*Article* **The Role of the Bridge in Single-Ion Magnet Behaviour: Reinvestigation of Cobalt(II) Succinate and Fumarate Coordination Polymers with Nicotinamide**

**Marek Brezovan <sup>1</sup> , Jana Juráková 2 , Ján Moncol <sup>1</sup> , L'ubor Dlhá ˇn 1 , Maria Korabik <sup>3</sup> , Ivan Šalitroš 1,2,4 , Ján Pavlik 1,\* and Peter Segl'a <sup>1</sup>**


**Abstract:** Two previously synthesized cobalt(II) coordination polymers; {[Co(*µ*<sup>2</sup> -suc)(nia)<sup>2</sup> (H2O)<sup>2</sup> ]· 2H2O}*n* (suc = succinate(2−), nia = nicotinamide) and [Co(*µ*<sup>2</sup> -fum)(nia)<sup>2</sup> (H2O)<sup>2</sup> ]*n* (fum = fumarate(2−)) were prepared and thoroughly characterized. Both complexes form 1D coordination chains by bonding of Co(nia)<sup>2</sup> (H2O)<sup>2</sup> units through succinate or fumarate ligands while these chains are further linked through hydrogen bonds to 3D supramolecular networks. The intermolecular interactions of both complexes are quantified using Hirshfeld surface analysis and their infrared spectra, electronic spectra and static magnetic properties are confronted with DFT and state-of-the-art ab-initio calculations. Dynamic magnetic measurements show that both complexes exhibit single-ion magnet behaviour induced by a magnetic field. Since they possess very similar chemical structure, differing only in the rigidity of the bridge between the magnetic centres, this chemical feature is put into context with changes in their magnetic relaxation.

**Keywords:** single-ion magnet; cobalt(II) coordination polymer; ab-initio calculations

### **1. Introduction**

Coordination polymers have been studied for a long time in terms of architecture, topology, and their potential applications in catalysis [1–3], gas adsorption [4–6], chemical adsorption [7], luminescence [8,9], and design of molecular magnetic materials [10–12]. The proper choice of relevant ligands and metal centre is the key to form fascinating and useful coordination polymers [13–23].

An extremely appealing class of molecular magnetic materials is formed by *single-molecule magnets* (SMMs) [24]. Very simply speaking, in these materials, the magnetic dipole moments tend to keep their orientation with respect to the molecular or polymeric frame. In reality, however, any imposed orientation disappears after some time, mostly due to their interference with thermal bath of molecular surroundings. In current SMMs it happens typically within milliseconds, albeit the limit of second has already been breached [25]. This measurable process is called *slow relaxation of magnetization* and its time constant is used as a characteristic of SMM systems. In special cases of 1D polymers, the term *single-chain magnets* (SCM) is used [26]. In both SMMs and SCMs, the slow relaxation of magnetization exists as a collective property of the magnetic centres. If, on the other hand, magnetically isolated centres are capable of slow relaxation of magnetization, a *single-ion magnet* (SIM) is encountered [27]. Counterintuitively, the chemical and magnetic structure of a system need not coincide, one can find, e.g., a chain of SIMs [28]. Although the best performing SIMs are based on the

**Citation:** Brezovan, M.; Juráková, J.; Moncol, J.; Dlhá ˇn, L'.; Korabik, M.; Šalitroš, I.; Pavlik, J.; Segl'a, P. The Role of the Bridge in Single-Ion Magnet Behaviour: Reinvestigation of Cobalt(II) Succinate and Fumarate Coordination Polymers with Nicotinamide. *Inorganics* **2022**, *10*, 128. https://doi.org/10.3390/ inorganics10090128

Received: 1 August 2022 Accepted: 26 August 2022 Published: 30 August 2022

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lanthanide and actinide central atoms [29], among few suitable 3*d*-elements, cobalt (II) occupies a prominent position forming SIMs with two-, three- four-, five-, six-, seven- and eightcoordinate Co(II) centres and various geometries of coordination environment [30]. The vast majority of them, however, are six-coordinate, which is thanks to the high unquenched angular momentum they bear [31]. The role of the angular momentum and symmetry of coordination environment plays important role for the mechanism of magnetic relaxation and there is a lot of attention being paid to the fine tuning of the relaxation process by design of the coordination environment. For example, the effect of linearity of coordinated pseudohalides was systematically addressed by Herchel et al. [32] or Wang et al. [33], and distortion of octahedral coordination environment was studied by groups of Pardo [34], Gao [35], Song [36,37], Herchel [38,39], or Colacio [40], concluding sometimes that the closest environment of Co(II) ion is decisive for SIM behaviour [41]. Nevertheless, there occur some clues that the focus on the central atom itself cannot uncover the full story behind slow relaxation of magnetization in SIMs. As discussed e.g., by Ren et al. [42] or Boˇca et al. [43] and very explicitly stated by Dunbar et al. [44]: " . . . *the deciding factor for SMM behavior is not the degree of distortion which, a priori, would be expected to be the case, but rather the interactions between neighboring molecules in the solid state*". Nonetheless, the stiffness of molecular and supramolecular structures is somehow overlooked in this context and the research in this sake is almost exclusively theoretical [29]. In one of very scarce works, Marinho et al. synthesized by carefully controlled conditions four variants of Co(II) coordination polymer which differed in their folding. The conformation of bridges manifested itself in the relaxation of the chain-arranged SIMs [45]. However, to the best of our knowledge no study yet addressed the question of the effect of rigidity of bridges connecting SIM centres.

Keeping this in mind, herein we attempted to compare the effect of bridge saturation upon the SIM behaviour in two analogous Co(II) coordination polymers. The succinate polymer {[Co(*µ*2-suc)(nia)2(H2O)2]·2H2O}*<sup>n</sup>* (suc = succinate(2−), nia = nicotinamide, complex **I**) was synthesized in 2009 by Demir et al. and characterized by single-crystal X-ray crystallography, IR spectroscopy, photoluminescence and TG-DTA [46]. The fumarate polymer [Co(*µ*2-fum)(nia)2(H2O)2]*<sup>n</sup>* (fum = fumarate(2−), complex **II**) was prepared in 2018 by Kansız et al. and characterized by FT-IR, X-ray crystallography and DFT calculations [47].

