1,3,5-Triamino-2,4,6-trinitrobenzene and Magnesium Interaction-A DFT Treatment

1,3,5-Triamino-2,4,6-trinitrobenzene, known as TATB, is an insensitive energetic material. On the other hand, certain metals like Al, Mg etc., are often involved in formulation of certain ammunition to increase the heat output of the composite. In the present study, the interaction of TATB and magnesium is considered in TATB+Mg and TATB+2Mg composites within the constraints of density functional theory at the level of B3LYP/6-311++G(d,p). The magnesium component disturbs TATB molecule mainly conformationally without causing any bond rupture. The composite formation is favorable, exothermic and they are electronically stable. As the magnesium content increases, the composites become more sensitive to impulse stimulus. Certain physicochemical, quantum chemical and spectral data are collected and discussed.


Introduction
For an high explosive (HE), thermal stability is of main concern regarding to the formulation, processing, and handling but also vital for its safety in the cases of fuel fires, propellant fires, and even including a potential for sympathetic detonation. It has been long known that 1,3,5-triamino-2,4,6-trinitrobenzene, abbreviated as TATB, is a reasonably powerful high explosive possessing thermal and shock stability which is considerably greater than that of any other known material of comparable energy. It is extremely insensitive to shock, vibration, fire, or impact. Because it is so difficult to detonate by accident, even under severe conditions, it has become preferred high 176 explosive for applications where extreme safety is required, such as the explosives used in nuclear weapons, where accidental detonation during an airplane crash or rocket misfiring would present extreme dangers. TATB was obtained years ago by Jacson and Wing by displacing bromines from structure of 1,3,5-tribromo-2,4,6-trinitrobenzene with cold alcoholic solution of ammonia [1,2]. The compound TATB has been known for its unusual thermal properties since the 1950s. TATB decomposes at 360ºC without melting [3]. It is a yellow-brown crystalline solid that is insoluble in most solvents. The best solvent is hot, concentrated sulfuric acid. TATB decomposes rapidly just below the melting point, however it has excellent thermal stability in the range 260-290ºC, which represents the upper temperature limit at which it may be used. In the years following II world war, research focused intensely on some high energetic materials in order to synthesize much safer and more heat resistant explosives [4]. One of the molecules fulfilling those criteria was TATB. The striking features of it is the strong and extensive hydrogen bonding (both inter-and intramolecular types) between NO 2 and NH 2 groups present [5,6]. Those electron acceptor and donor groups in the structure contribute its stability. The first important work in order to enlighten this unique stability was done in 1965 by Cady and Larson, who managed to determine the crystal structure of TATB [5]. Since then intense research has been published on TATB [7][8][9][10][11][12][13][14][15][16][17][18][19][20] which includes not only the experimental studies, but various computational work on TATB as well [21][22][23][24][25][26].
In the present work, the interaction of TATB and magnesium are investigated quantum chemically within the limitations of density functional theory (DFT) at the levels of B3LYP/6-311++G(d,p) level.

Method of Calculation
In the present study, firstly the initial structural optimizations of all the structures leading to energy minima have been achieved by using MM2 method followed by semiempirical PM3 self-consistent fields molecular orbital (SCF MO) method [27,28] at the restricted level [29,30]. The subsequent optimizations were achieved at Hartree-Fock level using various basis sets hierarchically. Then, the structural optimizations were managed within the framework of density functional theory (DFT) [31,32] at the levels of and B3LYP/6-311++G(d,p) [30,33]. 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 [32,34]. The correlation term of B3LYP consists of the Vosko, Wilk, Nusair (VWN3) local correlation functional [35] and Lee, Yang, Parr

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(LYP) correlation correction functional [36]. Additionally, 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 [37].
For NICS data, the absolute NMR shielding values [38] were calculated by employing the Gauge-Independent Atomic Orbital method [39] with the restricted closed shell formalism at the level of B3LYP/6-311++G(d,p). The NICS values were collected by calculating absolute NMR shielding values at the ring centers, NICS (0). The NICS (0) calculations of the present systems were performed by the use of the Gaussian 03 package program [40].

