CF4-n (SO3) n (n = 1–4): a new series of organic superhalogens

Superhalogens are species having higher electron affinity (EA) or vertical detachment energy (VDE) than those of halogen atoms. CF4 is a molecule having no positive EA or VDE. In the quest for new organic superhalogens, we substitute SO3 in the place of F in CF4 successively and study the resulting CF4-n (SO3) n (n = 1–4) neutral molecules and their anions using density functional theory and quantum theory of atoms in molecule at the ωB97xD/6-311 + G(d) and B3LYP/6-311 + G(d) levels, respectively. The EA of CF4-n (SO3) n and VDE of their anions, being greater than 5 eV, suggest that all these molecules behave as superhalogens. There is significant structural relaxation in C(SO3)4 molecule, leading to the remarkably high VDE of corresponding anions. The superhalogen properties have been explained on the basis of the electronic charge delocalisation over SO3 moieties. We believe that these findings will add a new chapter in the exploration of organic superhalogens. GRAPHICAL ABSTRACT


Introduction
A class of atomic clusters having higher electronic affinities (EAs) than halogens is referred to as superhalogen as proposed by Gutsev and Boldyrev [1]. According to them, superhalogens consist of a central atom or core connected to highly electronegative ligands such as fluorine (F), chlorine (Cl), or oxygen (O) atoms following the octet rule. Typical examples include LiF 2 , BF 4 , PF 6  electronegativity of the central core because of the delocalisation of electrons over electronegative atoms and hence, an increase in the EA of the systems. Various kinds of superhalogens have been explored in the last four decades following different electron counting rules such as octet rule [2][3][4][5][6][7][8][9][10], Wade-Mingos rule [11][12][13][14][15] and Huckel 4n+2 rule [16][17][18][19]. However, only a few studies [18][19][20][21] explored the superhalogen properties of organic species. Due to high EAs, these clusters can be used as strong oxidising agents. The application of superhalogens in the design of superacids has been well studied [14][15][16][22][23][24][25]. The use of superhalogens in the design of new materials for hydrogen storage [26] and new electrolytes for Li-ion batteries [12,17,27] has been also reported. Besides this, superhalogens appear in the organic superconductors [28]. The most recent study [29] suggests that superhalogens can be used as building blocks of ionic liquids. Jena [30] and Skurski [31] have reviewed and discussed the recent developments in this field. Ever-increasing applications of superhalogens make them worthy of investigation even today.
It should, however, be noticed that the electronegative atom such as F does not necessarily increase the EA of the system. Gutsev et al. [32,33] investigated the ground-state geometries of carbonfluorides (CF n ) clusters for n = 1-4 and calculated their EAs. They noticed that the increase in F atoms does not increase the EA of CF n clusters such that the EA of CF 4 is obtained to be negative, −1.94 eV [32] at LSDA and −1.22 eV [33] at the HF/6-31 + G(d) level. This is evidently due to the fact that carbon tertrafluoride or tetrafluoromethane (CF 4 ) is a highly stable compound, which does not react with acids or hydroxides. Therefore, we need to substitute F with some other ligand in order to increase the EA. In this paper, we consider the substitution of sulphur trioxide (SO 3 ) in CF 4 and study the resulting CF 4−n (SO 3 ) n (n = 1-4) molecules in neutral and anionic forms using density functional theory (DFT). We calculate their EAs and notice that they indeed behave as superhalogens.

