Theoretical design of highly energetic poly-nitro cage compounds

Abstract

In this work, we report on the design and full prediction of four poly-nitro cage compounds, octanitrooctaprismane (ONOP), octanitrooctaazaprismane (ONOAP), tetranitrooctaprismane (TNOP), and tetranitrooctaazaprismane (TNOAP) at the B3LYP/6-31G (d,p) level using density functional theory (DFT). The results show that all compounds possess large positive heats of formation (HOF) and specific enthalpies of combustion (ΔH_C). The detonation velocity (D) and pressure (P) are calculated using Kamlet–Jacobs equations, and ONOP, ONOAP, and TNOAP showed a superior performance in comparison to commonly used energetic materials, 1,3,5,7-tetranitro-1,3,5,7-tetrazocane (HMX) and 1,3,5-trinitro-1,3,5-triazinane (RDX). Calculation of the bond dissociation energy (BDE) is carried out and reveals good thermal stabilities for all compounds. In terms of sensitivity, molecules with four nitro groups (TNOP and TNOAP) display lower sensitivity than those with eight nitro groups (ONOP and ONOAP). Importantly, TNOAP outshines other molecules due to its superior energetic properties, compared to those of HMX, and good sensitivity, less than that of 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (CL-20) and comparable to that of RDX, so we recommend TNOAP as a promising HEDM candidate.

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Introduction

Energetic materials, including explosives, propellants and pyrotechnics, play an essential part in the fields of military affairs, national defense, and aerospace technology, as well as modern civilization.^1–4 Although tremendous progress has been made since World War II, conventional energetic materials cannot support the rapid development of contemporary military industry, which has inspired chemists and engineers to conduct deeper research on developing novel high-energy-density materials (HEDMs) with desirable properties.^5–8 It is known that energetic materials exhibit an excellent detonation performance, including high heat of formation (HOF), and high detonation velocity (D) and pressure (P); meanwhile, low sensitivity toward friction and impact is a requisite for HEDMs. Generally, the quantitative criteria of detonation performance employed to filter potential HEDM candidates are: crystal density ρ = 1.9 g cm⁻³, detonation velocity D = 9.0 km s⁻¹, and detonation pressure P = 40.0 GPa. In terms of thermal stability, HEDMs with a bond dissociation energy (BDE) of the initial step of thermolysis of more than 80 kJ mol⁻¹ are regarded to be thermally stable.⁹ Additionally, the impact sensitivity, h₅₀, can be evaluated by the characteristic height (h₅₀) at which the sample is impacted by a given mass and there is a 50% probability of causing an explosion.¹⁰ However, the detonation performance and stability/sensitivity of HEDMs are often contrary to each other. For example, the extensively used CL-20 (hexanitrohexaazaisowurtzitane) possesses outstanding detonation properties (D = 9.4 km s⁻¹, P = 44.1 GPa),^3,11 but it is too sensitive (h₅₀ = 14 cm).¹² On the other hand, the classic HEDM, TNT (2,4,6-trinitrotoluene), exhibits low sensitivity (h₅₀ = 100 cm) but the performance is poor in terms of the detonation velocity (6.9 km s⁻¹) and pressure (19.5 GPa),¹³ which has restricted its applications. Hence, further research is needed to reach a fine balance between a high explosive performance and low sensitivity for novel HEDMs.

