Density Functional Study of Structures and Electron Affinities of BrO4F/BrO4F−

The structures, electron affinities and bond dissociation energies of BrO4F/BrO4F− species have been investigated with five density functional theory (DFT) methods with DZP++ basis sets. The planar F-Br…O2…O2 complexes possess 3A′ electronic state for neutral molecule and 4A′ state for the corresponding anion. Three types of the neutral-anion energy separations are the adiabatic electron affinity (EAad), the vertical electron affinity (EAvert), and the vertical detachment energy (VDE). The EAad value predicted by B3LYP method is 4.52 eV. The bond dissociation energies De (BrO4F → BrO4-mF + Om) (m = 1–4) and De− (BrO4F− → BrO4-mF− + Om and BrO4F− → BrO4-mF + Om−) are predicted. The adiabatic electron affinities (EAad) were predicted to be 4.52 eV for F-Br…O2…O2 (3A′←4A′) (B3LYP method).


Introduction
In recent days, density functional theory (DFT) has been enjoying tremendous success in electronic structure calculations for molecules and solids alike [1][2][3][4][5][6][7][8]. The DFT methods are able to describe the electronic structure of these systems with accuracies comparable to traditional correlated molecular OPEN ACCESS orbital methods at a decreased computational cost. Furthermore these techniques are observed to assign more bonding character to the Lewis system in which the nucleophilic reaction occurs [9]. The DFT-based global and local properties (namely, DFT descriptors), such as Fukui functions, global and local hardness or softness [10,11], have already been used for reliable predictions in various types of electrophilic and nucleophilic reactions on a diversity of material structures [1][2][3][4][5][6][7][8][9][12][13][14][15][16]. In some sense, the DFT-descriptors provide us with more rigorous alternatives than the classical frontier orbital analysis. Chatterjee's group have already used the DFT-descriptors for predictions in electrophilic and nucleophilic reactions in the case of zeolites and clay materials with or without solvent environment [1][2][3][4][5][6][7].
On the other hand, the bromine, chlorine, and fluorine oxides are known to be important in lower stratospheric ozone depletion, and have been the subjects of intense studies in recent years [17-26, and references cited therein]. Relevant bromine oxide fluorides, represent intriguing ternary molecules involving covalent bond between highly electronegative atoms, possessing a large number of unpaired electrons, resulting in strong lone pair-lone pair repulsions. Therefore, the hypervalent structures of these species could be characterized. As early as 1972, Johnson et al. [27] reported the thermodynamic properties of Br(VII) FBrO 3 species. In 1976, Appelman et al. [28] characterized the molecular structure of gaseous perbromyl fluoride (FBrO 3 ), and Gillespie and Spekkens [29] prepared and characterized potassium difluorodioxobromate (BrO 2 F 2 -) and tetrafluoro-oxobromate (BrOF 4 -). In 1978, Christe et al. [30] reported the vibrational frequencies and assignment of BrOF 3 . In 2005, Lehmann et al. [31] reported synthesis and characterization of salts containing the bromine (VII) BrO 3 F 2 anion; last year, Lehmann et al. [32] also reported the characterization of BrO 3 F and ClO 3 F to [XO 2 ][SbF 6 ] (X = Cl, Br) by single crystal X-ray diffraction, raman spectroscopy, and computational methods. The results showed that of a few computational methods, the DFT functional, B3LYP in combination with the aug-cc-pVTZ basis set, and the QCISD and CCSD(T) calculations provided the most reliable correlation with the experimental geometry and vibrational frequencies of BrO 2 + [33] and likely provide reliable estimates of the geometric parameters and vibrational frequencies of BrO 3 + , as well as benchmarks for calculations involving bromine fluoride and oxide fluoride species [33]. Correspondingly, the density functional theory (DFT) in conjunction with DZP++ basis set has also localized these Br-hypervalent ternary structures to be minimum on the potential energy surfaces (PES) [34,35]. The planar/lineaer FBrO/FBrO-, pseudo-trigonal bipyramid F(F 2 )Br=O (C s symmetric) [34] and [F-(:BrO 2 )-F] -(C 2v ) anionic [29], and quasi-octahedral (OBr-F 4 ) -(C 4v ) [34,29] Br(V) structures have been found to be the lowest-lying isomers. However, the hypervalent FBrO 2 , FBrO 3 [35], and their corresponding anionic isomers are local minima on the PES. These DFT methods, especially the hybrid DFT methods (BHLYP and B3LYP) are reliable to predict the bond lengths and bond angles [32]. Besides the rich fluoride chemistry of the III and V oxidation states of Br oxides, the fluoride ion transfer reactions containing Br(VII) are scarce and have only been established by the syntheses of the ternary bromine oxide fluorides, BrO 3 F 2 - [31]. In this work, we report the systemic theoretical investigation of the similar BrO 4 F/BrO 4 Fspecies, which may be of importance in atmospheric chemistry. DFT/DZP++ scheme has been shown to be successful in prediction of electron affinities (EAs) of many species, such as BrOF n /BrOF n -, FBrO 2 /FBrO 3 , Br 2 O n /Br 2 O n -, BrClF n /BrClF n and SF 5 O n /SF 5 O n -(n = 1-3) species [34][35][36][37][38]. These studies and others have demonstrated that the DFT/DZP++ methods can predict electron affinities (EAs) in a good accuracy [39]. In addition, these methods are reliable for the geometry optimization of the neutral radicals and their anion.
