## 3 Results and Discussion
### Frontier Molecular Orbitals  
Based on the optimized geometry of the PMMA, PCL, PLGA, and QPhNO\({}_{2}\) molecules, we present the results of frontier molecular orbitals obtained from modeled molecules shown in Figure 1. Molecular frontier orbitals are crucial indicators of a molecule's reactivity, represented by the difference between the gap \(\Delta\)E = E\({}_{\text{LUMO}}-\) E\({}_{\text{HOMO}}\) values. Therefore, molecules that are chemically stable are indicated by the larger value of gap \(\Delta\)E. To observe how the frontier orbitals behave in each repeating unit, the surfaces presented in Figure 3 correspond to the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) for a group of six repeating units. Our simulations of the polymers with one, three, or six repeating unities showed that several properties changed, but not all. For example, band gap values vary little with increasing molecular weight. (For more details, see Table S1 in Supporting Information). The interaction between molecules occurs through the strong interaction between the HOMO region of one molecule and the LUMO region of another. It is expected that a molecule with a smaller orbital gap value is more polarizable and exhibits a significant degree of intramolecular charge transfer from the electron donor to the electron acceptor conjugation, which can influence the biological activity of the molecule [2; 6; 38]. The values of these selected properties can be seen in Table 2.  
Considering the information in Table 2 and the frontier molecular orbital (FMO) analysis (Figure 3), it is possible to infer important information about the potential interactions between the polymers and the QPhNO\({}_{2}\) molecule. As noted above, PMMA, PCL, and PLGA have high energy gaps, specifically 7.01 eV, 6.11 eV, and 6.78 eV, respectively, indicating more stable molecules compared to QPhNO\({}_{2}\) (2.78 eV). These properties may contribute to the stability of the encapsulated QPhNO\({}_{2}\) molecule, protecting it from undesired interactions with other molecules in the biological environment and preventing premature degradation. Figure 3: HOMO-LUMO energy diagrams (ground state) for different polymers and compounds, each represented with six repeating units. In each image pair, the letters indicate the corresponding orbital: (**A,B**) represent PMMA with HOMO and LUMO, respectively; (**C,D**) illustrate PCL; (**E,F**) show PLGA; and finally, (**G,H**) display QPhNO\({}_{2}\), highlighting the variation in electronic distribution between HOMO and LUMO in each material. The arrows represent the dipole moment vector of the molecule, indicating the direction and magnitude of the molecular polarity. The arrow points from the region of partial positive charge to the region of partial negative charge, and its length reflects the magnitude of the dipole moment. The calculated energy gaps (\(\Delta\)E) for the three polymers obtained using DFT calculations (B3 LYP/6-311++G) align well with the reported ranges in the literature. For instance, theoretical and experimental values for PMMA typically fall within the range of 6.8-7.2 eV [45; 46], while similar consistency is observed for PCL [38] and PLGA [47]. These results reinforce the reliability of our computational approach, demonstrating its ability to predict quantum chemical parameters. By examining the frontier molecular orbitals (HOMO and LUMO) of the polymers, we observe that the reactive regions are located near the end of the backbone. This is particularly evident for PCL, indicating that the number of intermediate repeating units is not significantly important for the location or energy values of these orbitals in this case. For the QPhNO\({}_{2}\) molecule (Figure 3), it is possible to identify preferred interaction sites and gain a better understanding of how encapsulation occurs. This information can be useful for optimizing the encapsulation efficiency.