Computational study of transition states for reaction path of energetic material TKX-50

ABSTRACT Dihydroxylammonium5,5′-bistetrazole-1,1′-diolate (TKX-50) is considered as one of the new ionic energetic materials. In this study, we employed density functional theory (DFT) method to calculate the reaction path of TKX-50 and search its optimized configurations of reactants, reactant complexes (RCs), transition states (TSs), product complexes (PCs), and products. We proposed 10 simple reactions in the reaction path, and determined their transition states. Among these TSs, six of them have lower energies than those of reactants. The equilibrium constants, which indicate the limitation of reactions, were computed from the difference of Gibbs free energy with temperature change. Based on the proposed reaction path, the reaction mechanism of TKX-50 was provided.


Introduction
Recently, the energetic material is one of the hot and significant topics (Dreger and Gupta 2013;Irikura 2013;Qiu, Gong, and Xiao 2008;Simpson et al. 1997;Xiao et al. 2004). Generally, energetic materials can be divided into two types: (1) molecules, in which contain energetic groups such an -C-NO 2 , -N-NO 2 and -O-NO 2 , rely on the rapid oxidation and reduction of intramolecular oxidation and combustible elements to generate a large amount of energies; and (2) high-energy nitrogen compounds such as TKX-50, which can release a lot of energies due to the high-energy-bonds N-N, N=N and C-N. The conventional energetic materials are widely used in civilian (such as mining and building) and military fields (Badgujar et al. 2008); however, they have critical defects. For example, 1,3,5-trinitro-1,3,5-triazinane(RDX), 1,3,5,7-tetranitro-1,3,5,7-tetrazocane (HMX) and 2,4,6,8,10,4,6,8,10, have toxicity to organisms and environment and high sensitivity to external stimuli of heating, friction, and impact (Sikder and Sikder 2004). HMX and CL-20 are complicated and expensive to synthesis. What is worse, CL-20 can change some properties spontaneously (Göbel et al. 2010). Many efforts and attempts are underway to design and synthesize new energetic materials with high performance (An et al. 2014a;Bolton and Matzger 2011;Dippold and Klapötke 2013;Talawar et al. 2009). Nitrogen-rich heterocycles (such as azole-based molecules) are promising candidacies which can lead to superior energy release compared to the conventional energetic materials.
The novel design of new energetic materials has been developed rapidly (Gao and Shreeve 2011;Göbel et al. 2010Göbel et al. , 2009Klapötke and Piercey 2011;Klapötke, Piercey, and Stierstorfer 2011;Li et al. 2010;Thottempudi and Shreeve 2011) with a long conventional source in chemical science. In order to seek high performance, low cost, safe, and green energetic materials, it is necessary to design and synthesize novel compounds. Fischer et al. synthesized an energetic ionic salt, namely dihydroxylammonium5,5′-bistetrazole -1,1′-diolate (TKX-50) (Fischer et al. 2012), which is more stable than other amines and azo-compounds because of the tetrazole. The triazole contains insufficient energy as energetic material, and pentazolate is an unstable chemical. So the tetrazole and its derivatives are good choices for having high energy and kinetic stability. It is the reason that tetrazole derivatives are selected as the research object. Compared with their nonionic analogs, energetic ionic salts show more stability, lower vapor pressures, higher heat of formation and lower toxicity to environment (Chand, Parrish, and Shreeve 2013;He and Shreeve 2015;He et al. 2013;Klapötke et al. 2015;Yin, Parrish, and Shreeve 2015;Zhang et al. 2015bZhang et al. , 2015a. TKX-50 is an azole-based energetic ionic salt with high density, high energy content, and insensitivity toward external stimuli (Fischer et al. 2012). What is more, it can be synthesized in a relatively simple way with compounds of low cost and low toxicity, making it a viable alternative green energetic material.
Due to its excellent performance and widespread application prospects, TKX-50 has attracted considerable attention as a new energetic material since Fischer et al. reported it (An, et al. 2014b;An et al. 2015;Dreger, Breshike, and Gupta 2017;Golubev and Klapötke 2014;Meng et al. 2016;Sinditskii et al. 2015). Researchers (Golenko et al. 2017;Ju et al. 2015;Zhu et al. 2014) also improved the synthetic routes based on the original synthetic route, making it simpler to synthesis. Dreger et al. (Dreger, Breshike, and Gupta 2017) used Raman spectroscopy to detect the high pressure-high temperature structural and chemical stability of TKX-50 crystal. They examined two high-temperature intermediates before the melting/decomposition of TKX-50, and a suppression of hydrogen-transfer led to the significant increase in the chemical stability of TKX-50 and intermediates. An et al. (An, et al. 2014b) used density functional based tight binding calculations and molecular dynamics (DFTB-MD) simulations to explore the initial thermal decomposition steps of TKX-50 crystal, and they predicted that the release of N 2 in the initial decomposition of TKX-50 could in turn provide adequate energy for the further decomposition. Meng et al. revealed that strong hydrogen bonding in TKX-50 crystal contributed to low impact sensitivity on its shear deformation and could deteriorate its thermal stability on thermal decomposition because that they promoted H-transfer when TKX-50 crystal was heated (Meng et al. 2016).
Although many properties have been studied, there are no reports on the transition states of a series of reactions in the synthetic routes of TKX-50. Based on the synthetic routes of Ju et al. (Ju et al. 2015), we simulate the transition states of a series of reactions in this paper. The geometries, energies, and vibrational frequencies of each stationary point are presented, i.e., reactants, reactant complexes (RCs), transition states (TSs), product complexes (PCs), and products. The synthetic routes of TKX-50 are given by the following scheme in Figure 1. We also calculate equilibrium constants to reveal the extent of the reactions.

