Supramolecular Diversity, Theoretical Investigation and Antibacterial Activity of Cu, Co and Cd Complexes Based on the Tridentate N,N,O-Schiff Base Ligand Formed In Situ

The four new complexes, [Cu(HL1)(L2)Cl] (1), [Cu(HL1)(L1)]∙Cl∙2H2O (2), [Co(L1)2]∙Cl (3) and [Cd(HL1)I2]∙dmso (4), have been prepared by one-pot reactions of the respective chloride or iodide metal salt with a non-aqueous solution of the polydentate Schiff base, HL1, resulted from in situ condensation of benzhydrazide and 2-pyridinecarboxaldehyde, while a ligand HL2, in case of 1, has been formed due to the oxidation of 2-pyridinecarboxaldehyde under reaction conditions. The crystallographic analysis revealed that the molecular building units in 1–4 are linked together into complex structures by hydrogen bonding, resulting in 1D, 2D and 3D supramolecular architectures for 1, 2 and 4, respectively, and the supramolecular trimer for 3. The electronic structures of 1–4 were investigated by the DFT theoretical calculations. The non-covalent interactions in the crystal structures of 1–4 were studied by means of the Hirshfeld surface analysis and the QTAIM theory with a special focus on the C–H⋯Cl bonding. From the DFT/DLPNO-CCSD(T) calculations, using a series of charged model {R3C–H}0⋯Cl− assemblies, we propose linear regressions for assessment of the interaction enthalpy (ΔH, kcal mol−1) and the binding energy (BE, kcal mol−1) between {R3C–H}0 and Cl− sites starting from the electron density at the bond critical point (ρ(rBCP), a.u.): ΔH = −678 × ρ(r) + 3 and BE = −726 × ρ(r) + 4. It was also has been found that compounds 1, 3 and 4 during in vitro screening showed an antibacterial activity toward the nine bacteria species, comprising both Gram-positive and Gram-negative, with MIC values ranging from 156.2 to 625 mg/L. The best results have been obtained against Acinetobacter baumannii MβL.


Introduction
The Schiff bases are recognized as an important class of organic ligands for the design and construction of the polymeric and polynuclear coordination compounds since they can be easily formed as novel ligand systems using the simple in situ condensation of a large and variable library of readily available aldehydes and amines [1,2]. Such complexes present many applications in catalysis, magnetochemistry, oxygen storage devices and show antitumoral and antiviral and antibacterial activity [1,[3][4][5]. The creation of effective antimicrobial agents is currently one of the most important challenges for medicinal chemistry. Due to the non-terminating development of the resistance of microorganisms (bacteria, fungi, viruses and parasites) to antimicrobial drugs, the search for new antimicrobial drugs still remains an essential and highly demanded task [6].
Nowadays, special attention is paid to the weak non-covalent interactions that often have predetermining role in the formation of supramolecular structures [7] as well as conformational changes in materials and bioactive molecules [8]. The molecular Schiff base complexes represent a good example for studying such types of intra-and intermolecular weak bonding due to the great diversity of Schiff base ligands [2]. The DFT theoretical calculation of the electron density and the extraction of its descriptors by means of quantum theory of atoms in molecules (QTAIM) provides a basis for the analysis of a weak interaction [9]. The search for the reliable correlation between the electron density at the bond critical points ρ(r BCP ) and the bond energy is an open question. Emamian and Lu described simple linear regressions that allow an easy estimation of the binding energy from ρ(r BCP ) for charged and neutral {X-H· · · Y} assemblies [10]. However, it is known that weak interactions (e.g., halogen bonding) are better described by regressions fitted to a specific data set rather than a broad one [11]. The C-H· · · Cl bonding is a case of particular interest because the respective contacts between chlorine-containing drugs and biological targets have a strong influence on the drug affinity and, therefore, the bioactivity [12][13][14]. Moreover, the interaction of a halide anion with C-H groups is the basis of many anion-selective receptors [12,15,16].

Synthesis
The complexes 1-4 (Scheme S1) were obtained using the two steps synthetic approach within the same reaction vessel: (1) in situ formations of a Schiff base ligand by condensation of benzhydrazide and 2-pyridinecarboxaldehyde and (2) reaction of the prepared Schiff base ligand (HL 1 , Scheme 1) with a metal precursor. The choosing strategy receives a broad application in the synthesis of Schiff base-containing coordination compounds and allows to use of the Schiff base ligand immediately after its formation. The interaction of metal chlorides (1)(2)(3) or iodide (4) with a non-aqueous (CH 3 OH for 1-3 and dmso for 4) solutions of HL 1 using a molar ratio of MX 2 :HL 1 = 1:2, resulted in green (1-2), brown (3) or yellow-orange (4) solutions obtained at the end of the reactions. All reactions were initiated and brought to completion by stirring and heating in the open air. Microcrystals 1 and 3 were formed in two days from the resulting solution, while microcrystals 2 were obtained from the filtrate of 1 in ca. one month. Microcrystals of 4 were obtained in two weeks after the addition of i PrOH into the resulting solution. Unexpectedly, in addition to the presence of desired HL 1 Schiff base ligand in 1, the single crystal X-ray analysis disclosed a presence of HL 2 , 2-pyridinecarboxylic acid (Scheme 1) as well. The formation of HL 2 can be understood by assuming aerobic oxidation of 2-pyridinecarboxaldehyde under reaction conditions since this process is known for aldehyde chemistry [34]. The IR spectra of 1-4 and the ligand HL 1 are depicted in Figures S1-S5.

