## 2 Structural Features and Methodology
### Cations  
The next step in constructing a clinoptilolite model is compensating the negative charge arising from substituting Si with Al at different T-sites with monovalent and/or divalent cations. Three main cation sites were spotted in clinoptilolites. According to [PERSON] [21], for the two samples (Alpe de Siusi and Agoura), 6 different cations occupied the same site; each site was not 100% occupied, and the least occupied site was the third site. The computational study in [10] stated that there are two sites in channel A, which are coordinated with the framework oxygen atoms from the side, and there is another site in channel B. One site in channel A is confined to the sides of the 10 MR and less exposed to the channel, such as those shown in Figure 2 (M1 and M2 sites), and the other is more in the middle of the channel; both are the preferred sites for monovalent cations such as Na\({}^{+}\) and K\({}^{+}\). Furthermore, their results predicted channel A to be a possible site for the divalent cation, Ca\({}^{2+}\); however, XRD studies [22] report that Ca\({}^{2+}\) atoms prefer channel B. Ba\({}^{2+}\) can be spotted in either channel A or channel B, with the former being the most favorable. On the same note, it was observed that K\({}^{+}\), Ca\({}^{2+}\), and Na\({}^{+}\) migrate towards the framework from their hydrated sites during dehydration [11]. [PERSON] et al. [13] analyzed the sites of the cations in clinoptilolite structures and found that Na\({}^{+}\) and K\({}^{+}\) are usually situated at the sides of the 10 MR at channel A. However, the reported distances in their work are somewhat different from the experimental results. These differences may be correlated to the fact that the structures are dehydrated. Indeed, water increases the coordination number of cations while weakening their engagement with the framework, thus resulting in longer distances between extra-framework cations and the framework content [13]. The following compositions were possible for each of the 84 configurations for the two different samples of [PERSON]'s work (Alpe de Siusi and Agoura): (a) Na\({}_{6}\)Al\({}_{6}\)Si\({}_{30}\)O\({}_{72}\), (b) Ca\({}_{3}\)Al\({}_{6}\)Si\({}_{30}\)O\({}_{72}\), (c) Ca\({}_{2}\)Na\({}_{2}\)Al\({}_{6}\)Si\({}_{30}\)O\({}_{72}\), and (d) Ca\({}_{2}\)NaKAl\({}_{6}\)Si\({}_{30}\)O\({}_{72}\). Figure 2: The possible cationic sites, M1 and M2, for Na\({}^{+}\), are shown in the 10 MR of channel A and the 8 MR of channel B, respectively, in one of the 84 possible configurations. Na-dominated clinoptilolite (Na\({}_{6}\)Al\({}_{6}\)Si\({}_{30}\)O\({}_{72}\)) is depicted in Figure 2. Na\({}^{+}\) was added to the large 10 MR (M1) and the 8 MR (M2) channels. Studying monocationic systems in clinoptilolite is valuable since it can aid in the synthesis of clinoptilolites and in the understanding of how natural zeolites could be tailored for specific applications, such as gas separations, adsorption, understanding diffusion characteristics, etc. [27; 28]. The next most dominant cation in clinoptilolites is Ca\({}^{2+}\). Therefore, likewise, a clinoptilolite dominated with Ca\({}^{2+}\) was also explored (Ca\({}_{3}\)Al\({}_{6}\)Si\({}_{30}\)O\({}_{72}\)), as shown in Figure 3. Ca\({}^{2+}\) was added to both M1 and M2 sites to study the most probable location of Ca\({}^{2+}\) in clinoptilolites. On the same note, to gain more insights into the behavior of the extra-framework content and how the different Al distributions affect the migration of those cations, clinoptilolites with both Ca\({}^{2+}\) and Na\({}^{+}\) cations were also investigated, such as Ca\({}_{2}\)Na\({}_{2}\)Al\({}_{6}\)Si\({}_{30}\)O\({}_{72}\), as shown in Figure 4.  
Finally, clinoptilolites with Na, Ca, and K cations were also included in the study, as depicted in Figure 5.  
Figure 4: One of our models and the possible Na\({}^{+}\) and Ca\({}^{2+}\) sites distributed over channels A and B, respectively.