Theoretical studies on the derivatives of tris([1,2,4]triazolo)[4,3-a:4′,3′-c:4′′,3′′-e][1,3,5]triazine as high energetic compounds

Abstract

A heterocyclic framework inherited from triazole and triazine was suggested for the design of new energetic compounds. The geometric and electronic structures, IR spectra, gas and condensed-phase heat of formation of tris([1,2,4]triazolo)[4,3-a:4′,3′-c:4′′,3′′-e][1,3,5]triazine (TTT) and its nitro, amino, nitramino, and azide functionalized derivatives have been studied with ab initio and density functional theory methods. The crystal structures of these compounds were predicted using the crystal packing model. The initial decomposition reactions in the gas phase were studied to examine their kinetic stability. Our calculated results indicate that these compounds are promising candidates for energetic materials. In particular, 3,7,11-trinitrotris([1,2,4]triazolo)[4,3-a:4′,3′-c:4′′,3′′-e][1,3,5]triazine (TNTTT) has a density of 2.031 g cm⁻³, heat of formation of 208.37 kcal mol⁻¹, detonation velocity of 10.55 km s⁻¹, pressure of 38.57 GPa, and high activation energy of 55.97 kcal mol⁻¹, which are in general better than the commonly used energetic materials.

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Introduction

Energetic materials are widely used in modern civil and military applications.^1–4 In order to meet a variety of requirements in reactivity, safety and environment, much effort has been taken to the design and synthesis of new energetic materials, referring to novel performances,^5–7 especially for the materials with great power and high safety. However, in most cases, it is very difficult to concentrate both desired properties into one compound. As one kind of interesting structure, high-nitrogen heterocyclic systems have attracted great attention for the development of high-energy compounds.^8–14 Because nitro and some other energetic groups are presented on the rings, this type of compound could be used for high performance explosives.^15–18 Moreover, nitrogen-containing aromatic heterocycles are insensitive because of their aromaticity.^1,18,19 Among these heterocycles, 1,2,4-triazole and triazine groups with good stability, high nitrogen content, high enthalpy of formation, etc. are efficient fragments to enhance the performance of high-energy compounds.^20–24 It is thus expected that a new backbone combining with 1,2,4-triazole and 1,3,5-triazine fragments would derive new energetic molecules with good performances both in power and insensitivity.

Tris([1,2,4]triazolo)[4,3-a:4′,3′-c:4′′,3′′-e][1,3,5]triazine (TTT) is one of the frameworks containing 1,2,4-triazole and 1,3,5-triazine. As shown in Scheme 1, three triazole units are fused into one triazine ring to form a large planar conjugated structure with high nitrogen content.²⁵ Although the framework inherited from triazole and triazine has good potential for high power and low sensitivity, as far as we know, no attention has been paid to this framework for energetic materials purpose. In this work the detonation and stability of TTT and several functionalized derivatives have been studied to examine our expectation by means of ab initio, density functional theory (DFT) and molecular mechanics methods. The crystal structures, electronic structures, heats of formation (HOFs), initial decomposition reactions, detonation velocities and pressures have been investigated to understand the energetics and stability of these compounds. Our study would be helpful for the experimental research about the energetic compounds with TTT framework and other nitrogen-enriched conjugated structures.

Scheme 1 The structures and atomic numbering of tris([1,2,4]triazolo)[4,3-a:4′,3′-c:4′′,3′′-e][1,3,5]triazine (TTT), four functionalized derivatives.

Computational methods

In this theoretical work, all ab initio and DFT calculations were performed with Gaussian 09 package.²⁶ For these heterocyclic compounds, geometry optimization of the molecular structures was carried out at the M06-2X/cc-pVTZ level.^27,28 The harmonic frequency calculations were performed at the same level in order to ensure that the structures are local minima on the potential energy surfaces. Molecular electrostatic potentials (MEPs) were obtained at the same level. Finally, the possible initial decomposition reactions were studied with M06-2X/cc-pVTZ to understand the stability referring to chemical processes directly, and all geometries of transition states were confirmed with their intrinsic reaction coordinates (IRC).