Among the diverse categories of HEDMs, poly-nitro compounds attract substantial attention because of their high energy content. Generally, the –NO₂ group is regarded as one of the most powerful energetic groups because it offers the oxygen needed for oxidation and combustion and therefore enhances the energy level of the resultant compounds. More importantly, the incorporation of the nitro group is beneficial to compounds with respect to high temperature and low pressure, which makes it possible for such HEDMs to be applied under special conditions. Typical HEDMs of this type include the well-known HMX (1,3,5,7-tetranitro-1,3,5,7-tetrazocane), RDX (1,3,5-trinitro-1,3,5-triazinane), TATB (2,4,6-trinitro-1,3,5-benzenetriamine), and TNT, which have been extensively studied and have various applications.¹⁴ Recently, poly-nitro cage compounds have aroused much interest because of the fact that their compact structures and the large strain energy of cage compounds contribute greatly to the density and HOF. Eaton et al. have successfully synthesized poly-nitro cubanes (tetra-, penta-, hexa-, hepta-, and octanitrocubane), among which ONC (octanitrocubane) showed a superior explosive performance compared to the well-known CL-20.¹⁵ Subsequently, a systematic theoretical study on ONC by Zhang and Xiao¹⁶ showed that the detonation performance of ONC is extremely high, namely, D = 10.26 km s⁻¹ and P = 52.08 GPa, which are in good accordance with the experimental results (D = 10.10 km s⁻¹ and P = 50.00 GPa).¹⁷ Further research on cubane derivatives by Gong et al. reported TNTAC (2,4,6,8-teranitro-1,3,5,7-tetraazacubane) with a detonation velocity of 10.42 km s⁻¹, a detonation pressure of 52.82 GPa, and good thermal stability, which showed an overall better performance than ONC.¹⁷ Additionally, polynitraminecubanes¹⁸ and polydinitroaminocubanes¹⁹ were investigated in the pursuit of HEDMs and some of the resulting compounds were deemed to be potential HEDMs, which were also designed based on the aforementioned strategy. Besides, two newly designed hexaprismane-based molecules, DNH (dodecanitrohexaprismane) and HNHAN (hexanitrohexaazaprismane) were investigated by Xiao et al.²⁰ and both were shown to exhibit better explosive performances (DNH1: D = 9.95 km s⁻¹, P = 43.50 GPa; DNH2: D = 10.05 km s⁻¹, P = 48.80 GPa; HNHAH: D = 9.62 km s⁻¹, P = 43.50 GPa) than HMX (D = 9.10 km s⁻¹, P = 39.00 GPa) and RDX (D = 8.75 km s⁻¹, P = 34.00 GPa).²¹ As for their sensitivity, DNH (DNH1: h₅₀ = 20 cm; DNH2: h₅₀ = 25 cm) has comparable sensitivity to HMX (h₅₀ = 29 cm) and RDX (h₅₀ = 26 cm),¹² whereas HNHAH is more insensitive (h₅₀ = 45 cm) than DNH and ONC (h₅₀ = 40 cm).²⁰ Furthermore, prismane is another commonly used and investigated cage compound with a large strain energy, based on which, our group have designed a series of HEDMs by incorporating –ONO₂ and –(NHNO₂)₂ groups into the prismane framework.^11,22 The results showed that all the eleven designed nitroesterprismane derivatives exhibit lower sensitivity than CL-20 (h₅₀ = 14 cm) and 1,2,3,4-tetranitroesterprismane has the best detonation properties (D = 9.28 km s⁻¹, P = 40.05 GPa) among them. In terms of the polydinitroaminoprismanes, five (C1, C2, D1, D2, D3) of the twelve designed compounds are more powerful than HMX and seven compounds (A, B1, B2, B3, C1, C2, C3) are less sensitive than CL-20.²² Other prismane derivatives, such as polynitroprismanes,²³ polynitramineprismanes,²⁴ polynitrosoprismanes,²⁵ and polyazidoprismanes,²⁶ turned out to have remarkable energetic performances.

Although the prominent advantages of nitro groups and cage frameworks have been successfully embodied in many poly-nitro cage compounds, to the best of our knowledge, there are very few studies on octaprismane derivatives for HEDMs. Karpushenkava et al. have theoretically investigated the thermal stability and strain energy of octaprismane, where the HOF and the strain energy were found to be 1193 kJ mol⁻¹ and 347 kJ mol⁻¹, respectively.²⁷ Thus, the resultant octaprismane-based compounds will be beneficial as HEDMs due to the following advantages: (1) the rigid structure of octaprismane significantly increases the density of the construction, (2) the large strain energy is conducive to a high HOF, thereby leading to a high energy content, (3) the presence of H atoms in the skeleton makes it possible to form hydrogen bonds, which may make an additional contribution to the stability of the compounds. Inspired by these clues, we designed four poly-nitro octaprismane compounds in the present work by incorporating nitro groups into octaprismane, namely, octanitrooctaprismane (ONOP), octanitrooctaazaprismane (ONOAP), tetranitrooctaprismane (TNOP), and tetranitrooctaazaprismane (TNOAP); see Fig. 1. Taking steric hindrance into account, ONOP is formed by substituting the H atoms at regular intervals using nitro groups. The replacement of C atoms with N atoms in ONOP results in a more nitrogen-rich compound, ONOAP, for which the energy content and detonation performance are expected to be improved. Further attempts have been made, based on ONOP and ONOAP, by reducing four nitro groups in each molecule, which yields another two molecules, TNOP and TNOAP, aiming at enhancing the stability/sensitivity level and ensuring the high energy density of the resultant compounds at the same time. The detonation performance and stability of the target compounds were investigated systematically using density functional theory (DFT) at the B3LYP/6-31G (d,p) level. We hope that the present work can provide useful insights for further research on novel HEDMs.

Fig. 1 Molecular structures of ONOP, ONOAP, TNOP, and TNOAP. For simplicity, the hydrogen atoms are not shown.

