Near-Infrared Emissive Cyanido-Bridged {YbFe 2 } Molecular Nanomagnets Sensitive to the Nitrile Solvents of Crystallization

: One of the pathways toward luminescent single-molecule magnets (SMMs) is realized by the self-assembly of lanthanide(3+) ions with cyanido transition metal complexes. We report a novel family of emissive SMMs, {Yb III (4-pyridone) 4 [Fe II (phen) 2 (CN) 2 ] 2 }(CF 3 SO 3 ) 3 · solv (solv = 2MeCN, 1 · MeCN ; 2AcrCN, 1 · AcrCN ; 2PrCN, 1 · PrCN; 2MalCN · 1MeOH; 1 · MalCN ; MeCN = acetonitrile, AcrCN = acrylonitrile, PrCN = propionitrile, MalCN = malononitrile). They are based on paramagnetic Yb III centers coordinating diamagnetic [Fe II (phen) 2 (CN) 2 ] metalloligands but differ in the nitrile solvents of crystallization. They exhibit a ﬁeld-induced slow magnetic relaxation dominated by a Raman process, without an Orbach relaxation as indicated by AC magnetic data and the ab initio calculations. The Raman relaxation is solvent-dependent as represented by the power “n” of the B Raman T n contribution varying from 3.07(1), to 2.61(1), 2.37(1), and 1.68(4) for 1 · MeCN , 1 · PrCN , 1 · AcrCN, and 1 · MalCN , respectively, while the B Raman parameter adopts the opposite trend. This was correlated with the variation of phonon modes schemes, including the number of available vibrational modes and their energies, dependent on the increasing complexity of the applied nitrile. 1 · MeCN and 1 · MalCN show the additional T -independent relaxation assignable to dipole-dipole interactions as conﬁrmed by its suppression in 1 · AcrCN and 1 · PrCN revealing longer Yb–Yb distances and the disappearance in the Lu III -diluted 1 · MeCN@Lu . All compounds exhibit Yb III –centered near-infrared photoluminescence sensitized by organic ligands. frameworks based on magneto-luminescent trinuclear cyanido-bridged {Yb III Fe II2 } 3+ cations, accompanied by triﬂuoromethanesulfonate counter-ions and nitrile solvent molecules of crystallization (MeCN, AcrCN, PrCN, and MalCN). We present the concept of using the neutral cyanido complexes of [Fe(phen) 2 (CN) 2 ] · 2H 2 O as the advanced metalloligands forming stable molecular systems with Yb(III) centers and non-innocent 4-pyridone ligands. Due to the presence of Yb 3+ ions, surrounded by 4-pyridone and


Introduction
Extensive scientific interest in novel functional materials is driven by the necessity of ensuring the development of hi-tech magnetic, optical, or electronic devices [1][2][3][4][5]. Technological progress needs the materials that fulfil requirements such as extreme miniaturization, high efficiency in demonstrating desired properties, and a low cost of production [6,7]. In this regard, the idea of multifunctional molecular materials emerged as they may realize diverse physical properties within a single-phase and the desired functionalities, e.g., magnetism, luminescence or ionic conductivity, and an ability to be programmed at the molecular level [8][9][10]. In the field of molecular materials, the application of lanthanide(3+) ions has been verified as a promising pathway [11]. They are the best candidates for single-molecule magnets (SMMs) that are molecular objects showing slow relaxation of magnetization [12][13][14][15]. This makes them promising for applications in data storage and molecular spintronics [16][17][18]. On the other hand, lanthanide(III) complexes have been investigated due to their luminescent properties originating from f-f electronic transitions [19,20]. The 4f-metal-based emissive materials were used for the development of light conversion systems, light-emitting devices, optical sensors, and bioimaging tools [21][22][23][24][25]. Moreover, they were recognized as great prerequisites for optical thermometers aimed at precise and contactless temperature detection at the nanoscale [26][27][28]. By combining magnetic and luminescent properties in a molecular system, white light, multicolored, or near-infrared (NIR) emissive molecular nanomagnets were obtained [29][30][31]. They offer a valuable correlation between magnetic anisotropy and luminescence, as both these properties originate from the electronic structure of 4f metal ions [32,33]. They also enable magnetic switching of emission and the construction of advanced opto-magnetic systems based on SMMs with optically self-monitored temperature [34,35].
Recently, NIR-emissive molecular nanomagnets, mainly based on Er(III) or Yb(III) complexes, have attracted considerable attention [29,[36][37][38]. This is partially related to the increasing interest in the NIR-luminescent functional materials. For instance, the use of low-energy radiation in fluorescence imaging enabled the non-invasive detection of pathological changes at the cellular level [39,40]. Traditional near-infrared (NIR I, 650-900 nm) light-emitting optical probes with low tissue absorption are extensively explored in bioimaging [41]. However, their sensitivity and penetration depth are still limited by the high-NIR-light scattering loss [42,43]. This problem may be solved by high-NIR-emission-intensity probes with large optical penetration depth using lower-energy (over 1000 nm) emissive Er(III) and Yb(III) complexes. The unique photophysical and photochemical performance of NIR-emissive materials also opens the application horizon in optical telecommunication, sensing, lasers, and energy conversion [44][45][46][47].