The aim of the present work is to apply five DFT methods to predict the electron affinities of ternary bromine oxide fluoride, BrO 4 F, as well as the equilibrium geometries, harmonic vibrational frequencies, and bond dissociation energies. Four forms of the electron affinities are calculated, evaluated as the neutral-anion energy separations in the following manners. The adiabatic electron affinities (EA ad ) are determined by, EA ad = E (optimized neutral ) − E (optimized anion) , zero-point corrected adiabatic electron affinities (EA zero ) are determined by, EA zero = E (zero-point corrected neutral) − E (zero-point corrected anion) , the vertical electron affinities (EA vert ) by, EA vert = E (optimized neutral) − E (anion at optimized neutral geometry) , and the vertical detachment energies (VDE) of the anion by, VDE = E (neutral at optimized anion geometry) − E (optimized anion) . The DFT descriptors, such as Fukui functions, global and local hardness or softness [10,11], also have been used for the reliable predictions in the stability of BrO 4 F isomers.

Theory
Just like Chatterjee et al. [1][2][3][4][5] rationalized the structure-property relationship in different clays and observed that the hydroxyl groups present in the clay structure play a crucial role in the catalytic activity. We have explored the role of O and F atoms on the structure and properties of different bromine oxygen fluoides [34,35].
The hard-soft acid-base (HSAB) principles categorize the interaction between acids and bases in terms of global softness. Pearson proposed the global HSAB principle [40]. The global hardness was the second derivative of energy with respect to the number of electrons at constant temperature and external potential, which includes the nuclear field. The nonchemical meaning of the word "hardness" is resistance to deformation or change.
The global softness is the inverse of this. Pearson also pointed out a principle of maximum hardness (PMH) [41], which stated that, for a constant external potential, the system with the maximum global hardness is the most stable.
DFT-based local properties, like Fukui functions and local softness [10], have already been used for reliable predictions of electrophilic and nucleophilic reactions [1][2][3][4][5][6][7][8]. Generally, compared to a gasphase calculation, the solvent environment alters the charge distribution of a molecule. There is an increase in the dipole moment of molecules such as water and BrF, which enhances the intrinsic reactivity of polar molecules toward nucleophilic and electrophilic attack [15]. Our aim in the current work is to explore the role of O n chain in the structure and bonding of BrO 4 F species. DFT-based local descriptors have been used for calculating the reactivity index within the helm of the HSAB principle [11][12][13][14][15]. It is used to determine the possible correlation between BrO 4 F isomers.
In density functional theory, hardness (η) [40] is defined as: where E is the total energy, N is the number of electrons of the chemical species, and μ is the chemical potential.
The global softness, S, is defined as the inverse of the global hardness, η: Using the finite difference approximation, S can be approximated as: where IE and EA are the first ionization energy and electron affinity of the molecule, respectively.