Computational method

All calculations were performed using the DFT-B3LYP method with the 6-31G (d,p) basis set in the Gaussian 09 software package,²⁸ except for the parameters related to ΔH_sub (the heat of sublimation) and ρ (the molecular density), which were performed at the B3PW91/6-31G (d,p) level. The atomic coordinates of the optimized molecules are listed in Tables S1–S4 in the ESI.†

We designed the following isodesmic reactions for each compound (eqn (1)–(4)) to obtain the gas-phase HOFs (ΔH_f,gas) of the title compounds, aiming at decreasing the calculation errors, viz.:

ONOP (C₁₆N₈O₁₆H₈) + 8CH₄ → C₁₆H₁₆ + 8CH₃NO₂ (1)

ONOAP (C₈N₁₆O₁₆) + 16NH₃ + 24CH₄ → 24CH₃NH₂ + 8CH₃NO₂ (2)

TNOP (C₁₆N₄O₈H₁₂) + 4CH₄ → C₁₆H₁₆ + 4CH₃NO₂ (3)

TNOAP (C₈N₁₂O₈H₄) + 16NH₃ + 20CH₄ → 24CH₃NH₂ + 4CH₃NO₂ (4)

Thus, the difference between the gas-phase HOFs of the products (ΔH_f,P) and the reactants (ΔH_f,R) at 298 K gives the heat of formation of the isodesmic reactions (Δ_rH₂₉₈) in eqn (5), which can also be expressed as eqn (6) in the absence of the experimental HOFs of ONOP, ONOAP, TNOP, and TNOAP:

Δ_rH₂₉₈ = ΔH_f,P − ΔH_f,R (5)

Δ_rH₂₉₈ = ΔE + ΔZPE + ΔH_T + ΔnRT (6)

here, ΔE is the difference between the total energies of the products and reactants at 0 K; ΔZPE is the difference between the zero-point energies of the products and reactants; ΔH_T stands for the thermal correction from 0 K to 298 K and ΔnRT is the work term.

The condensed-phase heats of formation (ΔH_f,solid) of the target compounds were then calculated using Hess's law of constant heat summation²⁹ via formulae (7) and (8):^30,31

ΔH_f,solid = ΔH_f,gas − ΔH_sub (7)

ΔH_sub = αA² + β(υσ_tot²)^0.5 + γ (8)

In eqn (8), A is the surface area of the 0.001 electrons per Bohr³ isosurface of the electronic density for the optimized structures, υ represents the degree of balance between the positive potential and negative potential on the molecular surface, and σ_tot² can be interpreted as an indicator of the variability of the electrostatic potential on the molecular surface. The computational procedures proposed by Bulat et al.³² were employed to obtain the three parameters mentioned above (A, υ, and σ_tot²) at the B3PW91/6-31G (d,p) level. The fitting parameters, α, β, and γ, were estimated by Rice et al. as α = 2.670 × 10⁻⁴ kcal mol⁻¹ A⁻⁴, β = 1.650 kcal mol⁻¹, and γ = 2.966 kcal mol⁻¹.³³

The detonation velocity (D) and pressure (P) were assessed by the Kamlet–Jacobs equations as follows:³⁴

D = 1.01(NM̄^1/2Q^1/2)^1/2(1 + 1.30ρ_c) (9)

P = 1.558ρ_c²NM̄^1/2Q^1/2 (10)

where D is the detonation velocity (km s⁻¹), P is the detonation pressure (GPa), N represents the moles of detonation gases per gram of explosive, M denotes the average molecular weight of gaseous products, and Q (kJ g⁻¹) is the heat of detonation. Typically, ρ_c (g cm⁻³) is the loaded density of explosives, measured through experiments for known explosives. Whereas for compounds not yet synthesized, ρ_c can be obtained in two ways: from the predicted crystal density (ρ_c) and by the Politzer method (ρ), which can be expressed as:³⁵where M is the molecular mass (g mol⁻¹), and V (0.001) is defined as the volume of the 0.001 electrons per Bohr³ contour of electronic density of the molecule (cm³ per molecule); α, β, and γ are coefficients determined as α = 0.9183, β = 0.0028, γ = 0.0443.³⁵

Results and discussion

Molecular geometry and electronic structure

Before discussing the diverse properties, it is necessary to examine the molecular geometries of the target compounds, since they are closely related to the physical and chemical properties. Table 1 lists some selected bond lengths at the B3LYP/6-31G (d,p) level. It is evident that either the C₁–C₂ bond of the octatomic ring or the C₁–C′₁ bond of the four-membered ring in the skeletons of ONOP and TNOP have little variation compared with those of octaprismane (C₁₆H₁₆). Meanwhile, both the C₁–N and the C₁–N′ bond lengths are shorter in ONOAP/TNOAP than in ONOP/TNOP and C₁₆H₁₆, indicating that these bonds may be stronger in ONOAP/TNOAP, which in turn confirms that the introduction of N atoms into octaprismane may stabilize the molecule through diminishing the molecular strain energy.¹⁷ Besides, the C–NO₂ bond lengths of each molecule vary slightly and the additional eight hydrogen bonds ranging from 2.17 to 2.30 Å in ONOP and 2.31 to 2.47 Å in TNOP (see Fig. 2) may serve to stabilize the structures.