Synthesis
The complexes 1-4 (Scheme S1) were obtained using the two steps synthet proach within the same reaction vessel: (1) in situ formations of a Schiff base liga condensation of benzhydrazide and 2-pyridinecarboxaldehyde and (2) reaction of th pared Schiff base ligand (HL 1 , Scheme 1) with a metal precursor. The choosing str receives a broad application in the synthesis of Schiff base-containing coordination pounds and allows to use of the Schiff base ligand immediately after its formation interaction of metal chlorides (1)(2)(3) or iodide (4) with a non-aqueous (CH3OH for 1dmso for 4) solutions of HL 1 using a molar ratio of MX2:HL 1 = 1:2, resulted in green brown (3) or yellow-orange (4) solutions obtained at the end of the reactions. All rea were initiated and brought to completion by stirring and heating in the open air. M crystals 1 and 3 were formed in two days from the resulting solution, while microcr 2 were obtained from the filtrate of 1 in ca. one month. Microcrystals of 4 were obt in two weeks after the addition of i PrOH into the resulting solution. Unexpectedly, dition to the presence of desired HL 1 Schiff base ligand in 1, the single crystal X-ray ysis disclosed a presence of HL 2 , 2-pyridinecarboxylic acid (Scheme 1) as well. Th mation of HL 2 can be understood by assuming aerobic oxidation of 2-pyridinecar dehyde under reaction conditions since this process is known for aldehyde chemistr The IR spectra of 1-4 and the ligand HL 1 are depicted in Figures S1-S5.
In the crystal lattice, the two closest neighboring molecules are strongly linked by hydrogen bonding between the oxygen atoms of the pyridine-carboxylates and the nitrogen atoms of Schiff base ligands ( Figure 2) [N3-H3· · · O1 a (a = 1 − x, 1 − y, 1 − z), D-A = 2.884(3) Å, D-H· · · A = 150.1 • ]. Moreover, the hydrogen bonds formed with the participation of the Schiff base ligands and coordinated chloride anions [C8-H8· · · Cl1 b (b = 1 − x, 1 − y, −z), D-A = 3.734(3) Å, D-H· · · A = 153.9 • ] tie together abovementioned supramolecular dimers into one-dimensional chains. The nearest Cu· · · Cu distance within the supramolecular chain in 1 are 6.1899(10) and 8.1024(10) Å.  In the crystal lattice, the two closest neighboring molecules are strongly linked by hydrogen bonding between the oxygen atoms of the pyridine-carboxylates and the nitrogen atoms of Schiff base ligands ( The single crystal X-ray analysis shows that 2 includes a [Cu(HL 1 )(L 1 )] + cation (Figure 3), one Clanion and two uncoordinated water molecules joined into supramolecular two-dimensional layers assisted by hydrogen bonds. The Schiff base ligands in 2 are present in both deprotonated and non-deprotonated forms and reveal the tridentate-chelating (N,N,O) coordination mode. Similarly to 1, the Cu(II) atom has a distorted elongated octahedral environment but with an O2N4 donor set formed by the Schiff bases. The Cu-X (X = O, N) bond lengths in the equatorial plain are in the range 1.931(2)-2.069(2) Å, and the apical Cu1-O2 and Cu1-N6 distances are 2.582(2) and 2.254(3) Å, respectively (Table S2). The O(N)-Cu-Ntrans bond angles vary from 144.32 (8) to 175.14(10)°.         Furthermore, the uncoordinated water molecules join the supramolecular dimers in 2, forming two-dimensional layers by means of strong O-H· · · O and O-H· · · Cl hydrogen bonding between dimers and chloride anions ( Figure 5 The chains formed by uncoordinated H 2 O molecules and Cl anions within the overall 2D structure of 2 can be considered as an independent supramolecular motif. They are built by {O H2O · · · O H2O · · · Cl} 2 synthons which are connected through O-H· · · O bridges ( Figure 5 (Table S3).  (Table S3).    In the solid state, the [Co(L 1 ) 2 ] + cations with uncoordinated Cl anions form supramolecular trimers by means of C-H· · · Cl bonding ( Figure 7 . Additionally, one more chlorine anion is connected by C-H· · · Cl contacts to each cobalt(III) moiety of this trimer [C26-H26· · · Cl2A, D-A = 3.480(4) Å, D-H· · · A = 154.6 • ]. The observed Co· · · Co intermolecular separation within the supramolecular trimer is 10.397 Å.
The crystal structure of the 4 is formed of discrete neutral [Cd(HL 1 )I 2 ] molecules ( Figure 8) and dmso molecules of crystallization, joined by strong hydrogen bonding with the formation of an extended supramolecular 3D structure (  (Table S4), while the angles at the Cd atoms vary from 66.86(9) to 135.73(9)°.     , involving nitrogen atoms from imine moieties of Schiff base ligands, oxygen atoms from uncoordinated dmso molecules, carbon atoms from Schiff bases and dmso molecules and coordinated I − anions, are responsible for the formation of the extended supramolecular three-dimensional framework ( Figure 9). The closest Cd· · · Cd intermolecular separation within the framework exceeds 7.48 Å.

