Density Functional Theory Study of CL-20/Nitroimidazoles Energetic Cocrystal Compounds in an External Electric Field

The external electric eld has a signicant inuence on the sensitivity of the energetic cocrystal materials. In order to nd out the relationship between the external electric eld and sensitivity of energetic cocrystal compounds 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane/1,4-dinitroimidazole (CL-20/1,4-DNI), 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane/1-methyl-2,4-dinitro-1H-imidazole (CL-20/2,4-MDNI) and 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane/1-methyl-4,5-dinitro-1H-imidazole (CL-20/4,5-MDNI). In this work, density functional theory (DFT) at B3LYP-D3/6-311+G(d,p) and M062X-D3/ma-def2 TZVPP levels was employed to calculate the bond dissociation energies (BDEs) of selected N-NO 2 trigger bonds, frontier molecular orbitals, electrostatic potentials (ESPs) and nitro group charges (QNO2) under different external electric eld. The results show that as the positive electric eld intensity increases, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energy gap and BDEs become smaller, and the local positive ESPs becomes larger, so that the energetic cocrystals tends to have higher sensitivity. In addition, the linear tting results show that the trigger bond length and nitro group charge changes are closely related to the external electric eld strength.


Introduction
In recent years, energetic cocrystal materials have attracted much attention due to their excellent detonation properties [1][2][3][4]. Studying the effect of external electric eld on energetic cocrystal molecules will help us understand the characteristics of this material and help us purposefully synthesize highperformance new explosives [5][6].
Usually, energetic materials have some energetic groups, which makes such materials release a large amount of energy under certain conditions, making them have great potential value in many elds such as military and propellant [7]. 2,4,6,8,10,12-Hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (CL-20) is a fourth-generation, caged nitroimine explosive. Also, it is the most powerful non-nuclear elementary explosive that can be used in practical applications [8]. However, the high mechanical sensitivity of CL-20 signi cantly impairs its safety and severely limit the application of CL-20. Co-crystallization technology is often used in the pharmaceutical industry to modify drug molecules to achieve speci c properties. In recent years, this technology has been introduced by researchers to reduce the sensitivity of explosives, and co-crystallization technology is receiving increasing attention in the eld of synthesizing new energetic materials [9][10][11][12][13][14]. By dissolving two explosives in the same solvent, according to the characteristics of the two explosive molecules, different methods are used to make the cocrystal precipitate in the solution, so that the two explosive molecules are combined into the same crystal lattice through weak intermolecular interactions. This kind of supramolecular thus has a speci c crystal structure and properties [15][16][17]. Using a material with lower mechanical sensitivity as a ligand to form a cocrystal with CL-20 is one of the effective methods to reduce the high mechanical sensitivity of CL-20.
Li et al [20] used theoretical calculations to study the changes in the structure and electrons of lead azide crystals induced by an electric eld. Ren et al [21][22] conducted a theoretical study on the possible trigger linkage theory prediction of CH 3 NO 2 and NH 2 NO 2 in an external electric eld and a theoretical study on the hydrogen transfer kinetics of the NH 2 NO 2 •••H 2 O complex in an external electric eld. Sun et al. [23] has studied the theoretical prediction of CL-20's trigger linkage, cage strain and explosive sensitivity under the external electric eld. Wu et al [24] studied the external electric eld induced conformational changes as a buffer to increase the stability of the CL-20/HMX cocrystal and its pure components. In recent years, since the trigger bond of nitroimine explosives is usually N-NO 2 , the role of electron and nitro oxygen transfer in the trigger reaction of energetic materials has attracted more and more attention [25]. Therefore, to reveal the essence of the in uence of the external electric eld on the sensitivity of the energetic cocrystal compounds, in this work, we used the theoretical calculation method based on DFT to study three kinds of cocrystal (CL-20/1,4-DNI, CL-20/2,4-MDNI, CL-20/4,5-MDNI), and explore the effects of different electric eld on the performance of the three cocrystals. This theoretical study will help us better understand the sensitivity change and the explosion mechanism of energetic cocrystal compounds under the external electric eld.

