Theoretical design of high-nitrogen energetic molecules: Performance prediction of pentazole-based derivatives

High nitrogen energetic compounds have always been a hot spot in energetic materials. In this work, we provide a new approach for the design of promising energetic molecules containing pentazole. Attractive energetic compounds include 5-amino-3-nitro-1H-1,2,4-triazole (ANTA) and 5-nitro-1,2,4-triazol-3-one(NTO) are used to effectively combine with pentazole to form a series of pentazole derivatives. Then, the NH 2 , NO 2 or NF 2 groups were introduced into the system to further adjust the property. Herein, the structures and densities of designed compounds as well as the heats of formation, detonation properties and impact sensitivities were predicted based on density functional theory (DFT). The results show that all ten designed molecules have excellent densities (1.81 g/cm 3 to 1.97 g/cm 3 ) and high heats of formation (621.66 kJ/mol to 1374.63 kJ/mol). Furthermore, detonation performances of compounds A3 (P = 41.16 GPa and D = 9.45 km/s) and A4 (P = 43.90 GPa and D = 9.69 km/s) are superior to 1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX), and lower impact sensitivity than HMX. It exhibited that they could be taken as promising candidates of high-energy density materials. This work provides a worthy way to explore the energetic compounds with excellent performance based on pentazole.


Introduction
Due to the superior performances over conventional explosives, high-energy density materials (HEDMs) have been a hot topic of interest and play a major role in the eld of military and civilian in recent years. With the increasing demand for HEDMs, researchers have continuously sought for new HEDMs to store signi cantly more chemical energy than the energetic materials currently used, which can release energy safely and have minimal impact on the environment. HEDMs can be achieved with the help of traditional chemistry, with novel chemistry dealing with polynitrogen compounds, or exotic physics such as metallic hydrogen. Potential HEDM can be applied in both explosives and propulsion systems. The decomposition of HEDMs releases lots of energy and produces environmentally friendly gas products (non-toxic in nature). In order to meet the above requirements, there should not be any metal atoms in the structure of HEDM. Nitrogen-rich high-energy materials are a kind of important HEDMs [1][2][3][4][5][6][7]. High-nitrogen energetic materials (HNEMs) are becoming a research hotspot in the eld of advanced HEDMs aimed at futuristic defense and space sector needs. The high energy content of HEDMs results from the existence of adjacent nitrogen atoms, which are ready to form nitrogen (N ≡ N). This transition is accompanied by a huge energy release, since the average bond energies of N-N (159kJ/mol) and N = N (419kJ/mol) are tremendously different from that of N ≡ N (946 kJ/mol) [8]. Due to the natural result of their chemical structures, HNEMs also produce large amounts of gas (N 2 ) per gram of high energetic materials projecting them as a good candidates for potentially environmentally friendly energetic materials [9][10][11].
The pentazole compounds, which are regarded as having enormous energy, are receiving signi cant attention in the eld of energetic materials. The cyclo-N 5 − was rst identi ed in aryl pentazoles in the late 1950s. Eventually, Zhang et al.
reported the rst synthesis of the cyclo-N 5 − in the solid phase (N 5 − ) 6 (H 3 O + ) 3 (NH 4 + ) 4 Cl − , which is highly stable with an initial thermal decomposition temperature of 390.15 K in 2017 [15]. Subsequently, a series of cyclo-N 5 − salts were successfully synthesized with good detonation properties. These studies indicate that the pentazole is a new generation of energetic compounds as well as one of the promising precursors in the family of full nitrogen compounds. Currently, there are few N 5 -based compounds in existence and more research is needed to design and investigate the structure and properties of N 5 -based energetic compounds further.
In 1979, Pevzner et al. [22] synthesized 5-amino-3-nitro-1H-1,2,4-triazole (ANTA) for the rst time as a raw HNEM containing triazole ring. It has the following characteristics: (1) the nitrogen content in the molecule is high (54%), relatively low carbon and hydrogen content, thereby improving the oxygen balance and increasing the energy density of the compound, (2) intermolecular hydrogen bond is formed between the hydrogen atom in the molecule and the oxygen atom in the nitro group, which increases the stability of the compound, (3) There are two reaction sites, -NH and -NH 2 , in the molecule, which can participate in a variety of chemical reactions, and a series of novel insensitive energetic compounds based on ANTA can be obtained. It is reported in the literature [23] that the sensitivity of high-energy insensitive explosive ANTA is similar to that of TATB, and its detonation performance is 7% higher than TATB. Thus, ANTA is an important insensitive explosive and rocket propellant. On account of ANTA containing acidic protons, its application is limited. However, there are active sites in the structure of ANTA, which has the basic characteristics of being a reaction intermediate in chemical synthesis and can eliminate the in uence of acidic hydrogen. In order to obtain high-energy insensitive materials with better performance, the synthesis of new high-energy insensitive compounds using ANTA as intermediate has become a research hotspot at home and abroad.
In 1966, the Soviet Union summarized the method of direct nitri cation and synthesis of NTO, and developed a two-step synthesis of NTO from semicarbazide hydrochloride and formic acid through condensation and nitration [25]. The method was used by later researchers since it was easier to get raw materials and more industrially friendly. In fact, the detonation performance of NTO is close to that of RDX, and its sensitivity is low, which is close to that of TATB. Moreover, NTO is similar to TNT in that only burns in case of re but does not explode [26], making it an ideal choice for high energy density and low sensitivity explosives. NTO has been as another high-energy insensitive compound with better performance.
In short, pentazoles, ANTA and NTO are greatly attractive and valuable HEDMs. If combined, are likely to form a new type of high-energy compound with good properties. Hence, in the work, a suite of HNEMs were designed by combining different numbers of PZ with ANTA and NTO (as shown in Fig. 1). Then, their structures and performance were theoretically predicted via using different methods including electrostatic potential (ESP) and the density functional theory (DFT).