Results and Discussion
TATB molecule possesses structures A and B as its two resonance forms. They have aromatic benzene ring and not-aromatic hexagonal ring, respectively. In the later case the nitro and amino substituents have exocyclic carbon-nitrogen double bonds. Structure-B is an interesting, highly charge separated resonance form originated from structure-A.
Omelchenko et al., studied geometrical parameters, aromaticity, and conformational flexibility of the set of polysubstituted benzenes with different number and position of nitro and amino groups [22] and concluded that the presence of nitro and amino groups in vicinal positions formed strong intramolecular resonance-assisted hydrogen bonds. Also they studied TATB molecule, which possesses alternatingly substituted nitro and amino groups and should have strong intramolecular resonance-assisted hydrogen bonds.
In the present study, TATB+Mg and TATB+2Mg composites have been considered Lemi Türker http://www.earthlinepublishers.com 178 which have the magnesium contents of 8.6 and 15.8%, respectively. In the present treatment, they have been respectively labeled as I and II. Figure 1 shows the optimized structures as well as the direction of the dipole moments of TATB and its magnesium composites considered.      Table 1 presents some properties of the structures considered. Note that composite-II has greater dipole moment and polarizability values compared to composite-I.  Table 2 lists some energies of the composite structures considered where E, ZPE and E C stand for the total electronic energy, zero point vibrational energy and the corrected total electronic energy, respectively. The data reveal that the composites are electronically stable. Energies in kJ/mol. Table 3 tabulates some of the thermodynamic values of the composite structures considered. According to the data the composites are exothermic and their formations are favorable.  Figure 4 shows the electrostatic potential charges (ESP) on the atoms of the structure optimized composites systems considered. 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 [37]. In both of the cases the magnesium atoms possess some positive charge accumulation. The loading of the second magnesium atom causes the first one to have less positive charge as compared to the previous case. Also positive charge development of the second one is less than the first magnesium atom. Note that locations of the magnesium atoms in structure-II are next to NH 2 and NO 2 groups, respectively. Also note that the direction of the dipole moment is from somewhere around that NH 2 group to that of NO 2 group mentioned.
Appearance of the electrostatic potential maps of the systems is shown in Figure 5 where red/reddish and blue/ green regions stand for negative and positive potential fields, respectively. It gives some idea about which NH 2 group(s) donates electron population at what extents and which NO 2 group(s) accepts.  Table 4 shows the HOMO, LUMO energies and the interfrontier molecular orbital energy gap (∆ε) values of the systems considered. As seen from the table magnesium atom(s) raises both the HOMO and LUMO energy levels of composite-I as compared to TATB case. Whereas in composite-II the HOMO level raises but the LUMO lowers down in the presence of magnesium atoms as compared to TATB case. Note that composite-II has higher HOMO but lower LUMO energy level as compared to composite-I. It means that the roles of two magnesium atoms are not the same in composite-II (see Figure 6 below).
On the other hand, presence of magnesium atoms decreases the HOMO-LUMO energy gap (interfrontier molecular orbital gap) more and more as its content increases. The narrowing of interfrontier molecular orbital (FMO) gap indicates that the composite should be more sensitive to impact stimuli because ∆ε values are related to impact sensitivity in explosives [41,42]. Namely, as the FMO energy gap (Δε) becomes less and less the impact sensitivity increases more and more. Energies in kJ/mol. Figure 6 shows the HOMO and LUMO patters of the structures considered. TATB seems to have π-symmetry whereas the composites have lost it somewhat. In composite-I the magnesium atom contributes very little in to the LUMO. In composite-II one of the Mg atoms (Mg2 in the figure) does not contribute in to the HOMO whereas the other one (Mg1) contributes almost nil to the LUMO. Figure 7 shows the time-dependent density functional (TDDFT) UV-VIS spectra of the systems of present concern. The spectrum of TATB is very symmetrical having only one λ max value. The figure also indicates that incorporation of magnesium shifts the spectrum of TATB to visible region more and more as the metal content increases. It is consistent with ∆ε values in Table 4. That is as the interfrontier molecular orbital energy gap values (∆ε) decrease bathochromic effect happens more profoundingly. The magnesium atom(s) disturbs the structure of TATB mainly conformationally without causing any bond cleavage. Meantime, various chromophoric moieties having different conjugation possibilities arise. Then, various electronic transitions occur to yield more than one λ max values to appear in the spectra of the composites.  Figure 8 shows the local ionization maps of the structures considered. In the local ionization potential map conventionally red regions on the density surface indicate areas from which electron removal is relatively easy, meaning that they are subject to electrophilic attack. On the other hand, regions having blue color represent areas where ionization is relatively difficult. Note that the red region in the case of structure-II locates nearby the magnesium atom which is next to the nitro group, whereas one of the blue region coincides on one of the NH 2 groups such that both regions lie in the direction of the dipole moment vector.

NICS
A combination of various properties in cyclic delocalized systems dictates aromaticity. In general, aromaticity is discussed in terms of energetic, structural and magnetic criteria [43][44][45][46][47][48][49]. Schleyer introduced a simple and efficient probe for aromaticity that is "nucleus-independent chemical shift" (NICS) [49]. It is the computed value of the negative magnetic shielding at some selected point in space such as at a ring or cage center. The data calculated and piled in the literature indicate that negative NICS values denote aromaticity (e.g., -11.5 for benzene, -11.4 for naphthalene) whereas positive NICS values denote antiaromaticity (28.8 for cyclobutadiene) while small NICS values are indicative of non-aromaticity (-2.1 for cyclohexane, -1.1 for adamantane).

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Presently, the NICS values of TATB, TATB+Mg and TATB+2Mg are -5.9888, -5.1804 and -4.2191, respectively. According to the data aromaticity of the ring decreases as the magnesium content of the composite increases. Note that aromaticity of the ring in TATB is rather low which could be explained (in the framework of valence bond theory) by referring the contribution of resonance structure-B like, charge separated structures which perturb the ring current essential for aromaticity.

Conclusion
The present study, performed within the restrictions of density functional theory has revealed that TATB and magnesium are compatible with each other up to 15% Mg content (present domain). However, magnesium somewhat perturbs TATB molecule by transferring some electron population to the organic component, acquiring some positive charge itself. Thus some properties of TATB molecule changes. The frontier molecular orbital energy gap narrows in the composites which should cause to arise systems more susceptible to impulse stimulus compared to TATB.