Symmetry in Recognition of Supramolecular Synthons–Competition between Hydrogen Bonding and Coordination Bond in Multinuclear CuII–4f Complexes with Bicompartmental Schiff Base Ligand

Classic Cu–O coordination bonds in 1 or elongated semi-coordination ones in 2 and 3 were applied to construct CuII–4f complexes composed of trinuclear subunits linked through μ-NO3 ions with formulae given as [Cu2Tm(H2tehy)2]2(NO3)6·H2O, (1), {[Cu2Ho(H2tehy)2(NO3)2][Cu2Ho(H2tehy)2 (H2O)2]}(NO3)4·2H2O, (2), and {[Cu2Er(H2tehy)2(H2O)]2([Cu2Er(H2tehy)2(NO3)]2}(NO3)10·2H2O· 4CH3OH, (3), where H2tehy = C19H20N2O4 is a tetrahydroxy Schiff base ligand. Topological analysis showed that the same characteristic motif of coordination accompanied by hydrogen bonds involving the uncoordinated nitrate oxygen atom and ligand’s phenoxy O atoms is responsible for linking trinuclear subunits into a hexanuclear one as well as for bridging the hexanuclear coordination units in 3 into a 1D supramolecular polymer, with the Cu–O distance being 3.19(1) Å, much longer than the limit of a semi-coordination bond (3.07 Å). The Cambridge Structural Database was used to discuss issues of crystallographic criteria (distance and angular preferences) for the assessment of the stabilizing or destabilizing effect of hydrogen bonding on coordination. The presented results show that the symmetrically repeated arrangement of molecules may provide a useful tool for identifying higher order non-covalently bonded supramolecular aggregates. The complexes 1–3 have been characterized by X-ray diffraction, FTIR, and thermal analysis. The magnetic studies indicated the ferromagnetic interaction between CuII and HoIII ions.