Theoretical Calculations
The mononuclear complex 1 represents a "classical" Cu(II) coordination compound with the S = 1/2 ground state and unpaired electron localized at the copper center (spin population of 0.710, according to the Löwdin population analysis of the quasi-restricted molecular orbitals). The HOMO orbital has large contributions from p z (30.1%) and p x (19.0%) orbitals of the oxygen atom and p z (17.4%) of the chlorine one ( Figure 10). The LUMO orbital is strongly delocalized over the atoms of the ligands.
In the supramolecular structure of 1 (Figure 2), one can select strongly bridged dimers, strengthened by the N-H· · · O and C-H· · · O hydrogen bonds as well as the π-π stacking. Analysis of the electron density ρ(r) and the bond critical points (BCPs) reveals two symmetrically equivalent sets of critical points (Figure 11), both formed by the oxygen atom O1 and H a atoms from N3 a , C12 a and C19 a ones (where the symmetry operation a is 1 − x, 1 − y, 1 − z). The sum electron density ρ(r) in these six BCPs is 7.1 × 10 −2 a.u. According to the model developed by Emamian and Lu [10], this value corresponds to the binding energy of −15.1 kcal mol −1 , which can be considered a strong H-bonded coupling.
The mononuclear complex 1 represents a "classical" Cu(II) coordination compound with the S = 1/2 ground state and unpaired electron localized at the copper center (spin population of 0.710, according to the Löwdin population analysis of the quasi-restricted molecular orbitals). The HOMO orbital has large contributions from pz (30.1%) and px (19.0%) orbitals of the oxygen atom and pz (17.4%) of the chlorine one ( Figure 10). The LUMO orbital is strongly delocalized over the atoms of the ligands. In the supramolecular structure of 1 (Figure 2), one can select strongly bridged dimers, strengthened by the N-H•••O and C-H···O hydrogen bonds as well as the π-π stacking. Analysis of the electron density ρ(r) and the bond critical points (BCPs) reveals two symmetrically equivalent sets of critical points (Figure 11), both formed by the oxygen atom O1 and H a atoms from N3 a , C12 a and C19 a ones (where the symmetry operation a is 1 − x, 1 − y, 1 − z). The sum electron density ρ(r) in these six BCPs is 7.1 × 10 −2 a.u. According to the model developed by Emamian and Lu [10], this value corresponds to the binding energy of −15.1 kcal mol −1 , which can be considered a strong H-bonded coupling.   In the supramolecular structure of 1 (Figure 2), one can select st mers, strengthened by the N-H•••O and C-H···O hydrogen bonds as we ing. Analysis of the electron density ρ(r) and the bond critical points ( symmetrically equivalent sets of critical points (Figure 11), both form atom O1 and H a atoms from N3 a , C12 a and C19 a ones (where the symm 1 − x, 1 − y, 1 − z). The sum electron density ρ(r) in these six BCPs is 7.1 × to the model developed by Emamian and Lu [10], this value correspo energy of −15.1 kcal mol −1 , which can be considered a strong H-bonded  The additional contribution to the binding energy of −1 kcal mol −1 comes from the interaction of phenyl and pyridine rings of the Schiff base ligands (Figure 12). The aromatic rings interact in the distorted parallel offset mode [35] with the angle of 25.4 • and ρ(r BCP ) = 3.9 × 10 −3 a.u. for the closest contacts. Optimization of the geometry of the dimer of 1 reveals that the parallel offset mode persists ( Figure S6), while the angle between planes formed by the aromatic rings becomes much smaller (10.0 • ). This suggests that rotation of the aromatic rings in the solid state is induced by the intermolecular interactions, not accounted for in the molecular geometry optimization. matic rings interact in the distorted parallel offset mode [35] with the angle of 25.4° and ρ(rBCP) = 3.9 × 10 −3 a.u. for the closest contacts. Optimization of the geometry of the dimer of 1 reveals that the parallel offset mode persists ( Figure S6), while the angle between planes formed by the aromatic rings becomes much smaller (10.0°). This suggests that rotation of the aromatic rings in the solid state is induced by the intermolecular interactions, not accounted for in the molecular geometry optimization. The broken symmetry calculations revealed the very small singlet-triplet splitting of −0.05 and −0.12 cm −1 (using B3LYP and ωB97X-D4 functionals, respectively, H = JS1S2 notation and J = 2(EHS − EBS)/(SA + SB) 2 formalism [37][38][39]). The calculated overlap between the magnetic orbitals (according to the analysis of unrestricted corresponding orbitals), containing unpaired electrons located on the copper atoms, constitutes 0.004 and 0.001 for B3LYP and ωB97X-D4 functionals, respectively. These values are ca. one order smaller than those expected for spin-coupled orbitals [40]. Thus, one can conclude that Cu(II) centers in 1 are almost magnetically isolated, but the existence of a small ferromagnetic coupling cannot be excluded.