Computational Details
In this work, all the calculations were performed with the Gaussian 16 software package [26]. The B3LYP-D3/6-311 + G(d,p) method was used to fully optimize the molecular structures of the three cocrystals under the external electric eld and no external electric eld. The stability of the cocrystal structures is judged by the criteria of "no imaginary frequency" and "reaching four convergence conditions".
Subsequently, the M062X-D3/ma-def2 TZVPP method was selected to calculate the single-point energy of the three cocrystal molecules.
After Laplace bond-level analysis, three kinds of cocrystal trigger bonds are obtained, all of which are N-NO 2, as shown in the red box in Fig. 1. Existing research shows that the external electric eld perpendicular to the direction of the trigger bond has no obvious effect on the strength of the trigger bond [27], and only the external electric eld parallel to the direction of the trigger bond can have a signi cant effect on the strength of the trigger bond. In order to explore the in uence of the applied electric eld on the trigger bond of the cocrystal explosive, the direction of the positive applied electric eld is de ned as N→NO 2 , and the direction of the negative applied electric eld is de ned as NO 2 →N. The eld strengths of the applied electric eld are as follow: 0.000, ± 0.005, ± 0.0075 and ± 0.010 a.u., respectively. Figure 1 shows the stable cocrystal molecular structures obtained after optimization on the B3LYP-D3/6-311 + G(d,p) level when no electric eld is applied.  To further explore the in uence of the external electric eld on the cocrystal sensitivity, the bond dissociation energy (EBDE) and interaction energy (Eint) of the three cocrystal molecules were calculated.
The calculation results are shown in Table 2. It can be seen from Table 2 that under the external electric eld, the variation trend of the Eint of the three cocrystal molecules is different, indicating that there are certain limitations in judging the cocrystal sensitivity from the Eint. As the positive electric eld intensity increases, the EBDE of trigger bonds is smaller and the cocrystal sensitivity is higher. When the negative electric eld intensity increases, the EBDE of trigger bonds increases and the cocrystal sensitivity decreases. Under the external electric eld, the order of the EBDE of the three cocrystals is as follows: CL-20/2,4-MDNI (48.88 kcal·mol-1) CL-20/1,4-DNI (47.37 kcal·mol-1) CL-20/4,5-MDNI (44.37 kcal·mol-1).
Therefore, the order of the sensitivity of the three cocrystals is: CL-20/4,5-MDNI CL-20/1,4-DNI CL-20/2,4-MDNI. The order of sensitivity obtained by calculating the EBDE is consistent with the order of sensitivity obtained by ESP analysis.

Frontier Molecular Orbitals
The highest occupied molecular orbital (HOMO) and the lowest occupied molecular orbital (LUMO) are two important aspects of the frontier molecular orbitals (FMOs) [29]. In addition to the orbitals, the energy gap between HOMO and LUMO also has important physical signi cance. It can determine the dynamic stability, chemical reactivity and optical polarizability of high-energy materials. The distribution of the HOMO and LUMO of CL-20/1,4-DNI, CL-20/2,4-MDNI and CL-20/4,5-MDNI along with their energy 8 gap is presented in Fig.3. It can be seen from Fig 3(a)

