Quantum chemical calculations of anion complex [B12Hx(NF2)12-x]2-, x = 9 – 12

The geometric, energetic, spectral and electronic properties of various isomers of B12Hх(NF2)12-х2− anion complex with x = 9 − 12 have been studied using Density Functional Theory (B3LYP/6-311++G**). It was shown that the most stable isomers are characterized by the preference to form the most symmetric structures with uniformly distributed charge densities. However, when replacing a hydrogen atom with difluoramino group, an inductive effect occurs. NF2 group pulls a part of electron density that leads to the polarization of the boron core. Blue shifts in the IR spectrum compared to the vibrations of the free radical NF2 ranging from 5 to 69 cm−1 for the most stable isomers with the minimum total energy are characteristic and points to the stability of B12Hх(NF2)12-х2− anions. The obtained results broaden the idea of aromaticity of B12H122− anion and will be useful in synthesis of new B12H122− derivatives.


Introduction
There are currently synthesized and investigated hundreds of compounds of dodecahydro-closododecaborate anions (B 12 Table), onium (alkyl-ammonium, -sulfonium, -phosphonium), and complex (transition metals with various organic ligands) cations [1][2][3][4]. The elemental composition of B 12 H 12 2− holds some promise for the preparation of compounds that can be used as energy-intensive components of energy-saturated materials for various purposes. However, because of the superior stability of the B 12 H 12 2− anion, the vast majority of its compounds are difficult to ignite and burn poorly because of the formation of boronoxycompounds on the surface of the burning particle melt. This fact does not allow the realization of the high energy intensity of these compounds. One of the ways to overcome this drawback is to incorporate the anions in mixed formulations with ultrafine polytetrafluoroethylene (UPTFE) [5]. Replacing the oxygen-containing oxidant (fully or partially) to UPTFE improves combustion of the borohydride fragment because the burning surface is constantly renewed by release of volatile boron trifluoride BF 3 or boron oxofluoride (BOF) 3 . In pure oxygen systems, boron release in the form of a boron oxide melt creates a protective film on the burning surface.
One of the most important features of the B 12 H 12 2− anion is its aromaticity, i.e. the ability to replace the terminal hydrogen atoms with other atoms or groups of atoms without destroying the core. Therefore, another possible method of improving the flammability of the boron anion may be the introduction of fluorinated groups to the exo-environment of B 12  Of particular fundamental and practical interest is the investigation of B 12 H 12 2− derivativesstructures with the hydrogen atoms replaced with other atoms or groups [1][2][3][4][5][6][7][8][9]. Previous quantum chemical calculations showed that the replacement of some hydrogen atoms in B 12 H 12 2− anion structure by fluoromethyl groups leads to the existence of stable anions [10]. Known is a number of nitrogen-substituted derivatives of В 12 Н 12 2− , for example, В 12 Н 11 NO 2− , В 12 Н 11 NH 3 − , В 12 Н 10 (NH 3 ) 2 , etc. [11]. Of particular theoretical interest is the substitution of oxygen and hydrogen atoms associated with a nitrogen atom to fluorine atoms. Nitrogen-fluorinated derivatives of В 12 Н 12 2− anion can be practically valuable as a power-consuming fuel, the combustion of which will lead to the release of boron in the form of volatile fluorides. In this case the amount of combustion gas can be increased by 25% in comparison with carbon-fluorinated derivatives since nitrogen will be evolved in a gas form.
The aim of the present work is to characterize the stability and some physico-chemical properties of the anion complex B 12 H х (NF 2 ) 12-х 2− (x = 9 -12) with the use of quantum-chemical calculations.

Computational Details
All the calculations were carried out within the GAMESS-US package [12] using the hybrid functional B3LYP [13,14] and the split-valence basis set 6-311++G** with diffuse and polarization functions. The choice of this computational method is based on the available literature data and our personal results. On the figure 2 we illustrated some of the results obtained with the use of various methods and split-valence basis sets. From these data it is well seen that even with the parallel computing, the computation time significantly increases with the addition of diffuse and polarization functions. But as far as we deal with the dodecahydro-closo-dodecaborate anion B 12 H 12 2− and its derivatives, the addition of diffuse functions is necessary for the correct description of the ionic nature, and the addition of polarization functions is important for the correct modeling of chemical bonds. Also, the calculated frequencies of the free radical NF 2 are in a better agreement with the known experimental value of ~1075 cm −1 [15] when using DFT method of calculations. Furthermore, B3LYP/6-311++G** shows a good correlation between accuracy and computational time.
The initial geometry of the B 12 H 12 2− structure was formed with I h symmetry. Further optimization of B 12 H 12 2− and B 12 H х (NF 2 ) 12-х 2− (х = 9 − 12) was executed without symmetry constraints. Anion structures with substituted difluoramino groups B 12 H х (NF 2 ) 12-х 2− , (х = 9 − 12) were formed by replacing of one to three hydrogen atoms with the appropriate number of NF 2 groups. To find the most stable structures, we compared total energies of all possible isomers of the given size. Harmonic vibrational frequency analysis was used to confirm the true local minima of the potential energy surface. If no imaginary frequencies were found, the structure was considered to be a global minimum. All energies were corrected by their zero-point energies (ZPE), and scaled by a factor of 0.9877 [16]. Bond orders between atoms and valence electron configurations were computed using Natural Bond Orbital (NBO) analysis [17].

