Theoretical study of the stabilities and detonation performance of 5-nitro-3-trinitromethyl-1H-1,2,4-triazole and its derivatives

Abstract

5-Nitro-3-trinitromethyl-1H-1,2,4-triazole (NTMT, A) and its substituted derivatives A–CH₃, A–OCH₃, A–NH₂, A–OH, A–NO₂, and A–ONO₂ were studied using density functional theory (DFT). For all of the molecules except for A–ONO₂, the C–NO₂ bond in the trinitromethyl group was found to be the weakest, and no transition state occurred during the scission of this bond. The weakest C–NO₂ of the trinitromethyl group bond dissociation energies for all of the molecules were all very similar. Most of the title molecules had similar frontier orbital distributions and comparable energy gaps between the frontier orbitals. The impact sensitivity (h ₅₀, in cm), predicted at various levels of theory, decreased in the order A–NH₂ (53.0–71.0) > A–CH₃ (53.0) > A (36.7) > A–OCH₃ (32.6–42.3) > A–OH (26.7–53.0) > A–NO₂ (5.6–7.4) > A–ONO₂ (4.6–6.1). Their detonation velocities (D), detonation pressures (P), and specific impulses (I _s) were 8.02–8.82 km/s, 29.92–35.54 GPa, and 214–260 s, respectively. Composite explosives made from hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) and A, A–OH, A–NH₂, A–NO₂, or A–ONO₂ as an oxidizer were found to possess much better detonation performance (D = 9.04–9.29 km/s, P = 37.25–39.26 GPa, and I _s = 270–281 s). Thus, introducing –OCH₃, –OH, and –NH₂ groups into A produced new explosives with acceptable stability and good detonation performance. A–OH and A–NH₂ appear to be promising candidates for oxidizers in composite explosives.

Introduction

Energetic materials attract great attention because of their wide range of military and industrial applications [1–4]. A multitude of explosives have been prepared in order to meet the various requirements for energetic materials. 1,3,5,7-Tetranitro-1,3,5,7-tetraazacyclooctane (HMX), 1,3,5-trinitro-1,3,5-triazacyclohexane (RDX), 2,4,6-trinitrotoluene (TNT), nitroglycerin (NG), and nitrocellulose (NC) [5–10] are the most commonly used and famous classical explosives. New explosives such as hexaazahexanitroisowurtzitane (CL-20), 2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105), 1,1-diamino-2,2-dinitroethylene (FOX-7), and 1,3,3-trinitroazetidine (TNAZ) have also been applied in military and civilian arenas [10–19]. The requirements of energetic materials—low sensitivity, high energy, and high oxygen balance (OB)—have resulted in a continuous search for new explosives. Polynitroazoles are the new stars in the field of energetic materials due to their high detonation performance and low sensitivities to friction and impact [20–25]. A variety of powerful nitroazoles have been prepared [26–31]. During ongoing efforts to find more powerful, less sensitive, and eco-friendly energetic nitroazole explosives, Shreeve’s team found a new molecule: 5-nitro-3-trinitromethyl-1H-1,2,4-triazole (NTMT, A in Fig. 1) [32]. This is a heterocyclic compound with high oxygen (48.7 %) and nitrogen (37.3 %) contents and low carbon (13.6 %) and hydrogen (0.4 %) contents, which results in a positive OB (9.2 %). NTMT has a high heat of formation (HOF, 123.2 kJ/mol^-1), which is helpful for improving detonation performance. Its positive OB, high HOF, environmentally benign decomposition products, and acceptable thermal stability (decomposition temperature T _d = 135 °C) and impact sensitivity (h ₅₀ = 36.7 cm, 2.5 kg drop hammer) [32] indicate that NTMT may be a potential candidate for an oxidizer.

Fig. 1

Structures of A and its derivatives

A substituted derivative of NTMT, 5-trinitro-3-trinitromethyl-1-methyl-1,2,4-triazole (NTMMT, A–CH₃), has also been prepared by mixing A with trimethylsilyl diazomethane [32]. A–CH₃ has good thermal stability (T _d = 153 °C) and impact sensitivity (h ₅₀ = 53.0 cm), a high HOF (95.6 kJ/mol^-1), and appealing detonation properties [32]. These attractive properties of A and A–CH₃ inspired us to search for new derivatives of NTMT with other functional groups, i.e., –OCH₃, –NH₂, –OH, –NO₂, and –ONO₂ (see Fig. 1). In order to assess the potential of these new derivatives as explosives, we predicted their thermal stabilities, impact sensitivities, chemical stabilities, and detonation properties in the solid state, as reported in this paper.

