Abstract
The dissociation of nitrogen trifluoride (NF3) is an important topic of study because the molecule is a highly dangerous greenhouse gas that can persist in the atmosphere for 740 years. In this study, changes in the geometry, orbital energy, spectral properties, and dissociation properties of NF3 when an external electric field was applied were studied by density functional theory. Results show that when the strength of the electric field was increased, the N–3F bond length became longer until it broke, and the energy gap decreased gradually. The dissociation barrier in the potential energy curve gradually decreased with the increase in the electric field strength. When the applied electric field reached 0.05 a.u., the dissociation barrier disappeared, indicating that under the action of a strong applied electric field, NF3 is degraded because of fracture of the N–3F bond. When the application of the electric field was continued, the potential barrier disappeared and dissociation occurred when the N–4F bond was scanned. The stepwise dissociation of nitrogen trifluoride molecules occurred under an electric field intensity of 0.05 a.u. The concerted dissociation of the N–3F and N–4F bonds occurred at an electric field intensity of 0.09 a.u. When the electric field direction was in the negative direction of the z-axis, the NF3 dissociated but no concerted dissociation occurred. These results offer insight into the degradation mechanism under an applied electric field.
1 Introduction
During chemical reactions, the formation and breaking of molecular bonds is one of the most basic concepts in science [1]. Because of their role in the catalytic destruction of stratospheric ozone, the photochemistry of compounds containing fluorine, chlorine, and bromine has attracted considerable attention [2,3,4]. In the lower part of the atmosphere, light-induced dissociation is usually a two-body phenomenon and that dissociation can be studied by relatively simple experiments. However, in a low-density environment such as that experienced in interstellar space and the stratosphere, it is easier for molecules to dissociate into many bodies. Because of the difficulties in predicting complex diabatic kinetics and in observing multiple dissociation products, the study of multibody dissociation has become a difficult problem for researchers to tackle [5,6]. Numerous molecular systems have been used for the study of three-body photodissociation dynamics, and in many fields stepwise or concerted reactions are significant processes [7]. For chemical dynamics, differentiating between a concerted (within one rotational period) and a stepwise process is also a hot issue.
In this work, nitrogen trifluoride (NF3) was chosen for the study of concerted and stepwise three-body photodissociation dynamics. There are three main reasons for this choice. First, and from the point of view of reaction kinetics, because it contains three equivalent N–F bonds it is an ideal molecule for studying the dissociation kinetics of three bodies. The stepwise dissociation and the concerted dissociation may occur under external electric fields even in its ground state. Second, at present, insufficient attention has been paid to the degradation of fluorine-containing compounds by electric fields. To clarify the mechanism of generating fluoride free radicals and understand the influence of fluorinated compounds on the atmospheric environment, it is necessary to study the dissociation kinetics of fluoride compounds under an external electric field. Third, under the action of an external electric field, molecules will undergo various physical and chemical changes, such as bond breakage, or changes in their molecular orbitals, crystal induction, or excitation spectra, for example [8,9,10]. In recent years, many scholars have studied the properties of external electric fields in various molecular systems and made progress, demonstrating that it is feasible to degrade molecules, including pollutant molecules, by an external electric field [11,12,13]. Although NF3 is indispensable in the electronics industry, it has been found to be a significant greenhouse gas, and its heat storage capacity is 17,000 times that of carbon dioxide [14]. Although its annual emissions are only 4,000 tons, the extent of its pollution to the atmosphere is equivalent to 67 million tons of carbon dioxide, and its life span in the atmosphere can be as long as 740 years. In 2008, NF3 was included in the list of controlled gases under the United Nations Framework Convention on Climate Change.
The past research on NF3 has mainly focused on the dissociation of the NF3 anion caused by the attachment of free electrons [15]. In that work, it was shown that under a high electron attachment energy, F fragments were produced through two different dissociation channels. Using a momentum imaging spectrometer, Wang et al. [16] studied the fragmentation kinetics of NF3 in an electron collision at 500 eV, and the results showed that all the dissociation channels involved the simultaneous cleavage of molecular bonds. To the best of our knowledge, the physical properties, spectral characteristics, and dissociation dynamics of NF3 when under an external field have not been previously investigated.
Based on density functional theory (DFT) (B3LYP/6-311G+(d,p)), the geometric configuration and spectral characteristics of NF3 under different electric field intensities were studied. By scanning the dissociation potential energy of the N–F bond, the stepwise dissociation and concerted dissociation of NF3 were studied.
