3.2.1. Synthesis of {[Co(*µ*2-suc)(nia)2(H2O)2]·2H2O}*<sup>n</sup>* (Complex **I**)

(a) From nicotinamide (nia)

Crystals of {[Co(*µ*2-suc)(nia)2(H2O)2]·2H2O}*<sup>n</sup>* (**I**) were obtained by dissolving cobalt(II) nitrate hexahydrate (2 mmol) with equimolar quantity of sodium succinate hexahydrate in 20 cm<sup>3</sup> of water. Nicotinamide (4 mmol) was dissolved in 20 cm<sup>3</sup> of *n*-pentanol. This solution was slowly added to an aqueous solution of cobalt(II) nitrate and Na2suc·6H2O (Scheme 1). The resulting solution was refluxed for 1 h and during the reflux the precipitate was formed. Then the solution was slowly cooled down. The solution was filtered and two layers were created—a layer of pink water solution, which was covered by *n*-Pentanol. These two layers were left to slowly diffuse at ambient temperature. After several weeks purple crystals of complex **I** were filtered off.

Yield: 54% based on Co. Elemental analysis for C16H24CoN4O<sup>10</sup> (M<sup>W</sup> = 491.32) found % (expected %): C 38.7 (38.3); N 11.0 (10.8); H 4.9 (4.7); Co 12.11 (12.30). IR (ATR, cm–1): 3424 sh, 3367 s, 3202 s, 3060 w, 2988 w, 2955 w, 1661 vs, 1559 vs, br, 1395 s, 1367 vs, 1151 m, 1138 m, 780 m, 652 vs, 516 vs. Electronic spectra (nujol mulls, nm): 223, 265, 330 sh, 480, 495 sh.

### (b) From *N*-(hydroxylmethyl)nicotinamide (hmnia)

Complex {[Co(*µ*2-suc)(nia)2(H2O)2]·2H2O}*n*, which has the same composition as complex **I**, was prepared by reaction of cobalt(II) chloride hexahydrate (2 mmol) with disodium succinate hexahydrate (2 mmol) and *N*-(hydroxymethyl)nicotinamide—hmnia (4 mmol) in 50 cm<sup>3</sup> of water (Scheme 2). The resulting solution was stirred under reflux. After 20 min of reflux the colour of the solution changed to purple and after another 20 min the colour changed to pink and a light precipitate was formed. After 2 h of reflux, the solution was slowly cooled down. The precipitate was filtered off and pink solution was left to evaporate at ambient temperature. After few days, purple crystals of complex {[Co(*µ*2-suc)(nia)2(H2O)2]·2H2O}*<sup>n</sup>* were collected.

Yield: 48% based on Co. Elemental analysis for C16H24CoN4O<sup>10</sup> (M<sup>W</sup> = 491.32) found % (expected %): C 38.8 (38.3); N 11.3 (10.8); H 5.1 (4.7); Co 12.2 (12.3). IR (ATR, cm–1): 3430 sh, 3360 sh, 3200 vs, 3061 w, 2989 w, 2959 w, 1656 s, 1597 s, 1546 vs, br, 1395 s, 1366 s, 1150 m, 1133 m, 779 m, 652 vs, 515 vs. Electronic spectra (nujol mull, nm): 208, 267, 325 sh, 480, 506 sh.

### 3.2.2. Synthesis of [Co(*µ*2-fum)(nia)2(H2O)2]*<sup>n</sup>* (Complex **II**)

Pink crystals of [Co(*µ*2-fum)(nia)2(H2O)2]*<sup>n</sup>* (**II**) were acquired by dissolving cobalt(II) nitrate hexahydrate (2 mmol), disodium fumarate (2 mmol) and nicotinamide (4 mmol) in 50 cm<sup>3</sup> mixture of water and methanol (1:1). Solution was refluxed for 2 h (Scheme 1). After 20 min of reflux the precipitate was formed. After 2 h, the solution was slowly cooled down and a pink precipitate was filtered off. The resulting pink solution was left to evaporate at ambient temperature. Pink crystals of complex [Co(*µ*2-fum)(nia)2(H2O)2]*<sup>n</sup>* were separated after few weeks.

Yield: 61% based on Co. Elemental analysis for C16H18CoN4O<sup>8</sup> (M<sup>W</sup> = 453.27) found % (expected %): C 41.8 (42.4); N 12.1 (12.4); H 4.2 (4.0); Co 12.2 (12.4). IR (ATR, cm–1): 3500 m, 3312 s, 3193 s, br, 3060 w, 1687 s, 1622 m, 1595 sh, 1573 vs, 1557 vs, 1393 s, 1368 vs, 1153 m, 1099 m, 754 m, 653 vs, 638 vs, 504 vs. Electronic spectra (nujol mull, nm): 229, 265, 320 sh, 472, 506 sh.

### *3.3. Analysis and Physical Measurements*

Analytical grade (Mikrochem, Pezinok, Slovakia; Acros Organics, Geel, Belgium and TCI Chemical, Tokyo, Japan) chemicals and solvents were used without further purification. Cobalt was determined by electrolysis after mineralization of the complexes; carbon, hydrogen and nitrogen were determined by microanalytical methods (Thermo Electron Flash EA 1112). Electronic spectra (9000–50,000 cm−<sup>1</sup> ) of the powdered samples in nujol

mull were recorded at room temperature on Specord 240 spectrophotometer (Carl Zeiss, Jena, Germany). Infrared spectra in the region of 400–4000 cm−<sup>1</sup> were recorded on a Nicolet 5700 FT-IR spectrometer (Thermo Scientific, Waltham, MA, USA). Spectra of the solid samples were obtained by ATR technique at room temperature. Magnetism of all complexes was measured using a SQUID magnetometer (MPMS-XL7, Quantum Design, San Deigo, CA, USA). The temperature dependence of magnetization was recorded at a constant magnetic field *B* = 0.1 (complex **I**) T or *B* = 0.5 T (complex **II**), corrected for diamagnetic contribution, and displayed as the product of temperature and molar susceptibility (in the cgs-emu unit system). The dependence of magnetization on the magnetic field was measured at two constant temperatures: *T* = 2.0 K and *T* = 4.6 K (complex **I**) or *T* = 2.0 K and *T* = 4.0 K (complex **II**).

### *3.4. Computational Details*

Fitting of the DC magnetic susceptibility and magnetization of both compounds was performed with the program PHI 3.1.3 [74]. Fitting of AC magnetic susceptibility was realized with the help of a home-made program. Calculations of magnetic exchange coupling parameter was performed within ORCA 5.0.2 [75] using model molecules **11** and **22** (Figure S18, see Supplementary Materials), all other calculations were carried out within the program ORCA 4.2.0 [76] with the model molecules **1** and **2** (Figures 3 and S17, see Supplementary Materials). Magnetic coupling was assessed with exchange-correlation density functional approximations B3LYP [77–79], PBE0 [80] and TPSSh [81]. The resolution of identity and chain-of-spheres approximations for Coulomb and exchange integrals (RIJCOSX) [82] were set on. For all atoms the Ahlrichs' basis set def2-TZVP [83,84] was used with an auxiliary basis set def2/J [85]. Prior to this calculation, the positions of all hydrogen atoms were optimized on the model molecules **11** and **22** using the method PBEh-3c [86] and all other atoms were kept in their positions as obtained from the X-ray analysis. The energy levels of crystal-field terms in mononuclear model molecules **1** and **2** were obtained using the state averaged complete active space self-consistent field method (SA-CAS[7,5]SCF) [87] complemented by strongly-contracted *N*-electron valence perturbation theory of second-order (NEVPT2) [88–90] and spin-orbit interaction [91,92]. All 10 spin quartet states and 40 spin doublet reference states were taken into account. The resolution of identity approximation for Coulomb and exchange integrals (RI-JK) [82] were set on. For all atoms the basis set def2-TZVP was used, this time with an automatically generated auxiliary basis set [93]. In all calculations the increased integration grid was set (level 5 in ORCA convention). The positions of all hydrogen atoms were optimized on the model molecules **1** and **2** using the same approach as for **11** and **22**. The molecular magnetization isosurface was visualized by a home-made program using the approach described in [38]. The infrared spectra were calculated at model molecules **1** and **2** with the abovementioned basis set and hybrid exchange-correlation density functional approximation B3LYP [77–79]. No negative vibration frequencies were obtained. The electronic spectra were calculated for molecules **1** and **2** using the time-dependent DFT method with the same setting of basis and exchange-correlation functional like it was for the IR spectra, asking for 15 roots.

### *3.5. Crystal Structure Determination*

Data collections and cell refinement were carried out using four-circle diffractometer STOE StadiVari using Pilatus3R 300K HPD detector, and microfocused X-ray source Xenocs Genix3D Cu HF (Cu*K*<sup>α</sup> radiation) at 100 K. The diffraction intensities were corrected for Lorentz and polarization factors. The absorption corrections were made by LANA [94]. The structures were solved with program SHELXT [95], and refined by the full-matrix least squares procedure of Independent Atom Model (IAM) [96] with SHELXL-2018/3 [97]. The Hirshfeld Atom Refinement (HAR) was carried out using IAM model as a starting point. The wave function was calculated using ORCA 4.2.0 software [76] with basis set def2- TZVPP [83,84] and hybrid exchange-correlation functional PBE0 [80]. The least-squares refinements of HAR model were then carried out with olex2.refine [98], while keeping the

same constrains and restrains as for the SHELXL refinement. The NoSpherA2 implementation [99] of HAR makes used for tailor-made aspherical atomic factors calculated on-the-fly from a Hirshfeld-partitioned electron density. For the HAR approach, all H atoms were refined isotropically and independently. All calculations and structure drawings were done in the OLEX2 package [100]. Final crystal data and HAR's refinement parameters are given in Table S1 (see Supplementary Materials).

### Hirshfeld Surface Analysis

The software Crystal Explorer [101] was used to calculate Hirshfeld surface [102,103] and associated fingerprint plots [104,105]. The Hirshfeld surfaces were obtained using CIF files from HAR model.

### *3.6. Powder X-ray Analysis*

PXRD data of **I** were collected within the 2Θ range 3◦–60◦ on a Brag-Brentano focusing powder diffractometer PHILIPS, model 1730/10. The instrument was equipped with X-ray tube providing Co α radiation, wavelength (0.179021 nm). The experimental conditions were as follow: exciting voltage: 40 kV, anode current: 35 mA, step size: 0.02◦ , time on step 2.4 s.

In the case of **II**, PXRD were collected within the 2Θ range 5◦–60◦ on a Brag-Brentano automated focusing powder diffractometer EMPYREAN. The instrument was equipped with X-ray tube providing Cu Kα radiation. wavelength (0.15405980 nm) and PIXcel3D-Medipix3 1 × 1 detector. The exciting voltage was 45 kV, and the anode current was 40 mA, continuous mode was used.

The simulated powder patterns of **I** and **II** were obtained from single-crystal data employing the Le Bail analysis in the computer program Jana 2006 [106].

### **4. Conclusions**

In conclusion, we have thoroughly reinvestigated two previously described analogous cobalt (II) coordination polymers, where the isolated metal centres are bridged by succinate or fumarate anion. The molecular structures of both compounds were determined with much higher accuracy then before, showing the shortest intermetallic distances in **I** and **II** about 9.5 Å and 9.7 Å, respectively, which imply isolated magnetic environments for both systems.

Static magnetic studies and ab-initio calculations further supported that the Co(II) centres can be considered magnetically isolated and they both show easy axis magnetic anisotropy pointing towards the connecting bridge.

The AC magnetic study showed that the fumarate analogue **II** relaxes comparatively faster at the field 0.1 T than the succinate complex **I**. Although the slow relaxation of magnetization is very susceptible to even small changes in local anisotropy of coordination environment, we can suppose that the enhanced rigidity of the bridge is a non-negligible factor for conservation of molecular magnetization. Indeed, as discussed in a few recent works [107–109], magnetic relaxation is faster if the material possesses low-lying avoidedcrossing points between acoustic and optical phonons, or, in simpler words, if the collective thermal vibrations spread easily to vibrations around the magnetic centre. In this sense we can state that in the studied couple of SIMs, the fumarate bridge could act as better "transmitter" of the vibrational perturbations onto the magnetic centre than the succinate bridge. We can thus conjugate that the less stiff bridges are more appropriate components for targeted design of single-molecule magnets.

**Supplementary Materials:** The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/inorganics10090128/s1, Figures S1–S7: Information on the molecular and supramolecular structure of complexes; Figures S8 and S9: PXRD spectra; Figures S10–S12: Experimental and theoretical IR spectra; Figures S13–S16: Experimental and theoretical electron spectra; Figure S17: NTOs of electron transitions in mononuclear model systems; Figure S18: Binuclear model molecules; Figure S19: Out-of-phase susceptibility component at 2 K; Figures S20–S25: AC susceptibility data at various fields; Tables S1–S4: Crystallographic data and parameters; Tables S5–S6: Characteristic band in IR spectra; Table S7: Calculated bands in electron spectra; Table S8: Calculated magnetic coupling interaction; Table S9: Calculated energies of Kramers' doublets; Tables S10 and S11: Conditions of AC magnetic experiments; Tables S12–S17: Parameters of the extended one-set Debye model, Tables S18–S22: Relaxation parameters using various combinations of mechanisms.