We demonstrated an alternative synthetic route for complex **I** employing *N*-(hydroxym ethyl)nicotinamde (hmnia) instead of nicotinamide. Crystal structures of both complexes were refined using aspheric atomic scattering factors by Hirshfeld Atomic Refinement and analysed using Hirshfeld surface analysis. Infrared and electronic spectra were interpreted and confronted with the prediction from DFT. The magnetic properties of complexes were measured and thoroughly interpreted with assistance of state-of-the-art quantum chemistry method CASSCF-NEVPT2-SOI. Finally, magnetic relaxation was discussed for these systems in context of mutual variances in their chemical structure.

### **2. Results**

### *2.1. Syntheses and Characterization*

Direct preparation of polymeric cobalt(II) carboxylates from nicotinamide—nia is represented in Scheme 1. Complex {[Co(*µ*2-suc)(nia)2(H2O)2]·2H2O}*<sup>n</sup>* (**I**) was also prepared from *N*-(hydroxymethyl)nicotinamide—hmnia (Scheme 2). Such a tendency of Co(II) salts to degradation of hmnia was not yet described in literature despite the fact that only very few Ni(II), Co(II) and Cu(II) complexes with hmnia are known [48–50]. A similar reaction occurs in the Chłopicki's preparation of the pyridinium salts of nicotinamide [51]. In Chłopicki's procedure the nitrogen atom of the amide group of nicotinamide is protected with methanal and after subsequent alkylation at the pyridine nitrogen atom, the methanal is released in water media at 37 ◦C. Cobalt (II) dichloride serves as Lewis acid, coordinating the pyridine nitrogen atom (instead of quarternization like it was in the patent) thus enabling easier methanal release (Scheme 2). In contrast with Chłopicki's procedure, however, in our case the reaction mixture was refluxed for two hours.

mide.

mide.

groscopic and stable in air and soluble in hot water.

groscopic and stable in air and soluble in hot water.

methanal is released in water media at 37 °C. Cobalt (II) dichloride serves as Lewis acid, coordinating the pyridine nitrogen atom (instead of quarternization like it was in the patent) thus enabling easier methanal release (Scheme 2). In contrast with Chłopicki's pro-

methanal is released in water media at 37 °C. Cobalt (II) dichloride serves as Lewis acid, coordinating the pyridine nitrogen atom (instead of quarternization like it was in the patent) thus enabling easier methanal release (Scheme 2). In contrast with Chłopicki's pro-

The preparation of complexes **I** and **II** was carried out by short refluxing from a water + n-pentanol (complex **I**, prepared from nia, Scheme 1), water + methanol (complex **I**, prepared from hmnia, Scheme 2) and water solution (complex **II**). The molar ratio of the reactants was 1:1:2 for cobalt(II) salts, sodium salts of dicarboxylic acids and nicotinamide or *N*-(hydroxymethyl)nicotinamide, respectively. To synthesize the discussed complexes, various molar ratios of cobalt(II) chloride hexahydrate or cobalt(II) nitrate hexahydrate to sodium carboxylate (succinate or fumarate)—Na2carb (where carb is suc or fum anion) and corresponding nicotinamide or *N*-(hydroxymethyl)nicotinamide were tested, specifically 1:1:1; 1:2:1; 1:1:2 and 1:2:2. Well-defined crystalline products were obtained only for the case of 1:1:2 (Schemes 1 and 2). The syntheses of complexes **I** and **II** was very well reproducible in terms of the product quality and yield. Prepared complexes are non-hy-

The preparation of complexes **I** and **II** was carried out by short refluxing from a water + n-pentanol (complex **I**, prepared from nia, Scheme 1), water + methanol (complex **I**, prepared from hmnia, Scheme 2) and water solution (complex **II**). The molar ratio of the reactants was 1:1:2 for cobalt(II) salts, sodium salts of dicarboxylic acids and nicotinamide or *N*-(hydroxymethyl)nicotinamide, respectively. To synthesize the discussed complexes, various molar ratios of cobalt(II) chloride hexahydrate or cobalt(II) nitrate hexahydrate to sodium carboxylate (succinate or fumarate)—Na2carb (where carb is suc or fum anion) and corresponding nicotinamide or *N*-(hydroxymethyl)nicotinamide were tested, specifically 1:1:1; 1:2:1; 1:1:2 and 1:2:2. Well-defined crystalline products were obtained only for the case of 1:1:2 (Schemes 1 and 2). The syntheses of complexes **I** and **II** was very well reproducible in terms of the product quality and yield. Prepared complexes are non-hy-

cedure, however, in our case the reaction mixture was refluxed for two hours.

cedure, however, in our case the reaction mixture was refluxed for two hours.

*Inorganics* **2022**, *10*, x FOR PEER REVIEW 3 of 18

**Scheme 1.** Synthesis of polymeric cobalt(II)dicarboxylate complexes (**I** and **II**) from nicotinamide. **Scheme 1.** Synthesis of polymeric cobalt(II)dicarboxylate complexes (**I** and **II**) from nicotinamide. **Scheme 1.** Synthesis of polymeric cobalt(II)dicarboxylate complexes (**I** and **II**) from nicotinamide.

**Scheme 2.** Synthesis of polymeric cobalt(II)succinate complex (**I**) from N-(hydroxymethyl)nicotina-**Scheme 2.** Synthesis of polymeric cobalt(II)succinate complex (**I**) from N-(hydroxymethyl)nicotina-**Scheme 2.** Synthesis of polymeric cobalt(II)succinate complex (**I**) from N-(hydroxymethyl) nicotinamide.