2 Materials and methods
Under an external electric field, the Hamiltonian of a molecular system can be written as:
The Hamiltonian in the absence of an external field is H 0, and the Hamiltonian generated by the interaction between the molecule and the electric field is H int. Under the dipole approximation, H int is given as:
where µ is the dipole moment of the molecule and F is the electric field. The electric field intensity used for the present work was 0–0.05 a.u. (where a.u. means atomic units, and 1 a.u. = 5.14225 × 1011 V/M).
According to the model proposed by Grozema et al. [17,18], the excitation energy, E exc, under the action of an external electric field has the following relationship with the electric field strength, F, the change in the electric dipole moment, ∆u, and the change in polarizability, ∆α:
where the colon in the formula represents a double wave function collapse. The excitation energy in a zero electric field is E exc(0) and the absorption oscillator strength, f lu, is
In Eq. (4), the centerline intensity, S, is in atomic units (
Various methods and basis sets were used to calculate the bond lengths in the molecules of ground state NF3. The results from these methods that were closest to the experimental values determined the calculation method that was then used to calculate the applied electric field. The properties of the NF3 molecule were then studied, including the bond length, energy, dipole moment, frontier orbital energy, IR spectrum, UV-vis absorption spectrum, dissociation potential energy curve, and relay potential energy surface. The Gaussian 09 [20] program package was used for all the calculations.
3 Results and discussion
Table 1 shows the calculated results for the NF3 molecule using different DFT functionals and basis sets. From Table 1, we can see that the bond length calculated with the B3LYP functional and 6-311G+(d,p) basis sets was 1.36480 Å, which was the most consistent with the experimental value of 1.38364 Å. Therefore, this method was used for the remainder of the study.
Partial bond length and bond angle of NF3 molecules using various methods and basis sets
| B3LYP/6-311G+DP | LSDA/3-21G | B3LYP/SDD | LSDA/6-311G | B3LYP/6-31G | Literature value [21] | |
|---|---|---|---|---|---|---|
| R(1–2)/Å | 1.382 | 1.448 | 1.454 | 1.446 | 1.447 | 1.365 |
| A(2,1,3)/° | 102.07 | 101.10 | 101.65 | 101.61 | 101.71 | 102.37 |
After selecting the above method and basis set, the molecular structure was optimized to give the stable configuration shown in Figure 1. The y-axis was selected as the direction of the external electric field. To avoid confusion and facilitate understanding, the opposite direction of the y-axis was the direction of the electric field, and the electric field intensity in this direction is shown as positive in all charts.
Stable configuration of NF3 molecule after optimization at B3LYP/6-311G+(d,p) (the left is a front view, and the right is a left view).
3.1 Effect of external electric field on dipole moment, total energy, and bond lengths
The structure of the NF3 molecule was optimized by B3LYP/6-311G+(d,p) under application of different electric fields (0–0.05 a.u.) along the y-axis and stable molecular structures were obtained. Table 2 shows the calculated total energy, dipole moment, and bond lengths of the NF3 molecules under the action of electric fields of various intensities. Figure 2 (left) is the change in the total energy and dipole moment of the NF3 molecule with an external electric field. With an increase in the applied electric field, the total energy of the NF3 molecules decreased and the dipole moment increased. From H = H
0
+ H
int, the total energy of the molecules is the sum of the energy at zero electric field and the interaction energy between an external electric field and the molecules. The interaction energy between the molecule system and the external electric field is
Changes in molecular energy, bond length, and dipole moment when various electric field intensities are applied
| F (a.u.) | 0 | 0.005 | 0.010 | 0.015 | 0.020 | 0.025 | 0.030 | 0.035 | 0.040 | 0.045 | 0.050 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| E/a.u. | −354.1968 | −354.1972 | −354.1982 | −354.1999 | −354.2023 | −354.2054 | −354.2092 | −354.2139 | −354.2192 | −354.2254 | −354.2326 |
| R(1,2)/Å | 1.38153 | 1.36741 | 1.35434 | 1.34224 | 1.33055 | 1.31920 | 1.30805 | 1.29695 | 1.28578 | 1.27443 | 1.26274 |
| R(1,3)/Å | 1.38153 | 1.38893 | 1.39674 | 1.40514 | 1.41415 | 1.42400 | 1.43488 | 1.44702 | 1.46075 | 1.47645 | 1.49468 |
| µ/Debye | 0.2903 | 0.4553 | 0.7559 | 1.0861 | 1.4310 | 1.7893 | 2.1635 | 2.5577 | 2.9771 | 3.4284 | 3.9207 |
Changes in energy and dipole moment when electric fields of various intensities are applied (left), and changes in bond lengths in NF3 when electric fields of various intensities are applied (right).
