## 3 Results and Discussion
### DFT Investigations
#### 3.2.3 HOMO and LUMO Molecular Orbitals and Reactivity  
The analysis of frontier molecular orbitals (FMOs), specifically the HOMO and LUMO, provides valuable insights into a compound's chemical reactivity, stability, biological activity, optical features, and electronic behavior [43]. The LUMO is associated with an electron's acceptance, while the HOMO signifies electron donation. Figure 5 presents the HOMO-1, HOMO, LUMO, and LUMO + 1 contributions for the **SQ** compound, highlighting the calculated values of \(\text{E}_{\text{HOMO-1}}\), \(\text{E}_{\text{HOMO}}\), \(\text{E}_{\text{LUMO}}\), and \(\text{E}_{\text{LUMO + 1}}\) and the energy gaps (\(\Delta\)E), determined using the DFT method at the B3 LYP/6-31 lg (d,p) level. A crucial parameter in understanding a compound's stability, reactivity, and potential biological effects is the HOMO-LUMO energy gap. Molecules with smaller energy gaps typically exhibit higher biological activity and chemical reactivity but lower stability than those with larger gaps [44]. In the SQ compound, the HOMO-LUMO analysis reveals that the electron density in the HOMO is concentrated primarily on the anionic \(\text{SO}_{3}-\) group, while the LUMO's electron density is distributed across the cationic regions, suggesting an electron transfer pathway from the \(\text{SO}_{3}-\) group to the cationic portions of the molecule. For SQ, the energy gap is calculated to be 1.87 eV, which is relatively low and implies enhanced reactivity and  
Figure 4: The MEP map of SQ (**5**) applying the DFT/B3 LYP/6-31 lg (d,p) level.  
biological activity. This narrow HOMO-LUMO gap indicates that the HOMO and LUMO energy levels are close, allowing for easy excitation of outer-layer electrons, which supports the compound's pronounced chemical and biological activity. Furthermore, the energy gap between HOMO-1 (\(-\)5.35 eV) and LUMO + 1 (\(-\)1.99 eV) is determined at 3.36 eV.  
In addition to fundamental calculations, a deeper quantum chemical analysis was conducted to further elucidate the reactivity of the compound. The key descriptors were evaluated, including absolute hardness (\(\eta\) = (E\({}_{\text{LUMO}}\) \(-\) E\({}_{\text{HOMO}}\))/2), which reflects the compound's resistance to charge transfer, and absolute softness (\(\sigma\) = 1/\(\eta\)), indicating its adaptability to electronic changes. This study also computed the absolute electronegativity (\(\chi\) = \(-\)(E\({}_{\text{HOMO}}\) + E\({}_{\text{LUMO}}\))/2), which describes the compound's affinity for electrons, as well as the chemical potential (P\({}_{\text{i}}\) = \(-\)\(\chi\)), representing the compound's tendency to release or accept electrons. Additional values, such as the additional electronic charge (\(\Delta\)N = \(-\)P\({}_{\text{i}}\)/\(\eta\)) and global electrophilicity (\(\omega\) = P\({}_{\text{i}}\)\({}^{2}\)/2\(\eta\)), which gauge its propensity to interact with electron-rich species, were calculated to provide a comprehensive view of the SQ compound's reactivity characteristics. The values of P\({}_{\text{i}}\), \(\omega\), \(\eta\), \(\chi\), \(\sigma\), and \(\Delta\)N for SQ are calculated to be \(-\)4.10 eV, 9.03 eV, 0.93 eV, 4.10 eV, 1.07 eV\({}^{-1}\), and 4.41, respectively. In the synthesized compound, the P\({}_{\text{i}}\) parameter is consistently negative, indicating that its structure remains stable and does not break down into fundamental elements. The \(\omega\) value suggests that this compound is capable of forming multiple binding modes with biological macromolecules [45], potentially enhancing its inhibitory effects. Additionally, the SQ compound shows a low absolute hardness of 0.93 eV, highlighting its increased reactivity.