NIR-emissive lanthanide SMMs are usually obtained by the attachment of the organic ligand to Er 3+ or Yb 3+ ions. The organic ligand serves as the sensitizer for 4f-based luminescence and constrains the lanthanide coordination geometry toward improved magnetic anisotropy [36][37][38]48]. Alternatively, cyanido transition metal complexes, that can efficiently transfer the energy to NIR-emissive lanthanides [49,50], can be used as advanced metalloligands for NIR-emissive SMMs [51][52][53][54]. In this context, we are continuously developing the idea of luminescent molecular magnets that can be achieved by inserting lanthanide ions into polycyanidometallate-based coordination systems. In the presented research, we used a neutral dicyanido iron(II) complex, [Fe II (phen) 2 (CN) 2 ] (phen = 1,10-phenanthroline) containing diamagnetic low-spin Fe(II) centers. Due to the strong visible light absorption and an efficient solvatochromic effect, this cyanido complex was recognized as a universal inorganic solvent polarity indicator [55][56][57][58] but here, we explore its ability to serve as a metalloligand for ensuring magnetic anisotropy and NIR luminescence of lanthanide ions. For this purpose, we selected Yb 3+ ions showing characteristic NIR emission in the 900-1100 nm range, which can be sensitized by UVto-vis-light absorbing chromophores [38,59,60]. The selected Yb III complexes also exhibit slow magnetic relaxation, which is usually dominated by the Raman relaxation rather than the Orbach relaxation that is typical for most of lanthanide SMMs [53,61]. Therefore, they are good systems for systematic studies on the structural and electronic factors that govern the Raman magnetic relaxation, which has been recently recognized as an important issue in the design of high-performance lanthanide SMMs [62][63][64]. Therefore, we report the structures as well as the magnetic and optical properties of novel molecular materials ({Yb III (4-pyridone) 4 [Fe II (phen) 2 (CN) 2 ] 2 }(CF 3 2MeCN  in 1·MeCN, 2AcrCN in 1·AcrCN, 2PrCN in 1·PrCN, and 2MalCN·1MeOH in 1·MalCN, where MeCN = acetonitrile, AcrCN = acrylonitrile, PrCN = propionitrile, MalCN = malononitrile, and MeOH = methanol), composed on trinuclear {YbFe 2 } molecules crystallized with four different nitrile solvents of crystallization. They are the first examples of NIR-emissive lanthanide-based molecular nanomagnets exploring the metalloligand application of dicyanido iron(II) complexes. They combine sensitized NIR Yb III emission with slow magnetic relaxation characterized by a Raman relaxation process sensitive to the type of nitrile solvent which was investigated by structural X-ray diffraction methods, AC magnetic data supported by the ab initio calculations, and solid-state photoluminescence experiments.
For the detailed investigation of the structural features governing magnetic relaxation effects in trinuclear {Yb III Fe II 2 } 3+ ions, we tested the formation of several analogs of 1·MeCN using more expanded nitrile solvents of crystallization, including acrylonitrile (AcrCN), propionitrile (PrCN), and malononitrile (MalCN). By modifying the synthetic procedure (see Materials and Methods), dark red crystals of 1·AcrCN, 1·PrCN, and 1·MalCN crystalline phases were obtained. They were characterized by elemental analyses, IR spectra and TGA, and their crystal structures were determined using a SC-XRD analysis (Figures 1 and 2, and Figures S1-S3, and S6-S12, Tables S2 and S4-S6). The obtained systems are very similar to 1·MeCN, crystallizing in the monoclinic C2/c space group and consisting of isomorphous {Yb III Fe II 2 } 3+ units, trifluoromethanesulfonate counter-ions, and respective nitrile solvent molecules (except for 1·MalCN also incorporating crystallization MeOH molecules). Thus, their composition is depicted by the general formula of {Yb III (4-pyridone) 4 [Fe II (phen) 2 2AcrCN in 1·AcrCN, 2PrCN  in 1·PrCN, and 2MalCN·1MeOH in 1·MalCN). Metric parameters and coordination geometries of {Yb III Fe II 2 } 3+ entities are very similar in the whole series of 1·MeCN, 1·AcrCN, 1·PrCN, and 1·MalCN ( Figure 1, Tables S3-S7). The structural differences are mainly related to the crystallization solvent content affecting features of supramolecular frameworks ( Figure 2 and Figure S12). In all compounds, solvent molecules are located between the supramolecular cationic layers of cyanido-bridged entities aligned within the ac crystallographic plane (Figure 2a). Starting from the smallest used nitrile of MeCN in 1·MeCN, through larger AcrCN in 1·AcrCN to the largest PrCN in 1·PrCN, the systematic increase in the a and b lattice constants and a slight decrease in the c lattice constant are observed ( Figure 2b). Surprisingly, the application of the most sterically expanded MalCN, even accompanied by additional MeOH molecules in 1·MalCN, drastically reduces the cell parameters of a and b while increasing the last one. This results in the pronounced differences in the closest distances between neighboring Yb 3+ ions ( Figure 2b and Figure S12, Table S8). As the nitrile size increases within the series of 1·MeCN, 1·AcrCN, and 1·PrCN, there is an increase of the closest Yb· · · Yb distances along all crystallographic directions, except the [001] one where this distance decreases similarly to the change of the c lattice constant. In 1·MalCN, along [011] and [101] directions, there is compliance with the first trend; however, in the case of other directions, there are visible inconsistencies. The most important feature seems to be the reduction of the Yb· · · Yb distances along the [110] and [101] directions, resulting in the closer alignment of Yb centers with the six of eight nearest lanthanide ions within the ac crystallographic plane. The above changes in the crystal structures related to the variation of the solvent are reflected in magnetic properties (see below). Changes in the position of the complexes within the ac plane should be particularly emphasized, as within this plane the rigid architecture of π-stacking interactions, possibly transmitting intermetallic dipolar interactions [66], is well-developed. The validity of the structural models for the bulk samples of all compounds was confirmed by the powder X-ray diffraction method ( Figure S13), which also proves the phase purity of all reported materials.
