*2.7. Hirshfeld Surface Study*

A Hirshfeld surface study was carried out to gain a fuller appreciation of the nature and quantitative contributions of intermolecular interactions to the supramolecular assembly of complexes **1**, **2** and **3**. The decomposition of contributions from different interaction types, which overlap in the full fingerprint, proved to be helpful to highlight graphically the surface regions that are involved in a specific type of intermolecular contact. The contributions to the Hirshfeld surface area from the various close intermolecular contacts are presented in the histogram in Figure 7.

**Figure 7.** Contributions to the Hirshfeld surface area from the various close intermolecular contacts.

The analysis shows that in compounds **1** and **3**, the Cl··· H interactions have the highest priority (the highest contribution to the Hirshfeld surface) and the N··· H interactions have the highest priority in **2**.

In this approach to assess and visualize the contribution of polar and non-polar interactions to the crystal packing forces, the two-dimensional fingerprint plots for **1**, **2** and **3** were delineated for different types of contacts, such as H··· H, Cl··· H, N··· H and S··· H, as shown in Figure 8. The decomposition of contributions from different interaction types proved to be helpful to highlight graphically the surface

regions that are involved in a specific type of intermolecular contact. The visual analysis of the different fingerprint plots show that the molecular environments are clearly different in each compound.

**Figure 8.** Fingerprint plots for H··· H, Cl··· H/H··· Cl, H··· N/N··· H and H··· S/S··· H contacts. The outline of the full fingerprint is shown in gray.

Despite the different crystal packing arrangements, in general the Hirshfeld analysis revealed that 50%–60% of the total surface areas can be identified with Cl/H, N/H and S/H contacts, which correspond to CH··· Cl, CH··· N or CH··· S hydrogen bonds.

The proportion of Cl··· H/H··· Cl interactions is almost the same in all structures and they contribute around 24% of the Hirshfeld surfaces for each compound. Furthermore, in all structures H··· N contacts are present; with the highest amount in **2** (24.9%) and decreasing gradually in **1** (22.7%) and **3** (15.1%).

The H/H contacts, which are less directed than H-bonds, are present on 2D fingerprint plots as bulk central areas. These contributions correspond to the van der Waals interactions and they represent less than 20% of the Hirshfeld surfaces (barely 6.5% in **1**), thus showing that these lattices are mostly stabilized by H-bonds rather than dispersion forces. The high percentage of other interactions, as shown in Figure 7, is consistent with the number of non-classical π··· π, Cl··· π or S··· π interactions present in the structures. These interactions are associated with C··· N, N··· N, Cl··· C/N and S··· C/N contacts and show that tetrazole units enhance the stacking interactions in the structures. Thus, as expected, another common feature in all of the structures is the relatively low area associated with C··· C interactions.

The presence of other interactions is particularly significant in the structures of **1** and **3**. The presence of water oxygen atoms in **1** produces O/H contacts that represent around 5% of the surface in this structure. Furthermore, the unsaturated coordination environment of the copper metal center in **3** gives rise to weak Cu··· Cl interactions that represent around 10.2% of the total surface. These contacts are almost negligible in the other structures due to their more saturated copper coordination environments.
