In recent days, density functional theory (DFT) has been enjoying tremendous success in electronic structure calculations for molecules and solids alike [1–8]. 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 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 [1–9,12–16]. 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 [1–7].

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) FBrO₃ species. In 1976, Appelman et al. [28] characterized the molecular structure of gaseous perbromyl fluoride (FBrO₃), and Gillespie and Spekkens [29] prepared and characterized potassium difluorodioxobromate (BrO₂F₂⁻) and tetrafluoro-oxobromate (BrOF₄⁻). In 1978, Christe et al. [30] reported the vibrational frequencies and assignment of BrOF₃. In 2005, Lehmann et al. [31] reported synthesis and characterization of salts containing the bromine (VII) BrO₃F₂⁻ anion; last year, Lehmann et al. [32] also reported the characterization of BrO₃F and ClO₃F to [XO₂][SbF₆] (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 BrO₂⁺ [33] and likely provide reliable estimates of the geometric parameters and vibrational frequencies of BrO₃⁺, 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(F₂)Br=O (C_s symmetric) [34] and [F-(:BrO₂)-F]⁻ (C_2v) anionic [29], and quasi-octahedral (OBr-F₄)⁻ (C_4v) [34,29] Br(V) structures have been found to be the lowest-lying isomers. However, the hypervalent FBrO₂, FBrO₃ [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, BrO₃F₂⁻ [31]. In this work, we report the systemic theoretical investigation of the similar BrO₄F/BrO₄F⁻ species, 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⁻, FBrO₂/FBrO₃, Br₂O_n/Br₂O_n⁻, BrClF_n/BrClF_n and SF₅O_n/SF₅O_n⁻ (n = 1–3) species [34–38]. 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, BrO₄F, 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 BrO₄F isomers.

Just like Chatterjee et al. [1–5] 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 [1–8]. Generally, compared to a gas-phase 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 BrO₄F species. DFT-based local descriptors have been used for calculating the reactivity index within the helm of the HSAB principle [11–15]. It is used to determine the possible correlation between BrO₄F isomers.

In density functional theory, hardness (η) [40] is defined as: η = ( 1 / 2 ) ( ∂ 2 E / ∂ N 2 ) v ( r ) = ( 1 / 2 ) ( ∂ μ / ∂ N ) vwhere 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: S = 1 2 η = ( ∂ N / ∂ μ ) v

Using the finite difference approximation, S can be approximated as: (1) S = 1 / ( I E − E A )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]: (2) f ( r ) = [ δ μ / δ v ( r ) ] N = [ ∂ ρ ( r ) / ∂ N ] v

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]: f − ( r ) = [ ∂ ρ ( r ) / ∂ N ] v −     ( governing   electrophilic   attack ) f + ( r ) = [ ∂ ρ ( r ) / ∂ N ] v +             ( governing   nucleophilic   attack ) f 0 ( r ) = ( 1 / 2 ) [ f + ( r ) + f − ( r ) ]     ( for   radical   attack )

In a finite difference approximation, the condensed Fukui function [16] of an atom, say x, in a molecule with N electrons is defined as: (3) f x + = [ q x ( N + 1 ) − q x ( N ) ]   ( for   nucleophilic   attack )   f x − = [ q x ( N ) − q x ( N − 1 ) ]   ( for   electrophilic   attack )   f x 0 = [ q x ( N + 1 ) − q x ( N − 1 ) ] / 2   ( for   radical   attack )where q_x is the electronic population of atom x in a molecule. The local softness s(r) can be defined as: (4) s ( r ) = ( δ ρ ( r ) / δ μ ) v

Equation(3) can also be written as: (5) s ( r ) = [ ∂ ρ ( r ) / ∂ N ] v [ ∂ N / ∂ μ ] v = f ( r ) S

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: (6)   s x + ( r ) = [ q x ( N + 1 ) − q x ( N ) ] S s x − ( r ) = [ q x ( N ) − q x ( N − 1 ) ] S s x 0 ( r ) = S [ q x ( N + 1 ) − q x ( N − 1 ) ] / 2

