Effect of the Alkaline Metal Ion on the Crystal Structure and Magnetic Properties of Heterometallic GdIII-VIV Complexes Based on Cyclobutane-1,1-Dicarboxylate Anions

A series of heterometallic GdIII-VIV compounds were synthesized by the reaction of VOSO4·3H2O with cyclobutane-1,1-dicarboxylic acid salts M2(cbdc) (M = Na, Rb, Cs). The new compounds were formed by [Gd(VO)2(cbdc)4(H2O)8] trinuclear anionic units that were similar in composition but differed in structure, depending on the nature of the alkali metal cation incorporated in the crystal structure of the compound. In the case of Na+, the {GdV2} units were characterized by identical V···Gd distances and were linked into the 1D-polymeric chain [NaGd(VO)2(cbdc)4(H2O)10]n (1). In the systems with Rb+ and Cs+, the V···Gd distances were different, and the {GdV2} units were linked into the 3D-framework {[RbGd(VO)2(cbdc)4(H2O)10]·2.5H2O}n (2) and the octanuclear molecule {[CsGd(VO)2(cbdc)4(H2O)11]·5H2O}2 (3), respectively. According to dc-magnetic measurements, the VIV and GdIII ions were ferromagnetically coupled in compound 1 (JVGd = 0.163± 0.008 cm−1), while in compounds 2 and 3, ferroand weak antiferromagnetic exchange interactions were observed (JVGd = 0.989 ± 0.028 and −0.089 ± 0.008 cm−1 for 2, 0.656 ± 0.009 and −0.050 ± 0.004 cm−1 for 3). Analysis of the EPR spectra of 1 revealed the presence of weak magnetic anisotropy of GdIII ions (D~0.08 cm−1 and E/D~0.1–0.15). Ac-susceptibility measurements showed an occurrence the field-induced slow relaxation of magnetization in 1–3.


Introduction
The interest in the directed synthesis of heterometallic compounds where 3d and 4f metal ions are combined in a single molecule is caused by the wide range of physicochemical properties they exhibit, including luminescent properties [1,2], molecular magnetism [3,4], magnetocaloric effect [5][6][7][8][9], and catalytic activity [10][11][12]. In addition, studies on such heterometallic compounds are of fundamental concern in order to elucidate the exchange interactions between paramagnetic centers of different nature, 3d and 4f metal ions, and the effect of these interactions on the dynamic characteristics of a single-molecule magnet (SMM), for example, the magnitude of the energy barrier to magnetization reversal ∆ eff . From this point of view, the most convenient objects for studies by physicochemical methods include systems with a 3d center containing one unpaired electron (S = 1/2, quantum spin), namely a Cu II (3d 9 ) or V IV (3d 1 ) ion. To date, a number of Cu II -4f systems, from molecular complexes to coordination polymers, have already been well

Crystal Structure Description
Compounds 1 and 2 crystallize in monoclinic space group C2/c. Compound 2 contained 2.5 solvate water molecules. Compound 3 crystallizes in triclinic space group P1 with 5 solvate water molecules. The basic structural unit of all the three compounds is the [Gd(VO) 2 (cbdc) 4 (H 2 O) 8 ] − ({GdV 2 } − ) anionic complex with a trinuclear metal core. In this unit, gadolinium is the central atom, while the vanadium atoms are terminal ones and belong to bis-chelate moieties {(VO)(cbdc) 2 (H 2 O)} (see Scheme 1). In complex 1, the vanadium atoms were crystallographycally equivalent (Figure 1), while the terminal vanadium atoms, V1 and V2, in compounds 2 and 3 were nonequivalent (Figures 2 and 3). The coordination polyhedron of vanadium (VO 6   The coordination polyhedra of gadolinium (GdO8) in 1-3 were analyzed using the SHAPE v2.1 program [46]. In 1, the GdO8 coordination polyhedron corresponded to a triangular dodecahedron [47]) formed by six O atoms of water molecules (O11, O12, O13) and two O atoms of carboxylate groups (O7) (Figure 1, Table S4). The GdO8 polyhedron in 2 can be described as a biaugmented (two-capped) trigonal prism [47]) with the basal planes formed by the O5, O8W, and O10W atoms on the one side, and the O18, O6W, and O13W atoms on the other side. The caps of the trigonal prism were formed by the O7W and O9W atoms located above the O6W-O8W-O10W-O13W and O5-O18-O6W-O8W faces, respectively ( Figure 2, Table S4). The geometry of the GdO8 coordination polyhedron in 3 was closest to a tetragonal antiprism [47] with the basal planes formed by eight O atoms: four O atoms of water molecules (O1W, O2W, O4W, O5W) on the one side, and two O atoms of carboxylate groups (O9, O16) and two O atoms of water molecules (O12W, O13W) on the other side ( Figure 3, Table S4).     