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A DFT study on the molecular properties of synthetic ester under the electric field

  • Yachao Wang , Xiaoran Lin EMAIL logo , Mei Wang and Jifang Wang
Published/Copyright: November 6, 2021
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Open Physics
From the journal Open Physics Volume 19 Issue 1

Abstract

Synthetic ester can replace the mineral oil traditionally used in transformers to avoid the environmental problems caused by oil leakage. However, the fast discharge phenomenon in a high electric field in transformers using synthetic ester seems to indicate its insulation property is inferior to that of mineral oil. In this paper, typical molecular models of synthetic ester, including F2, F4, F6, F8, and F10, are constructed. We studied the effect of electric fields on the molecular properties of the five molecules by density functional theory and time-dependent density functional theory. According to the electric field intensity required for discharge initiation and propagation in insulating oil, the electric field intensity applied in this study varied from 108 to 109 V/m. The results showed that the molecular bond lengths are obviously dependent on the electric field. The ionization potential (IP) of the F8 and F10 molecules decreases sharply under electric field intensities of 3.1 × 109 and 4.0 × 109 V/m. It can be inferred that the IP reduction of the long carbon chain molecules, such as F8 and F10, is the reason for the formation of fast discharge in the case of synthesis ester. Calculations for excited states show that the introduction of an electric field makes the electron transition more active. The results obtained by this work improve our understanding of the discharge mechanism in synthetic ester dielectrics and provide theoretical support for improvement in the performance of synthetic ester insulating oil.

Keywords: density functional theory; synthetic ester; discharge mechanism; molecular structure; excited state

1 Introduction

Synthetic ester is obtained by chemical synthesis and refining and is widely used as lubricating fluid in automobiles, aircraft, and other machinery [1]. In recent years, ester materials have been used as transformer oil for improved environmental performance [2,3,4,5]. Synthetic ester is degradable and can replace the traditional mineral oil in transformers to avoid the environmental problems caused by oil leakage [6,7]. Compared with traditional transformer oil, the higher ignition point of synthetic ester increases the security of power grids [8,9]. At present, synthetic ester is used in distribution transformers [10]. However, the application of synthetic ester in large power transformer needs further work. Discharge tests show that the breakdown voltage of synthetic ester is almost the same as that of traditional transformer oil under the condition of short oil gap [11]; however, under the condition of long oil gap, the breakdown characteristic of synthetic ester is obviously worse than with traditional mineral oil [12,13]. The fast discharge phenomenon is quick to appear in the case of synthetic ester in a high electric field [14]. Obviously, the molecular characteristics of synthetic ester in an electric field must be different from that of traditional mineral transformer oil. Basic physical research at the molecular level in this regard is still necessary.

The molecular structure of synthetic ester results from the esterification of a pentaerythritol molecule with four fatty acid molecules [14,15]. Figure 1 shows the molecular structure of synthetic ester. To improve the stability of materials, the fatty acid of synthetic ester used for insulating oil is usually saturated fatty acid. Functional group COOR can be the same or different. In this study, five fatty acids, including acetic acid (CH3COOH), butyric acid (CH3(CH2)2COOH), hexanoic acid (CH3(CH2)4COOH), octanoic acid (CH3(CH2)6COOH), and decanoic acid (CH3(CH2)8COOH), were selected to construct the synthetic ester molecule. If each synthetic ester contains only one kind of fatty acid, we can obtain five typical synthetic ester molecules, labeled as F2, F4, F6, F8, and F10. These five typical synthetic ester molecules were the objects of this research study.

Figure 1 Molecular structure of synthetic ester.
Figure 1

Molecular structure of synthetic ester.

Density functional theory (DFT) can be used to study the molecular properties of insulating materials [16,17,18]. The effect of C═C double bond on the ionization potential (IP) and electron affinity of unsaturated triglycerides was studied in ref. [16]; In ref. [17], the electronic structures and IPs of triolein and aromatic were compared, and the differences in discharge characteristics between natural ester and mineral oil were explained. The effect of electric fields on the IP and excitation energy of aromatic and alkane molecules was studied in ref. [18]. At present, few studies have been reported on the molecular characteristics of synthetic ester under electric field.

