It is well-known that electronic structure properties of the molecules, especially the electron affinity energy, are very sensitive to the DFT functionals and basis sets. In Figure 2, we plotted DFT calculated EA results with different functional and basis sets for c-C₄F₈ together with comparisons to experimental reference (0.63 ± 0.05 eV) (Chang et al., 1971). It is clearly shown that with basis set including f -type functions, long-range corrected or meta-hybrid functionals can generally give results much closer to experimental references than local or standard hybrid functions. Among them, M06-2X and ωB97-XD are shown to give smallest deviations (about −25 to 25% error). It is because in perfluoro-compounds, the large number of F atoms is associated with intense non-bonding interactions. Therefore, functional with long-range corrected or meta-hybrid functionals are required for the accurate calculation of the electronic structures of perfluoro-compounds.

As for the basis set, from Figure 2 one may also clearly notice that not only the diffused function but also f -type polarized function are necessary for an accurate theoretical prediction of EA for possible insulating gas molecules. It is shown that 6–311+g(d) basis set gives results with large deviations from experimental references for all of DFT functionals we adopted, while 6–311+g(3df), aug-cc-pVTZ and aug-cc-pVQZ basis sets can give more reasonable results. From the data shown in the Supporting Information, one can further notice that the basis set difference only causes slight distinctions in the optimized geometries and the EA difference by different basis sets mainly comes from the single point energy difference. Considering that the further incorporation of g-type (aug-cc-pVQZ) polarized function do not yield an obvious improvement of the calculated results, we finally decided to perform our further systematic DFT calculations with 6–311+g(3df) basis set to achieve a good compromise between accuracy and computational efficiency.

The equilibrium structures of the optimized molecules (1–7) in their both neutral and anion forms obtained from geometry optimization by DFT calculation at M06-2X/6–311g+(3df) level were shown in Figure 1, and the key structural parameters are listed in Table 1. It is shown that the molecule symmetry is decreased from D_2d to C_2v or C_s, C₂ or even C₁ with the increasing n for neutral forms of c-C₄F_8−nCl_n (n = 0, 1, 2), due to the symmetry break by chlorine substitution. Interestingly we notice that while the geometry of neutral c-C₄F₈ (1) is bent with D_2d symmetry (∠C₂C₁C₃C₄ around 164.4°), that of its anion form (1⁻) becomes planar with D_4h symmetry (∠C₂C₁C₃C₄ being 180.0°). This finding is consistent with earlier ESR experiments (ElSohly et al., 2005) and theoretical calculations (Choi et al., 2013). The previous computational results have shown that the added electron to c-C₄F₈ is delocalized in a “pi-like” orbital extending over the entire molecule, strengthening the four C-C bonds via π-bonding interactions, and weakening the eight C-F bonds via σ*-antibonding interactions. However, such a bent-to-planar transition was not observed for c-C₄F₈ derivatives upon attachment of an electron, due to the decrease of the symmetry by mono- and di-chloro-substitutions.

Figure 3 gives the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO) of the selected molecules 1, 2, and 6. For c-C₄F₈ (1), the LUMO is similar to a delocalized π-orbitals of the four carbon atoms, therefore, the attachment of an additional electron would make the carbon cycle more planar. On the contrary, for mono- and di-substituted molecules, the p-orbitals of chlorine atoms have much greater contributions to the LUMO, indicating a more localized feature at the Cl atom. As a consequence, the electron attached to the chloro-substitutes of c-C₄F₈ (2–7) will locate at the Cl atom to a great extent with an elongated C-Cl bond length and will not remarkably alter the planarity. This can be verified from the structure in Figure 1 and the data in Table 1, in which the ∠C₂C₁C₃C₄ change is less than 7° and the bond length difference between two C-Cl bonds are as large as 0.5–0.8 Å for the chloro-substitutes of c-C₄F₈ (2–7) upon electron attachment.

The results for binding energies and dipole moments for c-C₄F_8−nCl_n (n = 0, 1, 2) are listed in Table 2. The c-C₄F₈ (1) molecule is found to have the highest binding energy as compared to its mono- and di-chloro-substituted derivatives (2–7), and a zero dipole moment due to its relatively high symmetry of D_2d. At the same time, we notice that the binding energy is not sensitive to the different conformations for the isomers of c-C₄F₆Cl₂ (3–7), but the dipole moment is found to be highly dependent on them. Because recent multiple regression analysis (Rabie et al., 2013; Zhang et al., 2016) have shown that the magnitudes of dipole moment are correlated to the liquefaction temperature of the gases, this implies that searching for new insulating gases which can work in extremely areas should carefully examine the molecule's possible different dipole moments caused by various isomerized conformations.

As the electron affinity feature has been revealed to be highly correlated with the insulating properties of the potential new insulating gases (Rabie et al., 2013; Zhang et al., 2016), in this work we also performed calculations for various electron affinity parameters of c-C₄F_8−nCl_n (n = 0, 1, 2). The calculated EA_ad, EA_vert, and VDE by both ωB97-XD and M06-2X functionals are here listed in Table 3. As we have shown in Section Benchmark Tests for DFT Functional and Basis Set, by using suitable basis set (e.g., 6–311g+(3df)), DFT exchange-correlation functionals of ωB97-XD and M06-2X can yield very similar numerical results which are close to available experimental value. It is also shown that the electron affinity and VDA values are remarkably increased when the c-C₄F₈ (1) molecule is chloro-substituted. Considering that a larger EA value is beneficial to the improvement of relative electric strength (Rabie et al., 2013; Zhang et al., 2016), it would be useful to investigate the various halogen substitutions of currently used insulating gases of perfluoro-compounds for future improvement or replacement.

For the purpose of studying the greenhouse effect of the c-C₄F₈ and its derivatives, here we list the total infrared (IR) intensities and the cumulative IR intensities in the atmospheric IR “window” (800–1200 cm⁻¹) in Table 4, the latter of which is widely used as a descriptor for qualitatively measuring the gas's greenhouse effect (Sturges et al., 2000). All these values can be calculated by frequency analysis using Gaussian09 D.01 package. It is clear that both the total IR intensity and cumulative IR intensity in the atmospheric IR “window” are increased upon the attachment of an electron for c-C₄F_8−nCl_n (n = 0, 1, 2). Meanwhile, most chloro-substituted c-C₄F₈ compounds (4, 5, 7) show higher IR intensity in the atmospheric IR “window” than c-C₄F₈, implying a worse greenhouse effect. However, there are also some chloro-substituted c-C₄F₈ compounds (2, 3, 6) showing lower IR intensity in the atmospheric IR “window” than the c-C₄F₈ (1) molecule, implying a decreased greenhouse effect. Especially, a di-chloro-substituted c-C₄F₈ (6) has much less IR intensity (222.8 km × mol⁻¹) in the atmospheric IR “window” than that of the c-C₄F₈ (1) molecule (411.4 km × mol⁻¹). Therefore, new c-C₄F₈ derivatives like 6 can be expected to be possibly used as new insulating gases in electric equipment with much suppressed environmental problems.

Basic thermodynamic properties such as zero-point vibrational energy (ZPVE) and entropy as well as heat capacity have been also calculated for c-C₄F_8−nCl_n (n = 0, 1, 2), and the results are presented in Table 5. It is shown that while all the translational, rotational and vibrational movements contribute considerably to the total entropy, only vibrational ones make the dominant contributions to the total heat capacity. It can be also noticed that the ZPVE decreases upon chloro-substitution, but the entropy and the heat capacity increase upon chloro-substitution.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.