The Fukui function f(r) is defined by [10]: The function f is thus a local quantity, which has different values at different points in the species, N is the total number of electrons, μ is the chemical potential, and v is the potential acting on an electron due to all nuclei present. Since ρ(r) as a function of N has slope discontinuities, equation 1 provides the following three reaction indices [10]: In a finite difference approximation, the condensed Fukui function [16] of an atom, say x, in a molecule with N electrons is defined as: where q x is the electronic population of atom x in a molecule. The local softness s(r) can be defined as: Equation (3) can also be written as: Thus, local softness contains the same information as the Fukui function f(r) plus additional information about the total molecular softness, which is related to the global reactivity with respect to a reaction partner, as stated in the HSAB principle. Atomic softness values can easily be calculated by using equation 4, namely:

Methodology
The five different DFT exchange-correlation functionals employed in this work range from generalized gradient approximation (GGA) [BLYP, BP86] to hybrid-GGA [BHLYP, B3P86，and B3LYP]. These hybrid Hartree-Fock/density functionals include: (a) Becke's half and half HF/DFT hybrid exchange functional (BH) [42] with the Lee, Yang, and Parr correlation functional (LYP) [43] (BHLYP); (b) Becke's three parameter functional [44] (B3) plus Perdew's correlation functional (P86) [45] (B3P86); (c) B3 combined with LYP functionals (B3LYP) [44,43] The final contracted basis sets are thus designated as Br (15s12p6d/9s7p3d), O (10s6p1d/5s3p1d), and F (10s6p1d/5s3p1d). All of the molecular structures and the electron affinities have been determined using the Gaussian 03 program suite [50]. The fine integration grid (99 590) was used. All stationary point geometries were characterized by the evaluation of their harmonic vibrational frequencies at the five different levels of theory. Unless otherwise reported, the geometries in figures were found to be minima after determining the harmonic vibrational frequencies via analytical second derivatives for the corresponding stationary point structures for each function.
Besides the electron affinities, the bond dissociation energies for BrO 4 F/BrO 4 Fare also determined as the difference in total energies in the following manners: The bond dissociation energies for the neutrals refer to the reactions: The bond dissociation energies for the anions refer to the reactions: The natrural bond orbital (NBO) analysis [51] was carried out at the B3LYP/DZP++ level for some species, corresponding Wiberg bond index (WBI) and atomic charges are obtained. Unless otherwise stated, we use the B3LYP result for molecular structures and energetics. The counterpoise (CP) method [52] was used to correct the basis set superposition error (BSSE) [7,53] using the Boys-Bernardi method in the calculation of the binding energy for the current basis. For these complexes of Lewis species, the single point calculations of the cation and anion of each molecule at the optimized geometry of the neutral molecule were also carried out to evaluate Fukui functions, global and local softness [10]. The condensed Fukui function and atomic softness were evaluated using equations 3 and 6 in Section 2. Theory, respectively. The gross atomic charges were evaluated using the technique of Mulliken charges, due to the Br atomic charge can hardly be evaluated by using the technique of electrostatic potential (ESP) driven charges.

Results and Discussion
With the present five DFT methods, the optimized O-F bond length for single OF molecule ranges from 1.331 Å (BHLYP) to 1.385 Å (BLYP) (not shown). The trend of bond lengths predicted for O-F is BHLYP < B3P86 < B3LYP < BP86 < BLYP. The DZP++ B3LYP method gives the result closest to the experimental O-F bond length (r e ) of 1.3541 Å, obtained from Raman spectroscopy [18 and references cited therein]. The B3LYP method also obtain the best prediction result for dissociation energy (D e ) of OF [23] and BrO [21]. For a discussion of the reliability of B3LYP thermochemistry, see the recent work of Boese, Martin, and Handy [54]. Therefore, in the following discussion, unless otherwise stated, we use the B3LYP result for molecular structures and energetics.
