Thermal decomposition mechanisms of energetic CL-20-based co-crystals: quantum molecular dynamics simulations

The decomposition mechanisms of energetic CL-20:2,4-dinitro-2,4-diazapentane (DNP) and CL-20:2,4-dinitro-2,4-diazaheptane (DNG) co-crystals at high temperatures (1000, 2000, and 3000 K) were studied by density functional tight-binding molecular dynamics (DFTB-MD) simulations. At different temperatures, their decomposition mechanisms are very different. At 1000 K, conformational changes are observed only for the CL-20:DNG co-crystal, in which the CL-20 changes from β-CL-20 to γ-CL-20. When the temperature is increased to 2000 K, CL-20, DNP, and DNG begin to decompose, and there are five paths for the main initial mechanisms. Further increasing the temperature to 3000 K promotes a more complete decomposition. The initial reactions of CL-20 in the two co-crystals have two channels. There are two initial decomposition channels in the DNP molecule and only one channel in the DNG molecule. As the temperature increases, the decomposition products of the two co-crystals are different. Our work may provide the in-depth understanding of the decomposition mechanisms of high-energy CL-20-based co-crystals at high temperatures.


Introduction
High-energy density materials (HEDMs) with high energy and low sensitivity play an important role in many fields [1][2][3][4]. In recent years, with the advancement of technology, the requirements for HEDMs have been steadily increasing. Detonation performance and sensitivity have always been two important parameters that need to be considered [5]. However, they are difficult to meet at the same time. Many studies have been devoted to searching for new HEDMs with excellent detonation performance and low sensitivity through various methods, such as changing the components of energetic materials, controlling the morphology of the materials, reducing the size of particle, and synthesizing co-crystal explosives [6][7][8][9][10][11][12]. Among them, co-crystal explosives have attracted much attention because of their better performance. Therefore, some co-crystals based on two or more explosives have been synthesized in order to reduce their sensitivity and improve their energy properties [13][14][15][16][17][18].
2,4,6,8,10,12-Hexanitrohexaazaisowurtzitane (CL-20), one of the famous explosives, has high density and high detonation properties with a cage structure and several nitro groups [19]. Nowadays, there are many researches on cocrystal explosives combined with CL-20. Bolton et al. [15] showed the co-crystals with 1,3,5,7-tetranitro1,3,5,7-tetrazocane (HMX) and found that they possess higher power and lower impact sensitivity. Yang et al. [16] prepared a cocrystal explosive of CL-20 and benzotrifuroxan (BTF) and proved that the co-crystal explosive has better detonation power than BTF. Zhu et al. [20] synthesized the co-crystal of CL-20 with 3,4-dinitropyrazole and showed that the cocrystal has less sensitive and better detonation performance. These co-crystal explosives usually have good energy and enhancing stability, and so have the potential for practical applications.
Recently, many studies have detailed the decomposition of the crystal explosives through ab initio molecular dynamics (AIMD) simulations [21][22][23][24][25][26]. For instance, Xiang et al. [27] used AIMD to study the decomposition mechanisms of the α-RDX crystal under high temperatures coupled with detonation pressures. Isayev et al. [28] researched the initial decomposition of the CL-20 crystal using AIMD and pointed out there is only one initial reaction: the rupture of the N − NO 2 bond.
On the other hand, concerning higher temperature regimes, there are few studies available on the decomposition mechanism of the co-crystal explosives at high temperatures [29,30]. A comprehensive understanding of the decomposition mechanisms at the molecular level, including initial decomposition, subsequent reactions, and decomposition products, will provide better guidance for designing and synthesizing new co-crystal explosives.
In this work, the thermal decomposition of CL-20:2,4dinitro-2,4-diazapentane (DNP) and CL-20:2,4-dinitro-2,4-diazaheptane (DNG) co-crystals at different temperatures (1000, 2000, and 3000 K) were studied by density functional tight-binding molecular dynamics (DFTB-MD) simulations with NVE ensemble. The conformational changes and decomposition mechanisms of the two cocrystals were analyzed in details. Our results may contribute to the in-depth understanding of the decomposition mechanisms of high-energy CL-20-based co-crystals at high temperatures.

