## 3 Results and Discussion
### In Silico Study
#### 3.3.2 Study on Quantum Descriptors  
The energy of HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied MO) orbital determines the quantum chemical properties of molecules [69]. The energy gap (E\({}_{\text{LUMO}}\)-E\({}_{\text{HOMO}}\)) makes it possible to designate the kinetic stability and reactivity of a compound [69; 70; 71; 72]. The energy gap (E\({}_{\text{LUMO}}\)-E\({}_{\text{HOMO}}\)) makes it possible to designate the kinetic stability and reactivity of a compound [69; 70; 71; 72]. The HOMO and LUMO orbitals and their energy gap were calculated using the Gaussian09 package at the B3 LYP level using the 6-31 LG + (d,p) basis set [47]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Compound** & **MW** & **Csp\({}^{3}\)** & **nRt** & **nHA** & **nHD** & **TPSA** & **WLOGP** & **MLOGP** \\ \hline
**1** & 442.72 & 0.93 & 2 & 2 & 2 & 40.46 & 7.00 & 6.00 \\
**3** & 578.80 & 0.94 & 7 & 5 & 2 & 85.80 & 8.59 & 5.29 \\
**8a** & 720.91 & 0.88 & 12 & 9 & 2 & 146.24 & 9.74 & 5.34 \\ \hline \end{tabular}
\end{table} 
Table 7: Physicochemical parameters and predicted lipophilicity values of the selected compounds (SwissADME). \begin{table}
\begin{tabular}{c c c} \hline
**Compound** & **Drug-Likeness** \\ \hline
**1** & **Lipinski** & **Veber** & **Egan** \\ \hline
**1** & 1 & 0 & 1 \\  & \multicolumn{2}{c}{MLOGP \textgreater{} 4.15} & \multicolumn{2}{c}{WLOG \textgreater{} 5.88} \\
**3** & 2 & 0 & 1 \\  & \multicolumn{2}{c}{MW \textgreater{} 500, MLOGP \textgreater{} 4.15} & \multicolumn{2}{c}{WLOG \textgreater{} 5.88} \\
**8a** & 2 & 2 & 2 \\  & \multicolumn{2}{c}{MW \textgreater{} 500, MLOGP \textgreater{} 4.15} & nRt \textgreater{} 10, TPSA \textgreater{} 140 & WLOG \textgreater{} 5.88, TPSA \textgreater{} 131.6 \\ \hline \end{tabular}
\end{table} 
Table 8: Predicted drug likeness as the number of violated criteria for the selected compounds (SwissADME). As seen in Figure 5, the HOMO orbital is delocalized near the phosphonate group and E ring of betulin **1**, while the LUMO orbital is delocalized on betulin scaffold. The influence of the energy gap (\(\Delta\)E) on the reactivity of the compound; decreasing the \(\Delta\)G value increased the reactivity of the compound. Comparing the energy gap of compound **3** and betulin **1**[73] shows that the introduction of a phosphonate group led to an increase in the reactivity of the compound. The energies of the HOMO-LUMO orbital enable the calculation of the global reactivity descriptors, such as the ionization potential (I), electron affinity (A), hardness (n), softness (s), chemical potential (\(\mu\)), electronegativity (\(\chi\)), and electrophilicity index (\(\omega\)) [74]. Global reactivity descriptors are presented in Table 9.  
The values of ionization potential (I) and electron affinity (A) show that the derivatives have low reactivity with the electrophilic molecules. The high values of electronegativity (\(\chi\)) and electrophilicity index (\(\omega\)) indicate that compounds are good acceptors for the nucleophilic target [69; 74]. The molecular electrostatic potential map (MEP) is a useful tool to designate the electrophilic and nucleophilic region of the compound [75]. Surfaces with different charges are marked with different colors (negative--red, positive--blue, and neutral--green) (Figure 6) [76]. Figure 5: The HOMO and LUMO orbitals of compound **3**. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(\Delta\)**E (eV)** & **I (eV)** & **A (eV)** & \(\eta\) (eV)** & \(\mu\) (eV)** & \(\chi\) (eV) & \(\omega\) (eV) \\ \hline
6.071 & 6.883 & 0.811 & 3.036 & \(-\)3.847 & 3.847 & 2.438 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The global reactivity descriptors of **3**. For compound **3**, the nucleophilic regions are localized in three main areas. The first is localized near the phosphonate group. The second and third area include the oxygen atoms at positions C28 and C3, respectively. The electrophilic regions are localized near the hydrogen atom of the hydroxyl group at positions C3 and C28, respectively.