Counterion Effect and Isostructurality in a Series of Ag(I) Complexes Containing a Flexible, Imidazole Based Dipodal Ligand

The crystal structures of a series of Ag(I) complexes with 1,3-bis(imidazol-1-ylmethyl)-5-methylbenzene (L) and the counterions BF4− (1), PF6− (2), ClO4− (3), and CF3SO3− (4) were analysed to determine the effect of the latter on their formation. All resulting compounds crystallise in the non-centrosymmetric space group Cc of a monoclinic system and show the formation of cationic, polymeric 1D Ag(I) complexes. SCXRD analyses revealed that compounds 1–3 are isostructural, though 1 shows opposite handedness compared to 2 and 3, resulting in an inversed packing arrangement. The presence of the larger, elongated triflate counterion in 4 leads to a different ligand conformation, as well as different arrangements of the ligand in the cationic chain, and simultaneously results in a packing that exhibits fewer similarities with the remaining three compounds.


Introduction
The definition of isostructurality provided by the International Union of Crystallography (IUCr) states that 'Two crystals are said to be isostructural if they have the same structure, but not necessarily the same cell dimensions nor the same chemical composition, and with a 'comparable' variability in the atomic coordinates to that of the cell dimensions and chemical composition' [1].
The phenomenon is of high interest, especially for crystal engineers and the pharmaceutical industry, as it provides valuable information for crystal structure predictions. Many particular cases have been reported up till now [2][3][4][5][6][7]. Notably, a systematic study on the subject was initiated in the nineties of the last century by the Kálmán group. They tried to clarify the existing terminology and to determine the borders of isostructurality by introducing quantitative descriptors, such as a unit-cell similarity index and isostructurality indices [8,9], which resulted in the conception of the program ISOS [10,11]. Furthermore, the search for similarity of molecular arrangements on different levels (0-3 D dimensions) in diverse types of crystals led to the extension of the phenomenon of isostructurality to polymorphs [12][13][14][15]. To facilitate the identification of equal 'supramolecular constructs' and the quantification of their similarity, the program X-PAC was developed in 2005 [16].
In continuation of our work concerning metal complexes formed with imidazole based extended ligands [17][18][19], we recently reported the isostructurality of two polymeric 1D Ag(I) complexes containing the CF 3 SO 3 − counterion with two related ligands differing by the presence of a methyl group on the aromatic core, namely 1,3-bis(imidazol-1-ylmethyl)benzene and 1,3-bis(imidazol-1-ylmethyl)-5-methylbenzene (the latter has been further investigated here) [20]. In that report, we suggested that isostructurality is more likely to be achieved by polymeric coordination compounds of particular built, containing ligands differing by small structural modifications, than in the case of their parent ligands (discrete molecules). Following up on this work, two new Ag(I) complexes with 1,3-bis(imidazol-1-ylmethyl)-5-methylbenzene (L, Figure 1) and BF 4 − and PF 6 − were prepared and compared with the earlier reported Ag(I)L complexes containing the counterions isostructurality is more likely to be achieved by polymeric coordination compounds of particular built, containing ligands differing by small structural modifications, than in the case of their parent ligands (discrete molecules). Following up on this work, two new Ag(I) complexes with 1,3-bis(imidazol-1-ylmethyl)-5-methylbenzene (L, Figure 1) and BF4 − and PF6 − were prepared and compared with the earlier reported Ag(I)L complexes containing the counterions ClO4 − [21] and CF3SO3 − [20], in order to check the effect of the counterions on the crystal structure formation. One more study on an Ag(I) complex with NO3 -has been reported, but as the compound is a dihydrate and the water molecules obviously affect the crystal structure formed, it will not be further discussed here [22].

