*3.5. Vibration Mode Assignment of Raman Peaks*

The above results show that the theoretical Raman spectra of five PAEs (DMP, DEP, DBP, DEHP, and DINP) calculated by DFT B3LYP 6-311G(d, p) are the best in agreement with the experimental Raman spectra, and have the least spurious peaks. Combining the experimental and theoretical spectra, the Raman peaks of the five PAEs were assigned. Table 3 shows the common Raman peaks and vibrational mode assignments of the five PAEs. Table 4 shows the unique Raman peaks and vibrational mode assignments of the five PAEs. The five PAEs can be identified by their unique Raman peaks.


**Table 3.** Common Raman peaks and vibrational mode assignments of the five PAEs.

DMP: dimethyl phthalate; DEP: diethyl phthalate; DBP: dibutyl phthalate; DEHP: di(2-ethyl)hexyl phthalate; DINP: diisononyl phthalate;υ: telescopic vibration; β: in-plane bending vibration; γ: out-of-plane bending vibration; δ: deformation vibration; vs: very strong; s: strong; m: medium; w: weak.


**Table 4.** Unique Raman peaks and vibrational mode assignments of the five PAEs.

DMP: dimethyl phthalate; DEP: diethyl phthalate; DBP: dibutyl phthalate; DEHP: di(2-ethyl)hexyl phthalate; DINP: diisononyl phthalate;υ: telescopic vibration; β: in-plane bending vibration; γ: out-of-plane bending vibration; δ: deformation vibration; vs: very strong; s: strong; m: medium; w: weak.

#### **4. Conclusions**

In this study, the theoretical Raman spectra of five PAEs (DMP, DEP, DBP, DEHP, and DINP) were calculated using different theoretical methods and basis sets, and the best theoretical method was determined by comparing with the experimental spectra. Also, the common and unique Raman peaks the of five PAEs were identified, and the vibration modes were assigned to these peaks. The results indicate that DFT is more suitable for the theoretical study of PAEs than HF. In the DFT, the B3LYP method is more accurate than the B3PW91 method to calculated the theoretical spectra of PAEs, and 6-311G (d, p) is most suitable for the theoretical study of PAEs among these four basis sets. So, DFT B3LYP 6-311G(d, p) is the most applicable method for the theoretical calculation of the Raman spectra of PAEs, which can reduce the influence of spurious peaks and help to identify the Raman characteristic peaks of PAEs. This will be beneficial for the detection of trace PAEs and the discrimination of PAEs in food products or human blood in the future. Also, the results of this study will help us to establish a Raman fingerprint for PAEs. In the future, further studies must be considered to detect the trace PAEs in food products or human blood by Raman spectroscopy combined with DFT calculation.

**Author Contributions:** Conceptualization, Y.W. and T.S.; methodology, Y.W. and T.S.; software, Y.W.; validation, Y.W. and M.L.; formal analysis, Y.W. and T.S.; investigation, Y.W. and T.S.; resources, T.S. and D.H.; data curation, Y.W.; writing—original draft preparation, Y.W. and T.S.; writing—review and editing, T.S. and D.H.; visualization, Y.W. and T.S.; supervision, T.S. and D.H.; project administration, T.S. and D.H.; funding acquisition, T.S. and D.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Fundamental Research Funds for the Provincial Universities of Zhejiang (No. 2021TD002) and Talent launch project of Zhejiang A & F University Scientific Research Development Fund (No. 2019FR033).

**Data Availability Statement:** The data used to support the findings of this study can be made available by the corresponding author upon request.

**Conflicts of Interest:** The authors declare no conflict of interest.