Introduction
Symmetry and asymmetry are the fundamental features of mater in solids and liquids that help in the understanding of many physical phenomena and chemical reactions. Symmetry is often a useful clue for the recognition of supramolecular synthons.
The application of non-covalent interactions in crystal engineering is a thoroughly studied research area, among them hydrogen bonds [1][2][3][4][5][6][7], halogen bonds [8][9][10], dipole· · · dipole [11][12][13][14], and stacking [15][16][17][18][19][20] interactions should be mentioned. Such non-covalent interactions provide directional and stabilizing contacts that can be used successfully in the design of coordination compounds [21]. Additionally, there are also reports showing that hydrogen bonding can act as a pathway for magnetic interaction between metal ions [1,[22][23][24][25][26]. The coordination sphere plasticity for hexacoordinated copper(II) ions is known as the Jahn-Teller effect. This distortion from ideal symmetry usually exhibits as an elongation of two axial bonds in the tetragonal bipyramid polyhedron of the complex. The Jahn-Teller deformations are believed to be stabilized in the solid state by, e.g., hydrogen bonds. The observed crystal elongation has led to the introduction of a term of a "semi-coordination bond" by Brown et al. in 1967 [27]. The theoretical studies performed by Valach et al. resulted in the calculation of the limit of a semi-coordination bond being of 3.07 or 3.04 Å for the Cu-O bond located at the elongated out-of-plane axis [28,29]. Valach also found that transition from the bonded to non-bonded state in the elongated metal-ligand direction occurs discontinuously [28].
There are some interesting reports on semi-coordinated bonds found in crystal structures of Cu II cations staying within this Cu-O distance limits [29][30][31][32]. The strength of metal-ligand bonds depends on the bond length [33]. However, Nelyubina et al. proved that even very long and weak interatomic contacts (Cu· · · O 3.6 Å, 0.5 kcal/mol) may mediate magnetic super-exchange pathways [34]. On the other hand, non-covalent interactions have proved to be effective in the design of supramolecular polymers of exceptional properties [35][36][37][38].
The nitrate anion is often used in crystal engineering as a counterion since it has three oxygen atoms ready to form both coordinative and/or hydrogen bonds. However, the NO 3 − anion generally links the neighboring copper centers by two oxygen donors independently [24]. The hydrogen bonds are usually formed with the non-coordinated nitrate oxygen. A recurrent structural motif based on nitrate ions being the interplay between a coordination or semi-coordination bond and bifurcated hydrogen bonds has been found in the presented structures 1-3 ([Cu 2 Tm(H 2 tehy) 2 ] 2 (NO 3 ) 6 [39,40] (Scheme 1). The topologically analogous supramolecular arrangement has been found in 3, but this time linking not only the trinuclear subunits into hexanuclear ones but also the hexanuclear ones into a linear supramolecular aggregate, with a much longer Cu· · · O nitrate distance (3. 19(1) Å) which is above the limit of a semi-coordination bond (3.07 Å) [28] but still shorter than the distance where a very weak interaction has been reported by Nelyubina et al. (3.6 Å) [34].
Symmetry 2019, 11, x FOR PEER REVIEW 2 of 20 directional and stabilizing contacts that can be used successfully in the design of coordination compounds [21]. Additionally, there are also reports showing that hydrogen bonding can act as a pathway for magnetic interaction between metal ions [1,[22][23][24][25][26]. The coordination sphere plasticity for hexacoordinated copper(II) ions is known as the Jahn-Teller effect. This distortion from ideal symmetry usually exhibits as an elongation of two axial bonds in the tetragonal bipyramid polyhedron of the complex. The Jahn-Teller deformations are believed to be stabilized in the solid state by, e.g., hydrogen bonds. The observed crystal elongation has led to the introduction of a term of a "semi-coordination bond" by Brown et al. in 1967 [27]. The theoretical studies performed by Valach et al. resulted in the calculation of the limit of a semi-coordination bond being of 3.07 or 3.04 Å for the Cu-O bond located at the elongated out-of-plane axis [28,29]. Valach also found that transition from the bonded to non-bonded state in the elongated metal-ligand direction occurs discontinuously [28].
There are some interesting reports on semi-coordinated bonds found in crystal structures of Cu II cations staying within this Cu-O distance limits [29][30][31][32]. The strength of metal-ligand bonds depends on the bond length [33]. However, Nelyubina et al. proved that even very long and weak interatomic contacts (Cu···O 3.6 Å, 0.5 kcal/mol) may mediate magnetic super-exchange pathways [34]. On the other hand, non-covalent interactions have proved to be effective in the design of supramolecular polymers of exceptional properties [35][36][37][38].
The nitrate anion is often used in crystal engineering as a counterion since it has three oxygen atoms ready to form both coordinative and/or hydrogen bonds. However, the NO3⁻ anion generally links the neighboring copper centers by two oxygen donors independently [24]. The hydrogen bonds are usually formed with the non-coordinated nitrate oxygen. A recurrent structural motif based on nitrate ions being the interplay between a coordination or semi-coordination bond and bifurcated hydrogen bonds has been found in the presented structures 1-3  [39,40] (Scheme 1). The topologically analogous supramolecular arrangement has been found in 3, but this time linking not only the trinuclear subunits into hexanuclear ones but also the hexanuclear ones into a linear supramolecular aggregate, with a much longer Cu···Onitrate distance (3.19(1) Å) which is above the limit of a semi-coordination bond (3.07 Å) [28] but still shorter than the distance where a very weak interaction has been reported by Nelyubina  The series of Cu II -4f complexes presented here formed by a tetrahydroxy compartmental Schiff base ligand H4tehy (where H4tehy = C19H22N2O4) and nitrate anions offers an interesting object to study the influence of hydrogen bonding on the coordination and formation of a supramolecular network.
We present here the synthesis, crystal structure, FTIR spectra, and thermal and magnetic properties of complexes 1-3 where topological similarities are discussed in terms of crystallographic The series of Cu II -4f complexes presented here formed by a tetrahydroxy compartmental Schiff base ligand H 4 tehy (where H 4 tehy = C 19 H 22 N 2 O 4 ) and nitrate anions offers an interesting object to study the influence of hydrogen bonding on the coordination and formation of a supramolecular network.
We present here the synthesis, crystal structure, FTIR spectra, and thermal and magnetic properties of complexes 1-3 where topological similarities are discussed in terms of crystallographic distance limit of a Cu-O semi-coordination bond and the cooperative or competitive nature of coexisting coordination and hydrogen bonds.

Synthesis of Complexes
The heteronuclear compounds 1-3 were synthesized as follows: To 30 mL of methanolic solution of 0.1368 g Schiff base ligand (0.4 mmol) was added dropwise 10 mL of methanolic solution of 0.0799 g Cu(CH 3 COO) 2