( Figure 2b). Surprisingly, the application of the most sterically expanded MalCN, even accompanied by additional MeOH molecules in 1•MalCN, drastically reduces the cel parameters of a and b while increasing the last one. This results in the pronounced differences in the closest distances between neighboring Yb 3+ ions (Figures 2b and S12, directions, resulting in the closer alignment of Yb centers with the six of eight nearest lanthanide ions within the ac crystallographic plane. The above changes in the crystal structures related to the variation of the solvent are reflected in magnetic properties (see below). Changes in the position of the complexes within the ac plane should be particularly emphasized, as within this plane the rigid architecture of π-stacking interactions, possibly transmitting intermetallic dipolar interactions [66], is well-developed. The validity of the structural models for the bulk samples of all compounds was confirmed by the powder X-ray diffraction method ( Figure S13), which also proves the phase purity of all reported materials.

Magnetic Properties
Due to the presence of Yb III complexes in 1·MeCN, we investigated its magnetic properties including direct-current (dc) and alternate-current (ac) magnetic studies ( Figure 3 and Figures S14-S18). At 300 K, the magnetic susceptibility-temperature product, χ M T, reaches 2.45 cm 3 mol -1 , which is close to the theoretical value of 2.6 cm 3 mol -1 expected for a free Yb 3+ ion with a 2 F 7/2 ground multiplet ( Figure S14a,b) [33,38,48]. Upon cooling, the χ M T value gradually decreases as a result of the thermal depopulation of m J sublevels of the ground multiplet, finally reaching 1.2 cm 3 mol -1 at 1.8 K. The monotonous course of the χ M T(T) curve suggests the lack of strong magnetic interactions down to 1.8 K due to the separation of paramagnetic Yb(III) centers by diamagnetic [Fe II (phen) 2 (CN) 2 ] complexes and 4-pyridone ligands. Field dependence of magnetization at 1.8 K shows a featureless increase of the signal upon increasing the field up to 1.6 µ B at 70 kOe, which is in the range typically observed for isolated Yb III complexes [33,38,48], and supports the lack of magnetic correlation in the system ( Figure S14c,d).
cooling, the χMT value gradually decreases as a result of the thermal depopulation of mJ sublevels of the ground multiplet, finally reaching 1.2 cm 3 mol -1 at 1.8 K. The monotonous course of the χMT(T) curve suggests the lack of strong magnetic interactions down to 1.8 K due to the separation of paramagnetic Yb(III) centers by diamagnetic [Fe II (phen)2(CN)2] complexes and 4-pyridone ligands. Field dependence of magnetization at 1.8 K shows a featureless increase of the signal upon increasing the field up to 1.6 μB at 70 kOe, which is in the range typically observed for isolated Yb III complexes [33,38,48], and supports the lack of magnetic correlation in the system (Figure S14c,d).
As a next step, the alternate-current (ac) magnetic characteristics were gathered for 1•MeCN, clearly indicating the presence of slow magnetic relaxation effect of embedded Yb III complexes (Figures 3, S15 and S16). Due to the strong quantum tunneling of magnetization (QTM) typically observed for most of Yb III -based SMMs, slow magnetic relaxation under a zero dc field was not observed [53,67]. However, the QTM was suppressed by an external dc magnetic field for even a small value of 100 Oe (Figure 3a). The dc-field variable frequency dependences of out-of-phase (χM '' ) magnetic susceptibility clearly showed two maxima detectable in the 1-1000 Hz range, the high frequency one appearing immediately from 100 Oe, and the second, low frequency appearing above 1000 Oe (Figure 3a and S15). The maximum at high frequencies did not change significantly upon changes of dc field in the range of 100-1000 Oe, while for higher fields it underwent a shift towards higher frequencies. This indicates that the QTM is quickly quenched by the dc field, while high fields accelerate the relaxation by inducing a Figure 3. Field-and temperature-variable alternate-current (ac) magnetic susceptibility characteristics for 1•MeCN and 1•MeCN@Lu: (a,b) the respective frequency dependences of χM" under various dc fields, (c) the field-dependences of relaxation time, τ, (d,e) the respective frequency dependences of χM" under various temperatures, (f) the temperaturedependences of relaxation time, τ. Solid lines in the χM"(ν) plots present the best-fits using a generalized Debye model. Solid lines in the τ -1 (H) and ln(τ)(T -1 ) plots show the best-fits taking into account a QTM, a Raman process, and a field-induced direct process (Equation (1)). For details see Figures S15-S18 (Supporting Information). . Field-and temperature-variable alternate-current (ac) magnetic susceptibility characteristics for 1·MeCN and 1·MeCN@Lu: (a,b) the respective frequency dependences of χ M " under various dc fields, (c) the field-dependences of relaxation time, τ, (d,e) the respective frequency dependences of χ M " under various temperatures, (f) the temperaturedependences of relaxation time, τ. Solid lines in the χ M "(ν) plots present the best-fits using a generalized Debye model. Solid lines in the τ -1 (H) and ln(τ)(T -1 ) plots show the best-fits taking into account a QTM, a Raman process, and a field-induced direct process (Equation (1)). For details see Figures S15-S18 (Supporting Information).