In this study, we carry out a DFT study on the molecular properties of synthetic ester under the electric field. The molecules include F2, F4, F6, F8, and F10. The molecular properties refer to bond length, infrared spectrum, total energy, dipole moment, molecular orbital, IP and the excited state. Existing experimental results show that the electric field intensity required is 108 V/m for discharge initiation and 109 V/m for fast discharge [19,20,21]. So, the electric field intensity applied in this study varies from 108 to 109 V/m. The results obtained in the work are helpful to improve the understanding of discharge mechanism in synthetic ester dielectrics and provide theoretical support for the performance improvement of synthetic ester insulating oil.

2 Theoretical method

The Hamiltonian H of molecule and electric field system can be expressed as [22]

(1) H = H 0 + H int ,

where H 0 is the Hamiltonian without the electric field and H int is the Hamiltonian of the interaction between external electric field and molecule. H int can be expressed as

(2) H int = − μ ⋅ F ,

where μ is the dipole moment and F is the electric field.

Time-dependent density functional theory (TD-DFT) is also used to study the first six excited states. The expression for excitation energy E ex can be written as

(3) E ex ( F ) = E ex ( 0 ) − Δ μ ⋅ F − 1 2 Δ α F 2 ,

where Δ μ and ∆α are the variation of the dipole moment and the polarizability, respectively [23,24]. All the tests are carried out by the Gaussian 09 package [25].

Figure 2 shows the model of the F2 molecule. The red, blue, and gray atoms in the figure represent oxygen, hydrogen, and carbon, respectively, which are also marked by numbers. The F4, F6, F8, and F10 molecules have 2, 4, 6, and 8 more carbon atoms in each branch chain than the F2 molecule. The z-axis runs through the two atoms 1C and 2C. The molecular models of F2, F4, F6, F8, and F10 are optimized under the condition of without the electric field. Then, the electric fields of 0.0006, 0.0012, 0.0024, 0.0048, 0.0060, and 0.0078 a.u. are applied in the z-axis direction respectively. The electric field intensity of 1 a.u. stands for 5.1 × 1011 V/m. Consequently, the applied electric field are also 3.1 × 108, 6.2 × 108, 1.2 × 109, 2.5 × 109, 3.1 × 109, and 4.0 × 109 V/m, correspondingly. The molecular models are optimized again when the electric field is applied. Bond lengths, infrared spectra, total energy, dipole moment, and orbital energy are studied. Finally, the first six excited states are calculated by using the optimized molecular structure.

Figure 2 Model of F2 molecule with Cartesian axis.
Figure 2

Model of F2 molecule with Cartesian axis.

In terms of specific methods and basis set selection, this paper compares the results of SE/MP6, HF/6-31 G*, and B3LYP/6-31 + G* for the vibrational frequencies of main functional groups of molecules without electric field. 1.06, 0.90, and 0.96 are the scale factors [26]. The results are listed in Table 1. The experimental data for the functional groups are also listed in the table [27,28]. It can be found that the calculation results of B3LYP/6-31 + G* are closer to the experimental values than those of SE/MP6 and HF/6-31 G* scheme. The B3LYP/631 + G* method is selected for all other calculations in this paper.

Table 1

Comparison of the three methods

Molecule Method [26,27,28] Wave number (cm−1)
C–O–C C═O C–H
SE/MP6/1.06 1320.5 1936.6 2784.0
F2 HF/631 + G*/0.90 1250.6 1809.9 2945.7
B3LYP/631 + G*/0.96 1194.0 1751.2 2956.6
SE/MP6/1.06 1190.2 1931.8 2770.5
F4 HF/631 + G*/0.90 1187.6 1802.9 2873.7
B3LYP/631 + G*/0.96 1125.6 1744.7 2985.8
SE/MP6/1.06 1186.8 1932.4 2768.0
F6 HF/631 + G*/0.90 1181.6 1802.7 2868.2
B3LYP/631 + G*/0.96 1120.5 1744.5 2974.4
SE/MP6/1.06 1293.7 1932.4 2767.9
F8 HF/631 + G*/0.90 1179.2 1802.7 2926.1
B3LYP/631 + G*/0.96 1118.6 1744.5 2973.2
SE/MP6/1.06 1189.1 1932.4 2767.9
F10 HF/631 + G*/0.90 1178.2 1802.7 2868.1
B3LYP/631 + G*/0.96 1117.6 1744.5 2901.2
Experimental value 1,150–1,330 1,735–1,750 2,845–2,975