Methods
The elemental CHN analysis was performed using a CHN 2400 Perkin Elmer analyser. The contents of metals (copper, holmium, erbium, and thulium have been determined using ED XRF spectrophotometer (Canberra−Packard). The FTIR spectra of compounds in KBr pellets were recorded in the range of 4000 to 400 cm −1 on the M-80 spectrophotometer (Carl Zeiss Jena). Thermal analyses of 1-3 and H 2 tehy were conducted under air flow in the temperature range of 20 to 1000 • C (1-3) and 20 to 700 • C (H 2 tehy) at a heating rate of 10 • C·min −1 by the thermogravimetric (TG) and differential scanning calorimetry (DSC) methods with the use of the SETSYS 16/18 analyser (Setaram). The samples of 7.72 mg (1), 7.88 mg (2), 5.76 mg (3) were heated in Al 2 O 3 crucibles. The XRD powder diffractograms of the decomposition products were collected at room temperature on an Empyrean PANanalytical automated powder diffractometer (CuKα radiation λ = 1.54187 Å) in the 2θ range of 20 to 90 • . The magnetic susceptibility for finely ground crystalline samples was measured over the temperature range of 1.8 to 300 K at magnetic field 0.1 T using a Quantum Design SQUID-VSM magnetometer. The field dependences of magnetization were investigated at 2 K in the applied field up to 5 T and were corrected by subtracting the sample-holder signal and contribution χD estimated from Pascal's constants [43].
Diffraction intensities for 1-3 were measured on SuperNova X-ray diffractometer (with Atlas S2 CCD detector and the mirror-monochromatized CuKα radiation (λ = 1.54184 Å) at 294 K for 1 and at 120 K for 2-3, using the ω scan technique. The CrysAlis CCD and CrysAlis Red programs [44] have been applied for data collection, cell refinement, and data reduction. The molecular models were found by direct methods using SHELXS-97 and refined on F 2 by the full-matrix least-squares using the SHELXL-97 implemented in OLEX2 [45,46]. Non-hydrogen atoms (except the disordered part of the ligand molecule in 3 and selected nitrate and water molecules in 1-3) were refined anisotropically. The 2,2-dimethylpropyl bridge in 3 is disordered over two positions with site occupation factors (sof's) of the major part being of 0.6. The structure of 3 has been refined in a noncentrosymmetric space group as a two-component twin with the following twin law (−1 0 0, 0 1 0, 0 0 −1) (two-fold rotation about b axis with inversion twinning). The refined twin population parameter BASF (fractional contribution of twin domain calculated on batch scale factors) was 0.42. The conditions for the data collection and the crystal structure refinement parameters are shown in Table 1. The drawings were made in Mercury and Diamond software [47,48]. The experimental details and final atomic parameters for 1-3 were deposited with the Cambridge Crystallographic Data Centre as supplementary material (CCDC ID 1901698-1901700). Copies of the data can be obtained free of charge on request via www.ccdc.cam.ac.uk/data_request/cif, or by emailing data_request@ccdc.cam.ac.uk.

Molecular and Crystal Structure of Complexes 1-3
Compounds 1-3 were obtained by the same method of synthesis giving, however, crystal structures of different symmetry. The complexes show subtle differences in the coordination architecture and in the degree of Jahn-Teller distortion of Cu II ions.

Hexanuclear Complex of 1
Compound 1 form crystals in the monoclinic space group (C2/c) with half of the coordination unit being symmetrically independent ( Table 1). The asymmetric part consists of a trinuclear Cu II -Tm III -Cu II core linked by a bridging nitrate anion (lying on the two-fold axis) to the other half resulting in a hexanuclear coordination entity with the Cu2-O10 coordination bond length being 2.594(5) Å (Figures 1 and 2; Tables 2 and 3). This characteristic motif is supplemented by two O4-H4· · · O9 hydrogen bonds with a bifurcated acceptor O atom (Table 4). A similar characteristic arrangement of two trinuclear subunits linked by a bridging NO 3 − ion and hydrogen bonds has been discussed in structures of 2 and 3.
Symmetry 2019, 11, x FOR PEER REVIEW 4 of 20 been applied for data collection, cell refinement, and data reduction. The molecular models were found by direct methods using SHELXS-97 and refined on F 2 by the full-matrix least-squares using the SHELXL-97 implemented in OLEX2 [45,46]. Non-hydrogen atoms (except the disordered part of the ligand molecule in 3 and selected nitrate and water molecules in 1-3) were refined anisotropically. The 2,2-dimethylpropyl bridge in 3 is disordered over two positions with site occupation factors (sof's) of the major part being of 0.6. The structure of 3 has been refined in a noncentrosymmetric space group as a two-component twin with the following twin law (−1 0 0, 0 1 0, 0 0 −1) (two-fold rotation about b axis with inversion twinning). The refined twin population parameter BASF (fractional contribution of twin domain calculated on batch scale factors) was 0.42. The conditions for the data collection and the crystal structure refinement parameters are shown in Table 1. The drawings were made in Mercury and Diamond software [47,48]. The experimental details and final atomic parameters for 1-3 were deposited with the Cambridge Crystallographic Data Centre as supplementary material (CCDC ID 1901698-1901700). Copies of the data can be obtained free of charge on request via www.ccdc.cam.ac.uk/data_request/cif, or by emailing data_request@ccdc.cam.ac.uk.

Molecular and Crystal Structure of Complexes 1-3
Compounds 1-3 were obtained by the same method of synthesis giving, however, crystal structures of different symmetry. The complexes show subtle differences in the coordination architecture and in the degree of Jahn-Teller distortion of Cu II ions.

