## 3 Results and Discussion
### Theoretical Calculations
As evidence of this orbital phenomenon, it is the lowest electronic density on N3 and N12 compared to N1 (Table 6). The energy involved in the hyperconjugative interactions of the bonds between carbon and oxygen atoms of the carbonyl groups of molecule **4c**, give the most intense interactions and correspond to the highest degree of conjugation occurring in the \(\alpha\),\(\beta\)-unsaturated intramolecular system of aromatic ketones. \(\pi^{\bullet}\) (C\({}_{4}\)-O\({}_{21}\)) \(\rightarrow\)\(\pi^{\bullet}\) (C\({}_{13}\)-C\({}_{14}\)), 257 kcal/mol; \(\pi^{\bullet}\) (C\({}_{6}\)-O\({}_{22}\)) \(\rightarrow\)\(\pi^{\bullet}\) (C\({}_{15}\)-C\({}_{18}\)), 94.7 kcal/mol; \(\pi^{\bullet}\) (C\({}_{11}\)-O\({}_{23}\)) \(\rightarrow\)\(\pi^{\bullet}\) (C\({}_{15}\)-C\({}_{18}\)), 41.8 kcal/mol; \(\pi^{\bullet}\) (C\({}_{11}\)-O\({}_{23}\)) \(\rightarrow\)\(\pi^{\bullet}\) (C\({}_{16}\)-C\({}_{17}\)), 76.7 kcal/mol. In the analysis of the nonlinear optical properties (NLO) for **4c**, the polarization of the molecule, induced by an external radiation field, it often resembles the generation of a dipole moment induced by an external electric field. Under the weak polarization condition, a Taylor serial development in the electric field components can be used to demonstrate the dipole interaction with the electric field of external radiation. The first static hyperpolarizability (\(\beta_{0}\)) and its related properties (\(\beta\), \(\alpha_{0}\) and \(\Delta\alpha\)) were calculated using the B3 LYP/6-31G(d,p) level based on the finite field approach. The total static dipole moment \(\mu\), average polarizability \(\alpha_{0}\), anisotropy polarizability \(\Delta\alpha\) and hyperpolarizability of first average \(\beta_{0}\), using the components \(x\), \(y\) and \(z\) is defined as:  
\[\mu=\left(\mu_{x}^{2}+\ \mu_{y}^{2}+\ \mu_{z}^{2}\right)^{1/2} \tag{2}\]  
\[\alpha_{0}=\frac{1}{3}\big{(}\alpha_{xx}+\alpha_{yy}+\alpha_{zz}\big{)} \tag{3}\]  
\[\Delta\alpha=2^{-1/2}\Big{[}\big{(}\alpha_{xx}-\alpha_{yy}\big{)}^{2}+\big{(} \alpha_{yy}-\alpha_{zz}\big{)}^{2}+\big{(}\alpha_{zz}-\alpha_{xx}\big{)}^{2}+ 6\alpha_{xz}^{2}\Big{]}^{1/2} \tag{4}\]  
First order hyperpolarizability is  
\[\beta=\left(\beta_{x}^{2}+\beta_{y}^{2}+\beta_{z}^{2}\right)^{1/2} \tag{5}\]  
where  
\[\beta_{y}=\left(\beta_{yyy}+\beta_{yzz}+\beta_{yxx}\right) \tag{6}\]  
\[\beta_{z}=\left(\beta_{zzz}+\beta_{zxx}+\beta_{zyy}\right) \tag{7}\]  
\[\beta_{x}=\left(\beta_{xxx}+\beta_{xyy}+\beta_{zzz}\right) \tag{8}\]  
\[\beta=\left[\big{(}\beta_{xxx}+\beta_{xyy}+\beta_{zzz}\big{)}^{2}+\big{(} \beta_{yyy}+\beta_{yzz}+\beta_{yxx}\big{)}^{2}+\big{(}\beta_{zzz}+\beta_{zxx}+ \beta_{zyy}+\big{)}^{2}\right]^{1/2} \tag{9}\] \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Donor NBO (\(i\))**} & \multirow{2}{*}{**Acceptor NBO (\(j\))**} & \multicolumn{2}{c}{\(E_{2}\)} & \(E_{j}\)-\(E_{i}\) & \multicolumn{1}{c}{\(F(i\_{j})\)} \\ \cline{3-5}  & & **Kcal/mol** & **a.u** & **a.u** \\ \hline LP N\({}_{3}\) & \(\pi^{\bullet}\) N\({}_{1}\)-C\({}_{2}\) & 65.72 & 0.26 & 0.116 \\ LP N\({}_{3}\) & \(\pi^{\bullet}\) C\({}_{4}\)-O\({}_{21}\) & 44.57 & 0.30 & 0.104 \\ LP N\({}_{12}\) & \(\pi^{\bullet}\) C\({}_{13}\)-C\({}_{14}\) & 41.73 & 0.30 & 0.101 \\ LP N\({}_{12}\) & \(\pi^{\bullet}\) C\({}_{15}\)-C\({}_{18}\) & 39.97 & 0.30 & 0.101 \\ \(\pi^{\bullet}\) C\({}_{4}\)-O\({}_{21}\) & \(\pi^{\bullet}\) C\({}_{13}\)-C\({}_{14}\) & 256.96 & 0.01 & 0.080 \\ \(\pi^{\bullet}\) C\({}_{6}\)-O\({}_{22}\) & \(\pi^{\bullet}\) C\({}_{15}\)-C\({}_{18}\) & 94.72 & 0.02 & 0.076 \\ \(\pi^{\bullet}\) C\({}_{11}\)-O\({}_{23}\) & \(\pi^{\bullet}\) C\({}_{15}\)-C\({}_{18}\) & 41.82 & 0.04 & 0.075 \\ \(\pi^{\bullet}\) C\({}_{11}\)-O\({}_{23}\) & \(\pi^{\bullet}\) C\({}_{16}\)-C\({}_{17}\) & 76.69 & 0.03 & 0.075 \\ \hline \end{tabular}
\end{table} 
Table 7: Analysis perturbation theory second order in Fock matrix in NBO by level calculation B3 LYP/6-31G (d,p) for compound **4c**.