Table 1 Selected bond lengths (Å) of the optimized geometry for octaprismane (C₁₆H₁₆), ONOP, ONOAP, TNOP, and TNOAP at the B3LYP/6-31G (d,p) level. For atom labelling and numbering, see Fig. 1

Comp'd	C16H16	ONOP	ONOAP	TNOP	TNOAP
C1–C2/N	1.57	1.56	1.53	1.57	1.47
C1–C′1/N′	1.56	1.57	1.47	1.55	1.48
C–NO2	—	1.54	1.49	1.52	1.53

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Fig. 2 Eight intramolecular hydrogen bonds (dotted lines) and bond lengths (Å) in ONOP and TNOP. The carbon, nitrogen, oxygen, and hydrogen atoms are in gray, blue, red, and white, respectively.

The energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) usually determines the kinetic stability, chemical reactivity, optical polarizability, and chemical hardness-softness of a molecule.³⁶ It has been reported in previous studies that the smaller the energy gap is, the easier the electron transition will be.^37–39 Fig. 3 shows the HOMOs, LUMOs, and the energy gaps of the designed compounds. Apparently, the HOMO of ONOP is mainly located at the C atoms in the skeleton and the O atoms of the nitro groups, while the LUMO is distributed partly on C–N bonds and partly on O atoms. As for ONOAP, the HOMO and LUMO distributions are quite different from those of ONOP. In ONOAP, both the C–N/N′ bonds and –NO₂ groups participate in the HOMO and LUMO, and the C–NO₂ bonds make an additional contribution to the LUMO. Since the C–N/N′ orbitals of ONOAP participate in both the HOMO and the LUMO, this means that the removal of an electron from the HOMO level or addition of an electron to the LUMO level could weaken the skeletal framework.^38,40 Regarding the case of TNOP and TNOAP, the distributions of the HOMO and LUMO are similar; namely, all the C/N atoms in the skeleton and nitro groups participate in the HOMO, while the LUMO is mainly located at the nitro groups. The calculated energy gaps (ΔE) of ONOP, ONOAP, TNOP, and TNOAP are 5.62, 5.82, 5.42, and 5.25 eV, respectively, indicating that ONOAP is less active and more stable than the other three compounds in chemical or photochemical processes with electron transfers or leaps.⁴¹

Fig. 3 The HOMOs, LUMOs, and the energy gaps (ΔE, eV) of ONOP, ONOAP, TNOP, and TNOAP.

Heat of formation and enthalpy of combustion

The HOF is a fundamental parameter in the estimation of the explosive performance and usually acts as an indicator of the energy content for energetic materials. To be specific, a strongly positive HOF is invoked as being a very desirable property with respect to energy storage. Table 2 summarizes the calculated ΔH_f,gas, ΔH_f,solid and the specific enthalpies of combustion (ΔH_C) of ONOP, ONOAP, TNOP, and TNOAP. Quite noteworthy in Table 2 is that the ΔH_f,solid values of the target compounds are much larger (2011.81 kJ mol⁻¹ for ONOP, 4024.23 kJ mol⁻¹ for ONOAP, 1462.98 kJ mol⁻¹ for TNOP, and 3120.77 kJ mol⁻¹ for TNOAP) than those of the other two commonly used energetic compounds, HMX (75.24 kJ mol⁻¹) and RDX (79.00 kJ mol⁻¹).⁴² The extremely large positive HOFs of the four compounds may stem from the large strain energy and the rich C–N bonds in the framework. Furthermore, the HOF of ONOAP is almost double that of ONOP, implying large contributions from the doped N atoms. Similar cases can be found in TNOP and TNOAP. Hence, doping N into a cage framework proves to be an effective way to enhance the HOF of HEDMs.

Table 2 Gas-phase (ΔH_f,gas) and solid-phase (ΔH_f,solid) heat of formation and the specific enthalpy of combustion (ΔH_C) of ONOP, ONOAP, TNOP, TNOAP, HMX, and RDX calculated at the B3LYP/6-31G (d,p) level

Comp'd	ΔHf,gas (kJ mol^−1)	ΔHf,solid (kJ mol^−1)	ΔHC^a (kJ g^−1)
a The combustion reaction of the designed compounds: ONOP (C16N8O16H8) + 10O2 → 16CO2 + 4H2O + 4N2, ONOAP (C8N16O16) → 8CO2 + 8N2, TNOP (C16N4O8H12) + 15O2 → 16CO2 + 6H2O + 2N2, TNOAP (C8N12O8H4) + 5O2 → 8CO2 + 2H2O + 6N2.
ONOP	2228.89	2011.81	−16.64
ONOAP	4224.04	4024.23	−12.45
TNOP	1619.95	1462.98	−24.42
TNOAP	3268.57	3120.77	−17.27
HMX	—	75.24	−5.69
RDX	191.44	79.00	−9.53

