## 3 Results and Discussion
### Na-Ca-K Clinoptilolite  
In this clinoptilolite model, the cations were arranged as follows: two Ca atoms occupying the 8 MR of channel B--one positioned at the bottom of the structure and the other one at the left side of the structure, as illustrated in Figure 10. An Na atom occupies the right side of the 10 MR of channel A, while a K atom is sitting at the right side of the 8 MR of the smallest channel, C. This arrangement effectively neutralized the overall negative charge of the framework and led to a stable SCF convergence behavior since all cavities with cations were completely occupied. The DFT calculations in this study confirm that K atoms prefer occupying the third channel. As a matter of fact, according to [PERSON] [59], the presence of cations in the third channel prevents the structure from collapsing during heating. Figure 9: The movement of Ca in different Na\({}_{2}\)Ca\({}_{2}\)Si\({}_{30}\)Al\({}_{6}\)O\({}_{72}\) clinoptilolites in channel B: (**a**) Ca relocates towards the center of the channel and interacts with more framework oxygens, influenced by the presence of Al1 and Al2; (**b**) Ca further advanced to the middle of the channel due to the presence of 2 Al1, Al2, and Al3 atoms; (**c**) in this configuration, Ca migrated from the right side to the left side of the channel and in (**d**), Ca moves downward along the channel due to the presence of more Al atoms at the bottom. The presence of K cations in channels A and B is not favored by DFT calculations. Another experimental work [27] suggests that when K cations occupy these channels, they obstruct the molecular passage, thereby restricting diffusion primarily to channel C. This understanding of the precise positioning of cations within these channels could serve as a good starting point for guiding future experimental investigations. By analyzing cation distributions computationally, researchers can predict diffusion pathways and design experiments to optimize material performance for applications such as adsorption and molecular transport. Analyzing the 84 configurations for Na-Ca-K dinoptilolites, the following conclusions can be drawn. K shifts between the left and the right sides of the structure in response to the distribution of the Al atoms. K's behavior differs slightly from the pattern observed in Ca and contrasts with that of Na. As previously discussed, Na moves conservatively within channels, whereas Ca can traverse from one side to the other or from the upper to the lower parts of channel B. K, on the other hand, sits elegantly on the right side or the left side of the channel B.  
Figure 10: The movement of K and Ca in different Ca\({}_{2}\)NaKSi\({}_{30}\)Al\({}_{6}\)O\({}_{72}\) clinoptilolite models: (**a**) K is four-coordinated with the framework oxygens, influenced by the presence of four Al atoms at the left side of the channel; (**b**) K moved to the other side of channel C due to the presence of two Al1 atoms, whereas Ca is pointing toward Al2 and Al3; (**c**) in this configuration, Ca is pointing upwards due to the presence of Al2 and Al3 while K is three-coordinated to accommodate the four Al atoms and in (**d**) Ca points downward along the channel due to the presence of more Al atoms at the bottom while K accommodates oxygen atoms around Al1. side of channel C. It adjusts its position in response to the location of Al at T1 sites first, followed by those at the T3 sites, and then those at the T2 sites. The behavior of cations, in general, is attributed to where those Al atoms are sitting relative to the channel system of the clinoptilolites. That is, the framework oxygen atoms that surround Al at T2 sites will bind to the Ca atoms since those atoms align well with the same channel that Ca occupies.