Computational Methods
The optimizations of the molecular structures and the predictions of heat of formation (HOF) were performed by Gaussian 09 [27] package under the DFT-B3LYP method with the 6-311 + + G(d,p) basis set. All of the optimized structures have the local energy minimum on potential energy surfaces without imaginary frequencies.
The density of the compounds can be obtained by the following equation The gas-phase HOFs of ten novel compounds at 298 K were estimated on the basis of the following isodesmic reactions, respectively.
The heat of reaction ΔH 298 at 298 K can be calculated as the following equation, Meanwhile, the ΔH 298K can be calculated via the following expression, where ΔE 0 denotes the total energy difference between the products and the reactants at 0 K, ΔZPE stands for the difference between the zero-point energies of the products and the reactants at 0 K. ΔH T shows thermal correction from 0 to 298 K.
According to Hess's law of constant heat summation, the gas-phase HOF (ΔH f,gas ) and heat of sublimation (ΔH sub ) are used to evaluate the solid-phase HOF (ΔH f,solid ), ΔH f,solid = ΔH f,gas -ΔH sub (4) ΔH sub can be obtained by the empirical expression suggested by Politzer et al. [29], in which a, b, and c are 4.4307, 2.0599 and − 2.4825, respectively [29]. A denotes Overall surface area of the molecule.
The available free space per molecule in the unit cell (ΔV) were calculated by using the ESP methods proposed by Politzer group [31] as the following, where V eff is zero free space, V int stands for the intrinsic gas phase molecular volume. In above equation, V, A and were obtained through the Multiwfn program [32].