*2.2. Description of the Structures*  The crystal structure of both compounds **I** and **II** was previously determined using standard single-crystal X-ray diffraction at room temperature, and their models were refined using the standard IAM [46,47]. In this study, the structural parameters of both compounds are significantly more accurate as they were obtained by refining the structure model (all H atoms being refined isotropically and independently) using aspheric atomic scattering factors and the HAR method. Selected bond distances are given in Table S2 (see Supplementary Materials). *2.2. Description of the Structures*  The crystal structure of both compounds **I** and **II** was previously determined using standard single-crystal X-ray diffraction at room temperature, and their models were refined using the standard IAM [46,47]. In this study, the structural parameters of both compounds are significantly more accurate as they were obtained by refining the structure model (all H atoms being refined isotropically and independently) using aspheric atomic scattering factors and the HAR method. Selected bond distances are given in Table S2 (see Supplementary Materials). The preparation of complexes **I** and **II** was carried out by short refluxing from a water + n-pentanol (complex **I**, prepared from nia, Scheme 1), water + methanol (complex **I**, prepared from hmnia, Scheme 2) and water solution (complex **II**). The molar ratio of the reactants was 1:1:2 for cobalt(II) salts, sodium salts of dicarboxylic acids and nicotinamide or *N*-(hydroxymethyl)nicotinamide, respectively. To synthesize the discussed complexes, various molar ratios of cobalt(II) chloride hexahydrate or cobalt(II) nitrate hexahydrate to sodium carboxylate (succinate or fumarate)—Na2carb (where carb is suc or fum anion) and corresponding nicotinamide or *N*-(hydroxymethyl)nicotinamide were tested, specifically 1:1:1; 1:2:1; 1:1:2 and 1:2:2. Well-defined crystalline products were obtained only for the case of 1:1:2 (Schemes 1 and 2). The syntheses of complexes **I** and **II** was very well reproducible in terms of the product quality and yield. Prepared complexes are non-hygroscopic and stable in air and soluble in hot water.

### *2.2. Description of the Structures*

The crystal structure of both compounds **I** and **II** was previously determined using standard single-crystal X-ray diffraction at room temperature, and their models were refined using the standard IAM [46,47]. In this study, the structural parameters of both compounds are significantly more accurate as they were obtained by refining the structure model (all H atoms being refined isotropically and independently) using aspheric atomic scattering factors and the HAR method. Selected bond distances are given in Table S2 (see Supplementary Materials).

The cobalt atoms of both complexes lie in the centre of symmetry and are octahedrally coordinated by two oxygen atoms (O1) of the carboxyl groups of the succinate (**I**) [Co1–O1 = 2.0931(9) Å] or fumarate (**II**) [Co1–O1 = 2.0683(8) Å] anionic ligands, two nitrogen atoms (N1) of the pyridine rings of the nicotinamide ligands [Co1–N1 = 2.1672(12) Å for **I** and 2.1689(10) Å for **II**], and a pair of oxygen atoms (O1W) of the coordinated water

molecules [Co1–O1W = 2.1090(10) Å for **I** and 2.0924(9) Å for **II**] in trans positions (Figure 1). Both substances form 1D coordination chains formed by bonding of Co(nia)2(H2O)<sup>2</sup> units bridged through succinate (**I**) or fumarate (**II**) ligands. The closest Co· · · Co distances are 9.465 Å in **I** and 9.740 in **II**. molecules [Co1–O1W = 2.1090(10) Å for **I** and 2.0924(9) Å for **II**] in trans positions (Figure 1). Both substances form 1D coordination chains formed by bonding of Co(nia)2(H2O)2 units bridged through succinate (**I**) or fumarate (**II**) ligands. The closest Co···Co distances are 9.465 Å in **I** and 9.740 in **II**.

The cobalt atoms of both complexes lie in the centre of symmetry and are octahedrally coordinated by two oxygen atoms (O1) of the carboxyl groups of the succinate (**I**) [Co1–O1 = 2.0931(9) Å] or fumarate (**II**) [Co1–O1 = 2.0683(8) Å] anionic ligands, two nitrogen atoms (N1) of the pyridine rings of the nicotinamide ligands [Co1–N1 = 2.1672(12) Å for **I** and 2.1689(10) Å for **II**], and a pair of oxygen atoms (O1W) of the coordinated water

*Inorganics* **2022**, *10*, x FOR PEER REVIEW 4 of 18

**Figure 1.** Comparison of perspective view of the molecular structure of the complexes: (**a**) **I** and (**b**) **II**. Thermal ellipsoids are drawn at the 50% probability level. Symmetry codes: (i) 1 − *x*, 1 − *y*, 2 − *z*; (ii) −*x*, 2−*y*, 2 − *z*; (iii) 1 + *x*, −1 + *y*, +*z*; (iv) 1 − *x*, 1 − *y*, −*z*; (v) −*x*,−*y*, −*z*; (vi) 1 + *x*, 1 + *y*, +*z*. **Figure 1.** Comparison of perspective view of the molecular structure of the complexes: (**a**) **I** and (**b**) **II**. Thermal ellipsoids are drawn at the 50% probability level. Symmetry codes: (i) 1 − *x*, 1 − *y*, 2 − *z*; (ii) −*x*, 2−*y*, 2 − *z*; (iii) 1 + *x*, −1 + *y*, +*z*; (iv) 1 − *x*, 1 − *y*, −*z*; (v) −*x*,−*y*, −*z*; (vi) 1 + *x*, 1 + *y*, +*z*.

Several ideal six-coordinate geometries were compared with **I** and **II** through SHAPE structural analysis, proposed by S. Alvarez et al. [52–55] (Table S3, see Supplementary Materials). The obtained symmetry measure parameters undoubtedly prove the octahedral shape of coordination polyhedra of reported compounds (S(*O*h) ≈ 0.2 for **I** and 0.3 for **II**) and the next lowest values for the trigonal prism shape (S(*D*3h) ≈ 16.1 for both **I** and **II**) suggest that the Bailar twist does not occur in the reported complexes. Furthermore, the distortion parameter Σ [56,57], calculated from the twelve *cis* angles of the hexacoordinated polyhedron (Table S3, see Supplementary Materials) acquiring zero values when ideal octahedral symmetry is present, can express the degree of angular distortion of coordination polyhedra of reported compounds. Both reported complexes indicate only moderate angular distortion, although more pronounced in the complex **II** (**Σ** = 43°), since its value of distortion parameter is notably higher comparing the one observed in **I** (**Σ** = Several ideal six-coordinate geometries were compared with **I** and **II** through SHAPE structural analysis, proposed by S. Alvarez et al. [52–55] (Table S3, see Supplementary Materials). The obtained symmetry measure parameters undoubtedly prove the octahedral shape of coordination polyhedra of reported compounds (S(*O*h) ≈ 0.2 for **I** and 0.3 for **II**) and the next lowest values for the trigonal prism shape (S(*D*3h) ≈ 16.1 for both **I** and **II**) suggest that the Bailar twist does not occur in the reported complexes. Furthermore, the distortion parameter Σ [56,57], calculated from the twelve *cis* angles of the hexacoordinated polyhedron (Table S3, see Supplementary Materials) acquiring zero values when ideal octahedral symmetry is present, can express the degree of angular distortion of coordination polyhedra of reported compounds. Both reported complexes indicate only moderate angular distortion, although more pronounced in the complex **II** (**Σ** = 43◦ ), since its value of distortion parameter is notably higher comparing the one observed in **I** (**Σ** = 30◦ ).