Computational Methods
All calculations were carried out using the DMol3 (Delley 1990(Delley , 2000 with density functional theory (DFT) calculations under the generalized gradient approximation (GGA)/Perdew, Burke, and Enzerhof (PBE)/ double numerical plus polarization (DPN) (Perdew, Burke, and Ernzerhof 1996). Preliminary transitionstate geometries were obtained using the integrated linear synchronous transit/quadratic synchronous transit (LST/QST) method (Halgren and Lipscomb 1977). As shown in Fig. S1 (Supporting Information), the reactants, 12 RCs (RCn, n = 1-3, 5, and 7-14), 12 PCs (PCn, n = 1-3, 5, and 7-14), and products were identified with zero imaginary frequency (number of imaginary (NIMG) = 0), and each transition state (TSm, m = 1-14) was identified with one imaginary frequency (NIMG = 1). The structures and normal modes were shown and the normal mode corresponding to the reaction coordinate was observed to be consistent with the reaction of interest. We calculated equilibrium constant (Hassan and Vinjamur 2013), K eq , by the expression where ΔG is the Gibbs free energy difference between products and reactants, R is the universal gas constant, T is the temperature in Kelvins, and ω is the degeneracy of the conformation.

Optimization of Geometry
The geometries of TKX-50 and (C 2 O 2 N 8 ) 2− and the crystal of TKX-50 are from Fischer's work (Fischer et al. 2012) (Figure 2). Results of bond lengths, bond angles and dihedral angles of TKX-50 and (C 2 O 2 N 8 ) 2− are listed in Table S1 (Supporting Information). Compared with experimental results, the calculation results of bond lengths, bond angles and dihedral angles of TKX-50 change slightly. An interesting phenomenon were observed during optimizing TKX-50. No matter how much the dihedral angle of the initial bis-tetrazole rings is given, the optimized bis-tetrazole rings of (C 2 O 2 N 8 ) 2− are nearly perpendicular, but the dihedral angle of the bis-tetrazole rings is less than 20 degrees in the structure of TKX-50 as shown Figure 2(a-b). This implies that there is strong interaction between the (NH 3 OH) + and the (C 2 O 2 N 8 ) 2− , which leads to the bis-tetrazole ring approaching coplanar. Due to the geometry optimization for individual molecules in this work, the bis-tetrazole rings are not coplanar, but there is a clear trend towards co-planarity. So our study is in agreement with the experimental data (Fischer et al. 2012) in Figure 2(c). Table S2 (Supporting Information) shows the results of bond lengths, bond angles and dihedral angles of five molecules. The structure 1,1-BTO has similar geometry as TKX-50, and the bistetrazole rings of 1.1-BTO are almost coplanar. Compared with the initial structures, the geometries of other molecules have varying degrees of change. The bond lengths decrease less than 0.3 Å, and more or less, the changes of bond angles almost are less than 5 degrees. And the changes of dihedral angles are irregular and range from 0 to 55 degrees.