In 1, the {GdV2} − units were linked in a 1D-polymeric chain by Na atoms coordinating the O atoms of carboxylate groups (О1 and O3) and water molecules (O6) belonging to the {(VO)(сbdc)2(H2O)} moieties of the neighboring {GdV2} − units ( Figure 4, Tables 1 and S1). The shortest V···V distance was observed between two metal atoms of the adjacent {GdV2} − units (6.234 Å). The water molecules coordinated to Gd (O11, O12, O13), V (O6), Na (O14) atoms, the O2, O3, O7, O8, O9, O10 carboxylate atoms, the O5 atoms of {V=O} moiety, and the CH2 groups of the cyclobutane moieties of the ligand were involved in the formation of intra-and intermolecular hydrogen bonds which additionally stabilized the crystal structure of 1 (Table S5). The coordination polyhedra of gadolinium (GdO 8 ) in 1-3 were analyzed using the SHAPE v2.1 program [46]. In 1, the GdO 8 coordination polyhedron corresponded to a triangular dodecahedron [47]) formed by six O atoms of water molecules (O11, O12, O13) and two O atoms of carboxylate groups (O7) (Figure 1, Table S4). The GdO 8 polyhedron in 2 can be described as a biaugmented (two-capped) trigonal prism [47]) with the basal planes formed by the O5, O8W, and O10W atoms on the one side, and the O18, O6W, and O13W atoms on the other side. The caps of the trigonal prism were formed by the O7W and O9W atoms located above the O6W-O8W-O10W-O13W and O5-O18-O6W-O8W faces, respectively ( Figure 2, Table S4). The geometry of the GdO 8 coordination polyhedron in 3 was closest to a tetragonal antiprism [47] with the basal planes formed by eight O atoms: four O atoms of water molecules (O1W, O2W, O4W, O5W) on the one side, and two O atoms of carboxylate groups (O9, O16) and two O atoms of water molecules (O12W, O13W) on the other side ( Figure 3, Table S4).
Since the radius of Cs + ion is larger than that of Rb + , the former participated in linking not only with neighboring {GdV 2 } − anions but also with nonequivalent bis-chelate moieties {(VO)(cbdc) 2 (H 2 O)} within one {GdV 2 } − unit. As a result, a decrease in the V···V distance (6.077 Å) was observed in the {GdV 2 } − unit of 3 in comparison with that in 1 (6.391 Å) and 2 (7.010 Å), along with a sharp decrease in the dimensionality from 3D-polymeric to molecular structure. In addition, despite the structural similarity of the heterometallic trinuclear anions {GdV 2 } − in all the three compounds, the presence in their structures of different alkali metal cations involved in linking the {GdV 2 } moieties to each other affected not only the structure dimensionality but also the V···Gd distances within the {GdV 2 } moieties ( Figure 7).  (Table S7).   (4) Since the radius of Cs + ion is larger than that of Rb + , the former participated in linking not only with neighboring {GdV2} − anions but also with nonequivalent bis-chelate moieties {(VO)(cbdc)2(H2O)} within one {GdV2} − unit. As a result, a decrease in the V···V distance (6.077 Å) was observed in the {GdV2} -unit of 3 in comparison with that in 1 (6.391 Å) and 2 (7.010 Å), along with a sharp decrease in the dimensionality from 3D-polymeric to molecular structure. In addition, despite the structural similarity of the heterometallic trinuclear anions {GdV2} − in all the three compounds, the presence in their structures of different alkali metal cations involved in linking the {GdV2} moieties to each other affected not only the structure dimensionality but also the V···Gd distances within the {GdV2} moieties ( Figure 7).    