In order to get the standard gas-phase HOFs (Δ_fH^°_gas) at 298 K, a series of isodesmic reactions²⁹ were designed to obtain HOFs as shown as follows:

Scheme 2 Designed isodesmic reactions for four TTT derivatives.

For each isodesmic reaction, the Δ_fH^°_{gas,298 K} is calculated by the following equation:

Δ_fH^°_{gas,298 K} = ∑Δ_fH_P − ∑Δ_fH_R = ΔE₀ − ΔZPE + ΔH_T + ΔnRT (1)

where Δ_fH_P and Δ_fH_R are the HOFs of products and reactants at 298 K, respectively. ΔE₀ is the difference between the electron energies of products and reactants at 0 K. ΔZPE is the difference between the zero-point energies (ZPEs) of products and reactants, and ΔH_T is the thermal correction from 0 K to 298 K. ΔnRT is the work term, which is equal to zero because Δn is zero in Scheme 2. Since no measured values are available for the reference molecules, additional calculations were performed for their atomization reactions at the G3B3 level.³⁰ Further single point calculations for the M06-2X/cc-pVTZ optimized structures were performed with a larger aug-cc-pVTZ³¹ basis set.

Based on Hess's law,³² the condensed-phase HOFs (Δ_fH^°_Cond) were obtained by

Δ_fH^°_Cond = Δ_fH^°_gas − ΔH_sub (2)

where ΔH_sub is the heat of sublimation and can be evaluated by the Byrd and Rice method³³ in the framework of the Politzer approach:³⁴

ΔH_sub = α₁A² + α₂(νσ_tot²)^0.5 + α₃ (3)

Meanwhile, the density of energetic crystal was estimated with a similar empirical expression:^35,36

In these expressions, A and V are the area of isosurface of 0.001 electrons per bohr³, and the volume contained within such isosurface respectively. ν is the degree of balance between the positive and the negative potential on the molecular surface. σ_tot² is the measure of variability of the electrostatic potential. M is the molecular weight of compound. α_i, and β_i (i = 1, 2, 3) are empirical parameters that are fitted from experiment measures.^33,36 All of these parameters about surface were obtained in Multiwfn program³⁷ at the M06-2X/cc-pVTZ level. Combined with density and Δ_fH^°_Cond, the detonation velocities (D) and pressures (P) of these compounds were predicted with Explo5 (version 6.02) package which is based on the chemical equilibrium, steady-state model detonation.³⁸ The equilibrium composition of the detonation products can be estimated by the modified White, Johnson, and Dantzig's free energy minimization technique, combining with the Becker–Kistiakowsky–Wilson equation of state (BKW-EOS), which is used for gaseous detonation products and the Cowan–Fickett equation of state for solid carbon. The program is designed for predicting the detonation properties at the CJ point.

Because the energetic compounds are usually in solid, the possible polymorphs and crystal structure of the compounds were predicted by Dreiding force field and polymorph module of Materials Studio.³⁹ Because more than 80% organic compounds are crystallized in seven space groups (P2₁/c, P1̄, P2₁2₁2₁, Pbca, C2/c, P2₁ and Pna2₁) according to the statistical data,^40,41 the crystal prediction has been constrained to these most typical groups. The geometries which are optimized at the M06-2X/cc-pVTZ level were used for the polymorph search.

Results and discussion

Molecular geometry

In order to explore the TTT framework, nitro, amino, nitramino, and azide nitrogen-containing groups have been chosen to replace the hydrogen atoms in the derivatives shown in Scheme 1. These compounds should be obtained according to the syntheses of several known TTT's derivatives in the viewpoint of organic chemistry.^25,42,43 It is evident that three five-membered rings and one six-membered ring construct a framework with a C₃ axis for all compounds.