For neutral BrO 4 F species, the molecular chain FBr…OO…OO structure with a terminal F-Br moiety connected by OO…OO chain lies the lowest energetically. This structure in its 5 The FBr…OO…OO structures in 3 A' state (a: 3 A') optimized by three hybrid DFT methods (BHLYP, B3P86 and B3LYP) and in 1  The calculated energies (Table 1) show that the FBr…OO…OO structure in its 5 A' state or its dissociation products (FBr ... OO ( 3 A") + O 2 ( 3 Σ g -)) lies lower than the corresponding 3 A' (a) and 1 A' or 1 A (b) states by about 33 and 60 kcal/mol respectively with the B3LYP method. This state also lies much lower than the cis-, trans-BrOO…OOF (c: 1 A and d: 1 A) and BrOO 2 …OF (e: 1 A) isomers by ca.64, 64, and 95 kcal/mol (Table 1) respectively (B3LYP). The O 2 Br…OOF (f: 1 A) and FBrO 3 ...O (g: C 3v , 3 A 1 ) Br-hypervalent structures lie much higher than the 5 A' state by ca. 78 and 130 kcal/mol (Table 1) respectively. With a few exceptions, the two pure DFT methods (BP86 and BLYP) predict much smaller relative energies and the bond dissociation energies than three hybrid DFT methods. All these discrepancies indicate that BrO 4 F is a challenging target for DFT methods.  As can be seen from Figure 1, for the FBr…OO…OO structure in its 3 [55]. It is worthy to note that the geometries predicted using the five functionals are all similar, with small variations in bond lengths and angles. The general trend for the covalent bond lengths is BLYP > BP86 > B3LYP > B3P86 > BHLYP. According to previous studies on geometries of BrOF n /BrOF n -, FBrO 2 /FBrO 3 , BrClF n /BrClF n and BrF n species [34,35,37,56], the hybrid DFT methods (BHLYP, B3P86 or B3LYP method) are excellent methods for the prediction of covalent bond lengths. The B3LYP method taking the median position may be regarded as a compromise between the reliabilities of geometry and thermochemical parameter predictions. This order coincides with that predicted for the FO molecule [25] where comparison with experiment indicates the B3LYP method to be the most accurate in prediction of geometry, and for BrO in predictions of bond dissociation and adiabatic electron affinity (EA ad ) [21].
The attachment of an electron to FBr…OO…OO complex, results in the 4 A' ground state for anion (aa: 4 A' in Figure 2). As might be expected, this structure is more stable than other anionic BrO 4 F -Brhypervalent structures (ab: 2 A' and ac: 2 A' in Figure 2)    ) +O 2 ( 1 Δ g ) reaction being in the range of 7-48 kcal/mol, the BHLYP result is too small (7 kcal/mol). This is not unexpected, given the large fraction of exact exchange in the BHLYP method [57]. For the global minimum FBr…OO…OO anion (aa: 4   Generally, the theoretical dissociation energies (D e ) for BrO 4 F/BrO 4 Fspecies can be evaluated from the data in Tables 1 and 2. For the anionic BrO 4 Fspecies, all of five DFT methods predict almost consistent relative energies and bond dissociation energies, with the exception of the lowest BHLYP results (Table 2) (vide supra). In contrast, for the neutral BrO 4 F species (Table 1), the relative energies and bond dissociation energies predicted by BHLYP method are nearly the biggest. It is noted that BHLYP method perform poorly for bond-breaking process [57] due to the large (50%) contribution from Hartree-Fock or exact exchange. Based on the previous studies of the BrO n species [21] and the anionic BrO 4 Fspecies (vide supra), the B3LYP methods should predict reasonable dissociation energies and relative energies, however, caution is urged because of the complex of BrO 4 F ternary system.
At B3LYP level, for the lowest energies species, the theoretical bond dissociation energies for neutral BrO  ( 1 A') + O 3 (range from 48 to 101 kcal/mol, ca. 71 kcal/mol at B3LYP level), indicating the dissociation reaction is favored, which is consistent with the FBr…O 2 …O 2 complex structure.
