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. 2023 Aug 17;88(17):12481–12492. doi: 10.1021/acs.joc.3c01225

Can Catenated Nitrogen Compounds with Amine-like Structures Become Candidates for High-Energy-Density Compounds?

Xinbo Yang †,‡, Nan Li ‡, Yuchuan Li †,*, Siping Pang †,*
PMCID: PMC10476612  PMID: 37590038

Abstract

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The worthwhile idea of whether amine-like catenated nitrogen compounds are stable enough to be used as high-energy materials was proposed and answered. Abstracting the NH3 structure into NR3 (R is the substituent) yields a new class of amine-like catenated nitrogen compounds. Most of the azole ring structures have a high nitrogen content and stability. Inspired by this idea, a series of new amine-like catenated nitrogen compounds (A1 to H5) were designed, and their basic energetic properties were calculated. The results showed that (1) amine-like molecular structures are often characterized by low density; however, the density of these compounds increases as the number of nitrogens in the azole ring increases; (2) these catenated nitrogen compounds generally have extremely high enthalpies of formation (882.91–2652.03 kJ/mol), and the detonation velocity of some compounds exceeds 9254.00 m/s; (3) the detonation performance of amine-like catenated nitrogen compounds designed based on imidazole and pyrazole rings is poor due to their low nitrogen content; and (4) the bond dissociation enthalpy of trigger bonds of most compounds is higher than 84 kJ/mol, indicating that these compounds have a certain thermodynamic stability. In summary, amine-like catenated nitrogen compounds have the potential to become energetic compounds with excellent detonation properties and should be considered to be synthesized by experimental chemists.

1. Introduction

Ammonia is widely used in electronics, food, chemical industries, national defense, and other fields. Synthetic ammonia is a major achievement in the history of human science and technology.1 The H atom in its molecule is often replaced by other groups through an oxidation reaction, thus forming organic nitrogenous compounds. This compound formed by replacing the H atom in ammonia can be called the amine-like structure. In addition, the azole ring and the azine ring have a wide range of applications in the field of biomedicine.2 Replacing the H in the ammonia molecule with these rings as substituents will produce a series of amine-like catenated nitrogen compounds, which may have interesting properties.

Habitually, people often call energetic materials as catenated nitrogen compounds (catena-n nitrogen compounds, which are also called N-based energetic materials).3 These kinds of nitrogen-rich compounds have two characteristics: there are n nitrogen atoms directly connected in the molecule; and with the increase of the number of directly connected nitrogen atoms in the molecule, the stability of the molecule will generally decrease. A large number of studies have shown that when the value of n is larger than 4, the synthesis of nitrogen-rich structures will become extremely difficult, making the synthesis work always a challenging topic.4−8 Generally, there is a wide variety of synthetic nuclei for constructing nitrogen-rich compounds. For catena-n nitrogen compounds with n ≥ 5, their construction units mainly include triazole/triazene/triazine, tetrazole/tetrazene/tetrazine, and pentazole/pentazene/pentazine.3 From the perspective of increasing the catenation numbers (often referred to as N-extended π-systems), bridge linkage9 and fused ring10 strategies are often used to design new catenated nitrogen compounds. These two strategies increase the conjugation degree of the system, resulting in further expansion of the delocalization range of π electrons, thus effectively enhancing the molecular stability. For example, based on the fused ring strategy, Chavez et al.6 synthesized a 2,2′-diamino-5,5′-dinitro-[3,3′-bi(1,2,4-triazole)] from 5,5′-dinitro-bis-1,2,4-triazole as a starting material through N-amination and oxidative ring sealing, an N6-based energetic material, which is insensitive to impact, friction, and spark stimulation. Another example that can more reflect the fused ring strategy and stabilize the catenated polynitrogen compounds is the synthesis of 2,2′-diamino-4,4′,5,5′-tetranitro-[3,3′-bipyrazole] by Tang et al.7 This compound has not only high density and detonation velocity but also a high thermal decomposition temperature and friction sensitivity. In addition, the bridge linkage strategy has similar functions. For example, our laboratory has synthesized catena-8 nitrogen compounds4 with good thermal stability for the first time in the world by means of bridge linkage azo and 1,2,3-triazole (1,1′-azobis-1,2,3-triazole). The decomposition temperature of this compound is 193.8 °C, which is higher than the decomposition temperature of the hexazene structure11 and N5+,12 because the π electron delocalization effect of the catena-8 nitrogen structure contributes to the stability of this structure. Furthermore, Klapötke and Piercey5 synthesized the catena-10 nitrogen structure (1,1′-azobis(tetrazole)) according to the same method as 1,2,3-triazole (1,1′-azobis-1,2,3-triazole). Although the author mentioned in the article that the compound is extremely sensitive, the fact cannot be denied that a new type of catenated nitrogen compound can be constructed through the bridging strategy. This way of constructing Nn-based energetic materials by using an azo bond as the bridge linkage13 can expand the π electron delocalization range of the system, but it is undeniable that this chemical bond itself has certain instability. As mentioned previously, for 1,1′-azobis-1,2,3-triazole and 1,1′-azobis(tetrazole), in fact, the stability of these molecules is relatively poor. Recently, we have noticed that if the common azo bridge linkage is changed to a single nitrogen atom (ammonia molecule, NH3) connection, this may lead to a new class of catenated nitrogen compounds, which have amine-like structures (In this paper, the molecular structures of various nitrogen clusters14−21 will not be considered temporarily. Although the molecular structure characteristics of these nitrogen clusters meet the definition of catenated nitrogen compounds, the azoles used in this paper are all nitrogen-containing structures that have already existed in experiments, while most of the nitrogen cluster structures are only theoretical structures that cannot exist stably under actual conditions.) Interestingly, some studies have shown that N(NH2)3,22 N(NO2)3,23 N(NF2)3,24 N(N3)3,25 and N(1,2,4,5-tetrazin-3-yl)326−29 have been discussed. Although N(1,2,4,5-tetrazin-3-yl)3 has a low density (1.73 g/cm3), it has a very high enthalpy of formation (1386.2 kJ/mol), which can compensate for the lack of density, so its detonation velocity reaches 8322 m/s. Therefore, in order to answer whether these kinds of catenated nitrogen compounds, which are composed of azole rings, can become the candidates of high-energy-density materials, we designed a series of catenated nitrogen compounds with amine-like structures by replacing the hydrogen atoms in NH3 with the substituent groups of the azole rings (pyrazole, imidazole, triazole, tetrazole, pentazole) (see in Scheme 1), and the energetic properties of these compounds were evaluated. In addition, the effects of the azole ring skeleton on the crystal density and solid formation enthalpy of these catenated nitrogen compounds as well as the effect of the explosophoric groups on the bond dissociation enthalpy were discussed. Based on theoretical calculations, we preliminarily explored the basic properties of these new types of catenated nitrogen compounds, which provides an important reference value for the subsequent experimental synthesis.