Molecular geometry and electronic structure
The molecular structures of A1 to A5 and B1 to B5 were optimized via the method introduced above. As can be seen in Fig. 2 For the designed compounds, the energies of the highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO) and energy gaps (ΔE) were illustrated in Fig. 3. The energy of HOMO and LUMO decreases with the increase of the number of PZ attached to nitrogen in ANTA or NTO, showing that the addition of PZ could make the electron acceptance of ANTA or NTO easier and the electron loss more di cult. Since NH 2 is an electron-donor group and NO 2 and NF 2 are electron withdrawing groups, the introduction of NH 2 group increases the energy of HOMO and LUMO, while the introduction of NO 2 and NF 2 groups has an opposite effect. Conceptual density functional theory is a signi cant theory for the study of chemical reaction activities and sites. In this framework, there is a quantity called softness. Softness does not refer to the rigidity of the system, but re ects the activity of electrons and the distribution of easy deformation degree. For a series of similar systems, it is generally believed that the softer the molecule is, the more active its reactivity is. The softness is approximately equal to the reciprocal of HOMO-LUMO gap. In the chemical or photochemical process of electron transfer or transition, the energy gap is an important parameter to evaluate the reactivity. Thus, the smaller the Energy gap, the higher the reactivity. As shown in Fig. 3, all of the designed compounds have relatively large energy gaps, ranging from 4.14 eV to 5.31 eV, which indicates that these molecules show good stability in the chemical process. Moreover, A3 has the largest energy gap, while A5 has the smallest one among these compounds.

Density and heat of formation
For high-energy materials, density plays a signi cant role in detonation performance, since higher density means more energy per unit volume. Speci cally, the density can directly affect the detonation performance shown in the Kamlet−Jacobs equation. In this part, based on the combination of PZ and ANTA (A1 to A5)/NTO (B1 to B5), the effect of introducing different substituents on the density of energetic compounds with appropriate positions were studied. The density of the designed compounds ranges from 1.81 g/cm 3 to 1.97 g/cm 3 ( Table 2). In view of the second substitution site of NTO is adjacent to C-NO 2 , while that of ANTA is meta-substitution. When the same substituent is introduced, the repulsive force between substituents of series B derivatives is larger, and the corresponding substituents contribute more to the volume, so that the densities of series B derivatives are slightly lower than those of series A derivatives. It is found that the density increases in the order of A1 to A4, exhibiting that the introduction of NH 2 , NO 2 and NF 2 into the system increases the density. Since the above groups can signi cantly increase the molar mass of the compound, but have relatively little effect on the molecular volume. One should note that A5 (consisting of an ANTA and two PZ rings) has lower density, compared with A1, as a result of less coplanarity of its structure, reducing the packing regularity and increasing the spatial volume of the molecule with the addition of another PZ ring. In short, its contribution to volume is much greater than that to molecular weight. The change trend of the density of B and A series compounds is similar (except B2). Obviously, the in uence of the introduction of amino group on the volume is greater than that on molecular weight for B2.
Nitrogen content and oxygen balance (OB) are two momentous parameters for screening energetic compounds. The higher the nitrogen content of energetic materials is, the better the detonation performance is. Explosive reactions can release maximum heat when the oxygen balance is zero. Lower OB stands for more oxygen being needed from external surroundings during combustion transitioning to detonation, which could result in the decrease of detonation performance. Therefore, the energetic compounds with high nitrogen content and zero oxygen balance would have better detonation performance. For the designed molecules, the nitrogen content is higher than 58%, and the oxygen balance is between -26.29 % and 3.09 %. This displays that these molecules have good detonation properties. According to research ndings, the addition of another PZ ring could increase the solid-phase HOF of the system by about 640 kJ/mol. For A series compounds, the solid-phase HOF of A2, A3, A4 or A5 is larger than A1, indicating that the introduction of the NH 2 , NO 2 , NF 2 groups or consisting of an ANTA and two PZ rings could enhance HOF. While this positive in uence of NH 2 , NO 2 or NF 2 group is weaker than that of addition of another PZ ring, since A2 to A4 all have lower solid-phase HOFs than A5 to varying degrees. An analogical situation occurs in series B derivatives. Meanwhile, the similar solid-phase HOF values of series A and B show that the introduction of NF 2 (A4 and B4) cannot signi cantly increase the HOF. Therefore, in the formation of such compounds, in order to obtain high HOF, the introduction of NH 2 or NO 2 group as a substituent or combining with two PZ rings is a good choice.

