## 3 Results and Discussion
### Na-Dominant Clinoptilolite
#### 3.1.1 XC Functionals  
A comparison of the XC functionals was conducted on Na-clinoptilolite, starting from the relaxed atom positions and lattice parameters of the all-silica model. All available experimental ranges from the literature [9] pertaining to clinoptilolites are combined in Table 2. Table 3 presents the lattice parameters calculated using CP2K. A similar functional comparison was carried out by [PERSON] et al. [42; 43; 44]. Although the widely used PBE-D3 showed satisfactory convergence behavior and provided precise lattice parameter values with minimal deviation for the all-silica model, the same cannot be said for the Na clinoptilolite. The convergence behavior, the basis sets, and the XC functionals showed different behaviors as Al atoms and cations were added to our models. By looking at Table 2, one can readily conclude that PBE-D3 overestimated the \(a\) lattice parameter while underestimating the \(b\) lattice parameter, resulting in values that fall outside the range. Moreover, it is not the most appropriate choice, as convergence required a very long time for just one configuration--roughly three times longer than the time required by PBE-D3(BJ) to achieve comparable values. Both exhibited deviations beyond the range for the \(a\) and \(b\) lattice parameters: PBE-D3 showed a deviation of 0.71% for the former and 0.76% for the latter and PBE-D3(BJ) showed deviations of 0.69% and 0.79% for the \(a\) and \(b\) lattice parameters, respectively. One can observe that the greater deviation in the \(a\) lattice parameter corresponds to the lesser deviation for the \(b\) lattice \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Structure Type** & \(a\) [Å] & \(b\) [Å] & \(c\) [Å] & _β_ [\({}^{\circ}\)] \\ \hline HEU: clinoptilolites & & & & & \\ and heulandites & 17.62–17.74 & 17.81–18.05 & 7.39–7.53 & 116.13–116.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The unit cell parameters range for clinoptilolites that will be used in the XC functionals comparison. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Na-Clinoptilolite** & \(a\) [Å] & \(b\) [Å] & \(c\) [Å] & & \(\beta\) [\({}^{\circ}\)] & & **Volume [Å\({}^{3}\)]** \\ \hline Before optimization & 17.653 & 17.862 & 7.401 & 90 & 116.11 & 90 & 2095.51 \\ \hline
1. PBE-D3 & 17.778 & 17.727 & 7.426 & 89.65 & 116.77 & 89.94 & 2089.70 \\ \hline
2. PBE-D3(BJ) & 17.775 & 17.721 & 7.421 & 89.76 & 116.68 & 90.06 & 2088.69 \\ \hline
3. revPBE-D3 & 17.735 & 17.828 & 7.407 & 89.66 & 116.76 & 90 & 2090.99 \\ \hline
4. PBEsol-D3 & 17.697 & 17.719 & 7.402 & 89.74 & 117.01 & 90.02 & 2068.05 \\ \hline
5. B97-D3 & 17.735 & 17.847 & 7.416 & 89.71 & 116.33 & 90.20 & 2103.89 \\ \hline
6. TPSS-D3 & 17.747 & 17.790 & 7.408 & 89.89 & 116.13 & 90.10 & 2099.94 \\ \hline
7. optB86b-vdW & & & & & No convergence & & \\ \hline
8. rev-vdW-DF2 & 17.737 & 17.663 & 7.420 & 89.54 & 117.21 & 90.31 & 2067.65 \\ \hline
9. BEEF-vdW & 17.836 & 17.816 & 7.438 & 89.83 & 116.47 & 90.13 & 2115.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison between different functionals’ performance in Na-dominant clinoptilolite regarding the unit cell parameters. parameter. Indeed, this relationship can be understood as tension and compression within the cell during optimization: when the \(b\) lattice parameter is under tension, the \(a\) lattice parameter experiences compression, and vice versa. Conversely, revPBE-D3 and PBEsol-D3 demonstrated more favorable values; both maintained the \(a\) and \(c\) lattice parameters within the specified range, with only revPBE-D3 managing to keep the \(b\) lattice parameter within the range. The rev-vdW-DF2 showed the highest deviation for \(\beta\), causing it to exceed the acceptable range for both the \(b\) lattice parameter and angle \(\beta\), as well as being at the upper end of the range for the \(a\) lattice parameter. B97-D3 and revPBE-D3 presented identical deviations for the \(a\) lattice parameter and both were within the lower threshold of the acceptable range for the \(b\) lattice parameter.