Table 1 lists the selected bond lengths of the optimized structures. TTT exhibits a standard planar structure with C_3h symmetry. Three types of bonds, N–N, C=N, and C–N, exist in the framework. These bondlengths have very small changes when the H atoms are substituted. Take N4–C6 bond as an example, its length is about 1.385 Å in TTT, 2, and 3 and becomes 1.390 Å in 1. Although inheriting from the planar TTT, the frameworks in 1, 2, and 3 do not retain their perfect planes due to the steric effect of substituent groups. Moreover, most atoms in the nitro, amino, and nitramino groups are not located on the planes of the frameworks. In the four derivatives, all C3–R bonds are C–N single bonds with bond lengths of 1.461, 1.357, 1.385, and 1.379 Å, respectively. Overall, most of these compounds possess the compact symmetric structures.

Table 1 The bond-lengths of TTT and its derivatives (in Å)

Bond	TTT	R=NO2	R=NH2	R=NHNO2	R=N3
N1–N2	1.381	1.372	1.394	1.375	1.382
N2=C3	1.295	1.285	1.302	1.295	1.298
C3–N4	1.376	1.375	1.378	1.376	1.379
N4–C5	1.369	1.376	1.375	1.370	1.379
C5=N1	1.288	1.289	1.281	1.289	1.285
N4–N6	1.385	1.390	1.384	1.385	1.388
C3–R	1.076	1.461	1.357	1.385	1.379

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Crystal structure and density

The predicted lattice parameters of five compounds are presented in Table 2. All compounds are among three space groups, namely, P2₁/c, Pna2₁, and Pbca, according to their energy orders. Fig. 1 shows the cell structures of compound 1 and 3. Eight molecules of compound 1 and four molecules of compound 3 respectively construct two orthogonal cells with Pbca and Pna2₁ symmetries. And the predicted cell structures of compound TTT, 2 and 4 are presented in Fig. S1.†

Table 2 The cell parameters of possible molecular packings

Compound	Space groups	Z	ρ (g cm^−3)	a (Å)	b (Å)	c (Å)	α (°)	β (°)	γ (°)
TTT	P21/c	4	1.728	9.081	14.159	14.159	90.00	61.28	90.00
1	Pbca	8	2.031	7.577	12.237	23.716	90.00	90.00	90.00
2	Pna21	4	1.824	7.209	15.449	8.047	90.00	90.00	90.00
3	Pna21	4	1.905	9.069	10.089	14.528	90.00	90.00	90.00
4	P21/c	4	1.792	10.501	13.127	16.785	90.00	31.28	90.00

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Fig. 1 The cell structures of compound 1 and 3.

Density is one of the most attractive properties in energetic materials. Based on the cell structure, the crystal densities were estimated for these compounds, as listed in Table 2. Obviously, these TTT framework-containing compounds have high densities. The density of 1 with nitro-groups is as high as 2.031 g cm⁻³, close to 2.035 g cm⁻³, the density of ε-CL-20 (2,4,6,8,10,12-hexanitrohexaazaisowurtzitane). The density of 3 with nitramino-groups is 1.905 g cm⁻³, higher than those of β-HMX (1,3,5,7-tetranitro-1,3,5,7-tetrazocane, 1.903 g cm⁻³) and BTF (benzotrifuroxan, 1.901 g cm⁻³). For 2 and 4, the predicted densities are 1.824 and 1.792 g cm⁻³, respectively. At the same time, another series of density (ρ′) were obtained by using eqn (4), which are lower than those above, as shown in Table 3. For example, the predicted densities of 1 and 3 are 1.904 and 1.866 g cm⁻³, respectively. In short, compound 1 and 3 are expected to possess high densities, which is one of the indicators of good detonation performances.⁴⁴

Table 3 The calculated densities from eqn (4), heat of sublimation and formation, energy gaps, net charge on R group, and oxygen balance of the compounds

Compound	ρ′ (g cm^−3)	ΔfHgas (kcal mol^−1)	ΔHsub (kcal mol^−1)	ΔfHcond (kcal mol^−1)	Egap (eV)	Q(R) (e)	OB (%)
TTT	1.675	192.69	23.64	169.32	8.83	0.198	−59.7
1	1.904	176.45	29.41	208.37	7.91	−0.080	0.0
2	1.696	237.78	29.15	130.44	8.25	0.064	−58.5
3	1.866	245.18	37.36	207.82	8.26	−0.028	−6.3
4	1.803	439.07	36.68	402.40	7.74	0.047	−29.6

