## 2 Structural Features and Methodology
### Aluminum Distribution  
The five tetrahedral framework sites, shown in Figure 1, are primarily occupied by either Si and/or Al. The siting of the Al atoms can profoundly impact the extra-framework cations. According to the computational study of [PERSON] et al. [11], T2 sites are highly populated with Al while, in contrast, Al is unlikely to exist at T4 sites; they speculate that when Al occupies T4, the structure is unstable. Furthermore, Al atoms show lower occupancy for T1 than T3 sites [13; 15; 21]. However, for T5 sites, the experimental investigations of [PERSON] [21] show that there is a zero occupation of T5, and [PERSON] and [PERSON] [22] state that the lowest Al presence was at the T5 sites. In addition, ONIOM/PBC calculations in [10] showed that T5 sites for Al substitution are the least favorable for stabilizing large- and small-size cations. From the perspective of [PERSON] et al. [11] Al atoms appear at T5 sites according to a mixture of electrostatic and geometric considerations. For example, the extra-framework cations present in the 10 MR dictate the nature of the Al occupancy of T5; thus, if Ca\({}^{2+}\) is present, Al occupancy of T5 is favored which is otherwise not favorable if Na\({}^{+}\) is present. All the T-sites in clinoptilolites are shown in Figure 1c. Therefore, according to this discussion, we considered the following arrangement for our models: 35% of the Al atoms are present at the T2 sites, 25% are present at the T3 sites, which are the second most-preferred sites for Al, and finally, 10% are present at the T1 sites, leading to a total of 6 Al atoms and a Si/Al ratio of 5. T4 and T5 were left with no Al occupancy. This is because there is little evidence of the occupation of Al at T5 sites, and this would lead to a significant increase in the number of configurations to be studied. In fact, having 6 Al atoms that should be distributed over 24 tetrahedral sites (T1, T2, and T3) means we already have 134,596 possibilities. The computational time required to optimize all these configurations is simply prohibitive; hence, an alternative approach is needed to reduce this number to a computationally manageable one. Supercell program [23; 24] was utilized, which can transform a unit cell with partial occupancies to an ordered unit cell that is suited for calculations as well as detect symmetry-equivalent structures; this means that having 1568 configurations in total is doable, although still a demanding task. The general formula of an aluminosilicate zeolite, which allows for large chemical flexibility, has only one constraint: [PERSON]'s rule or the aluminum avoidance rule. This rule requires a minimum Si-to-Al ratio of 1:1, that is, no two AlO\({}_{4}\) tetrahedra are in direct contact with each other. On the one hand, [PERSON] et al. (2013) concluded, from extensively studying the distribution of Al atoms in dehydrated clinoptilolites, that the lowest-energy configuration obeys [PERSON]'s rule and [PERSON]'s rule. [PERSON]'s rule ([PERSON], 1955) states that alumina units are more likely to be sitting as far as possible from each other. On the other hand, some researchers ([PERSON], 1955) reported that Al-O-Si-O-Al helps bind divalent extra-framework cations; thus, these linkages are stable. Therefore, the  
Figure 1: (**a**) All-silica framework of clinoptilolite with 10 MR and 8 MR (channels A and B) parallel to the c-axis. (**b**) 8 MR (channel C) parallel to the a-axis. Blue and red spheres are the tetrahedral silicon and oxygen atoms, respectively. (**c**) Different T-sites, colored as follows: T1 (purple), T2 (orange), T3 (green), T4 (yellow), and T5 (cyan). An all-silica version is shown here to ease the understanding of the complex clinoptilolite structure. non-Lowensteinian configurations in our study were discarded, resulting in a total of 84 clinoptilolite structures out of 1568. With [PERSON]'s rule, we observed no discernible impact on the total energy of the structures, the cations' movement, or any other factor.