Complex 2 features the HOMO and LUMO quasi-restricted molecular orbitals strongly delocalized over the ligands' atoms ( Figure 13). The spin population (S = 1/2 ground state) of the copper center is similar (0.727) to that found for complex 1. The HOMO orbital of the diamagnetic complex 3 is totally located on one of the ligands, while the LUMO orbital is delocalized over two ligand moieties ( Figure 14). Both HOMO and LUMO molecular orbitals in the cation of 3 have negligible (less than 1%) contributions to the atomic orbitals of the cobalt atom. The same as for 3, the HOMO molecular orbital of the diamagnetic complex 4 is located at the halogen atoms and does not involve the cadmium center (Figure 15). Both iodine atoms have a high contribution, namely 39.1% of px orbital of I(1) and 22.8% pz and 22.1% of pz and py, respectively, of I(2). The broken symmetry calculations revealed the very small singlet-triplet splitting of −0.05 and −0.12 cm −1 (using B3LYP and ωB97X-D4 functionals, respectively, H = JS 1 S 2 notation and J = 2(E HS − E BS )/(S A + S B ) 2 formalism [37][38][39]). The calculated overlap between the magnetic orbitals (according to the analysis of unrestricted corresponding orbitals), containing unpaired electrons located on the copper atoms, constitutes 0.004 and 0.001 for B3LYP and ωB97X-D4 functionals, respectively. These values are ca. one order smaller than those expected for spin-coupled orbitals [40]. Thus, one can conclude that Cu(II) centers in 1 are almost magnetically isolated, but the existence of a small ferromagnetic coupling cannot be excluded.
Complex 2 features the HOMO and LUMO quasi-restricted molecular orbitals strongly delocalized over the ligands' atoms ( Figure 13). The spin population (S = 1/2 ground state) of the copper center is similar (0.727) to that found for complex 1. The HOMO orbital of the diamagnetic complex 3 is totally located on one of the ligands, while the LUMO orbital is delocalized over two ligand moieties ( Figure 14). Both HOMO and LUMO molecular orbitals in the cation of 3 have negligible (less than 1%) contributions to the atomic orbitals of the cobalt atom. The same as for 3, the HOMO molecular orbital of the diamagnetic complex 4 is located at the halogen atoms and does not involve the cadmium center ( Figure 15). Both iodine atoms have a high contribution, namely 39.1% of p x orbital of I(1) and 22.8% p z and 22.1% of p z and p y , respectively, of I(2).
The supramolecular structures of the complexes 1-3 reveal numerous C-H· · · Cl contacts of various strengths, where coordinated (1) or free (2 and 3) chloride anions are surrounded by the hydrogen atoms from the ligands. The Hirshfeld surface analysis [41] and the fingerprint plots disclose that the Cl· · · H contacts constitute the largest contribution to the intramolecular Cl· · · X interactions, being 100% for 3 ( Figure 16). The non-deprotonated form of the ligand (HL 1 ) is an excellent receptor for the anions due to the presence of three C-H groups directed approximately to a single point. Geometry optimization of the {HL 1 ·Cl} − assembly using the coordinates from structure 2 as the starting point shows that the chlorine atom is in the ligand's plane, forming three strong hydrogen bonds ( Figure 17). The enthalpy of the interaction between HL and Cl − was found to be −32.1 kcal mol −1 (ωB97X-D4/ma-def2-TZVP level).  The supramolecular structures of the complexes 1-3 reveal numerous C-H•••Cl contacts of various strengths, where coordinated (1) or free (2 and 3) chloride anions are surrounded by the hydrogen atoms from the ligands. The Hirshfeld surface analysis [41] and the fingerprint plots disclose that the Cl•••H contacts constitute the largest contribution to the intramolecular Cl•••X interactions, being 100% for 3 ( Figure 16). The non-deprotonated form of the ligand (HL 1 ) is an excellent receptor for the anions due to the presence of three C-H groups directed approximately to a single point. Geometry optimization of the {HL 1 •Cl} − assembly using the coordinates from structure 2 as the starting point shows that the chlorine atom is in the ligand's plane, forming three strong hydrogen bonds ( Figure  17). The enthalpy of the interaction between HL and Clwas found to be −32.1 kcal mol −1 (ωB97X-D4/ma-def2-TZVP level).  The supramolecular structures of the complexes 1-3 reveal numerous C-H•••Cl contacts of various strengths, where coordinated (1) or free (2 and 3) chloride anions are surrounded by the hydrogen atoms from the ligands. The Hirshfeld surface analysis [41] and the fingerprint plots disclose that the Cl•••H contacts constitute the largest contribution to the intramolecular Cl•••X interactions, being 100% for 3 ( Figure 16). The non-deprotonated form of the ligand (HL 1 ) is an excellent receptor for the anions due to the presence of three C-H groups directed approximately to a single point. Geometry optimization of the {HL 1 •Cl} − assembly using the coordinates from structure 2 as the starting point shows that the chlorine atom is in the ligand's plane, forming three strong hydrogen bonds ( Figure  17). The enthalpy of the interaction between HL and Clwas found to be −32.1 kcal mol −1 (ωB97X-D4/ma-def2-TZVP level).     It is known that the energies of weak interactions (including hydrogen bonds) can be approximately estimated through the evaluation of the electron density ρ(r) at the respective bond critical points (BCPs). This approach allows for the extraction of the energies of intramolecular interactions for which the individual energies of donor and acceptor sites It is known that the energies of weak interactions (including hydrogen bonds) can be approximately estimated through the evaluation of the electron density ρ(r) at the respective bond critical points (BCPs). This approach allows for the extraction of the energies of intramolecular interactions for which the individual energies of donor and acceptor sites cannot be calculated due to the inseparability of the whole molecule. While the BE vs. ρ(r) linear regressions (where BE is the binding energy) proposed by Emamian and Lu can be applied to a broad range of hydrogen bonds [10], re-examination of the BE vs. ρ(r) reference data for a certain X-H· · · Y pair may result in more precise coefficients of regression.