Computational details
The structures of CF 4−n (SO 3 ) n (n = 0, 1-4) molecules were optimised in their neutral and anionic forms using DFT at B3LYP level [34,35] with 6-311 + G(d) basis sets with the Gaussian 09 program [36]. No symmetry constraints were imposed during the geometry optimisation. The optimisation process was followed by frequency calculations to ensure that the optimised structures belong to at least some local minima. Some benchmark calculations suggest [37,38] the use of functionals other than B3LYP for the study of superhalogens. These B3LYP/6-311 + G(d) optimised structures were re-optimised using the dispersion-corrected ωB97xD functional [39] and 6-311 + G(d) basis set. The overall performance of ωB97xD is reasonably good among various GGA functionals as assessed by Mardirossiana and Head-Gordon [40]. Furthermore, this functional has been recommended for reliable thermochemical properties of main-group compounds by Grimme and coworkers [41]. The atomic charges were computed using the natural population analysis (NPA) [42] scheme as available in the Gaussian 09. The EA of CF 4−n (SO 3 ) n was calculated by the difference in the total energy of neutral and anion, both in their optimised structures. The VDE of CF 4−n (SO 3 ) n¯w as obtained by the difference of single-point energy of neutral structure at the optimised geometry of anion and total energy of the optimised geometry of anion.
To check the validity of the method employed, we have performed some test calculations on F, SO 3 and CF 4 using B3LYP, ωB97xD and single-point CCSD(T) calculations as given in Supplementary Table S1. The EA of F at the ωB97xD/6-311 + G(d) level (3.37 eV) agrees well with the corresponding experimental value of 3.40 eV [43,44] whereas the over-estimation of the EA of SO 3 (2.56 eV) as compared to the experimental value, 2.064 ± 0.085eV [45,46] is decreased as compared to B3LYP/6-311 + G(d) (2.71 eV). Although the EA of CF 4, measured to be −0.70 eV [47,48], is reproduced by B3LYP/6-311 + G(d) calculations, the ωB97xD/6-311 + G(d) result closely matches with the CCSD(T) calculations. These results suffice to establish the reliability of our results and the validity of the present scheme.

Results and discussion
The optimised molecular structures of CF 4−n (SO 3 ) n (n = 0, 1-4) are displayed in Figure 1 in both neutral as well as in anion forms and corresponding bond lengths along with the HOMO-LUMO gap (E gap ) are listed in Table 1. CF 4 molecule possesses a tetrahedral configuration (T d symmetry) with the C-F bond length of 1.321 Å, which agrees well with the experimental bond length, 1.330 ± 0.005 Å [49].
With the substitution of SO 3 , the C-F bond length is changed only marginally. The C-S bond length in CF 4−n (SO 3 ) n lies in the range 1.886-1.895 Å. The structures of CF 4−n (SO 3 ) n anions closely resemble those of their neutral counterparts. With the addition of an electron, however, the bond lengths are slightly changed as expected. For instance, the C-S and S-O bond lengths are slightly decreased, being in the range 1.874-2.883 Å and 1.462-1.474 Å, respectively.
In order to check whether there is any bonding between neighbouring O atoms of different SO 3 moieties, i.e., the possibility of peroxide (O-O) bonds, we have performed the quantum theory of atoms in molecule (QTAIM) analysis at the B3LYP/6-311 + G(d) optimised structures with AIMAll program [50]. It was already reported [51] that the QTAIM parameters are almost independent of the basis sets in the case of B3LYP. The molecular graphs of CF 4−n (SO 3 ) n (n = 2-4) and their anions are displayed in Figure 2 and corresponding parameters are listed in Table 2. In the framework of  Table 1. Neutral Anion QTAIM [52], the interaction between two atoms is governed by the presence of a bond critical point (BCP). From Figure 2, it is evident that there exist two O-O bonds in CF 2 (SO 3 ) 2 molecule and its anion with the bond distance of 2.117 and 3.118 Å, respectively (see Table 2). CF(SO 3 Table 2. The value of these parameters decides the nature and strength of the chemical interaction. Within the scheme of QTAIM, the stabilising interaction is characterised by ∇ 2 ρ > 0 and its strength can be estimated by [53] Table 2. Table 3 lists the NPA charges, EA of CF 4−n (SO 3 ) n (n = 0, 1-4), and VDE of corresponding anions. Since our primary objective is to investigate the superhalogen properties, we first analyse the EA and VDE values. Note that the EA of the CF 4 molecule and VDE of CF 4¯a re negative, as per the experimental findings [32,33,47,48]. This suggests that the molecule has no tendency to accept an electron. However, the substitution of SO 3 in the place of the F atom leads to a sudden increase in the EA of CF 3 SO 3 to 5.60 eV. This EA value slightly overestimates the experimental value of 5.29 eV for the CF 3 SO 3 molecule measured by the LPD method [54].
With the further substitutions of SO 3 , the EA of CF 2 (SO 3 ) 2 , CF(SO 3 ) 3 and C(SO 3 ) 4 molecules are calculated to be 5.10, 5.40, 4.73 eV, respectively. Thus, the substitution of more SO 3 molecules does not change the EA appreciably. Nevertheless, the EA of all CF 4−n (SO 3 ) n molecules for n = 1-4 exceeds 3.63 eV, the EA of the Cl atom. This suggests that all CF 4−n (SO 3 ) n molecules go to superhalogens for n = 1-4. These molecules are  significantly stabilised by adding an electron, i.e., in anionic states. We have also calculated the VDEs of these anions and listed them in Table 3. The EA of CF 4−n (SO 3 ) n molecules and VDE of corresponding anions are plotted in Figure 3 for a quick comparison. One can notice that the VDE of CF 4 , CF 3 SO 3, and CF(SO 3 ) 3 anions are almost equal to the EA of their neutral counterparts. Furthermore, it does not vary with the increase in the number of substitutions. This can be expected due to the fact that the peroxide Table 3. The electron affinity (EA) of CF 4−n (SO 3 ) n molecules, vertical detachment energy (VDE) of their anions, and NPA charges (q) on C atom, F atom, and SO 3 moiety at the ωB97xD/ 6-311 + G(d) level.