Electrostatic Potential
ESP is an important physical characteristic for studying the interaction, charge distribution and chemical reactivity on the surface of molecules [31]. This section uses the Multiwfn [32] software to calculate the surface ESP of three cocrystal molecules under the external electric eld, as shown in Fig.4~6. The maximum surface ESP, minimum surface ESP and the extreme values of the local positive ESP of the trigger bond are shown in Table 3.
It can be seen from Table 3 that with the increase of the electric eld intensity, the maximum and minimum surface ESP of CL-20/2,4-MDNI and CL-20/4,5-MDNI both increases. The change of surface ESP value is consistent with the gure of cocrystal surface ESP, which shows that the electric eld has a signi cant effect on the movement of the charge [33]. Under the external electric eld, combining Fig.4~6 and Fig.7, part of the blue area of CL-20/1,4-DNI and CL-20/4,5-MDNI turns red, indicating that part of the negative ESP has changed to positive ESP. Under the positive electric eld, as the electric eld intensity increases, the negative ESP on the molecular surface of CL-20/2,4-MDNI also transforms into the positive ESP. Under the negative electric eld, the situation is reversed. All the above changes indicate that the change of cocrystal charge distribution brings about the change of cocrystal sensitivity.
Politzer and Murray [34] point out that the smaller the local positive ESP (V s·max ) of the trigger bond, the lower the sensitivity of the energetic material and the more stable the energetic material. To explore the change of the trigger bond under the external electric eld, the local positive ESP of the trigger bonds of the cocrystal molecules are shown in Table 3. The obtained results show that as the intensity of the positive electric eld gradually increases, V s·max also increases, so the cocrystal sensitivity gradually increases. Therefore, the order of the sensitivity of the three cocrystals is: CL-20/4,5-MDNI CL-20/1,4-DNI CL-20/2,4-MDNI. Table.3 The maximum/minimum surface electrostatic potential and trigger bond local positive electrostatic potential extreme value of cocrystals at different electric eld.

Nitro Group Charge
Existing studies [35] have shown that the charge of the nitro group of an energetic material is a nonnegligible factor affecting its sensitivity. The more negative charge the group has, the lower the sensitivity of the energetic material, otherwise the higher the sensitivity. It can be seen from Table 4 that with the increase of the positive electric eld intensity, the charge of the nitro group gradually decreases, and the sensitivity of the cocrystal molecule decreases [36]. When a negative electric eld is applied, as the electric eld intensity gradually increases, the charge of the nitro group gradually increases, indicating that the sensitivity of the cocrystal molecule increases. In order to explore the variation of the nitro group charge (△ 2 ) under the electric eld, a linear tting was performed on the change of the nitro group charge in the electric eld. As shown in Fig.8, the linear correlation coe cients of the three cocrystals are 0.996 (CL-20/1,4-DNI), 0.989 (CL-20/2,4-MDNI) and 0.965 (CL-20/4,5-MDNI), respectively. There is a good linear correlation between the charge change of the nitro group and the external electric eld, indicating that the external electric eld has a signi cant in uence on the charge of the nitro group and the sensitivity of the energetic cocrystals [37].

Conclusion
In this work, DFT was used to systematically study the trigger bond, molecular orbital, electrostatic potential and nitro group charge of three CL-20/nitroimidazoles energetic cocrystal compounds in different electric eld. The results are summarized as follows: 1 By analyzing the bond length changes and BDEs of the trigger bonds in the electric eld, it can be concluded that as the positive electric eld intensity increases, the trigger bonds become longer and the BDEs become smaller, resulting in an increase of the cocrystal sensitivity. The situation is reversed in the negative electric eld.
2 Molecular orbital analysis shows that the positive electric eld reduces the HOMO-LUMO energy gap of the cocrystals. CL-20/2,4-MDNI has the smallest energy gap among the three cocrystals, and its chemical reaction activity is higher than other cocrystals. Therefore, the mechanical sensitivity of CL-20/2,4-MDNI is the highest among the three cocrystals. 3 The ESP analysis shows that as the positive electric eld intensity gradually increases, the V s·max of the three cocrystal molecules increases, so the sensitivity gradually increases. The situation is reversed in the negative electric eld. 4 The charge analysis of the nitro group shows that as the positive electric eld intensity increases, the charge of the nitro group decreases, resulting in a decrease in the sensitivity of the cocrystals. The situation is reversed in the negative electric eld.

Declarations
Funding: This study was funded by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (20KJB620001) and National Natural Science Foundation of China (Grant No.11702129).
Con icts of interest/Competing interests: No con ict of interest exits in the submission of this manuscript. The manuscript has not been published before nor submitted to another journal for the consideration of publication.
Availability of data and material: All data generated or analyzed during this study are included in this published article.