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ΔH_C in Table 2 is the molar enthalpy of combustion divided by the molar mass of the substance. It can be seen that the absolute values of ΔH_C for ONOP (−16.64 kJ g⁻¹), ONOAP (−12.45 kJ g⁻¹), TNOP (−24.42 kJ g⁻¹), and TNOAP (−17.27 kJ g⁻¹) are much higher than that of HMX (−5.69 kJ g⁻¹),⁴³ indicating the release of large amounts of energy during the combustion of the designed compounds. Moreover, the replacement of CH groups by N atoms in ONOAP results in a decrease in the number of H atoms, leading to a relatively smaller absolute value of ΔH_C for ONOAP (−12.45 kJ g⁻¹) than for ONOP (−16.64 kJ g⁻¹). This is in general consistent with the fact that each H atom contributes about 8 kJ g⁻¹ of energy or so through the formation of water during combustion, which can also explain the smaller absolute ΔH_C value for TNOAP than for TNOP. Hence TNOP possesses the largest absolute value of ΔH_C due to its rich CH content and may release more combustion energy than the other three compounds as energetic materials. Given the desirable HOFs and ΔH_C of the four new compounds, all the designed compounds can be expected to have high potential as HEDMs.

Crystal structure and density

It is well known that the packing motif is closely bound up with the condensed-phase properties, especially the densities. Molecular mechanics has an intensive application for the prediction of molecular packing of energetic compounds.¹⁷ Therefore we predict the crystal structures for each molecule using the polymorph predictor module in Materials Studio.⁴⁴ DMol3 was employed to optimize a single molecule and obtain the electrostatic potential charge of all atoms using the GGA-PBE functional. Then, the crystal structure prediction was performed using the Dreiding force field, which is capable of giving out reliable information about condensed-phase properties for a diversity of organic systems.^20,21,45,46 Recently, Li et al. have presented an investigation of the reliability of the predicted crystal structures and confirmed that the predicted structure is the same as dinaphtho-tetrathiafulvalene (DN-TTF).⁴⁷ Ten of the most common space groups (P2₁/c, P1̄, Pbca, C2/c, P2₁, Pna2₁, C2, CC, P2₁2₁2₁, and Pbcn) were chosen for the prediction of the target compounds. Table 3 presents the cell parameters for the target compounds with the lowest energy and the corresponding crystal structures are shown in Fig. 4. The predicted crystal densities of the designed compounds are in the range 1.60 to 2.07 g cm⁻³. TNOP, which belongs to the Pbca space group, has the smallest crystal density (1.60 g cm⁻³) in the given set of molecules as a consequence of it having fewer nitro groups, while TNOAP, with four nitro groups, shows roughly the same density as ONOAP, which has eight nitro groups. This is because ONOAP and TNOAP prefer the P2₁2₁2₁ space group, which has a smaller unit cell volume than that of the Pbca space group. Evidently, ONOAP and TNOAP even have slightly higher and comparable crystal densities in comparison with CL-20 (2.04 g cm⁻³), which has the highest density among all the synthesized C, H, O and N explosives,⁴⁸ implying an outstanding detonation performance for ONOAP and TNOAP.

Table 3 Crystal parameters of molecular packings for ONOP, ONOAP, TNOP, and TNOAP obtained with the Dreiding Force Field

Comp'd	Space group	Z^a	ρc (g cm^−3)	a (Å)	b (Å)	c (Å)	α (°)	β (°)	γ (°)
a The number of molecules per cell.
ONOP	P1̄	2	1.85	14.02	9.98	9.16	117.5	108.9	96.8
ONOAP	P212121	4	2.07	13.08	8.93	15.81	90.0	90.0	90.0
TNOP	Pbca	8	1.60	11.88	17.34	15.71	90.0	90.0	90.0
TNOAP	P212121	4	2.02	16.28	8.94	8.94	90.0	90.0	90.0

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Fig. 4 Crystal structures of ONOP, ONOAP, TNOP, and TNOAP.