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]; (d) incorporation of Becke’s 1988 exchange functional (B) [46] with Perdew’s correlation functional (P86) (BP86); (e) B along with LYP (BLYP) [46,43]. The standard double-ζ plus polarization (DZP) basis set augmented with diffuse functions (DZP++) were utilized. The basis set for bromine was comprised of Ahlrichs’ standard doublẹ-spd set plus a set of d-type polarization functions [α_d (Br) = 0.389] [47] plus diffuse functions [α_s (Br) = 0.0469 and α_p (Br) = 0.0465]. For oxygen and fluorine, the basis sets were composed of the standard Huzinaga-Dunning [48,49] doublẹ-ζ set plus one set of polarization functions [α_d (O) = 0.85, α_d (F) = 1.00] augmented with one set of diffuse functions [α_s (O) = 0.08227, α_p (O) = 0.06508, and α_s (F) = 0.1049, α_p (F) = 0.0826]. 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 BrO₄F/BrO₄F⁻ are also determined as the difference in total energies in the following manners:

The bond dissociation energies for the neutrals refer to the reactions: BrO 4 F → BrO 3 F + O ,   BrO 4 F → BrO 2 F + O 2 ,   BrO 4 F → BrOF + O 3 ,The bond dissociation energies for the anions refer to the reactions: BrO 4 F − → BrO 3 F − + O ,   BrO 4 F − → BrO 2 F − + O 2 ,   BrO 4 F − → BrOF − + O 3 , BrO 4 F − → BrO 3 F + O − ,   BrO 4 F − → BrO 2 F + O 2 − ,   BrO 4 F − → BrOF + O 3 −

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.

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 BrO₄F 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 ⁵A′ state (all of the five DFT methods) or ³A′ state (both BP86 and BLYP pure DFT methods) corresponds a very loose van der Waals complex between BrF…OO and O₂, possessing a binding energy of about zero and the very long Br…O (2.719–3.004 Å in ⁵A′ state and 2.618, 2.719 Å in ³A′ state) and (O)O^…O(O) (5.220–7.095 Å in ⁵A′ state, and 5.746, 6.014 Å in ³A′ state) distances (not shown). It is favorable to dissociate into BrF + 2O₂ (³Σ_g⁻) or BrF + O₂ (¹Δ_g) + O₂ (³Σ_g⁻).

The FBr…OO…OO structures in ³A′ state (a: ³A′) optimized by three hybrid DFT methods (BHLYP, B3P86 and B3LYP) and in ¹A′ (b: ¹A′) (BHLYP) or ¹A (b: ¹A) state (with the rest four DFT methods) are reported in Figure 1. The optimized geometries for both Br- and F-terminal structures, including cis- and trans- BrOO…OOF (c: ¹A and d: ¹A), and BrOO(O)…OF (e: ¹A), and those of Br-hypervalent structures, O₂Br…OOF (f: ¹A) and FBrO₃...O (g: C_3v, ³A₁) are also displayed in Figure 1. The optimized geometries for anionic BrO₄F⁻ species, including (FBr…OO)⁻…OO (aa: ⁴A′) chain, and [FBr(O₂)...OO]⁻ (ab: ²A′), (FO…BrO₃)⁻ (ac: ²A′) Br-hypervalent structures are shown in Figure 2. They may represent an important intermediate in atmospheric reactions.

The calculated energies (Table 1) show that the FBr…OO…OO structure in its ⁵A′ state or its dissociation products (FBr...OO (³A″) + O₂ (³Σ_g⁻)) lies lower than the corresponding ³A′ (a) and ¹A′ or ¹A (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: ¹A and d: ¹A) and BrOO₂…OF (e: ¹A) isomers by ca.64, 64, and 95 kcal/mol (Table 1) respectively (B3LYP). The O₂Br…OOF (f: ¹A) and FBrO₃...O (g: C_3v, ³A₁) Br-hypervalent structures lie much higher than the ⁵A′ 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 BrO₄F is a challenging target for DFT methods.

