## 3 Results and Discussion
### Na-Dominant Clinoptilolite
#### 3.1.2 Bond Lengths and Interatomic Distances  
In the following, we will discuss the bond lengths of the most stable configuration for both the revPBE-D3 and B97-D3 for both samples. For full details of Al-O, O-O, and Si-O's interatomic distances, as well as the distances between the framework and extra-framework cations, the reader is referred to the Supplementary Material. The bond lengths in this work were determined using the neighbor search module in Gemmi library (version 0.6.0) [57] in Python (v.3). The interatomic distances of the most stable configuration are shown in Tables 5 and 6, and both members of the GGA family performed well in this respect. The revPBE-D3 overestimates the interatomic distances while the B97-D3 provides a better estimate of the bond lengths. According to [PERSON]'s experimental refinements, the average distance between Si atoms in T1 with oxygen in the same tetrahedron was 1.625 A. Both functionals showed good agreement with Agoura clinoptilolite, while when using the Siusi clinoptilolite, only the B97-D3 showed better agreement, with a slight elongation of, at most, 0.007 A. For T2, the distances found by B97-D3 were shorter than those found for the revPBE-D3; both deviated from the experimental measurements because of the high percentage of Al atoms present in those sites. Speaking of which, the Al-O distances were between 1.718 A and 1.752 A, which, for the ONIOM and PBC calculations in [10], were further overestimated to be between 1.745 and 1.799 A and 1.757 and 1.769 A, respectively. This disagreement with the experiments in both studies stems from the fact that Si and Al occupy the same sites in nature, while, in both studies, Al had an occupation of 100% for the respective sites. Therefore, the largest deviation in both samples was observed in the site that has the highest Al percentage in nature, which was T2. T3 showed better agreement in both samples, with the B97-D3 showing a slight elongation of, at most, 0.002 A. revPBE-D3 showed less deviation for Si4-O when using the experimental measurements in Siusi clinoptilolite. Alternatively, B97-D3 with Agoura clinoptilolite showed better agreement, with a slight elongation of a few angstroms, at 0.006 A. For the Si-O in T5, B97-D3 showed better agreement, with a shortening of 0.004 A or elongation of 0.002 A, or complete agreement. Therefore, in summary, there was good agreement with the experiments and the strongest deviation was only observed at T2 sites where there was a high percentage of Al. For both samples, B97-D3 showed less deviation than the revPBE-D3 except for the T4 sites at the Siusi sample, which demonstrated more deviation in B97-D3 than when using revPBE-D3. In contrast, there was a stronger deviation in interatomic distances in [10,13], where both showed significant elongation or significant shortening for Si-O and the Al-O distances in pure siliceous clinoptilolites or clinoptilolites with cations. It should be noted at this point that all the results in the following sections were obtained with the B97-D3 functional. \begin{table}
\begin{tabular}{l l l l l} \hline
**Structure** & \(a\) **(Å)** & \(b\) **(Å)** & \(c\) **(Å)** & _β_ (\({}^{\circ}\)) \\ \hline Agoura\_revPBE-D3 & 17.63–17.73 & 17.71–17.76 & 7.37–7.39 & 116.84–117.03 \\ \hline Siusi\_revPBE-D3 & 17.65–17.71 & 17.72–17.76 & 7.37–7.39 & 116.73–117.04 \\ \hline Agoura\_B97-D3 & 17.72–17.77 & 17.68–17.81 & 7.41–7.42 & 116.25–116.52 \\ \hline Siusi\_B97-D3 & 17.70–17.74 & 17.82–17.87 & 7.39–7.41 & 116.12–116.35 \\ \hline \end{tabular}
\end{table} 
Table 4: revPBE-D3 and B97-D3 unit cell parameter ranges for both samples.