As a next step, the alternate-current (ac) magnetic characteristics were gathered for 1·MeCN, clearly indicating the presence of slow magnetic relaxation effect of embedded Yb III complexes ( Figure 3, Figures S15 and S16). Due to the strong quantum tunneling of magnetization (QTM) typically observed for most of Yb III -based SMMs, slow magnetic relaxation under a zero dc field was not observed [53,67]. However, the QTM was suppressed by an external dc magnetic field for even a small value of 100 Oe (Figure 3a). The dc-field variable frequency dependences of out-of-phase (χ M ") magnetic susceptibility clearly showed two maxima detectable in the 1-1000 Hz range, the high frequency one appearing immediately from 100 Oe, and the second, low frequency appearing above 1000 Oe (Figure 3a and Figure S15). The maximum at high frequencies did not change significantly upon changes of dc field in the range of 100-1000 Oe, while for higher fields it underwent a shift towards higher frequencies. This indicates that the QTM is quickly quenched by the dc field, while high fields accelerate the relaxation by inducing a field-induced direct process.
Thus, the faster relaxation reveals typical behavior for field-induced Yb III -based SMMs. In contrast, the second maximum of the slower relaxation process appeared only at higher dc fields and gradually changed the position by moving to lower frequencies upon increasing the external dc field. This suggests that its presence is related to the presence of some unquenched dipolar interactions between Yb centers, especially in the case of the compound 1·MeCN consisting of only one crystallographically independent Yb complex. To support this interpretation, we also investigated magnetic properties of the magnetically diluted sample of 1·MeCN built of Yb III complexes dispersed in the diamagnetic Lu III -based crystalline matrix. Such a diluted compound, 1·MeCN@Lu was characterized analogously to 1·MeCN, and its isostructurality was confirmed by the powder X-ray diffraction method (see the Experimental section and Figure S13). The concentration of Yb(III) in the diamagnetic matrix (Yb 0.07 Lu 0.93 ) was determined by a SEM-EDX microanalysis (Table S1). The ac magnetic data for 1·MeCN@Lu also show a field-induced magnetic relaxation represented by a single χ M "(ν) maximum, which also shifted towards slightly lower frequencies when compared with 1·MeCN ( Figure 3b). This confirms that the slower relaxation in 1·MeCN is due to the dipole-dipole interactions between insufficiently separated Yb III centers in the undiluted sample. Further proof of this interpretation is given by the temperaturedependence of dc χ M "(ν) maxima related to the slower relaxation investigated for 1·MeCN at a high dc field of 6 kOe ( Figure S16e) which shows the gradual disappearance of this maximum on heating without the characteristic shift to higher frequencies [68]. To discuss the single-ion properties of Yb III centers, we focused on the faster relaxation process in 1·MeCN and its temperature dependence through an investigation of the optimal dc field of 800 Oe related to the equilibrium between QTM and direct relaxation routes (Figure 3d and Figure S16). This condition allowed us to observe the displacement of the χ M " maxima towards higher frequencies in the 1.8−5.0 K range. Both Hand T-variable frequency dependences of χ M " were fitted using a generalized Debye model to extract the relaxation times (see comment to Figures S15-S24). The Equation (1) was used to parametrize the field-and T-dependences of relaxation time (Figure 3c,f, Figures S15 and S16): where the first term describes the Raman relaxation, the second represents the QTM, and the last reflects a field-induced direct process [33,38,48,61]. The Orbach relaxation pathway is usually inadequate for Yb III -based SMMs, thus it was removed from consideration. This assumption was supported by the results of ab initio calculations (see below). To fit the relaxation time using the Equation (1), the parameters of QTM and direct processes were firstly extracted from the H-dependence of relaxation time and used as a starting point for simultaneous fit of both Hand T-dependences. The resulting parameters for all processes lie within the limits expected for lanthanide molecular nanomagnets (Table 1) with the general case of the broadly variable n power of Raman relaxation due to the contributions of various phonon modes, and the variable m parameter of a direct process due to the hyperfine coupling [62][63][64]69,70]. The analogous procedure was performed for 1·MeCN@Lu ( Figure 3, Figures S17 and S18, Table 1). As we investigated the T-variable ac magnetism at the optimal dc field, the magnetic relaxation for both 1·MeCN and 1·MeCN@Lu was found to be dominated by the Raman relaxation. This process is depicted by the B Raman and n parameters of 81.68(5) s -1 K -3.07 and 3.07(1), respectively, for 1·MeCN which moderately change to 25.32(3) s -1 K -3.61 and 3.61(1), respectively, upon magnetic dilution in 1·MeCN@Lu. This can be partially explained by the non-negligible change in the phonon modes scheme occurring upon replacing Yb III with Lu III centers. However, this difference in the Raman parameters can be overestimated as the overall courses of ln(τ) versus T -1 plots for 1·MeCN and 1·MeCN@Lu mainly differ by the constant value, which can be assigned to the expected weakening of the QTM effect upon magnetic dilution (Figure 3f) [35].  1·MeCN, 1·MeCN@Lu, 1·AcrCN, 1·PrCN, and 1·MalCN.
