## 3 Results and Discussion
### The Complexes of Cadmium and Amino Acids
#### 3.1.4 The Complexes of Phe with Cd2+  
PheCd2+ a naturally aromatic amino acid, possesses a benzene ring with rich electrons; thus, the complexation of Cd with benzene was also considered. As shown in Figure 4, the calculated spectra of [COc, COc] were fairly consistent with the experimental IR spectra of the PheCd2+ complex. The main characteristic peaks of the actual IR were observed at 1520 and 1330 cm\({}^{-1}\), which corresponded with the bending vibration of N-H and the stretching  
Figure 2: The experimental (upper) and calculated (lower) FTIR spectra of GluCd2+. The gray, red, yellow, blue, and silver balls represent carbon, oxygen, cadmium, nitrogen, and hydrogen atoms, respectively.  
vibration of C-C of the [CO\({}_{\rm c}\), CO\({}_{\rm c}\)] structure. It is clearly seen that both of them fit the actual experimental IR well. Importantly, neither the bands of [N\({}_{\rm c}\), P] nor the [N\({}_{\rm c}\), CO\({}_{\rm c}\)] structure could be found in the experimental IR. Moreover, the lengths of the Cd-O/N bonds in [CO\({}_{\rm c}\), CO\({}_{\rm c}\)] (2.20 and 2.54 A) were much longer than those of the other amino acid-Cd complexes, which was attributed to the attractivity of the benzene ring (seen in Table 3).  
Figure 4: The experimental (upper) and calculated (lower) IR spectra of PheCd\({}^{2+}\). The gray, red, yellow, blue, and silver balls represent carbon, oxygen, cadmium, nitrogen, and hydrogen atoms, respectively.  
Figure 3: The experimental (upper) and calculated (lower) IR spectra of ThrCd\({}^{2+}\). The gray, red, yellow, blue, and silver balls represent carbon, oxygen, cadmium, nitrogen, and hydrogen atoms, respectively.  
3.1.5. The Theoretical Calculation of the Complex Energy  
From the FTIR spectra, the complex structures of Glu and Thr with Cd were found to be tridentate, while those of the others were bidentate. Based on these structures, the free energy of the dissolving processes (Equation (4)) and complex processes (Equation (5)) was calculated in the water phase as follows.  
\[L\text{Cd}^{2+}(s)\to L\text{Cd}^{2+}(l) \tag{4}\]  
\[\text{Cd}^{2+}(l)+L(l)\to L\text{Cd}^{2+}(l) \tag{5}\]  
As depicted in Table 4, all of the dissolving energies of the complexes were negative, indicating that all these complexes were easily dissolved in water and that all the complex processes in the water phase were spontaneous reactions. The complex energy of Cd and the amino acids followed the order Thr \(<\) Glu \(<\) Gly \(<\) Ala \(<\) Leu \(<\) Phe. The energy of the Cd and Thr complex process was the lowest, indicating that ThrCd\({}^{2+}\) was the most stable complex. In addition, the complex energies of ThrCd\({}^{2+}\) and GluCd\({}^{2+}\) were \(-24.33\) kcal/mol and \(-23.87\) kcal/mol, respectively, in the water phase, which were much lower than those of the other amino acid complexes with Cd. This might be attributed to the specific steric structures of Thr and Glu. Compared to other amino acids, the additional -OH and -COOH in the side chains of Thr and Glu might donate more electrons to Cd\({}^{2+}\)[43,44]. Thus, Thr and Glu are better electron donors for Cd ions than other amino acids. In addition, the structures of Gly, Ala, Leu, and Phe were bidentate steric structures, and the energy increased with increasing molecular weight. In the water phase, water molecules inhibit the mobility of the ligands. Thus, the larger the molecule of the amino acid, the more steric energy it will have.