Figure 8 shows the X-and Q-band EPR spectra of solid samples 1-3 vs. temperature. The spectra of 2 and 3 showed negligible changes in the temperature range of 5-295 K. The spectra of 1 did exhibit some changes in the spectral shape between 295 and 80 K; however, these changes were insignificant and might be due to a variation in the linewidth of the multiple overlapped signals. Therefore, we assumed that the exchange couplings in the triad were rather small, as it is typical of Gd III complexes and as magnetic susceptibility measurements confirm. Therefore, all paramagnetic centers should contribute to the resulting EPR spectra. Judging by the total spectrum width and shape, we concluded that the EPR spectrum was dominated by S = 7/2 signals of Gd III with noticeable zero-field splitting. The signals of two V IV ions with S = 1/2 had narrower spectra but much smaller integral intensity; therefore, they were buried in the much stronger signal  Figure 8 shows the X-and Q-band EPR spectra of solid samples 1-3 vs. temperature. The spectra of 2 and 3 showed negligible changes in the temperature range of 5-295 K. The spectra of 1 did exhibit some changes in the spectral shape between 295 and 80 K; however, these changes were insignificant and might be due to a variation in the linewidth of the multiple overlapped signals. Therefore, we assumed that the exchange couplings in the triad were rather small, as it is typical of Gd III complexes and as magnetic susceptibility measurements confirm. Therefore, all paramagnetic centers should contribute to the resulting EPR spectra. Judging by the total spectrum width and shape, we concluded that the EPR spectrum was dominated by S = 7/2 signals of Gd III with noticeable zero-field splitting. The signals of two V IV ions with S = 1/2 had narrower spectra but much smaller integral intensity; therefore, they were buried in the much stronger signal of Gd III (see Supplementary Materials for the supportive simulation). Figure 8 shows the X-and Q-band EPR spectra of solid samples 1-3 vs. temperature. The spectra of 2 and 3 showed negligible changes in the temperature range of 5-295 K. The spectra of 1 did exhibit some changes in the spectral shape between 295 and 80 K; however, these changes were insignificant and might be due to a variation in the linewidth of the multiple overlapped signals. Therefore, we assumed that the exchange couplings in the triad were rather small, as it is typical of Gd III complexes and as magnetic susceptibility measurements confirm. Therefore, all paramagnetic centers should contribute to the resulting EPR spectra. Judging by the total spectrum width and shape, we concluded that the EPR spectrum was dominated by S = 7/2 signals of Gd III with noticeable zero-field splitting. The signals of two V IV ions with S = 1/2 had narrower spectra but much smaller integral intensity; therefore, they were buried in the much stronger signal of Gd III (see Supplementary Materials for the supportive simulation). The zero-field splitting values D and E for 1 can be estimated simultaneously from the simulation of X/Q-band spectra (see Supplementary Materials). It was found that D was around ~0.08 cm −1 and E/D ~ 0.1-0.15. For the two other compounds, 2 and 3, the EPR spectra were less resolved (perhaps due to more efficient intermolecular exchange inter- The zero-field splitting values D and E for 1 can be estimated simultaneously from the simulation of X/Q-band spectra (see Supplementary Materials). It was found that D was around~0.08 cm −1 and E/D~0.1-0.15. For the two other compounds, 2 and 3, the EPR spectra were less resolved (perhaps due to more efficient intermolecular exchange interactions), but it is obvious that the zero-field splitting had comparable or even smaller values.

DC Susceptibility Measurements
The magnetic properties of compounds 1-3 were investigated by measuring the temperature dependences of molar magnetic susceptibility (χ M ) in the range of 2-300 K in a 5000 Oe dc-magnetic field. The experimental χ M T values at 300 K for 1-3 (8.64, 8.74, and 8.89 cm 3 K mol −1 , respectively, see  were similar to the spin-only value χ M T theor = 8.74 cm 3 K mol −1 expected for two non-interacting V IV ions (S = 1/2) and one Gd III ion (S = 7/2). The χ M T(T) dependencies for 2 and 3 were similar in shape. The χ M T values for 2 and 3 monotonically increased with decreasing temperature, reaching 8.99 and 9.03 cm 3 K mol −1 , respectively, at 45 K, then sharply grew to 9.75 and 9.71 cm 3 K mol −1 at 4 K, and finally decreased to 8.63 and 9.03 cm 3 K mol −1 at 2 K (Figures 9 and 10). The χ M T value for 1 monotonically increased with cooling, reached 8.94 cm 3 K mol −1 at 8 K, and then sharply decreased to 8.05 cm 3 K mol −1 at 2 K ( Figure 11).