3 Results and discussion

3.1 Bond length and infrared spectra

Bond length is the basic structural parameter of molecules, and the change of bond length plays a key role in the influence of molecular properties. Synthetic ester molecules contain a large number of chemical bonds. Limited to space, the bond lengths of some main chemical bonds of the F2 molecule under different electric fields are given in Table 2. It was found that the bond lengths are obviously dependent on the electric field. When the electric field intensity varies from 0 to 4.0 × 109 V/m, 2C–14O increases from 1.4380 to 1.4437 Å，and the bond length is extended by 0.0057 Å; 18C═19O increases from 1.2083 to 1.2148 Å，and the bond length is extended by 0.0065 Å. From Figure 2 and Table 2, it can be seen that the change of the same type of chemical bond under the electric field is not the same. That is because the angle between the chemical bond and the electric field direction is different. Generally, the variation of C–O with electric field intensity is larger than that of C═O and that of C–C.

Table 2

Bond length of tributyrin versus applied electric field

E (108 V/m) 1C–2C (Å) 2C–14O (Å) 11C–16O (Å) 18C═19O (Å) 18C–38C (Å) 20C═21O (Å) 24C–17O (Å) 24C═25O (Å)
0 1.5410 1.4380 1.4380 1.2083 1.5130 1.2083 1.3670 1.2083
3.1 1.5406 1.4385 1.4381 1.2087 1.5136 1.2085 1.3682 1.2077
6.2 1.5402 1.4391 1.4383 1.2091 1.5141 1.2087 1.3695 1.2070
12 1.5393 1.4404 1.4386 1.2099 1.5152 1.2091 1.3720 1.2057
25 1.5414 1.4405 1.4414 1.2121 1.5166 1.2111 1.3773 1.2031
31 1.5410 1.4417 1.4419 1.2131 1.5172 1.2117 1.3800 1.2018
40 1.5410 1.4437 1.4426 1.2148 1.5181 1.2128 1.3842 1.1999

The reason for the change of bond length is related to the electron charge transfer under the electric field. As we know, the atom is stable at the equilibrium distance under the internal stress of gravity and repulsion. The equilibrium distance is the bond length. When the electric field is applied, the amount of electronic charge on the atom’s transfers, the internal stress and equilibrium distance between atoms change, and the bond length changes accordingly.

Figure 3 shows the infrared spectrum of the F2 molecule under the electric field intensities of 0, 3.1 × 108, 1.2 × 109, and 3.1 × 109 V/m. In the absence of the electric field, the infrared spectrum of the F2 molecule is shown in Figure 2(a). The wavenumbers 1194.0 and 1194.3/cm are mainly contributed by the stretching vibration of C–O–C. The wave number 1751.1/cm is mainly contributed by the stretching vibration of C═O. The wavenumber range of 2938.6–3051.1/cm is mainly contributed by the stretching vibration of C–H.

Figure 3 Infrared spectra of the F2 molecule versus different electric field intensities, including 0 V/m (a), 3.1 × 108 V/m (b), 1.2 × 109 V/m (c) and 3.1 × 109 V/m (d).
Figure 3

Infrared spectra of the F2 molecule versus different electric field intensities, including 0 V/m (a), 3.1 × 108 V/m (b), 1.2 × 109 V/m (c) and 3.1 × 109 V/m (d).

When the electric field is applied, the infrared spectrum of the F2 molecule changes obviously, as shown in Figure 2(b–d). When the electric field changes from 0 to 3.1 × 109 V/m, the vibration frequency of C–O undergoes a redshift, and the wave number peak decreases from 1194.0–1194.3/cm to 1165.2–1190.4/cm. This is due to the increase of C–O bond length with the increasing of electric field intensity. The bond length of 2C–14O, 11C–16O, and 24C–17O is extended by 0.0037, 0.0039, and 0.0130 Å, respectively. With the increasing of the electric field intensity, the wave number peaks of C═O and C–H are broadened and the peak value decreases. In the absence of the electric field, C═O vibration has a main peak of 1751.1/cm; when an electric field intensity of 3.1 × 109 V/m is applied, the wave number peak of C═O vibration ranges from 1727.4 to 1780.3/cm. This is due to the changes of C═O bond length with the increasing of electric field intensity, which is similar to the reason mentioned above.