Computational details

Geometry optimizations for all compounds were performed at the M06-2X/6-311++G**, B3LYP/6-31G*, and B3PW91/6-31G** levels of theory using the Gaussian software package [33]. All geometries were verified to be the local energy minima via frequency analysis. Relaxed potential energy surface scans were carried out and the stretching of C–NO₂ in the trinitromethyl group C–C(NO₂)₃ and in C(R)–NO₂ (i.e., the C in the C–NO₂ group is in the ring) in all molecules, the stretching of N–NO₂ in A–NO₂, and the stretching of O–NO₂ in A–ONO₂ were investigated at the B3LYP/6-31G* level.

The bond dissociation energy (BDE), which is key to elucidating the mechanism of pyrolysis and thermal stability [34–37], was calculated at the M06-2X/6-311++G**, B3LYP/6-31G*, and B3PW91/6-31G** levels using the following equation:

$$ \mathrm{B}\mathrm{D}\mathrm{E}={E}_{\mathrm{R}1\cdotp }+{E}_{\mathrm{R}2\cdotp}\hbox{--} {E}_{\mathrm{R}1\hbox{---} \mathrm{R}2}, $$

(1)

where E _R1—R2, E _R1·, and E _R2· are the zero-point-corrected total energies of the parent molecule and the radicals produced by bond scission, respectively.

Q _Nitro is the algebraic sum of charges on the atoms in a nitro group, obtained using

$$ {Q}_{\mathrm{N}\mathrm{itro}}={Q}_{\mathrm{N}}+{Q}_{\mathrm{O}1}+{Q}_{\mathrm{O}2}. $$

(2)

The average value of Q _Nitro ($\left({\overline{Q}}_{\mathrm{Nitro}}\right)$ ) was calculated using

$$ {\overline{Q}}_{\mathrm{Nitro}}=\frac{1}{n}{\displaystyle \sum_{i=1}^n{Q}_{\mathrm{Nitro},i}}, $$

(3)

where n is the number of nitro groups in the molecule of interest.

The electrostatic potential V(r) created by the nuclei and electrons of a molecule in its environment was obtained using

$$ V(r)={\displaystyle \sum_A\frac{Z_A}{\left|{R}_A-r\right|}}-{\displaystyle \int \frac{\rho \left({r}^{\prime}\right)d{r}^{\prime }}{\left|{r}^{\prime }-r\right|}}. $$

(4)

Here, Z _A is the charge on nucleus A located at R _A , and ρ(r) is the electronic density.

σ ²₊ , σ ²₋ , and σ ²_tot are the positive, negative, and total variances of the surface electrostatic potential at r (V _s(r)). These reflect the range or variability of V _s(r) and were obtained using the following equations:

$$ {\sigma}_{+}^2=\frac{1}{n}{\displaystyle \sum_{i=1}^n{\left[{V}_{\mathrm{S}}^{+}\left({r}_i\right)-{V}_{\mathrm{S},\mathrm{a}\mathrm{v}\mathrm{e}}^{+}\right]}^2} $$

(5)

$$ {\sigma}_{-}^2=\frac{1}{m}{\displaystyle \sum_{j=1}^m{\left[{V}_{\mathrm{S}}^{-}\left({r}_j\right)-{V}_{\mathrm{S},\mathrm{a}\mathrm{v}\mathrm{e}}^{-}\right]}^2} $$

(6)

$$ \begin{array}{ccc}\hfill {\sigma}_{\mathrm{tot}}^2=\hfill & \hfill {\sigma}_{+}^2+\hfill & \hfill {\sigma}_{-}^2\hfill \end{array}. $$

(7)

Here, i and j are the indices of the sampling points in positive and negative regions, respectively. n and m are the number of positive and negative points on the surface, respectively. V ⁺_S (r _i ) and V ⁻_S (r _j ) are the electrostatic potentials at points i and j. V ⁺_S,ave and V ⁻_S,ave denote the average positive and negative electronic potentials on the surface, respectively.

v indicates the degree of balance between the positive and negative electrostatic potentials:

$$ v=\frac{\sigma_{+}^2{\sigma}_{-}^2}{{\left({\sigma}_{\mathrm{tot}}^2\right)}^2}. $$

(8)

The density was calculated using the equation below, in which the intermolecular interactions were taken into account via the electrostatic interactions on the molecular surface [38]:

$$ \rho ={\alpha}_1\frac{M}{V(0.001)}+{\beta}_1v{\sigma}_{\mathrm{tot}}^2+{\gamma}_1. $$

(9)

Here, M is the molecular mass in g/mol. V(0.001) is the volume that is encompassed by the 0.001-au contour of the molecule’s electronic density. Geometry optimizations and calculations of electrostatic parameters were performed at the B3PW91/6-31G** level of theory. The values of the coefficients α ₁, β ₁, and γ ₁ were taken from [38].

