Homolytic C-NO2 Bond Cleavage in Diaminodinitroethylene Isomers-A DFT Treatment

Diaminodinitroethylene (DADNE) has three isomers including the well known geminal isomer, FOX-7. In the present study, the homolytic cleavage of one of the C-NO2 bonds of these isomers has been considered within the constraints of density functional theory at the level of UB3LYP/6-311++G(d,p). Transition states for that type of bond rupture are obtained. Various quantum chemical properties of the parent compounds and the decomposed systems are obtained, compared and discussed. Also the activation energies are calculated. The transition state originating from cis DADNE and the one from the geminal DADNE are found to be the most and least stable ones, respectively among the all.


Introduction
Diaminodinitroethylene possesses three structural isomers. One of them, the geminal one, is well known FOX-7 [1]. The others are cis-and trans-isomers. FOX-7, 1,1diamino-2,2-dinitroethylene, is also known as DADNE or DADE. The FOI (Swedish Defense Research Agency) members synthesized it in 1998 [2,3] and its explosive potential was thoroughly investigated [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Its synthesis was also achieved by the nitration of 4,6-dihydroxy-2-methylpyrimidine and followed by hydrolysis [19]. 116 NO 2 NO 2 H 2 N H 2 N FOX-7 is a novel high-energy insensitive material having good thermal stability and low sensitivity. Albeit the fact that no structural resemblance exists among FOX-7, RDX and HMX they have the same C/H/N/O ratio but FOX-7 is much less sensitive than RDX (in terms of impact, friction, and electrostatic discharge sensitivities [20]). It exhibits excellent application performance in the field of insensitive ammunitions (IM) and solid propellants. FOX-7 shows abundant and surprising chemical reactivity although its molecular composition and structure is simple [21,22]. It is due to the amino and nitro groups (push-pull groups) it has. FOX-7 has many polymorphic forms. Of those, the α-form reversibly turns into β-form by heat treatment [23,24]. However, at higher temperatures, β-polymorph undergoes an irreversible conversion to γ-phase which undergoes decomposition at 504 K [23]. Its decomposition pathway has been extensively investigated [25]. Also the effect of high pressure on the crystal structure of FOX-7 has been searched [26]. FOX-7 is an attractive ingredient. It also possesses the ability of increasing the burning rate in propellants, thus it is of interest for high performance propellants [1]. In order to obtain a reduced or minimum smoke producing composite propellant with inherent IM-properties many FOX-7 based propellant formulations have been studied [27].
Thermo chemical calculations have indicated that PBX's based on FOX-7 and energetic binders could serve as a replacement of Comp-B even at rather low solid loadings. A plastic bound explosive based on FOX-7 and an energetic binder have been prepared, [28].
On the other hand, the effects of nitration and epoxidation on ballistic properties of FOX-7 were also investigated within the restrictions of density functional theory (DFT) [29]. Also, some ground state properties of FOX-7 were calculated based on B3LYP/aug-cc-pVDZ predictions [30]. The other isomers of DADNE are not as famous as FOX-7. In order to achieve the direct optical ignition of an insensitive explosive, laser ignitibility of FOX-7 was investigated [31]. Recently, some novel derivatives of FOX-7 (geminal DADNE) and their properties as energetic materials have been reported [32,33]. In the present study, homolytic C-NO 2 bond cleavage in DADNE isomers have been investigated within the constraints of density functional theory (DFT).

Method of Calculation
Structure optimizations leading to energy minima were initially achieved by using MM2 method which was followed by semi-empirical PM3 self-consistent fields molecular orbital (SCF MO) method [34,35] at the restricted level [36,37]. Subsequent optimizations were achieved at Hartree-Fock level by using various basis sets. Then, the optimizations were managed within the framework of density functional theory (DFT) using UB3LYP functional [38,39] at the level of 6-311++G(d,p). 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 [39,40]. The correlation term of B3LYP consists of the Vosko, Wilk, Nusair (VWN3) local correlation functional [41] and Lee, Yang, Parr (LYP) correlation correction functional [42]. The present vibrational analyses have been also done at the same level of calculations which had been performed for the optimizations. The total electronic energies (E) are corrected for the zero point vibrational energy (ZPE) to yield E c values. To minimize the basis set superposition error a rather high level basis set has been employed. 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. Whereas in each case the IR spectrum shows a single imaginary frequency for the transition state structure. All these calculations were done by using the Spartan 06 package program [43].

