## 3 Results and Discussion
### Quantum Chemical Calculation  
The HOMO and LUMO orbitals in the PCA-GLU can help us study the performance of the corrosion inhibitor theoretically. From Figure 6, the HOMO and LUMO distributions of polycitric acid (PCA) and PCA-GLU are located at both ends of the molecules, respectively. This distribution is conducive to the parallel adsorption of polymer molecules on the surface of Q235. The performance of the PCA-GLU can also be predicted by the following calculation parameters: the Highest Occupied Molecular Orbital (HOMO), Lowest Unoccupied Molecular Orbital (LUMO), Energy Gap (\(\Delta E\)), Mulliken Electronegativity (\(\chi\)), Global Hardness (\(\eta\)), parenting index (\(\omega\)), Chemical Potential (\(\mu\)), global softness (\(\sigma\)), and electron transfer fraction (\(\Delta N\)). The above parameter calculation results are obtained by the following formulas:  
\[\mu=\frac{(E_{LUMO}+E_{HOMO})}{2} \tag{4}\]  
\[\chi=-\mu \tag{5}\]  
\[\eta=\frac{E_{LUMO}-E_{HOMO}}{2} \tag{6}\]  
\[\sigma=\frac{1}{\eta} \tag{7}\]  
Figure 5: An equivalent circuit was used to fit the EIS data.  
\[\omega=\frac{\chi^{2}}{2\eta} \tag{8}\] \[\Delta E=E_{LUMO}-E_{HOMO}\] (9) \[\Delta N=\frac{(\chi Fe-\chi inh)}{2(\eta Fe+\eta inh)} \tag{10}\]  
Through the literature, we found that the value of \(\chi_{Fe}\) is 7.0 eV/mol, while the value of \(\eta_{Fe}\) is generally described as 0 eV/mol [28].  
Table 3 lists the quantum chemical parameters of four corrosives. \(E_{HOMO}\) reports the capacity of inhibitors to provide electrons to empty orbitals. The greater the \(E_{HOMO}\) value, the stronger the ability of corrosion inhibitors to supply electrons. \(E_{LUMO}\) reports the capacity of inhibitors to receive electrons, and the smaller the \(E_{LUMO}\) value, the stronger the capacity to accept electrons [29]. \(\Delta\)E can mirror the reaction property of the corrosion inhibitor. The smaller value of \(\Delta E\) generally means that the material has the possibility of becoming an excellent corrosion inhibitor [30]. From Table 3, we can see that the \(\Delta\)E order of the four corrosive agents is as follows: CA > GLU > PCA > PCA-GLU. However, it was found that the EHOMO value and ELUMO value of GLU are the highest values among the four compounds, proving that glutamic acid itself can donate electrons easily but cannot easily accept electrons. The rules for \(\chi\) are the same as for the \(E_{HOMO}\) value of the compound, and the rules for \(\omega\) are the same as for the \(E_{LUMO}\) value of the compound.  
The hardness (\(\eta\)) and softness (\(\sigma\)) go hand in hand with \(\Delta E\). The smaller \(\eta\), the greater the corrosion inhibition performance. The \(\eta\) value of the four corrosive agents is CA > GLU > PCA > PCA-GLU. The order agrees with \(\Delta\)E.  
\(\Delta\)N represents the probability of moving electrons from inhibitors to the surface. When \(\Delta N\) = 3.6, the inhibitor forms coordination bonds and transfers electrons to the metal surface. When \(\Delta N\) < 3.6, the inhibitory effect rises with increasing \(\Delta N\)[31]. The \(\Delta\)N value of the four inhibitors is less than 3.6 and the magnitude is as follows: GLU > PCA-GLU > PCA > CA.  
Based on the results of the above parameters, it can be inferred that PCA-GLU has a better anti-corrosion effect compared to PCA. This may be because the addition of glutamic acid improves the ability of electrons from the inhibitor to transfer to the iron surface,  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Inhibitors Additive** & **E\({}_{\text{LUMO}}\) (eV)** & **E\({}_{\text{HOMO}}\) (eV)** & \(\mu\) & \(\chi\) & \(\eta\) & \(\sigma\) & \(\omega\) & \(\Delta\)**N** & \(\Delta\)E \\ \hline PCA-GLU & \(-\)0.798 & \(-\)6.832 & \(-\)3.815 & 3.815 & 3.017 & 0.331 & 2.412 & 0.528 & 6.034 \\ \hline  
increasing the corrosion inhibitor to bind more firmly to the iron surface, thereby enhancing its corrosion inhibitory effect.