30°). The 1D coordination chains of both complexes are linked through hydrogen bonds to 3D supramolecular hydrogen-bonding networks. Parameters of hydrogen bonds are given in Table S4 (see Supplementary Materials). Figure S1 (see Supplementary Materials) shows the O–H···O hydrogen bonds between the two 1D coordination chains of compound **I** (top) and compound **II** (bottom). Two coordination chains of **I** are joined via O– H···O hydrogen bonds between coordinated water molecules (O1W) and oxygen atoms (O2) of the carboxyl groups of succinate anions of adjacent coordination chains [O1W– H1WB···O2, with O···O distance of 2.857(1) Å (Table S4, see Supplementary Materials)]. The oxygen atoms (O1W) of coordinated water molecules are linked by O–H···O hydrogen bonds to the oxygen atoms of uncoordinated water molecules (O2W) [O1W– H1WA···O2W, with O···O distance of 2.758(1) Å]. Uncoordinated water molecules (O2W) The 1D coordination chains of both complexes are linked through hydrogen bonds to 3D supramolecular hydrogen-bonding networks. Parameters of hydrogen bonds are given in Table S4 (see Supplementary Materials). Figure S1 (see Supplementary Materials) shows the O–H· · · O hydrogen bonds between the two 1D coordination chains of compound **I** (top) and compound **II** (bottom). Two coordination chains of **I** are joined via O–H· · · O hydrogen bonds between coordinated water molecules (O1W) and oxygen atoms (O2) of the carboxyl groups of succinate anions of adjacent coordination chains [O1W–H1WB· · · O2, with O· · · O distance of 2.857(1) Å (Table S4, see Supplementary Materials)]. The oxygen atoms (O1W) of coordinated water molecules are linked by O–H· · · ;O hydrogen bonds to the oxygen atoms of uncoordinated water molecules (O2W) [O1W–H1WA· · · O2W, with O· · · O distance of 2.758(1) Å]. Uncoordinated water molecules (O2W) are further involved as donor atoms in other O–H· · · O hydrogen bonds where the oxygen atoms (O1) of carboxyl groups [O2W–H2WA· · · O1, with O· · · O distance of 2.794(1) Å], and oxygen atoms (O3) of carboxamide groups of nicotinamide ligands [O2W–H2WB· · · O3, with O· · · O distance of 2.834(1) Å] serve as acceptor atoms of H-bonds. On the other hand, the O–H· · · O hydrogen bonds in crystal structure of **II** are observed only between the oxygen atoms (O1W) of the coordinated water molecules and the oxygen atoms (O2) of the carboxyl groups of fumarate anions [O1W–H1WB· · · O2, with O· · · O distance of 2.758(1) Å], and between the

oxygen atoms (O1W) of the coordinated water molecules and the oxygen atoms (O3) of carboxamide groups of nicotinamide ligands [O1W–H1WA· · · O3, with O· · · O distance of 2.822(1) Å].

The N–H· · · O and C–H· · · O hydrogen bonds of both complexes are shown in the Figures S2 and S3 (see Supplementary Materials). Crystal structures of both complexes show formation of supramolecular rings R<sup>2</sup> 2 (8) [58] by linking two carboxamide groups via a pair of N–H· · · O hydrogen bonds [N2–H2A· · · O3, with N· · · O distance of 2.943(1) Å for **I** and 2.972(1) Å for **II**, (Table S4 and Figure S2, see Supplementary Materials)]. The crystal structure of **II** also shows π-π stacking interactions of the pyridine rings [N1/C2–C5] of nicotinamide ligands (distances between two planes of 3.52 Å, centroid-centroid distance of 3.95 Å, shift distance of 1.77 Å [59]). In Figure S3 (see Supplementary Materials) the supramolecular rings R<sup>2</sup> 1 (7) [58] observed in the crystal structure of both complexes is displayed. These supramolecular rings form nicotinamide molecules and oxygen atoms (O2) of carboxylate groups of succinate (**I**) or fumarate (**II**) ligands through N–H· · · O hydrogen bonds between nitrogen atom (N2) of carboxamide group of nicotinamide ligand and carboxylate oxygen atom (O2) [N2–H2B· · · O2, with N· · · O distance of 3.046(1) Å for **I** and 2.901(1) Å for **II**, (Table S4 and Figure S3, see Supplementary Materials)], and C3–H3· · · O2 hydrogen bonds between carbon atom (C3) of pyridine ring of nicotinamide ligand and carboxylate oxygen atom (O2) [C3–H3· · · O3, with C· · · O distance of 3.357(1) Å for **I** and 3.232(1) Å for **II**].

### 2.2.1. Hirshfeld Surface Analysis

The intermolecular interactions of both complexes have been quantified using Hirshfeld surface analysis. Figures S4 and S5 (see Supplementary Materials) show transparent 3D Hirshfeld surface mapped over *d*norm shape index for complex **I** and complex **II**, respectively. Deep red spots on these surfaces indicate close-contact interactions majority of which is due to intermolecular hydrogen bonds. In the case of **II** π-π stacking interactions between pyridine rings of nicotinamide ligands are also visible (Figure S5, see Supplementary Materials). As shown in the 2D fingerprint plots (Figures S6 and S7, see Supplementary Materials), H· · · H interactions cover 37.3–40.6% range of the total Hirshfeld surface, H· · · O/O· · · H interactions span between 31.1–35.3%, H· · · C/C· · · H interactions cover between 9.1 and 11.1% and C· · · C interactions between 9.0 and 10.6%.

### 2.2.2. X-ray Powder Diffraction

The Le Bail analysis of both samples shows that they are of good crystalline quality without any significant amount of foreign impurity (Figures S8 and S9, see Supplementary Materials). A small residual intensity in difference plot can be assigned to the effect of real structure of powder sample. For example, artifacts of "first derivative" shape on difference plot originate from peak asymmetry of strong diffraction lines at low angle region. It can be concluded that both powder samples of **I** and **II** possess the same crystal structure as the structure of the corresponding single crystals.