Scheme 1. Amine-like Catenated Nitrogen Compounds Involved in a Previous Work and Designed in This Work.

Scheme 1

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2. Computational Methods

The initial geometries in this work were calculated by using the M06-2X30 exchange-correlation functional in conjunction with the 6-311G (d, p) basis set31 in the gas phase. All initial geometries were of alternate bond lengths, and the optimized structures discussed were characterized to be local minima without imaginary frequencies. The Gaussian 09 (D.01) program32 was employed for the quantum chemistry calculations for initial geometries. Molecular electrostatic potential (ESP)33 analyses were completed via the Multiwfn 3.8 (dev) code34 based on the formatted checkpoint files of Gaussian 09.

The isosurface maps of ESP were rendered by means of visual molecular dynamics (VMD) software35 based on the files exported from Multiwfn. The highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs), the electronic density, and the electrostatic potential (ESP) were calculated at the M06-2X/6-311G (d, p) level of theory.

The calculation of enthalpy of formation consists of the following parts. The double hybrid PWPB9536 level of theory functional in the ORCA program37 was used to calculate the final single-point energy of the stable molecular structure, and the input files of the ORCA program were prepared with the help of the Multiwfn code. The density functional theory (DFT) single-point energy calculations were conducted with ORCA applying TightSCF38 and Grid4 options. The quadruple-ζ def2-QZVP basis set39 was used for DFT calculations. The D3 London dispersion correction was generally applied for DFT calculations. The resolution-of-identity (RI) approximation for Coulomb (RIJ) and exchange (RIJK) integrals was used in combination with matching auxiliary basis sets as implemented in ORCA (def2/J, def2/JK options, def2-QZVPP/C for the MP2 correlation part)40 to speed up the DFT calculations. The vibration analysis files of the initial structure were used to calculate various thermodynamic constants by the Shermo program.41 As for the M06-2X functional, the resonant frequency correction factor of zero-point energy (ZPE) is 0.97. Finally, according to the definition of the enthalpy of formation, the enthalpy of formation in the gas phase42 was calculated.

Enthalpy of formation (ΔHf) is one of the most important parameters for energetic compounds. The definition of the enthalpy of formation (Scheme 2) is used to calculate the enthalpy of solid formation (ΔHf(solid, 298 K)) of a substance as shown in eq 1

2. 1

Scheme 2. Born–Haber Energy Cycle for the Formation of Energetic Materials.

Scheme 2

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The enthalpy of sublimation (ΔHsub) can be represented as eq 2

2. 2

where SA is the molecular surface area for an amine-like catenated nitrogen compound structure, σtot2 is an indicator of the variability of the electrostatic potential on the molecular surface, and υ is interpreted as showing the degree of balance between the positive and negative potentials on the molecular surface where a, b, and c are fitting parameters.

The gaseous enthalpy of formation (ΔH2) can be expressed as eq 3

2. 3

where H in eq 3 is the absolute enthalpy value.

The density was obtained using an improved equation proposed by Politzer et al.,43 which considers intermolecular interactions within the crystal

2. 4

where V (0.001) is the volume in cm3/molecule and is encompassed by the 0.001 au contour of the electronic density, M is the molecular mass in g/molecule, υσtot2 is derived from the molecular electrostatic potential calculation, and α, β, and γ are coefficients assigned through fitting eq 4 to the experimental densities of a series of 36 energetic compounds.