Detonation performance

Detonation velocity and pressure. Table 4 summarizes the OB (oxygen balance), Q (heat of detonation), D, P, theoretical density (ρ) and power index of the target molecules along with those of HMX and RDX for comparison. We calculated the densities of HMX and RDX using the Politzer method and found that the theoretical densities for HMX (1.80 g cm⁻³) and RDX (1.79 g cm⁻³) are in line with the experimental results (1.89 g cm⁻³ for HMX and 1.80 g cm⁻³ for RDX),⁴⁹ confirming the credibility of the method we adopted. Besides, the densities of ONOP (1.87 g cm⁻³) and ONOAP (2.07 g cm⁻³) calculated by the Politzer method are in perfect accordance with the predicted crystal densities (1.85 g cm⁻³ for ONOP and 2.07 g cm⁻³ for ONOAP), which in turn shows the consistency of both methods. It should be pointed out that the detonation performance (D and P) was assessed using the crystal densities in the present work. Apparently, the D and P of ONOP (10.87 km s⁻¹ and 53.70 GPa), ONOAP (11.24 km s⁻¹ and 60.70 GPa), TNOP (7.25 km s⁻¹ and 22.43 GPa), and TNOAP (10.06 km s⁻¹ and 46.30 GPa) are much larger than those of HMX (9.10 km s⁻¹ and 39.00 GPa) and RDX (8.75 km s⁻¹ and 34.00 GPa).⁵⁰ This means that ONOAP has a prominent explosive performance with a D and P higher than those of HMX by 24% and 54%, respectively. Hence, all the designed compounds, except for TNOP, may exhibit excellent detonation performances that are superior to HMX and RDX. The relatively poor detonation performance of TNOP can be attributed to the decrease in the number of nitro groups and the more negative OB value, which is given by the formula OB% = 100(2n_O − n_H − 2n_C − 2n_COO)/M (n_x is the number of certain atoms or groups) in this work. Generally, a positive OB means sufficient oxygen in the molecule for oxidation and combustion, which leads to an excellent detonation performance. Conversely, a negative OB value usually results in the incomplete release of energy/heat due to lack of oxygen and eventually a decrease in the detonation velocity and pressure,⁵¹ as is the case with TNOP. Hence, the relatively moderate OB of the studied compounds, except for TNOP, indicates that the oxygen content in ONOP, ONOAP, and TNOAP is adequate, allowing reaction with the available carbon and hydrogen. Therefore, these three compounds can be expected to give out a high heat of explosion during the detonation. In a word, based on the calculation results, we can conclude that ONOP, ONOAP, and TNOAP exhibit a comprehensively excellent detonation performance.

Table 4 Calculated oxygen balance (OB%), heats of explosion (Q, kJ g⁻¹), detonation velocity (D, km s⁻¹), detonation pressure (P, GPa), density (ρ, g cm⁻³), power index (%), and the specific impulse (I_s) of ONOP, ONOAP, TNOP, TNOAP, HMX, and RDX

Comp'd	OB%	Q (kJ g^−1)	D (km s^−1)	P (GPa)	ρ (g cm^−3)	Power index (%)	Is
a Experimental values from ref. 49.b Computed values using the Politzer method.
ONOP	−1.43	3902	10.87	53.70	1.87	269	20.58
ONOAP	2.78	2976	11.24	60.70	2.07	162	19.56
TNOP	−7.22	2037.38	7.25	22.43	1.69	102	22.94
TNOAP	−1.01	2887.91	10.06	46.30	1.90	199	22.11
HMX	0	1498	9.10	39.00	1.89^a (1.80)^b	166	14.43
RDX	0	1501	8.75	34.00	1.80^a (1.79)^b	168	14.13

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Power index. The power index was proposed as an indicator of the quantity of heat and gas products of the energetic materials.⁴³ The Kistiakowsky and Wilson rule⁴³ was employed to identify the gas products of decomposition and the products are shown in Table S5 in the ESI.† As shown in the following equation, the combination of the heat (Q) of explosion and the volume of gases (V) released per gram of explosives is defined as the explosive power. The value of the explosive power was then compared with the explosive power of a standard explosive (picric acid, PAc) to obtain the power index, viz.:

Explosive power = QV

Power index = [QV/Q_(PAc) × V_(PAc)] × 100

Table 4 lists the power indices of ONOP, ONOAP, TNOP, TNOAP, HMX, and RDX. Evidently, ONOP, ONOAP, and TNOAP have a better or comparable power index when compared to HMX/RDX, inferring that they may outperform HMX/RDX from the gaseous products and heat-releasing point of view. Unfortunately, TNOP has a smaller power index than the other three target molecules, therefore may display the poorest performance among these compounds, as reflected by D and P. This can be rationalized by the decrease in the nitro groups in the TNOP construction. To be specific, C atoms in the molecule cannot be fully oxidized to form CO/CO₂ due to the lack of oxygen, and they form carbon solids as products, therefore eventually leading to a reduction in the amounts of gas products and heat. However, we note that the trends of the given set of compounds are not consistent between D/P and the power index. Taking TNOAP and RDX, for example, a TNOAP molecule with a smaller power index (199%) is predicted to exhibit better explosive properties (D = 10.06 km s⁻¹, P = 46.30 GPa) than RDX (D = 8.75 km s⁻¹, P = 34.00 GPa) with a larger power index (168%). Therefore, we cannot judge the detonation properties only by the power index.

