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Cadmium-Inspired Self-Polymerization of {LnIIICd2} Units: Structure, Magnetic and Photoluminescent Properties of Novel Trimethylacetate 1D-Polymers (Ln = Sm, Eu, Tb, Dy, Ho, Er, Yb)

A series of heterometallic carboxylate 1D polymers of the general formula [LnIIICd2(piv)7(H2O)2]n·nMeCN (LnIII = Sm (1), Eu (2), Tb (3), Dy (4), Ho (5), Er (6), Yb (7); piv = anion of trimethylacetic acid) was synthesized and structurally characterized. The use of CdII instead of ZnII under similar synthetic conditions resulted in the formation of 1D polymers, in contrast to molecular trinuclear complexes with LnIIIZn2 cores. All complexes 1–7 are isostructural. The luminescent emission and excitation spectra for 2–4 have been studied, the luminescence decay kinetics for 2 and 3 was measured. Magnetic properties of the complexes 3–5 and 7 have been studied; 4 and 7 exhibited the properties of field-induced single-molecule magnets in an applied external magnetic field. Magnetic properties of 4 and 7 were modelled using results of SA-CASSCF/SO-RASSI calculations and SINGLE_ANISO procedure. Based on the analysis of the magnetization relaxation and the results of ab initio calculations, it was found that relaxation in 4 predominantly occurred by the sum of the Raman and QTM mechanisms, and by the sum of the direct and Raman mechanisms in the case of 7.


Introduction
The design and synthesis of new coordination compounds with two or more different physical properties that are promising for practical application, as well as the search for the ways to modify the physical properties (including their reversible change) are urgent problems of modern coordination chemistry and physical chemistry [1][2][3]. Such properties may include a combination of non-trivial magnetism and luminescence [4,5] or conductivity [6][7][8], a combination of magnetism and rotation of polarized light [9,10], sensitivity of magnetic properties to irradiation [11], or thermochromic properties [12], electrochromism [13], the ability to convert mechanic deformation into voltage and vice and the main geometrical parameters are compared ( Table 1). The complexes crystallize as solvates with one acetonitrile molecule per formula unit. In 1D polymeric chains, one can distinguish trinuclear linear fragments {LnCd 2 }, which play the role of monomeric fragments (Scheme 1, Figure 1a). In such units, metal centers are linked by carboxylate bridges from piv anions. The transition from Sm III to Yb III is accompanied by a change in the geometry of the LnO 8 polyhedron. The coordination environment of the Sm III ion in 1 has the geometry of a biaugmented trigonal prism, the environment of Eu III ion in 2 can be described as both a triangular dodecahedron and a biaugmented trigonal prism with a minimal deviation from an ideal polyhedron among 13 types of known 8-vertex polyhedra (Figure 1b). The geometry of the LnO 8 polyhedron in 3, 4, 6, 7 corresponds to a triangular dodecahedron (Table S2). Cadmium metallocentres are bound to oxygen atoms of bridging and chelate-bridging carboxylate groups as well as of one water molecule. The Cd1 ion is located in a pentagonal bipyramidal (D 5h ) CdO 7 environment, where the atoms O1, O2, O5, O6, and O14 are located in the equatorial plane. The geometry of the Cd 2 ion's environment (CdO 6 ) corresponds to both the trigonal prism (D 3h ) and octahedron (O h ). Hydrogen atoms of coordinated water molecules participate in the formation of H-bonds with the O atoms of the carboxylate groups (inside the polymer chain) and the N atom of the MeCN solvate molecule. Thus zigzag polymer chains are formed, the minimal distance between Ln ions (>10 Å) in the crystal corresponds to the distance in the polymer chain, while the shorter distance between Ln ions of neighboring chains is more than 11 Å (Figure 1b,c). Cd···Ln 3.6716(4), 3.6910 (4) 