The bond dissociation enthalpy (BDE) of the trigger bond is an important descriptor that can be used to describe the thermal stability of energetic materials.

2. 5

where BDE(AB) represents the bond dissociation enthalpy of AB, EA•(EB•) refers to the enthalpy of the free radical A•(B•), and EAB is the enthalpy of the compound AB.

The detonation parameters of energetic compounds including the detonation velocity (D) and pressure (P) were predicted by EXPLO 5 v6.05.44

3. Results and Discussion

3.1. Geometry and Frontier Molecular Orbital

The optimized structures of the title compounds are displayed in Figure 1 at the M06-2X/6-311G (d, p) level. We can intuitively find that when the hydrogen atom in ammonia gas is replaced by the azole rings (pyrazole, imidazole, triazole, tetrazole, and pentazole), the geometric configurations of some molecules retain a relatively high symmetry (A1, B1, C1, D1, E1, and H1). The symmetry of molecular geometry will change when there are substituents in the rings. For example, when there are nitro and difluoroamino groups (B2, B4, E2, E4, F2, F4, G2, G4, H2, and H4), the molecular structures are distorted greatly. This may indicate that the electron-withdrawing effect will reduce the aromaticity of the azole ring and lead to changes in the molecular geometries. Because the azido group and N-oxides are easily conjugated with the azole ring, some compounds can still maintain a high symmetry (B3, C3, D3, E3, A2, B5, C5, D5, and H5). Furthermore, N-oxides can also alter the symmetry of molecules in certain situations. For example, E5 and F5 have poor symmetry, and their intramolecular azole rings have a certain degree of twisting compared to E1 and F1, which do not have N-oxide structures. In addition, isomerism also has some influences on the molecular structures. For instance, the structures of B2, B3, B4, and B5 are different from those of E2, E3, E4, and E5. This is mainly due to the different atoms connected with the central nitrogen atom, resulting in the change of the electronic structure of the azole rings. In fact, the amine-like structure proposed in this paper can be regarded as a special case of designing energetic materials with the amino group as the bridging group. Some studies45−47 have shown that the use of the amino bridging strategy is an effective way to construct heat-resistant energetic compounds, which further suggests that the amine-like catenated nitrogen compounds designed in this paper are potential energetic materials.

Figure 1.

Figure 1

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Molecular structures of the amine-like catenated nitrogen compounds (A1–H5).

The frontier molecular orbitals (FMOs) are shown in Figure 2. FMOs include the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). The gap between the energy level of the HOMO orbital and the energy level of the LUMO orbital represents the energy required to overcome the electron transfer, which is an important parameter that can evaluate the reactivity in the chemical or photochemical processes with electron transfer or leap. The HOMOs, LUMOs, and energy gaps of amine-like catenated nitrogen compounds can be seen from Figure 2 as well as Scheme S1 and Table S1 in the Supporting Information (SI). The gap values of all compounds range from 7.05 to 9.55 eV, where A1 has the largest gap value and F5 has the smallest gap value. Compared with the gap value of RDX (9.22 eV), the gap values of A1, B1, D1, and E1 are higher, which indicates that these molecules are more difficult to undergo the charge transfer process than RDX under gas-phase conditions. In addition, some propeller-like multitetrazole molecules proposed by Zhang and Li48 are isomers of amine-like catenated nitrogen compounds proposed in this paper. For example, in their study, compounds D1, D2, D3, and D9 are isomers with B1, B3, B2, B4, E1, E3, E2, and E4, respectively. The gap values of compounds D1, D2, D3, and D9 are 6.40, 5.15, 4.56, and 5.71 eV, respectively, while the gap values of B1, B3, B2, and B4 are 9.29, 8.34, 7.92, and 9.06 eV, respectively (the gap values of E1, E3, E2, and E4 are 9.46, 7.83, 8.69, and 9.10 eV, respectively). It can be seen that the amine-like catenated nitrogen compounds (constructed from the tetrazole ring) designed in this paper are more difficult to undergo the charge transfer process than the propeller-like multitetrazole molecules.

Figure 2.

Figure 2

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HOMO (red bar chart) and LUMO (blue bar chart) energy levels of amine-like catenated nitrogen compounds (A1–E5). The red and blue dotted lines represent the HOMO orbit and the LUMO orbit of RDX, respectively.

3.2. ESPs on the Molecular Isosurface

Electrostatic potentials (ESPs)49 of amine-like catenated nitrogen compounds’ van der Waals (vdW) surfaces could be used for analyzing the chemical reactivity of energetic compounds. The molecules that are more sensitive have significant electron deficiencies (positive potentials) within the molecule. In the electrostatic potential isosurface, blue represents negative electrostatic potential, red represents positive electrostatic potential, and white represents zero electrostatic potential.