The choice of a calculation method for precise estimation of interaction energies in weakly bonded supramolecular assemblies is a topic of broad discussion, where the computational resources required to perform calculations at high levels are a crucial factor [42]. We selected several examples from the S66 dataset of the Benchmark Energy & Geometry Database (BEGDB) [43], where small molecules (such as water and methanol) form weak hydrogen bonds with other fragments. The original binding energies reported by Hobza et al. [43] were reconsidered several times [44,45]. Herein we used the BEs reported by Martin et al. [45] as a reference, where energies were calculated using a few sets of explicitly correlated methods with the basis sets near the limit along with counterpoise (CP) and other corrections. Since the accurate geometries and interaction energies in S66 were accurately determined [43,45], we tested several routine methods against the models 01, 03, 04, 09 and 18 of the S66 dataset. The geometries re-optimized at the ωB97X-D4/ma-def2-TZVP level showed only a slight difference from those reported in S66 (Table S8). The lowest deviation was found for the model 01 (HOH· · · OH 2 water dimer), while the highest one for the model 09 (interaction of methanol with methylamine). For these re-optimized geometries, we calculated the binding energies using the DLPNO-CCSD(T) scheme involving def2-TZVPPD and aug-cc-pV{D,T}Z, aug-ano-pV{D,T}Z and aug-ano-pV{T,Q}Z basis sets [46][47][48] with or without counterpoise correction [49] (Table S8). The extrapolated aug-ano-pV{T,Q}Z CP-corrected basis set gave excellent (<0.08 kcal mol −1 ) agreement with the reference data for 01 and 03 models (RMS = 0.09). However, this method is computationally demanding, and its use for heavier models was not justified under our conditions. Surprisingly, the second method of high accuracy was def2-TZVPPD without CP correction, which showed an RMS of 0.125 and the highest deviation of 0.21 kcal mol −1 (Table S8). A similar level of accuracy was observed for extrapolated aug-cc-pV{D,T}Z and aug-ano-pV{D,T}Z basis sets involving CP-correction (RMS = 0.161 and 0.182, respectively), while all extrapolated methods showed considerably higher RMS in the absence of counterpoise correction. Remarkably, the application of counterpoise correction along with the def2-TZVPPD basis set resulted in the highest RMS of 0.66 and BE deviation of almost 1 kcal mol −1 . It is known that, in certain cases, the errors of smaller basis sets may compensate for basis set superposition error (BSSE) and other systematic errors. For example, Antony and Grimme recommended SCS-MP2 with the triple-ζ basis sets (TZVPP and cc-pVTZ) without CP correction as the methods give reasonable results for large systems involving weak interactions [50]. In some cases, the half-counterpoise correction [10,51] or extrapolation to the basis set limit was found to better describe the reference data [52,53]. Although the BSSE largely affects the small (double-ζ) basis sets [54,55], the DFT scheme used herein for geometry optimizations (ωB97X-D4/ma-def2-TZVP) may suffer from the BSSE when calculating binding energies [54], also because estimation of the absolute electronic energy is a known weak point of the DFT. However, the geometrical parameters of the S66 models calculated at the DFT level are close to those obtained at the ab initio level (Table S8), while the DLPNO-CCSD(T) correction of the final energy allows approaching the reference BE values.
We checked how the H· · · Cl separation in the {CH 4 · · · Cl} − model assembly is influenced by the calculation level (Table S9). The ωB97X-D4/ma-def2-TZVP method affords d(H· · · Cl) = 2.689 Å. The application of the geometrical semi-empirical counterpoise correction (gCP) [56] along with the def2-TZVP basis set shortens the d(H· · · Cl) distance down to 2.591 Å (the pure def2-TZVP calculation gives d(H· · · Cl) = 2.575 Å), indicating that diffuse functions are essential for the present case of anion assembly. The increase of the basis set up to def2-QZVPPD, which is large enough to minimize BSSE until negligible level [57,58], results in H· · · Cl separation of 2.672 Å, which is slightly shorter than that for ma-def2-TZVP. A very similar distance of 2.673 Å was obtained for a very large aug-cc-pV6Z basis set (Table S9). While the ωB97M-V [59] and M06-2X [60] functionals showed similar tendencies, the SCS-MP2 method [61] gave much shorter d(H· · · Cl) = 2.603 Å for aug-cc-pV6Z, while for def2-QZVPPD the elongated distance of 2.713 Å was obtained. Finally, we optimized the {CH 4 · · · Cl} − geometry at the DLPNO-CCSD(T)/def2-QZVPPD level, which gave d(H· · · Cl) = 2.651 Å (Table S9). Thus, the geometry exhibited by the ωB97X-D4/ma-def2-TZVP method fits into the spread of d(H· · · Cl) distances. Considering this, as well as the success in the description of the selected S66 models (Table S8), we assume the precision of this DFT method to be sufficient for the present study.