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Vibration analysis and heats of formation

Infrared (IR) spectrum is often employed to identify the structures of substances and closely related to their thermodynamics properties. The simulated IR spectra of TTT and its derivatives are shown in Fig. 2. For the TTT framework, only one strong characteristic peak was characterized at 1683 cm⁻¹ corresponding to the asymmetrical stretching of N–C in the six-membered ring. When the hydrogen atoms are substituted by the functional groups, the peaks in compound 1, 3 and 4 remain around 1650 cm⁻¹, except the peak at 1729 cm⁻¹ in 2. Some additional peaks belonging to the substituent groups appear in the IR spectra. In compound 1, the strongest peak at 1743 cm⁻¹ is associated with the asymmetrical stretching vibrations of N–O bonds in the nitro groups, while the medium peaks at 1457 cm⁻¹ are mainly dominated by the stretching vibration of C–NO₂ bonds. In compound 2, the strongest peak at 1668 cm⁻¹ is assigned to the stretching of C–NH₂ bonds. The asymmetrical and symmetrical stretching modes of N–H bonds correspond to two medium peaks at 3565 and 3706 cm⁻¹, and the out-of-plane vibrations refer to the weak peak at 475 cm⁻¹. For compound 3, the strongest peaks are observed at 1770 cm⁻¹ referring to the stretching vibrations of N–NO₂ bonds. The three medium peaks at 1380, 1394 and 1430 cm⁻¹ respectively belong to the stretching of –C–NH–, the rocking modes of N–H, and the stretching of N–O. The out-of-plane and stretching modes of N–H refer to the weak peaks at 520 and 3581 cm⁻¹. For compound 4, the strongest peak at 2381 cm⁻¹ is assigned to the stretching vibration of =N=N bonds, and the stretching modes of –N=N= and C–N= refer to the medium peaks at 1291 and 1599 cm⁻¹.

Fig. 2 The M06-2X/cc-pVTZ simulated IR spectra of TTT and its derivatives.

Based on the vibrational analysis and statistic thermodynamic methods, the gaseous-phase HOFs of the compounds were estimated and tabulated in Table 3. Using atomization reaction at G3B3 level, HOF of TTT were predicted as high as 192.69 kcal mol⁻¹. Δ_fH^°_gas of compounds 1–4 were then obtained according to the isodesmic reactions in Scheme 2. Obviously, these four compounds inherit high positive Δ_fH^°_gas from TTT. Among these four compounds, 4 with –N₃ has the greatest Δ_fH^°_gas of 439.07 kcal mol⁻¹, followed by the –NHNO₂ derivative (245.18 kcal mol⁻¹) and the –NO₂ derivative (237.78 kcal mol⁻¹). 2 with –NH₂ has the smallest Δ_fH^°_gas of 176.45 kcal mol⁻¹.

According to eqn (3), the ΔH_sub values were predicted and presented in Table 3, which vary between 23.02 and 37.06 kcal mol⁻¹. The condensed-phase HOFs (Δ_fH^°_Cond) were then obtained with eqn (2). TTT and its derivatives in solid state have high HOFs ranging from 147.30 to 402.39 kcal mol⁻¹, which are greater than those of β-HMX (24.5 kcal mol⁻¹)⁴⁵ and ε-CL-20 (90.2 kcal mol⁻¹).⁴⁶ Among these compounds, 5 with –N₃ possesses the highest HOF of 402.39 kcal mol⁻¹. Moreover, 1 and 3 exhibit positively large HOFs of 208.37 and 207.82 kcal mol⁻¹, respectively, which are large enough to meet the requirements of energetic materials.