As can be seen from Figure 1, for the FBr…OO…OO structure in its ³A′ state, the covalent bond lengths are predicted to be 1.764–1.802 Å for the Br-F bond, and 1.227–1.232 Å for interim O-O and 1.216–1.219 Å for the terminal O-O bond, and the complex bond distances are 2.615–2.773 Å for Br…O, and 1.652–1.891 Å for (O)O^…O(O) with three hybrid DFT methods. At the B3LYP level, Br-F bond length, the interim O-O and terminal O-O bond lengths in the ³A′ state (a in Figure 1) are 1.802, 1.232, and 1.219 Å respectively, and Br…O or (O)O^…O(O) complex distance is 2.703 or 1.891 Å respectively. These structure parameters are similar to those of the corresponding ¹A′ state or ¹A state of (b in Figure 1), in which, the Br-F bond distance, the interim O-O and terminal O-O bond lengths (b in Figure 1) are slightly elongated (1.806, 1.239, and 1.223 Å respectively at B3LYP level), and Br…O or (O)O^…O(O) complex distance is significantly shortened (2.600 or 1.672 Å respectively). The geometric and electronic structures show that the F-Br terminal moiety connected by OO…OO chain structure in ³A′ (hybrid DFT methods) or in singlet state may be viewed as a van der Waals complex between BrF moiety and OO-OO covalent-like chain respectively. NBO analyses (B3LYP) show that the ³A′ state possesses stronger single Br-F (WBI: 0.795 vs 0.781) and double O-O (WBI: 1.462 vs 1.436 for interim O-O; 1.524 vs 1.519 for terminal O-O) bonds than the singlet state, and that the covalent OO-OO (WBI: 0.418 vs 0.717) and complex Br…O (WBI: 0.063 vs 0.089) bonds in ³A′ state are weaker than those in singlet state. Compared with the ³A″ state of FBr...OO [35], the Br-F and interim O-O bonds in ³A′ state of FBr^...OO-OO are slightly elongated by 0.01 Å, whereas Br^...O distance is significantly shorter by 0.26 Å (B3LYP), and the terminal O-O bond distance is very similar to that in free O₂ (³Σ_g⁻) (1.194–1.245 Å) [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⁻, FBrO₂/FBrO₃, 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 ⁴A′ ground state for anion (aa: ⁴A′ in Figure 2). As might be expected, this structure is more stable than other anionic BrO₄F⁻ Br-hypervalent structures (ab: ²A′ and ac: ²A′ in Figure 2) by 32 and 78 kcal/mol at B3LYP/DZP++ level. The covalent bond lengths are predicted to be 1.975–2.059 Å for the Br-F bond, and 1.284–1.302 Å for interim O-O and 1.194–1.270 Å for the terminal O-O bond, and the complex bond distances are 2.053–2.264 Å for Br…O, and 2.806–3.183 Å for (O)O^…O(O) in the ⁴A′ state of BrO₄F⁻. Comparison with the similar neutral isomer shows that there is a substantial change in geometry between neutral ³A′ state and anionic ⁴A′ state. The Br-F bond (2.013 Å at B3LYP level), the interim O-O bond (1.295 Å) and Br…O bond (2.157 Å) in anionic ⁴A′ state are analogous to those of (FBr-OO)⁻ (2.038 Å for Br-F, 1.302 Å for O-O, and 2.135 Å for Br…O) [35]; the terminal O-O bond in the ⁴A′ state of BrO₄F⁻ (1.230 Å) is similar to that of free O₂ (1.219 Å at B3LYP level) [55]; the (O)O^…O(O) distance of 2.806 Å in anionic BrO₄F⁻ is substantially longer than the corresponding (O)O^…O(O) distance (1.891 Å) in ³A′ state of neutral BrO₄F. Thus, this BrO₄F⁻ structure in ⁴A′ state could be regarded as a van der Waals complex between (FBr-OO)⁻ [35] and O₂ (³Σ_g⁻) due to suitable Br…O and (O)O…O(O) bonding distances, and the high negative charge of FBr-OO moiety (near to −1 from NBO analysis). Neither theoretical nor experimental values of BrO₄F/BrO₄F⁻ are available for comparison. For this structure in its doublet ²A′ state, the results of all five DFT methods are suspect due to the large spin contamination, with <S²> = 1.77 or 1.76.

For the cis- and trans- BrOO…OOF (c: ¹A and d: ¹A in Figure 1) structures, the bond lengths are calculated to be 1.846–2.123 Å for the Br-O bond (that in cis-form tinily shorter than in trans-like), 1.402–1.642 Å for the F-O bond, 1.401–1.987 Å for the central single O–O bond, and 1.233–1.374 Å for outer O–O bonds connected by Br and F. In the cis- BrOO…OOF, the O…OO fragment nearly in a planar, both BrO and FO bonds are almost perpendicular to this planar, however, in the trans- BrOO…OOF, the OO…OO chain nearly in a planar, the BrO and FO bonds are also almost perpendicular to this planar. At B3LYP level, both BrOO…OOF isomers nearly possess the same stability. This BrOO…OOF conformation could be viewed as a complex comprising of unstable BrOO and FOO molecules, furthermore, the DFT methods predict it thermodynamic instability with respect to dissociation into BrOO + FOO (not shown).