We considered a series of model complexes {R 3 C-H} 0 · · · Cl − , including radical forms (Tables S5 and S6, Figures S8-S10), for which BE vs. ρ(r) and ∆H vs. ρ(r) dependences were studied. Both binding energy and enthalpy data can be fitted to linear equations with R 2 of 0.92 and 0.91 and the RMS values of 1.60 and 1.55, respectively ( Figure 18).  [10].
The slope of the fitted line obtained for the BE vs. ρ(r) data (−726) significantly differs from that proposed by Emamian et al. for charged complexes (−332.34) [10]. Moreover, the latter equation is not able to describe the data in the region of strong interactions (Figure 18, right). To ensure that this discrepancy is not a result of differences in calculation methodology, we reproduced the geometries, electron densities and binding energies of several H-bonded assemblies used in [10]. We found that under our conditions, the energies of the assemblies and the slope of the BE vs. ρ(r) linear fit are almost identical to those reported by Emamian et al. [10] ( Figure S11). Therefore, one can conclude that the case of {R3C-H} 0 •••Cl − interactions is better described by the linear regression proposed herein. Further, we did not find a notable change in enthalpies when using larger basis sets (ma-def2-QZVPP and aug-cc-pVQZ) for DLPNO-CCSD(T) correction ( Figure S12). The pure DFT calculations (without the DLPNO-CCSD(T) correction) give the binding energies only slightly different from those for CCSD-corrected DFT data, maintaining the overall statistical distribution ( Figure S13).
From the proposed regressions, the interaction enthalpy of the {HL 1 •Cl} − assembly ( Figure 17) is expected to be -37.6 kcal mol −1 , which is rather close to the value found from the vibrational energies at the DFT level (−32.1 kcal mol −1 ). As the {HL 1 •Cl} − constitutes Figure 18. Dependences of the dissociation enthalpy (∆H, left) and the binding energy (BE, right) on the electron density ρ(r) at the H· · · Cl bond critical point in the set of model compounds featuring one (empty and black filled circles) or two (red filled circle) {R 3 C-H} 0 · · · Cl − hydrogen bonds ( Figure S8), where Cl is an isolated atom. The black-filled circles correspond to the radical species (triplet state); all others are in the singlet state. Solid red and green lines correspond to the least-squares linear fits: ∆H = −678 × ρ(r) + 3 and BE = −726 × ρ(r) + 4. Dash dot blue line (right) was calculated using the parameters reported by Emamian and Lu [10].
The slope of the fitted line obtained for the BE vs. ρ(r) data (−726) significantly differs from that proposed by Emamian et al. for charged complexes (−332.34) [10]. Moreover, the latter equation is not able to describe the data in the region of strong interactions (Figure 18, right). To ensure that this discrepancy is not a result of differences in calculation methodology, we reproduced the geometries, electron densities and binding energies of several H-bonded assemblies used in [10]. We found that under our conditions, the energies of the assemblies and the slope of the BE vs. ρ(r) linear fit are almost identical to those reported by Emamian et al. [10] ( Figure S11). Therefore, one can conclude that the case of {R 3 C-H} 0 · · · Cl − interactions is better described by the linear regression proposed herein. Further, we did not find a notable change in enthalpies when using larger basis sets (ma-def2-QZVPP and aug-cc-pVQZ) for DLPNO-CCSD(T) correction ( Figure S12). The pure DFT calculations (without the DLPNO-CCSD(T) correction) give the binding energies only slightly different from those for CCSD-corrected DFT data, maintaining the overall statistical distribution ( Figure S13).
From the proposed regressions, the interaction enthalpy of the {HL 1 ·Cl} − assembly ( Figure 17) is expected to be -37.6 kcal mol −1 , which is rather close to the value found from the vibrational energies at the DFT level (−32.1 kcal mol −1 ). As the {HL 1 ·Cl} − constitutes two C-H· · · Cl and one N-H· · · Cl bonds, we checked the applicability of the proposed model for {N-H} 0 · · · Cl − contacts: the DFT and regression model predicted ∆H for {CH 3 NH 2 · · · Cl} − equal to −9.8 and −9.7 kcal mol −1 , respectively. For the protonated ligand {H 2 L 1 } + interacting with the chloride anion, the regression predicts ∆H = −58.6 kcal mol −1 , while the DFT calculations give twice higher value ∆H of −112.8 kcal mol −1 . Such a strong interaction is illustrated by significant shortening of the N-H· · · Cl contact from 2.219 to 1.857 Å for {HL 1 ·Cl} − and {H 2 L 1 ·Cl} 0 , respectively ( Figure 17 and Figure S7), where the Löwdin charges at the respective H atoms in the free ligands are 0.219 and 0.241, respectively. Therefore, the linear regressions proposed herein should be used with care for the assessment of the stability of supramolecular assemblies with charges other than {R 3 C-H} 0 · · · Cl − .