Compound 1·MeCN  1·MeCN@Lu  1·AcrCN  1·PrCN  1·MalCN field-dependence of relaxation time (Figures 3 and 4, Figures S15, S17, S19, S21 and S23) temperature-dependence of relaxation time (Figures 3 and 4, Figures S16, S18 Despite excluding the Orbach relaxation process, we adapted the classical Arrhenius law of the T-activated process for the high-temperature range of the lnτ(T -1 ) plots: where U eff is the effective energy barrier and τ 0 is the microscopic attempt time. This procedure is often used to compare the magnetic properties of lanthanide SMMs, even if very different relaxation processes operate in the system. The fitting of the linear parts of the lnτ(T -1 ) plots for 1·MeCN and 1·MeCN@Lu provided similar and relatively low values of U eff = 12.5 K (8.69 cm -1 ) and 11.5 K (7.99 cm -1 ) for 1·MeCN and 1·MeCN@Lu, respectively, indicating moderate magnetic anisotropy of the generated Yb III complexes [67].
To further discuss magnetic relaxation in 1·MeCN, we determined the crystal field effect on Yb III complexes using the ab initio calculations of a CASSCF/RASSI/SINGLE_ ANISO type performed within an OpenMolcas package (Tables S9-S12 with the comment in the Supporting Information). For these calculations, we used the trinuclear {YbFe 2 } unit without non-coordinated CF 3 SO 3 anions and solvent molecules (Figure 1a). The resulting whole energy splitting of the 2 F 7/2 ground multiplet is close to 500 cm -1 , that is 509.5 cm -1 or 551.2 cm -1 for the small 1S and large 1L basis sets, respectively (Tables S9-S11). These values lie in the range expected for six-coordinated octahedral Yb 3+ complexes [53,61]. Using the 1L model, the ground sub-level was found to be composed of the mixture of |J, m J states of |7/2, ±7/2 (predominant contribution) and |7/2, ±1/2 , and can be described by the dominant g z of 5.95 but with the non-negligible values of g x and g y factors of 0.56 and 1.34, respectively (Table S11). This shows a significant magnetic anisotropy of Yb III complexes in 1·MeCN, revealing a desired magnetic easy axis type. It can be correlated with the arrangement of four 4-pyridone ligands, bearing a partial negative charge on donor O-atoms at the equatorial positions of the Yb III octahedral coordination sphere, as such an alignment is expected to stabilize the magnetic axiality in the Yb III complexes, revealing prolate electron density [71]. As the result, the magnetic easy axis is lying nearly perpendicular to the plane formed by four O-atoms of pyridine ligands, thus it is arranged close to the directions given by cyanido bridges (Figure 1a). However, this axiality is not perfect, as illustrated by the non-negligible values of g x and g y factors as well as by the significant admixture of |7/2, ±1/2 functions, which in particular facilitate the magnetic transition between two states of the ground Kramers doublet (due to the operating selection rule of ∆m J = 1 within the first-order perturbation theory). This explains the occurrence of a strong QTM effect and the lack of slow magnetic relaxation at the zero dc field. The first excited Kramers doublet of the 2 F 7/2 ground multiplet is located more than 250 cm -1 above the ground state (Tables S10 and S11), which is much higher than the experimental energy barrier estimated using the Arrhenius law (Table 1). Moreover, its application for the fitting of the T-dependence of overall magnetic relaxation gives unrealistic values for other parameters. All these strongly indicate the lack of Orbach relaxation pathway in 1·MeCN and the dominance of a Raman relaxation route. The validity of performed calculations is supported by the comparison with the experimental dc magnetic data, which are very well reproduced ( Figure S14b,d). The ab initio calculations also give insight into the energy of the excited 2 F 5/2 multiplet (Table S12). The bottom of the excited state in the 1L model is situated at 0.5 cm -1 , giving the estimation of emission wavelength (to the bottom of the ground multiplet) of circa 965 nm, which suits the experimental emission relatively well (see below).
The ac magnetic properties of 1·AcrCN and 1·PrCN are generally similar to those presented for 1·MeCN (Figure 4 and Figures S19-S22). In the frequency dependences of the χ M " magnetic susceptibility, the relaxation in both analogs is observed in the range of the applied dc field of 100-5000 Oe at a higher frequencies regime. However, 1·AcrCN  and 1·PrCN do not show the slower relaxation process which was observed in 1·MeCN and assigned to the dipole-dipole interactions between Yb III complexes, with only a very weak tail on the χ M "(ν) plots at lower frequencies. Such a feature can be explained by the better separation of Yb III complexes in the crystal structure due to the application of more expanded nitrile solvent molecules, AcrCN and PrCN ( Figure 2). In contrast, in 1·MalCN, two very distinct magnetic relaxation processes are observed in the ac magnetic characteristics under the applied dc field (Figure 4c, Figures S23 and S24). Moreover, the χ M "(ν) maxima assignable to the slower relaxation of a dipolar origin are stronger than in 1·MeCN. This suggests that the magnetic isolation of Yb III complexes in 1·MalCN is the worst within the whole investigated family of compounds. This can be correlated with the detailed analysis of the respective supramolecular frameworks, indicating the shortest Yb-Yb distances along the [110] and [101] directions in 1·MalCN that can lead to the strongest dipolar interactions (see Structural Studies and Figure 2 for details).
