Crystal structures and Hirshfeld surface analysis of transition-metal complexes of 1,3-azolecarboxylic acids

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Introduction
The understanding of the self-assembly process through both strong bonding (coordinative or covalent) and nonbonding interactions is a fundamental of crystal engineering (Seth et al., 2011), since properties of crystalline materials strongly depend on how structural components are organized with respect to one another (Yu, 2002;Bis et al., 2006). In contrast to the strong and directional bonding, the nature of nonbonding interactions, such as hydrogen bonding and aromaticinteractions, causes difficulties in crystal structure prediction (Braga et al., 2002). Supramolecular assembly regulated through a diverse range of these interactions is often explained and rationalized using the concept of molecular synthons (Kitagawa & Uemura, 2005;Shimizu et al., 2004), which have been well established for strong hydrogen bonds (Desiraju, 2002;Sherrington & Taskinen, 2001). The other weaker interactions, such as -, C-HÁ Á Á, lone pair-and halogen interactions, nonetheless play a significant role in selfassembly processes (Blake et al., 1999;Jayendran et al., 2019). Despite being weaker individually, the accumulation of these very weak interactions can be as substantial as the covalent bond (Desiraju, 2005).
To acquire a greater understanding on how molecular components interact with their local environment, the molecular Hirshfeld surface analysis has been introduced to visualize and quantify the interplay of these nonbonded interactions (Spackman & Jayatilaka, 2009), which otherwise cannot be readily obtained from conventional structure ISSN 2053ISSN -2296 # 2019 International Union of Crystallography analysis. Similarities and differences between intermolecular interactions, as well as information on the relative strengths of these interactions in crystal packing, can be quantified (Clausen et al., 2010;Wang et al., 2018). Although this approach has been widely used in the study of the polymorphism of small molecules (Munshi et al., 2010), it can also be useful for the investigation of interactions between different functionalities in supramolecular assemblies (Martin et al., 2015). The changing of tert-butyl on para-substituted phenols to benzyl and nitro, for example, diversified the dominant interactions within the crystal packing and therefore the crystal structures (Martin et al., 2010).
1,3-Azolecarboxylic acids, consisting of an azole ring and a carboxylic acid group, are an excellent choice of ligands owing to their structural adaptability to both the highly directional coordinative bonds, as well as the flexible nonbonding interactions (Sun et al., 2010;Furuya et al., 2001;Cheng et al., 2014;Cai et al., 2012;Rossin et al., 2011Rossin et al., , 2014Meundaeng et al., 2016Meundaeng et al., , 2017. The effects of thiazole-4-carboxylate, for instance, on the variation of supramolecular structures and therefore polymorphism in Co 2+ and Ni 2+ complexes have been reported (Meundaeng et al., 2016). Nevertheless, the effects of different heteroatoms, as well as the positions of the carboxylic acid group on the azole ring, on crystal packing has never been investigated.

Crystal structure determination
Crystal structure data for 1-5 are summarized in Table 1. All H atoms were refined freely and isotopically.