Results and Discussion
Fox-7 is a push-pull type structure. The amino groups present in its structure are capable of donating electrons whereas the nitro groups act as acceptors. In the cis and trans DADNE isomers this effect might be in varying extents. Note that the presently considered DADNE isomers are all isoconjugate with some even alternant hydrocarbon 118 anions [44][45][46]. This phenomenon is discussed in the literature that non-Kekulé alternant hydrocarbon isoconjugates may engender explosive materials when are subjected to suitable carbon-heteroatom perturbations [47]. Fox-7, the geminal DADNE isomer, is a non-Kekulé system having n*=7 and n ͦ =3 positions whereas the cis and trans isomers have n*= n ͦ =5, thus they are isoconjugate with Kekulé systems (anions) (see refs. 44 and 45 for details of Kekulé and non-Kekulé systems). So, they are not expected, as a first approximation, to be explosive systems. However, they are worth investigating at the molecular level for mare scientific interest.
On the other hand, the initial step in thermal decomposition of nitro compounds is often the rupture of C-NO 2 or N-NO 2 bond [48]. The C-NH 2 bond is known to have a very high bond dissociation energy [49]. Therefore, in the present study only the homolytic C-NO 2 bond cleavage of DADNE isomers are considered. Figure 1 shows the optimized structures of DADNE isomers (parents) as well as the composite systems (daughters) obtained from them after the homolytic bond dissociation has occurred. The does not preserve the cis configuration (see Figure 1 for the amino groups). When the double bond of parent structure is initially locked in the cis configuration the program yields cis B transition state structure.     Figure 4 shows the electrostatic potential (ESP) charges on the atoms of the transition state structures 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 [43].
The figure indicates that the NO 2 moiety in each case possesses some negative partial charge that is -0.353, -0.063, 0.063, -0.163 esu for the cases originated from geminal, cis A , cis B and trans isomers, respectively. The charge on the carbon atom from where NO 2 moiety is lost has the charge of -0.396, -0.598 and -0.420 esu, respectively for the isomers having the above mentioned sequence. Note that while a transition state progresses, some electron population can be conveyed from some other part of the molecule to the carbon atom at the terminus of the broken bond.  which lists Mulliken bond orders and bond lengths. A careful inspection of Figures 1-5 indicates that in the case of transition state geometry, called cis A form, it is actually trans (in terms of amino groups) in spite of the fact that the parent structure was cis. In other words while the cis structure approaches the transition state as C-NO 2 bond homolytically cleaves (whatever the mechanism is) the structure turns about C1-C2 bond and owes the trans geometry. The Mulliken analysis shows that C1C2 bond is single in cis A structure but delocalized in the cases of cis B and trans forms.   In each route, first vinylic type radical forms. In route I donation of electrons by the amino group, should form a radical anion but the electron pair of the anion and electron of the radical occupy different orbitals of the terminal carbon atom. Whereas in route II the electron pair and radical are on different carbons. Note that the anion formed in II is much better stabilized than the anion of route I because it is delocalized over a much larger space including the nitro group. Route III is less likely because it possesses three unpaired electrons. Note that electrons on the carbon atom of the reaction terminus occupy orthogonal orbitals, thus the initial vinylic radical does not gain extra stabilization by undergoing homolytic bond cleavage of the carbon-carbon double bond. Thus routes I and more likely route II result carbon-carbon single bond which allows rotation of the groups about it to access the trans orientation. Table 3 shows the total electronic energy (E), zero point vibrational energy (ZPE) and the corrected total electronic energy (E c ) of the present parent structures. The order of E C values is geminal < trans < cis. Note that the stability order is the reverse. These orders have to be dictated by the push-pull effects of the amino and nitro groups at different locations and different extents.   Figure 6 displays distribution of some of the molecular orbital energies of the transition Figure 6. Some of the molecular orbital energies of the transition states considered.
states considered. Whereas Table 5 shows the HOMO, LUMO energies and the interfrontier molecular orbital energy gaps (∆ε) of the parent and daughter systems.  Energies in kJ/mol. In each row the first and second entries stand for the parent and daughter, respectively. Figure 7 shows the HOMO and LUMO patterns of the transition states considered.
As seen in the figure, in the case of geminal and trans transition structures the NH 2 groups either contribute little or nil into the HOMO because the overall electron pull effect should have been decreased due to the absence of departing NO 2 moiety. It is known that in general electron donors raise up the frontier molecular orbital energies and electron acceptors lower them. The overall electron pull-push effect is mainly dictated by the orientation of the groups and the conjugative possibilities. All these effects dictate the molecular orbital energies as well as shape the HOMO and LUMO patters.   Table 6 shows the activation energies of the homolytic dissociations considered. Table 7 the ∆G ͦ ≠ values of the considered transition states are displayed.  Namely, the homolytic cleavage of C-NO 2 bonds of the parents follow the order of cis > trans > geminal. Obviously, this order should be dictated by various configurational, conformational factors and charge and bond dipole effects in these isomeric structures.

Conclusion
Within the restrictions of density functional theory at the level of UB3LYP/6-311++G(d,p), the present investigation of the homolytic C-NO 2 bond cleavage of DADNE isomers has revealed that cis DADNE is the most, whereas the geminal one is the least susceptible parent structures. The transition state search for cis DADNE yields an unexpected configuration in which the amino groups occupy trans orientation. A plausible mechanisms has been suggested to explain the rotation about the carbon-carbon bond to generate trans configuration of the transition state structure. When the cis geometry of the parent compound is fixed, a transition state structure having the cis configuration is obtained which is electronically the most stable transition state whereas the geminal one (from FOX-7) has the least stable transition state (the most energetic). It requires the greatest activation energy among the isomers to undergo the homolytic C-NO 2 bond rupture.