**Author Contributions:** Conceptualization, J.P. and P.S.; syntheses, M.B.; crystallographic measurements and interpretation, J.M.; spectroscopic measurements and interpretation, M.B. and P.S.; magnetism measurements, L'.D. and M.K.; magnetism interpretation, J.J., I.Š. and J.P.; computational studies. J.P.; writing—original draft preparation, M.B., J.M., I.Š., J.P. and P.S.; writing—review and editing, J.P.; supervision, J.P. and P.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** Grant Agencies (Slovakia: APVV-18-0197, APVV-18-0016, APVV-19-0087, VEGA 1/0029/22, KEGA 018-STU-4; Czech Republic: (GA C R 22-23760S) are acknowledged for the financial support. ˇ This article was written thanks to the generous support under the Operational Program Integrated Infrastructure for the project: "Strategic research in the field of SMART monitoring, treatment and preventive protection against coronavirus (SARS-CoV-2)", Project no. 313011ASS8, co-financed by the European Regional Development Fund.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** I.Š. acknowledges the financial support from institutional sources of the Department of Inorganic Chemistry, Palacký University Olomouc, Czech Republic. J.P. is grateful to the HPC centre at the Slovak University of Technology in Bratislava, which is a part of the Slovak Infrastructure of High-Performance Computing (SIVVP project, ITMS code 26230120002, funded by European regional development funds, ERDF), for computational time and resources made available. All authors are thankful to Vladimír Jorík (Slovak University of Technology in Bratislava) for PXRD measurements and analyses.

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

### **References**


### *Article* **Energy Levels in Pentacoordinate d<sup>5</sup> to d<sup>9</sup> Complexes**

**Ján Titiš, Cyril Rajnák and Roman Boˇca \***

Department of Chemistry, Faculty of Natural Sciences, University of SS Cyril and Methodius, 917 01 Trnava, Slovakia

**\*** Correspondence: roman.boca@ucm.sk

**Abstract:** Energy levels of pentacoordinate d<sup>5</sup> to d<sup>9</sup> complexes were evaluated according to the generalized crystal field theory at three levels of sophistication for two limiting cases of pentacoordination: trigonal bipyramid and tetragonal pyramid. The electronic crystal field terms involve the interelectron repulsion and the crystal field potential; crystal field multiplets account for the spin–orbit interaction; and magnetic energy levels involve the orbital– and spin–Zeeman interactions with the magnetic field. The crystal field terms are labelled according to the irreducible representations of point groups D3h and C4v using Mulliken notation. The crystal field multiplets are labelled with the Bethe notations for the respective double groups D'<sup>3</sup> and C'<sup>4</sup> . The magnetic functions, such as the temperature dependence of the effective magnetic moment and the field dependence of the magnetization, are evaluated by employing the apparatus of statistical thermodynamics as derivatives of the field-dependent partition function. When appropriate, the formalism of the spin Hamiltonian is applied, giving rise to a set of magnetic parameters, such as the zero-field splitting *D* and *E*, magnetogyric ratio tensor, and temperature-independent paramagnetism. The data calculated using GCFT were compared with the *ab initio* calculations at the CASSCF+NEVPT2 level and those involving the spin–orbit interaction.

**Keywords:** electronic terms; spin–orbit multiplets; zero-field splitting; pentacoordinate complexes

### **1. Introduction**

A correct interpretation of electronic spectra for transition metal complexes (d-d transitions), magnetometric data (magnetic susceptibility and magnetization), and spectra of electron spin resonance requires appropriate theoretical support. A traditional approach is represented by the crystal field theory, which is well elaborated for octahedral complexes (O<sup>h</sup> symmetry), even with tetragonal (trigonal) distortion (D4h, D3d) [1–5]. Analogously, tetrahedral patterns (Td) and their distortion daughters to prolate and/or oblate bispheoids (D2d) are also known. However, one is rather helpless when dealing with pentacoordination in its limiting cases represented by trigonal bipyramids (D3h) and tetragonal pyramids (C4v) and especially for intermediate geometries on the Berry rotation path (C2v).

A target of the present work is to elucidate a comprehensive view of the crystal field terms and crystal field multiplets in the case of pentacoordinate d<sup>5</sup> to d<sup>9</sup> complexes. Whereas multielectron crystal field terms are labelled according to Mulliken notation (A, B, E, T), the involvement of the spin–orbit interaction requires a passage from common symmetry point groups to double groups; therefore, crystal field multiplets are labelled according to Bethe notation (Γ<sup>1</sup> to Γ8).

Geometries belonging to point groups Oh, Td, D4h, or D2d are mostly omitted hereafter; numerical computer-assisted treatment is necessary when ligands occupy arbitrary positions. This approach is slightly more complicated, involving algebra of complex numbers due to the occurrence of complex spherical harmonic functions fixing the ligand positions. The treatment used below is termed the Generalized Crystal Field Theory, as outlined elsewhere [6].

**Citation:** Titiš, J.; Rajnák, C.; Boˇca, R. Energy Levels in Pentacoordinate d<sup>5</sup> to d<sup>9</sup> Complexes. *Inorganics* **2022**, *10*, 116. https://doi.org/10.3390/ inorganics10080116

Academic Editor: Wolfgang Linert

Received: 15 July 2022 Accepted: 5 August 2022 Published: 12 August 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

The eigenvalues of the model Hamiltonian refer to the energy levels at a given approximation. The eigenvectors bear all information about the symmetry of the wave function; therefore, they can be utilized to assign irreducible representations (IRs) either of the crystal field terms |*d n* : (*LS*); *G* : Γ*γa*i or the crystal field multiplets *d n* : (*J*); *G* 0 : Γ 0*γ* 0 *a* 0 . The irreducible representation within point group *G* is Γ, *γ* (its component when IR is degenerate), and *a* (the branching (repetition) number). The same holds true for double group *G* 0 .

### **2. Results**

The generalized crystal field theory (GCFT) applied below is fully described elsewhere, along with the closed formulae for the matrix elements of the involved operators in the basis set of the electronic atomic terms |Ψi = |*d n* : *νLSMLMS*i, where the apparatus of the irreducible tensor operators has been utilized [6,7]. (Here, the seniority number (*ν*) for the terms can distinguish between terms possessing the same set {*LS*}; the quantum numbers adopt their usual meaning [8]). These matrix elements refer to five operators:


The position of ligands (L) is arbitrary and fixed by the polar coordinates {*ϑL*, *ϕL*}. The model Hamiltonian involves three important cases:


The energy levels of crystal field multiplets for the half-integral spin (*S* = 1/2, 3/2, 5/2) appear as Kramers doublets and remain doubly degenerate in the absence of a magnetic field. This is the case of high-spin Fe(III), Mn(II), Co(II), and Cu(II) complexes.

Traditional crystal field theory operates with a set of collective parameters, such as 10*Dq* = ∆, *Ds*, *Dt*, etc., and is useful for cases certain symmetry, such as Oh, Td, and D4h, all of which are derived from the crystal field poles (*F*4(L) and eventually *F*2(L)), e.g.,


The crystal field poles originate in the partitioning of the matrix elements of the crystal field potential into radial (*R*) and angular (*A*) parts in the polar coordinates (*RK*, *ϑK*, *ϕK*).

$$
\left< \Psi'(\mathsf{R}, A) \middle| \hat{\mathcal{V}}\_{\mathrm{cf}}(\mathsf{R}, A) \middle| \Psi(\mathsf{R}, A) \right> = \left< \Psi'(\mathsf{R}) \middle| \hat{\mathcal{V}}\_{\mathrm{cf}}(\mathsf{R}) \middle| \Psi(\mathsf{R}) \right> \cdot \left< \Psi'(A) \middle| \hat{\mathcal{V}}\_{\mathrm{cf}}(A) \middle| \Psi(A) \right> \tag{1}
$$

The integration of the angular part yields some values (manually calculated for some cases, such as O<sup>h</sup> symmetry). This part contains the spherical harmonic functions *Yk*,*<sup>q</sup>* (*ϑK*, *ϕK*) for the positions of ligand *K*, and in general, it is a complex number. The radial part contains the metal–ligand distance (*RK*) and defines the crystal field poles:

$$\,^kF\_k(R\_K) = \int\_0^\infty R\_{nl}^\*(r) \frac{r\_<^k}{r\_>^{k+1}} R\_{nl}(r) r^2 \mathrm{d}r \approx \left\langle r^k \right\rangle / \,^k\!R\_K^{k+1} \tag{2}$$

(*k* = 0, 2, 4), where the integration runs over the electronic coordinates. The matrix elements of the crystal field operators can be expressed as:

$$\begin{aligned} & \left< l^{\text{tr}} \text{L} \text{SM}\_{L} \text{M}\_{S} \left| \hat{V}^{\text{cf}} \right| l^{\text{tr}} l' L' S' M\_{L}' M\_{\text{S}}' \right> \\ &= \delta\_{S,S'} \delta\_{\text{M}\_{S},\text{M}\_{S}'} \sum\_{k=0,2,4}^{2l} \left[ \left< l \left| \mathbf{C}^{k} \right| l \right> \left( \frac{4\pi}{2k+1} \right)^{1/2} \sum\_{K=1}^{N} z\_{K} F\_{\text{k}}(\mathbf{R}\_{K}) \cdot Y\_{\mathbf{k},q}^{\*} (\boldsymbol{\theta}\_{\mathbf{K}'} \boldsymbol{\varphi}\_{K}) \right] \\ & \cdot \left[ \left< l^{\text{tr}} \text{L} S \right| \left| \mathbf{U}^{\text{k}} \right| l^{\text{tr}} l' L' S' \right> (-1)^{L-M\_{\text{L}}} \cdot \left( \begin{array}{cccc} \text{L} & k & L' \\ -M\_{\text{L}} & q & M\_{\text{L}}' \end{array} \right) \right] \end{aligned} \tag{3}$$

where for the reduced matrix elements <sup>D</sup> *l <sup>n</sup>vLS* **U***k l nv* 0*L* 0*S* 0 E , D *l* **C** *k l* E and the 3j symbols, closed formulae exist [6,7] and can be evaluated with a desktop computer.

In practice, the crystal field poles are not subject to evaluation; they are taken as parameters of the theory and depend on the quality of the ligand (halide, amine, phosphine, cyanide, carbonyl, etc.), as well as the quality and oxidation state of the central atom. For practical applications, the spectroscopic series is used according to the ∆-value [4]. The values of ∆ can be deduced from the transitions observed in the electronic d-d spectra. Moreover, the ∆ value can be estimated based on the empirically determined increments *f* <sup>L</sup> for the ligands and *g*<sup>M</sup> for the central atoms

$$
\Delta = f\_{\mathbf{L}} \cdot \mathbf{g}\_{\mathbf{M}} \tag{4}
$$

However, the same ligand can produce different crystal field strengths depending on the actual metal–ligand distance (cf. Equation (2)). For instance, the -NCS– group can be attached at distance R(Ni–N) = 2.2 or 2.0 Å. In the second case, it produces a much stronger crystal field.

For the hexacoordinate complexes, value of *F*<sup>4</sup> = 5000 cm−<sup>1</sup> refers to ∆(Oh) = 8300 cm−<sup>1</sup> , which is a weak crystal field (appropriate for the halido ligand). Then, *F*<sup>4</sup> = 15,000 cm−<sup>1</sup> is equivalent to ∆(Oh) = 25,000 cm−<sup>1</sup> , which refers to the strong crystal field (appropriate for cyanido or carbonyl ligands). For tetrahedral complexes, *F*<sup>4</sup> = 5000 (15,000) cm−<sup>1</sup> refers to ∆(Td) = 3700 (11,100) cm−<sup>1</sup> .

### *2.1. Crystal Field Terms*

Figure 1 displays the relative energies of the crystal field terms (not to scale) for individual d*<sup>n</sup>* configurations. These result from the GCFT calculations using the weak crystal field characterized by the crystal field poles *F*4(L) = 5000 cm−<sup>1</sup> for each ligand. For the tetragonal pyramid (C4v), the angle L<sup>a</sup> -M-L<sup>e</sup> = 104 deg was maintained. The passage from the fully rotation group R<sup>3</sup> of a free atom to point group D3h or C4v is shown as the splitting of the atomic terms by the crystal field. The literature outlines the branching rules for such a reduction process [9].

The character tables for the point groups usually assign the dipole moment components to the IRs; these are useful in determining the selection rules for the excitation energies. For instance, within group D3h, the direct product of IRs is A 0 <sup>1</sup> ⊗ A 00 <sup>2</sup> = A 00 <sup>2</sup> ∈ *z*, meaning that the *z* component of the dipole moment is active in transition A 0 <sup>1</sup> → A 00 2 , yielding the non-zero transition moment A 0 1 |*µz*|A 00 2 6= 0 (orbitally allowed transition). On the contrary, A0 <sup>1</sup> ⊗ A 00 <sup>1</sup> = A 00 <sup>1</sup> <sup>∈</sup>/ *<sup>x</sup>*, *<sup>y</sup>*, *<sup>z</sup>* and thus transition A 0 1 *µx*,*y*,*<sup>z</sup>* A 00 1 = 0 are forbidden.

