## 4 Conclusions  
In this paper, THz spectral characteristics of 2,4-D, CPPU and IAA were studied by using THz-TDS. Eight window functions were applied to process the THz absorption spectra of these three PGRs. Among them, the function of the Blackman-Harris 4 term achieved the best spectral effect. Combined with THz optical parameters extraction models using Fresnel formula, the THz absorption coefficient spectra and refractive index spectra of PGRs in the band of 0.2-3 THz were obtained. The experimental results showed that the three kinds of PGRs had different characteristic absorption peaks in the THz band (2,4-D: 1.35, 1.57 and 2.67 THz, CPPU: 1.77 and 2.44 THz, IAA: 2.5 THz), and the refractive index changed at the location of each characteristic absorption peak. The density functional models of B3 LYP/6-31G and B3 LYP/6-31G (d, p) in DFT were used for geometric optimization and frequency calculation of single molecules of PGRs. The calculated spectra were in reasonable agreement with the experimental spectra. According to the calculation results of DFT, the vibrational frequencies of the experimental spectra were determined. The vibrational modes corresponding to the absorption peaks of THz spectra were mainly characterized by interior stretching vibration and external deformation vibration of molecular groups. Moreover, the vibration modes and amplitudes varied at different peaks. The results of this study provided the parameters for the detection of PGRs using THz technology. In addition, it provided theoretical guidance and experimental basis for the rapid identifying of PGRs species and the detection of PGRs residues in agricultural products.  
This work was supported in part by National keypoint research and invention program of the thirteenth (2016 YFD0700304) and Natural Science Foundations of China (Grant No. 61405175). The work presented here was carried out in collaboration between all authors. [PERSON] and [PERSON] conceived the idea. [PERSON], [PERSON], [PERSON] and [PERSON] co-worked on associated data collection and carried out the experimental work. [PERSON] drafted the manuscript, [PERSON] and [PERSON] provided their experience and co-wrote the paper. All authors contributed to, reviewed and improved the manuscript.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Calculation (THz)** & **Experiment (THz)** & **Deviation (THz)** & **Assignment** \\ \hline \hline \multicolumn{4}{c}{2,4-Dichlorophenoxyoxyacetic acid (2,4-D)} \\
1.32 (vs) & 1.35 & +0.03 & \(\upsilon\)(C-C)ip \\
1.55 (vw) & 1.57 & +0.02 & \(\delta\)(C-H)oop \\
1.98 (vw) & - & - & \(\upsilon_{\text{ring}}\),\(\delta\)(C-C-C)ip \\
2.53 (w) & 2.67 & +0.14 & \(\delta\)(C-O-C)ip+\(\upsilon\)(C-CL)ip \\
2.79 (w) & - & - & \(\upsilon_{\text{ring}}\),+\(\upsilon\)(C-C)ip \\ \hline \multicolumn{4}{c}{Forchlorofenuron (CPPU)} \\
1.70 (m) & 1.77 & +0.07 & \(\upsilon\)(C=O)ip+\(\delta\)(N-C-N)oop \\
2.53 (m) & 2.44 & \(-\)0.09 & \(\delta\)(C-N)oop \\ \hline \multicolumn{4}{c}{Indole-3-acetic acid (IAA)} \\
0.58 (w) & - & - & \(\delta\)(C-O)oop \\
2.5 (w) & 2.5 & \(\pm\)0 & \(\upsilon\)(C-C-C)ip \\ \hline \hline \multicolumn{4}{c}{vs: very strong, m: medium, w: weak, vw: very weak, \(\upsilon\): telescopic vibration, oop: surface external bending, ip: surface internal bending, \(\delta\): deformation vibration.} \\ \end{tabular}
\end{table}
Table 2: The assignment of the calculated absorption peaks.