Design and selection of pyrazolo[3,4-d][1,2,3]triazole-based high-energy materials

In this study, we design a series of bridged energetic compounds based on pyrazolo[3,4-d][1,2,3]triazole to screen potential energetic materials with excellent detonation properties and acceptable sensitivities. The electronic structures, heats of formation, detonation velocity, detonation pressure, and impact sensitivity of the designed compounds were calculated using density functional theory. The results showed that the designed compounds have high positive heats of formation in the range of 1035.4 (A7) to 2851.4 kJ mol−1 (D2). Moreover, the designed compounds have high crystal densities and heats of detonation, which significantly enhance detonation pressures and velocities. The detonation pressures and velocities are in the ranges of 6.23 (A1) to 9.65 km s−1 (D3) and 15.7 to 43.9 GPa (E8), respectively. The impact sensitivity data also suggest that the designed compounds have impact sensitivities in an acceptable range. Considering detonation pressures, detonation velocities, and impact sensitivities, six compounds (C3, C5, D3, D5, E3, and F3) were screened as potential materials with high-energy density, excellent detonation properties, and low impact sensitivities. Finally, the electronic structures of the screened compounds were simulated to provide further understanding on the physicochemical properties of these compounds.


Introduction
As a special important component of energy, energetic materials (such as propellant, explosive, and initiator) have played an important role in the development of military and its equipments [1][2][3][4][5][6]. In the face of increasing armed conflicts around the world, the leaders of different countries pay significant attention to the development of national armaments and desire higher performance of energetic materials and frequency of replacement. At present, research on energetic materials is focussed on nitrogen-rich compounds with high-energy density, excellent detonation performance, good thermal stability, and reduced amount of polluting gas in the process of explosion [7][8][9][10][11]. Scheme 1 shows the structures of some energetic compounds such as 1,3,5-trinitro-1,3,5triazinane (RDX), [12] 1,3,5,7-tetranitro-1,3,5,7-tetrazocane (HMX), [13] and cage structures 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazatetracyclododecane (CL-20) [14]. Among these structures, the detonation performance of cage-like energetic compounds is stronger than that of chainlike energetic compounds. However, the synthetic steps for the cage-like energetic compounds are more complex than those for the chain-like energetic compounds. The annular nitrogen-rich energetic compounds combine the benefits of the chain-like and cage-like energetic compounds and lead the field of energetic materials [15,16].