3.2 Total energy and dipole moment

Figure 4 shows the dipole moments of the five synthetic ester molecules under the different electric fields. It can be found that the dipole moments of these five molecules are all zero in the absence of the electric field, and they are all nonpolar molecules. When the electric field is applied, the positive and negative charge centers of the molecule no longer coincide, and the dipole moment of the molecule increases with the increasing of the electric field intensity. It should be noted that the dipole moment of molecule increases with the increasing of carbon chain length under the same electric field. For example, under the electric field intensity of 4.0 × 109 V/m, the dipole moment of the F10 molecule is more than two times that of the F2 molecule.

Figure 4 Dipole moment versus applied electric field.
Figure 4

Dipole moment versus applied electric field.

With the increasing of the carbon chain length, the volume of triglyceride molecule increases correspondingly. The distance between the positive and negative charge centers of the molecule increases correspondingly under the electric field, resulting in the increasing of dipole moment. In liquid dielectrics, the larger polarity of molecules will bring larger dielectric constant and dielectric loss, and reduce the insulation performance of dielectrics [29,30].

Figure 5 shows the total energy of the five synthetic ester molecules under the different electric fields. With the increasing of electric field intensity, the total energy decreases, which is contrary to the trend of dipole moment with the electric field. As mentioned in Section 2, according to formulas (1) and (2), the total molecular energy is negatively correlated with its dipole moment, so the total molecular energy will be the trend shown in Figure 5.

Figure 5 Total energy versus applied electric field.
Figure 5

Total energy versus applied electric field.

3.3 Orbital energy

The molecular frontier orbitals, including the highest occupied molecular orbital (HOMO) and the low unoccupied molecular orbital (LUMO), have an important influence on the molecular properties [31]. Figure 6 shows the frontier orbital energies of the five synthetic ester molecules under the different electric fields. The LUMO energies of these five molecules decrease with the increasing of the electric field intensity. The reduction of LUMO energy indicates the enhancement of the ability of molecules to obtain electrons. The HOMO energies of these five molecules increase with the increasing of the electric field intensity. when the same electric field intensity is applied, the HOMO energy increases with the increasing of the carbon chain length. The enlargement of HOMO energy indicates that the molecule is easier to lose the orbital electrons.

Figure 6 Frontier molecular orbital energy versus applied electric field.
Figure 6

Frontier molecular orbital energy versus applied electric field.

The LUMO energy minus the HOMO energy is the energy gap. The results are shown in Figure 7. The energy gap reflects the activity of molecules to a certain extent [32]. It can be seen from Figure 7 that the energy gaps of these five molecules decrease with the increasing of the electric field intensity. When the same electric field intensity is applied, with the increasing of carbon chain length, the molecular energy gaps also decrease.

Figure 7 Energy gap versus applied electric field.
Figure 7

Energy gap versus applied electric field.

Figure 8 shows the frontier orbital electron cloud of the F2 molecule under the electric field. The frontier orbital composition of the F2 molecule is given in Table 3, which is calculated by using Multiwfn 3.3.8 software package [33]. It can be seen from Figure 1, Figure 7, and Table 3 that the molecular configuration is obviously distorted under the electric field. In the absence of the electric field, the HOMO of the F2 molecule is mainly contributed by 19O(10.7%), 21O(13.2%), 23O(13.1%), and 25O(10.9%); the LUMO is mainly contributed by 1C(60.8%).

Figure 8 Electron cloud of the HOMO and LUMO of the F2 molecule versus applied electric field.
Figure 8

Electron cloud of the HOMO and LUMO of the F2 molecule versus applied electric field.