Hexanuclear Complex of 1
Compound 1 form crystals in the monoclinic space group (C2/c) with half of the coordination unit being symmetrically independent ( Table 1). The asymmetric part consists of a trinuclear Cu II -Tm III -Cu II core linked by a bridging nitrate anion (lying on the two-fold axis) to the other half resulting in a hexanuclear coordination entity with the Cu2-O10 coordination bond length being 2.594(5) Å (Figures 1,2; Tables 2,3). This characteristic motif is supplemented by two O4-H4···O9 hydrogen bonds with a bifurcated acceptor O atom (Table 4). A similar characteristic arrangement of two trinuclear subunits linked by a bridging NO3⁻ ion and hydrogen bonds has been discussed in structures of 2 and 3.
3.356 (7) Cu3-O10 1.952 (7) (5) * distance above the limit of 3.07Å for semi-coordination bond but recognized as a semi-coordinative assisted by hydrogen bonding. Table 3. Selected bond angles in degrees for 1-3. The smaller N 2 O 2 compartments are occupied by Cu II cations. Cu1 ion has the coordination number of five or six because one of the monodentate NO 3 − anions is disordered over three positions.
The Cu1· · · O16/O16A/O16B distance varies from 2.66(1) to 3.57(1) Å (Table 2), which differentiates the character of the interatomic contact (semi-coordination or non-bonding). The nitrate ion may be bonded directly to Cu1 cation by a coordinative bond, or it can act as a hydrogen bond acceptor in O8-H8· · · O14 interaction (Figures 1 and 2; Table 4). Cu2 cation is penta-coordinated. The apical position of the polyhedron is occupied by a bridging nitrato ion with Cu2-O10 bonds being of 2.594(5) Å. The Cu2 ion has also a long contact, above the limit of a semi-coordination bond (Cu2· · · O11 3.28(2) Å), to a nitrate anion hydrogen bonded through the same O11 atom to the phenoxy group (O3-H3· · · O11 interaction). The Tm III ion is octa-coordinated by two O 4 cavities of the perpendicularly oriented Schiff base ligands. In the crystal structure, there is only one uncoordinated solvent molecule-water linked strongly by a hydrogen bond to the H 2 tehy ligand (Table 4). Symmetry codes: i x, 1.5 − y, −0.5 + z; ii 1 − x, −y, −z; iii 2 − x, −y, 1 − z; iv x, 0.5 − y, 0.5 + z.

Dimer of Trinuclear Cores Linked by a Semi-Coordination Bond in 2
The − coordination unit in the monoclinic crystal 2 (P2 1 /c) is built of two symmetrically independent trinuclear Cu II -Ho III -Cu II coordination moieties linked by a bidentate nitrate ligand into one hexanuclear entity (Figures 3 and 4). However, the distances between the O nitrate atom and Cu II centers are different: 2.488(5) and 3.031(5) Å for Cu2-O24 and Cu3-O25 pairs of atoms, respectively. The first distance may be regarded as a classic coordination bond, whereas, the other one is very long but still within the limit of a semi-coordination bond (3.07 Å). Additionally, the coordination motif is again accompanied by two bifurcated hydrogen bonds O3-H3· · · O23 and O16-H16· · · O23 to the non-coordinated nitrate O atom, similar to 1. The hydrogen bonding seems to compete with the coordination bond causing the elongation of the Cu3-O25 distance above the conventional coordinative bond limit, but it seems to stabilize the whole motif. Because of the topological similarities between structures 1 and 2, the Cu3-O25 bond has been recognized as a semi-coordinative one, and the structure of 2 as a hexanuclear one.

Supramolecular Polymer Built of Hexanuclear Monomers in 3
Compound 3 crystallizes in the orthorhombic Pnc2 space group with two types of symmetrically independent hexanuclear coordination units composed of trinuclear subunits A and B linked by the NO3⁻ ions into AA and BB entities (Figures 5,6).

Supramolecular Polymer Built of Hexanuclear Monomers in 3
Compound 3 crystallizes in the orthorhombic Pnc2 space group with two types of symmetrically independent hexanuclear coordination units composed of trinuclear subunits A and B linked by the NO3⁻ ions into AA and BB entities (Figures 5,6).  there are two other positions which are disordered water molecules. This results in the change in conformation of the Schiff base ligands, which adopt a bent conformation instead of nearly planar as in 1. The remaining uncoordinated nitrate anions and water molecules interact through many hydrogen bonds (Table 4).