Frontier molecular orbital (FMO)
Highest occupied molecular orbitals (HOMO) and lowest non-occupied molecular orbitals (LUMO) are most frequently mentioned FMOs. They provide important information for predicting the chemical activity of compounds owing to their special status [19][20][21][22][23]. The energy gap Scheme 1 RDX, HMX, and cl-20 structures Scheme 2 The designed high-energy materials based on pyrazolo [3,4-d] [1,2,3]triazole between the HOMO and the LUMO is an expression of this information. Therefore, the values of HOMO, LUMO, and the energy gap (ΔE LUMO-HOMO ) are obtained from Gaussian calculations, and the results are summarised in Table 1.
The maximum values of HOMO and LUMO were −4.89 eV (B6) and −0.56 eV (B6), respectively, while their minimum values were −8.89 eV (E8) and −4.61 eV (D8), respectively. Moreover, the maximum and minimum values of ΔE LUMO-HOMO were 5.31 eV (A1) and 3.46 eV (B2), respectively. Therefore, we can make the conclusion that A1 was more stable than B2. Figure 1 shows the variation trend of the HOMO and LUMO values of the designed compounds with different substituent groups and bridging. As shown in the Fig. 1, the variations in the HOMO and LUMO values are consistent. For the designed compounds with substituents −N 3 , −NH 2 , and −NHNH 2 , the HOMO and LUMO values increased. However, the HOMO and LUMO values decreased for the designed compounds with substituents −CN, −NO 2 , −NHNO 2 , −CH(NO 2 ) 2 , and −C(NO 2 ) 3 . In addition, Fig. 1 shows the comparison between the HOMO values of the designed compounds with same substituents but different bridged connections. The compounds with -C = C-bridged connections were larger than those with other bridged connections. For the substituents -CN, -NO 2 , -NH 2 , -NHNO 2 , and -NHNH 2 , the HOMO value of the -N-N-bridged compounds was the lowest. Moreover, for the substituents -N 3 , -CH(NO 2 ) 2 , and -C(NO 2 ) 3 , the HOMO value of the -C-N-bridged compounds was the lowest. For same bridging connections, the HOMO values of the compounds with different substituents were compared. We found that for different bridging connections, the HOMO value of the compounds with the substituent -NHNH 2 was the highest. Furthermore, the HOMO value for the compounds with the substituent -C(NO 2 ) 3 was the lowest. Therefore, our results indicate that the -NHNH 2 energetic group, and -C = C-bridge was the most effective combination for increasing the HOMO value of the designed compounds. For a same bridging connection, the LUMO values of the compounds with different substituents were compared. It was found that the LUMO value of the compounds was the highest when the substituent was -NHNH 2 (except -C-C-) lowest when the substituent was -C(NO 2 ) 3 . Hence, we believe that for the designed compounds, the -NHNH 2 and -C(NO 2 ) 3 energetic groups could increase and decrease the LUMO values, respectively. The energy gap values of the compounds with a same substituent but different bridging connections, that is, the stability of the compounds, were compared. When the substituents were -N 3 , -NO 2 , -NHNO 2 , -NHNH 2 , and -C(NO 2 ) 2 , the ΔE LUMO-HOMO value of the designed compounds connected by -N-N-bridge was the largest. When the substituents were -CN, -NH 2 , and -NHNH 2 , the ΔE LUMO-HOMO value of the compounds connected by -N = N-bridge was the lowest. Moreover, when the substituents were -N 3 , -NO 2 , -NHNO 2, -CH(NO 2 ) 2 , and -C(NO 2 ) 3 , the ΔE LUMO-HOMO value of the compounds connected by -C = C-bridge was the lowest. We can conclude that the -N-N-bridge could increase the stability of the compounds, while the -C = C-and -N = N-bridges could decrease the stability of the compounds. The ΔE LUMO-HOMO values of the compounds with same bridging connections but different substituents were compared. The ΔE LUMO-HOMO values of the compounds with -N 3 substituent were the lowest. In the cases of -C-C-, -N-N-, and -C-N-connections, the ΔE LUMO-HOMO values of the compounds with the substituent -CN were the largest, thereby indicating that the -CN energetic group is the best, while the energetic group -N 3 is the worst among the eight substituents in enhancing the stability of the compounds.

Heats of formation
Heats of formation (HOF) is an indicator of energy content, which plays an important role in predicting the detonation characteristics of high-energy materials [24][25][26][27].

Detonation properties
As shown in Fig. 3, the substituent groups such as -N 3 , -NO 2 , -NHNO 2 , -CH(NO 2 ) 2 , and -C(NO 2 ) 3 can increase the density, detonation heat, detonation velocity, and detonation pressure of the designed compounds. In contrast, the substituent groups such as -CN, -NH 2 , and -NHNH 2 can decrease these quantities. In Fig. 3a, it can be seen that for a compound with same substituent group but different bridging groups, the rule is -C-C-< -C = C-< -C-N-< -N-N-< -C = N-< -N = N-. This indicates that the bridging group -N = N-can enhance the density of the designed compounds. Moreover, when the compounds are connected by the same bridge but have different substituents, the rule is -NHNH 2 < -NH 2 < -CN < -N 3 < -NHNO 2 < -NO 2 < -C H(NO 2 ) 2 < -C(NO 2 ) 3 , which indicates that the -C(NO 2 ) 3 substituent can increase the density of the designed compounds. From Table 3, the change trend of Q is basically the same as ρ, and the combination -N = N-/-C(NO 2 ) 3 plays an essential role in enhancing the explosion heat. We can conclude from Fig. 3b, c that different bridges have the same influence on D and P, that is, in the following order: -C-C-< -C = C-< -C-N-< -C = N-< -N-N-< -N = N-(except for the -C(NO 2 ) 3 energetic group). When the bridging connections are -C-C-, -C = C-, -N-N-, -C-N-, and -C = N-, the effect of different substituents on the designed compounds was in the following order: -CN < -NH 2 < -NHNH 2 < -N 3 < -NHNO 2 < -NO 2 < -C H(NO 2 ) 2 < -C(NO 2 ) 3 . When the bridge was -N = N-, the effect of different substituents on the compounds was in the following order: -CN < -NH 2 < -NHNH 2 < -N 3 < -NHNO 2 < -CH (NO 2 ) 2 < -NO 2 < -C(NO 2 ) 3 . The combination of -N = N-and -C(NO 2 ) 3 can significantly affect the energy performance of the designed compounds and enhance their energy. Figure 3d shows the comparison between the h 50 values of the compounds with different substituents but same bridge. For the bridges -C-C-, -N-N-, and -C-N-, the h 50 value of the compounds with the -NH 2 substituent was the highest. Furthermore, for the bridges -C = C-, -N = N-, and -C = N-, the h 50 value of the compound with the -N 3 substituent was the highest. Besides, we found that the -C(NO 2 ) 3 substituent would decrease the h 50 values of the designed compounds, while the -N 3 and -NH 2 substituents would increase the h 50 values. The h 50 values of the  compounds with the -C(NO 2 ) 3 were the lowest. When the compounds were connected with same bridge but different substituents, the h 50 values of the compounds bridged by -C-C-were the highest, while those of the compounds bridged by -N = N-were the lowest when the substituents were -NHNO 2 , -NHNH 2 , -CH(NO 2 ) 2 , and -C(NO 2 ) 3 .
In summary, six compounds (C3, C5, D3, D5, E3, and F3) were selected as candidates for energetic materials considering the detonation performance and impact sensitivity. For further analysis, their electronic structures, such as the FMO distribution and the electrostatic potential surface, were simulated.