In order to clarify the correctness of the assignment of the J values to the V1-Gd and V2-Gd fragments in the compounds 2 and 3, using a DFT method, we computationally considered two separate Gd III {VO(cbdc) 2 (H 2 O) 8 } units of 2 and 3 and analyzed the forms of natural orbitals responsible for the character of the exchange interactions in V IV -Gd III pairs of different type. Following from the shapes of natural orbitals ( Figure S24), there was an overlapping of the orbitals of the gadolinium(III) and oxygen atom of the vanadium fragment {V(2)O(cbdc) 2 (H 2 O), which provided an exchange channel leading to antiferromagnetic coupling in V(2) IV -Gd III pairs. In contrast, the orbitals of gadolinium and the closest oxygen atoms of {V(1)O(cbdc) 2 (H 2 O)} did not overlap, which resulted in ferromagnetic interactions between V(1) and Gd.
The magnetic properties of compounds 1-3 were investigated by measuring the temperature dependences of molar magnetic susceptibility (χM) in the range of 2-300 K in a 5000 Oe dc-magnetic field. The experimental χMT values at 300 K for 1-3 (8.64, 8.74, and 8.89 cm 3 K mol -1 , respectively, see  were similar to the spin-only value χMTtheor = 8.74 cm 3 K mol -1 expected for two non-interacting V IV ions (S = 1/2) and one Gd III ion (S = 7/2). The χMT(T) dependencies for 2 and 3 were similar in shape. The χMT values for 2 and 3 monotonically increased with decreasing temperature, reaching 8.99 and 9.03 cm 3 K mol -1 , respectively, at 45 K, then sharply grew to 9.75 and 9.71 cm 3 K mol -1 at 4 K, and finally decreased to 8.63 and 9.03 cm 3 K mol -1 at 2 K (Figures 9 and 10). The χMT value for 1 monotonically increased with cooling, reached 8.94 cm 3 K mol -1 at 8 K, and then sharply decreased to 8.05 cm 3 K mol -1 at 2 K ( Figure 11).
The interpretation of the experimental plots of χMТ vs. T for complexes 2 and 3 was carried out using PHI program [48] (for details see Supplementary Materials). The parameter of isotropic exchange between V IV ions was neglected. The best fits of the experimental plots of χMТ vs. T for 2 and 3 to the theoretically calculated curves were achieved with the following parameters: J1 (Gd···V1) = 0.989 ± 0.028 cm −1 , J2 (Gd···V2) = −0.089 ± 0.008 cm −1 , and g = 2.01 for 2 ( Figure 9) and J1 (Gd···V1) = 0.656 ± 0.009 cm −1 , J2 (Gd···V2) = −0.050 ± 0.004 cm −1 , and g = 2.03 for 3 ( Figure 10).  In order to clarify the correctness of the assignment of the J values to the V1-Gd and V2-Gd fragments in the compounds 2 and 3, using a DFT method, we computationally considered two separate Gd III {VO(cbdc)2(H2O)8} units of 2 and 3 and analyzed the forms of natural orbitals responsible for the character of the exchange interactions in V IV -Gd III pairs of different type. Following from the shapes of natural orbitals ( Figure S24), there was an overlapping of the orbitals of the gadolinium(III) and oxygen atom of the vanadium fragment {V(2)O(cbdc)2(H2O), which provided an exchange channel leading to antiferromagnetic coupling in V(2) IV -Gd III pairs. In contrast, the orbitals of gadolinium and the closest oxygen atoms of {V(1)O(cbdc)2(H2O)} did not overlap, which resulted in ferromagnetic interactions between V(1) and Gd.