3.6615(4), 3.6749 (4) 3.6554(2), 3.6652 (2) 3.6496(2), 3.6513 (2) 3.6370(5), 3.6415 (4) 3.6253 (5) Cd-Ln-Cd 153.954 (9) 153.890 (10) 153.617 (6) 153.420 (5) 153.324 (9) 153.061 (13) Cd-Cd-Ln 142.387(10), 149.957 (10) 142.508 (11), 149.818 (11) 142.526 (8), 149.706 (7) 142.463 (6), 149.219 (6) 142.535 (11), 149.411 (10) 149.232 (16)  It was previously shown that the combination of Ln III with Zn II ions gives molecular complex [EuZn 2 (piv) 6 (MeCN) 2 ] under the same conditions that are used herein for assembling Ln III -Cd II coordination polymers [46]. The zinc(II)-lanthanide(III) analog [EuZn 2 (piv) 6 (MeCN) 2 ] has a trinuclear metalcore with a central Eu III atom, which is similar to the crystallographically-independent unit of complex 2 (taking into account that positions of Zn II were occupied by Cd II in 2). All six piv anions in the compound have a bridging type of coordination and bind Eu III to Zn II atoms. Only one acetonitrile molecule is coordinated with both zinc(II) atoms in the terminal position and completes the formation of the molecular compound. The difference in ionic radii of Zn II and Cd II (r(Zn 2+ ) = 0.88 Å, r(Cd 2+ ) = 1.09 Å) [47] may be responsible for the difference in the structure of Ln-Zn and Ln-Cd complexes. As a consequence, the cadmium ion can have higher coordination numbers (CN = 5-7) compared to the zinc ion (CN = 4-6), and the Cd II ions can coordinate the oxygen atoms of neighboring trinuclear fragments {LnCd 2 (piv) 6 }. Thus, cadmium ions induce the polymerization of Cd 2 Ln fragments with the formation of polymeric Ln-Cd pivalates. A similar situation was previously observed for complexes [Ln 2 M 2 (pfb) 10 (phen) 2 ] (Ln = Eu, Gd, Tb, Dy; M = Zn, Cd; pfbis the anion of pentafluorobenzoic acid): Ln 2 Zn 2 complexes had a discrete molecular structure, while the Ln 2 Cd 2 species were molecular or 1D polymers as a result of changes in the functionality of bridging carboxylate groups and π-π interactions between aromatic fragments (pfb anion and phen ligand) of neighboring tetranuclear fragments [48]. Similarly, 1D polymer [CdEu 2 (pfb) 8 (Etypy)(H 2 O) 2 ] n (Etypy = 3-ethynylpyridine) was reported, where Cd II ion adopted coordination number 7 and could be bound in the chain [39]. It was previously shown that the combination of Ln III with Zn II ions gives molecular complex [EuZn2(piv)6(MeCN)2] under the same conditions that are used herein for assembling Ln III -Cd II coordination polymers [46]. The zinc(II)-lanthanide(III) analog In all these examples, as in the present study, the high ionic radius of Cd II and its ability to form a large number of coordination bonds at least contributed to the polymerization of Cd x Ln 2 (x = 1 or 2) moieties and, in some cases, were the main driving force behind the formation of coordination polymers. As expected, molecular complexes with Cd x Ln y pivalate cores were formed upon the addition of "capping ligands", which blocked the coordination sites of Cd II ions and prevented the formation of coordination bonds between these ions and pivalate oxygen atoms from the neighboring units [39,41,43,[48][49][50]. Among the heterometallic Cd-Ln carboxylates that do not contain specific capping ligands, only the compound [Cd 2 Eu(bzo) 6 (NO 3 )(MeCN) 2 (THF) 2 ] (bzo − = 3,5-di-tert-butylbenzoate anion) had a molecular structure, and the coordination positions of the terminal Cd II ions were blocked by coordinated THF and MeCN molecules [51]. Notably, this compound differs from all previous examples like the carboxylate ligand. Most likely, the formation of a molecular compound, in this case, is caused by the lower donor ability of O atoms of bzocompared to pivalate, however, other effects (such as the energy of the crystal lattice) cannot be excluded.
Complexes 1-7 are stable when stored in air, their phase purity and isostructurality were determined using PXRD ( Figures S1-S7).

