## 3 Results and Discussion
### Theoretical Calculations
The polarizability and hyperpolarizability data are reported in atomic units (a.u), by Gaussian 09, reason why were converted into electrostatic units (esu) (\(\alpha\): 1 au = 0.1482 \(\times\) 10\({}^{-24}\) esu; \(\beta\): 1 au = 8.639 \(\times\) 10\({}^{-33}\) esu). The mean polarization \(\alpha_{0}\) and total polarizability \(\Delta\alpha\) for **4c** are 45.46 \(\times\) 10\({}^{-24}\) esu and 30.66 \(\times\) 10\({}^{-24}\) esu, respectively. The total molecular dipole momentum and first order hyperpolarizability are 1.88 Debye and 3768.07 \(\times\) 10\({}^{-33}\) esu, respectively, see Table 8.  
These analysis frequently, are compared with the family of urea, as a reference for characterizing organic NLO materials [58; 59]. The total dipole moment of the molecule is about 2.22 times lower than urea, and hyperpolarizability first order is 5.89 times higher than urea (\(\mu\) and \(\beta\) for urea are 4.1775 Debye and 638.906 \(\times\) 10\({}^{-33}\) esu at the same calculation level). This result indicates the good non-linearity of the molecule. The intramolecular charge transfer process, is determined by the separation \(E\) between the HOMO (highest energy occupied molecular orbital) and LUMO (lowest energy unoccupied molecular orbital) levels. Energy susceptible to adjust to \(\lambda\) in the range of visible light or tunable laser, by controllable variations due to the nature donor-acceptor of the groups. As an indirect method for determining potential NLO properties, the basal and excited state of a molecule is calculated and these results are used in the qualitative estimation of the efficiency of the intramolecular charge transfer process [60; 61]. Which is related to the intramolecular electronic transfer in 5-arlyarly-2-methylthio-5,12-dihydrobenzo[g]pyrimidine[4,5-_b_]quinoline-4,6,11(3_H_)-trione derivatives, the carbonyl groups being the acceptors of this charge transfer. Finally, we compare the ground state energies of the optimized structures for 5-(4-methoxyphenylyl)-2-methylthio-5,12-dihydrobenzo[g]pyrimidine[4,5-_b_]quinoline-4,6,11(3_H_)-trione **4c** (obtained) and **5c** (Isomer angular uninsulated), with the aim to understand thermodynamic approach for the regiochemistry of the reaction shown Table 9. The calculated values show that 5c is thermodynamically more stable, however, is not formed. This suggests a kinetic control of the reaction. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Dipole Moment**} & \multicolumn{3}{c}{**Polarizability**} & \multicolumn{3}{c}{**First Order Hyperpolarizability**} \\ \hline
**Parameter** & **D** & **Parameter** & **a.u** & **esu (10\({}^{-24}\))** & **Parameter** & **a.u** & **esu (10\({}^{-33}\))** \\ \hline \(\mu_{x}\) & \(-0.28\) & \(\alpha_{xx}\) & 373.29 & 55.26 & \(\beta_{xxx}\) & 1497.24 & 12941.0 \\ \(\mu_{y}\) & \(-1.34\) & \(\alpha_{xy}\) & 7.513 & 1.11 & \(\beta_{xyy}\) & \(-165.57\) & \(-1431.10\) \\ \(\mu_{z}\) & \(-1.28\) & \(\alpha_{yy}\) & 336.29 & 49.78 & \(\beta_{xyy}\) & 665.94 & 5755.80 \\ \(\mu_{0}\) & \(1.88\) & \(\alpha_{xz}\) & 12.913 & 1.91 & \(\beta_{yyy}\) & \(-3426.60\) & \(-29\),616.0 \\  & & \(\alpha_{yz}\) & 55.10 & 8.15 & \(\beta_{xxz}\) & 420.33 & 3633.0 \\  & & \(\alpha_{xz}\) & 211.86 & 31.36 & \(\beta_{xyz}\) & 72.03 & 622.60 \\  & & \(\alpha_{0}\) & 307.15 & 45.46 & \(\beta_{yyz}\) & 438.54 & 3799.30 \\  & & \(\Delta\alpha\) & 207.15 & 30.66 & \(\beta_{yzz}\) & 20.44 & 176.73 \\  & & & & & \(\beta_{yzz}\) & \(-87.92\) & \(-759.93\) \\  & & & & & \(\beta_{zzz}\) & \(-25.13\) & \(-217.26\) \\  & & & & & & \(\beta_{0}\) 3768.07 \(\times\) 10\({}^{-33}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Electrical dipole moment, polarizability and first order hyperpolarizability of **4c** at the level DFT/B3 LYP/6-31G(d,p).