### *2.3. Spectral Characterization*

Infrared spectra of complexes **I** and **II** comprise bands confirming the presence of all characteristic functional groups. Some characteristic bands in the IR mid region of the nicotinamide (nia), the sodium salts (Na2suc·6H2O and Na2fum) and cobalt(II) complex **I** (prepared from nia and hmnia) and complex **II** are given in Table S5 (see Supplementary Materials).

IR spectra of model molecules **1** and **2** (Figures S10–S12, see Supplementary Materials) were calculated at the B3LYP/def2-TZVP level of theory after successful geometry optimization. Comparison of experimental and theoretical IR spectra is displayed in Figures S10–S12 and assigned bands of both complexes are collected in Table S5 (see Supplementary Materials).

In the IR spectra of **<sup>I</sup>**, **II** and Na2suc·6H2O the broad bands at ca. 3500 cm−<sup>1</sup> were assigned to ν(O–H) groups from coordinated and uncoordinated water molecules [60]. In theoretical spectra of **1** and **2** the O–H stretching modes were recorded at 3653 and 3628 cm–1 (Table S5, see Supplementary Materials).

In the experimental IR spectra of **I**, **II** and nia, the bands assigned to the symmetric and antisymmetric stretching vibrations of NH<sup>2</sup> groups from nicotinamide are observed in region about 3400–3140 cm−<sup>1</sup> (Table S5, see Supplementary Materials). In calculated spectra only symmetric *ν*s(NH2) (and none antisymmetric) stretching vibration modes were obtained at 3293 cm–1 for both model molecules.

The C–H aromatic stretching modes are observed in experimental spectra at the same wavenumber 3062 cm–1, while calculation gives 3012 cm–1 (complex **I**) and 3018 cm−<sup>1</sup> (complex **II**). Aliphatic stretching vibrations are observed only for complex **I**, the antisymmetric *ν*as(CH2) at 2988 cm–1 and symmetric *ν*s(CH2) at 2955 cm–1 while the calculation predicts 2957 cm−<sup>1</sup> and 2939 cm−<sup>1</sup> , respectively (Table S6, see Supplementary Materials).

Most characteristic bands for dicarboxylate complexes are due to symmetric *ν*s(COO−) and antisymmetric *ν*as(COO−) stretching vibrations of carboxylate groups [61]. While the former are observed at ca. 1370 cm–1, the latter occur at ca. 1560 cm–1 (Table S5, see Supplementary Materials). The difference (∆) between the wavenumber of antisymmetric and symmetric vibration of carboxylate group gives information on the carboxylate bonding mode of complexes. When confronted with disodium succinate (141 cm−<sup>1</sup> ) and disodium fumarate (188 cm−<sup>1</sup> ) which possess ionic carboxylic groups, complexes **I** and **II** show higher values of ∆ (180 cm−<sup>1</sup> and 201 cm−<sup>1</sup> , respectively) which are typical for monodentate *O*-coordination of carboxylate groups [61]. Bis(monodentate) bridging coordination mode of both carboxylate group in all complexes agrees with the structure of complexes as was determined by X-ray analysis.

In the recorded experimental IR spectra for the nia as well as for the complexes under study very strong or strong bands at about 1670, 1620 and 1390 cm–1 were assigned to Amide I (mainly ν(C=O)), Amide II (mainly δ(NH2)) and Amide III (mainly ν(C–N) stretching) (S4). The vibration mode of Amide II and Amide III was calculated at about 1610 and 1370 cm−<sup>1</sup> , respectively (Table S6, see Supplementary Materials). Relatively close positions of the bands assigned to Amide I, Amide II and Amide III for complexes under study to positions of bands in corresponding free molecules of nicotinamide are typical for non-coordinated amide groups [60].

In the UV-Vis absorption spectra, bands at about 220 and 265 nm can be observed, which are assigned to ligand (suc, fum and nia) internal transitions (Figures S13–S15, see Supplementary Materials). The shoulder at 350 nm is assigned to ligand-to-metal charge transfer transition [62] (LMCT, OαCo, NαCo). A band in the visible region between 470 and 480 nm with shoulder between 490 and 506 nm can be assigned to the <sup>4</sup>T1g(F) <sup>→</sup> <sup>4</sup>T1g(P) transition. Obtained electronic spectra are consistent with a strictoctahedral or a tetragonally-distorted-octahedral structure of coordination environment [63].

The electronic spectra of model molecules **1** and **2** were calculated at the same level of theory like the IR spectra. Only one dominant absorption was found for both cases, centred at 354 nm for **1** and 357 nm for **2** (Figure S16, Table S7, see Supplementary Materials). Inspection of the natural transition orbitals (NTOs) [64] associated with this electronic transition suggests that it corresponds to metal-to-ligand charge transfer in both cases (Figure S17, see Supplementary Materials) In both cases, a corresponding peak can be found in the experimental spectra, overlaid by strong intraligand absorption peak.

### *2.4. Static Magnetic Properties*

Magnetic behaviour of complexes **I** and **II** is displayed in Figure 2. In general, the decrease of magnetic moment with decreasing temperature is mostly due to local magnetic anisotropy and/or magnetic coupling interaction. Usually, the simple isotropic form of the interaction is applicable for octahedral Co(II) complexes [65]. A DFT assessment on model systems **11** and **22** (Figure S18, Table S8, see Supplementary Materials) indicated however its negligible contribution and studied systems cannot be considered single-chain magnets. The local magnetism of Co(II) complexes with octahedral coordination environment is

governed by both, spin magnetic momentum and angular magnetic momentum of the ground state [66]. Nevertheless, in some cases the angular momentum can be omitted, and it can be effectively described by simple spin Hamiltonian. As a rule of thumb this approximation can be applied if two lowest Kramers' doublets of the ground term <sup>4</sup>*T*1g are separated from excited doublets by more than 1000 cm−<sup>1</sup> [67]. environment is governed by both, spin magnetic momentum and angular magnetic momentum of the ground state [66]. Nevertheless, in some cases the angular momentum can be omitted, and it can be effectively described by simple spin Hamiltonian. As a rule of thumb this approximation can be applied if two lowest Kramers' doublets of the ground term 4*T*1g are separated from excited doublets by more than 1000 cm−1 [67]. environment is governed by both, spin magnetic momentum and angular magnetic momentum of the ground state [66]. Nevertheless, in some cases the angular momentum can be omitted, and it can be effectively described by simple spin Hamiltonian. As a rule of thumb this approximation can be applied if two lowest Kramers' doublets of the ground term 4*T*1g are separated from excited doublets by more than 1000 cm−1 [67].