In addition to the energy levels, Figure 1 also shows the allowed/forbidden polarized electronic dipole transitions, which are displayed as solid/dashed arrows. These data can be compared with the observations of the electronic d-d spectra [10].

**Figure 1.** Crystal field terms for d*<sup>n</sup>* configurations (energies not to scale). The electronic terms are labelled by exploiting the IRs of the point group, with the spin multiplicity as the superscript index and degeneracy in parentheses, e.g., <sup>4</sup>G(36). Dipole transitions: forbidden—dashed arrows, allowed—solid arrows.

### *2.2. Crystal Field Multiplets*

The crystal field terms represent a starting point for the further precision of the energy levels: upon introduction of the spin–orbit interaction, the crystal field terms are further spit into a set of crystal field multiplets (energy levels in the zero magnetic field) [11,12]. The basis set and the resulting multiplets contain 256, 210, 120, 45 and 10 members for electron configurations d<sup>5</sup> through d<sup>9</sup> , respectively. In this case, the energy levels are labelled using the Bethe notation for the IRs within double group G'. These symbols involve Γ<sup>1</sup> through Γ8, and their degeneracy is shown parentheses, e.g., Γ4(2). (The IR tables for the double groups are useful for practical reasons).

The spin and the orbital parts of the wave function are assessed independently. For instance, in D3h the level, <sup>6</sup>A<sup>1</sup> <sup>0</sup>(6) transforms its spin according to {2Γ<sup>4</sup> + (Γ<sup>5</sup> + Γ6)}. The orbital part matches A<sup>1</sup> = Γ1. Finally, the spin–orbit wavefunction transforms according to the direct product {2Γ<sup>4</sup> + (Γ<sup>5</sup> + Γ6)}⊗Γ1, and the result is {2Γ<sup>4</sup> + (Γ<sup>5</sup> + Γ6)}. In this special case, the levels (Γ<sup>5</sup> + Γ6) form a complex conjugate pair that can be abbreviated as Γ5,6(2) or simply Γ5(2). To this end, upon passage from the D3h to double group D'3, the crystal field term <sup>6</sup>A<sup>1</sup> <sup>0</sup>(6) is split into a set of {2Γ4(2) + Γ5,6(2)} multiplets. However, this part of the theory says nothing about the relative energies of the final three Kramers doublets; these result from numerical calculations by GCFT.

The principal result of the CGTF calculations with spin–orbit coupling in the complete space spanned by d*<sup>n</sup>* configurations is the spectrum of the crystal field multiplets. The lowest zero-field energy gaps are abbreviated as *δ*1, *δ*2, . . . , provided that the energy of the ground multiplet (*δ*0) is set to zero (Table 1). For the non-degenerate ground state (A or B type), the lowest multiplet gaps relate to the axial zero-field splitting parameter (*D*). For d 5 -Fe(II) (and, analogously, d<sup>5</sup> -Mn(III)), the sequence of the spin–orbit multiplet does not strictly follow *D* and 4*D* (there is a small difference (*δa*) around 4*D*). For Cu(II), the ground electronic term is not split by the spin–orbit interaction; however, the spin–orbit multiplets are slightly influenced by the spin–orbit coupling. The concept of the *D* parameter is strictly related to the spin–Hamiltonian theory.

**Table 1.** Multiplet gaps (in cm−1) calculated by GCFT for pentacoordinate systems.


The effect of the spin-orbit interaction leading to the passage from the crystal-field terms to the crystal-field multiplets is depicted in Figure 2.

**Figure 2.** Crystal field multiplets for d*<sup>n</sup>* configurations (energies not to scale). The crystal field multiplets are labelled by exploiting the IRs of the double group. Contributions to the Λ tensor: forbidden—dashed arrows, allowed—solid arrows.

### *2.3. Zero-Field Splitting*

The concept of the spin Hamiltonian is a popular and very useful tool for interpretation of the spectra of electron paramagnetic resonance, as well as for analysis of DC magnetometric data. The key formulae of the spin Hamiltonian are based on consideration of only the spin kets |*S*, *MS*i of non-degenerate ground term A or B. The second-order perturbation theory offers the Λ tensor in the following form:

$$
\Lambda\_{ab} = -\hbar^{-2} \sum\_{K \neq 0} \frac{\langle \mathbf{0} | \hat{L}\_a | \mathbf{K} \rangle \langle \mathbf{K} | \hat{L}\_b | \mathbf{0} \rangle}{E\_K - E\_0} \tag{5}
$$

where *K* runs over all excited electronic terms, and the magnetic tensors are expressed as follows:

• the *κ tensor* (reduced, temperature−independent paramagnetic susceptibility tensor):

$$
\kappa\_{ab}^{\text{para}} = \mu\_\text{B}^2 \Lambda\_{ab} \tag{6}
$$

• the *g tensor* (magnetogyric ratio tensor):

$$\mathbf{g}\_{ab} = \mathbf{g}\_{\mathbf{e}} \delta\_{ab} + 2\lambda \Lambda\_{ab} \tag{7}$$

• the *D tensor* (spin–spin interaction tensor):

$$D\_{ab} = \lambda^2 \Lambda\_{ab} \tag{8}$$

This approximation fails in the case of orbital (pseudo) degeneracy. The matrix elements of the angular momentum 0 *L*ˆ *a K* can be assessed by exploiting the symmetry of the ground and excited crystal field terms; the matrix element is non-zero only if the direct product (Γ<sup>0</sup> ⊗ Γ*<sup>K</sup>* = Γ*Lx*,*Ly*,*Lz* + . . .) contains the irreducible representation of at least one component of the angular momentum. For instance, within group D3h, A 0 <sup>1</sup> ⊗ E <sup>00</sup> = E <sup>00</sup> ∈ *Lx*,*<sup>y</sup>* and the common character tables indicate that the result contains the irreducible representation of *L<sup>x</sup>* and *Ly*.

The spin Hamiltonian parameters calculated via the GCFT are listed in Table 2. For Fe(III) and Mn(II), the ground electronic term <sup>6</sup>A does not allow transitions to excited terms with different spin multiplicities. Therefore, *D* = 0, *g<sup>i</sup>* = *g*<sup>e</sup> in this approximation. In this case, the spin Hamiltonian formalism is insufficient, so <sup>6</sup>A<sup>1</sup> + <sup>4</sup>T<sup>1</sup> terms must be considered for the O<sup>h</sup> symmetry [13].

**Table 2.** Calculated spin Hamiltonian parameters for pentacoordinate systems.


<sup>1</sup> SI unit for *χ*TIP is m<sup>3</sup> mol−<sup>1</sup> . Calculated according to the weak-field limit of *F*<sup>4</sup> = 5000 cm−<sup>1</sup> .

The spin Hamiltonian is often presented in the following form:

$$
\hat{H}^{\text{zfs}} = [D(\hat{S}\_z^2 - \hat{S}^2/3) + E(\hat{S}\_x^2 - \hat{S}\_y^2)] \hbar^{-2} \tag{9}
$$

where the *D* tensor is considered diagonal and traceless, yielding only two independent parameters: the axial zero-field splitting parameter (*D*) and the rhombic zero-field splitting parameter (*E*). This form is widely used for analysis of magnetometric and EPR data. According to convention, the rhombic part is minor: |*D*| > 3*E* > 0. *D* serves as a measure

of zero-field splitting. This energy gap can also be measured also by FAR-infrared spectroscopy (FIRMS and FDMRS techniques), inelastic neutron scattering, calorimetry, etc. [14].

As mentioned above, the case of d<sup>6</sup> -Fe(II) or d<sup>6</sup> -Mn(III) is specific, as for C4v geometry, the sequence of the spin–orbit multiplets differs depending on the exact multiplet splitting {0, *δ*1(2), *δ*220(1 + 1) and the spin Hamiltonian formalism {0, *D*(2), 4*D*(2)}; the number in parentheses corresponds to the multiplicity. The ground crystal field term is <sup>5</sup>B2; the orbital and spin parts transform as B<sup>2</sup> → Γ4, *S* = 2 → Γ<sup>1</sup> + Γ<sup>3</sup> + Γ<sup>4</sup> + Γ5, and their direct product is Γ4⊗(Γ<sup>1</sup> + Γ<sup>3</sup> + Γ<sup>4</sup> + Γ5) = Γ1(1) + Γ2(1) + Γ4(1) + Γ5(2). Only Γ5(2) is doubly degenerate, whereas the remaining multiplets are nondegenerate: Γ1(1), Γ2(1), and Γ4(1). The GCFT calculations for d<sup>6</sup> -Fe(II) in the complete basis set of 210 kets obtains Γ<sup>4</sup> as the ground multiplet and the multiplet splitting *<sup>E</sup>*(Γ5) <sup>−</sup> *<sup>E</sup>*(Γ4) = *<sup>δ</sup>*<sup>1</sup> = 0.31 cm−<sup>1</sup> ; *E*(Γ1) − *E*(Γ4) = *δ*<sup>2</sup> = 1.64 cm−<sup>1</sup> ; *E*(Γ2) − *E*(Γ4) = *δ*<sup>2</sup> <sup>0</sup> = 1.87 cm−<sup>1</sup> . This feature is reflected in the spectrum of electron paramagnetic resonance. Details about the symmetry rules are listed in Supplementary Information.

Table 3 shows a comparison of the d*<sup>n</sup>* configurations from the viewpoint of the spin Hamiltonian formalism. This table is also enriched by data for d<sup>1</sup> to d<sup>4</sup> configurations, as well as data for the intermediate geometry with C2v symmetry and *τ*<sup>5</sup> = 0.47. Table 4 analogously summarizes data for the hexacoordinate complexes.


**Table 3.** Review of the SH formalism for pentacoordinate systems <sup>1</sup> .

<sup>1</sup> The Addison structural parameter (*τ*<sup>5</sup> = (*<sup>β</sup>* <sup>−</sup> *<sup>α</sup>*)/60), where: *<sup>β</sup>* <sup>&</sup>gt; *<sup>α</sup>* are the two greatest valence angles of the coordination center [15]. Data on *D* and *E* in cm−<sup>1</sup> calculated with *F*<sup>4</sup> = 5000 cm−<sup>1</sup> .

**Table 4.** Review of the SH formalism for hexacoordinate systems with tetragonal distortion <sup>1</sup> .


1 JT points to a strong Jahn–Teller effect, owing to which a spontaneous symmetry descent proceeds. Data on *D* in cm−<sup>1</sup> calculated with *F*<sup>4</sup> = 5000 cm−<sup>1</sup> .

### *2.4. DC Magnetic Functions*

The magnetic energy levels *εi*,*a*(*Bm*) result from the diagonalization of the interaction matrix ((a) + (b) + (c) + (d) + (e)), which includes interelectronic repulsion, crystal field potential, spin–orbit coupling, and orbital and Zeeman terms in the applied magnetic field. Statistical thermodynamics offers formulae for magnetization and magnetic susceptibility

when the partition function is evaluated for three reference fields: *B<sup>m</sup>* = *B*<sup>0</sup> − *δ*, *B*0, *B*<sup>0</sup> + *δ* (allowing numerical derivatives):

$$Z\_{\mathbf{a}}(T, \mathcal{B}\_{\mathfrak{m}}) = \sum\_{i} \exp[\varepsilon\_{i, \mathfrak{a}}(\mathcal{B}\_{\mathfrak{m}})/k\_{\mathfrak{B}}T] \tag{10}$$

Hence, the molar magnetization is:

$$(M\_{\rm mol})\_a = \frac{RT}{Z\_a} \left(\frac{\partial Z\_a}{\partial B\_a}\right)\_T \tag{11}$$

The molar magnetic susceptibility is expressed as:

$$(\chi\_{\rm mol})\_{ab} = \mu\_0 \left( \frac{\partial (M\_{\rm mol})\_a}{\partial B\_b} \right)\_T \tag{12}$$

where the physical constants adopt their usual meaning. The index *a* refers either to the Cartesian coordinates {*x*, *y*, *z*} or to the grid point over a sphere along which the magnetic field is aligned, which is used to obtain the powder-sample average. Therefore, the magnetic susceptibility and magnetization are functions of discrete parameters (atomic parameters *B*M, *C*M, and *ξ*M; ligand positions *θ*<sup>L</sup> and *ϕ*L; crystal field poles *F*4(L); and eventually *F*2(L)), as well as the continuous parameters, such as the reference field (*Bm*) and temperature (*T*).

The modelling of the magnetization and susceptibility for pentacoordinate d*<sup>n</sup>* systems is presented in Figures 3 and 4. A counterpart of these graphs for the tetragonally distorted octahedral systems can be found elsewhere [16]. In the case of zero-field splitting with an orbitally non-degenerate ground term, the effective magnetic moment in the hightemperature limit of 300 K remains almost linear with zero slope; at low temperature, it is reduced. This is the case of d<sup>5</sup> -D3h, d<sup>5</sup> -C4v, d<sup>6</sup> -C4v, d<sup>7</sup> -D3h, and d<sup>8</sup> -C4v. For d<sup>9</sup> -D3h and d<sup>9</sup> - C4v, zero-field splitting is absent, so these systems follow the Curie law. The magnetization saturates to the value of *M*<sup>1</sup> = *M*mol/(*N*A*µ*B) = *g*av*S* when the zero-field splitting is small. This is the case of d<sup>5</sup> -D3h, d<sup>5</sup> -C4v, d<sup>6</sup> -C4v, d<sup>9</sup> -D3h, and d<sup>9</sup> -C4v; exceptions are d<sup>7</sup> -D3h and d 8 -C4v, with large zero-field splitting *D* parameters.