Hirshfeld surface analysis
The Hirshfeld surfaces and their associated two-dimensional (2D) fingerprint plots were analysed using Crystal-Explorer software (Version 17.5; Spackman & Jayatilaka, 2009), based on the solved and refined single-crystal structures. All bond lengths to the H atoms were set to the default values (C-H = 1.083 Å , O-H = 0.983 Å and N-H = 1.009 Å ) (Allen et al., 1987). Graphical plots of the Hirshfeld surface were mapped with the normalized contact distance (d norm ) ranging from À0.5 to 1.0 Å . The red-white-blue colour scheme was adopted for presentation. Whilst red indicates the shorter intermolecular contacts, white shows the contacts around the van der Waals (vdW) radii separation and blue represents the longer contacts. To study the relative contributions of different intermolecular interactions in the crystal structures, the 2D fingerprint plots were created from the research papers Hirshfeld surfaces. The colouring of each bin (essentially a pixel) of the resulting 2D histogram was presented as a function of the fraction of surface points in the particular bin, traversing from blue (few points) through green to red (many points). The plots were displayed in the standard 0.4-3.0 Å range for the scales of the d e and d i , axes, where d i is the closest internal distance from a given point on the Hirshfeld surface and d e is the closest contact point external to the surface. Complexes 1-3 are isostructural and crystallize in the monoclinic space group P2 1 /n. They are also isostructural with the previously reported compound [Zn(2-tza) 2 (H 2 O) 2 ] (Rossin et al., 2011). The asymmetric unit of 1 (as a representative of 1-3) contains one crystallographically unique Co 2+ atom, a single thiazole-2-carboxylate (2-tza À ) anionic ligand and a water molecule (Fig. 1). The operation of the inversion centre located at Co 2+ then completes the octahedral requirement, leading to the occupation of the equatorial plane by two equivalent 2-tza À ligands, with two water molecules at the axial positions. The 2-tza À ligand coordinates to Co 2+ in an N,O-chelating mode, generating the five-membered chelate ring as expected. The Co1-N1 bond length in 1 is 2.1161 (12) Å , while the Co1-O1 and Co1-O3 bond lengths are 2.1191 (10) and 2.1082 (10) Å , respectively. These bond lengths are comparable to those of the Ni 2+ and Cd 2+ analogues, as well as those of the Zn 2+ analogue (Rossin et al., 2011). Supramolecular assembly in the crystal structure of 1 is mainly directed by intermolecular hydrogen-bonding interactions, i.e. O-HÁ Á ÁO, C-HÁ Á ÁO and C-HÁ Á ÁS (Table 2). The molecular structure of 1, showing atoms drawn as 50% probability displacement ellipsoids and the atom-labelling scheme. [Symmetry code: (i) Àx + 1, Ày + 1, Àz + 1.] Table 1 Experimental details. For all structures: Z = 2. Experiments were carried out at 150 K with Mo K radiation using a Stoe IPDS2 diffractometer. Absorption was corrected for by multiscan methods (SORTAV; Blessing, 1995). All H-atom parameters were refined. The O-HÁ Á ÁO hydrogen bonds intriguingly form ring patterns of three different sizes, i.e. R 4 4 (12), R 2 2 (8) and R 2 2 (12) (Etter et al., 1990), all of which involve the water O3 and carboxylate O1 and O2 atoms. These rings, together with the other R 2 2 (7) ring engaging the neighbouring aromatic C2 atom and the water O3 atom, result in the supramolecular arrangement of the molecules in a 2D sheet (Fig. 2a). The other type of hydrogen-bonded ring, which results in the three-dimensional (3D) supramolecular architecture (Fig. 3a), is the R 2 1 (5) ring (Fig. 2b). This ring involves a bifurcated hydrogen bond between the aromatic H1 atom, the thiazole S1 atom and the uncoordinated carboxylate O2 atom of the adjacent plane. In the cases of 2 and 3, the hydrogen-bonding patterns are similar to those of 1. The hydrogen-bond distances found in 2 (Ni 2+ ) are slightly shorter than those in 1 (Co 2+ ) and 3 (Cd 2+ ), which is attributed to the differences in the vdW radii of the metal ions. If the discrete [M(2tza) 2 (H 2 O) 2 ] molecule is taken as a node, the hydrogenbonding networks in these isostructural complexes 1-3 can be simplified to the 8-connected uninodal bcu (body-centred cubic) net, with a point symbol 4 24 Á6 4 ( Fig. 3b) (Blatov et al., 2014).

Figure 3
Views of (a) the molecular structure of 1 in the unit cell and (b) the simplified 8-connected uninodal bcu net.

Figure 6
Views of (a) the molecular packing and (b) the simplified 8-connected uninodal bct net of 4.