Computational details
The NVE ensemble [31] combined with the first-principles London dispersion correction D3 [32] were used to perform the DFTB-MD [33][34][35] simulations, which were carried out through the CP2K package [36]. The initial structures of the CL-20:DNP and CL-20:DNG co-crystals taken from experiments [37] were optimized to get the most stable configurations. The SCC tolerance was set to 10 −5 a.u. The conjugate gradient (CG) method and limited memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) method [38] were used for geometric optimization. The optimized lattice parameters of the CL-20:DNP and CL-20:DNG co-crystals by DFTB were showed in Table 1. The calculation errors are all below 4%, indicating that these results are reasonable.
In order to avoid longer computational time and higher cost, a unit cell (8 CL-20 and 4 DNP) for the CL-20:DNP co-crystal and a 2 × 1 × 1 supercell (4 CL-20 and 4 DNG) for the CL-20:DNG co-crystal were used to simulate their decomposition, as shown in Fig. 1. Based on the optimized structures, DFTB-MD simulations were performed on the two co-crystals at high temperatures of 1000, 2000, and 3000 K, respectively. The total simulation time is 20 ps with a time step of 0.5 fs. For each co-crystal, three simulations were performed at each temperature for a total of 18 independent simulations. Table S1 of the Supporting Information lists the distance criteria for identifying small molecules during decomposition process [39][40][41][42][43]. During the simulations, all major decomposition products were present, indicating that primary and secondary chemical reactions occurred. Therefore, the decomposition mechanisms of the two cocrystals could be obtained.

Conformational change
CL-20 has five different crystalline polymorphs [44], as shown in Fig. S1 of the Supporting Information. The conformations of the CL-20 molecules in the CL-20:DNP and CL-20:DNG co-crystals are different, which will lead to different conformational changes of CL-20 at high temperatures.
At a temperature of 1000 K, there are no small molecules formed during the decomposition of the two co-crystals, only a conformational change occurs. The CL-20:DNG co-crystal underwent a conformational change, but the CL-20:DNP co-crystal did not. In the CL-20:DNP co-crystal, CL-20 presents γ form, which is more stable, so the conformation remains the γ form during 20 ps. However, in the CL-20:DNG co-crystal, all the CL-20 molecules change from β to γ and finally to ε conformation. The process of the conformation change at 1000 K was shown in Fig. 2. The optimized CL-20 molecular conformation is β form, whose stability is worse. Therefore, as the temperature rises to 1000 K, the conformation of the β-CL-20 molecules gradually becomes to the γ form at 1.5 ps. Then, they change to the ε form at 6.5 ps. Finally, at 20 ps, the β-CL-20 molecules Table 1 Experimental and calculation lattice parameters of the CL-20:DNP and CL-20:DNG co-crystals [a] The experimental values were taken from Ref. [37] [b] The values in parentheses are the relative errors between the experimental and calculation values completely transform into the γ and ε forms. The conclusion is consistent with the order of the conformational stability (ε > γ > β) [44]. Under the influence of the temperature, the CL-20 molecules change from the unstable β form to the more stable γ and ε forms.

Initial decomposition
At 2000 and 3000 K, the CL-20, DNP, and DNG molecules in the CL-20:DNP and CL-20:DNG co-crystals began to decompose. Figure 3 shows the initiation reactions of the CL-20, DNP, and DNG molecules. At 2000 K, the N − NO 2 bond in the five-member ring of the CL-20 molecule broke to release NO 2 in the CL-20:DNP co-crystal at 2.44 ps, whose bond length increases from 1.546 to 1.786 Å, as shown in Fig. 3a. At 5.38 ps, the N − NO 2 bond in the sixmember ring of the CL-20 molecule opened, whose bond length increases from 1.683 to 1.724 Å, as shown in Fig. 3b. The decomposition of DNP is much later than that of CL-20. At 14.11 ps, the C − N bond of DNP opened to form two small molecules and its bond length increases to 1.801 Å, as shown in Fig. 3c. The main product of the C − N bond breakage in DNP is CH 3 N(NO 2 )CH 2 , which immediately decomposed into NO 2 . When the temperature rises to 3000 K, the initial decomposition path of CL-20 is the same as that at 2000 K, but occurred earlier. The release time of the nitro groups in the five-member and six-member rings is about 0.5 ps. In all, increasing the temperature will promote the decomposition of CL-20, and the initial decomposition of DNP is the cleavage of N − NO 2 by releasing the nitro group. In the CL-20:DNG co-crystal, the decomposition of CL-20 at 2000 K was triggered by the cleavage of the N − NO 2 bonds in the five-member and six-member rings at 2.5 ps to form NO 2 . When the time reaches 6.56 ps, the DNG molecule began to decompose. The initial decomposition path of DNG is the N − NO 2 bond breaking to produce NO 2 . The N − NO 2 bond length increases from 1.430 to 1.962 Å, as seen in Fig. 3e. At 3000 K, the initial decomposition path is the same as that at 2000 K, but occurred earlier. The decomposition of CL-20 and DNG occurred at about 0.5 and 2.5 ps, respectively.
In summary, there are five initial decomposition paths of CL-20 in the two co-crystals, including the rupture of the N − NO 2 bond of the five-member and six-member rings in CL-20, consistent with experimental speculation and theoretical calculated results [28,45], and increasing the temperature can promote the decomposition. The initial decomposition reaction of DNP is the C − N bond and N − NO 2 bond cleavage, while that of DNG is only the N − NO 2 bond cleavage. Therefore, different temperatures could affect the initial decomposition mechanism of DNP.
The bond dissociation energies (BDEs) of the initial reactions were calculated by DFT. As shown in Fig. 4, the BDE of the N − NO 2 bond is 149.05 kJ/mol −1 in the five-member ring and 173.78 kJ/mol −1 in the six-member ring. This is why the N − NO 2 bond in the five-member ring decomposes first, which is in agreement with the previous report [28]. The BDE of the N − NO 2 bond is 178.88 kJ/mol −1 in DNP and 190.67 kJ/mol −1 in DNG, both higher than that in CL-20. So CL-20 first decomposes during the decomposition of the two co-crystals. It is worth noting that the BDE of the C − N bond in DNP is much higher, but it only decomposes first at 2000 K. This may be affected by the temperature and surrounding molecules.