Energetic properties
The detonation heat (Q), detonation pressure (P), and detonation velocity (D) of the title compounds have been assessed by the semi-empirical Kamlet-Jacobs formula, which has been proved to be applicable for predicting the explosive properties of energetic high-nitrogen compounds based on the predicted density and heat of formation. P and D are the most important parameters for evaluating energetic materials.
The P and D for two known explosives RDX and HMX were also calculated by above method. For molecules A1 to A4 and B1 to B4, with increasing sequence number, both corresponding P and D increases gradually, indicating that the introduction of NH 2 , NO 2 or NF 2 is bene cial for improving energetic properties. What's more, the molecule with NF 2 group (A4 or B4) has the best detonation performances while the compound with the NH 2 substituent (A2 or B2) has the worst detonation performances, indicating that the contribution of NF 2 group to the detonation performance of an energetic compound is greater than that of NH 2 group. When an NTO is combined with two PZ rings, both P and D are larger than those of B1 and B2. The reason is that the density and HOF of B5 advantage over those of B1 and B2. It is further proved that density and HOF are the decisive factors for evaluating the detonation performance of energetic materials. Both P and D of compounds A3, A4 and B4 are superior to HMX, A2, A5, B3 and B5 have approximate or exceeded P and D over HMX, whereas those of B1 and B2 are approximate or inferior to RDX, exhibiting that they can be taken as promising candidates of HEDMs apart from B1 and B2. These predictions further verify that modifying energetic molecules with appropriate substituents is a meritorious method to improve the energetic properties.

Sensitivity
The core problem in designing new explosives is to achieve the desired balance between high performance and low sensitivity. Therefore, in order to further investigate the practical application, an admissible sensitivity value is essential for a new high-energy compound. It is therefore signi cant to have some means of evaluating the likely sensitivities of compounds that have not yet been synthesized. In this part, the free space per molecule in the unit cell, designated ΔV, has been used to evaluate sensitivity of the proposed compounds, which has been proved to be reliable for predicting the sensitivity of energetic compounds [31,36]. The smaller value of ΔV is, the lower sensitivity of the explosive is.
In Fig. 4b, the second substitution site of NTO is adjacent to C-NO 2 , whereas that of ANTA is the meta-potition from C-

Conclusion
The connection of PZ with ANTA and NTO form A1 and B1, respectively. In order to adjust the property further, different substituents (NH 2 , NO 2 and NF 2 ) were introduced to form two series compounds A and B. The results showed that the formation heat of ANTA or NTO bonding two PZ rings increases by ~ 640 kJ/mol compared to those of ANTA or NTO bonding one PZ ring. In addition, better detonation performance and higher sensitivity are achieved when A1 or B1 combine with another PZ ring. Meanwhile, the second substitution site of NTO is adjacent to C-NO 2 , which has larger steric hindrance than ANTA, when introducing the same group into the frame. As a result, A-series derivatives have larger densities and lower sensitivities than B-series. The NH 2 , NO 2 and NF 2 groups increase the densities and HOFs, especially for the NO 2 and NF 2 groups. Moreover, all the compounds have high densities, heats of formation and great detonation performances. Among them, molecules A3 and A4 not only have better detonation performances than HMX, but also have comparable sensitivities, which further demonstrate that both NO 2 and NF 2 groups can availably regulate the energetic properties. The excellent energetic properties of A3 (P = 41.16 GPa and D = 9.45 km/s) and A4 (P = 43.90 GPa and D = 9.69 km/s) make them be potential candidates for HEDMs.

Declarations
Funding: This work was supported by the National Natural Science Foundation of China (No. 21975128, 21903044, 11972178).
Con icts of Interest/Competing interests: The authors declare no con ict of interest.
Availability of data and material: The work described is original that has not been published previously, and the data is available. Figure 1 Molecular structures of designed compounds.

Figure 2
Optimized structures of designed of compounds.

Figure 3
HOMO and LUMO energy levels and energy gaps of ten compounds.

Figure 4
A comparison of Q, P, D (a) and ΔV (b) of compounds.