Figure 3 shows the respective molecular electrostatic potential isosurface for A1 to D5, and the others (E1 to H5) are shown in Scheme S2 in the SI. On the whole, the regions with local maxima of positive electrostatic potentials are mainly distributed in the upper and lower sides of the azo ring plane in the amine-like catenated nitrogen compounds, while the regions with local minima of negative electrostatic potentials are mainly concentrated in the vicinity of nitrogen atoms and oxygen atoms with high electronegativity in the molecule. Surprisingly, this trend of electrostatic potential distribution is basically consistent with that of guanidine-based nitroazole-substituted compounds of energetic windmills studied by Zhang et al.50

Figure 3.

Figure 3

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ESP-mapped molecular vdW isosurface of amine-like catenated nitrogen compounds (A1 to D5).51 The 0.001 electron/bohr3 isosurface of electron density was evaluated at the M06-2X/6-311G (d, p) level.

However, it was found that the extreme value of the electrostatic potential near the F atom is close to zero (white region in the ESP-mapped molecular vdW surface) in some amine-like catenated compounds containing NF2 groups (B4, C4, D4, E4, and F4), which is not consistent with ordinary chemical intuition. Because in molecules, there is generally a more negative electrostatic potential around the atoms with high electronegativity, the atomic dipole moment-corrected Hirshfeld population (ADCH)52 values of these five molecules (see Figure 4) are further analyzed. In Figure 4, through the ADCH-mapped molecular diagrams, it can be found that the color of the NF2 in C4 is light blue, which indicates that the atomic charge on the amino group in the molecule has a weak negative charge (ADCH-2). In other molecules (B4, D4, E4, and F4), the ADCH-mapped molecular diagram shows that the color of the difluoroamino group in each molecule is close to white, suggesting that there are slightly positive atomic charges in these structures. These distributions of atomic charges determine that the color of the equivalent surface of the van der Waals surface electrostatic potential around the fluorine atoms in the NF2 is close to white.

Figure 4.

Figure 4

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ESP-mapped molecular vdW surface and ADCH-mapped molecular diagrams of amine-like catenated nitrogen compounds (B4 to F4).

3.3. Enthalpy of Formation and Density

The solid-phase enthalpy of formation (ΔHf (solid))53 of energetic materials is a critical index. It is usually obtained by deducting the sublimation enthalpy from the gas-phase formation enthalpy of molecules (see Table S2). It can be seen from Figure 5a that the ΔHf (solid) values of all amine-like catenated nitrogen compounds are between 882.91 and 2652.03 kJ/mol, which are higher than those of RDX (80.0 kJ mol–1) and HMX (104.8 kJ mol–1). These ultrahigh ΔHf (solid) values imply that these kinds of amine-like catenated nitrogen compounds have high energy and meet the design concept of high-energy materials. In addition, the order of influence of different substituents on the enthalpy of formation is N3 > NO2 > NF2 > N-oxides (except D4, D5, G4, and G5). For compounds D1, D2, D3, and D9 in Zhang’s work,48 their ΔHf (solid) values are 970.43, 2429.50, 1372.8, and 1324.10 kJ/mol, respectively. However, in our work, the ΔHf (solid) values of B1, B3, B2, and B4 are 1549.93, 1911.22, 1865.36, and 1779.86 kJ/mol, respectively (the ΔHf (solid) values of E1, E3, E2, and E4 are 1506.53, 2652.03, 1948.0, and 1930.05 kJ/mol, respectively). The results of ΔHf (solid) suggest that the amine-like catenated nitrogen compounds with tetrazole rings have a higher energy than the propeller-like multitetrazole molecules as a whole.

Figure 5.

Figure 5

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Radar maps of the solid-phase enthalpy of formation (a, kJ/mol) and density (b, g/cm3) of all amine-like catenated nitrogen compounds (A1 to H5).

The crystal density (ρ) (see Table S3) of energetic materials is directly related to the detonation velocity and pressure, which is another key index of energetic materials. The ρ distributions of all amine-like catenated nitrogen compounds are shown in Figure 5b. It can be seen that the ρ values of all compounds are between 1.42 and 2.04 g/cm3. The order of the effect of different substituents on the ρ of the compounds is NF2 > NO2 > N-oxides > N3. For compounds D1, D2, D3, and D9 in Zhang’s work,48 the ρ values are 1.75, 1.78, 1.93, and 2.06 g/cm3, respectively. However, in our work, the ρ values of B1, B3, B2, and B4 are 1.71, 1.75, 1.89, and 2.04 g/cm3, respectively (the ρ values of E1, E3, E2, and E4 are 1.69, 1.75, 1.87, and 1.97 g/cm3, respectively). The results of ρ suggest that the amine-like catenated nitrogen compounds with tetrazole rings have lower ρ than the propeller-like multitetrazole molecules as a whole. In addition, it is easy to find that when the substituents are changed from pentazole to imidazole, the density of the amine-like catenated nitrogen compounds formed gradually decreases. The reason for this phenomenon may be that the reduction of the number of nitrogen atoms in the molecule reduces the overall mass of the molecule, while the change of the molecular volume is small.