For the interpretation of the temperature dependence of χMТ for complex 1, in addi- For the interpretation of the temperature dependence of χMТ for complex 1, in addition to considering the magnetic exchange between Gd III and V IV ions, it is also necessary to take into account the exchange between V IV ions belonging to neighboring {GdV2}units, which can interact through bridging Na + ions (for details see Supplementary Materials). The best fit of the experimental plot of χMТ vs. T for 1, obtained by the use of PHI [48] program, was achieved with the following parameters: J1 (Gd···V) = 0.163 ± 0.008 cm −1 , J2 (V···V) = −1.095 ± 0.046 cm −1 , g = 2.01. Figure 11. Temperature dependencies of the χMT product (□) and χM (○) for compound 1. The red line shows the values calculated using PHI [48] program. Figure 11. Temperature dependencies of the χ M T product ( ) and χ M ( ) for compound 1. The red line shows the values calculated using PHI [48] program.
For the interpretation of the temperature dependence of χ M T for complex 1, in addition to considering the magnetic exchange between Gd III and V IV ions, it is also necessary to take into account the exchange between V IV ions belonging to neighboring {GdV 2 } − units, which can interact through bridging Na + ions (for details see Supplementary Materials). The best fit of the experimental plot of χ M T vs. T for 1, obtained by the use of PHI [48] program, was achieved with the following parameters: J 1 (Gd···V) = 0.163 ± 0.008 cm −1 , J 2 (V···V) = −1.095 ± 0.046 cm −1 , g = 2.01.
There are several examples of Gd III -V IV O complexes in the literature for which the magnetic properties have been analyzed. The exchange parameters J GdV obtained for 1-3 were within the range of known values ( Table 2) where interactions between paramagnetic centers can be ferro-or antiferromagnetic, as determined by the nature of the bridging moieties and the interatomic distance.

AC Susceptibility Measurements
It is known that slow relaxation of the magnetization effect can be observed both for Gd III - [36][37][38][39][40][41][42][43][44] and V IV -based complexes [49][50][51][52][53][54]. This fact inspired us to perform acmagnetic measurements for heterometallic Gd III -V IV compounds 1-3. As a result, all the synthesized complexes were found to exhibit field-induced slow relaxation of magnetization. However, in the zero dc-magnetic field, no out-of-phase signal was detected for 1-3 ( Figures S13-S16). To suppress the quantum tunneling of the magnetization process (QTM), which appeared to be the most likely reason for the absence of relaxation under the zero dc-field, the subsequent ac-measurements were carried out in dc-fields from 500 to 5000 Oe. In this way, we managed to quantify the optimal dc-field values for 1-3. The highest relaxation times were achieved by applying the optimal fields of 5000 Oe for 1 ( Figures S13 and S14), and 2500 Oe for 2 ( Figure S15) and 3 ( Figure S16). The optimal field was estimated at 8 K for 1, in contrast to 2 and 3 (2 K), because the low-temperature magnetic behavior of 1 under ac-field was quite difficult to explain.
To further study the relaxation dynamics, the isotherms of the in-phase and out-ofphase components of ac-magnetic susceptibility were measured for 1-3 under optimal H dc fields ( Figures S19-S21). To produce the temperature dependencies of relaxation time (τ vs. 1/T) for 1-3, the χ"(ν) isotherms were approximated by the generalized Debye model. The plots of τ vs. 1/T obtained in this way ( Figure 12) were approximated by the equations corresponding to different relaxation mechanisms and their combinations (see Tables S14-S16 in Supplementary Material). The best-fit parameters for the approximations of τ vs. 1/T plots for 1-3 are presented in Table 4. In the high-temperature range, all the τ vs. 1/T dependences were approximated using only the Orbach relaxation mechanism (τ = τ 0 ·exp{∆ eff /k B T}) to estimate the value of the effective anisotropic barrier.   (1, 1Y). Blue dashed lines represent fittings of the high-temperature range by the Orbach mechanism. Black solid lines represent fittings by the combinations of relaxation mechanisms presented in Tables 3 and 4. Thus, as follows from a comparison of ac-magnetic data for 1, 1Y, and 1Lu, the slow relaxation of magnetization in Gd III -V IV compounds can be determined by the contributions of both Gd III and V IV ions. Moreover, compounds 1, 1Y, and 1Lu demonstrated the highest Δeff values (according to the approximation by a single Orbach mechanism) compared with those of 2 and 3, which can be explained by longer V···V (6.234 Å for 1 Figure 12. τ vs. 1/T dependences for complexes 1-3, 1 Y , and 1 Lu under H dc fields of 2500 (2, 3, 1 Lu ) and 5000 Oe (1, 1 Y ). Blue dashed lines represent fittings of the high-temperature range by the Orbach mechanism. Black solid lines represent fittings by the combinations of relaxation mechanisms presented in Tables 3 and 4.