Structure Determination
The single-crystal X-ray diffraction data for 1 and 2 were collected on an SuperNova diffractometer (Oxford Diffraction) equipped with an Eos CCD detector and MoKa radiation, λ = 0.71073 Å. The crystals were mounted on a glass fibre and coated with Paratone-N oil. Data collection was carried out at 100(2) K to minimize solvent loss, possible structural disorder and thermal motion effects. Data frames were processed (unit cell determination, intensity data integration, correction for Lorentz and polarisation effects, and empirical absorption correction) by using the corresponding diffractometer's software package (CrysAlisPro Software System, version 1.171.39.46; Rigaku, Oxford, UK) [23]. The structures were solved by using direct methods with SHELXS-2018/3 [24] and refined by using full-matrix least-squares methods based on F2 by using SHELXL-2018/3 [25]. The programs Mercury [26] and POV-Ray [27] were both used to prepare molecular graphics. All non-hydrogen atoms were refined anisotropically, and the hydrogen atoms were positioned geometrically with C-H = 0.95 Å (aromatic), C-H = 0.98 Å (methyl) and 0.99 Å (methylene) and refined as riding, with Uiso(H) = 1.2 Ueq (C) and 1.5 Ueq (methyl C).
A summary of the data collection and structure refinement parameters is provided in Table 1 [20,21].

Structure Determination
The single-crystal X-ray diffraction data for 1 and 2 were collected on an SuperNova diffractometer (Oxford Diffraction) equipped with an Eos CCD detector and MoKa radiation, λ = 0.71073 Å. The crystals were mounted on a glass fibre and coated with Paratone-N oil. Data collection was carried out at 100(2) K to minimize solvent loss, possible structural disorder and thermal motion effects. Data frames were processed (unit cell determination, intensity data integration, correction for Lorentz and polarisation effects, and empirical absorption correction) by using the corresponding diffractometer's software package (CrysAlisPro Software System, version 1.171.39.46; Rigaku, Oxford, UK) [23]. The structures were solved by using direct methods with SHELXS-2018/3 [24] and refined by using fullmatrix least-squares methods based on F2 by using SHELXL-2018/3 [25]. The programs Mercury [26] and POV-Ray [27] were both used to prepare molecular graphics. All nonhydrogen atoms were refined anisotropically, and the hydrogen atoms were positioned geometrically with C-H = 0.95 Å (aromatic), C-H = 0.98 Å (methyl) and 0.99 Å (methylene) and refined as riding, with Uiso(H) = 1.2 Ueq (C) and 1.5 Ueq (methyl C).
A summary of the data collection and structure refinement parameters is provided in Table 1

Crystal Structures of Complexes 1-4: {[AgL]counterion}n
SCXRD analysis showed that all complexes crystallise in the same space group Cc of a monoclinic system with similar unit cell parameters (the biggest deviation is observed for the b parameter in 4). It also revealed the presence of one ligand molecule coordinated with one silver ion, as well as one counterion balancing the positive charge of the silver(I) complex in the asymmetric units of these complexes ( Figure 2).

Crystal Structures of Complexes 1-4: {[AgL]counterion}n
SCXRD analysis showed that all complexes crystallise in the same space group C of a monoclinic system with similar unit cell parameters (the biggest deviation is o served for the b parameter in 4). It also revealed the presence of one ligand molecule c ordinated with one silver ion, as well as one counterion balancing the positive charge the silver(I) complex in the asymmetric units of these complexes ( Figure 2).

Figure 2.
Representation of the asymmetric unit in 1 (left) and 2 (right); atomic displacement plo are shown with 50% probability.

