HMX/NMP cocrystal explosive: first-principles calculations

The band structure, total density of states, and atomic orbit projected density of states analysis were performed to investigate HMX/NMP cocrystal by using the first-principles calculations. Results show that the HMX/NMP cocrystal is equipped with a direct band gap and the interactions between HMX and NMP molecules are rather weak. The O orbits hybridize with H orbits, and the parts of charge transform from H to O atoms by analyzing the DOS. The HMX/NMP cocrystal possesses three types of intermolecular interactions between HMX and NMP; these interactions and the arrangement of two molecules in the structure are the main reasons for the low sensitivity of the cocrystal. The C-H…O type hydrogen bond is the key role in forming the structure, and the strength of the hydrogen bond interaction for C-H…O-N is higher than that of C-H…O-C.


Introduction
Energetic materials usually refer to organic compounds containing energy-containing groups (such as nitro, amino, and azide groups) in molecules, which release significant quantities of energy in an instant when there is a chemical reaction [1][2][3][4]. Energetic materials have a wide range of applications, for example, their chemical energy can be used to do work for missile launch and can be used as gas generators [5]. Explosives, propellants, and pyrotechnics are common energetic materials, which are widely used in civil and military fields [6][7][8]. A great deal of research has been done on energetic materials, such as 2,4,6-trinitrotoluene (TNT), hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX), and octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) [1,9]. Among these typical energetic materials, HMX is one of the most commonly used traditional explosives in propellants and explosives; it was first discovered as a byproduct of synthesis of RDX in 1930 [8], and its molecular structure is similar to RDX, with the characteristics of high energy density, high melting point, and high explosive performance [1,[8][9][10]. However, ideal energetic materials should have the advantages of good detonation performance as well as the low thermal and impact sensitivity [1,11]. It is difficult to meet the requirements of insensitive high density energetic materials (IHDEMs) [12,13] for HMX due to its moderate sensitivity [8,11], so the effective methods to reduce the sensitivity of HMX without significant energy reduction has aroused extensive attention in the academic circle [14,15].
Cocrystallization, which is the result of intermolecular interactions between two or more neutral molecules such as hydrogen bonds, π-stacking, and van der Waals forces [16,17]. Studies show that the sensitivity of HMX with inert molecules cocrystal is usually lower than that of pure HMX [8,18] and it is a promising method to solve this problem [16]. It is mainly because of the significant intermolecular interactions in the structure of HMX/NMP cocrystal explosive, which makes it less easily decomposed and exploded [16]. N-methyl-2-pyrrolidone (NMP) with a carbonyl group is a unique functional group, and it is a solvent molecule [4,18,19]. It is reported that the cocrystallization of HMX and NMP is helpful in reducing the sensitivity of the explosive without significant energy reduction [18,20]. In 1985, Haller and Rheingold et al. [21] prepared the HMX/NMP cocrystal by cooling crystallization for the first time and obtained the lattice parameters of the structure. In 2013, Lin and Zhu et al. [22] prepared the HMX/NMP cocrystal by solution evaporation method and investigated host-guest interactions of the structure by using the first-principles calculations. However, at present, it is necessary to further study the properties of HMX/NMP cocrystal explosive. On the one hand, in addition to the reports mentioned above, there are few studies on HMX/NMP cocrystal at the moment. The calculations of electronic properties for the HMX/NMP cocrystal by Lin et al. are inaccurate, as can be seen from the band structure and state density diagrams (the parts above the Fermi level are missing). On the other hand, for cocrystal, intermolecular interactions are the key to the formation of cocrystal structure and also one of the main reasons for reducing the sensitivity of explosives; thus, it is important to investigate the interactions [11,23]. Therefore, combined with the above situations, it is very meaningful to re-analyze the electronic properties and intermolecular interactions of the HMX/NMP cocrystal. The study of HMX/NMP cocrystal is helpful to provide theoretical evidence for exploration of low sensitivity energetic materials and the development of HMX cocrystal explosives.
In our study, we calculated the band structures and the density of states using the first principles and focused on analyzing its electronic properties and the possible intermolecular hydrogen bond interactions. The research results of this paper as the complement were published in 2013 by Lin et al. [22], and we hope to provide some reference and guidance for the design of HMX/NMP cocrystal in the future.