Transition State
The optimized geometries of reactants, reaction complexes, transition states, product complexes, and products of the reactions from 1,1-BTO to TKX-50 are shown in Fig. S1. We attempt several routes to search for transition states of each reaction, and then the reasonable search approaches were chosen. The energy level diagrams for the aimed reactions through all 14 TSs are given in Figure 3. The energy differences of RCs, TSs, PCs, and products with reactants are listed in Table 1. For 14  (Fischer et al. 2012). Blue represents nitrogen, gray represents carbon, white represents hydrogen, and red represents oxygen atoms in the structures.
TSs, 6 TSs (TS1, TS2, TS6, TS11, TS13, and TS14) have lower energies than the reactant's energies. For the 10 reactions except the second one in the third reaction and the first one in the fourth reaction, the reactants always form a weakly bound reactant complexes (RCs) before proceeding to TSs, and then break up to form a weakly bound product complexes (PCs) before proceeding to the products (Dash and Rajakumar 2012). Therefore, they go through the following process.
Reactants ! RCs ! TSs ! PCs ! Products There are 10 reactions shown in Figure 3, and the third reaction and the fourth reaction, respectively, include three reaction channels. It is worth noted that, in the reactions from DAG to 1,1-BTO, the transition state structures cannot converge in the search processes among considerable attempts. Fortunately, we find a reasonable channel to gain the TSs (TS11 and TS12). It may be that the reaction is a self-cyclization reaction. The energy differences between the reactant complexes (RC1, RC2, RC3, RC5, RC7, RC8, RC9, RC10, RC11, RC12, RC13 and RC14) and the reactants are 231. 54, 27.62, 43.98, 0.54, 2.17, 0.04, −32.36, 11.48, 0.04, 0.24, 58.56, and 46.66 kcal·mol −1 , respectively. The energy differences between product  Here we mainly analyze the reactions from 1,1-BTO to TKX-50. This is a reaction of NH 2 OH abstracting the hydrogen atom on OH group of 1,1-BTO. Two types of attractive interactions were observed in RC13 and RC14. One of these interactions is observed to be strong between the hydrogen atom of the OH group and one of the oxygen atoms of 1,1-BTO. The other interaction is formed between the nitrogen atom in N=C and the hydrogen taken from the 1,1-BTO. On the whole, the later hydrogen bond is stronger than that of the first one, and nine-membered ring-like structures in RC13 and RC14 were formed. The stable hydrogen bond lengths of reactant complexes (RC13 and RC14) in the two small steps are 2.91 and 2.27 Å, respectively. Similar situations also appear in PC13 and PC14.
TS13 and TS14 are found to be influenced by strong hydrogen bonding in two reactions from 1,1-BTO to TKX-50. It is important to know that hydrogen bonding influences energetics. The hydrogen bonds of TS13 and TS14 are formed between the hydrogen atom of the OH group of NH 2 OH and the oxygen of bis-tetrazole, and the hydrogen bond lengths are 1.936 and 2.087 Å, respectively. Energy barriers of TS13 and TS14 are −42.59 and −30.20 kcal·mol −1 , respectively. Theoretically, the two reaction channels are same, but it is significantly observed that bis-tetrazole rotation amplitude of TS13 is stronger than TS14, in which bis-tetrazole of TS13 is almost coplanar while there is clear dihedral angle on bis-tetrazole of TS14. The reason is that there are different structures of reactants (5(1,1-BTO), and 5ʹ). The two tetrazole rings of 5(1,1-BTO) of first small step similarly contain OH group, while the two tetrazole rings of the reactant of second small step contain OH group, and O anion, respectively. There is attractive interaction between oxygen anion of (C 2 O 2 N 8 H) − and nitrogen atom of (NH 3 OH) + , which suppresses the free rotation of bis-tetrazole. The detailed results of entropy, heat capacity, enthalpy and free energy of the reaction for all reactions are given in Table 2.

Equilibrium Constants of Reaction
In this work, the equilibrium constants of reactions were calculated by Gibbs free energy in the temperature range of 250 and 400 K with an interval of 25 K. The results of equilibrium constants are shown in Table S3 (Supporting Information). At 298 K, the equilibrium constants of each reaction are 0.08889, 3.7032, 1.2831 × 10 −4 , 0.03745 and 2.8441 × 10 −19 , respectively. The equilibrium constant of the reaction of 1,1-BTO to TKX-50 is much smaller and is about magnitude of 10 −19 , which manifests the reaction is ionization for TKX-50. This is clearly consistent with the actual situation, and this reaction is an acid-base neutralization reaction. Figure 4 shows the ln(K eq ) vs 1/T plot, with the increase of 1/T, the ln(K eq ) of two reactions (glyoxal →glyoxime and glyoxime → dichloroglyoxime) gradually increases, while other reactions (dichloroglyoxime → DAG, DAG → 1,1-BTO and 1,1-BTO → TKX-50) show the opposite trend. In other words, the equilibrium constants of the first two reactions decrease with temperature increasing, but the equilibrium constants of the latter three reactions have the opposite results. What is more, only the ordinate in Figure 4(b) is positive, indicating that the equilibrium constants of other four reactions are less 1. The red points in Figure 4(b-e) are almost evenly distributed on the black fitting lines, but the red points in Figure 4(a) slightly deviate from the black fitting line. The slope of the fitting lines show the following rank order of the extent influenced by temperatures for the reactions studied glyoxime → dichloroglyoxime > 1,1-BTO → TKX-50 >DAG → 1,1-BTO > glyoxal →glyoxime > dichloroglyoxime → DAG.

Conclusions
In this paper, the transition states of reaction paths for the synthesized TKX-50 are successfully explored. By employing DFT calculations, the structures of all molecules are optimized at the PBE/ DNP level. Transition states occur between the reaction complexes and the product complexes, indicating the importance of the complex for a reaction. Due to the restriction of the spatial structures, the reactions of two small steps are not the same. The equilibrium constants of each reaction were calculated to reveal the limitation of the reaction. The equilibrium constants were obtained from the difference of Gibbs free energy with temperature increasing from 250 K to 400 K. And the results show that the equilibrium constants are slightly affected by temperatures.