Systems with E-type orbitally doubly degenerate ground terms, such as d<sup>6</sup> -D3h, d<sup>7</sup> - C4v, and d<sup>8</sup> -D3h behave differently. The effective magnetic moment is enlarged, and it passes through a round maximum. The magnetization is also suppressed and does not reach saturation until *B* = 10 T.

A positive slope of the effective magnetic moment reflects the effect of the low-lying excited electronic terms mixed considerably with the ground term via the spin–orbit interaction. This results in temperature-independent paramagnetism, *χ*TIP > 0. This term, along with the underlying diamagnetism (*χ*dia < 0), need be subtracted from the measured temperature dependence of the magnetic susceptibility. With respect to the underlying diamagnetism, a method of additive Pascal constants is useful and frequently utilized. However, for temperature-independent paramagnetism, the amount of information is considerably limited [6,7].

**Figure 3.** Magnetization functions at *T* = 2.0 K calculated by GCFT for a weak (strong) crystal field with *F*<sup>4</sup> = 5000 (15,000) cm−<sup>1</sup> .

**Figure 4.** DC susceptibility functions at *B* = 0.1 T (Equation (12)) converted to the effective magnetic moments as calculated by GCFT for a weak (strong) crystal field with *F*<sup>4</sup> = 5000 (15,000) cm−<sup>1</sup> .

### *2.5. AC Magnetic Susceptibility*

In the oscillating magnetic fields (usually with a low amplitude of *B*AC = 0.3 mT and a frequency range of *f* = 10−2–10<sup>5</sup> Hz), the measured magnetic moment of the specimen has two components: in-phase and out-of-phase. This is easily transformed into two components of AC susceptibility: *χ* 0 (dispersion) and *χ*" (absorption). The absorption component is a measure of the resistivity of the sample used to alter its magnetization; it provides information about the relaxation time, which is a function of temperature, frequency (*f*), and the external applied field (*B*DC). The relaxation time can be inferred from the position of the maximum at the out-of-phase susceptibility (*f* "max) with the following formula: *τ* = 1/(2π*f* "max). It has been reported that the sample can exhibit two or more relaxation channels and that their absorption curves can overlap or merge to form a shoulder. The whole AC susceptibility can be fitted by exploiting the generalized Debye equation [17,18]:

$$\chi(\omega) = \chi\_{\rm S} + \sum\_{k}^{K} \frac{\chi\_{k} - \chi\_{k-1}}{1 + (\mathrm{i}\omega \tau\_{k})^{1-a\_{k}}} \tag{13}$$

where *K* is the number of relaxation channels, *χ*<sup>S</sup> is the common adiabatic susceptibility (high-frequency limit), *χ<sup>k</sup>* is the thermal susceptibilities, *α<sup>k</sup>* is the distribution parameters, *τk* is the relaxation times, and the circular frequency is *ω* = 2π*f*. This complex equation can be decomposed into a real and imaginary part.

The slow magnetic relaxation includes several mechanisms that can be collected to a single equation for the reciprocal relaxation time:

$$\tau^{-1} = \tau\_0^{-1} \exp(-\mathcal{U}\_{\text{eff}}/k\_{\text{B}}T) + \mathcal{C}\_{\text{R}}T^{\text{ll}} + \mathcal{C}\_{\text{pb}}T^{\text{l}} + AB^{\text{mt}}T + D\_1/(D\_2 + B^2) \tag{14}$$

The first term describes the thermally activated Orbach process, which is associated with the height of the barrier to spin reversal (*U*eff); the second is the Raman term, with the temperature exponent typically *n* = 5–9; next is the phonon bottleneck term, with *l* ~ 2; the fourth term describes the direct relaxation process, with *m* = 2–4; the last term refers to the quantum tunnelling of magnetization throughout the barrier to spin reversal. The reciprocating thermal behavior was recently registered with a term analogous to the phonon bottleneck but a negative temperature exponent (*l* ~ −1) [18].

The effectiveness of the slow magnetic relaxation is, as a rule, evaluated by the value of *U*eff (when the Orbach process applies). It is assumed that it is related to the axial zero-field splitting parameter (*D*), which must be negative, and the molecular spin (*S*) [19]:

$$\mathcal{U}\_{\rm eff} = \left| D \right| (S^2 - 1/4),\tag{15}$$

which holds true for Kramers systems with half-integral spin (e.g., *S* = 3/2 for CoII); for non-Kramers systems with an integer spin, the factor <sup>1</sup> 4 is dropped (e.g., *S* = 1, for NiII). It is common practice for the *U*eff and the pre-exponential factor (*τ*0) to be subtracted using the Arrhenius-like plot ln(*τ*) vs. 1/*T* (Figure 5-left): a few high-temperature points are fitted by the straight line, tangential of which refers to *U*eff. However, "high-temperature points" refer to the highest temperature among the data considered in our analysis, so there still could be points yielding a higher tangential and thus *U*eff. A preferred approach involves plotting ln(*τ*) vs. ln(*T*), where the temperature exponent recovering the high-temperature data refers to the slope (Figure 5, right). When the temperature coefficient is *n* > 9, instead of the Raman process the Orbach process is applied.

**Figure 5.** Contributions to the relaxation time. (**Left**): Orbach process (high-temperature, black, *U*eff/*k*<sup>B</sup> = 37 K). (**Right**): direct process (low-temperature, green, *m* ~ 1, Raman process; intermediate temperature, blue, *n* > 5; red *n* < 9). Data adapted from [20] for a mononuclear FeIII complex. Straight-line formula: *y* = b [0] + b [1]*x*.

For high-spin Co(II) complexes with *S* = 3/2, eqn (15) implies a relationship of *U* = 2|*D*|. A collection of experimental data for a series of tetracoordinate CoII complexes is shown in Figure 6 based on the analysis of higher-temperature, high-frequency relaxation data in terms of the Orbach process. Evidently, a correlation of *U* vs. 2|*D*| fails. *D* is a field-independent quantity, whereas the extracted value of *U* depends upon the applied magnetic field. A positive value of *D* contradicts the *D*-*U* paradigm; however, SIMs behavior can occur (the Raman mechanism is likely the leading term). With increased barrier to spin reversal (*U*), the extrapolated relaxation time (*τ*0) is shortened, irrespective of the sign of the *D* parameter. A violation of the *D*-*U* paradigm has been discussed elsewhere with consideration of anharmonicity contributions [21].

**Figure 6.** Collection of relaxation data for tetracoordinate Co(II) complexes, *S* = 3/2. Full points for *D* < 0, empty for *D* > 0. Dashed line—a hypothetical *D*-*U* paradigm. (1/*k*B) = 1.439 K/cm−<sup>1</sup> .

### **3. Discussion**

The GCFT approach enables fast and "continuous" mapping of the energy levels, such as electronic terms and the spin–orbit multiplets: one is free to changing the ligand positions {*θ*L, *ϕ*L} from regular coordination polyhedra to distorted polyhedra and to alter the crystal field poles *F*4(L) and, eventually, *F*2(L). On the contrary, the modern ab initio calculations provide high-quality data on energy levels but only for the unique geometry of the complex under investigation. Therefore, it is interesting to utilize and compare both approaches.

*Ab initio* calculations have been performed using ORCA software [22] with respect to the experimental geometry of the complexes resulting from X-ray structural analysis (the corresponding cif files are deposited in the Cambridge Crystallographic Data Centre). The relativistic effects were included in the calculations with a second-order Douglas–Kroll– Hess (DKH) procedure. An extended basis set TZVP of Gaussian functions was used, e.g., BS1 = [17s11p7d1f] and BS2 = [17s12p7d2f1g] for Ni(II). The calculations were based on state-average complete active-space self-consistent field (SA-CASSCF) wave functions. The active space of the CASSCF calculations comprised eight electrons in five metal-based dorbitals. The state-averaged approach was used, whereby all 10 triplet and 15 singlet states were equally weighted. The spin–orbit effects were included according to quasi-degenerate perturbation theory, whereby the spin–orbit coupling operator (SOMF) was approximated according to the Breit–Pauli form. The electronic terms were evaluated at the CASSCF + NEVPT2 level, and the multiplets by considering the spin–orbit interaction (Table 5). Effective Hamiltonian was used to evaluate the spin Hamiltonian parameters.


**Table 5.** Energy levels for representative Ni(II) complexes calculated by ab initio method 1.

<sup>1</sup> Abbreviations: mag—magnetometry, EPR—(high-field/high-frequency) electron paramagnetic resonance, FDMRS—frequency-domain magnetic resonance spectroscopy, FIRMS—far infrared magnetic spectroscopy; SHAPE index (consistency with the regular coordination polyhedron) [23]: TBPY—trigonal bipyramid, SPY square pyramid, vOC—vacant octahedron; electronic terms a3A—ground-spin triplet, b3A—first excited spin triplet, a3E—ground-orbital doublet, b3E—first excited orbital doublet; ground spin–orbit multiplet at zero; *δ*—separation of the lowest multiplets: three from term a3A (consistent with the spin Hamiltonian formalism), six from a3E (beyond the spin Hamiltonian formalism). Structural and experimental data according to Refs. [24–28]. *Ab initio* calculations were carried out according to the same protocol.

The *ab initio* calculations refer to in silico state, i.e., intermolecular interactions and other solid-state effects are ignored. This is not the case for experimental magnetometric or spectroscopic data, which could be influenced by the environment. The *ab initio* data, in general, are consistent with those obtained by experimental techniques.

When comparing the CGTF calculations with *ab initio* calculations, calculated transition energies can be assessed. With a proper set of crystal field poles, the CGTF can reproduce first allowed transitions; however, the electronic spectrum, has a smaller width with respect to *ab initio* data.

An extended set of similar pentacoordinate Ni(II) complexes based on the fixed skeleton of a pentadentate Schiff base (Figure 7) was investigated by magnetometry and *ab initio* calculations with respect to the experimental geometry; these are listed in Table 6.

**Figure 7.** Schematic representations of pentacoordinate Ni(II) complexes. **<sup>1</sup>**: R<sup>1</sup> = R3<sup>=</sup> <sup>−</sup>CH<sup>3</sup> , R <sup>2</sup> <sup>=</sup> <sup>−</sup>C(CH<sup>3</sup> )3 , R<sup>4</sup> = H; **<sup>2</sup>**: R<sup>1</sup> <sup>=</sup> <sup>−</sup>CH<sup>3</sup> , R<sup>2</sup> = R<sup>4</sup> = H, R3= Br; **<sup>3</sup>**: R<sup>1</sup> <sup>=</sup> <sup>−</sup>CH<sup>3</sup> , R<sup>2</sup> = R<sup>4</sup> = H, R3= I; **4**: R <sup>1</sup> <sup>=</sup> <sup>−</sup>CH<sup>3</sup> , R<sup>2</sup> = R<sup>3</sup> <sup>=</sup> <sup>−</sup>C(CH<sup>3</sup> )3 , R<sup>4</sup> = H; **<sup>5</sup>**: R<sup>1</sup> <sup>=</sup> <sup>−</sup>CH<sup>3</sup> , R<sup>2</sup> = R<sup>3</sup> = R<sup>4</sup> = H; **6**: R<sup>1</sup> = R<sup>3</sup> = R<sup>3</sup> = H, R <sup>4</sup> <sup>=</sup> <sup>−</sup>CH<sup>3</sup> .

**Table 6.** Magnetometric and *ab initio* data for a set of pentadentate Ni(II) complexes comprising Schiff base ligands <sup>1</sup> .


<sup>1</sup> Data from ref. [29].

The experimentally reported and calculated *D* values cover a broad interval of positive and negative values over a wide range of the *τ*<sup>5</sup> parameters. These were used to plot *D* vs. *τ*5, which can be termed the *second magnetostructural D-correlation* for Ni(II) complexes (MSDC). (The first magnetostructural *D* correlation for hexacoordinate Ni(II) complexes is outlined elsewhere [30].) The MSDC can be approximated by a straight line (Figure 8) when the *τ*<sup>5</sup> parameter guarantees that the ground electronic term is not orbitally quasidegenerate (the energy gap ∆ > 2000 cm−<sup>1</sup> ). In the opposite case, the calculated *D* values tend to diverge. The value of the D parameter switches between positive and negative values at *τ*<sup>5</sup> ~ 0.2–0.3. Furthermore, the E parameter plays a role that has not be considered so far.

**Figure 8.** Dependence of the *D* parameter in pentacoordinate Ni(II) complexes on the distortion parameter (*τ*<sup>5</sup> ). Yellow squares—magnetometric data; red pica—*ab initio* calculations; solid—correlation line, dashed—confidence intervals, dotted—prediction intervals.

