# A Computational (DFT) Study on the Anti-Malarial Drug: Lumefantrine
## 3 Results and Discussion
### Molecular Orbitals Surfaces (HOMO-LUMO) Analysis and UV-Vis Spectra  
Highest Occupied Molecular Orbital (HOMO) represents the highest energy level in which at least one electron exists around the molecule. Lowest Unoccupied Molecular Orbital (LUMO) gives the lowest energy level around the molecule in which there is no electron. The gap between these two values is very significant in the biological and chemical reactivities of the molecules. The molecules with small energy gaps are accepted as soft molecules and expected to involve in chemical reactions easily. These energy levels also determine the acidity and basicity of the molecules.  
In Lumefantrine, the energy gap between HOMO-LUMO was calculated to be 9.9 eV, 9.6 eV, 3.5 eV and 3.7 eV, according to the methods, respectively. As can be seen easily, DFT methods give dramatically smaller values than the HF calculations (Tables 2 and 3). According to these values, Lumefantrine can be supposed to be a semi-rigid molecule (Figure 4). The larger HOMO-LUMO gap gives the molecule greater kinetic stability and lower chemical reactivity. The molecule's hardness can be predicted via Equation (2), and softness (S) can be derived from hardness via Equation (3).  
\[\eta=(\epsilon\text{LUMO}-\varepsilon\text{HOMO}) \tag{2}\]  
Figure 4: Electron transitions and corresponding E and \(\Delta\)E values for Lumefantrine.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**HF**} & \multicolumn{2}{c}{**DFT**} & \multicolumn{2}{c}{**DFT**} & \multicolumn{2}{c}{**DFT**} & \multicolumn{2}{c}{**DFT**} & \multicolumn{2}{c}{**DFT**} \\ \cline{2-10}  & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**BD3 LYP**} & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**BDF2**} & \multicolumn{1}{c}{**BD3 LYP**} \\ \cline{2-10}  & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**HDF2**} \\ \cline{2-10}  & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**HDF2**} & \multicolumn{1}{c}{**HDF2**} \\ \hline C1 & \(-\)0.087 & \(-\)0.019 & 0.093 & 0.083 & H1 & 0.310 & 0.265 & 0.181 & 0.177 \\ C2 & \(-\)0.178 & \(-\)0.195 & \(-\)0.199 & \(-\)0.190 & H2 & 0.310 & 0.261 & 0.176 & 0.172 \\ C3 & \(-\)0.194 & \(-\As can be easily guessed, molecules with large energy gaps, defined as hard molecules, do not change their electron density very easily. On the other hand, molecules with small energy gaps, called soft molecules, change their electron densities relatively easily [31; 32]. The calculated \(\lambda\)max can be calculated from the differences between MO energies as seen in Table 4. Calculated UV-Vis spectra can be seen in Figure 5.