Specific impulse. To obtain a comprehensive insight into the detonation properties of the designed compounds, we carried out an additional study on the specific impulse (I_s). Desirable HEDM candidates should possess not only high density, high detonation velocity and pressure but also high I_s, which is assessed through the following idealized stoichiometric decomposition reactions based on the exothermic principle; namely, all nitrogen atoms are assumed to form N₂, and carbons to form CO₂ (if there are enough oxygen atoms) or C, while oxygen atoms preferentially form H₂O (if hydrogen atoms are available):⁵²

ONOP (C₁₆N₈O₁₆H₈) → 4H₂O + 6CO₂ + 4N₂ + 10C

ONOAP (C₈N₁₆O₁₆) → 8CO₂ + 8N₂

TNOP (C₁₆N₄O₈H₁₂) → 6H₂O + CO₂ + 2N₂ + 15C (s)

TNOAP (C₈N₁₂O₈H₄) → 2H₂O + 3CO₂ + 6N₂ + 5C (s)

The expression of this approach is:

I_s ≈ T_C^1/2N^1/2

where T_C is the combination of the absolute temperature in the combustion chamber and N is the number of moles of gases produced per unit weight of explosive. It is assumed that the heat of combustion is fully used to heat the product gases to the combustion temperature so that

−ΔH_comb = C_P,gases(T_C − T₀)

where ΔH_comb is the enthalpy of combustion, C_P,gases represents the total heat capacity of the gas products, and T₀ and T_C are the initial and combustion temperatures, respectively.

Table 4 presents the I_s values and Table S6† displays the corresponding parameters related to I_s of ONOP, ONOAP, TNOP, TNOAP, HMX, and RDX. It is clear that the I_s values of the four designed molecules are much higher than those of HMX (14.43) and RDX (14.13),⁵² owing to the extremely large ΔH_comb. This indicates that the four designed compounds can be anticipated to exhibit eminent detonation properties, taking the high I_s values into consideration.

In view of the detonation performance reflected by the detonation velocity, detonation pressure, power index, and the specific impulse, ONOP, ONOAP, and TNOAP are expected to be excellent energetic materials with remarkable detonation performances among the CHON-containing explosives.

Thermal stability and sensitivity. Another main concern regarding the explosives is whether they are stable/safe enough to store or transfer. In most cases, an enhancement of the detonation performance results in poor stability, rather than concomitantly improving it, which impedes the application of the newly synthesized energetic materials to some extent. Previous studies have shown that the assessment of the BDE and the h₅₀ for the studied compounds is an effective and straightforward way of estimating the thermal stability and sensitivity of energetic materials.^22,53 Therefore, an investigation of the thermodynamic stability through calculating the BDEs of the trigger bonds was performed to determine whether the designed compounds are thermally stable enough, and to obtain an insight into the decomposition mechanism. Previous studies^54–56 have shown that for poly-nitro cage explosives with structures similar to CL-20 and ONC, two possible initial steps in the decomposition are C–C cleavage in the cage and C–NO₂ bond breaking. Thus, both bond types were considered in this study and the BDE of the trigger bond was evaluated in terms of the formula:

BDE₀(A–B) = E₀(A˙) + E₀(B˙) − E₀(A–B)

The bond dissociation energy with zero-point energy (ZPE) correction is calculated by equation:

BDE(A–B)_ZPE = BDE(A–B) + ΔZPE

where ΔZPE is the difference between the ZPEs of the products and the reactants.

As shown in Table 5, both the C–C′ bonds between the two octatomic rings in ONOP (83.08 kJ mol⁻¹) and the C–N (N′) bonds in each octatomic ring in ONOAP, TNOP, and TNOAP have smaller BDEs (129.67, 197.50, and 117.89 kJ mol⁻¹, respectively) than the C–NO₂ bonds, indicating that the C–C/N bonds in the cage are weaker than the C–NO₂ bonds; thereby, all compounds may firstly decompose through C–C/N cleavage rather than C–NO₂ breaking. This is in agreement with previous studies, where the C–C bond breaking in the cage is the initial decomposition step for ONC, and with respect to TNTAC (2,4,6,8-teranitro-1,3,5,7-tetraazacubane), the skeleton C–N bond has much a smaller BDE (140.63 kJ mol⁻¹) than the side chain C–NO₂ (196.72 kJ mol⁻¹), suggesting that the breaking of the C–N bond in the cage is much easier and is the pyrolysis initiation step during pyrolysis in the gas phase.^16,20 Although the BDEs of the trigger bonds of ONOP, ONOAP, and TNOAP are smaller than those of HMX and RDX (145.62 and 160.41 kJ mol⁻¹, respectively), they have satisfied the stability requirement suggested previously; that is, for a viable HEDM candidate, the BDE should be larger than 80 kJ mol⁻¹ and for an exploitable HEDM, 120 kJ mol⁻¹.⁵⁷

