# ZIF-75 under Pressure: Negative Linear Compressibility and Pressure-Induced Instability
## 3 Results  
### Crystal Structure  
The computed crystal structure of ZIF-75 is shown in Figure 1. According to [PERSON] et al. [2], ZIF-75 is tetragonal, space group \(I41/a\). The composition of the unit cell of the framework is Zn(Im\({}_{2}\)), where the imidazolate ligand has molecular formula Im \(\equiv\) C\({}_{3}\)H\({}_{2}\)N\({}_{2}\). The structure of the imidazolate ligand is shown in Figure 2. According to [PERSON] et al. [3] and the _Reticular Chemistry Structure Resource_ (_RSCR_) [125], ZIF-75 belongs to GIS topology and has the zeolite code GIS. The size of the diameter of the largest sphere that will fit into the channels without contacting the framework atoms is 8.6 A. As can be observed, the crystal structure of ZIF-75 contains large empty channels expanding along the [1 0 0] direction of two types. The main channels are shown at the center of Figure 1, and the secondary ones are shown on the left- and right-hand sides of the main channels. The main channels are very large, having horizontal and vertical dimensions of \(\omega=10.6\) and \(h=7.0\) A, respectively, as measured by the distance between opposite hydrogen atoms (see Figure 1). The computed lattice parameters of ZIF-75 are shown in Table 1. As can be seen in the second row of Table 1, the unit cell parameters of ZIF-75 are well-reproduced despite the complexity and large size of the unit cell of this framework material. The computed  
Figure 1: View of crystal structure of ZIF-75 from [1 0 0] crystallographic direction. The meaning of the horizontal and vertical dimensions of the main channels in ZIF-75, \(\omega\) and \(h\), is also explained in the figure. Color code: Zn—green; N—blue; C—gray; H—white. Figure 2: The structure of the imidazolate ligand. The ligand is shown within an orange box. As observed in the figure, the ligand may link with other carbon atoms through the N atoms. Color code: N—blue; C—gray; H—white. unit cell volume overestimates the experimental one by 11.4%. The inclusion of dispersion corrections is fundamental for ZIF-75 as the uncorrected PBE functional (first row of Table 1) leads to an extremely large overestimation of the lattice parameters. The PBE unit cell volume overestimation is huge, at 32.4%. As mentioned in the Section 2, the geometry optimizations were in fact performed first, relaxing all symmetry constraints. The tetragonal symmetry was broken and, by finding the space symmetry of the resulting optimized structure, a monoclinic symmetry, space group (C2/c), was found. The unit cell parameters of the fully optimized monoclinic structure are given in the third row of Table 1. This structure is reported in the Supplementary Material of this paper as a file in the CIF (crystallographic information file) file format. While the bonding structure in the monoclinic structure is analogous to that of the tetragonal one, the difference in the unit cell volumes is about 8 A\({}^{3}\) and the monoclinic structure is more stable than the tetragonal one with a difference of enthalpy of about 3.9 Kcal-mol\({}^{-1}\). We cannot claim that the tetragonal space symmetry of ZIF-75 is not correct since the structure was determined by Rietveld refinement from powder X-ray diffraction data at room temperature (293 K), and the results of the present calculations refer to zero temperature. The Rietveld refinement of X-ray diffraction data at low temperatures could be used to verify the theoretical result. The volume and enthalpy differences for the structures having tetragonal (\(I41/a\)) and monoclinic (\(C2/c\)) structures of ZIF-75 are rather small. The description of the behavior under pressure of ZIF-75 in the full range of pressure studied (from \(P=-1.0\) to 1.0 GPa) is analogous. Therefore, the results provided in the next sections were obtained using the tetragonal structure, but it must be emphasized that essentially the same conclusions were obtained independently of the space symmetry employed.