Magnetic behaviour of complexes **I** and **II** is displayed in Figure 2. In general, the decrease of magnetic moment with decreasing temperature is mostly due to local magnetic anisotropy and/or magnetic coupling interaction. Usually, the simple isotropic form of the interaction is applicable for octahedral Co(II) complexes [65]. A DFT assessment on model systems **11** and **22** (Figure S18, Table S8, see Supplementary Materials) indicated however its negligible contribution and studied systems cannot be considered singlechain magnets. The local magnetism of Co(II) complexes with octahedral coordination

Magnetic behaviour of complexes **I** and **II** is displayed in Figure 2. In general, the decrease of magnetic moment with decreasing temperature is mostly due to local magnetic anisotropy and/or magnetic coupling interaction. Usually, the simple isotropic form of the interaction is applicable for octahedral Co(II) complexes [65]. A DFT assessment on model systems **11** and **22** (Figure S18, Table S8, see Supplementary Materials) indicated however its negligible contribution and studied systems cannot be considered singlechain magnets. The local magnetism of Co(II) complexes with octahedral coordination

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*2.4. Static Magnetic Properties* 

*2.4. Static Magnetic Properties* 

**Figure 2.** Product of magnetic susceptibility and temperature as a function of temperature (left) and magnetization as a function of magnetic field (right) per one magnetic centre for: (**a**) **I** and (**b**) **II**. Circles: experiment, solid line: optimum parameter fit. **Figure 2.** Product of magnetic susceptibility and temperature as a function of temperature (left) and magnetization as a function of magnetic field (right) per one magnetic centre for: (**a**) **I** and (**b**) **II**. Circles: experiment, solid line: optimum parameter fit. **Figure 2.** Product of magnetic susceptibility and temperature as a function of temperature (left) and magnetization as a function of magnetic field (right) per one magnetic centre for: (**a**) **I** and (**b**) **II**. Circles: experiment, solid line: optimum parameter fit.

To obtain this kind of insight, the magnetic energetic levels of mononuclear model systems **1** and **2** (Figure 3) were inspected using the method SA-CAS[7,5]SCF-NEVPT2- SOI. The resulting energy values of relevant Kramers' doublets are presented in Table S9 (see Supplementary Materials) revealing that the spin Hamiltonian is not justified in these systems (separation of Γ*c* and Γ*b* by 420.1 cm−1 and 272.9 cm−1 for **1** and **2**, respectively). To obtain this kind of insight, the magnetic energetic levels of mononuclear model systems **1** and **2** (Figure 3) were inspected using the method SA-CAS[7,5]SCF-NEVPT2-SOI. The resulting energy values of relevant Kramers' doublets are presented in Table S9 (see Supplementary Materials) revealing that the spin Hamiltonian is not justified in these systems (separation of Γ*<sup>c</sup>* and Γ*<sup>b</sup>* by 420.1 cm−<sup>1</sup> and 272.9 cm−<sup>1</sup> for **1** and **2**, respectively). To obtain this kind of insight, the magnetic energetic levels of mononuclear model systems **1** and **2** (Figure 3) were inspected using the method SA-CAS[7,5]SCF-NEVPT2- SOI. The resulting energy values of relevant Kramers' doublets are presented in Table S9 (see Supplementary Materials) revealing that the spin Hamiltonian is not justified in these systems (separation of Γ*c* and Γ*b* by 420.1 cm−1 and 272.9 cm−1 for **1** and **2**, respectively).

**Figure 3.** A cut-off from respective polymeric systems **I** and **II** forming a neutral mononuclear model molecule: (**a**) **1**; (**b**) **2** (right). The yellow transparent surface shows calculated directional dependence of molecular magnetization.

Therefore, more appropriate Griffith-Figgis Hamiltonian was employed instead [19,38,66], which in atomic units adopts the form of Equation (1).

$$\hat{H} = \sigma \lambda \stackrel{\rightarrow}{\hat{L}} \cdot \stackrel{\rightarrow}{\hat{S}} + \sigma^2 \Delta\_{\text{ax}} \left( \hat{\mathcal{L}}\_z^2 - \hat{L}^2 / \mathfrak{3} \right) + \sigma^2 \Delta\_{\text{rh}} \left( \hat{\mathcal{L}}\_x^2 - \hat{\mathcal{L}}\_y^2 \right) + \left( \sigma \stackrel{\rightarrow}{\hat{L}} + \hat{\mathcal{G}} \stackrel{\rightarrow}{\hat{S}} \right) \cdot \stackrel{\rightarrow}{\hat{B}} \tag{1}$$

Here → *L*ˆ and → *S*ˆ are vector operators of angular momentum and spin, respectively, and → *B* is vector of magnetic field. Parameters of the model are the constant of spinorbit interaction λ, combined parameter *σ* (accounting for covalence of chemical bonds between central ion and ligands along with configuration interaction between ground and excited terms of matching symmetry), parameter of crystal field of axial symmetry ∆*ax*, parameter of crystal field of rhombic symmetry ∆*rh* and gyromagnetic factor *g* which was fixed equal to 2.00. In this Hamiltonian the convention with *σ* <sup>2</sup> absorbed in to ∆*ax* and ∆*rh* can be often encountered [66]. To improve the agreement between the model and experiment the effect of molecular field was included in the fitting procedure (quantified by parameter *zj*). The optimum values of parameters ∆*ax*, ∆*rh*, *σ* and λ obtained from fitting of experimental curves are collected in Table 1 and the match of experimental and optimum fit curves is displayed in Figure 2. The product of error residuals *R*(*χT*) × *R*(*M*) gains value considerably lower than 0.05 indicating very good accordance between model and experiment. The values resulting from ab-initio calculation are collected in Table 2. Comparing the calculated and fitted values, a satisfactory agreement can be concluded for the constant of spin-orbit interaction and parameter of crystal field of axial symmetry, for the parameter of rhombic splitting; however, there is a discrepancy of one order of magnitude in the case of couple **I**/**1**. Since the values obtained as optimum fit of experimental data (Table 1) are model-dependent and simultaneous fit for **II** is not perfect, the values obtained by ab-initio calculation (Table 2) can be considered somewhat more reliable. Finally, the visual assessment of directional dependence of molecular magnetization derived from all SA-CAS[7,5]SCF-NEVPT2-SOI states [38,67] shows, that magnetic anisotropy is of axial-like type (which is in accordance with negative value of parameter ∆*ax*) and that the preferred orientation of molecular magnetization is towards the connecting bridge (Figure 3).

