## 3 Results and Discussion  
### Geometry Optimization  
Geometry optimization and frequency calculation for ACA, MAY, and LUT were performed in order to analyze their properties at the lowest energy configuration. The optimized geometries shown in Figure 1 were obtained by the M06/6-31G(d) methodology. Along with the properties regarding molecular geometry, the Fukui functions (FF) have been successfully used in studies on site selectivity in molecules [29]. The susceptibility to an electrophilic and nucleophilic attack in the atoms can be explained by these entities (FF). This information could be used in future work for the application of carrier vehicles with the studied molecules. The analysis of the FF values must be complemented with the examination of the torsion angles of each ligand. These dihedral angles can exhibit possible steric impediments that ligands could have within the active site of the maltage-glucoamylase (NtMGAM). Furthermore, the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) were used to identify the pharmacophore of the ACA, MAY, and LUT.  
As can be observed in Figure 1A, the ACA geometry is non-planar due to the four torsion angles present in the structure, which are C23-N26-C1-C6 with \(-107.06^{\circ}\), H78-N26-C1-C44 with \(-5.93^{\circ}\), and C2-O28-C24-C16 with \(105.64^{\circ}\). Additionally, in the opposite extreme of the molecule, the dihedral angle is formed among O29-C3-C25-C17 with a value of \(105.49^{\circ}\). These dihedral angles are related to the steric impediment of the cyclohexane and saccharide moieties present in the ACA ligand, affecting the binding energy with the active site of the NtMGAM. Likewise, the electrophilic and nucleophilic attack sites were determined through the FF, which were calculated in a minimum energy state of the ACA. According to FF, the most susceptible site for an electrophilic attack is located on the N26 atom that corresponds to the secondary amine of the ACA, and the nucleophilic attack site is on the C22 atom of the cyclohexane unit (Figure 1A).  
A non-planar geometry was obtained for the MAY molecule, mainly in the ketofucosyl moiety, which showed a dihedral angle of \(92.80^{\circ}\) for O57-C51-C5-C3. While for the L-rhamosyl, the torsion angle regarding C52-O67-C31-C32 registered \(58.79^{\circ}\). Moreover, in the opposite extreme of the structure, a dihedral angle is formed between O8-C15-C16-C21 atoms with a value of \(-178.98^{\circ}\). The dihedral angles obtained in ketofucosyl and L-rhamnosyl groups increased the rotational degrees of the MAY molecule. According to FF the most susceptible site for an electrophilic attack is the C17 atom which is located in the B ring, and the nucleophilic attack is for the C13 atom of the C ring (Figure 1B).  
The LUT molecule exhibited a planar geometry with dihedral angles very close to \(+/-180^{\circ}\), except the O8-C15-C16-C21 angle which is equal to \(-8.87^{\circ}\). For this molecule, only the B ring presented rotational degrees relative to the A-C rings. Additionally, FF values determined the most susceptible site for an electrophilic attack, which is the C14 atom which corresponds to the double bond C=C in the C ring, while the nucleophilic attack is in the O6 atom which belongs to the oxo group located in the same ring (Figure 1C).  
Figure 1: Optimized molecular structure of the ligands at the M06/6-31G(d) level of theory: (**A**) acarboxylate (ACA), (**B**) maysin (MAY), and (**C**) luteolin (LUT).