*2.3. Theoretical Calculation*

The Hartree–Fock method (HF) is one of the ab initio methods, which is based on the Schrodinger equation [24]. DFT is a method for studying the electronic structure of multielectron systems, which has a wide range of applications in the study of the properties of molecules and condensed matter. It is one of the most commonly used methods in the field of computational materials science and computational chemistry in condensed matter physics [25–27]. There are many hybrid methods in DFT. The hybrid methods of B3LYP (Becke-3 exchange with Lee–Yang–Parr gradient-corrected correlation functional) and B3PW91 (B3 exchange + PW91 correlation) are the most used in the calculation of organic matter [28]. Both B3LYP and B3PW91 are exchange-correlated general functions with similar calculated results [29], but the specific results are related to the studied substances.

The basis set is the second component of the theoretical calculation, and using a basis set means selecting a region of space where each electron is located [30]. For example, 6-311G+(2d, p): the first 6 refers to the six Gaussian functions describing the inner layer electrons; the latter 311 means that each valence orbit is represented by three basis functions, which are fitted by 3, 1, and 1 original functions, respectively; G means Gaussian basis set; d means one additional polarization function for each heavy atom (non-hydrogen atom); p means one additional polarization function for the hydrogen atom adds a polarization

function; + means to add a dispersion function to the heavy atom; if the hydrogen atom also wants to add a dispersion function, then + is replaced by ++ [31]. The larger the basis set, the fewer the constraints imposed on the electrons and the more accurate the approximation of the true molecular wave function. The choice of the basis set depends on different accuracy requirements, theoretical approaches, and research object systems, etc. [32–34].

In this study, structural models of five PAEs(DMP, DEP, DBP, DEHP, and DINP) were constructed. Then, the two theories of DFT and HF with 6-31G(d) were used to calculate the theoretical Raman spectra of five PAEs, and the spectra of five PAEs calculated by DFT and HF were compared in order to obtain the suitable theory for PAEs. In DFT theory, the hybrid methods of B3LYP and B3WP91 were chosen, and the spectra calculated by B3LYP and B3WP91 of DFT were compared to determine which specific method would be more suitable. After that, different basis sets, (3-21G, 6-31G(d), 6-311G(d, p), and 6-311G+(d, p), were used to simulate theoretical spectra of five PAEs, and the results were compared to choose the most applicable basis set for PAEs. Finally, the most applicable theoretical Raman spectra combined with experimental Raman spectra were analyzed to assign the Raman vibrations to the Raman peaks. All the theoretical calculations are prepared using the Gaussian09 (version 9.5), software.

#### **3. Results**

### *3.1. Molecular Structure of PAEs*

The structural models of the five PAEs (DMP, DEP, DBP, DEHP, and DINP) and their molecular formulae are shown in Figure 2a–e. It can be found that the structure of DMP consists of a benzene ring, two carboxyl groups, and two methyl groups, and the structure of DMP is the simplest among these PAEs. The study of DMP has important reference values for other PAEs [35]. Also, the other four PAEs are relatively typical structures, which are important for the study of PAEs [36].

**Figure 2.** Optimized molecular structure diagram of PAEs and its molecular formula. (**a**): DMP; (**b**): DEP; (**c**): DBP; (**d**): DEHP; (**e**): DINP. DMP: dimethyl phthalate; DEP: diethyl phthalate; DBP: dibutyl phthalate; DEHP: di(2-ethyl)hexyl phthalate; DINP: diisononyl phthalate.

#### *3.2. Experimental Raman Spectra of PAEs*

Figure 3 shows the experimental Raman spectra of five PAEs. From Figure 3, it can be seen that the Raman peaks in the range of 2800~3200 cm−<sup>1</sup> are very heterogeneous, and the peaks in this interval overlap with those of many solvents such as ethanol. Therefore, the range of 300~2000 cm−<sup>1</sup> is chosen for this study. From Figure 3, it can be seen that the common Raman peaks of the five PAEs are 400, 650, 1040, 1120, 1160 1284, 1450, 1580, 1600, and 1726 cm<sup>−</sup>1. The unique Raman peaks of DMP are 818 and 964 cm−1; the unique Raman peaks of DEP are 352, 784, and 848 cm<sup>−</sup>1; the unique Raman peaks of DBP are 810, 842, 940, and 962 cm<sup>−</sup>1; the unique Raman peaks of DEHP are 834, 858, 894, and 956 cm−1; and the unique Raman peaks of DINP are 822, 900, and 960 cm<sup>−</sup>1. The partial experimental Raman peaks of PAEs in this study are consistent with the peaks of 650, 1040, 1580, 1600, and 1726 cm−<sup>1</sup> for DEHP and DBP in the literature [22]. They are basically consistent with the peaks of 1038, 1120, 1578, 1599, and 1723 cm−<sup>1</sup> for DEHP, DEP, and DBP in the literature [20], and the peaks of 403, 653, 1043, 1127, 1167, 1585, 1605, and 1731 cm−<sup>1</sup> for eight PAEs in the literature [37].

**Figure 3.** Experimental Raman spectra of phthalic acid esters. DINP: diisononyl phthalate; DEHP: di(2 ethyl)hexyl phthalate; DBP: dibutyl phthalate; DEP: diethyl phthalate; DMP: dimethyl phthalate.