The best approximations of τ vs. 1/T dependences for complexes 1 and 3 were achieved using the Orbach and direct relaxation mechanisms (τ −1 = τ 0 −1 ·exp(−∆ eff /k B T) + A direct TH 4 ). The other combinations of the two relaxation mechanisms, as well as the single Orbach and Raman mechanisms, failed to fit the high-temperature range of the experimental data. The addition of a third relaxation mechanism led to overparameterization in all cases. In contrast, an ensemble of the Orbach, Raman, and QTM relaxation mechanisms (τ −1 = τ 0 −1 exp(−∆ eff /k B T) + C Raman T n_Raman + B) was used for the best-fit of the experimental data for 2. Adjunction of the third relaxation mechanism in this instance resulted in an improvement of the approximation in comparison with all options involving two relaxation mechanisms.
In our previous paper [55], we reported on two structural analogs of 1, [NaLn(VO) 2 (cbdc) 4 (H 2 O) 10 ] n (1 Y : Ln = Y, 1 Lu : Ln = Lu). However, the SMM properties of those compounds were thoroughly studied in the present study (Figures S17, S18, S22 and S23). The corresponding fitting parameters of the τ vs. 1/T plots ( Figure 12) are presented below ( Table 3). The τ(1/T) best-fits in the entire temperature range for 1 Y and 1 Lu were achieved using the cooperative contribution of Orbach and Raman mechanisms (τ −1 = τ 0 −1 ·exp(−∆ eff /k B T) + C Raman T n_Raman ) for 1 Lu and the Orbach, Raman, and QTM mechanisms for 1 Y . Other combinations of relaxation mechanisms either failed to fit the experimental data or led to over-parametrization.
At low temperatures, the relaxation of 1 was strikingly different from the relaxation of 2 and 3. A decrease in the relaxation time with a temperature decrease was observed. Because of this, the low-temperature section of the τ vs. 1/T plot cannot be approximated by a sum of any relaxation mechanisms. Such a change may originate from the absence of a network of hydrogen bonds in 1, in contrast to the structures of compounds 2 and 3.
The minimum V···V distance (6.077 Å) and one of the Gd···V distances (4.547 Å) in compound 3 led to the largest dipole-dipole interaction between ions in the Gd III ···V IV and V IV ···V IV pairs. These interactions possibly give rise to additional pathways of magnetization relaxation, and hence acceleration of relaxation [56]. Therefore, for compound 3, the effective magnetization reversal barrier, estimated from the high-temperature section by the Arrhenius equation, was the smallest.
Thus, as follows from a comparison of ac-magnetic data for 1, 1 Y , and 1 Lu , the slow relaxation of magnetization in Gd III -V IV compounds can be determined by the contributions of both Gd III and V IV ions. Moreover, compounds 1, 1 Y , and 1 Lu demonstrated the highest ∆ eff values (according to the approximation by a single Orbach mechanism) compared with those of 2 and 3, which can be explained by longer V···V (6.234 Å for 1 and 6.216 Å for 1 Y ) and Gd···V distances (5.722 Å for 1) weakening the dipole-dipole interaction between paramagnetic ions. (1 Y : Ln = Y, 1 Lu : Ln = Lu) were synthesized according to procedures described previously [56]. The IR spectra of complexes 1-3 were measured using a Spectrum 65 FT-IR spectrometer (Perkin-Elmer) by the ATR method in the range of 4000-400 cm −1 . Elemental C,H,N-analysis was carried out using an EuroEA 3000 automatic analyzer (EuroVector).