Figure 5
The hydrogen-bonded-ring patterns found in 4.
R 2 2 (9), are formed ( Fig. 8). They are very similar to those found in 4. The fact that the water O atom is always part of the established hydrogen-bonding patterns is intriguingly common in every assembly, generating the R 2 2 (7) and R 2 2 (8) rings. The R 2 1 (4) and R 2 2 (9) rings in 5 are formed via the weak C-HÁ Á ÁO interaction. The similarity in the hydrogen-bonding interaction patterns of 4 and 5 leads to very similar crystal packing and the same network topology of bct for both supramolecular arrangements (Blatov et al., 2014). Hirshfeld surfaces of (a)-(d) 1, (e)/(f) 4 and (g)/(h) 5, viewed from different angles.

Figure 8
The hydrogen-bonded-ring patterns found in 5. 2016), are alike, the packing of the molecular units in the crystal structures differs significantly. The apparent diversity in the crystal packing evidently derives from the differences in supramolecular interactions which stem from differences in the heteroatom of the ligand and the positions of the carboxylic acid group.
Whilst the S atom of 2-tza À in 1 acts as a hydrogen-bond acceptor, the N-H group of 2-Hima À in 4 functions as a hydrogen-bond donor. The diverse function of the heteroatoms, i.e. S and N-H, then leads to the establishment of smaller hydrogen-bonded rings in 4, i.e. R 2 2 (9) and R 2 1 (4), compared with those found in 1, i.e. R 4 4 (12), R 2 2 (12) and R 2 1 (5), in spite of their identical position in relation to the coordinating carboxylate group. The effect of the different heteroatoms on the supramolecular assembly in 5 (4-oxa À ) and [Co(4-tza) 2 (H 2 O) 2 ] (Meundaeng et al., 2016) is nonetheless minimal since these heteroatoms are not involved in the hydrogen-bonding interactions.
The position of the carboxylic acid group relative to the heteroatom on the azole ring has a profound influence on the crystal packing though hydrogen-bond formation. As the carboxylate group of 2-tza À in 1, for example, promotes the participation of the S atom in hydrogen-bond formation, that of 4-tza À in [Co(4-tza) 2 (H 2 O) 2 ] prevents the engagement of the S atom in hydrogen-bond interactions. The critical significance of the hydrogen-bond interactions in regulating the assembly process is also apparent.

Hirshfeld surface analysis
To gain a quantitative insight into the relative contribution of the hydrogen-bond interactions, the 3D Hirshfeld surfaces of the molecular units and the 2D fingerprint plots of any possible short interactions were established from the singlecrystal data of 1 (as a representative of 1-3), 4 and 5. In each structure, the predominance of the O-HÁ Á ÁO interactions, which are represented by the vivid red areas on the Hirshfeld surfaces, is evident (Fig. 9). The 2D fingerprint plots consis-tently showed the greatest percentages for the HÁ Á ÁO/OÁ Á ÁH contacts, accounting for ca 40 (1), 46 (4) and 57% (5) (Fig. S1-S3 in the supporting information). Apparently, the variation is in the other nonbonding interactions. The second strongest interactions in 1 are the C-HÁ Á ÁS interactions, which contribute ca 17% for SÁ Á ÁH/HÁ Á ÁS contacts and the N-HÁ Á ÁO interactions are the next biggest contributors in 4, although the percentage is less than 5% for NÁ Á ÁH/HÁ Á ÁN contacts. These interactions are shown as pale-red areas on the Hirshfeld surfaces. Noticeably, there is a higher proportion of HÁ Á ÁH contacts on the surface of 4 compared with 1, which can be accounted for by the presence of the N-H group in the azole ring of 2-Hima À (4).
The existence of OÁ Á ÁH/HÁ Á ÁO contacts in 5 is the most substantial among the reported complexes, accounting for ca 57% of the Hirshfeld surface, which is derived primarily from the higher proportion of O atoms in the molecular structure. Intriguingly, the azole O atom does not participate in these quantified OÁ Á ÁH/HÁ Á ÁO contacts. It interacts, on the other hand, with an aromatic O atom from an adjacent discrete molecule and ascribes to ca 5% of the OÁ Á ÁO contacts on the surface. Compared with [Co(4-tza) 2 (H 2 O) 2 ] (Meundaeng et al., 2016), the formation of the hydrogen-bond-ring patterns between these two crystal structures are very similar, resulting in the same crystal packing. However, it is evidenced from the Hirshfeld surface analyses that the fractional contribution of the intermolecular interactions involved in the solid-state assembly can be altered by changing the heteroatom on the azole ring (Fig. 10). This information is not readily apparent  from a conventional analysis of the crystal packing diagrams alone.
The Hirshfeld surface analyses not only provided 3D visualization of the nature and direction of all the possible nonbonding interactions present in the structures but also quantitative information on those interactions. These data then allowed a better understanding of the relationship between the supramolecular interactions and the self-assembling behaviours of the studied molecular structures.