For the BrOO₂…OF (e: ¹A) structures, the bond lengths are calculated to be 1.768–1.792 Å for the Br-O bond, 1.345–1.408 Å for the F-O bond, 1.200–1.230 Å for the central double O–O bond and 1.573–1.946 Å, 1.7514–1.884 Å for outer single O–O bonds connected by Br and F, respectively. At B3LYP level, the Br-O (1.781 Å) or F-O (1.376 Å) bond is slightly longer than that in BrO [21] or FO [25]. Thus, this BrOO₂…OF (e: ¹A) structures could be regarded as a complex comprising of simple BrO, O₂ and FO molecules. The hybrid DFT methods predict it thermodynamic instability with respect to dissociation into BrO + O₂ + OF (not shown), whereas the pure DFT methods predict the reaction energy of about 10 (BP86) and 6 kcal/mol (BLYP) for BrOO₂…OF (e: ¹A) → BrO + O₂ + OF (not shown).

For Br-hypervalent structures: O₂Br…OOF (f: ¹A), the bond lengths are predicted to be 1.592–1.682 Å for Br-O_term (with an oxygen atom at the terminal position), 1.981–2.501 Å for Br-O_mid (with O atom at the middle position), and 1.246–1.319 Å for O-O, and 1.408–1.638 Å for F-O. The predicted Br-O_term length is comparable to that of OBrO (1.649 Å) [21], F-O or O-O bond distances are slightly shorter or longer than those in FOO (1.649 or 1.200 Å) [18]. This structure could be thought as a complex between BrO₂ and FOO. Likewise, the hybrid DFT methods predict it thermodynamic instability with respect to dissociation into BrO₂ + FOO (not shown), and the pure DFT methods predict the dissociation energy of O₂Br…OOF (f: ¹A) → BrO₂ + FOO reaction is about 2.3 (BP86) and 0.5 kcal/mol (BLYP) respectively (not shown).

For the rare Br(VII) FBrO₃...O (g: C_3v, ³A₁) complex between FBrO₃ and O atom, the bond lengths are predicted to be 1.573–1.639 Å for Br-O, 1.738–1.832 Å for Br-F, and 3.039–3.168 Å for Br…O. At B3LYP level, Br-O bond long is 1.604 Å, analogous to that in BrO₄⁻ (1.603 Å) [21] or BrO₃F₂⁻ (1.601 Å) [31], and longer than that in FBrO₃ (1.582 Å) [35], however, significantly shorter than that in BrO₃⁻ (1.648 Å) [21]. The Br-F bond length is 1.804 Å, being significantly shorter than that in BrO₃F₂⁻ (1.872 or 1.849 Å) [31], while substantially longer than that in FBrO₃ (1.708 Å) [35]. ∠FBrO and ∠OBrO angles are 101.4 and 116.2° respectively, slightly narrower than those in FBrO₃ theoretically (101.9 and 115.9) or experimentally (103.3 and 114.9°) [27]. Generally, the predicted lengths are comparable to those of FBrO₃ (C_3v) and BrO₃F₂⁻ anion [31]. The DFT methods predict the dissociation energy of FBrO₃...O (g: C_3v, ³A₁) → FBrO₃ (C_3v) + O reaction is about 1 kcal/mol (Table 1), demonstrating that this Br(VII) FBrO₃...O (g: C_3v, ³A₁) hypervalent structure is bound for dissociation to FBrO₃ and O.

The corresponding anion eventually to dissociation into FBr(O₂)⁻...OO (ab: ²A′) complex structure, Br-F and Br-O bonds are elongated to be 2.036 and 1.639 Å (B3LYP), the Br…O complex distance and O-O bond length are about 2.3 and 1.30 Å. The DFT methods predict the dissociation energy of FBr(O₂)⁻...OO (ab: ²A′) → BrF⁻ + O₂ (³Σ_g⁻) +O₂ (¹Δ_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: ⁴A′), the predictions of five different DFT methods for the dissociation energies for aa to dissociate to its components [FBr...OO⁻(²A″) + O₂, FBr...OO (³A″) + O₂⁻, or BrF⁻+ 2O₂(³Σ_g⁻)] show the same trend, i.e. the pure DFT (BP86 and BLYP) methods predict higher dissociation energies than the hybrid DFT methods, and the BHLYP result is the smallest.