The most reliable B3LYP method predicts the dissociation energy (D e ) for F-Br…O 2 …O 2 ( 5 A') → BrF + 2O 2 and (F-Br…O 2 …O 2 ) -( 4 A') → BrF -+ 2O 2 are only 0.0 and 9.1 kcal/mol, respectively (Tables 1 and 2      Isodesmic reactions, which have been typically used to obtain the heats of formation for many molecules, are those in which the reactants and products contain the same types of bonds, i.e., the number of bonds broken and formed is conserved [58]. An isodesmic reaction scheme requires that the heats of formation of all the molecules involved in the reaction to be known with the exception of the heat of formation of the particular isomer. Because of this property, errors in the energy that might occur due to defects in the basis set and electron correlation cancel, to a large extent. The isodesmic scheme used here is BrOOOOF + 4HOH → 3HOOH + HOBr + HOF. During the calculation of the heat of formation of BrOOOOF using the isodesmic scheme, literature values for the heats of formation of HOH (-57.10 kcal mol -1 ) [59], HOOH (-31.02 kcal mol -1 ) [59], and HOBr (-10.93 kcal mol -1 ) [60], HOF (-22.47 kcal mol -1 ) [61], were used. Using these results we were able to calculate the heats of reaction. For cis BrOOOOF (c), the heat of formation is predicted to be 50 kcalmol -1 at B3LYP level of theory (Table 5). Using the relative energies (Table 1) along with the heat of formation of BrOOOOF (c), we obtained a value of 19 kcal mol -1 for FBrOOOO(a), 83 kcal mol -1 for BrOO2…OF (e), 64 kcal mol -1 for O 2 Br…OOF (f), and 116 kcal mol -1 for FBrO 3 …O (g) (shown in Table 6). To further assess these results, we have listed all five DFT methods heats of formation of the isomers in Table 6. At present, there are no experimental measurements to which be mainly due to the incompleteness of the basis sets and only partial allowance for electron correlation.  For these complexes of Lewis acid (BrF) and base (lone pair O m chains), we treated as a local version of the hard and soft acid base (HSAB) principle [40]. The DFT-based local reactivity descriptors such as the global or local softness or hardness, condensed Fukui functions can be used to explain the stability of isomers. The predicted global hardness (η) and softness (GS) for the minimum-energy BrO 4 F structures (a, b, c, d, e, f, and g isomers) with five DFT methods are shown in Tables 7  and 8 structures (a, b, c, d, e, f, and g isomers) at the B3LYP/DZP++ level are tabulated in Table 9. According the Pearson's PMH suggestion [41], the Br(VII) structure (g) FBrO 3 …O in this work has the largest global hardness (Table 7), and smallest global softness (Table 8), thus triplet state FBrO 3 …O structure is the most stable isomer. For BrO 4 F isomers, the maximum value (from 5.1 to 8.2, at B3LYP/DZZ++ level, as 8.2) of global hardness (Table 7) set in the highest symmetric Br(VII) FBrO 3 ...O structure (g), whereas the minimum value (from 2.9 to 3.2) of hardness assign to singlet BrOO...OOF isomer (b), inversely, the isomers (g) or (b) possesses the smallest or largest global softness (Table 8), respectively, namely, from 0.06 to 1.0, or from 0.16 to 0.17. For Br in the different isomers presents almost either the largest or smallest S x -/S x + values (Table 9), corresponding to different bonds stabilities. An important finding from this investigation is that Br may reveal the flexibility in which the bromine atom shares valence electrons and orbitals to form a variety of hypervalent species, even the extend hypervalent system.    F (a, b, c, d, e, f, and g)

Conclusions
The structures, electron affinities and bond dissociation energies of BrO 4 F/BrO 4 F − species have been studied with five DFT methods. The B3LYP method is the most reliable method for predicting the geometry and electron affinities for this ternary species. The EA ad value predicted by the B3LYP method is 4.52 eV for BrO 4 F. The EA ad values for OBrF [34], FBrOO, and FBrOOO [35] species are 3.64, 5.83 and 4.43 eV, respectively. and close to those of other interhalogen compounds, such as BrCIF n and BrF n [37,56]. Those with odd n (n = 1 and 3, closed shell) have smaller EA ad than those of even n (n = 2 and 4) species, which are open-shell triplet state. These substantial electron affinities suggest that the corresponding anion may have the lifetimes as independent species under atmospheric conditions.
Similar to the case of the electron affinities, the hybrid DFT methods especial BHLYP predict the discrepant values of bond dissociation energies for BrO 4 F/BrO 4 F − dissociation reactions and relative energies from two pure DFT methods, demonstrating that this system is a challenge for DFT methods.
Although the FBr-O 2 -O 2 /(FBr-O 2 -O 2 )chain structures have been found to be the most stable isomers, yet there is no workable reaction mechanism for the formation of these species considering only BrF or BrF -, BrO and O 2 or O 2 as starting materials. According recently report on bromine (VII) BrO 3 F 2 anion [31], we conclude that the Br(VII) structure, FBrO 3 ...O (g: C 3v , 3 A 1 ) are the most likely structure for neutral BrO 4 F, and the BrO 4 Fmay have Br(V) (FO…BrO 3 ) -(ac: 2 A') complex structure. The DFT-based local reactivity descriptors such as the global or local softness or hardness, condensed Fukui functions can demonstrate this suggestion. The DFT methods are able to describe the electronic structure of these systems with accuracies comparable to traditional correlated molecular orbital methods at a decreased computational cost. Furthermore these DFT-based local descriptors techniques are observed to assign more bonding character to the BrO 4 F Lewis system.