Computational methods
In this work, the first-principles calculation of HMX/NMP cocrystal were performed using the CASTEP (Cambridge Sequential Total Energy Package) code [24] based on density functional theory (DFT) [25,26] with GGA [27] in the scheme of Perdew-Burke-Ernzerhof (PBE). The cutoff energy of 380.0 eV for the plane wave was used, and the K-points in the Brillouin zone were set to 1 × 1 × 1 throughout all calculations. The electronic configurations of the ions used for the calculation are 2s 2 2p 2 of C, 1s 1 of H, 2s 2 2p 4 of O, and 2s 2 2p 3 of N. We used the experimental data and related coordinate information in the reference [21] as the basis for calculations and optimized the atomic coordinates. The atom coordinates for HMX/NMP cocrystal are shown in Table 1; the values in parentheses correspond to the experimental data [21]. In addition, we calculated the electrostatic potentials of HMX molecule, NMP molecule, and HMX/ NMP cocrystal by using the Dmol3 module in Materials Studio software [24].

Crystal structures
The selected bond lengths in HMX/NMP cocrystal along with the corresponding experimental data [21] are shown in Table 2. For HMX molecules, it can be seen that the bond lengths compare well with experimental values which indicate that our results agree well with the experimental values [21]. Moreover, the trigger bond is N-NO 2 bond for nitro energetic materials. In general, the longer the trigger bond is, the more unstable the crystal structure is [2]. We can find that the lengths of N-NO 2 bonds in HMX/NMP cocrystal (1.370;1.387) are shorter than that in pure HMX crystal (1.379;1.392) by comparing their N-NO 2 bonds in the same place of their structures [22]. Therefore, from the comparison of trigger bonds, we preliminarily concluded that the structure of HMX/ NMP cocrystal is more stable than that of HMX crystal, which is consistent with previous research results [21,22].  Because it has been verified by predecessors, its sensitivity will not be studied in more detail but only make a preliminary judgment here. For NMP molecules, we have carried out geometric optimization on the isolated NMP molecule and listed their geometric parameters in brackets of Table 2 for comparison. It is worth noting that the geometric parameters of the NMP molecule in HMX/NMP cocrystal are different from those of the optimized isolated NMP molecule; this is because the noncovalent interactions between NMP and HMX influence its structure in HMX/NMP cocrystal to some extent [21,22]. The calculated structure of the HMX/NMP cocrystal model and the molecular structures of HMX and NMP are shown in Fig. 1. As can be seen from the Fig. 1a, HMX and NMP molecules are arranged in a staggered manner in the structure, which makes the whole crystal structure compact and contributes to the stability of the crystal structure [28][29][30][31]. From the Fig. 1b, we can observe that the structure of HMX/NMP cocrystal along the y-axis, HMX, and NMP molecules are arranged in six disordered layers in the structure. The HMX/NMP cocrystal is a trigonal structure with the space group R‾3c, and the lattice parameters are a = b = 16.607 Å and c = 31.506 Å [21]; the molecular formula is C 9 H 17 N 9 O 9 . Figure 1c and d show the HMX molecule and NMP molecule with atom numbering.  [8]. As can be seen in Fig. 1c, the HMX molecule shows the chairchair ring conformation [19,20] in HMX/NMP cocrystal, and there are four nitro groups on the same side of the C 4 N 4 ring [32]. In Fig. 1d, it can be observed that the NMP molecule has a crystallographic twofold rotation axis, and the C3, C6, and O5 atoms lie on this axis [21]. Moreover, we can also see that the NMP molecules in cocrystal are distorted due to their interactions with HMX molecules. Figure 2 shows more detailed structural information of the HMX/NMP cocrystal. The arrangement of HMX and NMP molecules viewed along the z-axis is shown in Fig. 2 [21]; it can be seen that these two molecules are in a disordered arrangement in the cocrystal.

Electronic properties
The calculated energy band structures along the high symmetry direction of the Brillouin zone is shown in Fig. 3; the vertical dashed line at 0 eV is Fermi level. It can be seen that the valence band minimum (VBM) and the conduction band maximum (CBM) are both located at G point; this indicates that the HMX/NMP cocrystal shows direct bandgap behavior; the value of direct bandgap is 0.958 eV.
In addition, the valence bands and conduction bands of band structures are quite flat along different symmetry directions in the Brillouin zone, which suggests that it is limited for overlap between orbitals on neighboring molecule, and the interaction between HMX and NMP molecules is rather weak in the cocrystal [33,34].
In order to get more information about the electronic properties of the HMX/NMP cocrystal, we calculated the DOS (density of states) as shown in Fig. 4. Furthermore, we need to explain here that the non-covalent interactions between NMP and HMX molecule lead to the distortion of the valence band in the NMP structure, so that the charge separation of NMP molecule in the HMX/NMP cocrystal is increased. Combining with TDOS (total density of states) and PDOS (partial density of states), the main characteristics of DOS can be summarized as follows. (1) These peaks are sharp and localized from PDOS; this indicates that the interactions in the cocrystal are weak; these peaks are associated with previous flat band structure (Fig. 3).

