## 2 Computational Method
Moreover, in reference [32], the B3 LYP and triple-\(\zeta\) basis set were used to obtain the electrostatic potential around the molecules and partial charges, while in reference [30], the B3 LYP calculations of atomic charges were correlated to a conformational \begin{table}
\begin{tabular}{c c} \hline \hline
**Number of Carbons in AATEAB Aliphatic Chain** & **R\({}_{\text{popul}}\)** \\ \hline C3 & 5.5 \\ C4 & 4.5 \\ C6 & 3.5 \\ C9 & 5.5 \\ C10 & 8.0 \\ C11 & 1.5 \\ C12 & 3.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Ratio between the group with the maximum number of conformers (\(pcg\)) and the group containing the conformers with smaller \(h\) among the thirty most stable (\(sc\)) populations. AATEAB—acryloxylylethylammonium bromides. study. Finally, B3 LYP with 6-31G (d) basis set was also applied to calculate a set of quantum chemistry properties of eleven quaternary ammonium compounds [33]. In particular, in this work, DFT-based descriptors were used to derive quantitative structure-activity relationships enabling the correlation of the computed properties with the toxicity of quaternary ammonium compounds on green alga _Chlorella vulgaris_ with good results [33]. This investigation showed that the alkyl chain lengths and the most positive net atomic charges on the hydrogen atoms of quaternary group, as well as entropy, are the major descriptors (properties) governing the structure-activity relationship models. The optimizations of the quantum region of the investigated surfactants and the entire geometries in the successive pure DFT optimizations were performed using the analytical energy gradients and the quasi-Newton algorithm with an approximate energy Hessian. The maximum and root mean square gradient thresholds of 4.5 \(\times\) 10\({}^{-3}\) and 3.0 \(\times\) 10\({}^{-3}\), respectively, were used as the convergence criteria in conjunction with the maximum and root mean square of the nucleus Cartesian displacement vectors, equal to 5.4 \(\times\) 10\({}^{-3}\) and 3.6 \(\times\) 10\({}^{-3}\) (a.u. ), respectively. The QAS electronic proprieties were calculated with good results using B3 LYP and a similar or smaller basis set. The interactions between the surfactant and water molecules may change both the solute geometry and the charge distributions, thus the QM/MM optimizations were carried out to take into account this effect. The model in Figure 3 was used in the QM/MM calculations. In particular, the CH\({}_{2}\)N(CH\({}_{2}\)CH\({}_{3}\))\({}_{3}\) group was considered as the quantum region, while the rest of the surfactant was considered as the classical part, in addition to the water molecules randomly collocated around the solute (Figure 3). This model is consistent with the environment encountered by the AATEABs, as some of them are used as surfactants to prepare oil/water polarizable bi-continuous micro-emulsions [20]. Thus, self-assembled surfactants are not consistent with the oil/water micro-emulsion environment. For the same reason, periodic boundary conditions were not used. The dimensions of the box in Figure 3, correlated with the water content, depend on the surfactant sizes; however, appropriate dimensions were chosen so as to guarantee a sufficient number of water molecules, in order to investigate the possible water bridge between the carbonyl and ammonium hydrogens. Specifically, for all of the investigated AATEABs, a box with the following dimensions was considered: L\({}_{\rm x}\) = 1.5 nm, L\({}_{\rm y}\) = 1.5 nm, and L\({}_{\rm z}\) = 2.5 nm. The geometry of the quantum region was optimized according the aforementioned procedure, while the classic region was optimized by using an Amber99 force field; the steepest descent algorithm and a threshold for the total energy convergence of 10\({}^{-6}\) were also used. Figure 3: Model used for the quantum/molecular mechanics (QM/MM) calculations. Red = oxygen; white = hydrogen; grey = carbon; and blue = nitrogen.