Antibacterial Activity Studies
Complexes 1, 3 and 4 were screened for antibacterial activity with a following evaluation of the minimal inhibitory concentration (MIC) ( The MIC values ranged between 156. 25

Experimental
All chemicals were of reagent grade and used as received. All chemical experiments were carried out in air. Elemental analyses for CHN were provided by the Microanalytical Service of the Taras Shevchenko National University of Kyiv. Infrared spectra (4000-400 cm −1 ) were recorded in KBr pellets using a PerkinElmer 1600 FT-IR (PerkinElmer Inc., Waltham, MA, USA) instrument. Benzhydrazide (0.27 g, 2 mmol) and 2-pyridinecarboxaldehyde (0.19 mL, 2 mmol) were dissolved in CH 3 OH (20 mL), forming a light-yellow solution which was magnetically stirred at 50-60 • C (30 min). Then, CuCl 2 ·2H 2 O (0.17 g, 1 mmol) was added, and the resulting mixture was stirred for 1 h. The brown precipitate, which was immediately formed after cooling the obtained solution, was filtered, and the resulting solution was kept at r.t. Dark green crystals of 1, suitable for the X-ray crystallographic study, were formed in two days. Yield: 0.1 g. Anal. calc. for C 19 (4) Benzhydrazide (0.27 g, 2 mmol) and 2-pyridinecarboxaldehyde (0.19 mL, 2 mmol) were dissolved in dmso (20 mL), forming a light-yellow solution which was magnetically stirred at 50-60 • C (30 min). Then, CdI 2 (0.37 g, 1 mmol) was added, and the resulting mixture was stirred for 2 h. Yellow-orange crystals of 4, suitable for X-ray crystallographic study, were formed two weeks after the addition of 4 mL of i PrOH. Yield: 0.14 g, 21%. Anal. calc. for C 15

Crystallography
Single-crystal X-ray data for all compounds were collected on a Gemini A diffractometer (Agilent Technologies Inc., Santa Clara, CA, USA) equipped with an Atlas CCD detector, using graphite monochromated MoKα radiation. The data were treated using the CrysAlisPro software suite program package [66]. Analytical absorption corrections were applied to all data sets. All structures were solved using the dual-space algorithm of the SHELXT [67] program implemented in the Olex2 (version 1.5) crystallographic software [68]. Structure refinement was performed with SHELXL-2014 software [69]. The atom O4 in 2 was found to be disordered over two positions, O4A and O4B, with occupancies of 0.74(2) and 0.26 (2), respectively. Details of the data collection and processing, structure solution and refinement are summarized in Table 2. Crystallographic data for the structures reported can be obtained free of charge from the Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/ cif quoting the deposition numbers CCDC 2209507 (1), 2209509 (2), 2209508 (3), and 2209510 (4).

Theoretical Calculations
The ORCA 5.0.3 package was used for all calculations [70][71][72]. Unless stated otherwise, the calculations were performed using ωB97X-D4 functional [73] with the minimally augmented ma-def2-TZVP basis sets [74,75]. The effective core potentials (ECP) included in the ma-def2-TZVP basis set were used to describe the core electrons of Cd and I atoms. Grimme's atom-pairwise dispersion correction was employed [76]. The SCF and optimization convergence criteria were settled with VeryTightSCF and TightOPT keywords, respectively. Integration grids of high density (Defgrid3 keyword) were used. The CCSD calculations were performed through the DLPNO-CCSD(T) scheme [77] using the def2-TZVPPD basis set [46,75] and the TightPNO keyword. For calculations of singlet molecules, the "UseFullLMP2Guess false" command was applied to adjust the energies of closed-shell and open-shell calculations. AutoAux keyword [78] was used to generate auxiliary basis sets in all cases. To obtain the binding energy (BE) of the X· · · Y assembly, the whole geometry was optimized at the DFT level, and individual electronic energies E XY , E X and E Y were calculated at the DLPNO-CCSD(T) level with no structural relaxation of the X and Y components. The final BE was calculated according to the equation BE XY = E XY − E X − E Y . The counterpoise (CP) correction [49] was not applied unless stated otherwise. The interaction enthalpy ∆H was obtained from the vibrational energies calculated on the DFT-optimized structures of dimers and relaxed monomers, where the electronic energies were corrected at the DLPNO-CCSD(T) level for relaxed geometries of the monomers. The root mean square deviation (RMS) was defined as RMS =

2
, where E calcd. and E fit.
are energies or enthalpies obtained from DFT/DLPNO-CCSD(T) calculations and linear regression, respectively. Visualization of molecular orbitals was made using Avogadro 1.2 program [79]. Analysis of bond critical points and non-covalent interactions indexes [36] was performed using Multiwfn 3.8 program [80]. Hirshfeld analysis and surface visualization were made using the CrystalExplorer 17.5 program [81]. Cartesian coordinates of the DFT-optimized structures are given in Listing S1.

Strains Culturing Conditions and Antibacterial Assay
Gram-negative bacteria (Escherichia coli ATCC 25922, Pseudomonas aeruginosa ATCC 27853, Klebsiella pneumoniae ATCC 700603, Acinetobacter baumannii ATCC BAA 747, Pseudomonas aeruginosa HUI PAMβL) and Gram-positive bacteria (Staphylococcus aureus ATCC 25923, Staphylococcus aureus HUI MRSA, Staphylococcus aureus ATCC MR 43300, Staphylococcus haemolyticus HUI MRCNS). All strains were stored as frozen stocks in 25 (v/v)% glycerol at −80 • C. Pseudomonas aeruginosa HUI PAMβL, Staphylococcus aureus HUI MRSA, Staphylococcus haemolyticus HUI MRCNS were obtained from Ukrainian hospitals. The Kirby-Bauer disc-diffusion assay was used to determine the antimicrobial susceptibility as the diameter (mm) of inhibition or minimum inhibitory concentration (MIC) value after incubation for two days and interpreted according to the European Committee on Antimicrobial Susceptibility Testing (EUCAST) guidelines [82]. Antibiotic susceptibilities of the studied strains are listed in Tables S10 and S11.