For the higher-lying hypervalent anionic (FO…BrO₃)⁻ complex structure (ac: ²A′), the bond lengths are predicted to be 1.635–1.702 Å for Br-O bonds, 1.355–1.451Å for F-O bond, 1.355–1.451Å for F-O bond, and 2.568–2.774 Å for Br…O complex bond. The theoretical dissociation energies for (FO…BrO₃)⁻ → BrO₃⁻ (C_3v) + FO is in the range of 2.8–17.9 kcal/mol (Table 2). Likewise, the pure DFT methods predict higher dissociation energies, and the BHLYP result is the lowest.

Generally, the theoretical dissociation energies (D_e) for BrO₄F/BrO₄F⁻ species can be evaluated from the data in Tables 1 and 2. For the anionic BrO₄F⁻ species, 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 BrO₄F 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 BrO₄F⁻ species (vide supra), the B3LYP methods should predict reasonable dissociation energies and relative energies, however, caution is urged because of the complex of BrO₄F ternary system.

At B3LYP level, for the lowest energies species, the theoretical bond dissociation energies for neutral BrO₄F refer to the reactions: BrO₄F→ BrO_4-mF + O_m (m = 1–4). For BrO₄F → BrO₂F (³A″) [35] + O₂, the theoretical reaction energies (ca. zero) are much smaller than those of BrO₄F→ BrO₃F (¹A’) + O (range from 84 to 109 kcal/mol, about 100 kcal/mol at B3LYP level) and BrO₄F→ BrOF (¹A’) + O₃ (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…O₂…O₂ complex structure.

The most reliable B3LYP method predicts the dissociation energy (D_e) for F-Br…O₂…O₂ (⁵A′) → BrF + 2O₂ and (F-Br…O₂…O₂)⁻ (⁴A′) → BrF⁻ + 2O₂ are only 0.0 and 9.1 kcal/mol, respectively (Tables 1 and 2), suggesting a weak van der Waals interaction between the BrF or BrF⁻ and O₂ moieties.

For the anionic BrO₄F⁻ species, the D_e of BrO₄F⁻ → BrO_4-mF⁻ + O_m and BrO₄F⁻ → BrO_4-mF + O_m⁻predicted (Table 2). The bond dissociation energies for BrO₄F⁻ → BrO₂F⁻ + O₂ are smaller positive values, from 1.0 to 1.5 kcal/mol for three hybrid DFT methods and 4.4 or 4.9 kcal/mol for BP86 or BLYP (two pure DFT) methods. The D_e values predicted by BHLYP method are too low to be reliable. The D_e value of 1.4 kcal/mol predicted by B3LYP is much smaller than those of BrO₄F⁻ → BrO₃F⁻ + O (71 kcal/mol) and BrO₄F⁻ → OBrF⁻ + O₃ (60 kcal/mol).

For BrO₄F⁻ → BrO_4-mF + O_m⁻ reactions, the higher bond dissociation energies are predicted, the D_e value (58 kcal/mol) of BrO₄F⁻ → BrO₂F + O₂⁻ is also smaller than those of BrO₄F⁻ → BrO₃F + O⁻ (136 kcal/mol) and BrO₄F⁻ → OBrF + O₃⁻ (81 kcal/mol), and demonstrating that complex BrO_nF [34,35] species have higher electron affinities than the free O_m species [55]. For the challenging BrO_mF/BrO_mF⁻ (m = 1–4) species, minima on PES were found with all of DFT methods employed. However, the thermodynamic stabilities decrease with n (vide supra).