Apart from the slower relaxation appearing at high dc fields in 1·MeCN and 1·MalCN, all compounds exhibit the relaxation, which is strongly temperature-dependent. It was investigated at the optimal dc field of 800 Oe in the range of 1.8-5 K (Figures 3d and 4d-f). All resulting Hand T-variable frequency dependences of ac susceptibility were fitted using the generalized Debye model to extract the relaxation times which were further analyzed by following the Equation (1) (Figure 4g,h). As the course of ac magnetic data was similar within the whole series, we excluded the Orbach relaxation from the consideration in all compounds, as it was completed and discussed with the support of ab initio calculations for 1·MeCN (see above). The resulting best-fit parameters are presented in Table 1, while the differences between obtained compounds are visualized in Figure 4g,h.  Similarly to 1·MeCN, the magnetic relaxation of 1·AcrCN, 1·PrCN, and 1·MalCN is dominated by the Raman relaxation, thus the varying parameters of B Raman and n represent the modulation of slow magnetic relaxation effect by the nitrile solvent change. The B Raman parameter is the smallest, 81.68(5) s -1 K -3.07 , for 1·MeCN, then increases significantly for 1·AcrCN (208.28(2) s -1 K -2.37 ) and 1·PrCN (128.09(1) s -1 K -2.61 ), and reaches the highest value of 527.08(2) s -1 K -1.68 for 1·MalCN, which directly leads to the slowest relaxation time at 1. 8 K for 1·MeCN, faster for 1·AcrCN and 1·PrCN, and the fastest for 1·MalCN  (Figure 4h). However, the power n of Raman relaxation reveals the opposite trend; the highest value of 3.07(1) was observed for 1·MeCN, lower for 1·AcrCN (2.37(1)) and 1·PrCN (2.61(1)), and the lowest value of 1.68(4) was found for 1·MalCN. This means that the weakest T-dependence of Raman relaxation was observed in 1·MalCN, thus this compound should show the slowest relaxation times at the temperatures higher than the investigated range of 1.8-5 K. Nevertheless, a significant influence of the nitrile solvent content was found on the Raman relaxation features, which could be assigned to the variable phonon modes schemes [62][63][64]72]. In this context, the increasing trend of the B Raman parameter may be correlated with the increasing amount of available phonon modes going from simple MeCN, to more expanded AcrCN and PrCN, up to the most complex MalCN molecules accompanied by MeOH solvent. On the other hand, the decreasing trend of the power n may be attributed to the rising of the energies of critical vibrational modes engaged in the magnetic relaxation going within the series of 1·MeCN, 1·AcrCN, 1·PrCN,  and 1·MalCN. However, the detection of such critical phonon modes is a very difficult task and stays beyond the scope of this article [73]. The variation of the power n of the Raman relaxation results in the variation of effective energy barriers, U eff , obtained from the Arrhenius-type plots (Equation (2), Table 1). The highest value of U eff of 12.50(58) K was found for 1·MeCN, lower for 1·AcrCN (7.86 (27) series of 1·MeCN, 1·PrCN, 1·AcrCN,  and 1·MalCN. increasing trend of the BRaman parameter may be correlated with the increasing amount of available phonon modes going from simple MeCN, to more expanded AcrCN and PrCN, up to the most complex MalCN molecules accompanied by MeOH solvent. On the other hand, the decreasing trend of the power n may be attributed to the rising of the energies of critical vibrational modes engaged in the magnetic relaxation going within the series of 1 •MeCN, 1•AcrCN, 1•PrCN, and 1•MalCN. However, the detection of such critical phonon modes is a very difficult task and stays beyond the scope of this article [73]. The variation of the power n of the Raman relaxation results in the variation of effective energy barriers, Ueff, obtained from the Arrhenius-type plots (Equation (2), Table 1). The highest value of Ueff of 12.50 (58) properties of 1·AcrCN, 1·PrCN, and 1·MalCN: (a-c) the frequency dependences of χ M " under various dc fields at T = 1.8 K, (d-f) the frequency dependences of χ M " under various temperatures for the optimal H dc , (g) the field-and (h) the temperature-dependences of relaxation time, τ. For comparison, in (g,h), the experimental data for 1·MeCN were shown (taken from Figure 3). Solid lines in the χ M "(ν) plots present the best-fits using a generalized Debye model. Solid lines in the τ -1 (H) and ln(τ)(T -1 ) plots show the best-fits taking into account QTM, Raman, and direct processes (Equation (1)). Solid lines in the τ -1 (H) and ln(τ)(T -1 ) plots present the best-fits using a generalized Debye model. For details, see Figures S15-S24 (Supporting Information).

