## 3 Experimental Study
### Screening of Molecular Descriptors  
The molecular descriptors are generated by the following methods:  
* Construction of molecular structure. This is performed using Chemdraw Ultra 7.0 software. * Optimization of molecular structure. The molecular structure is further optimized in Hyper Chem 7.5 software. * Calculation of molecular descriptors. The optimized molecular structure is imported into CODESSA software and the corresponding molecular descriptors are obtained by calculation. Through molecular descriptor computing software, 733 molecular descriptors are generated and some of the molecular descriptors are closely related to each other. When modeling, it is necessary to filter a large number of calculated molecular descriptors in order to select the descriptors which are the most closely related to the research questions. The quality of the QSPR model depends on the way to determine molecular descriptors to a large extent. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number of Compounds** & **Experimental pKa** & **References** \\ \hline
31 & 0.70–4.99 & [50; 51] \\
34 & 5.00–6.99 & [50; 51; 52] \\
16 & 7.00–7.99 & [50; 51; 52] \\
46 & 8.00–8.99 & [50; 51; 52] \\
80 & 9.00–9.99 & [50; 51; 52] \\
45 & 10.00–10.99 & [50; 51; 52] \\
16 & 11.00–13.80 & [50; 51] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistical table of experimental data. In this study, the CAPSO algorithm is used to screen a large number of calculated molecular descriptors. The implementation process of filtering molecular descriptors with CAPSO is described as follows:  
Step 1. Population initialization. To set the population size and initialize the population individual as a molecular descriptor; to set the number of iterations and the maximum number of iterations. Step 2. Adaptive evaluation. To calculate the fitness of all the molecular descriptors of a population. Step 3. Molecular descriptor selection. To select the next generation of molecular descriptors based on individual fitness values. Step 4. Population renewal. To iterate the molecular descriptors in the population and obtain the next generation of molecular descriptor population. Step 5. Re-evaluation of individual adaptive values. To calculate the fitness of all of the molecular descriptors of the population through iterative evolution and re-evaluate the merits and demerits of the individuals. Step 6. Iteration. To judge whether the iteration condition is satisfied. If it is satisfied, the evolution is ended, otherwise turn to Step 3 and continue to perform the iteration. Finally, five molecular descriptors were selected through CAPSO's search for molecular descriptors (Table 2). Five molecular descriptors belonging to four types were selected by CAPSO: constitutional descriptors, topological descriptors, electrostatic descriptors, and quantum descriptors. The relative number of N atoms (molecular descriptor 1 (MD1)) is a constitutional descriptor and usually proportional to the density of the electron cloud. When the polarity of the positive and negative charge of a molecule increases, its pKa value decreases. The relative number of N atoms can be used to characterize the composition of the molecular structure. The Randic index (order 3) (MD2) is a topological descriptor for molecular size, shape, branching degree, and dispersion force. As the molecular dispersion increases, the molecular volume increases, leading to the decrease of pKa value. The Randic index (order 3) can represent the topological structure of molecules. RNCG relative negative (QMNEG/QTMINUS) (quantum-chemical PC) (MD3) and RNCS relative negative charged SA (SAMNEG * RNCG) (Zefirov's PC) (MD4) are electrostatic descriptors, which depend on the distribution of the charges on the molecule. The negative coefficient of the relative negative charge is inversely proportional to the pKa value and the probability that positive ions replace protons is inversely proportional to the contact area and the pKa value of the negative atomic solvent.