Table 5 Calculated BDE, ΔV, and h₅₀ of ONOP, ONOAP, TNOP, TNOAP, HMX, RDX

Comp'd	BDE (kJ mol^−1)			ΔV (Å^3)	h50
	C–NO2	C–N (N′)^a	C–N (N′)^b
a Bonds in each octatomic ring.b Bonds between the two octatomic rings.c Experimental values from ref. 60.
ONOP	189.73	190.00	83.08	57.40	8
ONOAP	178.65	129.67	165.74	53.80	7
TNOP	218.46	197.50	208.94	33.94	53
TNOAP	196.25	117.89	193.58	45.61	19
HMX	145.62	—	—	49	29^c
RDX	160.41	—	—	46	26^c

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The sensitivity of the target compounds was estimated by calculating the characteristic height (h₅₀, using the methods proposed by Politzer et al.⁵⁸) and the free space per molecule in the unit cell (ΔV). Politzer et al. have proposed that ΔV can be used to estimate the impact sensitivity of energetic compounds.⁵⁹ ΔV is expressed as ΔV = V_eff − V_int, where V_eff is the difference between the effective volume per molecule and V_int is the intrinsic gas-phase molecular volume. In general, the impact sensitivities show an overall tendency to increase as ΔV becomes larger. The predicted ΔV and h₅₀ values are given in Table 5 for each molecule. As observed, the results from ΔV and the h₅₀ values are consistent with each other; namely, the sensitivity behavior of the designed molecules follows the sequence TNOP < TNOAP < ONOP = ONOAP. That is to say, the decrease in the number of nitro groups positively reduces the sensitivity of the resultant compounds. Therefore, adjusting the nitro content in the framework is still an efficient and straightforward strategy to improve the sensitivity. Relatively rich nitro groups make ONOP and ONOAP more sensitive than HMX and RDX, but they are predicted to be less sensitive than bis(trinitroethyl)nitramine (h₅₀ = 5 cm).⁶⁰ Moreover, although TNOAP displays a slightly poorer explosive performance than ONOP and TNOAP, the sensitivity of TNOAP is much lower than ONOP and ONOAP. More importantly, TNOAP displays superior explosive properties compared to HMX and a lower sensitivity than CL-20 (h₅₀ = 14 cm).²² This may suggest that properly replacing the carbon atoms by nitrogen atoms in cage explosives with super high energy may be a useful way to make them less sensitive without reducing their energy too much.²⁰ Overall, TNOAP may be the most promising candidate as a highly suitable energetic material, taking the comprehensive detonation performance coupled with thermal stability and sensitivity into consideration.

Conclusions

Four novel nitro-cage molecules, ONOP, ONOAP, TNOP, and TNOAP have been theoretically designed in this work. The geometric and crystal structures, gas-phase and condensed-phase HOFs, enthalpies of combustion, detonation performance, thermal stability and sensitivity of the target compounds are systematically investigated based on DFT calculations. Note that quite a few poly-nitro cage compounds^61,62 and octaprismane analogues⁶³ have been successfully synthesized experimentally. In this light, it is reasonable to conjecture that the poly-nitro octaprismane derivatives designed in our theoretical work can be synthesized in practice.

The results show that ONOP, ONOAP, and TNOAP possess high crystal densities (1.85, 2.07, and 2.02 g cm⁻³, respectively), which give them superior detonation velocities (10.06–11.24 km s⁻¹) and pressures (46.30–60.70 GPa). The bond dissociation energy of the molecules indicates that all the compounds display excellent thermal stability, except for ONOP, which also meets the thermal stability requirement as an HEDM. Besides, it is found that the C–C/N bond in the skeleton is the trigger bond during thermolysis, rather than the C–NO₂ bond. The sensitivity is assessed by calculating h₅₀ and ΔV values, both of which illustrate that molecules with four nitro groups are less sensitive than those with eight nitro groups, and TNOP (h₅₀ = 53 cm, ΔV = 33.94 ų) is found to be the most insensitive compound, followed by TNOAP (h₅₀ = 19 cm, ΔV = 45.61 ų). In all, TNOAP is found to be a highly powerful compound with appropriate sensitivity, thus we recommend this molecule as the best candidate for advanced HEDMs for the next generation.

Acknowledgements

This study is financially supported by the National Natural Science Foundation of China (21473010, 21303007).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra05352a

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