Electronic structures
To investigate the electronic structure and properties of these compounds, the LUMO-HOMO and electrostatic potential (ESP) orbitals were studied. Figure 4 shows the LUMO and HOMO distributions of the selected compounds (C3, C5, D3, D5, E3, and F3). It can be clearly seen that the LOMO and HOMO distributions of each compound are different. The LUMOs of C3, C5, and E3 were mainly distributed on the energetic groups and rings on one side, while those of D3, D5, and F3 were mainly distributed on the energetic groups and bridging structures. The HOMOs of C3, C5, D3, D5, and F3 were mainly distributed on the parent structure, while that of E3 was mainly distributed on the energetic group and ring on one side. The ΔE LUMO-HOMO values of the six screened compounds (C3, C5, D3, D5, E3, and F3) were in the range of 4.01 eV(D5) to 4.92 eV (C3), which were relatively stable. Therefore, we conclude that the compound C3 has the most stable structure.
The molecular surfaces of the six screened compounds were quantitatively analysed using the Multiwfn software, [31] and then the distribution of the ESP was obtained using the VMD software [32]. The molecular interactions and chemical reaction sites could be visualised on the ESP surface [33][34][35]. Figure 5 shows the ESP analysis of the selected compounds (C3, C5, D3, D5, E3, and F3). In Fig. 5, the positive and negative potentials are represented by red and blue colours, respectively. In addition, the area ratio of the positive and negative potentials is also provided. The positive potential was mainly distributed on the ring and the hydrogen atoms, while the negative potential was mainly distributed on the outer ring and the energetic groups. Global

Conclusions
In this study, the HOF, ρ, Q, D, P, and h 50 of the designed compounds were calculated using density functional theory. The calculated results show that all the designed compounds have high positive values of HOF owing to their coplanar structures, which resulted in higher values of HOF of the designed compounds compared to RDX and HMX. Besides, we found that the combination of the -N = N-bridge and -N 3 substituent was most effective in enhancing the HOF of the designed compounds. Our findings suggested that the combination of the -N = N-bridge and -C(NO 2 ) 3 substituent was most effective in increasing the D and P values of the designed compounds. The -C-C-bridge and -N 3 /-NHNH 2 substituents were most effective increasing the impact sensitivity of the designed compounds. By comparing the detonation performance (D and P) and impact sensitivity, six compounds (C3, C5, D3, D5, E3, and F3) with excellent overall performance and great potential for military applications were screened. Availability of data and material The data sets supporting the results of this article are included within the article and its additional files.

Declarations
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Conflict of interest/Competing interests
The authors declare no competing interests.