Crystal Structures of Complexes 1-4: {[AgL]counterion} n
SCXRD analysis showed that all complexes crystallise in the same space group Cc of a monoclinic system with similar unit cell parameters (the biggest deviation is observed for the b parameter in 4). It also revealed the presence of one ligand molecule coordinated with one silver ion, as well as one counterion balancing the positive charge of the silver(I) complex in the asymmetric units of these complexes ( Figure 2
The involvement of particular interactions stabilising the crystal structures was estimated by Crystal Explorer [32] a program enabling the visualisation of the molecular packing in a 3D surface (Hirshfeld surface), which can be transposed to a 2D representation of intermolecular distances. These so called fingerprints plot the distances going from the Hirshfeld surface to the closest atoms inside and outside the surface, which are marked as d e and d i , respectively [33]. Though these fingerprint plots are unique for each molecule, those for 1-3 are similar in shape as the compounds show isostructurality (Figure 4). The contribution of H···F/F···H (1-2) and H···O/O···H (3) intermolecular contacts establishing the formation of weak hydrogen bonds stabilising these structures, was calculated as 25.4%, 30.2% and 34.0% for 1-3, respectively (Figure 4). The higher percentage of former contacts in the case of 2 compared to 1 is not surprising as the compound contains more F atoms. The C-H···F interactions present in 2 involve all available H atoms from both imidazole rings, whereas in case of 1, the H atoms from C4 and C5 are not involved (see Table 2). Furthermore, H···H type contacts are also frequently encountered in these structures, contributing 32.4%, 26.7% and 29.4% respectively.
With respect to the unit cells parameters of 1-3, the biggest discrepancy can be observed for the pair 1 and 2, with an elongation of the b parameter of ca. 0.6 Å in 2. This is caused by the presence of counterions of different volume (38 Å 3 for BF 4 − (1), 54 Å 3 for PF 6 − (2), 47 Å 3 for ClO 4 − (3), [34]) and the geometry of these anions, facilitating different types of interactions. The cell similarity index (Π) in this case is equal to 0.03 and the isostructurality index I(20) = 59.4%. However, these values (in particular the latter) are not fully representative as they are influenced by the big difference in size of the counterions [35]. The cell similarity indices for the pairs 1 and 3 and 2 and 3, with a smaller, almost equal difference in size between the counterions, show Π values of ca. 0.01 and I(20) = 84.5%/79.8%, respectively. The slightly higher value of the isostructurality index for the pair 1-3 versus 2-3 might arise from the same geometry of the counterions in the former case. The most striking difference in molecular arrangement of the compounds 1 and 2/3 is caused by the opposite handedness of the isolated crystals, leading to equal but inversed packing motives ( Figure 5). Therefore, it might be more appropriate to refer to this phenomenon as inversed isostructurality. With respect to the unit cells parameters of 1-3, the biggest discrepancy can be observed for the pair 1 and 2, with an elongation of the b parameter of ca. 0.6Å in 2. This is caused by the presence of counterions of different volume (38Å 3 for BF4 − (1), 54 Å 3 for PF6 − (2), 47Å 3 for ClO4 − (3), [34]) and the geometry of these anions, facilitating different types of interactions. The cell similarity index (П) in this case is equal to 0.03 and the isostructurality index I(20) = 59.4%. However, these values (in particular the latter) are not fully representative as they are influenced by the big difference in size of the counterions [35]. The cell similarity indices for the pairs 1 and 3 and 2 and 3, with a smaller, almost equal difference in size between the counterions, show П values of ca. 0.01 and I(20) = 84.5%/79.8%, respectively. The slightly higher value of the isostructurality index for the pair 1-3 versus 2-3 might arise from the same geometry of the counterions in the former case. The most striking difference in molecular arrangement of the compounds 1 and 2/3 is caused by the opposite handedness of the isolated crystals, leading to equal but inversed packing motives ( Figure 5). Therefore, it might be more appropriate to refer to this phenomenon as inversed isostructurality. The CF3SO3 − ion present in 4, has an elongated shape which differs from the remaining counterions, as well as a much bigger anion volume (77 Å 3 ) [36], which influence the formation of the crystal structure. Furthermore, it is equipped with O and F atoms, both capable of forming weak hydrogen bonds. As mentioned above, its presence causes a change in the conformation of the ligand. Moreover, a closer look at the formed 1D chain reveals that the monomeric complex units alternating in the chain are related by an inversion centre, causing a different orientation of the methylene group in the mesitylene ring compared to 1-3. This leads to the presence of more free space between the layers allowing a bigger-sized counterion to fit in (Figure 6), which results in an elongation of the b axis of ca. 1.6 Å in comparison with 1 (the closest distances between adjacent chains located in neighbouring layers are ca. 3.6 Å in 1 and 2, 3.7 Å in 3 and 4.4 Å in  With respect to the unit cells parameters of 1-3, the biggest discrepancy can be observed for the pair 1 and 2, with an elongation of the b parameter of ca. 0.6Å in 2. This is caused by the presence of counterions of different volume (38Å 3 for BF4 − (1), 54 Å 3 for PF6 − (2), 47Å 3 for ClO4 − (3), [34]) and the geometry of these anions, facilitating different types of interactions. The cell similarity index (П) in this case is equal to 0.03 and the isostructurality index I(20) = 59.4%. However, these values (in particular the latter) are not fully representative as they are influenced by the big difference