Table 3

Composition of the frontier molecular orbitals of the F2 molecule versus applied electric field

E (108 V/m) Composition of the frontier orbitals (>2%)
0 HOMO 1C:4.4, 2C:4.5, 5C:5.7, 8C:4.4, 11C:5.6, 14O:2.3, 15O:2.9, 16O:2.9, 17O:2.4, 19O:10.7, 21O:13.2, 23O:13.1, 25O:10.9, 26C:3.0, 34C:2.5, 38C:2.4
LUMO 1C:60.8, 8C:2.1, 11C:2.1, 18C:5.8, 22C:5.7, 24C:5.7
3.1 HOMO 1C:4.6, 2C:4.4, 8C:14.9, 14O:2.2, 17O:7.8, 19O:9.8, 25O:34.5, 34C:7.7, 38C:2.4
LUMO 1C:47.7, 2C:2.0, 5C:3.4, 8C:1.7, 11C:3.7, 18C:14.7, 24C:9.8, 38C:5.1
6.2 HOMO 1C:4.8, 2C:2.2, 8C:17.4, 17O:9.3, 19O:4.1, 24C:5.0, 25O:41.8, 34C:8.9
LUMO 1C:23.4, 2C:8.2, 5C:4.0, 8C:2.3, 11C:4.6, 18C:22.9, 24C:10.0, 26C:2.3, 30C:2.3, 38C:12.8
12 HOMO 1C:4.6, 8C:16.9, 17O:10.3, 24C:5.6, 25O:45.5, 34C:9.6
LUMO 2C:26.6, 8C:3.8, 11C:2.3, 18C:26.1, 24C:4.8, 26C:2.7, 30C:3.0, 38C:22.8
25 HOMO 1C:6.3, 8C:8.1, 17O:12.2, 24C:6.4, 25O:51.5, 34C:10.9
LUMO 1C:4.4, 2C:39.8, 5C:24.4, 18C:12.7, 38C:12.3
31 HOMO 1C:6.2, 8C:6.3, 17O:12.6, 24C:6.5, 25O:52.4, 34C:11.0
LUMO 1C:4.3, 2C:38.2, 5C:23.3, 18C:13.9, 38C:14.7
40 HOMO 1C:5.9, 8C:4.3, 17O:13.2, 24C:6.6, 25O:53.1, 34C:11.2
LUMO 1C:4.1, 2C:33.3, 5C:21.5, 11C:2.3, 18C:15.9, 38C:18.8

When the electric field is applied, with the increasing of the electric field intensity, the electron cloud of HOMO moves in the opposite direction of the electric field, and the electron cloud of LUMO moves in the positive direction of the electric field. When an electric field intensity of 4.0 × 109 V/m is applied, the HOMO is mainly contributed by 25O(53.1%), 17O(13.2%), and 34C(11.2%); the LUMO is mainly contributed by 2C(33.3%), 5C(21.5%), 38C(18.8%), and 18C(15.9%). The movement of the frontier orbit to the far end of the molecule under the electric field makes it easier for the molecule to gain or lose electrons.

The discharge process in liquid dielectrics is very complicated. Under the strong electric field, the neutral molecules of dielectric ionize to form positive ions and electrons. The positive ions and electrons move to the cathode and anode respectively under the action of electric field force. In this process, electrons can be trapped by neutral molecules to form negative ions. During the whole discharge process, there occurs recombination of positive and negative ions, recombination of positive ions and electrons, and strong acousto-optic phenomena concomitantly. The ionization of neutral molecules runs through the whole discharge process and plays an important role in the development of discharge. Molecular IP can represent the difficulty of molecular ionization. Koopman’s theorem holds that the molecular IP is equal to the opposite number of HOMO energy [34]. According to this theorem, the IP of molecules can be estimated. Koopman’s theorem assumes that when a molecule loses an electron, its molecular structure and orbital energy level remain unchanged, so the IP obtained from this theorem may not be very accurate. However, in liquid dielectrics composed of various molecular components, the discharge process is usually determined by molecules with low IP, so it is still of practical significance to compare the relative value of intermolecular IP [35].