3.2 Effect of external electric field on charge distribution
Using the same method, the effects of applying different electric fields on the charge distribution (Millikan charge) of NF3 were studied, as shown in Table 3. Under the action of electric field, intramolecular electrons move with the direction of electric field, resulting in the increase in electronegativity of 3F and 4F atoms, the increase in positive charge density of N and 2F atoms, and the negatively charged 2F atoms become positively charged. The charges on the 3F and 4F atoms were equal, indicating that the symmetry of the NF3 molecule on the y-axis did not change when the external electric field was applied.
Changes in the molecular charge distribution of NF3 under various electric field intensities
| F (a.u.) | 0 | 0.005 | 0.010 | 0.015 | 0.020 | 0.025 | 0.030 | 0.035 | 0.040 | 0.045 | 0.050 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.022 | 0.023 | 0.023 | 0.023 | 0.024 | 0.025 | 0.027 | 0.029 | 0.032 | 0.036 | 0.043 |
| 2F | −0.007 | 0.021 | 0.050 | 0.078 | 0.106 | 0.135 | 0.165 | 0.195 | 0.227 | 0.260 | 0.296 |
| 3F | −0.007 | −0.022 | −0.036 | −0.051 | −0.065 | −0.080 | −0.096 | −0.112 | −0.129 | −0.148 | −0.169 |
| 4F | −0.007 | −0.022 | −0.036 | −0.051 | −0.065 | −0.080 | −0.096 | −0.112 | −0.129 | −0.148 | −0.169 |
Figure 3 shows the electrostatic potential distribution of NF3 molecules placed under electric field intensities of 0, 0.03, and 0.05 a.u. We can see from the figure that the charge in the molecule was evenly distributed in the zero electric field. The increase in the electric field strength resulted in the directional transfer of positive and negative charges under the action of the electric field, which is consistent with the changes demonstrated in Table 3.
The electrostatic potential of NF3 molecules with external electric fields of 0, 0.03, and 0.05 a.u. (blue represents positive charge and red represents negative charge).
It can be seen from the above research that NF3 has high symmetry in the absence of external electric field, but the symmetry in other directions is destroyed after the electric field is applied in the Y direction, and the symmetry in the Y direction is still good.
3.3 Influence of an external electric field on the frontier orbital energy and energy gap of NF3 molecule
Using the same method, we calculated the lowest unoccupied molecular orbital (LUMO) energy, E L, the highest occupied molecular orbital (HOMO) energy, E H, and the energy gap, E G, of NF3 when an electric field of 0–0.05 a.u. was applied. Table 4 shows the physical parameters that were calculated, where E G was calculated by
Changes in the HOMO energy, LUMO energy, and E G of NF3 under different electric field intensities
| F (a.u.) | E L (a.u.) | E H (a.u.) | E G (eV) |
|---|---|---|---|
| 0 | −0.025 | −0.382 | 9.716 |
| 0.005 | −0.030 | −0.382 | 9.595 |
| 0.010 | −0.036 | −0.383 | 9.430 |
| 0.015 | −0.043 | −0.383 | 9.264 |
| 0.020 | −0.050 | −0.384 | 9.089 |
| 0.025 | −0.058 | −0.385 | 8.906 |
| 0.030 | −0.067 | −0.387 | 8.714 |
| 0.035 | −0.076 | −0.389 | 8.514 |
| 0.040 | −0.086 | −0.391 | 8.307 |
| 0.045 | −0.096 | −0.392 | 8.091 |
| 0.050 | −0.108 | −0.397 | 7.867 |
Many properties of molecules are influenced by their frontier orbitals. E H indicates the ability of a molecule to lose electrons, and this ability increases with an increase in E H. The ability of molecules to acquire electrons increases with a decrease in E L. The ability of electrons to transition from the HOMO to the LUMO, or E G, is indicative of whether it is easy for a chemical reaction to occur. Figure 4 (left) shows the change in E L and E H when an electric field was applied.
Changes in molecular energy levels of NF3 when external electric fields are applied (left) and changes in the molecular E G of NF3 when external electric fields are applied (right).
From Figure 4 (left), the LUMO energy and HOMO energy gradually decreased when the applied electric field was increased, and the change in the LUMO energy was clearer than in the HOMO energy. Figure 6 shows the change in E G, and it decreased with the increase in the external electric field, indicating that the external electric field makes the electrons easy to excite to the empty orbital. Consequently, the molecule is more prone to react by, for example, the N–F bond breaking.
