Compatibility of Diborane and Borane with FOX-7-A DFT Treatment

FOX-7 as an energetic material is getting more and more popular as the constituents of various ammunitions. On the other hand, boronic species attract attention as fuels in rocket engineering. The present study, within the constraints of density functional theory, considers some composites of them, that is FOX-7+B2H6, FOX-7+2BH3 and FOX7+BH3. The calculations at the B3LYP/6-311++G(d,p) level indicate that all the components are structurally stable in the composites although they interact with each other electronically. Various quantum chemical and QSAR data are obtained and discussed.


Introduction
Diborane is an interesting compound having the formula of B 2 H 6 in which two threecentered bonds exist [1]. It is a gas (m.p. −165.5°C, b.p. −92.5°C) and stable up to 100°C [2,3]. All the evidence indicates that it is a diamagnetic material hence the molecule contains no unpaired electrons. The molecule is electron deficient, reacts with ammonia and certain amines and hydrazine [2][3][4][5]. In its structure each boron atom is tetrahedrally hybridized [6][7][8].
Diborane is used as a reducing agent, as a rubber vulcanizer, as a catalyst for hydrocarbon polymerization, as a flame-speed accelerator, and as a doping agent. It is also used in electronics to impart electrical properties in pure crystals [4][5][6]13]. During 1950s, a considerable effort was expended in the search for diborane and organoboranes that could serve as efficient and easy-to-handle high-energy rocket propellants [14][15][16][17][18].

Method of Calculation
In the present study, the initial structural optimizations of all the structures leading to energy minima have been achieved by using MM2 method followed by semi-empirical PM3 self-consistent fields molecular orbital (SCF MO) method [42,43] at the restricted level [44,45]. Subsequent optimizations were achieved at Hartree-Fock level using various basis sets. Then, the structural optimizations were managed within the framework of density functional theory (DFT) [46,47] at the level of B3LYP/6-311++G(d,p) [45,48]. The exchange term of B3LYP consists of hybrid Hartree-Fock and local spin density (LSD) exchange functions with Becke's gradient correlation to LSD exchange [47,49]. The correlation term of B3LYP consists of the Vosko, Wilk, Nusair (VWN3) local correlation functional [50] and Lee, Yang, Parr (LYP) correlation correction functional [51]. Also, the vibrational analyses have been done. The total electronic energies are corrected for the zero point vibrational energy (ZPE). The normal mode analysis for each structure yielded no imaginary frequencies for the 3N-6 vibrational degrees of freedom, where N is the number of atoms in the system. This indicates that the structure of each molecule corresponds to at least a local minimum on the potential energy surface. All these calculations were done by using the Spartan 06 package program [52].

Results and Discussion
The presently considered composites are FOX-7+B 2 H 6 , FOX-7+2BH 3 and FOX-7+BH 3 . It is to be mentioned that BH 3 is the dissociation product (at least one of them) of B 2 H 6 . It is known that both B 2 H 6 and BH 3 are electron deficient reagents [7]. On the other hand FOX-7, also known as geminal diaminodinitroethene (DADNE), is a pushpull type olefinic compound classified as insensitive high explosive.    Figure 2 shows the ESP charges on the atoms of the composites. Note that the ESP charges are obtained by the program based on a numerical method that generates charges that reproduce the electrostatic potential field from the entire wavefunction [52]. In the diborane composite, the boron atoms acquire some partial negative charges contrary to the bridge hydrogens (three-centered bond owners). In the case of FOX-7+2BH 3 , the boron atom next to the amino groups has some positive partial charge whereas the other boron atom which is next to the NO 2 group possesses negative partial charge. However, in FOX-7+BH 3 composite, the boron atom which is next to the amino groups has negative partial charge. In all the cases, the ESP charges on the respective atoms of the FOX-7 moieties are quite different from each other. These variations dictate the appearance of the electrostatic potential maps of the composites shown in Figure 3 where red/reddish and blue/ green regions stand for negative and positive potential fields, respectively. where ε HOMO and ε LUMO are the energies of the highest occupied and lowest unoccupied molecular orbitals, respectively (see below paragraphs for the ε HOMO and ε LUMO values).
The hardest and most electronegative composite is FOX-7+BH 3 . FOX-7+B 2 H 6 is harder but less electronegative than its isomeric composite.   composite is more favorable as compared to FOX-7+2BH 3 case which is entropically more favored. Energies in kJ/mol. Table 4 shows the HOMO and LUMO energies as well as the interfrontier molecular orbital energy gaps (∆ε) of the composites. The order of the HOMO energies is FOX-7+BH 3 < FOX-7+B 2 H 6 < FOX-7+2BH 3 . Whereas, the LUMO energies follow the order of FOX-7+BH 3 < FOX-7+2BH 3 < FOX-7+B 2 H 6 . As a consequence of these orders, the ∆ε values exhibit the order of FOX-7+BH 3 < FOX-7+B 2 H 6 < FOX-7+2BH 3 . Table 4 also  Figure 4 shows some of the molecular orbital energy levels of the components of the composites. As seen in Table 4 and Figure 4, the HOMO and LUMO energy orders of the    Table 5. Accordingly, the interaction between FOX-7 and B 2 H 6 seems to be almost equally HOMO B2H6 -LUMO FOX-7 and HOMO FOX-7 -LUMO B2H6 controlled. Whereas, the interaction with BH 3 seems to be mainly HOMO FOX-7 -LUMO BH3 controlled. Energies in kJ/mol. Figure 5 shows some of the molecular orbital energy levels of the composites considered. As seen in Table 4 and Figure 4 the dissociation of B 2 H 6 into BH 3 raises up the HOMO but lowers the LUMO levels of FOX-7+B 2 H 6 yielding molecular orbital energy levels of FOX-7+2BH 3 composite. Meantime ∆ε values get smaller (narrowing of the interfrontier molecular orbital energy gap). Since ∆ε value of an explosive is associated with its sensitivity to impact [53,54], FOX-7+2BH 3 composite should be more sensitive than the diborane composite. However, note that BH 3 dimerizes at atmospheric pressure to yield diborane [55][56][57]. Also it is worth mentioning that the dissociation of B 2 H 6 is not as simple as B 2 H 6 2BH 3 . Some series of interconversions of the boronic species occur [7].  Figure 5. Some of the molecular orbital energy levels of the composite species considered. Figure 6 shows the HOMO and LUMO patterns of the components of the composites. Whereas the respective patterns of the composites are shown in Figure 7.  highly affects them. Figure 8 shows the LUMO maps of the composites. A LUMO map displays the absolute value of the LUMO on the electron density surface. The blue color stands for the maximum value of the LUMO and the color red, the minimum value. Hence, a nucleophile attacks on the atom having the blue color.

Conclusion
Within the restrictions of the applied DFT methodology, the composites considered are found to be structurally stable and thermodynamically favorable although their components interact with each other. FOX-7+B 2 H 6 composite is more stable than its isomeric composite FOX-7+2BH 3 . The later composite is characterized with higher HOMO but lower LUMO energy as compared to its isomeric one. Among the all, FOX-7+2BH 3 has the smallest and FOX-7+BH 3 has the largest HOMO-LUMO energy gap. If the impact sensitivities are considered, and correlated with ∆ε values, as B 2 H 6 in the composite undergoes dissociation, increasing number of BH 3 molecules should turn the composite to be more and more sensitive to impact.