Figure 9 compares the IPs of the five molecules under the different electric fields. The molecular IP decreases with the increasing of carbon chain length. This is because with the increasing of the carbon chain length, the molecular volume becomes larger, the molecule’s attraction to the outermost electrons is weakened, and the molecule is more likely to lose the electrons. It is worth noting that the IPs of the F8 and F10 molecules decrease sharply under the electric field intensities of 3.1 × 109 and 4.0 × 109 V/m. The IP of the F10 molecule is 5.26 eV under the electric field intensity of 4.0 × 109 V/m, which is 2.50 eV lower than that without the electric field, and the decrease rate is more than 30%. The relationship between the molecular IP and the electric field intensity can be expressed as IP ( E ) = IP ( 0 ) − γ ∣ E ∣ , where IP(0) is the molecular IP under the electric field intensity of 0 V/m and γ is a constant [36]. The IP of molecules decreases and the charge production increases under the strong external electric field, which leads to the rapid development of discharge in liquid dielectrics [35,37]. From this point of view, it can be inferred that the long carbon chain molecules, such as the F8 and F10 molecules, are the reason for the formation of fast discharge in the synthesis ester.

Figure 9 IP of different molecules under electric field.
Figure 9

IP of different molecules under electric field.

Tunnel ionization may occur under an intense field, accompanied by molecular dissociation [38,39]. Therefore, the applied electric field intensity has an upper limit. When it exceeds this upper limit, molecular dissociation may occur. The tunnel ionization rate of the molecule can be written as

(4) ω = 4 ω 0 ∣ E ∣ ( 2 IP ) 5 2 ⋅ exp − 2 3 ( 2 IP ) 3 2 ∣ E ∣ ,

where ω 0 is the atomic unit of frequency (ω 0 = 4 × 1016/s), ∣ E ∣ is the electric field intensity, and IP is the ionization potential. The t = 1 / ω is the average tunnel ionization time of the molecule. The vibration period can be written as T = 1 / ( c k ) , where c is velocity of light and k is the wavenumber. With the increasing of electric field density, the value of t will decrease. When t < T, the tunneling effect is obvious and accompanied by molecular decomposition. The electric field density corresponding to t = T is the upper limit of electric field density.

In this study, the maximum applied electric field density is 4.0 × 109 V/m (0.0078 a.u.). The IP of the F10 molecule is 5.26 eV (0.1933 a.u.). According to the formula mentioned above, the value of t is 4.39 × 10−10 s. The wavenumber corresponding to the slowest vibration mode is about 198.1/cm. So, the value of T is 1.68 × 10−13  s. Obviously, t > T. This shows that the electric field in our work is not large enough to cause molecular dissociation. In fact, when the electric field density reaches 6.7 × 109 V/m (0.0132 a.u.), the value of t decreases rapidly to 1.66 × 10−13 s, which is t < T. Molecular dissociation may occur under the electric field.

3.4 Excited state

The excited states of molecules are calculated by time-dependent density functional method. Table 4 shows the excitation energy E ex, transition wavelength λ, and oscillator strength f of the F2, F6, and F10 molecules under the typical electric field intensity. The first six excited states are studied in this work. It is found that the excitation energy of each molecule in each excited state decreases with the increasing of electric field intensity, and the transition wavelength increases accordingly. In the absence of electric field, the oscillator strengths of the three molecules from the ground state to the first two singlet excited states are all zero, which belongs to the forbidden transition. When the field intensity is greater than 3.1 × 109 V/m, the oscillator strength is not zero, and the electronic transition can occur from the ground state to the first and second excited states. Hence, the introduction of electric field makes the electron transition more active. In the discharge test, stronger electric field will be accompanied by stronger light effect. It should be noted that the reduction of excitation energy is much smaller than that of IP under the same electric field. In ref. [36], the IP and excitation energy of molecules, including p-diaminobenzene, 2-propanol, and cyclohexane, is compared under electric field, and the conclusion is similar with ours.