Figure 4 (right) also shows the HOMO and LUMO of the NF3 when the electric field intensity was changed. From Figure 4 (right), in the case of the zero electric field, the electron cloud was evenly distributed around the NF3. Because of the attraction of the external electric field to the electron cloud, the lowest empty orbital of the NF3 molecule moved in the direction that the electric field increased. It can be directly observed that the impact of the electric field on the lowest orbital was far greater than on the highest occupied orbital.
3.4 Effect of external electric field on infrared spectrum (IR) spectrum
Changes in the IR spectrum of NF3 can provide much physical or chemical information. Using the static method (the scale factor is 0.967), the NF3 molecules are simulated and calculated. The second derivative of the energy to the atomic displacement is obtained under the simple harmonic approximation, and the relative intensity of each vibration mode is calculated according to the relationship that the absorption intensity is proportional to the square of the corresponding transition dipole distance, shown in Table 5. The calculated values were close to the experimental values, which further illustrates the appropriateness of the calculation methodology applied in this study.
Vibration frequencies calculated for NF3 and experimental values
| Mode | Vibrational frequency (cm−1) | |
|---|---|---|
| Calculated value | Experimental value [23] | |
| Sym str | 1034.23 | 1032.00 |
| Sym deform | 645.38 | 647.00 |
| Deg str | 874.65 | 907.00 |
| Deg deform | 484.95 | 492.00 |
Using the same method, the IR spectra of NF3 molecules were calculated by adding electric fields with different intensities along the y-axis. Figure 5 shows the IR spectra of NF3 molecules under various electric fields. From the calculation results, there were two degenerate vibrations at 874.58 cm−1 at zero electric field, namely, the degree stretch vibrations of the N–3F and N–4F bonds and the degree stretch vibration of the N–2F bond. When the external electric field was applied, the vibration peak underwent a Zeeman effect and split into two peaks. When the electric field strength was increased, the two peaks red shifted at the same time, then a slight blue shift occurred at 0.04 a.u., before they continued to shift to the red. This demonstrated that the energy required for the vibration became low and the N–3F and N–4F bonds became unstable before they were likely to break soon after.
Changes in the vibration frequency and infrared spectrum of NF3 when external electric fields are applied.
3.5 Effect of applied electric field on UV-vis absorption spectrum
On the basis of the above research, the UV-vis absorption spectra of the first 10 excited states of NF3 under an electric field intensity of 0–0.05 a.u. were calculated by time-dependent DFT using B3LYP/6-311G+(d,p).
Figure 6 shows that when the electric field was varied from 0 to 0.05 a.u., the absorption intensity of the NF3 decreased and the peak deformation widened. The overall curve peak intensity decreases and the peak width widens, indicating that the molecular polarity increased and the electronic state transition energy decreased.
Changes in the UV-vis spectrum of NF3 when external electric fields are applied.
3.6 Effect of electric field on dissociation potential energy
Using the same method, the basis-state energy curves were calculated by rigid scan for a NF3 molecule with bond lengths of 1–2.5 Å without an external electric field and with application of electric fields of 0–0.05 a.u., Figure 7. As the electric field gradually decreased from 0–0.05 a.u., the potential energy curve of the N–3F bond became shallower, which means that the potential barrier gradually disappeared. The N–3F bond became unstable, and the potential barrier was relatively flat at 0.05 a.u., showing that the N–3F bond was about to break at that field strength. In the process of dissociation, because fluorine atoms are more electrophilic, the electron pairs shared by covalent bonds will be captured by fluorine atoms, resulting in the Heterolytic fission.
Changes in the N–3F bond dissociation potential energy curves of NF3 molecules when external electric fields are applied.
After the dissociation of N–3F, we continued scanning of the N–4F bond. The potential energy curves for the N–4F bond under electric fields of 0.04 a.u. and 0.05 a.u. were plotted, Figure 8. It was found that the potential energy curve was also relatively flat at 0.05 a.u., indicating that under that electric field intensity, the potential barrier disappeared and the N–4F bond broke. Therefore, nitrogen trifluoride molecules will dissociate stepwise when an external electric field of this strength is applied.
Changes in the potential energy curve of the N–4F bond dissociation in an NF2 molecule when external electric fields are applied.
After the N–3F and N–4F bonds were broken, we continued to scan along the N–2F bond. Figure 9 plots the potential energy curve when electric field intensities of 0–0.06 a.u. were applied. It can be seen that the applied electric field had little effect on N–2F, thus showing that after the first two F atoms break away, NF becomes stable and does not continue to break.
Changes in the potential energy curve of the N–2F bond dissociation in an NF molecule when electric fields are applied.