In addition, in order to further study the influence of different molecular skeletons of amine-like catenated nitrogen compounds on their solid formation enthalpy and crystal density, the solid formation enthalpy and crystal density of amine-like catenated nitrogen compounds (A1 to H1) are counted in Figure 6. The results show that with the decrease of the number of nitrogen atoms in the azole rings (pentazole to diazole), the crystal density (Figure 6a) and solid formation enthalpy (Figure 6b) of amine-like catenated nitrogen compounds (A1 to H1) appear to show a decreasing trend on the whole. This implies that in these catenated nitrogen systems, the appropriate azole rings should be selected to construct ammonia-like structures to ensure an appropriate size of crystal density and solid formation enthalpy. Furthermore, in Figure 6b, the enthalpies of solid formations of F1 and H1 are higher than those of D1 and G1, respectively. The reason for this phenomenon is that the numbers of catenated nitrogen atoms of F1 (N10) and H1 (N7) are higher than those of D1 (N7) and G1 (N3), respectively.

Figure 6.

Figure 6

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Effects of different molecular skeletons on the crystal density (a, g/cm3) and enthalpy of formation (b, kJ/mol) of amine-like catenated nitrogen compounds (A1 to H1).

3.4. Bond Dissociation Enthalpy

Here, the bond dissociation enthalpy (BDE) is used to further describe the molecular thermodynamic stability. For the designed amine-like catenated nitrogen compounds, two ways of dissociation are considered, one is the N–N single bond formed by connecting the central nitrogen atom with the azole ring, and the other is the C–N single bond formed by connecting the nitrogen-containing substituents on the azole ring with the azole ring (see Figure 7). Table 1 contains the bond dissociation enthalpies of the trigger bonds that may break in the molecules of amine-like catenated nitrogen compounds. According to the literature, when the bond dissociation enthalpy of the trigger bond in the molecule is higher than 84 kJ/mol,54 the compound may exist stably in theory. Therefore, most of the amine-like catenated nitrogen compounds designed in this paper can exist under theoretical conditions.

Figure 7.

Figure 7

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Model diagram of an amine-like catenated nitrogen compound with possible dissociation methods: (1). N–N bond homolysis; and (2). C–N bond homolysis. The pentagon represents azole ring structures such as pentazole, tetrazole, triazole, diazole, and corresponding N-oxide derivatives, and R represents N3, NO2, and NF2.

Table 1. Bond Dissociation Enthalpy (BDE, kJ/mol) Computed at the PWPB95(D3)/def2-QZVP//M06-2X/6-311+G (d, p) Level for Amine-like Catenated Nitrogen Compounds.

compounds BDEC–Na BDEN–Nb compounds BDEC–Na BDEN–Nb
N(N3)3   79.35 E1   238.39
N(NF2)3   74.90 E2 280.27 227.08
N(NO2)3   108.69 (122.0023) E3 409.36 154.19
A1   234.34 E4 305.08 193.17
A2   38.08 E5   32.71
B1   204.20 F1   215.80
B2 276.91 204.99 F2 297.18 225.80
B3 403.68 157.97 F3 392.17 165.75
B4 277.78 162.98 F4 312.67 207.20
B5   60.52 F5   55.31
C1   204.47 G1   141.54
C2 294.71 231.45 G2 278.85 150.08
C3 399.28 170.88 G3 396.13 111.34
C4 309.80 214.85 G4 300.12 137.28
C5   55.48 G5   5.06
D1   225.26 H1   209.66
D2 283.52 234.10 H2 303.27 194.35
D3 401.95 150.43 H3 397.05 163.23
D4 306.27 186.15 H4 314.83 183.74
D5   65.35 H5   64.10
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a

The BDE of the C–N single bond formed by connecting the nitrogen-containing substituents with the azole ring.

b

The BDE of the N–N single bond formed by connecting the central nitrogen atom with the azole ring.

However, it is easy to find that the enthalpies of dissociation of the trigger bonds of these catenated nitrogen structures are very small when there are N-oxide structures on the azole rings. For example, the N–N bond dissociation enthalpies of A2, B5, C5, D5, E5, F5, G5, and H5 are 30.08, 60.52, 55.48, 65.35, 32.71, 55.31, 5.06, and 64.10 kJ/mol, respectively. These very weak bond dissociation enthalpies suggest that amine-like catenated nitrogen compounds with N-oxide structures may be difficult to exist under general conditions. In addition, the bond dissociation enthalpies of the C–N bond are higher than those of the N–N bond on the whole, which further suggests that these kinds of catenated nitrogen compounds have certain challenges in the actual synthesis process. The smaller N–N bond dissociation enthalpy indicates that the process of completely replacing H in the ammonia molecule with the azole ring structure can easily lead to the occurrence of dissociation between the azole ring and the central amino-nitrogen atom. Therefore, to date, there has been no relevant experimental research on amine-like catenated nitrogen compounds.