Optical Studies
Optical properties of 1·MeCN, 1·AcrCN, 1·PrCN, and 1·MalCN, including solidstate UV-vis-NIR absorption and photoluminescence characteristics, are presented in Figure 5 and Figures S25 and S26 (Supporting Information). All compounds exhibit strong absorption in the UV-vis range, which is responsible for their dark red color ( Figure S25). The absorption spectrum consists of two main parts, including the strong band located at higher wavelengths (380-650 nm) corresponding to the metal-to-ligand charge transfer (MLCT) from Fe(II) centers to phen ligands within [Fe(phen) 2 (CN) 2 ] units [55][56][57][58]. In comparison to the [Fe(phen) 2 (CN) 2 ]·2H 2 O precursor, the CT band is shifted to lower wavelengths. This is related to the coordination of the lone electron pair located on the N-atom of the CNligand to Yb 3+ ions, which strengthens the π-bonding interaction between Fe 2+ and CNions but weakens the interaction between the Fe 2+ ion and the phen ligand. The second, higher energy band observed in the UV range of 220-280 nm is related to the sum of spin-allowed π-π* transitions of 1,10-phenanthroline and 4-pyridone ligands [35,74]. Following the absorption spectra, the powder samples of all compounds were irradiated by the UV light of 270 nm to investigate the photoluminescent properties ( Figure 5). 1·MeCN, 1·AcrCN, and 1·PrCN exhibited well-developed room-temperature NIR emission with the main maximum at circa 975 nm, originating from the 2 F 5/2 2 F 7/2 f-f electronic transition of Yb 3+ ions (Figure 5a-c) [19,38,53]. The related excitation spectra consisted of two main components, the first ranging from 240 to 280 nm and the second ranging from 280 to 380 nm of the UV range. Both bands corresponded to the ligands spin-allowed π-π* transitions observed in the absorption spectrum. The absorption of 4-pyridone was represented by the main peak of the much narrower UV range (220-280) with a maximum at circa 255 nm, and the absorption spectrum of phen consisted of a few bands ranging from the deep UV to 380 nm with the maxima at 260 and 330 nm [35,74]. Therefore, it can be postulated that this NIR emission for the obtained compounds is realized by the energy transfer process from organic ligands to Yb 3+ ions. On the other hand, there were no clear bands in the excitation spectra that could be assigned to the MLCT states of the [Fe(phen) 2 (CN) 2 ] units (they should lie in the visible range), suggesting these states are not sensitizing the Yb III -based emission. However, they did not show a disturbing impact, as the effective sensitization of NIR Yb III emission in 1·MeCN, 1·AcrCN,  and 1·PrCN by organic ligands led to a pronounced signal that was easily detectable at room temperature. At low temperatures (77 K), four distinct bands located at circa 975 nm (~10260 cm -1 ), 1020 nm (~9815 cm -1 ), 1050 nm (~9530 cm -1 ), and circa 1060 nm (~9410 cm −1 ) were observed ( Figure S26). They could be tentatively assigned to four expected transitions from the lowest m J level of the excited 2 F 5/2 multiplet to four sublevels of the ground 2 F 7/2 multiplet. However, they suggested a much larger energy scale of the crystal field splitting of the ground multiplet (~850 cm -1 ) than found in the ab initio calculations (~550 cm -1 , see above) which indicates that part of these bands, e.g., those at higher energies, can be at least partially related to the remaining hot-bands from the higherlying sublevel of the emissive multiplet. Both high-and low-temperature emission spectra of 1·MalCN differ significantly from the emission spectra of other compounds (Figure 5d and Figure S26d). They consist of a single broad band covering the 870-1050 nm range with the maximum at 967 nm, also revealing a noticeably lower intensity. The assignment of this emission was identical to other compounds, as proven by the analogous shape of excitation spectra. However, the weaker signal and its broadband character are special and could be assigned to the distinguishable structure of 1·MalCN (Figures 1 and 2). In all compounds, the nitrile solvent molecules interact by weak H-bonds with 1,10-phenanthroline ligands and/or trifluoromethanesulfonate anions. Unlike the rest, additional methanol molecules are also present in 1·MalCN. They directly interact with 4-pyridone ligands that are coordinated to Yb 3+ ions. Thus, the additional O-H oscillators appearing in the vicinity of the NIR-emissive ion may lead to the weakening and broadening of the observed luminescent signal.  1•MeCN, 1•AcrCN, 1•PrCN, and 1•MalCN, including the excitation spectra for the indicated monitored emission (left panel) and the emission spectra for the indicated excitation wavelengths (right panel) gathered for (a) 1 •MeCN, (b) 1•AcrCN, (c) 1•PrCN, and (d) 1•MalCN.

X-Ray Diffraction Analysis
SC-XRD data for all samples, 1·MeCN, 1·AcrCN, 1·PrCN, and 1·MalCN, were collected using a Bruker D8 Quest diffractometer (Billerica, MA, USA) equipped with a Pho-ton50 CMOS detector, Mo Kα (0.71073 Å) irradiation source, a graphite monochromator, and an Oxford Cryostream cooling system. The SC-XRD measurements were performed at 100(2) K. The absorption correction was executed using the TWINABS program [77]. All crystal structures were solved by an intrinsic phasing method using SHELXT-2014/5 and refined by a full-matrix least squares technique on F 2 using SHELXL-2018/3 within the WinGX system (Glasgow, UK) [78,79]. All non-hydrogen atoms were refined anisotropically. Hydrogen atoms for 4-pyridone and phen ligands, as well as of solvent molecules, were calculated in their idealized positions, and refined using a riding model. Because of the significant structural disorder on trifluoromethanesulfonate anions, the significant number of restraints of the DFIX and ISOR types, as well as some of the DELU and SIMU types were applied for the selected non-hydrogen atoms to ensure the propose geometry and the convergence of the refinement procedure. Moreover, some ISOR and DFIX restraints were used for part of the atoms in 4-pyridone, phen, and solvent molecules. Also, the FLAT restraint was applied for one of the 4-pyridone rings in 1·MalCN to ensure its proper geometry. Using all these procedures, satisfactory refinement parameters were achieved. The reference CCDC numbers for 1·MeCN, 1·AcrCN, 1·PrCN, and 1·MalCN are 2082295, 2082298, 2082296, and 2082297, respectively. Details of crystal data and structure refinement are summarized in Table S2, while the representative structural parameters are gathered in Tables S3-S6. Structural figures were prepared using the Mercury 3.10.3 software (Cambridge, UK). The P-XRD data were collected using a Bruker D8 Advance Eco powder diffractometer equipped with a CuKα (1.5419 Å) radiation source (Billerica, MA, USA). The P-XRD measurements were conducted at room temperature for the polycrystalline samples inserted into a glass capillary (diameter of 0.5 mm).