**Table 1.** Magnetic parameters extracted from optimum fit for complexes **I** and **II**.



**Table 2.** Calculated magnetic parameters for model molecules **1** and **2**.

### *2.5. Dynamic Magnetic Properties*

To examine the presence of the slow relaxation of magnetization (SRM), which is the proof of SIM behaviour, the temperature and frequency dependence of the alternatingcurrent (AC) susceptibility was measured at low temperatures for both complexes (see Supplementary Materials, Tables S10 and S11 for a detailed experimental description of AC susceptibility measurements and data analysis). The DC field scan for a limited number of frequencies over four orders of magnitude shows that out-of-phase component of AC susceptibility is silent at *B*DC = 0 T (Figure S19, see Supplementary Materials). This indicates very fast SRM, probably due to the quantum tunnelling of magnetization induced by hyperfine interactions with the nuclear spin and/or dipolar interactions between the spin centres in the lattice. In order to determine the optimal *B*DC to suppress the quantum tunnelling effect, AC susceptibility measurements under various *B*DC fields were applied at 2 K (Figure S19). Upon increasing DC field up to *B*DC = 0.8 T, the out-of-phase component varies, but differently for individual frequencies. This confirms that compounds **I** and **II** show field-induced SRM and the subsequent temperature and frequency dependent measurements were carried out by choosing *B*DC fields at which the out-of-phase components

*χ*" reach the maximal response (*B*DC = 0.1 T for **I** and *B*DC = 0.2 T for **II**). Furthermore, in order to detect changes in mechanisms of the SRM upon the various static magnetic fields, the temperature variable AC susceptibility measurements have been recorded also at *B*DC = 0.02 T for complex **I** as well as at *B*DC = 0.05 T, *B*DC = 0.1 T and *B*DC = 0.15 T for complex **II** (Figures S20–S25). *Inorganics* **2022**, *10*, x FOR PEER REVIEW 10 of 18

> At 2 K and 0.1 T, the out-of-phase component *χ*" of **I** does not yet show maximum, which indicates that the SRM acquires relaxation times *τ* longer than 0.16 s (Figure 4a). However, the reduction of static magnetic field to 0.02 T has already caused the appearance of maxima even at the lowest temperatures of measurement (14 Hz, *τ* = 73 ms at 1.8 K; Figure S20, Table S12). At both fields, the increase of temperature resulted in the obvious shift of the maxima in the *χ*" vs. f dependencies towards higher frequencies and proves that **I** is field-induced SIM. On the contrary, the out-of-phase component *χ*" of complex **II** shows maxima around 63 Hz at 1.8 K which indicates much faster relaxation of magnetisation (*τ* ≈ 2.54 ms) in comparison to complex **I**. Also here, the increase of temperature shifts those maxima towards higher frequencies (shorter relaxation times). All herein reported AC susceptibility measurements recorded at various static magnetic field *B*DC were satisfactorily fitted by one-set Debye model for a single relaxation channel relaxation of magnetisation (Equations (S1) and (S2), see Supplementary Materials). This analysis resulted in the set of four parameters—adiabatic *χ<sup>S</sup>* and isothermal *χ<sup>T</sup>* susceptibilities, the distribution parameters *α*<sup>i</sup> and relaxation times *τ*<sup>i</sup> (see Supplementary Materials, Tables S12 and S13 for **I**, Tables S14–S17 for **II**). hexacoordinated Co(II) single-ion magnets [67,71,72]. The values of Raman exponent were fixed to the recommended value *n* = 9 for Kramers' systems, pre-exponential constant *C*are rather field independent and pre-exponential factor of direct process *A* (if *m* = 4 for Kramers' system [68,69]) has an decreasing trend when the static magnetic field is increased. To put the observed changes in magnetic relaxation in context with the change of geometry of coordination environment, the difference of symmetry measure parameter S(*O*h) from 0.198 (**I**) to 0.306 (**II**) is associated with decrease of relaxation time limit τ0 from 3.2·10−4 s to 1.0·10−5 s at the field of 0.1 T. For comparison, a recent work by Liu et al. [73] reported the effect of subtle geometry changes in isolated octahedral complexes with the same coordination environment CoN2O4 but an easy-plane magnetic anisotropy. In their work, the difference of symmetry measure parameter from S(*O*h) = 0.025 (Co1) and S(*O*h) = 0.067 (Co2) to S(*O*h) = 0.117 induced a small increase of relaxation time limit τ0 from 1.67·10−8 s to 1.88·10−8 s at the field of 0.2 T.

**Figure 4.** (**a**) Frequency dependent out-of-phase *χ*″ components of AC susceptibility for compound **I** recorded at the applied static magnetic field *B*DC = 0.1 T (Solid lines present fits using the onecomponent Debye's model, Equations (S1) and (S2); see Supplementary Materials); (**b**) The ln*τ* vs*.*  1/*T* dependency obtained from AC susceptibility measurements at two static magnetic fields. **Figure 4.** (**a**) Frequency dependent out-of-phase *χ*" components of AC susceptibility for compound **I** recorded at the applied static magnetic field *B*DC = 0.1 T (Solid lines present fits using the one-component Debye's model, Equations (S1) and (S2); see Supplementary Materials); (**b**) The ln*τ* vs. 1/*T* dependency obtained from AC susceptibility measurements at two static magnetic fields.