In addition, the influence of explosophoric groups on BDE was further discussed. Since the energy required for breaking the N–N bond is lower than that of the C–N bond, the effect of the explosophoric groups on the dissociation enthalpy of the N–N bond is only discussed here. In Figure 8, the relationship between the change of bond dissociation enthalpy (ΔBDE) and the explosophoric groups of the N–N bonds of most amine-like catenated nitrogen compounds is fully discussed. ΔBDE represents the difference between the N–N bond dissociation enthalpy in derivative structures containing explosophoric substituents on the azole rings and the N–N bond dissociation enthalpy in structures without explosophoric substituents (B1, C1, D1, E1, F1, G1, H1) on the azole rings (see Table S4), reflecting the effect of explosophoric groups on the N–N bond dissociation enthalpy. From Figure 8, it can be found that the order of the influence of various explosophoric groups on the dissociation enthalpy of N–N bonds is NO2 < N3 < NF2 < N–O. The reason for this phenomenon may be that NO2, NF2, and N3 are directly connected to the carbon atom in the azole ring, which can form a certain conjugation with the azole ring without reducing the electron density of the catenated nitrogen structure. In the N–O structure, the oxygen atom is directly connected to the nitrogen atom in the azole ring. Since the electronegativity of the oxygen atom is greater than that of the nitrogen atom, it may lead to a decrease in the electron density of the catenated nitrogen structure, which will eventually lead to a decrease in the bond dissociation enthalpy of N–N bonds.

Figure 8.

Figure 8

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Effects of different types of explosive groups on the change of the bond dissociation enthalpy (ΔBDE) of the N–N bond dissociation model in amine-like catenated nitrogen compounds. B to H represent the series code names of each series of amine-like catenated nitrogen compounds designed in Figure 1 in this article, respectively.

3.5. Detonation Performances

Detonation performance represents the energy properties of energetic materials, which mainly include detonation velocity (VD), detonation pressure (P), detonation heat (Q), and specific impulse (Isp). Table 2 lists the relevant detonation parameters.

Table 2. Physical and Detonation Properties of the Newly Designed Amine-like Catenated Nitrogen Compounds as Explosives.

compounds OBa [%] Nb [%] ρc [g/cm3] ΔHfd[kJ/mol] VDe [m/s] Pf [GPa] Qg [kJ/kg] Isph [s]
N(N3)3 0 100.00 1.61 1344.90 9854.5 39.1 9643 358.4
N(NH2)3 –77.31 90.25 1.25 274.10 9482.7 25.5 5988 270.8
N(NO2)3 63.14 36.85 1.90 328.60 7401.2 21.2 2238 183.8
N(NO)3 46.14 53.86 1.73 482.30 8212.3 26.8 4622 254.0
N(NF2)3 28.23 32.95 2.26 230.20 5769.7 16.8 2854 154.9
N(tetrazin-3-yl)3 –83.98 70.80 1.73 1386.2 8322.0 (8017.8) 26.4 (23.5) (4963) (234.2)
A1 0 100.00 1.79 1977.99 10523.2 47.0 8902 345.9
A2 17.64 82.36 1.92 2218.29 10633.3 50.6 8051 321.5
B1 –54.26 82.34 1.71 1549.93 9238.9 32.9 6838 280.3
B2 0 62.93 1.89 1865.36 10080.1 44.9 8118 300.5
B3 –42.72 89.53 1.75 1911.22 9441.3 37.5 7078 286.6
B4 –12.83 48.67 2.04 1779.86 9106.7 39.7 8349 273.5
B5 –26.75 67.66 1.80 1652.09 9862.5 40.1 8083 317.4
C1 –109.99 64.20 1.60 1277.23 7941.5 22.2 5603 245.3
C2 –33.97 51.56 1.79 1460.89 9125.1 36.4 6968 291.4
C3 –63.30 78.00 1.66 2375.13 8511.9 27.4 6564 270.1
C4 –45.26 49.06 1.89 1410.98 8378.1 30.6 7515 269.8
C5 –72.13 52.62 1.72 1339.99 8623.5 30.2 6962 277.2
D1 –109.99 64.20 1.58 1070.69 7559.6 19.6 4693 227.5
D2 –33.98 51.56 1.82 1268.59 9038.9 35.5 6480 280.0
D3 –63.30 78.00 1.67 2134.11 8407.6 26.4 5899 258.7
D4 –45.26 49.06 1.90 1199.30 8296.4 29.7 6973 262.3
D5 –72.13 52.62 1.72 1205.14 8468.9 28.7 6484 268.1
E1 –54.26 82.34 1.69 1506.53 9106.1 31.7 6645 277.2
E2 0 62.93 1.87 1948.07 10020.9 43.9 8280 303.7
E3 –27.89 89.53 1.75 2652.03 9408.3 35.8 7535 297.2
E4 –12.83 48.67 1.97 1930.05 8987.1 37.8 8734 278.6
E5 –26.75 67.66 1.82 1728.41 10005.4 44.8 8365 322.2
F1 –109.99 64.20 1.56 1185.66 7625.0 20.0 5196 237.7
F2 –33.97 51.56 1.79 1534.64 9163.2 36.7 7156 295.6
F3 –63.30 78.00 1.69 2350.51 8603.3 28.2 6506 269.0
F4 –45.26 49.06 1.88 1546.12 8413.7 30.8 7855 274.4
F5 –72.13 52.62 1.76 1413.02 8870.9 32.3 7246 281.9
G1 –167.26 45.56 1.48 882.91 6497.6 14.9 3875 197.1
G2 –68.53 40.00 1.76 1071.50 8080.3 27.3 5916 254.3
G3 –99.32 66.26 1.58 1943.58 7501.9 20.2 5333 238.6
G4 –78.21 38.04 1.84 1001.60 7896.3 25.4 6583 264.4
G5 –118.53 37.25 1.67 1014.21 7610.1 21.9 5791 242.8
H1 –167.26 45.56 1.42 993.36 6520.3 16.1 4373 207.9
H2 –68.53 40.00 1.75 1193.41 8126.7 27.6 6229 261.5
H3 –99.32 66.26 1.58 2116.68 7598.1 21.5 5801 247.1
H4 –78.21 38.04 1.84 1127.77 7978.5 26.1 6914 269.0
H5 –118.53 37.25 1.60 1088.60 7415.9 20.7 6026 248.5
RDX –21.61 37.84 1.81 80.00 8872.0 34.7 6320 267.8
HMX –21.61 37.84 1.90 104.80 9254.0 39.2 6190 265.6
Open in a new tab
a