3.7 Effect of external electric field on potential energy surface
To explore whether nitrogen trifluoride molecules will undergo concerted dissociation, we increased the two-dimensional potential energy curve to a three-dimensional potential energy surface. Using the same method and basis sets, the three-dimensional potential energy surfaces of NF3 molecules 3F and 4F were calculated, as shown in Figure 10. It can be seen from the figure that when the electric field intensity was zero, the molecule was in the bound state of the high potential barrier. When the electric field intensity was increased to 0.05 a.u., the barrier on both sides was slight, indicating that at that time, there will be fracture of the N–F bond. This was consistent with the descriptions in Figures 7 and 8. There was a barrier at the diagonal position, representing the path of concerted dissociation. However, when the electric field strength was increased to 0.09 a.u., not only did the curve collapse on both sides of the potential energy surface, but there was collapse at the diagonal position, indicating that concerted dissociation of NF3 molecules occurs under an external electric field of 0.09 a.u.
Potential energy surfaces of NF3 when external electric fields are applied.
3.8 Effect of external electric field on four-body dissociation
We next studied the four-body dissociation of a NF3 molecule. Changing the direction of the electric field to the opposite direction of z-axis and applying an electric field in this direction as shown in Figure 11 (left), we studied the fracture of three bonds in a NF3 molecule. The reason for choosing the z-direction was that the electric field in that direction had the same effect on each of the three bond lengths. Applying different electric field intensities, we scanned along the direction to obtain the surfaces shown in Figure 11 (right). There was a potential barrier in the molecule at a zero applied electric field. The molecular barrier decreased when the electric field intensity was 0.06 a.u. When the electric field intensity was 0.12 a.u., the N–2F bond did not dissociate, but the N–3F bond did dissociate. This shows that NF3 will not undergo four-body dissociation in this direction.
Schematic diagram of applied electric field in the z-axis direction of NF3 molecule (left), the potential energy surface of NF3 molecule (right), when the electric field direction is z-axis.
4 Conclusion
An electric field was applied to study changes in the geometric configuration, spectral characteristics, and dissociation characteristics of NF3. The effect of the external electric field on these properties was analyzed and the following conclusions were obtained. The properties of NF3 changed when the external electric field strength was varied. An increase in the applied electric field increased the N–3(4)F bond length and made it easier to break. Changing the electric field intensity from 0 a.u. to 0.05 a.u. resulted in the increase in molecular dipole moment, indicating that the molecular polarity also increased. On comparing with the experimental values, the IR spectrum of NF3 obtained by DFT calculations was shown to be reasonably accurate. By increasing the electric field intensity from 0–0.05 a.u., the bond stretching frequency generally shifted to the red. From the observed decrease in the energy gap, E G, and the observed changes in the peak wavelength in the UV-vis spectrum, it was demonstrated that an increase in the applied electric field intensity reduced the transition energy of the electronic state, thus making the molecules more easily excited. The increase in the external electric field was beneficial for the degradation of the NF3 molecule. The potential barrier of the N–3F bond of the nitrogen trifluoride molecule gradually decreased in height when the applied electric field strength was increased, meaning that the molecule was more easily dissociated. When the electric field intensity was 0.05 a.u., the barrier gradually disappeared and dissociation occurred. The concerted dissociation of NF3 was also studied. It was found that when the external electric field was increased to 0.09 a.u., a diagonal potential energy barrier representing the concerted dissociation disappeared, and the synergistic dissociation of the N–3F and N–4F bonds occurred. When the opposite direction to the z-axis is chosen as the electric field direction acting on the three fluorine atoms, four-body dissociation will not occur. The research described herein provides a theoretical basis for the external electric field degradation of NF3, and also provides an important reference for further research into this important area of study. Meanwhile, the method can be used for dissociating NF3 molecules in experiments and reducing the heat storage capacity of the NF3 molecules so as to achieve the purpose of protecting the environment.
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Funding information: This research was funded by the National Natural Science Foundation of China (No. 21763027), Innovation team for monitoring of emerging contaminants and biomarkers (No. 2021D14017), Xinjiang Regional Collaborative Innovation Project (No. 2019E0223), Scientific research program of colleges and universities in Xinjiang (No. XJEDU2020Y029), “13th Five-Year” Plan for Key Discipline Physics Bidding Project of Xinjiang Normal University (No. 17SDKD0602), Teaching Reform Project of Postgraduate Education in Xinjiang (XJ2021GY25), Undergraduate Teaching Research and Reform Project of Xinjiang Normal University (SDJG2021-12), Outstanding Youth Fund of Xinjiang Autonomous Region (No. 2022D01E12).
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Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Conflict of interest: The authors state no conflict of interest.
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Data availability statement: The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.
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