Physical Techniques
The CHNS elemental analyses were performed on an Elemental Vario Micro Cube analyzer. IR absorption spectra were measured on selected single crystals using a Thermo Scientific Nicolet iN10 Fourier transform infrared (FTIR) spectrometer in the 4000−700 cm −1 range (Thermo Fisher Scientific, Waltham, MA, USA). The solid-state UV−vis−NIR absorption spectra in the 220−1270 nm range were collected for thin films of the powder samples dispersed in the NVH immersion oil using a Shimadzu UV-3600i Plus spectrophotometer equipped with three detectors (photomultiplier, InGaAs and PbS) and the LabSolutions™ UV software (Shimadzu, Tokyo, Japan). The TGA curves were collected under a nitrogen atmosphere using a TG209 F1 Libra thermogravimetric analyzer with Al pans as holders (Netzsch, Selb, Germany). The TGA data were gathered in the 20−400 • C temperature range with a heating rate of 1 • C·min −1 . Solid-state photoluminescent spectra, including emission and excitation spectra, were measured on a Horiba Jobin-Yvon Fluorolog-3 (FL3-211) spectrofluorometer (model TKN-7, Kyoto, Japan), equipped with a Xe lamp (450 W) as an excitation source and an InGaAs photodiode detector DSS-IGA020L cooled by liquid nitrogen. The emission and excitation data were analyzed using the FluorEssence software. Part of the data were gathered at 77 K using the optical cryostat filled with liquid nitrogen. Investigation of magnetic properties was performed using a Quantum Design MPMS-3 Evercool magnetometer on the powder samples, protected by paraffin oil, and closed with cotton wool in a polycarbonate capsule (Quantum Design, San Diego, CA, USA).

Calculations
Continuous Shape Measure (CSM) analyses for determination of the coordination geometry of Yb III and Fe II complexes in 1·MeCN, 1·AcrCN, 1·PrCN, and 1·MalCN were conducted using the SHAPE software, version 2.1 (Barcelona, Spain) [80,81]. The details of the ab initio calculations of a CASSCF/RASSI/SINGLE_ANISO type, performed for the molecular fragment of 1·MeCN, are described in Supplementary Materials (Tables S9-S12, with the related comment).

Conclusions
We report a novel family of luminescent molecular nanomagnets generated in the supramolecular frameworks based on magneto-luminescent trinuclear cyanido-bridged {Yb III Fe II 2 } 3+ cations, accompanied by trifluoromethanesulfonate counter-ions and nitrile solvent molecules of crystallization (MeCN, AcrCN, PrCN, and MalCN). We present the concept of using the neutral cyanido complexes of [Fe(phen) 2 (CN) 2 ]·2H 2 O as the advanced metalloligands forming stable molecular systems with Yb(III) centers and non-innocent 4-pyridone ligands. Due to the presence of Yb 3+ ions, surrounded by 4-pyridone and cyanido ligands within the deformed octahedral geometry, the obtained materials exhibit a field-induced SMM behavior which is modulated by the nitrile molecules. Firstly, the additionally appearing magnetic relaxation associated with the dipole-dipole interaction between Yb 3+ ions can be suppressed due to the extension of the distances between the Yb(III) centers within the supramolecular frameworks by the proper choice of more expanded nitrile solvents, AcrCN and PrCN. Secondly, the variation of phonon modes schemes due to the nitrile solvent exchange strongly affects the Raman relaxation process which is dominant in the observed Yb III -centered slow magnetic relaxation effects. This nitrile solvent impact on the Raman contribution to the overall magnetic relaxation was found to be extensive. The increasing complexity of the nitrile in the series of MeCN, AcrCN, PrCN, and MalCN, increases the B Raman parameter, which was correlated with the increasing number of available vibrational modes. Simultaneously, it results in the decrease of the power n, which seems to be related with the increasing the energies of phonon modes critical for the occurrence of the relaxation process. This phenomenon is not fully clarified and will be the subject of future work. Nevertheless, we present an efficient pathway for modulation of slow magnetic relaxation of Yb III complexes by subtle structural changes involving only the variation of nitrile solvent of crystallization. Additionally, all obtained molecular systems exhibit pronounced Yb III -centered NIR photoluminescence under UV irradiation. Further development of such emissive molecular nanomagnets with magnetic and optical properties tunable by sensitivity to chemical and physical stimuli is planned in our laboratory.
Supplementary Materials: The following are available online: https://www.mdpi.com/article/10.3 390/magnetochemistry7060079/s1, Table S1: results of SEM-EDXMA analysis, Figure S1: IR spectra, Figure S2: TG curves, Table S2: summary of crystal data and structure refinement, Tables S3-S6: detailed structural parameters, Figures S3-S11: additional structural views, Table S7: results of Continuous Shape Measure analysis, Figure S12, Table S8: visualization and analysis of closest Yb-Yb distances within the crystal structures, Figure S13: P-XRD patterns, Figure S14: direct-current magnetic properties, Figures S15-S24: set of detailed alternate-current magnetic characteristics for all obtained compounds under variable temperature and magnetic field, Table S9: description of the basis sets employed in the ab initio calculations, Tables S10-S12: results of the ab initio calculations with the comment on the details of these calculations, Figure S25: UV-vis-NIR absorption spectra, Figure S26: additional low-and high-temperature excitation and emission spectra.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author. The data are not publicly available, as all essential results related to this work are already included in the manuscript and Supplementary Materials.