Supramolecular Polymer Built of Hexanuclear Monomers in 3
Compound 3 crystallizes in the orthorhombic Pnc2 space group with two types of symmetrically independent hexanuclear coordination units composed of trinuclear subunits A and B linked by the NO 3 − ions into AA and BB entities (Figures 5 and 6).  In a topological sense, compound 3 may be regarded as a 1D supramolecular polymer AA-BB-AA-BB running as a folded chain along the a axis with hexanuclear entities AA and BB linked by an elongated semi-coordinative bond (Cu4-O20 3.01(1) Å) and by a long contact of the same topology but probably of a different nature of interaction (Cu2-O18 3.19(1) Å). Each of these semi-coordination bonds or contacts is accompanied by a specific array of hydrogen bonds forming the characteristic motif found in 1 and 2 ( Figure 6).
The assumption of an attractive character of this long contact is based on topological similarities of the recurrent supramolecular motif found in 1-3 and on the results of studies performed by Nelyubina et al. [34]. The stabilizing effect is provided by the accompanying hydrogen bonds O3-H3···O19, O11-H11···O19, and O11-H11···O20 (Table 4), wherein it is important that the hydrogen bonding occurs through the non-coordinated O nitrate atoms. The Er III cation is octa-coordinated as Tm III in 1. Cu1 (CN = 6) has H2O molecule in the apical position and μ-NO3⁻ ion at the other apex of a tetragonal bipyramid. The nitrate anion links by a semi-coordination bond (Cu1-O30 2.83(1) Å) two related by a two-fold rotation Cu1 ions into a hexanuclear unit. The apical ligands of Cu2 ion (CN = 6) are one methanol molecule and one NO3⁻ anion with a very long Cu2-O18 contact distance (3.19(1) Å) bridging to Cu4 cation. The Cu4 (CN = 6) is linked further to a repeated by a two-fold axis to another Cu4 ion. Cu3 (CN = 5) ion coordinates one monodentate nitrate ion. The Cu3···O38 (3.613(8) Å) contact was not identified as a coordinative because of the In a topological sense, compound 3 may be regarded as a 1D supramolecular polymer AA-BB-AA-BB running as a folded chain along the a axis with hexanuclear entities AA and BB linked by an elongated semi-coordinative bond (Cu4-O20 3.01(1) Å) and by a long contact of the same topology but probably of a different nature of interaction (Cu2-O18 3.19(1) Å). Each of these semi-coordination bonds or contacts is accompanied by a specific array of hydrogen bonds forming the characteristic motif found in 1 and 2 ( Figure 6).
The assumption of an attractive character of this long contact is based on topological similarities of the recurrent supramolecular motif found in 1-3 and on the results of studies performed by Nelyubina et al. [34]. The stabilizing effect is provided by the accompanying hydrogen bonds O3-H3· · · O19, O11-H11· · · O19, and O11-H11· · · O20 (Table 4), wherein it is important that the hydrogen bonding occurs through the non-coordinated O nitrate atoms. The Er III cation is octa-coordinated as Tm III bridging to Cu4 cation. The Cu4 (CN = 6) is linked further to a repeated by a two-fold axis to another Cu4 ion. Cu3 (CN = 5) ion coordinates one monodentate nitrate ion. The Cu3· · · O38 (3.613(8) Å) contact was not identified as a coordinative because of the long distance and a competitive influence of O15-H15· · · O38 hydrogen bond (interaction to the same O nitrate atom).

The Geometric Criteria for a Semi-Coordination Bond on the Base of CSD Search
For the search of Cambridge Structural Database (CSD, ver. 5.40 Nov. 2018) the Conquest software (ver. 2.0.0.) was used, the restrictions were as follows R values <5%, no disorder, no powder structures [47]. The search for Cu· · · O-NO 2 distances up to 4 Å without determining the type of bonding or contact gave 1068 results. The number of occurrences of a given Cu-O distance (Figure 7) clearly confirm the Jahn-Teller distortion: 1) the first sharp peak with the maximum at ca. 1.9 Å corresponds to the shorter in-plane coordination bonds, 2) the next population of longer Cu-O distances has a wider range with a lower maximum at ca. 2.5 Å (Cu-O distance to the out-of-plane ligands). Next, the number of occurrence of Cu· · · O contacts seems to be nearly constant from three until ca. 3.5 Å, where it starts to grow with a small increase at ca. 3.1 Å. From the crystallographic point of view, this plot does not indicate any sharp border between coordination and semi-coordination bonding nor the sharp border of the second one.

The Geometric Criteria for a Semi-Coordination Bond on the Base of CSD Search
For the search of Cambridge Structural Database (CSD, ver. 5.40 Nov. 2018) the Conquest software (ver. 2.0.0.) was used, the restrictions were as follows R values <5%, no disorder, no powder structures [47]. The search for Cu···O-NO2 distances up to 4 Å without determining the type of bonding or contact gave 1068 results. The number of occurrences of a given Cu-O distance (Figure 7) clearly confirm the Jahn-Teller distortion: 1) the first sharp peak with the maximum at ca. 1.9 Å corresponds to the shorter in-plane coordination bonds, 2) the next population of longer Cu-O distances has a wider range with a lower maximum at ca. 2.5 Å (Cu-O distance to the out-of-plane ligands). Next, the number of occurrence of Cu···O contacts seems to be nearly constant from three until ca.    long distance and a competitive influence of O15-H15···O38 hydrogen bond (interaction to the same Onitrate atom).