The isodesmic reaction method was employed to predict the gas-phase HOFs (∆_f H(g)) of the title compounds:

(10)

The enthalpy of reaction (∆_r H ₂₉₈) at 298 K for this isodesmic reaction was calculated using the following equation:

$$ \begin{array}{c}\hfill {\varDelta}_{\mathrm{r}}{H}_{298} = \sum {\varDelta}_{\mathrm{f}}{H}_{\mathrm{P}}\hbox{--} \sum {\varDelta}_{\mathrm{f}}{H}_{\mathrm{R}}\hfill \\ {}\hfill =\varDelta {E}_0+\varDelta {E}_{\mathrm{zpv}}+\varDelta {H}_{\mathrm{T}}+\varDelta nRT\hfill \end{array}, $$

(11)

where ∆_f H _P and ∆_f H _R are the HOFs of the products and the reactants, respectively. ∆E ₀ is the difference in total energy between the products and the reactants at 0 K. The MP2/6-311++G**//B3LYP/6-31G* level of theory was employed in this work to predict ∆E ₀ more accurately. ∆E _zpv is the difference in zero-point energy (E _zpv) between the products and the reactants, and ∆H _T is the thermal correction from 0 K to 298 K, which were both calculated at the B3LYP/6-31G* level. ∆nRT is the work term, which equals zero here. Since the HOFs of A, NH₃, NH₂NH₂, and CH₃NH₂ are available [32, 39], the HOFs of the others (NH₂OCH₃, NH₂OH, NH₂NO₂, and NH₂ONO₂) were estimated using the atomization reaction method at the G3 level.

The HOF in the solid state (∆_f H(s)) was estimated using the following equation:

$$ {\varDelta}_{\mathrm{f}}H\left(\mathrm{s}\right) = {\varDelta}_{\mathrm{f}}H\left(\mathrm{g}\right)\ \hbox{--} {\varDelta}_{\mathrm{sub}}H. $$

(12)

Here, ∆_sub H is the enthalpy of sublimation estimated using the equation below, as suggested by Rice and Politzer et al. [40, 41]:

$$ {\varDelta}_{\mathrm{s}\mathrm{ub}}H={\alpha}_2{A_{\mathrm{s}}}^2+{\beta}_2{\left(\nu {\sigma}_{\mathrm{tot}}^2\right)}^{0.5}+{\gamma}_2. $$

(13)

In this equation, A _s is the surface area of the 0.001-au isosurface of the electron density, and ν and σ ²_tot were obtained at the B3LYP/6-31G* level of theory. The values of the coefficients α ₂, β ₂, and γ ₂ were taken from [40].

Detonation velocity (D) and detonation pressure (P), which are important properties of energetic materials, were estimated via the empirical Kamlet–Jacobs equations [42] as follows:

$$ D = 1.01\ \left({N}^{0.5}{M_{\mathrm{ave}}}^{0.25}{Q}^{0.25}\right)\left(1 + 1.30\rho \right) $$

(14)

$$ P = 1.558{\rho}^2N\kern0.5em {M_{\mathrm{ave}}}^{0.5}{Q}^{0.5}. $$

(15)

Here, N is the number of moles of gaseous detonation products per gram of explosives, M _ave is the mean molecular mass of the detonation products, and Q is the detonation energy (cal/g). N, M _ave, and Q are determined based on the maximum exothermicity principle [42].

The specific impulse (I _s) was calculated with a widely adopted method [43] using the following equation:

$$ {I}_{\mathrm{s}}=k{T_{\mathrm{C}}}^{0.5}{N}^{0.5}. $$

(16)

k (19.26) was determined via the experimentally evaluated I _s value of CL-20, and this constant was then used to accurately reproduce the I _s values of TNAZ (1,3,3-trinitroazetidine) and RDX (hexahydro-1,3,5-trinitro-1,3,5-triazine). T _C is the temperature in the combustion chamber, calculated using

$$ -\varDelta {H}_{\mathrm{c}}={C}_{\mathrm{p},\mathrm{g}}\left({T}_{\mathrm{C}}\hbox{--} {T}_0\right), $$

(17)

where ∆H _c represents the enthalpy of combustion and C _p,g is the total heat capacity of the gaseous products. T ₀ is the initial temperature.

