## 2 Results and Discussion
### Computational Studies
#### 2.2.2 Global Reactivity Descriptors  
Density functional theory (DFT) was utilized to understand the chemical reactivity and site selectivity of the molecular systems. As highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are the orbitals that are the most likely to be involved in chemical reactivity, where the HOMO (\(\pi\) donor) is the highest energy orbital that is still occupied; therefore, energetically, it is the orbital which is easiest to remove electrons from, thus acting as a Lewis base. On the other hand, the LUMO (\(\pi\) acceptor) is the lowest lying orbital that is empty; therefore, energetically, this orbital is the easiest to add more electrons to (acts as Lewis acid). The energy gap = \(E\)HOMO \(-\)\(E\)LUMO and clarifies the inevitable charge exchange interaction inside the molecule. The global electrophilicity index (\(\omega\)), chemical potential (\(\mu\)), electronegativity (\(\chi\)), global softness (S),and global hardness (\(\eta\)), are determined by the well-known equations [40] and the data are listed in Table 1.  
\[\chi=-1/2\ (E_{\text{LUMO}}+E_{\text{HOMO}}) \tag{1}\]  
\[\mu=-\chi=1/2\ (E_{\text{LUMO}}+E_{\text{HOMO}}) \tag{2}\]  
\[\eta=1/2\ (E_{\text{LUMO}}-E_{\text{HOMO}}) \tag{3}\]  
\[S=1/2\ \eta \tag{4}\]  
\[\omega=\mu^{2}/2\ \eta \tag{5}\]  
The softness \(\sigma=1/\eta\) (6)  
From the obtained data we can deduced that:  
1. The values of Frontier molecular orbitals energies (FMOs) namely \(E_{\text{HOMO}}\) and \(E_{\text{LUMO}}\) as well as their neighboring orbitals are negative, indicating the stability of the synthesized antipyrinyl-thiazole derivatives [41].
2. Based on FMOs theory, the reaction occurs with maximum overlap between the HOMO on one molecule and the LUMO on the other and this is a controlling factor in many reactions. Therefore, orbitals of the derivative with the largest value of molecular orbital coefficients may be considered as the sites of electron donation. Thus, the HOMO level is mostly localized on N(2), N(3), S(17), C(16), C(18), C(19), C(4), and O(14) atoms, see Figures 1 and 2, indicating the most preferable sites for attack of the incoming nucleophile.
3. It is well documented that the smaller the energy gap (\(\text{E}_{\text{HOMO}}-\text{E}_{\text{LUMO}}\)) of a molecule the greater the reactivity, polarizability, and readiness to offer electrons to an acceptor and the molecule is considered to be \"soft\", which in turn affects its biological activity. Thus, the title compounds follow the order: **10b** > **10c** > **6** > **7a** > **7b** > **10a** > **5** > **14** > **4** > **9** > **2** > **12**. This means that compound **10b** possesses the smallest energy gap and the highest electrophilicty index (\(\omega=30.864\)) among all newly synthesized thiazoles and, therefore, has the highest softness, polarizability, and reactivity [13].
4. Furthermore, it is obvious that the values of the binding energy increase for the new 4-antipyrinylthiazole derivatives (except thiazole compound **9**) when compared to that of the starting compound (i.e., 4-antipyrinyl-2-chloroacetamidothiazole), revealing higher stability of the newly-formed thiazoles. The newly synthesized thiazoles can be arranged according to stability as: **7b** > **7a** > **10a** > **5** > **4** > **10b** > **6** > **10c** > **12** > **14** > **2** > **9**.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Cpd. No.** & **HOMO** & **LUMO** & \(\text{E}_{\text{HOMO}}-\text{E}_{\text{LUMO}}\) & \(\chi\) & \(\mu\) & \(\eta\) & \(\mathbf{S}\) & \(\omega\) & \(\sigma\) & **Binding Energy \({}^{*}\)** \\ \hline
**2** & \(-3.090\) & \(-1.705\) & \(-1.385\) & \(2.397\) & \(-2.397\) & \(0.692\) & \(0.722\) & \(4.150\) & \(1.444\) & \(-5683.573\) \\
**4** & \(-3.389\) & \(-2.232\) & \(-1.157\  
Figure 1: The electron density, the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) frontier orbitals of 4-antipyrinylthiarole derivatives **2**, **4**, **5**, **6**, and **7**.