Photoluminescence Properties of 2-4
Figures 2-4 display the excitation and emission spectra of polycrystalline samples of compounds 2-4, measured at ambient temperature. Compounds exhibit bright luminescence in the red (2) or green (3 and 4) regions of the spectrum. The absence of broad bands of the ligands in the excitation spectra indicates the inability of sensitization through ligands. The high triplet level of the piv ligand (determined earlier as 27,470 cm −1 [46] does not promote the energy transfer to lanthanide ions, nevertheless, the characteristic red and green emission of Eu 3+ and Tb 3+ ions can be observed with the naked eye under ultraviolet excitation. The emission spectrum of complex 2 demonstrates characteristic narrow bands at 579, 590, 616, 651, and 700 nm associated with the 5 D0-7 FJ (J = 0-4) transitions of Eu 3+ , respectively. The most intense 5 D0-7 F2 transition, named hypersensitive, is highly dependent on changes in the Eu III ion environment. In contrast, the probability of the 5 D0-7 F1 magnetic dipole transition in the first approximation can be considered constant, therefore, this transition is often used as a measure of the luminescence intensity. The ratio of the integrated intensities I( 5 D0-7 F2)/I( 5 D0-7 F1) is 4.8 for 2 and indicates the absence of an inversion center at the Eu 3+ position [53]. The single symmetric line of the 5 D0-7 F0 transition, as well as the monoexponential decay of the luminescence, indicate the presence of a unique crystal site of Eu III . These data agree with the single-crystal X-ray diffraction data. The emission spectrum of 3 ( Figure 3) demonstrates the typical Tb III luminescence bands at 486, 542, 585, and 620 nm associated with transitions from the 5 D4 excited state of Tb 3+ to the 7 FJ multiplets (J = 6-3), respectively. The 5 D4-4 F2 transition demonstrates low intensity at 640 nm. The most intense band corresponds to the 5 D4-7 F5 transition; its intensity is about 62% of the total integrated intensity.  The emission spectrum of 3 ( Figure 3) demonstrates the typical Tb III luminescence bands at 486, 542, 585, and 620 nm associated with transitions from the 5 D4 excited state of Tb 3+ to the 7 FJ multiplets (J = 6-3), respectively. The 5 D4-4 F2 transition demonstrates low intensity at 640 nm. The most intense band corresponds to the 5 D4-7 F5 transition; its intensity is about 62% of the total integrated intensity.    The excitation spectra of complexes 2, 3, and 4 (Figures 2-4) demonstrate a series of narrow bands corresponding to the 4f-4f transitions of lanthanide ions and the absence of the broad absorption bands of the ligands. The excitation spectrum of 3 features a strong broadband with a maximum at ~31,000 cm −1 , which is absent in the spectra of 2 and 4 and may belong to the 4f-5d parity allowed transition of Tb III .
The luminescence decay curves for 2 and 3 are well fitted by monoexponential functions ( Table 2). The lifetimes of the metal-centered luminescence were long due to the absence of low-lying energy levels contributing to the depopulation of the 5 D0 (Eu III ) and 5 D4 (Tb III ) excited states, as well as the lack of efficient quenchers in the closest surrounding of lanthanide ions. The ligand environment prevents the coordination of solvent molecules to the lanthanide ion, which leads to a low rate constant of the non-radiative decay of the Eu III excited state.  The emission spectrum of complex 2 demonstrates characteristic narrow bands at 579, 590, 616, 651, and 700 nm associated with the 5 D 0 -7 F J (J = 0-4) transitions of Eu 3+ , respectively. The most intense 5 D 0 -7 F 2 transition, named hypersensitive, is highly dependent on changes in the Eu III ion environment. In contrast, the probability of the 5 D 0 -7 F 1 magnetic dipole transition in the first approximation can be considered constant, therefore, this transition is often used as a measure of the luminescence intensity. The ratio of the integrated intensities I( 5 D 0 -7 F 2 )/I( 5 D 0 -7 F 1 ) is 4.8 for 2 and indicates the absence of an inversion center at the Eu 3+ position [53]. The single symmetric line of the 5 D 0 -7 F 0 transition, as well as the monoexponential decay of the luminescence, indicate the presence of a unique crystal site of Eu III . These data agree with the single-crystal X-ray diffraction data.
The emission spectrum of 3 ( Figure 3) demonstrates the typical Tb III luminescence bands at 486, 542, 585, and 620 nm associated with transitions from the 5 D 4 excited state of Tb 3+ to the 7 F J multiplets (J = 6-3), respectively. The 5 D 4 -4 F 2 transition demonstrates low intensity at 640 nm. The most intense band corresponds to the 5 D 4 -7 F 5 transition; its intensity is about 62% of the total integrated intensity.