Results and discussion

Bond stability

Bond stability is a conventional index that reflects the thermal stability of explosives [35–37, 44–48]. To evaluate the thermal stabilities of the title molecules, the stabilities of several bonds of A and its derivatives were predicted. These included the weakest C–NO₂ bond in the trinitromethyl group, the C(R)–NO₂ bond (i.e., where the C atom is in the ring), the C–C(NO₂)₃ bond, the N–NO₂ bond for A–NO₂, and the O–NO₂ bond for A–ONO₂. Since the bond-breaking processes for the weakest C–NO₂ of trinitromethyl group, C(R)–NO₂, and C–C(NO₂)₃ bonds of the derivatives are similar to those of A, only those of A are shown in Fig. 2. The simulated processes of N–NO₂ and O–NO₂ bond dissociation are also similar to those presented in Fig. 2.

Fig. 2

Plots showing how the energy changes as the lengths of the C–NO₂, C(R)–NO₂, and C–C(NO₂)₃ bonds in A are varied

Figure 2 shows that the energy of A increases as the weakest C–NO₂ bond of the trinitromethyl group, C(R)–NO₂, and C–C(NO₂)₃ bonds lengthen, the slopes of the curves gradually decrease, and the energy ultimately plateaus. This behavior reveals that transition states (TSs) do not occur during the dissociation processes for these bonds, and the products are two radicals. Therefore, the required energies for these processes are the differences between the total energies of the radical products and the reactant (i.e., the BDEs). Different methods (M06-2X/6-311++G**, B3LYP/6-31G*, and B3PW91/6-31G**) were employed to evaluate the BDE, and the results obtained are listed in Table 1. The three levels of theory applied provided the same results: the weakest C–NO₂ bonds of the trinitromethyl group were found to have significantly smaller BDEs than the C(R)–NO₂ and C–C(NO₂)₃ bonds did, so breaking the former bonds should be much easier than breaking the C(R)–NO₂ and C–C(NO₂)₃ bonds. The BDE of the N–NO₂ bond is larger than that of the weakest C–NO₂ bond of the trinitromethyl group in A–NO₂, so the former is stronger than the latter. For A–ONO₂, the BDE of the O–NO₂ bond is significantly smaller than that of the weakest C–NO₂ of the trinitromethyl group, i.e., scission of the O–NO₂ bond should be the initial step in the decomposition of A–ONO₂. In conclusion, the weakest C–NO₂ bond of the trinitromethyl group is the weakest bond, so it breaks first in all of the molecules aside from A–ONO₂.

Table 1 Predicted BDEs (in kJ/mol) of the bonds C–NO₂, C(R)–NO₂, and C–C(NO₂)₃, calculated at various levels of theory^a

As shown in Fig. 3, the BDE of the weakest C–NO₂ bond of the trinitromethly group decreases in the order A > A–CH₃ > A–OCH₃ > A–NO₂ > A–OH > A–NH₂. It is noteworthy that the maximum differences in BDE (ΔBDE = BDE(A) – BDE(A–NH₂)) in Fig. 3 are 4.3, 5.0, and 5.2 kJ/mol^-1 when calculated at the M06-2X/6-311++G**, B3LYP/6-31G*, and B3PW91/6-31G** levels of theory, respectively. This indicates that the weakest C–NO₂ bond of A is slightly weakened by the introduction of substituents. This conclusion further implies that the other derivatives in which the weakest bond is the weakest C–NO₂ bond in the trinitromethyl group may also have BDEs of the weakest C–NO₂ of the trinitromethyl group that are similar to that of A.

Fig. 3

Variation in the BDE of the weakest C–NO₂ bond of the trinitromethyl group, as calculated at various levels of theory

The BDE of the weakest C–NO₂ bond of the trinitromethyl group was 159.7–164.0, 105.1–110.1, and 110.3–115.5 kJ/mol^-1 when calculated at the M06-2X/6-311++G**, B3LYP/6-31G*, and B3PW91/6-31G** levels of theory, so the B3LYP/6-31G* level yields the smallest values. BDEs obtained at the M06-2X/6-311++G** level are considerably larger than those obtained at the other levels of theory. To identify the most reliable results, the BDEs of the C–NO₂ bonds of nitrobenzene, 4-aminonitrobenzene, and 1,3-ditrinitrobenzene (all of which have experimentally available BDE values) were calculated at the three levels of theory. The results are listed in Table S1 of the “Electronic supplementary material” (ESM). The BDEs obtained at the B3LYP/6-31G* and B3PW91/6-311G** levels were smaller than the corresponding experimental BDEs, while those obtained at the M06-2X/6-311++G** level were bigger. The average deviation of the computed BDE from the experimental one was smallest for the results obtained at the B3LYP/6-31G* level (−6.8 kJ/mol^-1), rather than the M06-2X/6-311++G** (14.9 kJ/mol^-1) and B3PW91/6-31G** (−13.3 kJ/mol^-1) levels. Therefore, the results computed at the B3LYP/6-31G* level of theory should be the most reliable.