OB, oxygen balance.

b

N, nitrogen content.

c

ρ, density.

d

ΔHf, enthalpy of formation.

e

VD, detonation velocity predicted by EXPLO 5 v6.05.

f

P, detonation pressure predicted by EXPLO 5 v6.05.

g

Q, detonation heat predicted by EXPLO 5 v6.05.

h

Isp, specific impulse predicted by EXPLO 5 v6.05.

First of all, the oxygen balance describes the difference between the actual oxygen content in the explosive and the oxygen required to completely oxidize carbon and hydrogen in the explosive. It is generally believed that the value of oxygen balance is zero, which means that in theory, the oxygen element contained in the system can just completely oxidize combustible elements, which is conducive to the maximum power of explosives. For example, in our design of amine-like catenated nitrogen compounds, A1, B2, and E2, which belong to zero oxygen balance, exhibit excellent detonation performance. In addition, the detonation performance of N(NH2)3 was also studied. Surprisingly, although this compound has a very negative oxygen balance (−77.31%), low density (1.25 g/cm3), and low solid formation enthalpy (274.1 kJ/mol), it has excellent detonation velocity (9482.7 m/s). The reason for this phenomenon may be that N(NH2)3 has better gas production and average product molecular weight. Due to many factors affecting the detonation performance of energetic materials, this research cannot accurately give the relationship between oxygen balance and detonation performance. Second, compared to the nitrogen content of RDX and HMX (37.84%), most of the amine-like catenated nitrogen compounds designed in this paper have a higher nitrogen content (except G5 and H5) between 38.04% and 100%, which can be considered as compounds with a high nitrogen content.

In addition, amine-like catenated nitrogen compounds (A1 to H5) have a high enthalpy of formation as a whole, which can be attributed to the catenated nitrogen structures in their molecules. Due to the ultrahigh enthalpy of formation and high nitrogen content and density (except A1 1.79 g/cm3), the detonation velocities of A1, A2, B2, E2, and E5 all exceed 10000 m/s, which are 10523.2, 10633.3, 10080.1, 10020.9, and 10005.4 m/s, respectively. Finally, owing to the low nitrogen content of the imidazole ring and the pyrazole ring, the densities of most of them (G1 to H5) are less than 1.80 g/cm3 (1.84 g/cm3 except for G4 and H4), and their detonation velocities (G1 to H5) are between 6497.6 m/s and 8126.7 m/s. As a typical case of amine-like energetic materials, the synthesis of N(1,2,4,5-tetrazin-3-yl)3 (abbreviated as N(tetrazin-3-yl)3 in Table 2) is of great significance. The typical feature of this compound is a polynitrogen compound obtained by replacing three hydrogen atoms in the ammonia molecule with three tetrazine rings, which is similar to the amine-like polynitrogen compound in this paper. We note that although N(tetrazin-3-yl)3 has a low density (1.73 g/cm3), it has a very high enthalpy of formation (1386.2 kJ/mol), so its detonation velocity reaches 8322 m/s.

Detonation heat (Q) is an important factor to maintain the stable propagation of the detonation wave, which is closely related to detonation velocity (VD). Compared with the detonation heat of RDX (6320 kJ/kg) and HMX (6190 kJ/kg), most amine-like catenated nitrogen compounds composed of triazole rings, tetrazole rings, and pentazole rings have a higher detonation heat. Among them, the detonation heat of A2 (8051 kJ/kg), B2 (8188 kJ/kg), B4 (8349 kJ/kg), B5 (8083 kJ/kg), E2 (8280 kJ/kg), E4 (8734 kJ/kg), and E5 (8365 kJ/kg) are higher than 8000 kJ/kg; the reason why these structures have ultrahigh detonation heat is the high nitrogen content in the molecules of these compounds. This also suggests that some amine-like catenated nitrogen compounds are potential high-energy materials with high detonation heat.