Subsequent decomposition
The detailed subsequent decomposition process of CL-20 in the two co-crystals after two initiation reactions were shown in Fig. 5. After the decomposition of CL-20 was triggered by two different initial decomposition reactions, the cage-opening reactions of CL-20 have four paths. It can be seen from  decomposition of CL-20 is the cage opening by the cleavage of two C − N bonds to form a five-member ring. Int2 was formed by the N − NO 2 breaking in the six-member ring, and then, they mainly decomposed in two paths: (a) through the cleavage of a C − C bond, the cage was broken to form Int2-1, which opened the tricycle by the two C − N bonds cleavage and (b) Int2-2 was produced by the cleavage of N − NO 2 and C − C bonds. Then, it further decomposed by the C − N and C − C bonds cleavage. This is a step for producing seven-and nine-member heterocycles, which have also been reported in previous research [28].
Above all, these decomposition pathways mainly involve the cage opening of CL-20 in the CL-20-based co-crystals and CL-20 decomposed more thoroughly at high temperature. The decomposition mechanism of CL-20 in the two co-crystals is consistent with previous studies [46].
Meanwhile, subsequent decomposition processes of DNP and DNG in the two CL-20 co-crystals are shown in Fig. 6.
It is found that the DNP molecules have two decomposition channels: C − N bond cleavage and N − NO 2 bond breakage. Also, there are cleavage of C − N bonds to form small radicals C 2 H 5 N, CH 3 N 2 O 2 , and NO 2 . In addition, the decomposition mechanism of the DNG molecule is roughly the same as that of the DNP molecule. DNG began to decompose by the N − NO 2 bond cleavage. After that, the C − N bonds also broke to form small segments. These decomposition substances are all highly reactive intermediates. They easily reacted with the decomposition species of CL-20 in the two co-crystals.

Decomposition products
The time evolution of the number of CL-20, DNP, DNG, and main decomposition species in the two co-crystals at 2000 and 3000 K were presented in Fig. 7. As shown in Fig. 7a, both the CL-20 and DNP molecules began to decompose When the temperature rises to 3000 K, all CL-20 and DNP happened to decompose. CL-20 first began to decompose and lasted 1.2 ps. Then at about 2.0 ps, DNP took place to decompose. As the temperature increases, the decomposition becomes more complete. From Fig. 7b, it can be found that the situation in the CL-20:DNG co-crystal is similar to that in the CL-20:DNP co-crystal. All CL-20 decomposed at 2000 K and only one DNG began to decomposed. After the temperature rising to 3000 K, all CL-20 and DNG happened to decomposed. The average decomposition duration of DNG is 10.2 ps, indicating that the stability of DNG at high temperatures is better than that of DNP.
The main decomposition products of the two CL-20 cocrystal are NO 2 , NO, N 2 , CO, and H 2 O. The most important product is NO 2 , which is produced by the N − NO 2 bond cleavage during the initial decomposition. As the decomposition reaction continues at 2000 K, the amount of NO 2 gradually increases, but at 3000 K, the amount of NO 2 increases rapidly and then decreases after reaching the maximum value. This is because NO 2 will be consumed in subsequent reactions to form intermediates, such as NO and HONO. The subsequent production of NO at 3000 K is also higher than that at 2000 K. It is generally believed that H 2 O and CO may be the final decomposition products of the two co-crystals. It can be seen that the number of CO and H 2 O produced at 3000 K is the same as that at 2000 K, but the former was produced earlier. This indicates that the increasing temperature will promote the decomposition of the two co-crystals. The presence of N 2 indicates that the decomposition completed at 3000 K. For the CL-20:DNG co-crystal, the changing trends of the products NO 2 , NO, and N 2 are the same as those in the CL-20:DNP co-crystal, but their difference is that no H 2 O produced. This indicates that the CL-20:DNG co-crystal completely decomposed, and the decomposition of the CL-20:DNP co-crystal at high temperature is more thorough than that of the CL-20:DNG co-crystal.
The main product N 2 has an important feature in the decomposition process. Figures 8 and 9 present the release mechanisms of the nitrogen gas during the decomposition of the CL-20:DNP and CL-20:DNG co-crystals, respectively. After the initial decomposition began, the CL-20 molecules gradually decomposed into rings and some long chains with carbon-rich heterocycles. There are two N 2 generation mechanisms in the CL-20:DNP co-crystal, as shown in Fig. 8. However, the release mechanism of the nitrogen gas in the CL-20:DNG co-crystal is different from that in the CL-20:DNP co-crystal, as shown in Fig. 9. During the decomposition of the CL-20:DNG co-crystal, N 2 was generated by the C − N bond breaking from the long chains at 2.880 and 15.115 ps, respectively. The release mechanism of the nitrogen gas in the CL-20:DNG co-crystal is the same as that in the thermal decomposition of the high-energy crystal TEX [47]. Due to the differences in the structures of the two CL-20 co-crystals, their release mechanisms of the nitrogen gas are different.