Impact sensitivity

A continuing major concern in the area of energetic materials is their tendency to explode due to external stimuli. Impact sensitivity is the degree of vulnerability of an energetic material to an external impact. It is widely used to reflect the stability of explosives, and is commonly measured via the parameter h ₅₀. The smaller the value of h ₅₀, the higher the impact sensitivity. In order to assess the impact sensitivities of A and its derivatives, the nitro group charge method (NGCM) [19]—which makes use of the roughly linear relation between the reciprocal of impact sensitivity $\left(\frac{1}{h_{50}}\right)$ and ${\overline{Q}}_{\mathrm{Nitro}},$ and has been used in some investigations [32, 49]—was applied to predict the h ₅₀ values of the title molecules. Thus, ${\overline{Q}}_{\mathrm{Nitro}}$ values were calculated (Table 2) at the M06-2X/6-311++G**, MP2/6-311++G**, and B3PW91/6-31G** levels of theory. Since the structures of the title molecules are similar, a strong linear relationship between their $\frac{1}{h_{50}}$ values and their ${\overline{Q}}_{\mathrm{Nitro}}$ values was expected. The experimental h ₅₀ values of A and A–CH₃ are available [32]. Three linear equations linking the ${\overline{Q}}_{\mathrm{Nitro}}$ values obtained at the three levels of theory with the $\frac{1}{h_{50}}$ values of A and A–CH₃ were fitted to allow the h ₅₀ values of the other molecules to be predicted:

Table 2 Predicted ${\overline{Q}}_{\mathrm{Nitro}}$ values and h ₅₀ values of the title molecules, calculated at three levels of theory

$$ \begin{array}{ll}\mathrm{M}06-2\mathrm{X}:\hfill & \frac{1}{h_{50}}=0.26189+1.67601{\overline{Q}}_{\mathrm{Nitro}}\hfill \\ {}\mathrm{B}3\mathrm{P}\mathrm{W}91:\hfill & \frac{1}{h_{50}}=0.31217+2.39427{\overline{Q}}_{\mathrm{Nitro}}\hfill \\ {}\mathrm{M}\mathrm{P}2:\hfill & \frac{1}{h_{50}}=0.5801+1.97177{\overline{Q}}_{\mathrm{Nitro}}.\hfill \end{array} $$

The predicted h ₅₀ values are listed in Table 2 and depicted graphically in Fig. 4. Although the calculated ${\overline{Q}}_{\mathrm{Nitro}}$ values vary depending on the level of theory applied, the predicted h ₅₀ values show similar variations among the derivatives of A whatever the level of theory used; the deviations between the values obtained at the three levels are not significant. A–NH₂ possesses the lowest impact sensitivity (53.0–71.0 cm). A–NO₂ and A–ONO₂ are the most sensitive of the derivatives: their h ₅₀ values are about 4.6–7.4 cm. The h ₅₀ value of A–OCH₃ (32.6–42.3) is comparable to that of A (36.7 cm). Generally speaking, the impact sensitivities of all the molecules aside from A–NO₂ and A–ONO₂ were found to be lower than that of RDX (26 cm) [30], a widely used explosive, meaning that their impact sensitivities are acceptable. The very positive Q _Nitro values of the extra –NO₂ groups in A–NO₂ and A–ONO₂ result in less negative ${\overline{Q}}_{\mathrm{Nitro}}$ values, which evidently make A–NO₂ and A–ONO₂ more attractive to electrons and further increase their impact sensitivities.