The emission spectrum of 4 consists of three lines at 480, 575, and 665 nm, corresponding to the 4 F 9/2 -6 H 15/2 , 4 F 9/2 -6 H 13/2, and 4 F 9/2 -6 H 11/2 transitions of Dy 3+ , respectively ( Figure 4). The 4 F 9/2 -6 H 13/2 transition is dominant; its intensity is about 64% of the total intensity. The excitation spectra of complexes 2, 3, and 4 ( Figures 2-4) demonstrate a series of narrow bands corresponding to the 4f-4f transitions of lanthanide ions and the absence of the broad absorption bands of the ligands. The excitation spectrum of 3 features a strong broadband with a maximum at~31,000 cm −1 , which is absent in the spectra of 2 and 4 and may belong to the 4f-5d parity allowed transition of Tb III .
The luminescence decay curves for 2 and 3 are well fitted by monoexponential functions ( Table 2). The lifetimes of the metal-centered luminescence were long due to the absence of low-lying energy levels contributing to the depopulation of the 5 D 0 (Eu III ) and 5 D 4 (Tb III ) excited states, as well as the lack of efficient quenchers in the closest surrounding of lanthanide ions. The ligand environment prevents the coordination of solvent molecules to the lanthanide ion, which leads to a low rate constant of the non-radiative decay of the Eu III excited state. [Tb(phbz) 3 ] n 0.75 24 [63] pfb is pentafluorobenzoate, bzo is 3,5-di-tert-buthylbenzoate, phbz is 4-phenylbenzoate, 4-TBA is trifluoromethylbenzoate, tpc is thiophene-2carboxylate, pyr is pyrrol-2-carboxylate, fbz is 2-fluorobenzoate, f 2 bz is 2,5-difluorobenzoate, f 3 bz is 2,3,6-trifluorobenzoate, f 4 bz is 2,3,4,5tetrafluorobenzoate, FBA is 4-fluorobenzoate, phen is 1,10-phenantroline, pz is pyrazine, py is pyridine, lut is 2,3-lutidine, bpy is 2,2 -bipyridine. The intrinsic quantum yield (Q Ln Ln ) calculated for 2 turned out to be higher than for Eu(NO 3 ) 3 ·6H 2 O [54], and is comparable with that of aromatic carboxylate complexes of Eu III ( Table 2). The lifetimes of the excited state (τ obs ) of complexes 2 and 3 are comparable to those for the Ln III -Zn and Ln III -Cd heterometallic complexes with aromatic carboxylate ligands, as well as for the Ln III pivalate complexes with coordinated aromatic N-donors, in which radiative decay prevails over nonradiative (for Eu III -containing complexes) ( Table 2). These results confirm that the presence of "antenna" ligands and the absence of water molecules in the coordination sphere of the Ln III ion contribute to an increase of the lifetime, effective sensitization of emission, as well as a high quantum yield.
We also used the SINGLE_ANISO code and the results of SA-CASSCF/SO-RASSI calculations for model clusters 4m and 7m to simulate the χ M T temperature dependences for 4 and 7 (see Section 3.6, Figures S9 and S11, Supplementary material). Indeed, our ab initio modeling, which takes into account the temperature-dependent population of Kramers doublets of isolated model clusters (Table 3), is in good agreement with experiment for 7 and in reasonable agreement-For 4 ( Figure 5). To investigate the magnetization dynamics, alternating current (ac) magnetic susceptibility measurements were performed for polycrystalline samples of 3-5 and 7. The studied complexes did not demonstrate the presence of slow magnetic relaxation in the zero magnetic field. The application of dc-magnetic field made it possible to observe non-zero values of the imaginary component of magnetic susceptibility for 4 and 7. Such a change in the magnetic behavior in the presence of an external magnetic field usually indicates a rather strong contribution of quantum tunneling of magnetization (QTM) to the relaxation process, which significantly accelerates the rate of relaxation. For 3 and 5, the deviation from zero of the χ" value was within the instrument error range even in non-zero dc-magnetic fields (Figures S13 and S14). The high efficiency of QTM in complexes 4 and 7 is due to their insufficiently high magnetic axiality, as evidenced by the rather high values of g x , g y (Table 3), which leads to large values of the corresponding matrix elements between components of KDs of the transversal magnetic moment (Figures S10 and S12) [64].