### **4. Conclusions**

Experimental data on magnetic susceptibility, magnetization, and electron paramagnetic resonance require an appropriate model in order be analyzed correctly. For some shapes of coordination polyhedra, such as octahedron Oh, tetragonal bipyramid D4h, trigonal antiprism D3d, tetrahedron Td, and bispehoid D2d, the crystal field theory offers such a support, and the spin Hamiltonian formalism defines relationships for the set of magnetic parameters (*D*, *E*, *gx*, *gy*, *gz*, *χ*TIP). A dearth in the literature with respect to pentacoordinate systems, such as the trigonal bipyramid D3h and tetragonal pyramid C4v symmetry, is filled by this publication. The working tool is the generalized crystal field theory in the form of its fully numerical, computer-assisted tool [31]. The advantage of this approach is that the positions of the ligands can be arbitrary, making it applicable to any geometry of the chromophore and any ligands. Only the set of Racah parameters of the interelectronic repulsion (*B*<sup>M</sup> and *C*M), the spin–orbit coupling constant (*ξ*M), polar angles (or Cartesian coordinates) of each ligand {*θ*L, *ϕ*L}, the crystal field poles *F*4(L) and, eventually, *F*2(L) are required. This method enables evaluation of the energies of the multielectron crystal field terms, spin–orbit crystal field multiplets, and the magnetic energy levels at the applied magnetic field. Then, the magnetic susceptibility and magnetization can be evaluated as functions of the temperature field via derivatives of the partition function. The eigenvectors provide complete information about the symmetry and can be used to automatically label terms/multiplets.

**Supplementary Materials:** The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/inorganics10080116/s1, Tables S1–S5: Reduction and selection rules for d5–d<sup>9</sup> configurations; Table S6: Reduction of the (2*S* + 1) states; Table S7: Decomposition of the direct product.

**Author Contributions:** All three authors contributed equally to the individual parts of the manuscript. "Conceptualization, R.B.; methodology, R.B.; software, R.B.; validation, J.T and C.R.; formal analysis, J.T; investigation, J.T.; resources, C.R.; data curation, C.R.; writing—original draft preparation, R.B.; writing—review and editing, R.B.; visualization, C.R.; supervision, R.B.; project administration, J.T.; funding acquisition, C.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** Slovak Research and Development Agency (APVV 18-0016, APVV 19-0087 and VEGA 1/0086/21, VEGA 1/0191/22) are acknowledged for their financial support.

**Data Availability Statement:** The experimental susceptibility and magnetization data and protocols of the CGTF and *ab initio* calculations are available from authors upon reasonable request.

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

### **References**


*Perspective* 

### *Perspective* **Bis(benzimidazole) Complexes, Synthesis and Their Biological Properties: A Perspective Bis(benzimidazole) Complexes, Synthesis and Their Biological Properties: A Perspective**

**Zdenˇek Šindeláˇr and Pavel Kopel \* Zdeněk Šindelář and Pavel Kopel \*** 

> Department of Inorganic Chemistry, Faculty of Science, Palacky University, 17. listopadu 12, 779 00 Olomouc, Czech Republic 779 00 Olomouc, Czech Republic; zdenek.sindelar@upol.cz **\*** Correspondence: pavel.kopel@upol.cz; Tel.: +420-585-634-352

Department of Inorganic Chemistry, Faculty of Science, Palacky University, 17. listopadu 12,

**\*** Correspondence: pavel.kopel@upol.cz; Tel.: +420-585-634-352

**Abstract:** Benzimidazoles are a very well-known, broad group of compounds containing nitrogen atoms in their structure that can mimic properties of DNA bases. The compounds show not only biological activities but also are used for spectral and catalytic properties. Biological activity of benzimidazoles can be tuned and accelerated in coordination compounds. This minireview is focused on preparation of bis(benzimidazoles), their complexes, and biological properties that can be found from 2015. atoms in their structure that can mimic properties of DNA bases. The compounds show not only biological activities but also are used for spectral and catalytic properties. Biological activity of benzimidazoles can be tuned and accelerated in coordination compounds. This minireview is focused on preparation of bis(benzimidazoles), their complexes, and biological properties that can be found from 2015.

**Abstract:** Benzimidazoles are a very well-known, broad group of compounds containing nitrogen

**Keywords:** bis(benzimidazole); mixed ligand complexes; antibacterial; anticancer **Keywords:** bis(benzimidazole); mixed ligand complexes; antibacterial; anticancer

### **1. Introduction 1. Introduction**  The benzimidazole is a bicyclic molecule composed of benzene ring and imidazole

The benzimidazole is a bicyclic molecule composed of benzene ring and imidazole ring. The compound is isostructural with naturally occurring nucleotides [1]. Its similarity to natural molecules led to the preparation of derivatives that can be utilized in medicinal chemistry. The very broad spectrum of biological activities that it treats include antimicrobial, antibiofilm, antifungal, antiviral, antioxidant, anti-inflammatory, antidiabetic, antiparasitic, anthelmintic, anticoagulant, antiallergic, antiprotozoal, anticonvulsants, anticancer and cytotoxic activities. There are drugs already used in medicine, such as Albendazole, Bendamustine, Omeprazole, Pimonbendane, Benomyl, Carbendazim, Telmisartan, Pantoprazole, Etonitazene, and Thiabendazole (some of them are depicted in Scheme 1). ring. The compound is isostructural with naturally occurring nucleotides [1]. Its similarity to natural molecules led to the preparation of derivatives that can be utilized in medicinal chemistry. The very broad spectrum of biological activities that it treats include antimicrobial, antibiofilm, antifungal, antiviral, antioxidant, anti-inflammatory, antidiabetic, antiparasitic, anthelmintic, anticoagulant, antiallergic, antiprotozoal, anticonvulsants, anticancer and cytotoxic activities. There are drugs already used in medicine, such as Albendazole, Bendamustine, Omeprazole, Pimonbendane, Benomyl, Carbendazim, Telmisartan, Pantoprazole, Etonitazene, and Thiabendazole (some of them are depicted in Scheme 1).

**Citation:** Šindeláˇr, Z.; Kopel, P. Bis(benzimidazole) Complexes, Synthesis and Their Biological Properties: A Perspective. *Inorganics* **2023**, *11*, 113. https://doi.org/ 10.3390/inorganics11030113 Bis(benzimidazole) Complexes, Synthesis and Their Biological Properties: A Perspective. *Inorganics*  **2023**, *11*, x. https://doi.org/10.3390/xxxxx Academic Editors: Peter Segľa and

**Citation:** Šindelář, Z.; Kopel, P.

Academic Editors: Peter Segl'a and Ján Pavlik Received: 15 February 2023 Revised: 27 February 2023

Received: 15 February 2023 Revised: 27 February 2023 Accepted: 7 March 2023 Published: 9 March 2023 Accepted: 7 March 2023 Published: 9 March 2023

Ján Pavlik

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

*Inorganics* **2023**, *11*, x. https://doi.org/10.3390/xxxxx www.mdpi.com/journal/inorganics

nating atoms.

Moreover, benzimidazoles can be utilized as optical sensors for bioimaging and in photovoltaics. There are not only many papers but also many reviews on the topic, such as the one on lanthanide complexes by Cruz-Navarro et al. [1], by Hernández-Romero et al. on first-row transition metal complexes [2], and Suarez-Moreno et al. on second- and third-row transition metal complexes [3]. The last two reviews contain information about the anticancer and antitumor activities of benzimidazole complexes. the anticancer and antitumor activities of benzimidazole complexes. In this review, we have focused on the preparation of bis(benzimidazoles) and their complexes that show biological activities. These compounds can be utilized as bridges among metal centers, chelating ligands with nitrogen atoms, or oxygen or sulfur coordi-

In this review, we have focused on the preparation of bis(benzimidazoles) and their complexes that show biological activities. These compounds can be utilized as bridges among metal centers, chelating ligands with nitrogen atoms, or oxygen or sulfur coordinating atoms. **2. Bis(benzimidazole) Synthesis and Some Examples of Complex Preparation** 

### **2. Bis(benzimidazole) Synthesis and Some Examples of Complex Preparation** There are many ways for benzimidazole and benzimidazole derived ligands. Some examples of the preparations are mentioned hereafter. The work of Matthews et al. de-

Moreover, benzimidazoles can be utilized as optical sensors for bioimaging and in

photovoltaics. There are not only many papers but also many reviews on the topic, such as the one on lanthanide complexes by Cruz-Navarro et al. [1], by Hernández-Romero et

third-row transition metal complexes [3]. The last two reviews contain information about

There are many ways for benzimidazole and benzimidazole derived ligands. Some examples of the preparations are mentioned hereafter. The work of Matthews et al. described symmetric as well as asymmetric bis(benzimidazoles) [4]. The general method can be seen in Scheme 2. scribed symmetric as well as asymmetric bis(benzimidazoles) [4]. The general method can be seen in Scheme 2.

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**Scheme 2.** General synthesis of bis(benzimidazoles). (X = O, S, NH). **Scheme 2.** General synthesis of bis(benzimidazoles). (X = O, S, NH).

For example, preparation of 4-(2-Benzimidazolyl)-3-thiabutanoic acid and 2-(1*H*-ben-For example, preparation of 4-(2-Benzimidazolyl)-3-thiabutanoic acid and 2-(1*H*benzimidazol-2-ylmethylsulfanylmethyl)-1*H*-benzimidazole is given.

zimidazol-2-ylmethylsulfanylmethyl)-1*H*-benzimidazole is given. Thiodiacetic acid and o-phenylenediamine in a solution of 4 M HCl are refluxed for a total of 72 h and allowed to cool to room temperature. A green precipitate was filtered and dried. The precipitate was dissolved in distilled water. The solution was stirred and Thiodiacetic acid and o-phenylenediamine in a solution of 4 M HCl are refluxed for a total of 72 h and allowed to cool to room temperature. A green precipitate was filtered and dried. The precipitate was dissolved in distilled water. The solution was stirred and basified with ammonia solution to pH 9. A precipitate of bis(benzimidazole) was filtered and dried. The filtrate was treated with concentrated HCl until pH 7. White precipitate gave 4-(2-Benzimidazolyl)-3-thiabutanoic acid.

basified with ammonia solution to pH 9. A precipitate of bis(benzimidazole) was filtered and dried. The filtrate was treated with concentrated HCl until pH 7. White precipitate gave 4-(2-Benzimidazolyl)-3-thiabutanoic acid. Similarly, 4-(2-benzimidazolyl)-3-oxabutanoic acid was prepared. These acids were used for condensation with 4-nitro-o-phenylenediamine, N-methyl-o-phenylenediamine, Similarly, 4-(2-benzimidazolyl)-3-oxabutanoic acid was prepared. These acids were used for condensation with 4-nitro-o-phenylenediamine, N-methyl-o-phenylenediamine, or 4,5-dimethyl-o-phenylenediamine to form asymmetric bis(benzimidazoles) [4]. The ligands were used for the preparation of copper(II) complexes. The complexes were prepared by equimolar addition of ligand to the copper bromide or perchlorate dissolved in methanol. The ligands were tridentate chelating.

or 4,5-dimethyl-o-phenylenediamine to form asymmetric bis(benzimidazoles) [4]. The ligands were used for the preparation of copper(II) complexes. The complexes were pre-Caymaz et al. reported synthesis of 2,20 -bis-(imidazo [1,2-*a*]pyridine-8-yl)-1*H*,1*H*0 - [5,50 ]-bisbenzimidazole [5]. The syntheses of compound were performed by reacting the imidazo(1,2-*a*)pyridine-8-carbaldehyde with 3,30 -diaminobenzidin (see Scheme 3).

imidazo(1,2-*a*)pyridine-8-carbaldehyde with 3,3′-diaminobenzidin (see Scheme 3).

methanol. The ligands were tridentate chelating.

pared by equimolar addition of ligand to the copper bromide or perchlorate dissolved in

[5,5′]-bisbenzimidazole [5]. The syntheses of compound were performed by reacting the

Caymaz et al. reported synthesis of 2,2′-bis-(imidazo [1,2-*a*]pyridine-8-yl)-1*H*,1*H*′-

**Scheme 3.** 2,2′-bis-(imidazo[1,2-*a*]pyridine-8-yl)-1*H*,1*H*′-[5,5′]-bisbenzimidazole. **Scheme 3.** 2,20 -bis-(imidazo[1,2-*a*]pyridine-8-yl)-1*H*,1*H*0 -[5,50 ]-bisbenzimidazole. **Scheme 3.** 2,2′-bis-(imidazo[1,2-*a*]pyridine-8-yl)-1*H*,1*H*′-[5,5′]-bisbenzimidazole.