Fig. 4

h ₅₀ values of A and its derivatives, obtained at three levels of theory

Surface electrostatic potentials

Murray [50] and Politzer et al [51] pointed out that, for the C–NO₂ bond, a more positive V _s,max (the positive extreme of the surface electrostatic potential) value usually corresponds to a smaller bond dissociation energy, and the most sensitive molecules generally have higher anomalous charge imbalances. To assess the relative sensitivities of the title molecules, the positive and negative variances (σ ²₊ and σ ²₋ ) and the v and V _s,max values of the three C–NO₂ bonds of the trinitromethyl group were evaluated at the B3PW91/6-31G(d,p)//B3PW91/6-31++G(3d,2p) level used in the literature [51], and the results are listed in Table 3. As is evident from this table, σ ²₊ is far larger than σ ²₋ , which shows that the strength and variability of the positive surface potential are stronger and larger than those of the negative surface potentials, which agrees well with the characteristics of energetic compounds. The v values of the derivatives are closer to 0.25 than they are to A, reflecting the idea that the introduction of functional groups onto A helps to improve the balance between the positive and negative surface potentials. The maximum V _s,max value among the three C–NO₂ bonds in each title molecule decreases in the order A–OH > A–NO₂ > A–ONO₂ > A > A–NH₂ > A–OCH₃ > A–CH₃. Although this order is not exactly the same as the order of C–NO₂ bond BDEs among these molecules, or the order of predicted h ₅₀ values among them, the order of molecules is very similar for all three parameters, meaning that V _s,max is a good indicator of the relative sensitivities of the title molecules. In addition, the V _s,max values of A–NO₂ are larger than those of A, i.e., the introduction of the extra –NO₂ group weakens the original C–NO₂ bonds and lowers their BDEs, which is reflected in the smaller BDE of the C–NO₂ bond of A–NO₂ in comparison with that of A.

Table 3 Predicted σ ²₊ , σ ²₋ , v, and V _s,max values of the three C–NO₂ bonds in the trinitromethyl group

Chemical stability

The energy gap (E _g) between the frontier orbitals is a widely used parameter that reflects the stability of a molecule to chemical or photochemical processes involving electron transitions or jumps [52, 53]. The E _g values of A and its derivatives were calculated at the three levels of theory and the results are tabulated in Table 4. The E _g values of all of the molecules except for A–NH₂ were similar whichever level of theory was used, which means that the chemical stabilities of the derivatives are comparable to that of A. In other words, introducing a functional group (aside from an –NH₂ group) onto A barely affects its chemical stability.

Table 4 Predicted E _HOMO, E _LUMO, and E _g values (all in eV) of A and its derivatives, and contributions of the substituents in these molecules to their frontier orbitals (in %)^a

It is clear that A–NH₂ presents far smaller E _g values than the other compounds. Why is this? Figure 5 shows that the E _HOMO values and E _LUMO values of A–OH, A–CH₃, A–OCH₃, and A–ONO₂ are very similar to those of A, which leads to similar E _g values too. The E _HOMO and E _LUMO values of A–NO₂ are lower than those of A, and the drop in E _LUMO is slightly larger than the drop in E _HOMO with respect to A. For A–NH₂, E _LUMO is comparable to that of A, but its E _HOMO is much higher than that of A, which leads to its smaller E _g.

Fig. 5

Trends in E _HOMO, E _LUMO, and E _g among the title compounds, as calculated at the M06-2X/6-311++G** level

The frontier orbital distributions were computed to determine their effects on E _HOMO and E _LUMO. Since A, A–CH₃, A–OCH₃, A–OH, and A–ONO₂ show similar HOMO and LUMO distributions, only those of A and A–CH₃ are shown in Fig. 6, along with the HOMOs and LUMOs of A–NH₂ and A–NO₂. The percentage contributions of the substituents to the HOMO and LUMO were evaluated using the Multiwfn program [54], and the results are listed in Table 4. The HOMOs of A and A–CH₃ are mainly located at the C–N bonds in the triazole ring and the O atoms in the trinitromethyl group, while the LUMOs are mainly associated with the three N atoms in the ring and the C(R)–NO₂ group. The –CH₃ group makes minor contributions to the HOMO and LUMO (3.5 % and 0.7 %). The similar HOMO and LUMO distributions for A and A–CH₃ result in similar E _HOMO values, E _LUMO values, and E _g values for these molecules, and the same is true of A–OCH₃, A–OH, and A–ONO₂. For A–NH₂, the –NH₂ group makes a considerable contribution (41.9 %) to the HOMO, causing a significant increase in E _HOMO. The LUMO is barely affected by the introduction of the –NH₂ group, so the E _LUMO of A–NH₂ is close to that of A. The LUMO distribution of A–NO₂ and the contribution of the –NO₂ group (49.4 %) to it both show that the –NO₂ group considerably affects the LUMO distribution, which may be responsible for the smaller E _LUMO of A–NO₂ than A.