Table 4

Excited state of synthesis ester molecules versus applied electric field

E (108 V/m) m = 1 m = 2 m = 3 m = 4 m = 5 m = 6
0 E ex (eV) 5.6571 5.6578 5.6603 5.6605 6.7224 6.7225
λ (nm) 219.17 219.14 219.04 219.03 184.43 184.43
f 0 0 0.0014 0.0014 0.0106 0.0104
3.1 E ex (eV) 5.6542 5.6572 5.6577 5.663 6.7183 6.722
F2 λ (nm) 219.28 219.16 219.14 218.94 184.55 184.44
f 0 0.0014 0.0003 0.0011 0.0105 0.0106
31 E ex (eV) 5.5967 5.6075 5.6175 5.6923 6.374 6.4994
λ (nm) 221.53 221.1 220.71 217.81 194.51 190.76
f 0.0005 0.001 0.0008 0.0008 0.0012 0.0059
0 E ex (eV) 5.6971 5.6978 5.7007 5.7007 6.7458 6.746
λ (nm) 217.63 217.6 217.49 217.49 183.79 183.79
f 0 0 0.0005 0.0005 0.0093 0.0092
3.1 E ex (eV) 5.6947 5.6977 5.6981 5.7019 6.7426 6.7465
F6 λ (nm) 217.72 217.6 217.59 217.44 183.88 183.78
f 0 0.0001 0.0004 0.0004 0.0095 0.009
31 E ex (eV) 5.6294 5.6498 5.6598 5.7231 6.3722 6.5159
λ (nm) 220.24 219.45 219.06 5.7231 194.57 190.28
f 0.0002 0.0004 0.0003 0.0002 0.0014 0.0054
0 E ex (eV) 5.6959 5.6966 5.6996 5.6996 6.7405 6.7408
λ (nm) 217.67 217.65 217.53 217.53 183.94 183.93
f 0 0 0.0004 0.0004 0.0104 0.0103
3.1 E ex (eV) 5.6931 5.6965 5.6973 5.7017 6.7357 6.7398
F10 λ (nm) 217.78 217.65 217.62 217.45 184.07 183.96
f 0 0.0004 0.0001 0.0004 0.0103 0.0103
31 E ex (eV) 5.6319 5.6487 5.6611 5.7185 6.3833 6.5126
λ (nm) 220.14 219.49 219.01 216.81 194.23 190.37
f 0.0002 0.0004 0.0003 0.0002 0.0017 0.0053

4 Conclusion

In this study, DFT and TD-DFT are used to calculate the molecular properties of the typical synthetic ester molecules under the electric field. The results show that the molecular structure changes under the electric field, and the molecular bond lengths are dependent on the electric field. The dipole moment increases with the increasing of electric field intensity and the carbon chain length. The IPs of the F8 and the F10 molecules decrease sharply under the electric field intensities of 3.1 × 109 and 4.0 × 109 V/m, which is the reason for the formation of fast discharge in the synthesis ester. The calculation results for excited states show that the introduction of electric field makes the electron transition more active. The excitation energy decreases with the increasing of electric field intensity. However, the reduction of excitation energy is much smaller than that of IP under the same electric field. The results obtained in the work are helpful to improve the understanding of discharge mechanism in synthetic ester dielectrics and provide theoretical support for the performance improvement of synthetic ester insulating oil.

  1. Funding information: The authors acknowledge the Science and Technology Research Project of Higher Education of Hebei Province (Grant No. QN2019069) and the Research Foundation of Hebei University of Economics and Business (Grant Nos. 2019YB11). The resources on the computation are provided by National Supercomputing Center in Shenzhen, China.

  2. Author contributions: All authors have accepted responsibility for the entire content of this article and approved its submission.

  3. Conflict of interest: The authors state no conflict of interest.

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Received: 2021-07-02
Revised: 2021-09-29
Accepted: 2021-10-15
Published Online: 2021-11-06

© 2021 Yachao Wang et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/phys-2021-0077
Keywords for this article
density functional theory; synthetic ester; discharge mechanism; molecular structure; excited state
Creative Commons
BY 4.0

Articles in the same Issue

  1. Regular Articles
  2. Circular Rydberg states of helium atoms or helium-like ions in a high-frequency laser field
  3. Closed-form solutions and conservation laws of a generalized Hirota–Satsuma coupled KdV system of fluid mechanics
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  59. Review Articles
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  62. Rapid Communications
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  102. Intensification of thermal stratification on dissipative chemically heating fluid with cross-diffusion and magnetic field over a wedge
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