In order to clearly show the distribution of the detonation performance of all compounds, Figure 9 uses the radar maps to further compare the detonation parameters of A1 to H5 with that of RDX and HMX. It can be found from Figure 9 that (1) the different detonation parameters (red curves) of compounds A1 to H5 are basically the same as a whole; (2) the amine-like catenated nitrogen compounds (G1 to H5) constructed by the imidazole ring and the pyrazole ring have a lower detonation velocity, detonation pressure, detonation heat (except for G4 and H4), and specific impulse than RDX and HMX, which may be due to the low nitrogen content in the imidazole and pyrazole rings; (3) the amine-like catenated nitrogen compounds (A1 to B5 and E1 to E5) constructed from pentazole and tetrazole rings usually have more excellent detonation properties than RDX; (4) the amine-like catenated nitrogen compounds (C1 to C5, D1 to D5, and F1 to F5) constructed by the triazole ring have a small number of compounds with a higher detonation velocity and detonation pressure than RDX and HMX, while most compounds have a higher detonation heat and specific impulse than RDX and HMX, which further suggests that density and enthalpy of formation have a great influence on the detonation velocity and detonation pressure of energetic materials, while nitrogen content has an important influence on the detonation heat and specific impulse.

Figure 9.

Figure 9

Open in a new tab

Radar maps of detonation parameters of all amine-like catenated nitrogen compounds (A1 to H5). a–d represent the detonation velocity (VD, m/s), detonation pressure (P, GPa), detonation heat (Q, kJ/kg), and specific impulse (Isp, (s)), respectively.

The results of the detonation performance (Figure 9) not only reflect that the strategy of replacing the three hydrogen atoms in the ammonia molecule with three azole rings (pyrazole, imidazole, triazole, tetrazole, pentazole) is an effective strategy for constructing new catenated nitrogen compounds but also prove that the structural characteristics of the azole ring itself have different effects on the energetic performance. The detonation performance of the amine-like catenated nitrogen compounds constructed by imidazole and pyrazole rings is worse than that of the compounds constructed by triazole, tetrazole, and pentazole rings. This suggests that people should focus on the use of azole rings containing more nitrogen atoms in the process of constructing amine-like catenated nitrogen compounds.

4. Conclusions

In summary, a strategy for designing novel high-nitrogen energetic compounds is proposed in this article. Through detailed theoretical simulations, the basic energy-containing performance parameters and stability of these kinds of amine-like catenated nitrogen compounds have been deeply revealed in theory, and the potential of these compounds to become high-energy-density compounds has been answered. Using the nitrogen atom in the ammonia molecule as a linking group, the catenated nitrogen compounds were obtained by combining three azole rings of the same kinds of azoles. The amine-like catenated nitrogen compounds have an ultrahigh enthalpy of solid formation, up to 2652.03 kJ/mol. Remarkably, some compounds have outstanding detonation parameters, with detonation velocities up to 10,633.3 m/s and detonation pressures up to 50.6 GPa. Most amine-like catenated nitrogen compounds have a certain stability, and the bond dissociation enthalpy is higher than 84 kJ/mol, indicating that these compounds can exist stably in theory. In particular, the effect of the number of nitrogen atoms in the azole ring skeleton on the density and enthalpy of formation and the effect of explosophoric groups on the bond dissociation enthalpy are also analyzed. The results show that the greater the number of nitrogen atoms in the azole ring, the greater the crystal density and solid formation enthalpy of amine-like catenated nitrogen compounds; the order of the influence of explosophoric groups on the addition and dissociation enthalpy was NO2 < N3 < NF2 < N–O. This paper proposes and theoretically proves the rationality of the existence of amine-like catenated nitrogen compounds and their potential and possibility as high-energy-density materials, which will be beneficial to further promote the development of polynitride compounds. In addition, we hope that researchers who are interested in such new catenated nitrogen compounds will participate in the related synthesis exploration work of such compounds.

Acknowledgments

The authors would like to acknowledge the National Natural Science Foundation of China (22135003 and 21975023) for providing funding for conducting experiments.

Data Availability Statement

The data underlying this study are available in the published article and its Supporting Information.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.joc.3c01225.

  • HOMO, LUMO, and energy gaps, enthalpy of formation (ΔHf), density (ρ), total energy (E0), zero-point energy (ZPE), and thermal correction to H (HT), Cartesian coordinates of A1 to H5 (Tables S1–S3 and S5 and S6); change in the bond dissociation enthalpy (ΔBDE) of the N–N bond in B1 to H5 (Table S4); HOMO and LUMO energy levels of F1 to H5 (Scheme S1); and ESP-mapped molecular vdW isosurface of E1 to H5 (Scheme S2) (PDF)

The authors declare no competing financial interest.

Supplementary Material

jo3c01225_si_001.pdf (1.7MB, pdf)

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Associated Data

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Supplementary Materials

jo3c01225_si_001.pdf (1.7MB, pdf)

Data Availability Statement

The data underlying this study are available in the published article and its Supporting Information.

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