The obtained thermal dependency of relaxation time, presented in the form ln *τ* vs. 1/*T*, was analysed according to extended relaxation Equation (2) [68,69]

$$\frac{1}{\tau} = \frac{1}{\tau\_0} \exp(-\frac{\mathcal{U}}{\mathcal{k}T}) + \mathcal{C}T^\mathrm{n} + A\mathcal{B}^\mathrm{m}T,\tag{2}$$

where the terms correspond to thermally activated Orbach, Raman and direct processes, respectively (Tables S18–S22, see Supplementary Materials). At first, the high temperature regions of ln *τ* vs. 1/*T* dependencies were fitted to the Arrhenius-like plot, which considers the Orbach relaxation process only (Figures 4b and 5b, dashed lines). Such simple analysis resulted in the preliminary evaluation of the effective energy barrier of spin reversal *U*, which in the case of **I** showed a decrease upon the increase of the *B*DC from 0.02 T (*U* = 52 K) to 0.1 T (*U* = 38 K). On the other hand, complex **II** shows field-independent

**II** recorded at the applied static magnetic field *B*DC = 0.05 T (Solid lines present fits using the onecomponent Debye's model, Equations (S1) and (S2); see Supplementary Materials); (**b**) The ln*τ* vs. 1/*T* dependency obtained from AC susceptibility measurements at four static magnetic fields.

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1.67·10−8 s to 1.88·10−8 s at the field of 0.2 T.

creased.

hexacoordinated Co(II) single-ion magnets [67,71,72]. The values of Raman exponent were fixed to the recommended value *n* = 9 for Kramers' systems, pre-exponential constant *C* are rather field independent and pre-exponential factor of direct process *A* (if *m* = 4 for Kramers' system [68,69]) has an decreasing trend when the static magnetic field is in-

To put the observed changes in magnetic relaxation in context with the change of geometry of coordination environment, the difference of symmetry measure parameter S(*O*h) from 0.198 (**I**) to 0.306 (**II**) is associated with decrease of relaxation time limit τ0 from 3.2·10−4 s to 1.0·10−5 s at the field of 0.1 T. For comparison, a recent work by Liu et al. [73] reported the effect of subtle geometry changes in isolated octahedral complexes with the same coordination environment CoN2O4 but an easy-plane magnetic anisotropy. In their work, the difference of symmetry measure parameter from S(*O*h) = 0.025 (Co1) and S(*O*h) = 0.067 (Co2) to S(*O*h) = 0.117 induced a small increase of relaxation time limit τ0 from

values that are twice as small (*U* = 26 K) in the range 0.1–0.2 T, while the linear fit of the low field measurement at 0.05 T has not yielded reliable results (Table S18). component Debye's model, Equations (S1) and (S2); see Supplementary Materials); (**b**) The ln*τ* vs*.*  1/*T* dependency obtained from AC susceptibility measurements at two static magnetic fields.

**Figure 4.** (**a**) Frequency dependent out-of-phase *χ*″ components of AC susceptibility for compound **I** recorded at the applied static magnetic field *B*DC = 0.1 T (Solid lines present fits using the one-

**Figure 5.** (**a**) Frequency dependent out-of-phase *χ*″ components of AC susceptibility for compound **II** recorded at the applied static magnetic field *B*DC = 0.05 T (Solid lines present fits using the onecomponent Debye's model, Equations (S1) and (S2); see Supplementary Materials); (**b**) The ln*τ* vs. 1/*T* dependency obtained from AC susceptibility measurements at four static magnetic fields. **Figure 5.** (**a**) Frequency dependent out-of-phase *χ*" components of AC susceptibility for compound **II** recorded at the applied static magnetic field *B*DC = 0.05 T (Solid lines present fits using the one-component Debye's model, Equations (S1) and (S2); see Supplementary Materials); (**b**) The ln*τ* vs. 1/*T* dependency obtained from AC susceptibility measurements at four static magnetic fields.

In the more complex analysis of ln τ vs. 1/*T* dependencies, combinations of two or all three relaxation processes from Equation (2) have been used for the fitting procedure (Tables S18–S22, see Supplementary Materials). The most reliable results were obtained for the combination of Orbach and Raman processes in the case of complex **I** and for the combination of all three relaxation processes in the case of complex **II** (Figures 4b and 5b) [68,69].

Although the contribution of Orbach process to the overall slow relaxation magnetisation in hexacoordinated Co(II) complexes is quite rare [70], some recent studies suggest that this two-phonon thermally activated relaxation can be operative also in this type of SIMs [70,71]. Obtained values of energy barriers *U* are relatively small for the class of hexacoordinated Co(II) single-ion magnets [67,71,72]. The values of Raman exponent were fixed to the recommended value *n* = 9 for Kramers' systems, pre-exponential constant *C* are rather field independent and pre-exponential factor of direct process *A* (if *m* = 4 for Kramers' system [68,69]) has an decreasing trend when the static magnetic field is increased.

To put the observed changes in magnetic relaxation in context with the change of geometry of coordination environment, the difference of symmetry measure parameter S(*O*h) from 0.198 (**I**) to 0.306 (**II**) is associated with decrease of relaxation time limit <sup>τ</sup><sup>0</sup> from 3.2 <sup>×</sup> <sup>10</sup>−<sup>4</sup> s to 1.0 <sup>×</sup> <sup>10</sup>−<sup>5</sup> s at the field of 0.1 T. For comparison, a recent work by Liu et al. [73] reported the effect of subtle geometry changes in isolated octahedral complexes with the same coordination environment CoN2O<sup>4</sup> but an easy-plane magnetic anisotropy. In their work, the difference of symmetry measure parameter from S(*O*h) = 0.025 (Co1) and S(*O*h) = 0.067 (Co2) to S(*O*h) = 0.117 induced a small increase of relaxation time limit <sup>τ</sup><sup>0</sup> from 1.67 <sup>×</sup> <sup>10</sup>−<sup>8</sup> s to 1.88 <sup>×</sup> <sup>10</sup>−<sup>8</sup> s at the field of 0.2 T.

### **3. Materials and Methods**

### *3.1. Chemical Reagents*

The chemicals were of reagent grade (Sigma-Aldrich, Darmstadt, Germany) and used without further purification. The organic reagents were purchased from Sigma-Aldrich (Darmstadt, Germany) and TCI Chemicals (Tokyo, Japan); their purity was checked by IR spectra.

### *3.2. Syntheses of the Complexes*