For the most effective neutralization of the QTM effect, it is necessary to determine the optimal field at which the relaxation time is the longest. Measurement of the ac-magnetic susceptibility in the dc-field range from 0 to 5000 Oe at 2 K made it possible to determine the optimal field value, at which the maximum values of the imaginary component of the ac-susceptibility are shifted to the lowest frequencies; these field values were equal to 1000 Oe for both 4 and 7 ( Figure 6). process, which significantly accelerates the rate of relaxation. For 3 and 5, the deviation from zero of the χ″ value was within the instrument error range even in non-zero dcmagnetic fields (Figures S13 and S14). The high efficiency of QTM in complexes 4 and 7 is due to their insufficiently high magnetic axiality, as evidenced by the rather high values of gx, gy (Table 3), which leads to large values of the corresponding matrix elements between components of KDs of the transversal magnetic moment (Figures S10 and S12) [64].
For the most effective neutralization of the QTM effect, it is necessary to determine the optimal field at which the relaxation time is the longest. Measurement of the ac-magnetic susceptibility in the dc-field range from 0 to 5000 Oe at 2 K made it possible to determine the optimal field value, at which the maximum values of the imaginary component of the ac-susceptibility are shifted to the lowest frequencies; these field values were equal to 1000 Oe for both 4 and 7 ( Figure 6). The results of measuring the ac-magnetic susceptibility of complex 4 in the optimal dc-field are shown in Figure 7. The relaxation time τ0 = 1/2πνmax was determined by processing the dependences χ′(ν) and χ″(ν) using the generalized Debye model. Approximation of the high-temperature part of the τ(1/Т) dependence using the Arrhenius equation (Orbach relaxation mechanism, τOrbach = τ0exp{ΔЕeff/kBT}) led to an evaluation of the effective energy barrier of magnetization reversal and the characteristic relaxation time, ΔEeff/kB = 15 K and τ0 = 5.6·10 −7 s, respectively (Figure 8). The results of measuring the ac-magnetic susceptibility of complex 4 in the optimal dc-field are shown in Figure 7. The relaxation time τ 0 = 1/2πν max was determined by processing the dependences χ (ν) and χ"(ν) using the generalized Debye model. Approximation of the high-temperature part of the τ(1/T) dependence using the Arrhenius equation (Orbach relaxation mechanism, τ Orbach = τ 0exp {∆E eff /k B T}) led to an evaluation of the effective energy barrier of magnetization reversal and the characteristic relaxation time, ∆E eff /k B = 15 K and τ 0 = 5.6·10 −7 s, respectively (Figure 8).
The results of measuring the ac-magnetic susceptibility of complex 4 in the optimal dc-field are shown in Figure 7. The relaxation time τ0 = 1/2πνmax was determined by processing the dependences χ′(ν) and χ″(ν) using the generalized Debye model. Approximation of the high-temperature part of the τ(1/Т) dependence using the Arrhenius equation (Orbach relaxation mechanism, τOrbach = τ0exp{ΔЕeff/kBT}) led to an evaluation of the effective energy barrier of magnetization reversal and the characteristic relaxation time, ΔEeff/kB = 15 K and τ0 = 5.6·10 −7 s, respectively (Figure 8). For compound 7, the maxima on the frequency dependence of χ" were observed in an optimal field of 1000 Oe in the temperature range 2-4 K ( Figure 6). The τ values were evaluated as in the previous case. ∆E eff /k B and pre-exponential factor (τ 0 ) were determined by approximation of the high-temperature data using the Arrhenius law and found to be 13 K and 5.7 × 10 −7 s, respectively (Figure 9). To approximate the experimental data in the entire temperature range the sum of Orbach, Raman, and direct mechanisms were used.
The following values of the parameters were obtained: ∆E eff /k B = 7.2 K, τ 0 = 7.1 × 10 −6 s, C Raman = 2.8 K −7 s −1 , n Raman = 7, A direct = 1.8 × 10 −9 s −1 Oe −4 K −1 , n direct = 4, R 2 = 0.99996, where R 2 was determined using formula.  On the other hand, it should be borne in mind that the Orbach process does not always contribute to the relaxation process, which has already been observed for some Er and Yb complexes [73]. The absence of such a contribution can be evidenced by the ab initio prediction of the energy of the first excited state, which exceeds the effective barrier by two times for 4 and by an order of magnitude for 7 (Table 3), as well as by sufficiently large values of τ 0 . The relaxation times characteristic of the over-barrier magnetization reversal corresponding to the Orbach mechanism should be~10 −10 -10 −12 s. For 4 and 7, the values of τ 0 are very far from these limits. Thus, we tried to explain the experimental data excluding the Orbach regime from the analysis of relaxation processes according to ref. [74].
