## 3 Results and Discussion
### Quantum Mechanical Calculations and Molecular Docking Study
Electron density is represented by a color gradient, with red representing a higher electron density and dark blue representing a lower electron density. In a further stage of the docking study, an interaction analysis was performed for the best position from each complex using the Protein Ligand Interaction Profiler (PLIP) server [39] (Table 5). The analysis showed that the tested dimers **8** and **8a** bind in different parts of the pocket, depending on the software used. Both docking programs indicated that dimer **8** had fewer binding sites than dimer **8a**. In the complexes obtained using the DiffDock server, the ligands bind near the zinc atom, Phe168 and His198 amino acids, while the complexes obtained using the AutoDock software in the left part of the pocket also interact with Phe168 (Figure 4). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Pose** & \begin{tabular}{c} **DiffDock** \\ **Confidence** \\ \end{tabular} & \begin{tabular}{c} **Autodock Vina** \\ **Binding Affinity** \\ **[kcal/mol]** \\ \end{tabular} & \
\begin{tabular}{c} **DiffDock** \\ **Confidence** \\ \end{tabular} &
\begin{tabular}{c} **AutoDock Vina** \\ **Binding Affinity** \\ **[kcal/mol]** \\ \end{tabular} \\ \cline{2-5}  & & **8** & & **8a** \\ \hline
3 & \(-1.46\) & \(-8.74\) & \(-1.51\) & \(-8.98\) \\
4 & \(-1.61\) & \(-8.65\) & \(-1.59\) & \(-8.93\) \\
5 & \(-1.91\) & \(-8.61\) & \(-1.60\) & \(-8.91\) \\
6 & \(-2.06\) & \(-8.61\) & \(-1.73\) & \(-8.85\) \\
7 & \(-2.18\) & \(-8.58\) & \(-1.93\) & \(-8.53\) \\
8 & \(-2.38\) & \(-8.50\) & \(-1.98\) & \(-8.61\) \\
9 & \(-3.25\) & \(-8.48\) & \(-2.08\) & \(-8.54\) \\
10 & \(-3.67\) & - & \(-4.15\) & - \\ Average & \(-2.11\) & \(-8.65\) & \(-1.94\) & \(-8.82\) \\ Deviation & \(0.81\) & \(0.13\) & \(0.81\) & \(0.20\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._  
Figure 4: Picture of the pockets occupied by docked compounds **8** and **8a**. The light-pink color indicates the pocket where compounds are docked with DiffDock and the light-blue color indicates the pocket where compounds are docked with AutoDock Vina. The orange sticks indicate the following amino acids: Phe168 and His198. The obtained results were also compared with the position of the trifluoromethyl ketone inhibitor in the structure of the tested protein. This inhibitor binds to the pocket into which test compounds **8** and **8a** were docked using DiffDock software (Figure 5). Analyzing the interactions of both dimers in this binding pocket, it can be noticed that dimer **8** is located at a considerable distance from the zinc atom and interacts only with Phe168 and His198 (Figure 6). Figure 5: Position of the trifluoromethylketone inhibitor in the ligand-binding pocket obtained using DiffDock docking. The dark-blue sphere indicates the zinc atom. Orange sticks indicate the following amino acids: Phe168 and His198. Figure 6: Position of dimer **8** in the binding pocket obtained using DiffDock docking and the interaction with amino acids, which are indicated by black dashed lines. The dark-blue sphere indicates the zinc atom. The orange sticks indicate the following amino acids: Phe168 and His198. Meanwhile, the **8a** dimer, having a lutidine system in its structure, is located closer to the zinc atom compared to its analog **8**, and has four interactions with the following amino acids: Phe168, Phe277, His153, and His198 (Figure 7). The performed quantum mechanical studies and preliminary molecular docking in relation to histone deacetylase explain the weak anticancer activity of the tested compounds compared to previously obtained active dimers with a lutidine linker.