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The compound binds to DNA grooves and has peroxide mediated DNA-cleavage properties. It was tested on cell lines HepG2, DLD-1, and MDA-MB-231, and was found to have high cytotoxic activities [5]. The compound binds to DNA grooves and has peroxide mediated DNA-cleavage properties. It was tested on cell lines HepG2, DLD-1, and MDA-MB-231, and was found to have high cytotoxic activities [5]. properties. It was tested on cell lines HepG2, DLD-1, and MDA-MB-231, and was found to have high cytotoxic activities [5]. Synthesis of (2-((1*H*-benzo[d]imidazol-2-yl)methylthio)-1*H*-benzo[*d*]imidazol-6-

The compound binds to DNA grooves and has peroxide mediated DNA-cleavage

Synthesis of (2-((1*H*-benzo[d]imidazol-2-yl)methylthio)-1*H*-benzo[*d*]imidazol-6 yl)(phenyl)methanone [BIPM] and its Pd complex was reported by Kumar et al. [6]. In the first step, (2-mercapto-1*H*-benzo[*d*]imidazol-6-yl)(phenyl)methanone is prepared in methanol in presence of KOH by reaction of carbon disulfide with 3,4-diaminobenzophenone. Then, 2-(chloromethyl)-1*H*-benzo[*d*]imidazole was prepared by condensing chloroacetic acid and o-phenylenediamine in 4 M hydrochloric acid. Finally, (2-((1*H*-benzo[*d*]imidazol-2-yl)methylthio)-1*H*-benzo[*d*]imidazol-6-yl)(phenyl)methanone [BIPM], was obtained by a reaction of above-mentioned components in methanol (see Scheme 4). Synthesis of (2-((1*H*-benzo[d]imidazol-2-yl)methylthio)-1*H*-benzo[*d*]imidazol-6-yl) (phenyl)methanone [BIPM] and its Pd complex was reported by Kumar et al. [6]. In the first step, (2-mercapto-1*H*-benzo[*d*]imidazol-6-yl)(phenyl)methanone is prepared in methanol in presence of KOH by reaction of carbon disulfide with 3,4-diaminobenzophenone. Then, 2-(chloromethyl)-1*H*-benzo[*d*]imidazole was prepared by condensing chloroacetic acid and o-phenylenediamine in 4 M hydrochloric acid. Finally, (2-((1*H*-benzo[*d*]imidazol-2 yl)methylthio)-1*H*-benzo[*d*]imidazol-6-yl)(phenyl)methanone [BIPM], was obtained by a reaction of above-mentioned components in methanol (see Scheme 4). yl)(phenyl)methanone [BIPM] and its Pd complex was reported by Kumar et al. [6]. In the first step, (2-mercapto-1*H*-benzo[*d*]imidazol-6-yl)(phenyl)methanone is prepared in methanol in presence of KOH by reaction of carbon disulfide with 3,4-diaminobenzophenone. Then, 2-(chloromethyl)-1*H*-benzo[*d*]imidazole was prepared by condensing chloroacetic acid and o-phenylenediamine in 4 M hydrochloric acid. Finally, (2-((1*H*-benzo[*d*]imidazol-2-yl)methylthio)-1*H*-benzo[*d*]imidazol-6-yl)(phenyl)methanone [BIPM], was obtained by a reaction of above-mentioned components in methanol (see Scheme 4).

**Scheme 4.** Synthesis of (2-((1*H*-benzo[*d*]imidazol-2-yl)methylthio)-1*H*-benzo[*d*]imidazol-6-yl)(phe-**Scheme 4.** Synthesis of (2-((1*H*-benzo[*d*]imidazol-2-yl)methylthio)-1*H*-benzo[*d*]imidazol-6-yl)(phenyl)methanone (BIPM). **Scheme 4.** Synthesis of (2-((1*H*-benzo[*d*]imidazol-2-yl)methylthio)-1*H*-benzo[*d*]imidazol-6-yl)(phenyl) methanone (BIPM).

nyl)methanone (BIPM). There are many papers on coordination compounds with 2,6-bis(1*H*-benzo[*d*]imidazol-2-yl)pyridine (BBP) and its derivatives (see Scheme 5, top left). These ligands are multidentate ligands and can be coordinated to metal atoms in different metal–ligand ratios. Substitution of the N–H bond in the benzimidazole ring by alkyl groups can lead to the formation of hydrogen bonds, and complexes are studied for interesting optical and magnetic properties [1]. BBP can be obtained by the reaction of pyridine-2,6-dicarboxylic acid and o-phenylenediamine in the presence of polyphosphoric acid (PPA). Higher yields can be obtained with phosphorus oxide or HCl and reaction in microwave oven. There are many papers on coordination compounds with 2,6-bis(1*H*-benzo[*d*]imidazol-2-yl)pyridine (BBP) and its derivatives (see Scheme 5, top left). These ligands are multidentate ligands and can be coordinated to metal atoms in different metal–ligand ratios. Substitution of the N–H bond in the benzimidazole ring by alkyl groups can lead to the formation of hydrogen bonds, and complexes are studied for interesting optical and magnetic properties [1]. BBP can be obtained by the reaction of pyridine-2,6-dicarboxylic acid and o-phenylenediamine in the presence of polyphosphoric acid (PPA). Higher yields can be obtained with phosphorus oxide or HCl and reaction in microwave oven. Instead of pyridine-2,6-dicarboxylic acid, pyridine-2,6-dicarbaldehyde can be used, but There are many papers on coordination compounds with 2,6-bis(1*H*-benzo[*d*]imidazol-2-yl)pyridine (BBP) and its derivatives (see Scheme 5, top left). These ligands are multidentate ligands and can be coordinated to metal atoms in different metal–ligand ratios. Substitution of the N–H bond in the benzimidazole ring by alkyl groups can lead to the formation of hydrogen bonds, and complexes are studied for interesting optical and magnetic properties [1]. BBP can be obtained by the reaction of pyridine-2,6-dicarboxylic acid and o-phenylenediamine in the presence of polyphosphoric acid (PPA). Higher yields can be obtained with phosphorus oxide or HCl and reaction in microwave oven. Instead of pyridine-2,6-dicarboxylic acid, pyridine-2,6-dicarbaldehyde can be used, but the yields are low [1].

Instead of pyridine-2,6-dicarboxylic acid, pyridine-2,6-dicarbaldehyde can be used, but the yields are low [1]. the yields are low [1]. N-substituted ligands derived from BBP can be obtained by condensing pyridine-2,6-dicarboxylic acid with N-alkyl-o-phenylenediamine derivative. The other possible

perature.

group led to the final product.

way is to deprotonate N3 with a base, followed by a reaction with alkyl or aryl halides. Some examples are given below. The 2,6-bis-(6-nitrobenzimidazol-2-yl)pyridine (BNBP) (see Scheme 5, top right) was prepared by reaction of BBP with concentrated sulfuric acid and nitric acid. The complex [Ru(BBP)Cl3] was prepared by a reaction of BBP with ruthenium(III) chloride. The nucleophilic substitution of BBP with 3,5-di-*tert*-butylbenzyl bromide or 4-*tert*-butylbenzyl chloride, in basic heated DMSO solution, led to preparation of derivatives depicted in Scheme 5 (bottom) [7]. Scheme 5, top right) was prepared by reaction of BBP with concentrated sulfuric acid and nitric acid. The complex [Ru(BBP)Cl3] was prepared by a reaction of BBP with ruthenium(III) chloride. The nucleophilic substitution of BBP with 3,5-di-*tert*-butylbenzyl bromide or 4-*tert*-butylbenzyl chloride, in basic heated DMSO solution, led to preparation of derivatives depicted in Scheme 5 (bottom) [7].

N-substituted ligands derived from BBP can be obtained by condensing pyridine-2,6-

to deprotonate N3 with a base, followed by a reaction with alkyl or aryl halides. Some examples are given below. The 2,6-bis-(6-nitrobenzimidazol-2-yl)pyridine (BNBP) (see

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**Scheme 5.** 2,6-*bis*(1*H*-benzo[*d*]imidazol-2-yl)pyridine (BBP), BNBP = 2,6-bis-(6-nitrobenzimidazol-2-yl)pyridine), [Ru(BBP)Cl3] (middle) [8]. The substituted ligands (bottom) were obtained via the nucleophilic substitution of 2,6-bis(1*H*-benzimidazole-2-yl)pyridine [7] with 3,5-di-*tert*-butylbenzyl bromide or 4-*tert*-butylbenzyl chloride in the presence of KOH in DMSO solvent at an elevated tem-**Scheme 5.** 2,6-*bis*(1*H*-benzo[*d*]imidazol-2-yl)pyridine (BBP), BNBP = 2,6-bis-(6-nitrobenzimidazol-2 yl)pyridine), [Ru(BBP)Cl<sup>3</sup> ] (middle) [8]. The substituted ligands (bottom) were obtained via the nucleophilic substitution of 2,6-bis(1*H*-benzimidazole-2-yl)pyridine [7] with 3,5-di-*tert*-butylbenzyl bromide or 4-*tert*-butylbenzyl chloride in the presence of KOH in DMSO solvent at an elevated temperature.

Another example of BBP derivative on pyridine ring was recently reported by Orvos et al. The synthetic route of the ligand is outlined in Scheme 6 [9]. The 4-azidopyridine derivative was prepared from dimethyl 4-chloropyridine-2,6-dicarboxylate by the basic hydrolysis of with LiOH. Diamide was obtained with *o*-phenylenediamine using *O*-(ben-Another example of BBP derivative on pyridine ring was recently reported by Orvos et al. The synthetic route of the ligand is outlined in Scheme 6 [9]. The 4-azidopyridine derivative was prepared from dimethyl 4-chloropyridine-2,6-dicarboxylate by the basic hydrolysis of with LiOH. Diamide was obtained with *o*-phenylenediamine using *O*-(benzotriazol-1-yl)- *N*,*N*,*N*0 ,*N*0 -tetramethyluronium tetrafluoroborate (TBTU) in DMF. Hydrogenation on Pd/C in MeOH gave an amino derivative. NH2-bis(benzimidazole)pyridine was obtained by heating in acetic acid. The reaction of nitrosobenzene with the amino group led to the final product.

zotriazol-1-yl)-*N*,*N*,*N*′,*N*′-tetramethyluronium tetrafluoroborate (TBTU) in DMF. Hydrogenation on Pd/C in MeOH gave an amino derivative. NH2-bis(benzimidazole)pyridine was obtained by heating in acetic acid. The reaction of nitrosobenzene with the amino

**Scheme 6.** The azidopyridine derivative of BBP preparation [9]. **Scheme 6.** The azidopyridine derivative of BBP preparation [9].

### **3. Biologically Active Bis(benzimidazole) Complexes 3. Biologically Active Bis(benzimidazole) Complexes**

Deng et al. have prepared ruthenium complexes that have potential applications as sensitizers for use in cancer radiotherapy [8]. They prepared [Ru(BBP)Cl3] (1), [Ru(BBP)2]Cl2 (2a), and [Ru(BNBP)2]Cl2 (2b). Complex 2b was found to be particularly effective in sensitizing human melanoma A375 cells toward radiation. Moreover, it was found that complex 2b is not toxic to normal cells. Mechanism of action is formation of intracellular reactive oxygen species (ROS) with glutathione (GSH) followed by DNA strand breaks. The subsequent DNA damage induces phosphorylation of p53 (p-p53) and upregulates the expression levels of p21, which inhibits the expression of cyclin-B, leading to G2M arrest. Moreover, p-p53 activates caspases-3 and -8, triggering cleavage of Deng et al. have prepared ruthenium complexes that have potential applications as sensitizers for use in cancer radiotherapy [8]. They prepared [Ru(BBP)Cl3] (1), [Ru(BBP)2]Cl<sup>2</sup> (2a), and [Ru(BNBP)2]Cl<sup>2</sup> (2b). Complex 2b was found to be particularly effective in sensitizing human melanoma A375 cells toward radiation. Moreover, it was found that complex 2b is not toxic to normal cells. Mechanism of action is formation of intracellular reactive oxygen species (ROS) with glutathione (GSH) followed by DNA strand breaks. The subsequent DNA damage induces phosphorylation of p53 (p-p53) and upregulates the expression levels of p21, which inhibits the expression of cyclin-B, leading to G2M arrest. Moreover, p-p53 activates caspases-3 and -8, triggering cleavage of poly(ADP-ribose) polymerase (PARP), finally resulting in apoptosis [8].

poly(ADP-ribose) polymerase (PARP), finally resulting in apoptosis [8]. BODIPY iridium(III) complexes containing 2,2′-bis(benzimidazole) show selectivity for cancerous cells over normal cells [10]. The tetranuclear (2 + 2) complexes were prepared through the self-assembly of benzimidazole and BODIPY ligands with dichloro (pentamethylcyclopentadienyl) iridium dimer. Cytotoxicity studies revealed that the complex is highly selective for cervical cancer cells (HeLa) and human glioblastoma (U87) BODIPY iridium(III) complexes containing 2,20 -bis(benzimidazole) show selectivity for cancerous cells over normal cells [10]. The tetranuclear (2 + 2) complexes were prepared through the self-assembly of benzimidazole and BODIPY ligands with dichloro (pentamethylcyclopentadienyl) iridium dimer. Cytotoxicity studies revealed that the complex is highly selective for cervical cancer cells (HeLa) and human glioblastoma (U87) cancer cells [10].