X = 12.
Before studying the anion structures with substituted difluoramino groups, it was necessary to analyse the electronic and geometric structure of the initial B 12 H 12 2− anion. To be sure that the singlet is the most energetically stable structure, we also computed the B 12 H 12 2− cluster in the triplet state. The results of the calculations confirmed the 0.2 eV preference in energy of the singlet over the triplet, so the singlet anion structures will be considered in further discussion.
In the initial B 12  2− anion reveals that the oscillation near 2490 cm −1 is characteristic of the nearly isolated B-H stretch. These given geometric and spectroscopic parameters are in a good agreement with the known experimental and theoretical results [3,4,6,8,11,18,19].
The calculated Mulliken charges of the boron and hydrogen atoms are listed in table 1. As seen, in the initial B 12 H 12 2− anion the charge is uniformly distributed in the core: boron atoms are positively charged, whereas negative charge is distributed over the hydrogen atoms. According to the NBO analysis, the valence electron configuration of B and H is: 2s 0.65 2p 2.50 3p 0.02 and 1s 0.99 , respectively.

X = 11.
The B 12 H 11 NF 2 2− anion structure, shown in figure 3a have been found by replacing of one hydrogen atom of the optimized B 12 H 12 2− structure by difluoramino group. The anion structure with one NF 2 group is seen to have decreased B-B and B-H bond distances near the B atom related to the NF 2 group, when compared to the initial B 12 (table 2).
In any case, when replacing a hydrogen atom with an electron-withdrawing difluoramino group, an inductive effect occurs due to the transfer of electron density from the boron core. As a result, the charge on the boron atom related to the substituted NF 2 group (В7, figure 3a) and on the neighboring to the B7 boron atoms (connected by a common edge, i.e. B3, B4, B8, B11 and B6) increases. At the

X = 10.
To find the most stable anion structures with two or three substituted difluoramino groups of B 12 H х (NF 2 ) 12-х 2− , various isomers fully optimized without symmetry constraint were obtained. Some of the results are summarized in tables 2, 3 and the energetically most favourable structures are shown in figure 3. By analogy with the disubstituted benzenes, the following prefixes indicating the positions of the substituent can be used: ortho-, meta-, para-. Thus, the position of NF 2 groups substituted on the adjacent boron atoms (connected by a common edge, e.g. B7 and B8) will be called ortho-, the position with NF 2 groups substituted on the boron atoms separated by one or two boron atoms of the same plane (not connected by an edge, e.g. B7 and B2) -meta-, and the position with NF 2 groups that are substituted at a maximum distance from each other (e.g. B7 and B1) -para-position.
The calculated features of the possible isomers of B 12 H х (NF 2 ) 12х 2− with х = 9, 10 show a large influence of the position of NF 2 groups. As seen from the figure 3, where the most stable isomers of B 12 H х (NF 2 ) 12х 2− with х = 9 − 11 are shown, para-position with NF 2 groups substituted on hydrogen atoms bonded to B7 and B1, is the most favourable one (table 3). The energy preference of this position over ortho-and meta-positions is 0.27 and 0.16 eV, respectively. A broader range of B-B and B-H bond lengths in the B 12 H 10 (NF 2 ) 2 2− anion is observed when compared to the structure with one NF 2 group (x = 11). Thus, substitution of hydrogen atoms by NF 2 groups leads to the increase of the charge on the boron atoms conjugated with nitrogen atoms of difluoramino groups (table 1) and polarization of the boron atoms of the core. For the most stable isomers 1 and 2-1 the total charges on NF 2 groups are equal to -0.588 and -0.644 e (the average value), respectively. For other possible isomers of B 12 H х (NF 2 ) 12х 2− with x = 10 the total charges on NF 2 groups are equal −0.642 e for metaand −0.575 e for ortho-positions. As seen from the table 3, for the most stable isomer 2-1 the dipole moment is equal to 0.00 D while for others (less symmetric structures) the dipole moment is much higher. The difference in values of the dipole moments is the greater, the greater the difference in energies among the energetically most favorable isomer with the energy taken as a zero, and other isomers. Table 3. Calculated relative energies (∆E), dipole moments (d), IR frequencies (ν(NF 2 )) and frequency shifts (∆ν(NF 2 )) of B 12 H х (NF 2 ) 12х 2− structures, х = 9 -11.

