## 3 Results and Discussion
### Theoretical Calculation of THz Spectra by DFT  
In order to identify the formation mechanism of the characteristic absorption peaks, the Gaussian 2009 software was used to conduct the quantum chemistry calculation of the three PGRs. DFT was applied for the geometric optimization and frequency calculation of single molecular of PGRs. On the basis of the traditional Hartree Fock theory, the method of calculating various electronic energy information in the molecule was added in DFT. Therefore, the results of DFT were more accurate and the calculation speed was faster. The density functional model of B3 LYP Becke with three parameters (B3 LYP/6-311G, Lee-Yang-Parr functional) in DFT was used to calculate the molecules of 2,4-D and IAA. Additionally, the model of B3 LYP/6-31G (d, p) was used to calculate the molecule of CPPU. These models could be used to calculate the geometric configuration and zero-point energies. They had obvious advantages in geometric optimization of the molecular structure and no imaginary frequency appeared in the optimization result. Therefore, the stable molecular conformation could be obtained. Figure 4 showed the simulated molecules and the calculated spectra of the three PGRs by DFT. Among them, the simulated results of 2,4-D obtained five absorption peaks, which were located at 1.32, 1.55, 1.98, 2.53 and 2.79 THz, respectively. Two absorption peaks were obtained from the simulated results of CPPU, which were located at 1.70 and 2.53 THz. The two calculated absorption peaks of IAA were located at 0.58 and 2.5 THz, respectively. It could be seen that there were discrepancies of absorption peak position and intensity between the experimental and theoretical results. The reason was that the experimental samples were crystals, while the objects of theoretical calculation were molecules. Moreover, the sample thickness, the crystal field effect, the crystal resonance and the interaction between molecules were not taken into account in the theoretical calculation. Additionally, the theoretical spectra had irregular deviations compared with the experimental spectra. The reason was that the experiment was carried out at laboratory temperature (294 K), but the theoretical calculation was based on a temperature of 0 K, and thus ignored this kind of thermal effect. In addition, the number of absorption peaks obtained by theoretical spectra was larger than that obtained by experimental spectra. The main reason was probably that some of the absorption peaks were not detected due to the limitation of the THz experimental instruments. Figure 3: Absorption coefficients and refractive indexes of PGRs. (**A**) Absorption coefficient of 2,4-D; (**B**) absorption coefficient of CPPU; (**C**) absorption coefficient of IAA; (**D**) refractive index of 2,4-D; (**E**) refractive index of CPPU; (**F**) refractive index of IAA. The characteristic absorption peaks could be assigned and analyzed using the visualization function of GaussView 5.08. The results showed that these absorption peaks were mainly generated by the collective vibration and twisting of molecules. Table 2 lists the vibration modes of the theoretically calculated absorption peaks. The molecular structures were represented by Descartes coordinates. The absorption peak of 2,4-D at 1.32 THz was attributed to the stretching vibration and external deformation vibration of C-C (13 C, 16 C) in the X-Z plane with \(Z\) axis. The absorption peak of 2,4-D at 1.55 THz was ascribed to the interior stretching vibration and external deformation vibration of C-O-C (3 C, 12 O, 13 C) in X-Z plane with \(Z\) axis. The absorption peak of 2,4-D at 2.53 THz was attributed to the interaction between the surface stretching vibration of C-O-C (3 C, 12 O, 13C) and the interior surface stretching vibration of C-CL (2 C, 11 CL, 10 CL). The absorption peak of CPPU at 1.70 THz was attributed to the interaction between the external deformation vibration of N-C-N (11 N, 13 C, 15 N) and the interior stretching vibration of C=O (13 C, 14 O) in Y-Z plane with \(Z\) axis.