Similar to the case of 4, the approximation of the temperature dependency of the relaxation time for 7 ( Figure 10) was performed with sufficient confidence, taking into account the direct and Raman mechanisms of relaxation with the following parameters: C Raman = 1040 ± 100 K −n_Raman s −1 , n Raman = 2.9 ± 0.1, A direct = (7.4 ± 1.0) × 10 −12 K −1 Oe −4 s −1 , n direct = 4, R 2 = 0.9959. Thus, we propose that the magnetization relaxations in compounds 4 and 7 take place predominantly by the direct and Raman mechanisms.
A large number of Dy III complexes exhibit SMM properties, but the search for conditions leading to the formation of a certain geometry of the coordination environment of a metal ion and its isolation from other paramagnetic ions is a rather difficult task. The proposed method of incorporating Dy III into a polymeric chain of Cd II ions and pivalate ligands made it possible to isolate metal ions from each other, but the geometry of the coordination environment did not favor to slow magnetic relaxation by the Orbach mecha-nism. The creation of a certain geometry of the coordination environment is apparently governed by the unpredictable action of several factors. For example, diamagnetic dilution of Dy III ions by Zn II in the heterometallic trinuclear {DyZn 2 } complex with a Schiff-base and carboxylate ligands was associated with the formation of DyO 8 polyhedron with the geometry of square antiprism (Dy···Dy 9.736 Å) [75]. This {DyZn 2 } complex possessed a field-induced slow magnetic relaxation with ∆E eff /k B ≈ 12.3 K (2 kOe) [75]. On the other hand, in the case of 1D-polymer [Dy 2 (piv) 5 (OH)(H 2 O)] n based on tetranuclear fragment {Dy 4 (piv) 6 (µ 3 -OH) 2 } [76], the field-induced slow relaxation of magnetization was revealed using the ac-magnetic data analysis, but the barrier was much lower (∆E eff /k B ≈ 4.5 K), this lower value was presumably caused by intramolecular exchange interactions between Dy III ions (Dy···Dy 3.790−4.175 Å). The same paper [76] reported on the binuclear complex [Dy 2 (piv) 6 (phen) 2 ] (Dy···Dy 5.391 Å), for which the field-induced slow magnetic relaxation was also observed and the barrier was estimated using the Arrhenius equation as ≈ 28.4 K.  Figure 9. Frequency dependences of the real (χ′, (a)) and imaginary (χ″, (b)) components of the acmagnetic susceptibility for complex 7 in the 1000 Oe dc-field. The lines are the best-fits by the generalized Debye model. A large number of Dy III complexes exhibit SMM properties, but the search for conditions leading to the formation of a certain geometry of the coordination environment of a metal ion and its isolation from other paramagnetic ions is a rather difficult task. The proposed method of incorporating Dy III into a polymeric chain of Cd II ions and pivalate ligands made it possible to isolate metal ions from each other, but the geometry of the coordination environment did not favor to slow magnetic relaxation by the Orbach mechanism. The creation of a certain geometry of the coordination environment is apparently governed by the unpredictable action of several factors. For example, diamagnetic dilution of Dy III ions by Zn II in the heterometallic trinuclear {DyZn2} complex with a Schiffbase and carboxylate ligands was associated with the formation of DyO8 polyhedron with the geometry of square antiprism (Dy…Dy 9.736 Å) [75]. This {DyZn2} complex possessed a field-induced slow magnetic relaxation with ΔEeff/kB ≈ 12.3 K (2 kOe) [75]. On the other hand, in the case of 1D-polymer [Dy2(piv)5(OH)(H2O)]n based on tetranuclear fragment {Dy4(piv)6(μ3-OH)2} [76], the field-induced slow relaxation of magnetization was revealed using the ac-magnetic data analysis, but the barrier was much lower (ΔEeff/kB ≈ 4.5 K), this lower value was presumably caused by intramolecular exchange interactions between Dy III ions (Dy…Dy 3.790−4.175 Å). The same paper [76] reported on the binuclear complex [Dy2(piv)6(phen)2] (Dy…Dy 5.391 Å), for which the field-induced slow magnetic relaxation was also observed and the barrier was estimated using the Arrhenius equation as ≈ 28.4 K.