Label
Atom

X = 9.
As the number of NF 2 groups increases the substituted groups prefer to occupy positions such that the electron density in the core is most uniformly distributed. This corresponds to the symmetrical arrangement of NF 2 groups on the vertices of the core. Among all the isomers that meet this condition, 3-6 isomer with three substituted NF 2 groups bonded to B10, B7 and B5 shown on the figure 3c has the lowest total energy. Behaviour similar to the above-mentioned features was observed for this B 12 H 10 (NF 2 ) 3 2− structure. Boron atoms related to the NF 2 group, and especially NF 2 groups itself, pull a part of electron density from the boron core. As a result, an excess positive charge appears around the boron atom related to the NF 2 group. The diagonally arranged boron atoms B3 and B9 have a negative charge that, presumably, partly compensate the large positive charge. The total charges on the NF 2 groups decrease with the increasing number of NF 2 groups and are equal to −0.588 e for the anion structure with x = 11 and −0.594 e for x = 9. The electron configuration of the most stable 3-6 isomer according to the results of NBO analysis can be described as following: B 2s 0.67 2p 2.48 3p 0.02 , B* 2s 0.57 2p 2.21 3p 0.04 , B** 2s 0.57 2p 2.21 3s 0.01 3p 0.03 , H 1s 0.95 , N 2s 1.52 2p 3.32 3p 0.02 3d 0.01 , F 2s 1.90 2p 5.39 , where B* indicates the B5, B10 and B** -B7. In comparison with the electron configuration of the most stable structure of B 12 H х (NF 2 ) 12-х 2− with the larger x, there is a tendency of increasing electrons on 2s orbitals and decreasing of electrons on 2p orbitals of B atoms, wherein hydrogen atoms donate electrons, that reflects in the decreasing of electrons on its 1s orbitals.
Changes in the electron structure of B 12 H х (NF 2 ) 12-х 2− reflect in the changes of its geometry. Thus, substitution of one or more hydrogen atoms with the appropriate number of NF 2 groups leads to the weakening of the bonds in the core, and the formation of strong ionic bond B-NF 2 . This is indicated by the calculated bond distances and bond orders. With the increasing number of NF 2 groups bond length between the boron atoms of the core is increased, the length of the B-H, B-N and N-F decreases; and, on the contrary, the order of the B-B bond decreases, B-N and B-F -increases. These changes indicate to the better binding of NF 2 groups with the core for B 12 H х (NF 2 ) 12-х 2− with x = 9 in comparison with the anion structures with x = 10 and 11.
In the infrared spectra of B 12 H х (NF 2 ) 12-х 2− with х = 9 − 11 the most intense bands appear in the 1076 − 1156 cm −1 region and are assigned to the vibrations of the difluoramino group. The calculated shifts compared to the vibrations of the free radical NF 2 are accompanied with the structural changes of B 12 H х (NF 2 ) 12 are characteristic for the most stable isomers with the minimum total energy, namely, 1, 2-1 and 3-6 isomer, and points to a stronger bonding between NF 2 and the core. For x = 9 four isomers with blue shifts are observed but as it is seen from the table 3, the most stable isomer 3-6 is characterized by the greater values of ν(NF 2 ). The smaller values of frequency shifts and red shifts are typical for the less stable structures.

Conclusions
Within the present study, we examined the geometric, energetic, spectral and electronic features of the dodecahydro-closo-dodecaborate anion B 12 H 12 2− and its difluoramino-substituted derivatives. The results of quantum chemical calculations of the most stable isomers of B 12 H x (NF 2 ) 12-x 2− (х = 9 − 12) at the B3LYP/6-311++G** level of theory showed that as the number of NF 2 groups increases, they preferentially occupy symmetrical positions relatively to the core, such that the charge density in the complex achieves the most uniform distribution. The details of such distribution and the stability of the anion complex B 12 H х (NF 2 ) 12-х 2− (x = 9 -12) have been discussed. We hope that these results will aid in the investigation of B 12 H 12 2− derivatives and will broaden the idea of one of the most important features of B 12 H 12 2− anion -its aromaticity.