Electronic structure and stability

The highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) are called as frontier molecular orbitals (FMOs). The energy gap (E_gap) between HOMO and LUMO is related to many molecular properties including kinetic stability and chemical reactivity.⁴⁷ The M06-2X/cc-pVTZ computed E_gap of TTT is 8.83 eV, much higher than that of BTF (6.75 eV), which is planar with three five-membered rings and one six-membered ring. The E_gap of compounds with –NO₂, –NH₂, –NHNO₂ and –N₃ are 7.910, 8.254, 8.256, and 7.740 eV, respectively. The TTT framework is characterized by its π-electron delocalization in the triazole and triazine rings. Every N atom in the framework forms three σ-bonds through sp² hybridization, making 18 p electrons including 6 π–n electrons delocalize over the framework to form a large conjugated system. Fig. 3 shows one of the π-bonding orbitals in TTT and 1. The HOMO of TTT consists of π orbitals, and its LUMO concentrates on the nitrogen atoms in the framework and the atoms in the substituent groups.

Fig. 3 HOMOs, LUMOs, and π orbitals of TTT and compound 1.

Table 3 gives the net charge on substituent groups (Q(R)). In general, Q(R) varies between −0.080 and 0.198e. It's noted that although as an electron-withdrawing group, –N₃ indeed transfers 0.047e to framework in the participation of conjugated system. The molecular electrostatic potential (MEP), which is related to intermolecular interaction and the impact sensitivity of the energetic compounds,⁴⁸ is definitely affected by the substituent groups. Fig. 4 illustrates the MEPs computed at the M06-2X/cc-pVTZ level for these compounds. The MEPs are scaled with color. Red denotes the most negative potential (−0.02 hartree) and blue the most positive potential (0.06 hartree). For all those compounds, the positive potential concentrates mainly on the triazine ring, while the negative potential is near to the atoms with lone-pair electrons in the five-membered rings and the substituent groups. In TTT the positive potential is at the center of the six-membered ring, while the negative potential is around the lone pairs of the N–N structure. Along with the replacement of the hydrogen atoms with the electron-withdrawing groups, such as –NO₂ and –NHNO₂, the electrons distributed on the heterocycle decrease and leave a positive potential on the frameworks. When the electron-donating group of –NH₂ are incorporated in the compounds, the blue region moves to the center of six-membered rings.

Fig. 4 The MEPs of the compounds at the M06-2X/cc-pVTZ level.

To evaluate the kinetic stability of these compounds, the transition states were identified for breaking these weak bonds. The results are shown in Fig. 5. In TTT framework the breaking of C3–N4 bond climbs over the energy barrier of 56.21 kcal mol⁻¹, which is the lowest barrier among the reaction channels. The breaking of N4–C6 bond has a higher barrier of 93.36 kcal mol⁻¹, and the N1–N2 bond is found difficult to break with a continuing rise of energy. In view of the energy barriers, C3–N4 breaking is the most important reaction channel for TTT. Compared to the bond breaking barriers of N–NO₂ in HMX (42.8 kcal mol⁻¹)⁴⁹ and C–NO₂ in TNT (61.7 kcal mol⁻¹),⁵⁰ one can conclude that TTT is a kinetically stable structure. The stability of TTT framework is also reflected by the other compounds. As listed in Table 4, the barriers range from 45.07 kcal mol⁻¹ of –NHNO₂ derivative to 55.97 kcal mol⁻¹ of –NO₂ derivative. It is evident that TTT brings a stable framework for these derivatives.

Fig. 5 The calculated initial reactions for compounds TTT, 1, 3 and 4 at the M06-2X/cc-pVTZ level.

Table 4 The energy barriers for bond breaking reactions in kcal mol⁻¹

R	ΔE		ΔG
	TS	PRO	TS	PRO
(C3–N4)
–H	51.54	41.24	56.21	45.46
–NO2	55.97	46.31	61.79	51.62
–NH3	—	46.46	—	54.35
–NHNO2	45.07	43.79	55.16	53.26
–N3	49.58	46.77	56.49	52.96
–H(N4–C5)	93.36	91.96	97.46	96.30
–H(N4–C6)	100.97	99.64	105.35	101.55
–H(N1–N2)	—	—	—	—
–NO2(C3–NO2)	73.65	66.11	79.60	58.44
–NHNO2(N–NO2)	45.30	38.09	55.84	33.87
–N3(N–N2-1)	5.23	3.57	15.52	13.36
–N3(N–N2-2)	38.21	−5.57	44.27	−10.64

