## 3 Results and Discussion
### Quantum Mechanical Calculations and Molecular Docking Study  
In order to understand and explain the differences in the activity and inactivity of the dimers with an \(m\)-xylene and lutidine linker, measurements of the electron density of the selected dimer **8** containing 2,7-diazphenothiazazine in its structure and its analog with the lutidine **8a** system were performed using the Gaussian program [32]. Dimer **8** was selected for quantum mechanical studies and molecular docking because it was the only one that showed inactivity against all of the tested cancer cell lines (IC\({}_{50}\)\(>\) 100 uM). A visualization of the obtained results is presented in Figures 2 and 3 using the Avogadro program [33]. These measurements show that the presence of the lutidine system in dimer **8a** causes a differentiation of the electron charges on the thiazine nitrogen atom in 1,4-thiazine rings directly connected to the CH\({}_{2}\) moiety (Figure 3). Additionally, the lutidine system contains a basic nitrogen atom with a lone electron pair, which causes the entire molecule to be enriched with electrons. This situation was not observed in dimer **8** with the \(m\)-xylene linker (Figure 2). Additionally, bond length measurements were made, with particular attention paid to the connecting linkers. In the dimer **8a** containing lutidine, there are CH2-Clutidine bonds with a length of 1.516 A and a characteristic Clutidine-Nlutidine bond with a length of 1.362 A. These bonds are essentially shorter than the analogous bonds found in dimer **8** (CH2-Cm-xylene with a length of 1.521 A; Cm-xylene-Cm-xylene bond with a length of 1.405 A) (Supplementary Materials File S1). The structural analysis carried out using quantum mechanical calculations to some extent explains the differences in the structure of isomeric dimers **8** and **8a**, which had a direct impact on the affinity for protein molecular targets. In the next step, in order to more deeply explain the weak activity of the dimers with the \(m\)-xylene system, preliminary molecular docking studies of dimer **8** and its lutidine derivative **8a** were performed in relation to the histone deacetylase (HDAC4), indicated as a molecular target by the PASS program. The selected histone deacetylase (HDAC4) and the dimers **8** and **8a** were prepared for docking according to the literature data (see Section 2.6) [34; 35; 36]. Two types of docking were performed using two kinds of software. The first one was performed using the DiffDock software Version 1.1.2 [37] with the default settings. The second docking was also performed using the AutoDock Vina software Version 4.2.6 [39], implemented on the TAMARIND BIO server, where the docking site was defined as the inhibitor-binding pocket in the crystallographic structure. This pocket was also detected during blind docking using DiffDock software when analyzing the selected ligands. The docking results are summarized in Table 4, which presents the confidence values of the DiffDock software, as well as the binding affinity calculated by the AutoDock software. The results indicate that both dimers **8** and **8a** dock with a similar strength. \begin{table}
\begin{tabular}{c c c c c} \multirow{2}{*}{**Pose**} & \multirow{2}{*}{\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
1 & \(-1.26\) & \(-8.88\) & \(-1.38\) & \(-9.03\) \\
2 & \(-1.34\) & \(-8.77\) & \(-1.42\) & \(-9.01\) \\ \end{tabular}
\end{table} 
Table 4: Docking results obtained from the DiffDock and AutoDock Vina tools. Figure 3: Visualization of the electron density of the structural analog **8a** with a lutidine system as a linker (electron density was calculated in the Gaussian program, visualized in the Avogadro program).