## 3 Results and Discussion
### Frontier Molecular Orbitals
It is important to emphasize that different polymers may exhibit distinct encapsulation properties due to their chemical structures and physical properties. For example, PCL and PLGA are biodegradable and biocompatible polymers, making them ideal in biomedical applications, including drug nanoencapsulation [20; 21]. These polymers may be particularly suitable for controlled-release systems of molecules like QPhNO\({}_{2}\) due to their ability to degrade in the body and release the encapsulated drug in a controlled manner. In contrast, PMMA is a non-biodegradable polymer, which may limit its applicability in some biomedical applications [19]. However, its optical and insulating properties can be exploited in other applications, such as protecting the QPhNO\({}_{2}\) molecule from light or undesired redox reactions [48]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **QPhNO\({}_{2}\)** & **PMMA** & **PCL** & **PLGA** \\ \hline Structural formula & C\({}_{20}\)H\({}_{16}\)N\({}_{2}\)O\({}_{5}\) & (C\({}_{5}\)H\({}_{8}\)O\({}_{2}\))\({}_{6}\) & (C\({}_{6}\)H\({}_{10}\)O\({}_{2}\))\({}_{6}\) & (C\({}_{3}\)H\({}_{4}\)O\({}_{2}\))\({}_{6}\) + \\ Weight (amu) & 364.357 & 630.722 & 700.907 & 782.610 \\ Dipole moment (Debye) & 9.05 & 6.54 & 2.97 & 14.01 \\ HOMO energy (eV) & \(-\)6.29 & \(-\)7.37 & \(-\)7.02 & \(-\)7.53 \\ LUMO energy (eV) & \(-\)3.51 & \(-\)0.36 & \(-\)0.91 & \(-\)0.75 \\ PSA (A\({}^{2}\)) & 84.461 & 115.159 & 124.564 & 254.494 \\ log P & 3.49 & 7.14 & 5.18 & 3.49 \\ HBD count & 1 & 0 & 0 & 0 \\ HBA count & 7 & 0 & 7 & 0 \\ Polarizability (10\({}^{-30}\) m\({}^{3}\)) & 68.99 & 93.52 & 102.04 & 96.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Calculated molecular properties for QPhNO\({}_{2}\), PMMA, PCL, and PLGA molecules, utilizing the DFT approach, B3 LYP model, and 6-311++G basis set in a vacuum for equilibrium geometry in the ground state. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Quantum Parameters** & **QPhNO\({}_{2}\)** & **PMMA** & **PCL** & **PLGA** \\ \hline Gap energy (\(\Delta\)E) (eV) & 2.78 & 7.01 & 6.11 & 6.78 \\ Ionization energy (I) (eV) & 6.29 & 7.37 & 7.02 & 7.53 \\ Electron affinity (A) (eV) & 3.51 & 0.36 & 0.91 & 0.75 \\ Electronegativity (x) (eV) & 4.90 & 3.87 & 3.97 & 4.14 \\ Hardness (\(\eta\)) (eV) & 1.39 & 3.51 & 3.06 & 3.39 \\ Softness (\(\sigma\)) (eV\({}^{-1}\)) & 0.72 & 0.29 & 0.33 & 0.29 \\ Chemical potential (\(\mu\)) (eV) & \(-\)4.90 & \(-\)3.87 & \(-\)3.97 & \(-\)4.14 \\ Global electrophilicity (GE) (eV) & 8.64 & 2.13 & 2.57 & 2.53 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Calculated quantum chemical parameters of the compounds studied in this work. According to Table 2, QPhNO\({}_{2}\) has a higher electronegativity value (4.90 eV) compared to the polymer molecules. Electronegativity is defined as a measure of a molecule's ability to attract electrons to itself in a bond. As shown, the electronegativity values follow the trend PMMA < PCL < PLGA (3.87 < 3.97 < 4.14). For the most stable conformers of QPhNO\({}_{2}\), PMMA, PCL, and PLGA compounds, additional quantum chemical parameters, such as ionization potential (I), electron affinity (A), chemical potential (\(\upmu\)), global electrophilicity index (GE), and hardness (\(\upmu\)), are also calculated and reported in Table 2.  
The chemical potential (\(\upmu\)) represents the tendency of electrons to escape from a stable system. The negative chemical potential indicates that a complex is stable and does not spontaneously decompose into its elements. Hardness refers to the resistance to the deformation of the electronic cloud of the chemical system under minor disturbances encountered during the chemical process. From the values shown in Table 2, we can observe that hardness increases in the following order: QPhNO\({}_{2}\) < PCL < PLGA < PMMA (1.39 < 3.06 < 3.39 < 3.51). A soft, more reactive molecule is one with a small HOMO-LUMO gap as opposed to one with a big HOMO-LUMO gap.