The EA_ad for FBr-O₂-O₂ (a: ³A′← aa: ⁴A′) are predicted to be 4.95 eV(BHLYP), 4.97 eV(B3P86), and 4.52 eV(B3LYP), zero-point corrected EA_ad (EA_zero) is only increased about 0.05 eV. At B3LYP level, EA_zero is 4.57 eV, larger than those of FBr-OOO [35] and FBrO [34] by about 0.1 and 1.9 eV respectively, and much smaller than those of FBr-OO by 1.3 eV (B3LYP). Those with odd n (n = 1 and 3, closed shell) have smaller EAs than those of species for the even number of n (n = 2 and 4), which are open-shell triplet state. The EA_vert values range from 2.13 to 3.55 eV. The range of VDE is from 4.49 to 4.98eV. No experimental data are available.

The harmonic vibrational frequencies and IR active intensities of BrO₄F/BrO₄F⁻ species predicted by B3LYP method are available in Tables 3 and 4. For triplet state FBr...O₂...O₂ (a) (C_s, ³A′), the calculated infrared spectrum is characterized by three strong bands around 1561 (terminal O-O symmetri stretch(s.s.)), 1440 (middle O-O s.s.), 628 cm⁻¹(F-Br s.s.), all other modes give rise to weak intensities. For singlet state FBr...OOOO (b) (C₁, ¹A), the bands of ca. 1508 (terminal O-O s.s.), 1391 (middle O-O s.s.), and 620 cm⁻¹(F-Br s.s.) possess the stronger intensities. For BrOO...OOF chain structures (c) and (d), the predicted infrared spectrum are characterized by three stronger bands around 1223, 1376 (F-connected O-O s.s.), 1107, 1276 (Br-connected O-O s.s.), and 720, 667 cm⁻¹(F-O-O bend), respectively, the rest modes yield weak intensities. For BrOO2...OF structure (e), four bands around 1209, 934, 862, and 718 cm⁻¹ exist the stronger intensities, the corresponding modes are O-O (O2) s.s., F-O s.s., Br-O s.s., and O...O stretch.

For O₂Br...OOF structure (f), four bands around 1529, 1055, 732, and 618 cm⁻¹ possess the stronger intensities, the corresponding modes are O-O stretch, OBrO asymmetric bend, OBrO symmetric bend, and FOO bend. For the highest symmetric Br(VII) FBrO₃...O (g), theoretical infrared spectrum are characterized by the stronger bands around θ: 955 cm⁻¹ (BrO₃ asymmetric stretch (a.s.)); η: 864 cm⁻¹ (BrO₃ symm.bend); ζ: 567 cm⁻¹(F-Br s.s.); ɛ: 364 cm⁻¹(OBrO in the planar bend); δ: 345 cm⁻¹ (OBrO out of planar bend), the harmonic vibrational frequencies of BrO₃ radical are larger than the corresponding BrO₃⁺ [32] (966, 850, 329, and 231 cm⁻¹). For anionic quartet state FBr...OO...OO (aa) (C_s, ⁴A′) species, four bands around 1532, 1226, 383, and 227 cm⁻¹ possess the stronger intensities. For anionic hypervalency structure [FO...Br(O)O₂] ⁻ (ac) (C_s, ²A′), four bands around 957, 812, 805, 789 cm⁻¹ possess the stronger intensities.

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 O₂Br…OOF (f), and 116 kcal mol⁻¹ for FBrO₃…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 BrO₄F structures (a, b, c, d, e, f, and g isomers) with five DFT methods are shown in Tables 7 and 8 respectively. The local softness (S_x⁺ and S_x⁻), and ratios of them (S_x⁻/S_x⁺) for the minimum BrO₄F 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) FBrO₃…O in this work has the largest global hardness (Table 7), and smallest global softness (Table 8), thus triplet state FBrO₃…O structure is the most stable isomer. For BrO₄F 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) FBrO₃...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.

The structures, electron affinities and bond dissociation energies of BrO₄F/BrO₄F⁻ 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 BrO₄F. 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 BrO₄F/BrO₄F dissociation reactions and relative energies from two pure DFT methods, demonstrating that this system is a challenge for DFT methods.

Although the FBr-O₂-O₂/(FBr-O₂-O₂)⁻ 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 O₂ or O₂⁻ as starting materials. According recently report on bromine (VII) BrO₃F₂⁻ anion [31], we conclude that the Br(VII) structure, FBrO₃...O (g: C_3v, ³A₁) are the most likely structure for neutral BrO₄F, and the BrO₄F⁻ may have Br(V) (FO…BrO₃)⁻ (ac: ²A′) 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 BrO₄F Lewis system.