in size of the counterions [35]. The cell similarity indices for the pairs 1 and 3 and 2 and 3, with a smaller, almost equal difference in size between the counterions, show П values of ca. 0.01 and I(20) = 84.5%/79.8%, respectively. The slightly higher value of the isostructurality index for the pair 1-3 versus 2-3 might arise from the same geometry of the counterions in the former case. The most striking difference in molecular arrangement of the compounds 1 and 2/3 is caused by the opposite handedness of the isolated crystals, leading to equal but inversed packing motives ( Figure 5). Therefore, it might be more appropriate to refer to this phenomenon as inversed isostructurality. The CF3SO3 − ion present in 4, has an elongated shape which differs from the remaining counterions, as well as a much bigger anion volume (77 Å 3 ) [36], which influence the formation of the crystal structure. Furthermore, it is equipped with O and F atoms, both capable of forming weak hydrogen bonds. As mentioned above, its presence causes a change in the conformation of the ligand. Moreover, a closer look at the formed 1D chain reveals that the monomeric complex units alternating in the chain are related by an inversion centre, causing a different orientation of the methylene group in the mesitylene ring compared to 1-3. This leads to the presence of more free space between the layers allowing a bigger-sized counterion to fit in (Figure 6), which results in an elongation of the b axis of ca. 1.6 Å in comparison with 1 (the closest distances between adjacent chains located in neighbouring layers are ca. 3.6 Å in 1 and 2, 3.7 Å in 3 and 4.4 Å in 4), as well as a lower packing efficiency with Kitaigorodskii packing indices of 67.7% in 4 versus 72.8%, 71.2% and 70.9% in 1-3, respectively. The CF 3 SO 3 − ion present in 4, has an elongated shape which differs from the remaining counterions, as well as a much bigger anion volume (77 Å 3 ) [36], which influence the formation of the crystal structure. Furthermore, it is equipped with O and F atoms, both capable of forming weak hydrogen bonds. As mentioned above, its presence causes a change in the conformation of the ligand. Moreover, a closer look at the formed 1D chain reveals that the monomeric complex units alternating in the chain are related by an inversion centre, causing a different orientation of the methylene group in the mesitylene ring compared to 1-3. This leads to the presence of more free space between the layers allowing a bigger-sized counterion to fit in (Figure 6 The latter is a consequence of the irregular shape of CF3SO3 − which excludes fully efficient molecular packing and leads to the presence of free space. Mapping with the application PLATON [37] indicates a volume of 46.9 Å 3 per unit cell, accounting for 2.5% of the total cell volume (grid = 0.2 Å, probe radius 1.2 Å), which is not available in complexes 1-3 ( Figure 7). Furthermore, the differences between 4 and 1-3 are reflected in a lower cell similarity index oscillating around 0.1 between 4 and each of the remaining compounds, as well as a different shape of the fingerprint plot (Figure 7). The latter indicates the stabilisation of the structure by a different set of intermolecular interactions, with H···F/F···H and H···O/O···H contacts contributing more or less equally for a total of 34% (the same input was observed for H···O/O···H contacts in 3), whereas the contribution of H···H contacts with a percentage of 21.5% is lower than in compounds 1-3. It is worth mentioning that the larger volume of the trifluoromethanesulfonate anion was reported to preclude ion exchange with perchlorate or hexafluoridophosphate ions [38]. Interestingly, even though 4 is not isostructural with 1-3, it shows isostructurality with an Ag(I) complex of an analogous ligand without methyl substituent on the benzene ring, namely 1,3-bis(imidazol-1-ylmethyl)benzene. In this case, the volume of the voids between the formed layers was calculated as 124.6 Å 3 per unit cell, which could indicate that even the lack of a methyl group situated on the ligand's benzene ring is not sufficient to gain enough free space to fit CF3SO3 between the layers formed by the polymeric chains, as is the arrangement in 1-3.  The latter is a consequence of the irregular shape of CF 3 SO 3 − which excludes fully efficient molecular packing and leads to the presence of free space. Mapping with the application PLATON [37] indicates a volume of 46.9 Å 3 per unit cell, accounting for 2.5% of the total cell volume (grid = 0.2 Å, probe radius 1.2 Å), which is not available in complexes 1-3 ( Figure 7). Furthermore, the differences between 4 and 1-3 are reflected in a lower cell similarity index oscillating around 0.1 between 4 and each of the remaining compounds, as well as a different shape of the fingerprint plot (Figure 7). The latter indicates the stabilisation of the structure by a different set of intermolecular interactions, with H···F/F···H and H···O/O···H contacts contributing more or less equally for a total of 34% (the same input was observed for H···O/O···H contacts in 3), whereas the contribution of H···H contacts with a percentage of 21.5% is lower than in compounds 1-3. It is worth mentioning that the larger volume of the trifluoromethanesulfonate anion was reported to preclude ion exchange with perchlorate or hexafluoridophosphate ions [38]. Interestingly, even though 4 is not isostructural with 1-3, it shows isostructurality with an Ag(I) complex of an analogous ligand without methyl substituent on the benzene ring, namely 1,3-bis(imidazol-1-ylmethyl)benzene. In this case, the volume of the voids between the formed layers was calculated as 124.6 Å 3 per unit cell, which could indicate that even the lack of a methyl group situated on the ligand's benzene ring is not sufficient to gain enough free space to fit CF 3 SO 3 between the layers formed by the polymeric chains, as is the arrangement in 1-3.