cancer cells [10]. [MnBr(CO)3L2] (3, L2 = 2,2′-bisbenzimidazole), [MnBr(CO)3L3]·CH3OH (4, L3 = BBP = 2,6-bis(benzimidazole-2′-yl)pyridine), and *fac*-[MnBr(CO)3L4] (5, L4 = 2,4-bis(benzimidazole-2′-yl) pyridine) were prepared by reactions of MnBr(CO)5 with appropriate ligands L2–L4, respectively, and characterized by single crystal X-ray diffraction, NMR, IR, UVvis, and fluorescence spectroscopy [11]. The CO-release properties were investigated using the myoglobin assay and CO detection, and the results show that all of the complexes could release CO rapidly upon exposure to 365 nm UV light. The fluorescence imaging show that the Mn(I) complexes can be taken up by human liver cells (HL-7702) and liver cancer cells (SK-Hep1), and are suitable for bioimaging. A cell viability assay for SK-Hep1 [MnBr(CO)3L2] (3, L2 = 2,20 -bisbenzimidazole), [MnBr(CO)3L3]·CH3OH (4, L3 = BBP = 2,6 bis(benzimidazole-20 -yl)pyridine), and *fac*-[MnBr(CO)3L4] (5, L4 = 2,4-bis(benzimidazole-20 -yl) pyridine) were prepared by reactions of MnBr(CO)<sup>5</sup> with appropriate ligands L2–L4, respectively, and characterized by single crystal X-ray diffraction, NMR, IR, UV-vis, and fluorescence spectroscopy [11]. The CO-release properties were investigated using the myoglobin assay and CO detection, and the results show that all of the complexes could release CO rapidly upon exposure to 365 nm UV light. The fluorescence imaging show that the Mn(I) complexes can be taken up by human liver cells (HL-7702) and liver cancer cells (SK-Hep1), and are suitable for bioimaging. A cell viability assay for SK-Hep1 shows that the anticancer activity of 3 is highest in the studied complexes [11].

shows that the anticancer activity of 3 is highest in the studied complexes [11]. Pd(II) complex with (2-((1*H*-benzo[*d*]imidazol-2-yl)methylthio)-1*H*-benzo[*d*]imidazol-5-yl)(phenyl)methanone (BIPM) was prepared by reaction of palladium acetate with BIPM in a 1:1 molar ratio [6]. BIPM is bidentate N,S chelating ligand, and the other two positions are occupied by oxygen atoms from two acetate anions. The in vitro antiproliferative effect of the BIPM and complex were tested against the MCF7, A549, Ehrlich ascites carcinoma (EAC), and Daltons lymphoma ascites (DLA) carcinoma cell lines. The mechanism is the antiangiogenic effect and promotion of apoptosis. The potential photo-induced binding mode on double-stranded calf thymus DNA and protein cleavage activity study Pd(II) complex with (2-((1*H*-benzo[*d*]imidazol-2-yl)methylthio)-1*H*-benzo[*d*]imidazol-5-yl)(phenyl)methanone (BIPM) was prepared by reaction of palladium acetate with BIPM in a 1:1 molar ratio [6]. BIPM is bidentate N,S chelating ligand, and the other two positions are occupied by oxygen atoms from two acetate anions. The in vitro antiproliferative effect of the BIPM and complex were tested against the MCF7, A549, Ehrlich ascites carcinoma (EAC), and Daltons lymphoma ascites (DLA) carcinoma cell lines. The mechanism is the antiangiogenic effect and promotion of apoptosis. The potential photo-induced binding mode on double-stranded calf thymus DNA and protein cleavage activity study on pBR322 DNA of the complex confirmed apoptosis. The molecular docking study proved its interaction with DNA [6].

Ruthenium mixed ligand complex with 2-(1*H*-benzimidazol-2-ylmethylsulfanylmethyl)- 1*H*-benzimidazole and Schiff base (2-((*E*)-1*H*-1,2,4-triazol-5-yliminomethyl) phenol) was reported by Sur et al. [12]. The antibacterial effect of the complex was studied against *Staphylococcus aureus*, vancomycin-resistant *Staphylococcus aureus* (VRSA), methicillin-resistant *Staphylococcus aureus* (MRSA), and *Staphylococcus epidermidis*. Very high antibacterial activity was observed on growth curves and by fluorescence imaging. Moreover, in vivo tests on VRSA-infected mice proved better healing of skin wounds. thyl)-1*H*-benzimidazole and Schiff base (2-((*E*)-1*H*-1,2,4-triazol-5-yliminomethyl) phenol) was reported by Sur et al. [12]. The antibacterial effect of the complex was studied against *Staphylococcus aureus*, vancomycin-resistant *Staphylococcus aureus* (VRSA), methicillin-resistant *Staphylococcus aureus* (MRSA), and *Staphylococcus epidermidis*. Very high antibacterial activity was observed on growth curves and by fluorescence imaging. Moreover, in vivo tests on VRSA-infected mice proved better healing of skin wounds. Mononuclear, binuclear, and multinuclear silver complexes of composition

on pBR322 DNA of the complex confirmed apoptosis. The molecular docking study

Ruthenium mixed ligand complex with 2-(1*H*-benzimidazol-2-ylmethylsulfanylme-

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proved its interaction with DNA [6].

Mononuclear, binuclear, and multinuclear silver complexes of composition [Ag2(methacrylate)2(Etobb)2]·CH3CN **1**, [Ag(methacrylate)(Bobb)] **2**, and [Ag2(methacrylate)2(Aobb)]<sup>n</sup> **3**, where Etobb = 1,3-bis(1-ethylbenzimidazol-2-yl)-2-oxapropane, Bobb = 1,3-bis(1-benzylbenzimidazol-2-yl)-2-oxapropane, Aobb = 1,3-bis(1-allylbenzimidazol-2-yl)-2-oxapropane were prepared by Zhang et al. [13]. Synthesis of the ligands is in Scheme 7. The three complexes have been prepared by reaction of silver nitrate with sodium methacrylate and corresponding ligand. Single-crystal X-ray diffraction revealed that complex **1** is binuclear, and the silver atom is coordinated by two N atoms to two Etobb ligands and oxygen of methacrylate. The complex **2** is mononuclear with a chelating ligand, but the oxygen atom of bis(benzimidazole is not involved in coordination. Complex **3** is a metal–organic compound with a diamond-like multinuclear silver center, with each silver atom bridged by two Aobb ligands and two methacrylate ions to form 1-D single-coordination polymer chain structures that extend into 2-D frameworks through π–π interactions. The binding modes of DNA were checked through absorption titration experiments of CT-DNA with complexes at 270 nm. A binding to DNA through intercalation with strong π–π stacking to the DNA base pairs was proved. Hydroxyl radical scavenging activity revealed the inhibitory effect of the complexes on OH˙ radicals. [Ag2(methacrylate)2(Etobb)2]·CH3CN **1**, [Ag(methacrylate)(Bobb)] **2**, and [Ag2(methacrylate)2(Aobb)]n **3**, where Etobb = 1,3-bis(1-ethylbenzimidazol-2-yl)-2-oxapropane, Bobb = 1,3-bis(1-benzylbenzimidazol-2-yl)-2-oxapropane, Aobb = 1,3-bis(1-allylbenzimidazol-2 yl)-2-oxapropane were prepared by Zhang et al. [13]. Synthesis of the ligands is in Scheme 7. The three complexes have been prepared by reaction of silver nitrate with sodium methacrylate and corresponding ligand. Single-crystal X-ray diffraction revealed that complex **1** is binuclear, and the silver atom is coordinated by two N atoms to two Etobb ligands and oxygen of methacrylate. The complex **2** is mononuclear with a chelating ligand, but the oxygen atom of bis(benzimidazole is not involved in coordination. Complex **3** is a metal–organic compound with a diamond-like multinuclear silver center, with each silver atom bridged by two Aobb ligands and two methacrylate ions to form 1-D single-coordination polymer chain structures that extend into 2-D frameworks through π–π interactions. The binding modes of DNA were checked through absorption titration experiments of CT-DNA with complexes at 270 nm. A binding to DNA through intercalation with strong π–π stacking to the DNA base pairs was proved. Hydroxyl radical scavenging activity revealed the inhibitory effect of the complexes on OH˙ radicals.

**Scheme 7.** Synthetic way for ligands (Etobb, Bobb, Aobb), where R = -CH2CH3 (Etobb), R = -CH2-ph (Bobb), R = CH2CHCH2. **Scheme 7.** Synthetic way for ligands (Etobb, Bobb, Aobb), where R = -CH2CH<sup>3</sup> (Etobb), R = -CH<sup>2</sup> -ph (Bobb), R = CH2CHCH<sup>2</sup> .

Rodriguez-Cordero et al. have characterized ZnLBr2 complexes with bis(benzimidazole) prepared by reaction of citraconic acid with o-phenylenediamine or its derivative obtained by following reaction with benzylbromide in DMF [14]. Tetrahedral zinc coordination was proven by single crystal X-ray analysis. Zinc is coordinated by two Br atoms and a chelating N-N ligand. UV spectra of ligands and complexes showed decreases in peak intensities when increasing amounts of CT DNA. These spectral changes are con-Rodriguez-Cordero et al. have characterized ZnLBr<sup>2</sup> complexes with bis(benzimidazole) prepared by reaction of citraconic acid with o-phenylenediamine or its derivative obtained by following reaction with benzylbromide in DMF [14]. Tetrahedral zinc coordination was proven by single crystal X-ray analysis. Zinc is coordinated by two Br atoms and a chelating N-N ligand. UV spectra of ligands and complexes showed decreases in peak intensities when increasing amounts of CT DNA. These spectral changes are consistent with intercalation or partial intercalation of the ligands and complexes into the DNA.

sistent with intercalation or partial intercalation of the ligands and complexes into the DNA. Pan et al. have prepared and proved structures of [Cu(bmbp)(HCOO)(H2O)](ClO4)·DMF (1), [Co(bmbp)2]2(ClO4)4·DMF·H2O (2) and [Zn(bmbp)2]2(ClO4)4·DMF·H2O (3), where bmbp is 4-butyloxy-2,6-bis(1-methyl-2-benzimidazolyl)pyridine, complexes by single crystal X-ray analysis [15]. Complex 1 has square-pyramidal geometry, and complexes 2 and 3 are distorted octahedral. The complexes and bmbp were tested on a human esophageal cancer cell line

(Eca109). Inhibition of the growth was proven, and complex 1 showed that it was the most active (IC50 = 26.09 µM). age of plasmid pBR322, in the presence of H2O2 [16]. Very interesting ligand synthesis and copper complexes are presented by Suwalsky

Pan et al. have prepared and proved structures of [Cu(bmbp)(HCOO)(H2O)](ClO4)·DMF (1), [Co(bmbp)2]2(ClO4)4·DMF·H2O (2) and [Zn(bmbp)2]2(ClO4)4·DMF·H2O (3), where bmbp is 4-butyloxy-2,6-bis(1-methyl-2-benzimidazolyl)pyridine, complexes by single crystal X-ray analysis [15]. Complex 1 has squarepyramidal geometry, and complexes 2 and 3 are distorted octahedral. The complexes and bmbp were tested on a human esophageal cancer cell line (Eca109). Inhibition of the growth was proven, and complex 1 showed that it was the most active (IC50 = 26.09 μM). Mixed ligand Cu(II) complexes [Cu(BBP)(L)H2O]SO4 (where L = 2,2′ bipyridine (bpy), and ethylene diamine (en)), have been prepared, and DNA-binding properties proved by absorption spectroscopy, fluorescence spectroscopy, viscosity measurements and thermal denaturation methods. DNA intercalation mechanism was suggested as well as the cleav-

*Inorganics* **2023**, *11*, x FOR PEER REVIEW 7 of 11

Mixed ligand Cu(II) complexes [Cu(BBP)(L)H2O]SO<sup>4</sup> (where L = 2,20 bipyridine (bpy), and ethylene diamine (en)), have been prepared, and DNA-binding properties proved by absorption spectroscopy, fluorescence spectroscopy, viscosity measurements and thermal denaturation methods. DNA intercalation mechanism was suggested as well as the cleavage of plasmid pBR322, in the presence of H2O<sup>2</sup> [16]. et al. [17]. The authors have prepared tetradentate Bis(2-methylbenzimidazolyl)(2-methylthioethyl)amine (L1) (see Figure 1A), and bis(1-methyl-2-methylbenzimidazolyl)(2-methylthioethyl)amine (L1Me). The first ligand was prepared by refluxing 1-tert-butoxycarbonyl-2-cloromethylbenzimidazole and 2-methylthioethylamine in the presence of K2CO3 and NaI in CH3CN. The second ligand was prepared similarly with 1-methyl-2-chloro-

Very interesting ligand synthesis and copper complexes are presented by Suwalsky et al. [17]. The authors have prepared tetradentate Bis(2-methylbenzimidazolyl)(2 methylthioethyl)amine (L1) (see Figure 1A), and bis(1-methyl-2-methylbenzimidazolyl)(2 methylthioethyl)amine (L1Me). The first ligand was prepared by refluxing 1-tert-butoxycarbonyl-2-cloromethylbenzimidazole and 2-methylthioethylamine in the presence of K2CO<sup>3</sup> and NaI in CH3CN. The second ligand was prepared similarly with 1-methyl-2-chloromethylbenzimidazole. The complexes were prepared by reaction of copper perchlorates with ligands. The effect on the morphology of human erythrocytes and antiproliferative effect was tested on HeLa, REH, A546, and K-562 cells. methylbenzimidazole. The complexes were prepared by reaction of copper perchlorates with ligands. The effect on the morphology of human erythrocytes and antiproliferative effect was tested on HeLa, REH, A546, and K-562 cells. Similar Bis(benzimidazole)thio- and selenoether ligands and their nickel(II) complexes were prepared by the same group of authors [18]. This time, 1-methyl-2-(chloromethyl)benzimidazole reacted with (2-phenylethylthio)ethylamine (for L3Me) or (2 phenylseleno)ethylamine (for L4Me). Mononuclear and binuclear Ni(II) complexes were obtained by a reaction of nickel chloride with the ligands. Their structures can be seen in Figure 1.