Conclusions
Heterocyclic ligands, i.e. thiazole-2-carboxylate (2-tza À ), imidazole-2-carboxylate (2-Hima À ) and oxazole-4-carboxylate (4-oxa À ), provide a predictable chelating coordination mode to transition-metal ions. Although the molecular structures of the resulting complexes are relatively similar, the packing of the molecular units in their crystal structures, as well as the established nets for the hydrogen-bonding interactions, are significantly different, depending on the types of heteroatom and the positions of the carboxylate group in the ligand structures. Structural characterization also reveals that the solid-state assembly of the molecular structures is crucially governed by the hydrogen-bonding interactions, resulting in the 3D supramolecular architectures. The molecular Hirshfeld surfaces, the 2D fingerprint plots, as well as the enrichment ratios, have been used as tools to quantify these interactions, revealing the priority of these nonbonding interactions. Through the systematic variation in type of the heteroatom and position of the carboxylate group on 1,3-azolecarboxylic acids, the structure-directing features of these ligands through nonbonding interactions have been elucidated.  (Blessing, 1987(Blessing, , 1989. Program(s) used to solve structure: SHELXT2014 (Sheldrick, 2015a) for Co-2tza, Ni-2tza, Cd-2tza, Co-2Hima; SHELXS86 (Sheldrick, 2008) for Co-4oxa. For all structures, program(s) used to refine structure: SHELXL2018 (Sheldrick, 2015b).

Diaquabis(thiazole-2-carboxylato-κ 2 N,O)cobalt(II) (Co-2tza)
Crystal data Special details Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. Refinement. X-ray diffraction intensity data of 1</b->-5 were collected in the series of w-scans using Stoe IPDS2 image plate diffractometer operated with Mo Kα radiation at 150 (2) K. The multi-scan absorption corrections were applied for every collected data set (Blessing, 1987;Blessing, 1989). The structures were solved using dual-space methods within SHELXT and full-matrix least squares refinements were carried out within SHELXL-2018/3 via the WinGX program interface (Sheldrick, 2015). All non-hydrogen positions were located in the direct and the difference Fourier maps and refined using anisotropic displacement parameters.

Diaquabis(thiazole-2-carboxylato-κ 2 N,O)cadmium(II) (Cd-2tza)
Crystal data Special details Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. Refinement. X-ray diffraction intensity data of 1</b->-5 were collected in the series of w-scans using Stoe IPDS2 image plate diffractometer operated with Mo Kα radiation at 150 (2) K. The multi-scan absorption corrections were applied for every collected data set (Blessing, 1987;Blessing, 1989). The structures were solved using dual-space methods within SHELXT and full-matrix least squares refinements were carried out within SHELXL-2018/3 via the WinGX program interface (Sheldrick, 2015). All non-hydrogen positions were located in the direct and the difference Fourier maps and refined using anisotropic displacement parameters.

sup-12
Acta Cryst. (2019). C75, 1319-1326 Special details Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. Refinement. X-ray diffraction intensity data of 1</b->-5 were collected in the series of w-scans using Stoe IPDS2 image plate diffractometer operated with Mo Kα radiation at 150 (2) K. The multi-scan absorption corrections were applied for every collected data set (Blessing, 1987;Blessing, 1989). The structures were solved using dual-space methods within SHELXT and full-matrix least squares refinements were carried out within SHELXL-2018/3 via the WinGX program interface (Sheldrick, 2015). All non-hydrogen positions were located in the direct and the difference Fourier maps and refined using anisotropic displacement parameters.