## 3 Results and Discussion
### Theoretical Calculation and Analysis  
For detailed analysis of spectral characteristics, DFT was applied to 2,4-D geometry optimization and frequency calculation. Figure 2 shows the comparison between the 2,4-D experimental spectrum and the theoretical spectrum calculated by B3 LYP with three basis sets in the range of 1.1-2.8 THz. Furthermore, in order to analyze the absorption spectrum more intuitively, the baseline correction was conducted to the experimental obtained spectrum. In addition, the assignment of the calculated absorption peaks are summarized in Table 1.  
It can be seen from Figure 2 that there were four DFT-calculated absorption peaks of 2,4-D for all the three basis sets. The four absorption peaks calculated by three basis sets had similar peak positions, at around 1.36, 1.57, 1.93, and 2.59 THz, respectively. Moreover, according to the frequency RMSD (root-mean-square deviation) values of 2,4-D theoretical absorption peaks, compared to experimental absorption peaks in Table 1, it shows that all the basis sets had good calculation results. Comparing spectra calculated by 6-31G with 6-31G (d, p), it can be seen that the addition of a polarization function caused all the absorption peaks to blue shift. Moreover, it shows that theoretical spectra calculated by 6-31G (d, p) and 6-31G++ (d, p) had better consistency with the experimental spectrum on the first two absorption peak positions than theoretical spectra calculated by 6-31G. The theoretical spectra absorption peaks had a good consistency with experimental spectra, especially at 1.36 and 1.60 THz, which indicated that the theoretical calculation was feasible. However, there were some slight discrepancies between experimental absorption spectra and DFT-calculated absorption spectra. For instance, there was a blue shift phenomenon for the absorption peak at \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Experiment** & **B3 LYP/** & **B3 LYP/** & **B3 LYP/** & **Assignment** \\  & **6-31G** & **6-31G(d, p)** & **6-31G++(d, p)** & \\ \hline
1.36 & 1.32 & 1.37 & 1.36 & \(\
u\)ring+8(3C-12O-13C)oop \\
1.60 & 1.55 & 1.58 & 1.57 & \(\
u\)ring+8(13C-14/15H)oop+8(2C-11 CL)oop \\ - & 1.92 & 1.94 & 1.93 & \(\
u\)(6C-18 CL)ip+\(\
u\)(2C-11 CL)ip+\(\
u\)(13C-12O)ip \\
2.38 & 2.59 & 2.64 & 2.56 & \(\
u\)(3C-12O-13C)ip+\(\
u\)(6C-10 CL)ip \\
**RMSD** & 0.13 & 0.15 & 0.11 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The assignment of the calculated absorption peaks. Figure 2: Comparison between experimental and theoretical absorption spectra of 2,4-dichlorophenoxyoxyacetic acid. (**A**) Theoretical spectra calculated by B3 LYP/6-31G; (**B**) Theoretical spectra calculated by B3 LYP/6-31G (d, p); (**C**) Theoretical spectra calculated by B3 LYP/6-31G++ (d, p). around 2.38 THz in the theoretical spectra. First, the theoretical calculation was to calculate isolated molecule without considering the intermolecular forces. Second, it might be that theoretical spectra were calculated based on the environment of 0 K, while the experimental spectra were performed at 294 K. The experimental spectra obtained at 294K showed broader absorption than theoretical spectra, especially at 2.38 THz, which was mainly due to the high temperature of the molecule (294 K, or 25 meV) compared with the THz photon energy (2-8 meV). Therefore, a lower energy resonance will have a contribution from hot-band transitions, which results in broadening [37]. An absorption peak at around 1.92 THz was not detected in the previous experiment, which might be caused by limitation of apparatus performance. In order to further analyze the formation mechanism of the terahertz fingerprint peaks, the vibrational modes of 2,4-D molecular at the absorption peaks of 1.36, 1.60, and 2.38 THz are shown in Figure 3. The experimental results showed that the absorption peaks of 2,4-D at these three peaks were caused by the action of different bonds. The absorption peak at 1.36 THz was mainly caused by the joint motion of the two parts.