**Figure 1.** Molecular structures of (**A**) [L1CuCl]; C (gray), N (blue), S (yellow), Cl (green), and Cu (red), (**B**) [Ni(L1Me)(H2O)(Cl)]Cl, Ni (great green), O (red), (**C**) Ni2(L2Me)2(μ-Cl)3]Cl, (**D**) [Ni2(L3Me)2(μ-Cl)2][NiCl4], (**E**) [Ni2(L4Me)2(μ-Cl)2][NiCl4], Se (gold). **Figure 1.** Molecular structures of (**A**) [L1CuCl]; C (gray), N (blue), S (yellow), Cl (green), and Cu (red), (**B**) [Ni(L1Me)(H2O)(Cl)]Cl, Ni (great green), O (red), (**C**) Ni<sup>2</sup> (L2Me)<sup>2</sup> (µ-Cl)<sup>3</sup> ]Cl, (**D**) [Ni<sup>2</sup> (L3Me)<sup>2</sup> (µ-Cl)<sup>2</sup> ][NiCl<sup>4</sup> ], (**E**) [Ni<sup>2</sup> (L4Me)<sup>2</sup> (µ-Cl)<sup>2</sup> ][NiCl<sup>4</sup> ], Se (gold).

The stability of complexes in aqueous solutions was monitored for 72 h by UV–vis spectroscopy, and these are stable in solutions. The cytotoxicity of complexes was screened against SK-LU-1 (human lung adenocarcinoma), HeLa (human cervical carcinoma), and HEK-293 (non-tumoral human embryonic kidney) cell lines using an MTT. It Similar Bis(benzimidazole)thio- and selenoether ligands and their nickel(II) complexes were prepared by the same group of authors [18]. This time, 1-methyl-2-(chloromethyl)benzimidazole reacted with (2-phenylethylthio)ethylamine (for L3Me) or (2-phenylseleno)ethylamine (for L4Me). Mononuclear and binuclear Ni(II) complexes were obtained by a reaction of nickel chloride with the ligands. Their structures can be seen in Figure 1.

The stability of complexes in aqueous solutions was monitored for 72 h by UV–vis spectroscopy, and these are stable in solutions. The cytotoxicity of complexes was screened against SK-LU-1 (human lung adenocarcinoma), HeLa (human cervical carcinoma), and HEK-293 (non-tumoral human embryonic kidney) cell lines using an MTT. It was found that the complexes are less cytotoxic in comparison with cisplatin, but they are selective to tumor cell lines.

1-(1*H*-benzimidazol-2-yl)-*N*-(1*H*-benzimidazol-2-ylmethyl)methanamine (abb) and 2-(1*H*-benzimidazol-2-ylmethylsulfanylmethyl)-1*H*-benzimidazole (tbb) have been prepared and characterized [19]. The trinuclear complex [Ni3(abb)3(H2O)3(µ-ttc)](ClO4)3, was where ttcH<sup>3</sup> = trithiocyanuric acid was prepared and characterized by X-ray (depicted in Figure 2A1,A2). The complex and ligands were tested on bacteria strains *Staphylococcus aureus*, *Escherichia coli*, and *Saccharomyces cerevisiae*. The complex was more active than ligands.

The same complex was used together with another trinuclear complex [Ni3(tebb)3(H2O)3(µttc)](ClO4)3, tebb = 2-[2-[2-(1*H*-benzimidazol-2-yl)ethylsulfanyl]ethyl]-1*H*-benzimidazole, to study cytotoxicity on breast cell lines T-47D, MCF-7 and non-malignant HBL-100 (complex cation shown in Figure 2B) [20]. ands. The same complex was used together with another trinuclear complex [Ni3(tebb)3(H2O)3(μ-ttc)](ClO4)3, tebb = 2-[2-[2-(1*H*-benzimidazol-2-yl)ethylsulfanyl]ethyl]-1*H*-benzimidazole, to study cytotoxicity on breast cell lines T-47D, MCF-7 and non-malignant HBL-100 (complex cation shown in Figure 2B) [20].

was found that the complexes are less cytotoxic in comparison with cisplatin, but they are

1-(1*H*-benzimidazol-2-yl)-*N*-(1*H*-benzimidazol-2-ylmethyl)methanamine (abb) and 2-(1*H*-benzimidazol-2-ylmethylsulfanylmethyl)-1*H*-benzimidazole (tbb) have been prepared and characterized [19]. The trinuclear complex [Ni3(abb)3(H2O)3(μ-ttc)](ClO4)3, was where ttcH3 = trithiocyanuric acid was prepared and characterized by X-ray (depicted in Figure 2A1,A2). The complex and ligands were tested on bacteria strains *Staphylococcus aureus*, *Escherichia coli*, and *Saccharomyces cerevisiae*. The complex was more active than lig-

*Inorganics* **2023**, *11*, x FOR PEER REVIEW 8 of 11

selective to tumor cell lines.

**Figure 2.** Molecular structures of complex cations: (**A1**,**A2**) [Ni3(abb)3(H2O)3(μ-ttc)]; Ni (green), O (red), C (gray), N (blue), S (yellow), (**B**) [Ni3(tebb)3(H2O)3(μ-ttc)], (**C1**,**C2**) [Ni(tebb)2]. The abb = 1- (1*H*-benzimidazol-2-yl)-*N*-(1*H*-benzimidazol-2-ylmethyl)methanamine, ttcH3 = trithiocyanuric acid, tebb = 2-[2-[2-(1*H*-benzimidazol-2-yl)ethylsulfanyl]ethyl]-1*H*-benzimidazole. **Figure 2.** Molecular structures of complex cations: (**A1**,**A2**) [Ni<sup>3</sup> (abb)<sup>3</sup> (H2O)<sup>3</sup> (µ-ttc)]; Ni (green), O (red), C (gray), N (blue), S (yellow), (**B**) [Ni<sup>3</sup> (tebb)<sup>3</sup> (H2O)<sup>3</sup> (µ-ttc)], (**C1**,**C2**) [Ni(tebb)<sup>2</sup> ]. The abb = 1-(1*H*-benzimidazol-2-yl)-*N*-(1*H*-benzimidazol-2-ylmethyl)methanamine, ttcH<sup>3</sup> = trithiocyanuric acid, tebb = 2-[2-[2-(1*H*-benzimidazol-2-yl)ethylsulfanyl]ethyl]-1*H*-benzimidazole.

It was found that complexes are very cytotoxic (24IC50 = 9.5 μM). The complex with abb was encapsulated in ferritin modified with folic acid to overcome toxicity to normal cells and enable transport to cancer cells. For a comparison of cytotoxicity of trinuclear complex with a mononuclear tebb complex, [Ni(tebb)2](ClO4)2 has been prepared (the cation shown in Figure 2C1,C2) [21]. The complex is readily uptaken by malignant MDA-MB-231 and CACO-2 cells and is not toxic to Hs27 fibroblasts. The lowest IC50 values were found for MDA-MB-231 cells (5.2 μM). DNA cleavage, DNA fragmentation leads to the formation of reactive oxygen species [21]. Antibacterial study against *Staphylococcus aureus* and *Escherichia coli* on [Ni3(tebb)3(H2O)3(μ-ttc)](ClO4)3 was reported by Ashrafi [22]. It was found that complexes are very cytotoxic (24IC50 = 9.5 µM). The complex with abb was encapsulated in ferritin modified with folic acid to overcome toxicity to normal cells and enable transport to cancer cells. For a comparison of cytotoxicity of trinuclear complex with a mononuclear tebb complex, [Ni(tebb)2](ClO4)<sup>2</sup> has been prepared (the cation shown in Figure 2C1,C2) [21]. The complex is readily uptaken by malignant MDA-MB-231 and CACO-2 cells and is not toxic to Hs27 fibroblasts. The lowest IC50 values were found for MDA-MB-231 cells (5.2 µM). DNA cleavage, DNA fragmentation leads to the formation of reactive oxygen species [21]. Antibacterial study against *Staphylococcus aureus* and *Escherichia coli* on [Ni3(tebb)3(H2O)3(µ-ttc)](ClO4)<sup>3</sup> was reported by Ashrafi [22].

### **4. Conclusions**

**4. Conclusions**  The goal of the mini review was to perform a literature search of the current state of the art of chemistry of bis(benzimidazole) syntheses and the preparation of complexes with the ligands. There are plenty of papers on the topic and many reviews. We have The goal of the mini review was to perform a literature search of the current state of the art of chemistry of bis(benzimidazole) syntheses and the preparation of complexes with the ligands. There are plenty of papers on the topic and many reviews. We have focused on complexes that were studied for their biological properties in the last 7 years.

focused on complexes that were studied for their biological properties in the last 7 years. Bis(benzimidazoles) were selected from the broad collection of papers dealing with benzimidazole complexes because bis(benzimidazoles) are structurally interesting and offer chelating and as well as bridging modes of coordination to central atoms. Plenty of these complexes have been known for ages, though these were prepared as models mimicking biological systems, so the data on biological activities was often missing. These known compounds can be further studied for biological properties and can find their potential to be used as drugs, for example, in cases where known antibiotics are insufficient to fight against resistant bacteria. From the literature, it is obvious that the complexes were mostly studied as antiproliferative, anticancer, and antitumor agents. From this point of view the studies are concerned on non-platinum metal-based drugs. Except of ruthenium, palladium and iridium complexes were found. There are some recent results on copper, cobalt, and zinc, and nickel, although nickel is mentioned in studies as a toxic metal. There are not many papers on silver complexes, and metals such as gold or iron can be other way to diversify our knowledge on biological properties of coordination compounds [2,3,23]. Very promising are combinations of ligands such as benzimidazoles with other biologically active ligands, for example Schiff bases. Some benzimidazoles contain sulfur or selenium that can increase their biological action or they can contain arms with the atoms to be more strongly coordinated to central atoms [18]. It should also be of interest to include P ligands to combine them with benzimidazoles to increase bioactivity, for example in the case of 2,6-bis(2-(diphenylphosphanyl)-1*H*-imidazol-1-yl)pyridine [24].

Fewer studies have been performed on bacteria strains. There are some papers on copper, zinc, and nickel bis(benzimidazole) complexes and their antibacterial properties, but the data are not available for all of the already known species. These can be future trends of studies on benzimidazole biological active complexes. Probable toxicity of prepared complexes can be overcome by using transporters on the base of nanoparticles that can deliver the complexes without side effects to healthy cells.

**Author Contributions:** Conceptualization, P.K.; resources, Z.Š. and P.K.; writing—original draft preparation, Z.Š. and P.K.; writing—review and editing, Z.Š. and P.K.; visualization, P.K.; supervision, P.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** Authors acknowledge financial support from the institutional sources of the Department of Inorganic Chemistry, Palacky University Olomouc, Czech Republic.

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

### **Abbreviations**

BIPM = 2-((1*H*-benzo[*d*]imidazol-2-yl)methylthio)-1*H*-benzo[*d*]imidazol-6-yl)(phenyl)methanone; BBP = 2,6-bis(1*H*-benzo[*d*]imidazol-2-yl)pyridine; PPA = polyphosphoric acid; BNBP = 2,6-bis- (6-nitrobenzimidazol-2-yl)pyridine; TBTU = *O*-(benzotriazol-1-yl)-*N*,*N*,*N*0 ,*N*0 -tetramethyluronium tetrafluoroborate; Etobb = 1,3-bis(1-ethylbenzimidazol-2-yl)-2-oxapropane; Bobb = 1,3-bis(1-benzylbenzimidazol-2-yl)-2-oxapropane; Aobb = 1,3-bis(1-allyl-benzimidazol-2-yl)-2-oxapropane; bmbp = 4-butyloxy-2,6-bis(1-methyl-2-benzimidazolyl)pyridine; abb = 1-(1*H*-benzimidazol-2-yl)-*N*- (1*H*-benzimidazol-2-ylmethyl)methanamine; tbb = 2-(1*H*-benzimidazol-2-ylmethylsulfanylmethyl)- 1*H*-benzimidazole; tebb = 2-[2-[2-(1*H*-benzimidazol-2-yl)ethylsulfanyl]ethyl]-1*H*-benzimidazole; ttcH<sup>3</sup> = trithiocyanuric acid; Bcl-2 = B-cell lymphoma 2; BSA = bovine serum albumin; HBL-100 = human breast epithelial cell line; MDA-MB-231 human breast adenocarcinoma cancer cell line; MIC = minimum inhibitory concentration; MOF = metal–organic framework; ROS = reactive oxygen species; SOD—superoxide dismutase.

### **References**


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