The Geometric Criteria for a Semi-Coordination Bond on the Base of CSD Search
For the search of Cambridge Structural Database (CSD, ver. 5.40 Nov. 2018) the Conquest software (ver. 2.0.0.) was used, the restrictions were as follows R values <5%, no disorder, no powder structures [47]. The search for Cu···O-NO2 distances up to 4 Å without determining the type of bonding or contact gave 1068 results. The number of occurrences of a given Cu-O distance (Figure 7) clearly confirm the Jahn-Teller distortion: 1) the first sharp peak with the maximum at ca. 1.9 Å corresponds to the shorter in-plane coordination bonds, 2) the next population of longer Cu-O distances has a wider range with a lower maximum at ca. 2.5 Å (Cu-O distance to the out-of-plane ligands). Next, the number of occurrence of Cu···O contacts seems to be nearly constant from three until ca. 3.5 Å, where it starts to grow with a small increase at ca. 3.1 Å. From the crystallographic point of view, this plot does not indicate any sharp border between coordination and semi-coordination bonding nor the sharp border of the second one. The plot of Cu···O-N(O2) angle shows three maxima at ca. 7, 75, and 115° ( Figure 8). The highest maximum at ca. 115° corresponds to the optimal orientation of oxygen lobes toward the positive charge of the Cu center in coordination bonding, the peaks at ca. 7 and 75° are related to the angles between Cu and the non-interacting nitrate oxygen atoms. It shows a clear directional preference in the orientation of nitrate ions toward the Cu metal centers (semi-coordination Cu···O-N(O2) angle in the range of ca. 100 to 140°). It is even more pronounced at the scatter plot of Cu···O-N(O2) angle vs Cu···O distance values (Figure 9). The It shows a clear directional preference in the orientation of nitrate ions toward the Cu metal centers (semi-coordination Cu· · · O-N(O 2 ) angle in the range of ca. 100 to 140 • ). It is even more pronounced at the scatter plot of Cu· · · O-N(O 2 ) angle vs Cu· · · O distance values ( Figure 9). The directionality is sustained until ca. 3.65 Å and only above this distance limit does the distribution of Cu· · · O-N(O 2 ) valence angles start to be more random. directionality is sustained until ca. 3.65 Å and only above this distance limit does the distribution of Cu···O-N(O2) valence angles start to be more random. At the scatter plot ( Figure 9) six groups of data can be distinguished: 1) the group of classic coordination bond to the in-plane ligands with short Cu···O distance (up to ca. 2.2 Å) and Cu···O-N(O2) angle being in the range of 90 to 130°; 2) and 3) are clearly distinctive groups with low valence angles 5 to 10° and 60 to 90° and ranges of Cu···O distances above 3.65 Å and 2.3-3.7 Å, respectively. They correspond to the non-bonding contacts to the neighborly located oxygen atoms within the same coordinated NO3⁻ molecule; 4) the elongated coordination or semi-coordination bond to the out-of-plane ligands (Cu-O bond ca. 2.3-3 Å, Cu···O-N(O2) angle ca. 110-140°); 5) the extended area for very long interactions of a different character but still with a high degree of directionality (Cu···O distance ca. 3-3.65 Å, Cu···O-N(O2) angle ca. 100-150°), could be probably hydrogen bond assisted coordination bonds. Additionally, in this group, if the regarded Cu···O-N(O2) contact was not included as a coordination, nearly all of the copper(II) centers were tetra-or penta-coordinated and the nitrate anion was located at the "free" non-coordinated side of the central ion closing, at least in a topological sense, the coordination sphere of copper; 6) Group of contacts above 3.65 Å showing no specific directional preferences. A similar distribution of Cu-O distances and Cu-O-X(O2) angles was observed in the group of other oxo complexes, where X was C or N; 7226 data, Figure S1 in Supplementary Materials).  Figure S1 in Supplementary Materials).

Infrared Spectra
The obtained Cu II -4f complexes show similar FTIR spectral features ( Figure 10 and Figures  S2-S4). A strong band at 1620 cm −1 from ν(C=N imine ) is red-shifted by 20 cm −1 in comparison to the free H 4 tehy ligand indicating a decrease of the C=N bond order because of the formation of the coordination bond to the copper(II). The broad band with a maximum at ca. 3400 cm −1 comes from ν(O-H) stretching vibrations of coordinated and/or solvated water/methanol molecules and from the undeprotonated hydroxyl groups of the H 2 tehy ligand. The strong phenolic ν(C-O) stretching vibration band was observed at 1240 cm −1 for free H 4 tehy ligand, whereas, in complexes there was a doublet with peaks at 1252 and 1220 cm −1 , confirming the coordination through these groups [49][50][51][52][53]. The obtained Cu II -4f complexes show similar FTIR spectral features (Figures 10 and S2-S4). A strong band at 1620 cm -1 from ν(C=Nimine) is red-shifted by 20 cm -1 in comparison to the free H4tehy ligand indicating a decrease of the C=N bond order because of the formation of the coordination bond to the copper(II). The broad band with a maximum at ca. 3400 cm -1 comes from ν(O-H) stretching vibrations of coordinated and/or solvated water/methanol molecules and from the undeprotonated hydroxyl groups of the H2tehy ligand. The strong phenolic ν(C-O) stretching vibration band was observed at 1240 cm −1 for free H4tehy ligand, whereas, in complexes there was a doublet with peaks at 1252 and 1220 cm −1 , confirming the coordination through these groups [49][50][51][52][53].