A direct comparison of the magnetic properties of heterometallic complexes of lanthanides with Zn II or Cd II cations is hampered by the small number of such complexes with similar geometric parameters. Since the Zn II and Cd II ions are diamagnetic, the difference in their effect on the magnetism of the Zn-Ln and Cd-Ln compounds is exclusively due to their influence on geometric characteristics. As noted above, the larger ionic radius A direct comparison of the magnetic properties of heterometallic complexes of lanthanides with Zn II or Cd II cations is hampered by the small number of such complexes with similar geometric parameters. Since the Zn II and Cd II ions are diamagnetic, the difference in their effect on the magnetism of the Zn-Ln and Cd-Ln compounds is exclusively due to their influence on geometric characteristics. As noted above, the larger ionic radius of the Cd II cation and, accordingly, its higher possible coordination numbers in comparison with Zn II are the main sources of differences in geometric characteristics. For the above zinc complexes, in one case, two relaxation pathways were observed, which is quite typical for heterometallic Dy III complexes. The existence of two relaxation pathways can be associated with several asymmetric units and, possibly, with low-temperature isomers/conformers or Ln-Ln interactions, which perturb the electronic structure of some Ln III ions. In the CdLn complexes, we observed only one relaxation pathway, which indicates that, in this particular case, the Cd-based structure was more symmetric and/or rigid in view of the changes caused by temperature (as shown in [37]). In Cd-Ln complexes, the higher separation of Ln III ions may be responsible for their better magnetic isolation and the absence of disturbing interactions. However, there are currently insufficient data to formulate general conclusions.

Materials and Methods
The compounds were synthesized in the air using commercial MeCN solvent (>99%  [77]. Elemental analysis was carried out on an EA1108 Carlo Erba automatic CHNS-analyzer. IR spectra of the compounds were recorded on a Perkin Elmer Spectrum 65 spectrophotometer equipped with a Quest ATR Accessory (Specac, Orpington, UK) by the attenuated total reflectance (ATR) in the range 400-4000 cm −1 . Luminescent spectra were measured with a Perkin Elmer LS-55 spectrofluorometer.

Synthesis of the Compounds
0.28 mmol Ln(NO 3 ) 3 ·xH 2 O (x = 5 for Ln = Dy, Ho, Er and 6 for Ln = Sm, Eu, Tb, Yb) was added to a solution of 0.20 g [Cd(H 2 O) 2 (piv) 2 ] (0.57 mmol) in 20 mL of MeCN. The reaction mixture was stirred for 20 min at 80 • C, cooled to room temperature, and filtered. The solution was kept at room temperature and colorless crystals of complexes precipitated after 72 h. The crystals were filtered off, washed with cold MeCN (t = −5 • C), and dried in air at t = 20 • C.

X-ray Diffraction Studies
Single crystal X-ray studies of crystals 1-4, 6 and 7 were carried out on a Bruker Apex II diffractometer equipped with a CCD detector (MoK α , λ = 0.71073 Å, graphite monochromator) [78]. A semiempirical adjustment for absorption was introduced for all complexes [79]. Using Olex2 [80], the structures of the compounds obtained were solved by direct methods and refined in the full-matrix least-squares anisotropic approximation using the SHELX software complexes [81]. The hydrogen atoms in the ligands were calculated geometrically and refined in the "riding" model. The crystallographic parameters and the structure refinement statistics are shown in Table S1. CCDC numbers 2044967 (for 1), 2044968 (for 2), 2044970 (for 3), 2044972 (for 4), 2044971 (for 6), 2044969 (for 7) contains the supplementary crystallographic data for the reported compounds. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via http: //www.ccdc.cam.ac.uk/data_request/cif (accessed on 14 July 2021).

Magnetic Measurements
Magnetic susceptibility measurements were performed with a Quantum Design susceptometer PPMS-9. This instrument works between 1.8 and 400 K for DC applied fields ranging from −9 to 9 T. For AC susceptibility measurements, an oscillating AC field of 1 or 5 Oe with a frequency between 10 and 10,000 Hz was employed. Measurements were performed on polycrystalline samples sealed in polyethylene bags and covered with mineral oil to prevent field-induced orientation of the crystallites. The paramagnetic components of the magnetic susceptibility χ were determined taking into account the diamagnetic contribution evaluated from Pascal's constants as well as the contributions of the sample holder and mineral oil.