Conclusions
Comparison of the crystal structures of a series of Ag(I) complexes formed with 1,3-bis(imidazol-1-ylmethyl)-5-methylbenzene and a range of counterions (BF 4 − , PF 6 − , ClO 4 − and CF 3 SO 3 − ; in molar ratio 1:1) revealed that the first three anions lead to isostructurality, with the highest structural similarity indices observed for compounds containing counterions of similar size and geometry, in particular BF 4 − and ClO 4 − . SCXRD analyses of the complex containing CF 3 SO 3 − , a counterion of much larger size and different shape, revealed that it crystallises in the same space group with similar unit cell parameters as the other three complexes. However, after deeper structural analysis, the initial impression of its isostructurality with the remaining complexes had to be revised, as it indicated changes already on the molecular level, namely a different conformation of the ligand caused by the flip of one of the imidazole rings. Together with the difference in distribution of the monomeric units in the polymeric cationic chain compared to 1-3, this facilitates the presence of more free space between the formed supramolecular layers to accommodate the larger, elongated counterion. Interestingly, this compound is isostructural with an analogue formed with a ligand without a methyl group on the benzene ring, namely {[Ag(1,3-bis(imidazol-1-ylmethyl)benzene]CF 3 SO 3 } n . Further studies on additional representatives of this family of complexes and their packing preferences are ongoing.