Single Crystal X-ray Diffraction
Single crystal X-ray diffraction study for the crystals of 1-3 was carried out on a Bruker SMART APEX II diffractometer equipped with a CCD detector (Mo-K α , λ = 0.71073 Å, graphite monochromator) [57]. Semi-empirical absorption correction was applied by the SADABS program [58]. The structures were solved by direct methods and refined by the full-matrix least squares in the anisotropic approximation for non-hydrogen atoms. The calculations were carried out by the SHELX-2014 program package [59] using Olex2 1.2 [60]. The hydrogen atoms in structures 1-3 were positioned geometrically and refined using the riding model. The crystallographic parameters for 1-3 and the structure refinement details are given in Table 5.

Powder X-ray Diffraction
The purity of the samples for magnetic measurements and EPR spectroscopy was achieved by powder X-ray diffraction. The powder patterns were obtained at room temperature on a Bruker D8 Advance diffractometer with a LynxEye detector in Bragg-Brentano geometry, with the sample dispersed thinly on a zero-background Si sample holder, λ(CuKα) = 1.54060 Å, θ/θ scan with variable slits (irradiated length 20 mm) from 4 • to 65 • 2θ, step size 0.020 • (Figures S25-S27).

EPR Spectroscopy
Variable-temperature continuous wave X/Q-band EPR spectra were obtained using a Bruker Elexsys E580 spectrometer equipped with an Oxford Instruments temperature control system (T = 4-300 K). All spectral simulations were done using the EasySpin toolbox for Matlab [61].

Magnetic Measurements
Magnetic susceptibility measurements were performed with a Quantum Design PPMS-9 susceptometer. Dc-magnetic susceptibility measurements were performed in the 2-300 K temperature range in a 5000 Oe dc-magnetic field. For ac-susceptibility measurements, oscillating ac-magnetic fields of 5, 3, and 1 Oe within frequency ranges 10-100, 100-1000, and 1000-10,000 Hz, respectively, were applied. Measurements were performed on polycrystalline samples sealed in a polyethylene bag and covered with mineral oil in order to prevent field-induced orientation of the crystals. Magnetic data were corrected for the diamagnetic contribution evaluated from Pascal's constants, the sample holder, and mineral oil.

DFT Calculations
The density functional theory calculations were performed by using the Gaussian 09 program package [62] with the UB3LYP functional [63]. The standard 6-31G (d,p) basis set was used for all atoms with the exception of Gd, for which the SDD basis set with effective core potential was employed. The relativistic effects were incorporated via the Douglas-Kroll-Hess (DKH) [64,65] method.

Conclusions
The radius of the alkali metal cation (Na, Rb, Cs) was shown to affect the structure of trinuclear heterometallic anions [Gd(VO) 2 (cbdc) 4 (H 2 O) 8 ] − and their mutual arrangement in a crystal. With Na + , trinuclear {GdV 2 } − moieties were characterized by identical V···Gd distances and were connected into 1D-polymeric chains in the case of 1. With Rb + and Cs + , the V···Gd distances were different, and [GdV 2 ] − fragments were linked into a 3D-framework for 2 and a molecular complex for 3, respectively. Based on EPR spectroscopy data for 1, the presence of weak magnetic anisotropy of Gd III ions was identified (D~0.08 cm −1 and E/D~0.1-0.15). Fitting the χ M T-temperature plots (excluding the magnetic anisotropy contributions of metal ions) showed the presence of ferromagnetic exchange interactions between Gd III and V IV ions in the trinuclear unit of 1, and both ferro-and antiferromagnetic exchange channels in 2 and 3. Ac-susceptibility measurements showed field-induced slow relaxation of magnetization in 1-3 that can be described using the sum of Orbach and direct mechanisms for 1 and 3, or the sum of Orbach, Raman, and QTM mechanisms for 2. Moreover, of all the compounds obtained, the highest values of the effective anisotropic energy barrier (according to the approximation by a single Orbach mechanism) were obtained for 1 and its structural analogs with diamagnetic Y III and Lu III ions.

Conflicts of Interest:
The authors declare no conflict of interest.