## 3 Results and Discussion
In particular, a _pcg_ conformer was used to obtain the structure of Figure 7a, while the structure of Figure 7b was obtained using an initial geometry belonging to _sc_. A weak hydrogen bonding or electrostatic interaction is present between C=O and a hydrogen of the ammonium group (Figure 7b), in fact the C=O-H distance is 2.895 A. This interaction, absent in the structure obtained starting from a _pcg_ conformer, can explain the gap between the values of the ammonium charge (Figures 6b and 5d) of C4 obtained when _pcg_ and _sc_ conformers are used as initial geometries in the quantum optimizations. As pointed out, the antibacterial activity of the PQASs is correlated with the interaction between the ammonium positive charge and the LPS (peptidoglycan) thin layer of the bacteria. Although the number of aliphatic carbons influences the AATEABs antibacterial activity, as measured in reference [19], this influence is not correlated with an increase in the positive charge on the ammonium group. Figure 6: DFT calculated net charge of the ammonium group as a function of the carbons number of the AATEABs aliphatic chain ((**a**) Löwdin, (**b**) ESP). The maximum length of the AATEABs as a function of carbons in the main chain was calculated and shown in Figure 8, while Figure 9 reports using the structures of the surfactants optimized at a QM/MM level. Similar to previous Figures, the diamonds refer to the \(h\) values obtained from the optimizations, where the \(pcg\) isomer is used as the initial geometry, while circles indicate values derived from optimizations where the shortest isomer is used. Figure 8: AATEABs maximum length versus carbons number of the surfactant’s aliphatic chain using the DFT optimized structures. Figure 7: (**a**) DFT optimized structure of the C4 surfactant obtained using a conformer of the \(pcg\) as initial geometry; (**b**) DFT optimized structure of C4 obtained using a conformer of \(sc\) as initial geometry. Unlike the partial charges, a different trend was obtained for the maximum length of the surfactants. Using the _pcg_ initial geometries, \(h\) increases non-linearly as the number of aliphatic carbons increases, whereas when considering \(sc\) as the initial geometry, the maximum length does not increase. As molecular conformations, water effects, and dispersion interactions were considered in the modeling, the trends in Figures 8 and 9 are not trivial; the winding of the main aliphatic chain with the increase of the carbon number was in fact taken into account. The difference between the \(h\) values obtained using the _pcg_ and \(sc\) initial geometries widened, going from C3 to C12, however, the average value increases with the number of C atoms in the aliphatic chain. The surfactant should show an adequate length so that the positive ammonium group can effectively interact with the bacteria LPS structure; this distance is estimated at 1.5 nm [38; 39]. Considering this threshold as a reference, the trends shown in Figures 8 and 9 are in good agreement with the measured antibacterial activity of the AATEABs [19]  
The suppressive effect due to the solvated polyanions interacting with the ammonium group is other aspect that should be considered; PQASs with alkyl chains capable of protecting the quaternary nitrogen showed a better antibacterial activity [10; 11]. For the investigated surfactants, this shielding effect can be correlated to the molecular aspect ratio. A molecule assumes spherical form when its aspect ratio tends to one, whereas it will be elongated when the latter gets closer to two or higher values. Thus, the aspect ratio of the surfactants was evaluated using both QM/MM and DFT optimized structures. In Table 2, the QM/MM aspect ratios of the syntetized surfactants, shown in Figure 2, were reported; the DFT calculated values were quite similar. The aspect ratio of C6 was near two when considering the structure obtained from a _pcg_ initial conformer, while the aspect ratio of C9 was 1.34.