Fig. 6

HOMOs (top) and LUMOs (bottom) of A, A–CH₃, A–NH₂, and A–NO₂

Detonation properties

The energy content of an energetic molecule can be gauged from its heat of formation, which is an important parameter of energetic materials. In this paper, the gas-phase HOFs (∆_f H(g) values) of A and its derivatives were predicted by the isodesmic reaction method. The results listed in Table 5 show that the ∆_f H(g) values are 114.7–298.2 kJ/mol^-1. The fact that the ∆_f H(g) values are highly positive reveals that these molecules store a large amount of heat, which improves their detonation properties. As a matter of fact, most explosives exist in the solid state under normal conditions, so solid HOFs (∆_f H(s) values) are required to be able to evaluate the detonation performance of solid molecules. In order to obtain ∆_f H(s) values, we determined the ΔH _sub values of the title molecules (cf. Table 6). The data in Table 6 show that all of the molecules except for A–CH₃ have positive ∆_f H(s) values, which aid detonation performance.

Table 5 The total energy (E ₀), zero-point energy (E _ZPV), thermal correction (H _T), and heat of formation in the gas phase (∆_f H(g)) for various compounds^a

Table 6 Calculated enthalpy of sublimation (Δ_sub H) and heat of formation in the solid (∆_f H(s)) for each of the title compounds

Detonation velocity, detonation pressure, and specific impulse are the most important detonation characteristics of energetic materials, and Q and ρ are the most influential factors in these detonation characteristics. The predicted Q, ρ, D, P, and I _s values are shown in Table 7. We see that introducing a –CH₃, –OCH₃, or –NH₂ group decreases the density of A, while introducing a –OH, –NO₂, or –ONO₂ group increases it. Only the addition of –OCH₃ or –NH₂ helps to improve Q and I _s. The solid detonation properties of A–OCH₃, A–NH₂, and A–OH are better than those of A, due to their larger Q and ρ values. The D values (8.59–8.82 km/s) and P values (33.72–35.54 GPa) of A, A–OCH₃, A–NH₂, and A–OH are comparable to or larger than those of RDX (D = 8.75 km/s and P = 34.00 GPa), so these molecules can be used as single compound explosives.

Table 7 Detonation properties of the title molecules

A plot of Q versus oxygen balance (OB) (see Fig. 7) shows that Q initially increases but then decreases with increasing OB, and it achieves its maximum value when OB equals −2.72, which the closest plotted OB value to zero. As the absolute value of OB shifts further away from zero, Q gets smaller and smaller. The excess O atoms in molecules (i.e., explosives) with positive OB values are converted into O₂ molecules during explosions, and these O₂ molecules extract some of the heat from the explosion, which results in smaller Q values for the explosives. When the OB of the explosive is negative, some of the C and H atoms are not oxidized during the explosion, so maximum heat release is impossible, leading to a smaller Q value. On the whole, the smaller the absolute value of OB, the higher the Q value.

Fig. 7

Plot of Q versus oxygen balance (OB)

The presence of excess oxygen atoms lowers the detonation performance of A, A–OH, A–NH₂, A–NO₂, and A–ONO₂ when they are used as single compound explosives, but they can be fully utilized in composite explosives as oxidizers. Our previous studies [55, 56] showed that composite explosives containing both oxygen-rich explosives and oxygen-poor explosives present enhanced detonation performance. Thus, composite explosives of RDX using A, A–OH, A–NH₂, A–NO₂, and A–ONO₂ as oxidizers were studied. The weight ratios of these composite explosives were adjusted to make the OBs of the mixtures zero. The explosive reactions of these composite explosives are as follows:

$$ \begin{array}{ll}\mathrm{A}/\mathrm{R}\mathrm{D}\mathrm{X}\hfill & 2\mathrm{C}3\mathrm{H}\mathrm{O}8\mathrm{N}7\ \left(\mathrm{s}\right) + \mathrm{C}3\mathrm{H}6\mathrm{N}6\mathrm{O}6\ \left(\mathrm{s}\right) = 9\mathrm{C}\mathrm{O}2\ \left(\mathrm{g}\right) + 4\mathrm{H}2\mathrm{O}\ \left(\mathrm{g}\right) + 10\mathrm{N}2\ \left(\mathrm{g}\right)\hfill \\ {}\mathrm{A}\hbox{-} \mathrm{O}\mathrm{H}/\mathrm{R}\mathrm{D}\mathrm{X}\hfill & 6\mathrm{C}3\mathrm{H}\mathrm{O}9\mathrm{N}7\ \left(\mathrm{s}\right) + 5\mathrm{C}3\mathrm{H}6\mathrm{N}6\mathrm{O}6\ \left(\mathrm{s}\right) = 33\mathrm{C}\mathrm{O}2\ \left(\mathrm{g}\right) + 18\mathrm{H}2\mathrm{O}\ \left(\mathrm{g}\right) + 36\mathrm{N}2\ \left(\mathrm{g}\right)\hfill \\ {}\mathrm{A}\hbox{-} \mathrm{N}\mathrm{H}2/\mathrm{R}\mathrm{D}\mathrm{X}\hfill & 3\mathrm{C}3\mathrm{H}2\mathrm{O}8\mathrm{N}8\left(\mathrm{s}\right) + \mathrm{C}3\mathrm{H}6\mathrm{N}6\mathrm{O}6\ \left(\mathrm{s}\right) = 12\mathrm{C}\mathrm{O}2\ \left(\mathrm{g}\right) + 6\mathrm{H}2\mathrm{O}\ \left(\mathrm{g}\right) + 15\mathrm{N}2\ \left(\mathrm{g}\right)\hfill \\ {}\mathrm{A}\hbox{-} \mathrm{N}\mathrm{O}2/\mathrm{R}\mathrm{D}\mathrm{X}\hfill & 3\mathrm{C}3\mathrm{O}10\mathrm{N}8\ \left(\mathrm{s}\right) + 4\mathrm{C}3\mathrm{H}6\mathrm{N}6\mathrm{O}6\ \left(\mathrm{s}\right) = 21\mathrm{C}\mathrm{O}2\ \left(\mathrm{g}\right) + 12\mathrm{H}2\mathrm{O}\ \left(\mathrm{g}\right) + 24\mathrm{N}2\ \left(\mathrm{g}\right)\hfill \\ {}\mathrm{A}\hbox{-} \mathrm{O}\mathrm{N}\mathrm{O}2/\mathrm{R}\mathrm{D}\mathrm{X}\hfill & 3\mathrm{C}3\mathrm{H}\mathrm{O}8\mathrm{N}7\ \left(\mathrm{s}\right) + 5\mathrm{C}3\mathrm{H}6\mathrm{N}6\mathrm{O}6\ \left(\mathrm{s}\right) = 24\mathrm{C}\mathrm{O}2\ \left(\mathrm{g}\right) + 15\mathrm{H}2\mathrm{O}\ \left(\mathrm{g}\right) + 27\mathrm{N}2\ \left(\mathrm{g}\right)\hfill \end{array} $$

The calculated detonation properties of these mixtures are tabulated in Table 8. The densities of these mixtures are 1.88–1.89 g/cm³, which are between those of the corresponding oxidizer and RDX. The Q values of these composite explosives are far larger than those of their components when they are used as single compound explosives. These considerable improvements in Q can be attributed to the full utilization of the excess oxygen present in the oxidizers, which means that no heat is lost to the excess oxygen of the oxidizers and full oxidization of the carbon and hydrogen atoms in RDX occurs, releasing more heat. The D values and P values of these mixtures are 9.04–9.29 km/s and 37.25–39.26 GPa, respectively. The detonation performance of each composite explosive is obviously better than those of its components, and is comparable to that of HMX. The I _s values of these mixtures are close to or even better than that of CL-20 (278.8 s) [57].

Table 8 Detonation properties of composite explosives that include A or derivatives of it

Conclusions

The C–NO₂ bond of the trinitromethyl group is the weakest bond in A, A–CH₃, A–OCH₃, A–NH₂, A–OH, and A–NO₂, and no TS occurs during the decomposition of this bond. The BDEs of the weakest C–NO₂ bonds of the trinitromethyl group in these molecules are very similar, whatever the level of theory used to calculate them. The contributions of –CH₃, –OCH₃, –OH, and –ONO₂ to the HOMO and LUMO distributions are small, meaning that their E _g values are comparable to that of A. The impact sensitivities of A, A–CH₃, A–OCH₃, A–NH₂, and A–OH are acceptable (26.7–71 cm), while those of A–NO₂ and A–ONO₂ are quite high (4.6–7.4 cm).

The D, P, and I _s values of A and its derivatives are 8.02–8.82 km/s, 29.92–35.54 GPa, and 214–260 s, respectively. A, A–OCH₃, A–NH₂, and A–OH show moderately good detonation performance when used as single compound explosives. Composite explosives containing RDX and A, A–OH, A–NH₂, A–NO₂, or A–ONO₂ as an oxidizer have much better detonation properties (D = 9.04–9.29 km/s, P = 37.25–39.26 GPa, and I _s = 270–281 s) than those of A or its derivatives.