube (Elementar Analysensysteme GmbH) equipment. Both ac and dc magnetic properties were measured using Physical Properties Measurements System PPMS-9 (Quantum Design) in the temperature range of T = 2-300 K under a magnetic field up to B = 7 T. The samples in the polycrystalline (powder) form were loaded into an insulating capsule. The experimental data were corrected for the sample holder. The diamagnetic contribution from the ligand was calculated using Pascal's constants.

X-Ray Data Collection, Structure Solution and Refinement
X-ray diffraction data for 1-Dy, 2-Dy, 4-Er and 5-Tb were obtained on a Bruker SMART APEX II diffractometer (CCD detector, Mo Kα, λ = 0.71073 Å, graphite monochromator) using ω-scan mode at the Laboratory for X-Ray Diffraction Studies INEOS RAS. X-ray diffraction data for 3-Ho were collected on the 'Belok' beamline [90] (λ = 0.79272 Å) of the Kurchatov Synchrotron Radiation Source (National Research Center "Kurchatov Institute", Moscow, Russian Federation) in the φ-scan mode using a Rayonix SX165 CCD detector at 100 K. The data were indexed, integrated and scaled using the Bruker SAINT program (SAINT; Bruker AXS Inc., Madison, WI, USA, 2016) and the XDS program suite [91]. The reflection intensities were corrected for absorption using the SADABS software (SADABS; Bruker AXS Inc., Madison, WI, USA, 2016) for complexes 1-Dy, 4-Er and 5-Tb, the TWINABS software (Bruker TWINABS 2012/1. Bruker AXS Inc., Madison, WI, USA) for 2-Dy and the XDS program [91] for compound 3-Ho. The structures were solved by direct methods and refined by full-matrix least squares on F 2 with anisotropic displacement parameters for non-hydrogen atoms in general positions, and isotropically in the case of disordered carbon atoms (complexes 1-Dy and 2-Dy). The residual electron density arises from the extremely disordered neutral solvent molecules in 1-Dy and 3-Ho was removed with the SQUEEZE tool [92]. Wherever possible, the acidic hydrogen atoms were derived from electron density map and refined isotropically, or initially the hydrogen atoms positions were derived from the electron density map followed by the placement of the hydrogen atoms in ideal positions and refinement in the riding model. All other hydrogen atoms were placed in calculated positions and refined using the riding model with Uiso(H) = 1.5 × Ueq(C, O) for the methyl and hydroxyl groups and 1.2 × Ueq(C) for hydrogen atoms of the ligand and methylene groups. SADI, DFIX and EADP instructions were applied on disordered atoms of molecules and solvents, and other atoms were refined without any constraints or restraints. In addition, twinned data in 1-Dy and 2-Dy were handled with TWIN instruction on HKLF 4 and HKLF 5, respectively. Calculations were carried out using the SHELXTL program suite [93,94]. Crystallographic data for 1-5 have been deposited with the Cambridge Crystallographic Data Center, № 1987371-1987375 (deposit@ccdc.cam.ac.uk, https://www.ccdc.cam.ac.uk/structures/).

Simulation of Static Magnetic Properties and CF Calculations
Crystal-field (CF) analysis for complexes 1-4 was carried out with the conventional CF theory for f-electrons based on the Wyborne parameterization scheme [64][65][66] in combination with the superposition CF model [67][68][69] adapted for low-symmetry metal sites. Simulation of magnetic susceptibility was performed in terms of the Gerloch-McMeeking equation [71] using computational routines described elsewhere [72][73][74]. •CH3OH•CHCl3 (6-Tb). These reactions also led to nine coordinate complexes as byproducts, of which terbium complex [Tb(L)(NO3)(H2O)2]•2DME (5-Tb) was isolated and characterized by X-ray diffraction analysis. Complexes 1-4 contained two ligands, one of which was dianionic (L 2− ), and the second was monoanionic (HL − ). The Ln 3+ ions were coordinated by six nitrogen and four oxygen atoms forming a ten-coordinate bicapped square antiprism LnN6O4. Although all four complexes had very similar molecular structures, their crystal structures and space groups were different. The structures of the 1-Dy and 3-Ho complexes contained two crystallographically independent molecules and the hydrogen atom was localized at one of the two amido nitrogens of the monoanionic ligand. In contrast, the 2-Dy and 4-Er contained only one symmetry independent molecule in the unit cell, and the hydrogen atom was localized in the erbium complex and disordered over two nitrogen positions in 2-Dy. AC magnetic measurements revealed that 1-Dy, 2-Dy and 4-Er were field-induced SMMs, while 3-Ho was not. Magnetic properties of 1-4 and their electronic structure were analyzed in terms of theoretical calculations based on the superposition CF model. In particular, this analysis showed that SMM-silent behavior of 3-Ho was due to a non-magnetic character of the ground state of non-Kramers Ho 3+ ion. The behavior of magnetic relaxation in complexes 1-Dy, 2-Dy and 4-Er varied significantly. The 1-Dy shows two separate relaxation processes, which was explained by the presence of two crystallographically independent molecules in its structure, while in 4-Er one type of curves with maximum was present on the frequency dependences of the imaginary component of the ac susceptibility. The 2-Dy complex exhibited complicated dynamics of relaxation, which was likely affected by the disorder in the structure of this compound. The magnetization barriers for the 1-Dy and 2-Dy complexes correlated with the theoretical calculations of electronic structures for these complexes. Compounds 1-4 refer to a rare class of ten-coordinate lanthanide complexes formed by two planar pentadentate ligands with interpenetrating N3O2 chelating rings producing a LnN6O4 polyhedron shaped as a distorted bicapped square antiprism.