Radial distribution function
The radial distribution function (RDF) is used to examine the structural properties of materials. The formula for calculating RDF is as follows [48]: where g(r) is the probability that another particle exists in a spherical space of radius r to r + δr. N is the number of atoms, V is the volume of the system, and r ij is the distance between i and j atoms.
In the DFTB-MD simulation process, the co-crystals began to decompose at high temperatures and their structures change from ordered to disordered. Figure 10 shows the RDFs of the N···O atom pair in the CL-20:DNP and CL-20:DNG co-crystals at different temperatures.
As seen in Fig. 10a, at 0 ps, the maximum peak of the N···O atom pair in the CL-20:DNP co-crystal is at 1.2 Å, which is the length of N − O bond in NO 2 . At 5 ps, the peaks at 1000 and 2000 K have little change, the intensity of the RDF peak at 3000 K becomes weaker, whose shape is smoothed from the sharp peaks, indicating that the co-crystal transforms from an ordered structure to a disorder state at a temperature of 3000 K [49]. At 2000 K, the intensity of the RDF peak becomes weaker at 15 ps, indicating that the decomposition began at 15 ps. With the increase of the time, the peaks of the RDF at 2000 and 3000 K become more and more small, indicating that the CL-20:DNP co-crystal gradually decomposes. As the temperature rises, the molecular decomposition occurs earlier, and the generated molecules move irregularly, making the system disorderly. The higher the temperature is, the lower the peak is, and the more violent the CL-20:DNP co-crystal decomposes.
For the RDF of the N···O atom pairs in the CL-20:DNG co-crystal, as shown in Fig. 10b, a similar trend with that of the CL-20:DNP co-crystal can be observed. At 0 ps, the RDF of the N···O atom pairs indicates that the co-crystal is in the crystal state, whose shape is sharp. The shape and intensity of the RDF peaks at the three temperatures started to change at Fig. 9 Release mechanisms of N 2 in the decomposition of the CL-20:DNG co-crystal 5 ps. The RDF peak shape at 3000 K is smoother than that at 1000 K. The peak shape of RDF at 2000 K began to decrease until 15 ps. Over time, the shape of the RDF peak became smoother and smaller. Compared the RDF of the N···O atom pair in the two co-crystals at the same time, it can be seen that the peak positions are the same, but their shape and intensity are different.

Conclusions
In this work, the conformational changes and decomposition mechanisms of the CL-20:DNP and CL-20:DNG co-crystals at high temperatures were studied using DFTB-MD. The results show that the decomposition mechanisms of the CL-20-based co-crystals are different at different temperatures.
At 1000 K, the CL-20 molecule in the CL-20:DNP cocrystal does not undergo a conformational change. However, there is mainly a conformational change from β-CL-20 to γ-CL-20 in the CL-20:DNG co-crystal. When the temperature is set to 2000 K, CL-20, DNP, and DNG in the co-crystals begin to decompose. There are five paths for the initial mechanisms observed during their thermal decomposition. The increasing temperature will promote the decomposition, and moreover, the more high the temperature is, the more complete the decomposition is. The initial decomposition pathway of CL-20 in the two cocrystals has two channels. The DNP molecule has two initial decomposition channels, while the DNG molecule has one initial decomposition channel. As the temperature increases, the decomposition products of the two cocrystals are different.
These results may contribute to the in-depth understanding of the decomposition mechanisms of high-energy CL-20-based co-crystals at high temperatures.
Author contribution All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Li Tang. The first draft of the manuscript was written by Li Tang and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.  Data availability The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Competing interests
The authors declare no competing interests.