Magnetic Properties
The plots of temperature-dependent molar susceptibility (χMT versus T) were shown in Figure   12, where χM is the molar magnetic susceptibility, and T is the absolute temperature. The magnetic properties of the complexes result from the interplay between three factors: the Cu II ···Cu II and Cu II -Ln III interactions, as well as the thermal population of the Stark components of the lanthanide(III) ions. The χMT values of the complexes studied at room temperature were calculated theoretically by the Equation (1) where N is Avogadro constant, β is the Bohr magneton, and k is Boltzman's constant. In this equation gLn is the g factor of the ground J terms of Ln III and is expressed as in Equation (2)

Magnetic Properties
The plots of temperature-dependent molar susceptibility (χ M T versus T) were shown in Figure 12, where χ M is the molar magnetic susceptibility, and T is the absolute temperature. The magnetic properties of the complexes result from the interplay between three factors: the Cu II · · · Cu II and Cu II -Ln III interactions, as well as the thermal population of the Stark components of the lanthanide(III) ions. The χ M T values of the complexes studied at room temperature were calculated theoretically by the Equation (1) assuming four Cu II and two magnetically isolated Ln III ions.
where N is Avogadro constant, β is the Bohr magneton, and k is Boltzman's constant. In this equation g Ln is the g factor of the ground J terms of Ln III and is expressed as in Equation (2): In Cu II 4-Tm III 2 (1) complex the χMT value of 14.85 cm 3 Kmol -1 observed at 300 K corresponds to the value of 15.80 cm 3 Kmol -1 expected for two Tm III ( 3 H6, S = 1, L = 5, J = 6, g = 3/2) and four Cu II (S = 1/2, g = 2) magnetically isolated ions. This value steadily decreased as T was lowered to reach 6.99 cm 3 Kmol -1 at 1.8 K. For Cu II 4-Ho III 2 (2) the χMT value experimentally determined at 300 K (28.04 cm 3 Kmol -1 ) is slightly lower than the value of 29.63 cm 3 Kmol -1 expected for two Ho III ( 5 I8, J = 8, L = 6, S = 2, g = 5/4) and four Cu II (S = 1 /2, g = 2) noninteracting metal ions. With the lowering of the temperature the χmT remained constant until 120 K, then it decreased to 27.00 cm 3 Kmol -1 at 19 K and next increased to reach a value of 28.48 cm 3 Kmol -1 at 6.6 K. Finally, it showed a small decrease to 22.07 cm 3 Kmol -1 at 1.8 K. For the compound Cu4 II -Er2 III (3) the experimental value of χMT at room temperature was equal to ca. 24.83 cm 3 Kmol -1 corresponding to the calculated value of 24.45 cm 3 Kmol -1 for two uncoupled Er III ( 4 I15/2, S = 3/2, L = 6, J = 15/2, g = 6/5) and four uncoupled Cu II ions (S = 1/2, g = 2). As shown in Figure 12, this value decreased with the lowering of the temperature to 13.93 cm 3 Kmol -1 at 1.8 K.
The lowering of χMT at low temperature in 1 and 3, is caused most probably by the crystal field splitting of Ln III ion, and/or a combination of the contribution of the overall antiferromagnetic interactions of metal ions. The profile of the χMT vs T curve in 2 strongly suggests the existence of two competitive phenomena. The decrease of χMT on temperature lowering was most probably caused by the depopulation of the Ho Stark sublevels, or the presence of magnetic anisotropy, or the antiferromagnetic coupling between ions, whereas, the increase of the χMT at lower temperatures may arise because of the ferromagnetic Cu II −Ho III interaction.