Neutral Anion
Systems  linkages (O-O) provide destabilisation as the number of SO 3 substitutions increases. It should also be noted that the VDE of C(SO 3 ) 4 anion exceeds the EA of neutral C(SO 3 ) 4 by more than 5 eV. Note that the calculations of VDE do not account for the structural relaxation upon detachment of an electron from an anion. This is evidently due to the appreciable structural relaxation in C(SO 3 ) 4 anion by detaching an electron as reflected due to a decrease in the peroxide linkage explored by QTAIM analysis (see Table 2), which results in the high VDE of the anion. In order to explain the superhalogen properties of CF 4−n (SO 3 ) n molecules, we have analysed the NPA charges on various fragments of neutral CF 4−n (SO 3 ) n molecules and their anions. One can see that the extra electron added to CF 4 is delocalised over the whole molecule. This leads to no positive EA of CF 4 . With the substitution of SO 3 , however, only 18% of the extra electronic charge is localised on the central C atom and almost 70% charge is delocalised over SO 3 moiety. This leads to an enhanced EA of 5.60 eV for CF 3 SO 3 . Note that the importance of charge delocalisation in achieving superhalogen properties has been indicated in several previous studies [55][56][57][58]. On the contrary, although the extra electronic charge is completely delocalised over SO 3 moieties in the case of C(SO 3 ) 4 , its EA is reduced to 4.73 eV. This can be expected due to the destabilisation in the C(SO 3 ) 4 anion caused by the increase in the peroxide linkages.

Conclusion
We have systematically studied the substitution of SO 3 in CF 4 molecule in neutral and anionic forms using B3LYP and ωB97xD levels with 6-311 + G(d) basis sets. We have analysed their structures and calculated EA of neutral and VDE of anionic CF 4−n (SO 3 ) n molecules. We notice that their EAs, ranging between 4.73 and 5.60 eV, suggest that all these molecules go to superhalogens for n = 1-4. The difference between EA and VDE for n = 4 has been explained on the basis of structural relaxation in these molecules. Interestingly, these two superhalogens have closed-shell structures. The NPA charges and molecular orbitals analyses have been employed to explain the superhalogen properties of these molecules. Although the high EA of CF 4−n (SO 3 ) n molecules results due to charge delocalisation over SO 3 moieties, the destabilisation caused by peroxide linkages tends to reduce the EA as the number of SO 3 substitutions is increased.
Acknowledgements AKS thanks Prof. N. Misra for providing computational facilities.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Funding
The funding received from University Grants Commission through start-up grant 30-466/2019(BSR) is also acknowledged.

Supporting information
The test calculations (Supplementary Table S1) and Cartesian coordinates of the optimised structures are given in Supplementary Information.