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Furthermore, the initial decomposition reactions including the breaking of the nitro, nitramino, and azide-groups were studied. It is apparent in Fig. 5 that the barrier of C–NO₂ breaking is 73.65 kcal mol⁻¹, about 17.68–28.58 kcal mol⁻¹ higher than those of C3–N4 bonds. The barrier of N–NO₂ bond is 45.30 kcal mol⁻¹, close to that of C3–N4 in 3. For 5 with –N₃, the C3–N4 bond breaks with N₂ release and lead to a low barrier of 38.21 kcal mol⁻¹, indicating that 4 is less stable than other compounds. Therefore, compound 1 and 3 have overall good stability among these compounds.

Detonation properties

Oxygen balance (OB) is an index to measure the deficiency or excess of oxygen in a molecule required to convert all carbon into carbon monoxide (or carbon dioxide), and all hydrogen into water. In this work, the OB values of molecules with CaHbNcOd have been calculated as

OB (%) = 1600 × [d − a − b/2]/M (based on CO and HX).

where a, b, c, d are the number of carbon, hydrogen, nitrogen and oxygen atoms in the molecule. Table 3 lists the OB values for the compounds and more than half of them possess good OB values, indicating that these compounds have a good potential to release a large amount of power.

The detonation velocity (D) and the pressure (P) are evaluated with Explo5 6.02. Fig. 6 summarizes the detonation properties of these compounds, which were obtained based on the density from crystal packing. For a comparison, D and P of the well-known explosives TNT,⁵¹ HMX,⁵¹ and CL-20 ⁵¹ were also presented in the figure. D and P of all these compounds are much greater than those of TNT. It is worth to note that D of 1 reaches 10.55 km s⁻¹, greater than that of CL-20. Moreover, compound 3 exhibits good performances close to HMX. Even if using the low density predicted with eqn (4), the obtained performances of 1 and 3 are comparable to those of HMX (ESI Table 1†). Therefore, compound 1 and 3 promising powerful energetic materials among the C/H/N/O-containing organic compounds.

Fig. 6 Detonation parameters predicted with Explo5 for TTT, four functionalized derivatives, TNT, HMX, and CL-20.

Conclusion

In this work, a conjugated framework combining with triazole and triazine was proposed for heterocyclic energetic compounds. Tris([1,2,4]triazolo)[4,3-a:4′,3′-c:4′′,3′′-e][1,3,5]triazine (TTT), and its nitro, amino, nitramino, and azide-functionalized derivatives have been studied theoretically. Ab initio, DFT methods were used to investigate their geometrical and electronic structure, gas and condensed-phase heat of formation. The crystal structures of these compounds were predicted with molecular packing calculations. All the compounds were predicted to possess large HOFs and high densities, which lead to great detonation performances. Compound 1 (3,7,11-trinitrotris([1,2,4]triazolo)[4,3-a:4′,3′-c:4′′,3′′-e][1,3,5]triazine, TNTTT) exhibits the remarkable D of 10.55 km s⁻¹ and P of 38.57 km s⁻¹, which are better than those of HMX and CL-20. Compound 3 (N,N′,N′′-(tris([1,2,4]triazolo)[4,3-a:4′,3′-c:4′′,3′′-e][1,3,5]triazine-3,7,11-triyl)trinitramide, TNATTT) also possesses good detonation properties (D = 9.40 km s⁻¹ and P = 34.78 km s⁻¹).

Calculations on the initial decomposition reaction in gas-phase indicate that the TTT framework is stable with high activation energies about 56 kcal mol⁻¹ at the M06-2X/cc-pVTZ level, which is much higher than that of HMX. TNTTT and TNATTT were then characterized with good stability. Considering both the detonation properties and stabilities, the compounds with triazole and triazine, particularly TNTTT, are promising candidates of high-energy density material with low sensitivity and high performance.

Acknowledgements

The authors gratefully acknowledge the support of the National Natural Science Foundation of China (No. 11402240), and the China Postdoctoral Science Foundation (No. 2014 2014M552381).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra22524h

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