Intermolecular interactions
Intermolecular interactions are the primary drive forces for the formation of cocrystal, and they contribute to the stability of the crystal structure [35,36]. The hydrogen bonding is considered as one of the intermolecular interactions in numerous studies [37][38][39][40][41], and they are usually expressed in terms of X-H…Y [42][43][44]. For HMX/NMP cocrystal, the intermolecular hydrogen bond interactions between HMX molecule and NMP molecule are the main forces for the formation of HMX/NMP cocrystal, especially the hydrogen bond interaction between nitro group in HMX and neighboring hydrogen [35,36]. In most of the examples of hydrogen bonds, the distance between H and Y atoms is less than the sum of their van der Waals radii [37,38,45]. Therefore, it can be preliminarily inferred the existence of hydrogen bond between O and H atoms when their distance is less than the sum of their van der Waals [45] for HMX/ NMP cocrystal [8,33,38,46]. In this study, we used 1.20 Å and 1.52 Å as the van der Waals radii of H and O [45], respectively.
Based on this method, we find the possible existence of hydrogen bonds between O5 and H16, O5 and H17, O6 and H19, O6 and H25, O7 and H19, O8 and H24, O9 and H20, O9 and H24, O9 and H26, O10 and H21, and O11 and H21. The possible hydrogen bonds between HMX and NMP moleculars are shown in Fig. 5. In Fig. 5a, the hydrogen bonds are indicated by the dotted lines; the HMX and NMP moleculars are connected to each other by these possible hydrogen bonds. The H atoms of the methylene groups in HMX or the H atoms in the NMP molecular serve as proton donors, and the O atoms of the nitro groups in HMX or the O atoms in the NMP molecular serve as proton acceptors. We can see that there are three different intermolecular interactions between HMX and NMP moleculars in HMX/ NMP cocrystal from Fig. 5b. These three types of intermolecular interactions play important roles in stabilizing cocrystal, combined with other weak interactions such as C…N interactions, finally form the structure. The distances and angles of possible hydrogen bonds found in cocrystal have been listed in Table 3; the labeled atoms are shown in Fig. 5b. In these possible hydrogen bonds, the shortest contact is C11H24…O8 with 2.091 Å and the longest one is C8H19…O6 with 2.611 Å. In addition, their bond angles are above 110° except the C10H20…O9 and C11H26…O9. It is reported in previous literature [37,38] that the hydrogen bond angle should preferably be above 110°, the bond angles of these bonds are basically consistent with this conclusion. HMX and NMP molecules are alternately arranged in the cocrystal structure and connected by these hydrogen bonds, which increase the stability of the structure and safety of the cocrystal explosive. And this is one of the reasons for the decreased sensitivity of this cocrystal explosives [28][29][30][31][47][48][49]. The electronic overlap in PDOS is generally interpreted as one of the evidence of the interaction for non-bond atoms [32,33,46]. In order to further study these interactions, we present the PDOS of the correlative O and H atoms (O5, O6, O7, O8, O9, O10, O11, H16, H17, H19, H20, H21, H24, H25, H26) in the HMX/NMP cocrystal as shown in Fig. 6. From Fig. 6a, it can be observed that resonance is found between O5 and H16 from − 7 to − 5 eV. The resonance is also found between O5 and H17 from − 6 to − 5 eV, especially their peaks appear at the same level with − 5.5 eV. This indicates that hydrogen bond interactions occur between O5 and H16 and O5 and H17. Similarly, in Fig. 6b, there are hydrogen bond interactions between O6 and H119 states in the energy range of − 10 to − 9 eV. And in the energy range of − 4 to − 2 eV, there are hydrogen bond interactions between O6 and H25 states. As Fig. 6c-e show, the hydrogen bond interactions also occur between O9 and H20, O9 and H26, O7 and H19, and O8 and H24. This is basically consistent with the previous results obtained by the distance method to determine the existence of hydrogen bond interactions. In addition, these hydrogen bond interactions can be divided into two types: C-H…O-C and C-H…O-N hydrogen bonds. The hydrogen bond interactions between O5-2p in NMP Fig. 7 The electrostatic potential of a NMP molecule, b HMX molecule, c HMX/NMP cocrystal, d HMX/NMP cocrystal viewed along z-axis molecules and H-1 s states (H16 and H17) belong to C-H… O-C hydrogen bonds, the other hydrogen bond interactions between other O-2p (O6, O7, O8, and O9) states in HMX molecules and H-1 s states belong to C-H…O-N hydrogen bonds. It can be seen from Fig. 6 that the hydrogen bonds in HMX/NMP crystal mainly comes from the C-H…O-N hydrogen bonds. Therefore, the strength of the hydrogen bond interactions for C-H…O-N is higher than C-H…O-C hydrogen bonds in the HMX/NMP cocrystal explosive.
Electrostatic potential has been widely used in the study of interaction and has become one of the common means to analyze the interaction between molecules [50,51]. Electrostatic potential computed on molecular surfaces plays an important role in the design of new cocrystal materials [52]. Therefore, we calculated the electrostatic potentials of HMX/NMP and its related molecules. Figure 7 shows the electrostatic potential on the surface of HMX molecule, NMP molecule, and HMX/ NMP cocrystal. Different colors represent different electrostatic potential values, red represents positive, and blue represents negative potential. As shown in Fig. 7a, for the electrostatic potential of individual NMP molecule, the positive electrostatic potential region is mainly distributed around the hydrogen atom, and the negative electrostatic potential region is mainly distributed around the oxygen atom and nitrogen atom. For the electrostatic potential distribution of HMX molecule, as shown in Fig. 7b, the positive electrostatic potential region is mainly distributed in its eight-membered ring; the negative electrostatic potential region is distributed near the O atom of N-O bond, and its surface electrostatic potential is axisymmetric [53]. Figure 7c and d show the electrostatic potential of HMX/NMP cocrystal; it can be seen from the figure that the electrostatic potential distribution of the two molecules in the cocrystal is different from that of the two molecules when they exist alone. This is mainly due to the superposition of the positive and negative electrostatic potential regions in the two molecules, which changes the potential in their contact regions. The results indicate that there are interactions between HMX and NMP molecules in HMX/NMP cocrystal [54,55], which is consistent with our previous analysis results. Moreover, combined with the results of electrostatic potential analysis and the previous reports by Politzer and Murray [50-52, 54, 55], we can also know that the interactions should be the involving extended regions of positive and negative potentials; their sites do not always correspond to particular atoms.

