## 3 Results and Discussion
### Theoretical Calculations  
To unambiguously define the structures of **4**, we attempted to obtain a crystal of suitable for X-ray analysis (Figure 2). Crystal of 5-(4-methoxyphenyl)-2-methylthio-5,12-dihydrobenzo[g]pyrimido [4,5-\(b\)]quinoline-4,6,11(3\(H\))-trione 4c was grown in ethanol (95%) using the slow evaporation method at room temperature (RT) [45]. In accordance with the X-ray structural analysis of 5-(4-methoxyphenylyphenyl)-2-methylthio-5,12-dihydrobenzo[g]pyrimido[4,5-\(b\)]quinoline-4,6,11(3\(H\))-trione **4c**, the computational studies indicate that the dihydropyridine ring in these compounds has a boat conformation due to the presence of a _sp\({}^{3}\)_ hybridized C5-atom in which the aryl ring occupies the pseudo-axial position. The orientation of the additional substituent on the C5-aryl ring (CH\({}_{3}\)O) located on the _para_-positions with respect to the heterocyclic ring may be _syn_-orientated to the C5-H bond (synperiplanar, C5-H _sp_), or may lie above the heterocyclic ring and anti-orientated to the C5-H bond (antiperiplanar, C5-H _ap_) (Figure 3). Figure 3: Conformation of the dihydropyridine ring in the structure of compound **4c**. Figure 2: X-ray structure of 5-(4-methoxyphenyl)-2-methylthio-5,12-dihydrobenzo[g]pyrimido[4,5-\(b\)]quinoline-4,6,11(3\(H\))-trione **4c**: (**Left**) ORTEP (Oak Ridge Thermal Ellipsoid Plot diagram), displacement ellipsoids are drawn at the 30% probability level. (**Middle**) The optimized structure with B3 LYP/6-31G(d,p) level, ball and bond type. (**Right**) The optimized structure with B3 LYP/6-31G(d,p) level. The optimized structures of the compound considered in the present study are illustrated in Figure 3, in which the CH\({}_{3}\)O group has the more stable planar conformation. Structural and bonding analysis of these compounds is started by comparison of the selected bond lengths, and bond dihedral angles. Orientation of the CH\({}_{3}\)S group with respect to the heterocyclic ring pyrimidine is denoted by a dihedral angle\(\tau\)1 (N\({}_{1}\)-C\({}_{2}\)-S\({}_{19}\)-C\({}_{20}\)), inter-ring dihedral angles defining orientations of the aryl ring towards the heterocyclic ring are indicated as \(\tau\)2 (C\({}_{14}\)-C\({}_{5}\)-C\({}_{24}\)-C\({}_{29}\)), and the inner dihedral angles of the dihydropyridine ring are denoted by \(\tau\)3 (N\({}_{12}\)-C\({}_{13}\)-C\({}_{14}\)-C\({}_{5}\)) and \(\tau\)4 (N\({}_{12}\)-C\({}_{18}\)-C\({}_{15}\)-C\({}_{5}\)), and dihedral angle \(\tau\)5 (C\({}_{28}\)-C\({}_{27}\)-O\({}_{44}\)-C\({}_{45}\)) the 4-metoxi group the 5-aryl, which are extracted from the optimized structures of compound **4c** (Figure 3) and listed in Table 3. These orientations may influence the molecular energy content and the changes of some characteristic bond lengths, bond angles and bond dihedral angles. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Parameter** & & & **Parameter** & \\ \hline
**Bond Length (Å)** & **Experimental X-ray** & **6-31G(d,p)** & **Bond Length (Å)** & **Experimental X-ray** & **6-31G(d,p)** \\ \hline N\({}_{1}\)-C\({}_{2}\) & 1.31 (4) & 1.33 & C\({}_{11}\)-C\({}_{17}\) & 1.50 (4) & 1.49 \\ N\({}_{1}\)-C\({}_{13}\) & 1.37  
To study the vibrational characteristics and structural parameters of 5-(4-methoxyphenyl)-2-methylthio-5,12-dihydroxy-driborbenzo[\(g\)]pyrimidin0[4,5-\(b\)]quinoline-4,6,11(3\(H\))-tritone **4c**, we performed a theoretical study at DFT level, which allows us to set the geometric and energetic parameters of the title compound. The optimized structure with B3 LYP/6-31G(d,p) level is shown in Figure 2[46; 47; 48; 49; 50]. The calculated geometric parameter (bond lengths, bond angles and dihedral angles) at same levels of calculation for title compound was compared with the experimental parameters, see Table 3, showing very good correlation.