Conclusion
The nuclearity of the presented complexes 1-3 was tuned by the interplay between coordination and hydrogen bonds involving nitrate anions. The recurrent array of coordination or semi-coordination bonds and hydrogen bonding presented here can be added to the crystal engineering library as a building motif. The coordination bond may be weakened and elongated until it transforms into a non-covalent interaction when a competitive influence of hydrogen bonding will occur. It is worth to underline that even at long distances (above the limit of semi-coordination bond 3.07 Å) the directionality of the Cu···O-NO2 contact (100-150°) may be sustained up to ca. 3.65 Å, which also correlates well with the reports of Nelyubina et al. about weak but still attractive in nature interactions (Cu···O 3.6 Å, 0.5 kcal/mol), which was involved in the magnetic super-exchange [34]. These may be regarded as crystallographic criteria for the searching In Cu II 4 -Tm III 2 (1) complex the χ M T value of 14.85 cm 3 Kmol −1 observed at 300 K corresponds to the value of 15.80 cm 3 Kmol −1 expected for two Tm III ( 3 H 6 , S = 1, L = 5, J = 6, g = 3/2) and four Cu II (S = 1/2, g = 2) magnetically isolated ions. This value steadily decreased as T was lowered to reach 6.99 cm 3 Kmol −1 at 1.8 K. For Cu II 4 -Ho III 2 (2) the χ M T value experimentally determined at 300 K (28.04 cm 3 Kmol −1 ) is slightly lower than the value of 29.63 cm 3 Kmol −1 expected for two Ho III ( 5 I 8 , J = 8, L = 6, S = 2, g = 5/4) and four Cu II (S = 1 / 2 , g = 2) noninteracting metal ions. With the lowering of the temperature the χ m T remained constant until 120 K, then it decreased to 27.00 cm 3 Kmol −1 at 19 K and next increased to reach a value of 28.48 cm 3 Kmol −1 at 6.6 K. Finally, it showed a small decrease to 22.07 cm 3 Kmol −1 at 1.8 K. For the compound Cu 4 II -Er 2 III (3) the experimental value of χ M T at room temperature was equal to ca. 24.83 cm 3 Kmol −1 corresponding to the calculated value of 24.45 cm 3 Kmol −1 for two uncoupled Er III ( 4 I 15/2 , S = 3/2, L = 6, J = 15/2, g = 6/5) and four uncoupled Cu II ions (S = 1/2, g = 2). As shown in Figure 12, this value decreased with the lowering of the temperature to 13.93 cm 3 Kmol −1 at 1.8 K.
The lowering of χ M T at low temperature in 1 and 3, is caused most probably by the crystal field splitting of Ln III ion, and/or a combination of the contribution of the overall antiferromagnetic interactions of metal ions. The profile of the χ M T vs T curve in 2 strongly suggests the existence of two competitive phenomena. The decrease of χ M T on temperature lowering was most probably caused by the depopulation of the Ho Stark sublevels, or the presence of magnetic anisotropy, or the antiferromagnetic coupling between ions, whereas, the increase of the χ M T at lower temperatures may arise because of the ferromagnetic Cu II −Ho III interaction.

Conclusions
The nuclearity of the presented complexes 1-3 was tuned by the interplay between coordination and hydrogen bonds involving nitrate anions. The recurrent array of coordination or semi-coordination bonds and hydrogen bonding presented here can be added to the crystal engineering library as a building motif. The coordination bond may be weakened and elongated until it transforms into a non-covalent interaction when a competitive influence of hydrogen bonding will occur. It is worth to underline that even at long distances (above the limit of semi-coordination bond 3.07 Å) the directionality of the Cu· · · O-NO 2 contact (100-150 • ) may be sustained up to ca. 3.65 Å, which also correlates well with the reports of Nelyubina et al. about weak but still attractive in nature interactions (Cu· · · O 3.6 Å, 0.5 kcal/mol), which was involved in the magnetic super-exchange [34]. These may be regarded as crystallographic criteria for the searching of elongated semi-coordination bonds when assisted by hydrogen bonding. On the basis of these results, the following conclusions can be drawn: That depending on the supramolecular topology and symmetry of the analyzed system, the hydrogen bonding can stabilize the coordination, or it can disrupt it. It seems that the stabilizing effect on semi-coordination bonding is observed when the accompanying hydrogen bond is directed to the non-coordinated O nitrate atom (see sets of contacts in crystal 3: O3-H3· · · O19 and Cu2· · · O18; bifurcated O11-H11· · · O19/O20 and Cu4· · · O20). The destabilizing effect occurs when coordination and hydrogen bonding compete for the same O atom (see the pairs of contacts in 1: O13-H13· · · O11 and Cu2· · · O11; in 2: O8-H8· · · O35 and Cu1· · · O35; O4-H4· · · O26 and Cu2· · · O26). Additionally, the border of 3.07 Å for a semi-coordination bond can be probably extended when the "hydrogen bond assisted" coordination occurs, but additional angular preference factor must be considered.
The presented results show that hydrogen bonding has a significant influence on the coordination bonds being responsible for the weakening and the elongation of the axial out of plane bonds in structures disturbed by the Jahn-Teller effect. Irrespective of the semi-coordination bond distance limit, topological analysis of crystal structures should always be performed since even minor structural features may help in better understanding of physicochemical properties of coordination compounds, as well as in designing of self-assembling materials or in protein-ligand docking methods.