Antibacterial activity of 1, 3 and 4 was studied by the MICs method using the broth microdilution approach. The compounds were dissolved in dmso:H 2 O = 1:1 mixture under heating in a water bath for 1 h to achieve a stock concentration of 1.25 µg/mL. Further, the resulting solutions were incubated at 37 • C for 12 h. Separately, the control of the growth in the experiments with sterile distilled water or solvent mixture without the addition of coordination compounds was carried out. If the solutions with high concentrations of dmso (50% and 25%) showed antibacterial activity, such an effect was not associated with the activity of the studied complexes and was neglected.
All bacteria were cultured in Cation-adjusted Mueller-Hinton broth (CAMHB) at 37 • C overnight. Then a sample of each culture was then diluted 40-fold in fresh broth and incubated at 37 • C for 1.5-3 h. The resultant mid-log phase cultures were diluted (CFU/mL measured by OD 600 ) and added to each of the compound-containing plates, giving a cell density of 5 × 10 5 CFU/mL and a total volume of 50 µL. All the plates were covered and incubated at 37 • C for 18 h without shaking. Growth inhibition of all bacteria was determined by measuring absorbance at 600 nm (OD 600 ) using a Tecan M1000 Pro (Tecan Austria GmbH, Grödig, Austria) monochromator plate reader. The percentage of growth inhibition was calculated for each well using the negative control (media only) and positive control (bacteria without inhibitors) on the same plate as the references. The growth rates for bacteria had a variation of ±10%, which is within the reported normal distribution of bacterial growth.
The MIC was determined as the lowest concentration at which the growth was fully inhibited, defined by an inhibition ≥ 80%. In addition, the maximal percentage of growth inhibition is reported as DMax, indicating any compounds with partial activity.
We evaluated the non-covalent interactions in structures 1-3 with special attention to the C-H· · · Cl contacts. After DFT and QTAIM analysis of a series of model {R 3 C-H} 0 · · · Cl − assemblies, we propose the linear regressions ∆H = −678 × ρ(r BCP ) + 3 and BE = −726 × ρ(r BCP ) + 4 which coefficients differ from those proposed earlier for charged X-H· · · Y hydrogen bonds [10]. Although the R 2 and MAD values of the present regression demonstrate that the dispersion of the data is not negligible, we believe these regressions will help in the assessment of energies of charged {C-H· · · Cl} − contacts.
Complexes 1, 3 and 4 were screened against some bacteria strains and were found to be active against nine Gram-negative and Gram-Positive bacteria. The MIC obtained for these compounds showed that the best activity was observed against Acinetobacter baumannii MβL, and 4 was the most effective against all the tested organisms.
Supplementary Materials: The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/molecules27238233/s1, Scheme S1: Schematic representation of the coordination compounds 1-4. Figure S1: IR spectrum of 1; Figure S2: IR spectrum of 2; Figure S3: IR spectrum of 3; Figure S4: IR spectrum of 4; Figure S5: IR spectrum of HL 1 ; Figure S6: Dimeric structure of 1 optimized at the DFT level, Figure S7: DFT-optimized structure of the {H 2 L 1 ·Cl} 0 assembly, the plot of Laplacian of electron density, reduced density gradient plot; Figure S8: DFToptimized model assemblies 1m-16m; Figure S9: plot of Laplacian of electron density and reduced density gradient plot for 1m; Figure S10: plot of Laplacian of electron density and reduced density gradient plot for 16m; Figure S11: Plot of the BE vs. ρ(r BCP ) dependence obtained for three reference assemblies from [10]; Figure S12: Plot of the ∆H vs. ρ(r BCP ) data obtained using different basis sets; Figure S13: Plot of the ∆H vs. ρ(r BCP ) data with and without DLPNO-CCSD(T) correction of the electronic energy; Table S1. Selected geometrical parameters for 1; Table S2. Selected geometrical parameters for 2; Table S3. Selected geometrical parameters for 3; Table S4. Selected geometrical parameters for 4; Table S5. DFT and DLPNO-CCSD(T)-corrected total energies and enthalpies of the model assemblies 1m-16m; Table S6. Thermodynamic parameters of the model assemblies 1m-16m and electron densities at the H· · · Cl bond critical points; Table S7. Binding energies of the model assemblies 1m-16m calculated using different basis sets; Table S8. Geometry and binding energies of the selected model H-bonded assemblies from the S66 dataset calculated at different theory levels; Table S9. Selected properties of the {CH 4 · · · Cl} − assembly optimized at various levels of theory. Table S10. The susceptibility of studied gram-positive strains to some known antibiotics. Table S11. The susceptibility of studied gram-negative strains to some known antibiotics. Listing S1. Cartesian coordinates (Å) of the monomers and dimers of the {R 3 C-H· · · Cl} − and selected S66 model assemblies optimized at the ωB97X-D4/ma-def2-TZVP level.