Conclusions
In summary, based on the density functional theory, we have studied the electronic properties and intermolecular interactions by analyzing its band structure and the density of states. The main results and conclusions were summarized as follows in this study: (1) There is a direct band gap in the HMX/NMP cocrystal. (2) The interaction between HMX and NMP molecules is rather weak due to its bands being quite flat, and its peaks from PDOS are localized. (3) There are hybridization interactions between N-2p and O-2p states, O-2p and H-1 s states, N-2p and C-2 s states, and C-2p and H-1 s. (4) There is interaction between the O atom and H atom; the parts of charge transform from H to O atoms. (5) The structure of HMX/NMP cocrystal is more stable than that of HMX crystal. Three types of intermolecular interactions play important roles in stabilizing the HMX/NMP cocrystal, and the C-H…O hydrogen bond interaction is the key role. (6) The arrangement of HMX and NMP molecules in the structure and the hydrogen bonds between them are the main reasons for the decrease of the sensitivity of the cocrystal. (7) The strength of the hydrogen bond interactions for C-H…O-N is higher than that of C-H…O-C hydrogen bond interactions.
Author contribution Yi-Hua Du: writing-original draft, formal analysis, investigation, methodology, and software.
Fu-Sheng Liu: data curation, methodology, and writing-review and editing.
Qi-Jun Liu: conceptualization, project administration, resources, supervision, and writing-review and editing.
Bin Tang: methodology, software, and writing-review and editing. Mi Zhong: data curation, writing-review and editing, and visualization.
Funding This project was supported by the Fund of the Key Laboratory of National Defense Science and Technology (Grant No. 6142A03182008).

Data availability
The datasets supporting the results of this work are included within the article; the other datasets generated during the current study are available from the corresponding author on reasonable request.
Code availability Not applicable.

Declarations
Ethics approval Not applicable.

Competing interests
The authors declare no competing interests.