The magnetization relaxation times τ = 1/2πν max and the α factors, which account for the distribution in relaxation processes, were obtained by fitting the χ (ν) and χ"(ν) plots using the generalized Debye model (see SI).

Photo-Physical Measurements
Luminescent measurements were performed with a Horiba-Jobin-Yvon Fluorolog FL 3-22 (Horiba Scientific, Kyoto, Japan) spectrometer, which has a 450 W xenon arc lamp as an excitation source for steady state measurements and a 150 W xenon pulse lamp for kinetic experiments. An R-928 PMT tube (Hamamatsu Photonics K.K, Hamamatsu, Japan) was used as a detector. The spectra were corrected for instrumental responses. Lifetimes were measured with the same instrument using a xenon flash lamp. The quantum yield measurements were carried out on solid samples with a Spectralone-covered G8 integration sphere (GMP SA, Renens, Switzerland) under ligand excitation, according to the absolute method. Each sample was measured several times under slightly different experimental conditions. The estimated error for quantum yields was ±10%. All complexes studied were powdered before measurements.

Details of Quantum Chemical Calculations
Coordination polymers were divided into smaller structural fragments of individual spin centers, which then could be treated by ab initio computational methods. Calculations were performed for DyCd 2 and YbCd 2 clusters using the truncated XRD geometry with the tr Bu groups substituted by Me groups in the piv ligand (hereinafter referred to as 4m, 7m, Supplementary Materials, Figures S8 and S10). The SA-CASSCF/SO-RASSI approach [83][84][85], implemented in the MOLCAS 8.2 suite of programs [86], was used for calculations. The ANO-RCC-VTZP relativistic basis sets for lanthanides and oxygen atoms with the smaller ANO-RCC-VDZ for other atoms were employed [87]. The scalar relativistic effects were taken into account using the DKH2 Hamiltonian [88]. For the dysprosium complex, 21 sextet, 128 quintet, and 130 doublet states (the energy region up to~50,000 CM −1 ) were taken into account with the active space consisted of 9 electrons distributed on 7 f-orbitals. For the ytterbium complex, seven singlet and seven triplet states were accounted with the active space consisted of 13 electrons on 7 f-orbitals.
The g-tensors for Kramers doublets, their orientations in the molecular axes, and temperature dependence of the molar magnetic susceptibility were evaluated using results of the SA-CASSCF/SO-RASSI calculations and SINGL_ANISO code [89].

Conclusions
A series of new LnCd 2 heterometallic 1D polymers [LnCd 2 (piv) 7 (H 2 O) 2 ] n ·nMeCN (Ln = Sm, Eu, Tb, Dy, Ho, Er, Yb) with pivalic acid anions were synthesized and characterized by various methods. Due to the larger ionic radius of Cd II and its ability to have higher coordination numbers in comparison with Zn II , the trinuclear units LnCd 2 undergo polymerization, forming 1D chains, in contrast to the discrete Zn 2 Ln analogs. The polymers [LnCd 2 (piv) 7 (H 2 O) 2 ] n ·nMeCN are isostructural; according to the single-crystal X-ray data, the geometry of the LnO 8 polyhedron changes from a biaugmented trigonal prism for Ln = Sm and Eu to a triangular dodecahedron for Ln = Tb, Dy, Er, and Yb. In the polymeric chain, lanthanide ions are isolated from each other by two Cd ions (the minimal Ln···Ln distance is more than 10 Å) and coordinates only the oxygen atoms of the bridging carboxylate groups. This type of the closest coordination environment, where efficient quenching groups are absent, gives rise to higher values of the intrinsic quantum yield of luminescence for 2 (EuCd 2 core) than for Eu(NO 3 ) 3 ·6H 2 O, and the quantum yield comparable to that for Eu III aromatic carboxylate complexes. The excited state lifetimes for 2 and 3 (EuCd 2 and TbCd 2 cores) are comparable to the similar lifetimes of the Ln-Zn and Ln-Cd heterometallic carboxylates. Complexes 4 and 7 (DyCd 2 and YbCd 2 cores) exhibit the properties of field-induced SMMs. Based on the analysis of the relaxation of magnetization and the results of high-level ab initio calculations, the contribution of the Orbach relaxation mechanism was excluded. The sum of the Raman and QTM mechanisms was dominant in the magnetization relaxation for 4, and the sum of the direct and Raman processes was the dominant relaxation mechanism in the case of 7.