A DFT study of five-membered nitrogen-containing fused heterocycles for insensitive highly energetic materials

Abstract

A series of molecules with conjugated backbones combined with two five-membered nitrogen-containing rings is suggested for the design of new energetic compounds. With the participation of both –NH₂ and –NO₂, seven planar derivatives were characterized with aromaticity and intramolecular hydrogen bonds. The geometrical and electronic structures, gas and condensed-phase heats of formation (HOFs) and strengths of the hydrogen bonds were studied using density functional theory methods. The crystal structures of these compounds were predicted using molecular packing calculations. The bond dissociation energies (BDEs) were investigated to understand their stabilities. Our calculated results indicate that these compounds are promising candidates for energetic materials. Among them, two compounds with a B4 backbone, B4-1 and B4-2, possess high densities, great HOFs and detonation properties. B4-2 has not only a high density of 2.263 g cm⁻³, heat of formation of 106.91 kcal mol⁻¹, detonation velocity of 9.74 km s⁻¹ and pressure of 47.79 GPa, but also a high BDE of 62.72 kcal mol⁻¹ and layered crystal packing, and can be considered as a potential candidate for high energetic materials with great insensitivity.

---

Introduction

Energetic materials (EMs), including explosives, propellants, and pyrotechnics, are used extensively for both civilian and military applications.^1,2 With the continuing requirements for improved EMs, many researchers have been attracted to the design and synthesis of new EMs with novel performances, especially for the development of materials with great power and high safety levels.^3–6 However, the power seems to be contrary to the stability and insensitivity, which causes the development of EMs to meet a great challenge.⁷

To balance the power and sensitivity, several good backbones have been chosen for the development of new EMs. Among them, nitrogen-rich heterocycles have been receiving considerable attention, such as triazole, tetrazole, triazine, and tetrazine.^8–16 EMs derivated from these backbones not only bring high power because of a high nitrogen content, a high heat of formation and high density, but also exhibit excellent kinetic and thermal stabilities owing to their aromaticity.^17,18 Many researchers have focused on constructing derivatives of the heterocycles with functional groups including –NO₂, –NHNO₂, and –N₃. However, the presence of too many energetic groups still tends to increase the instability of the materials, though the power properties will be enhanced. Although the power might be sacrificed to some extent, amino groups are introduced to construct intra/inter-molecular hydrogen bonds (HBs) with the nitro groups, which can increase the density, decrease sensitivity and improve the thermal stability.

Actually, the combination of a conjugated structure and intra/inter-molecular hydrogen bonds is always applied to obtain low sensitivity EMs.^7,19,20 1,3,5-triamino-2,4,6-trinitrobenzene (TATB)¹ and 1,1-diamino-2,2-dinitroethylene (FOX-7)²¹ are typical carbon-based 4n + 2π electron aromatic systems with hydrogen bonding between –NH₂ and –NO₂. They possess excellent sensitivity with good detonation properties. Moreover, 2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105)² and dihydroxylammonium-5,5′-bistetrazole-1,1′-diolate (TKX-50)²² with nitrogen-containing aromatic heterocycles and hydrogen bonding also have a good balance between power and safety. Recently, Chavez et al. reported a di-N-aminated 3,3′-dinitro-5,5′-bi-1,2,4-triazole, which possesses a satisfying thermal stability, a good density, an insensitivity close to that of TATB, and a power approaching that of RDX.²³ Together with hydrogen bonding, nitrogen-containing polycyclic compounds should offer many opportunities for the design and development of new EMs.

In this work, four five-membered nitrogen-containing cyclic compounds, including pyrrole, pyrazole, imidazole and triazole, were focused on to construct di-cyclic backbones. Although many backbones can be obtained from these four rings, four planar structures with inversion symmetry were chosen since they have enough sites for the substituents and aromaticity with 10π electrons, as shown in Fig. 1. With the participation of both –NH₂ and –NO₂, a series of energetic compounds with intramolecular HBs was designed for obtaining candidates with high explosive performance and insensitivity. Through density functional theory (DFT) methods, the geometric and electronic structures, heats of formation, crystal packing mode and density, and detonation performance of these compounds were studied. The stabilities are discussed based on their electronic structures including the energy gaps (E_gap) and bond dissociation energies (BDEs). Our study will promote experimental research on energetic compounds with these backbones, and improve the understanding of the properties of nitrogen-enriched conjugated structures and intramolecular HBs.

Fig. 1 The di-cyclic aromatic backbones with 10π electrons studied in this work.

Methods

The geometries of these heterocyclic compounds were optimized using the hybrid functional M06-2X²⁴ with a 6-311+G(p) basis set. The harmonic vibrational frequencies were calculated at the same level to confirm the structures located at the local minima on the potential energy surfaces and calculate thermochemical parameters. Molecular electrostatic potentials (MEPs) were obtained at the same level.

The crystal packing density (ρ) is one of the critical parameters for energetic materials. In this work, the crystal densities were obtained from the results of the crystal prediction. According to statistical data, more than 80% of organic compounds crystallize in seven space groups (P2₁/c, P1̄, P2₁2₁2₁, Pbca, C2/c, P2₁ and Pna2₁).²⁵ Meanwhile, the density of the energetic crystals was also evaluated using an empirical expression proposed by Politzer et al.:²⁶

In this expression, M is the molecular weight of the compound and V is the volume within the 0.001 a.u. isosurface of an electron. ν is the degree of balance between the positive and the negative potential on the molecular surface. σ_tot² is a measure of the variability of the electrostatic potential. a_i (i = 1, 2, 3) are empirical parameters that were determined by Rice et al.²⁷

The HOF is the other important parameter for energetic compounds. In order to obtain accurate standard gas-phase HOFs (Δ_fH^o_gas) at 298 K, a series of isodesmic reactions²⁸ were designed to evaluate the HOFs (see Scheme S1†). The Δ_fH^o_{gas,298 K} can be obtained using the following equation:

Δ_fH^o_{gas,298 K} = ∑Δ_fH_P − ∑Δ_fH_R = ΔE₀ − ΔZPE + ΔH_T + ΔnRT (2)

where Δ_fH_P and Δ_fH_R are the HOFs of the products and reactants at 298 K, respectively; ΔE₀ is the difference between the electron energies of the products and reactants at 0 K; ΔZPE is the difference between the zero-point energies (ZPEs) of the products and reactants; ΔH_T is the thermal correction from 0 K to 298 K; and ΔnRT is a work term, which equals zero for Δn = 0. For the reference molecules, corresponding values were obtained from experimental measurements or additional calculations using an atomization reaction at the G3B3 level.²⁹ Thus, the condensed-phase HOFs (Δ_fH^o_Cond) were obtained according to Hess’s law,³⁰

Δ_fH^o_Cond = Δ_fH^o_gas + E_latt (3)

for which the lattice energy can be calculated directly based on the predicted crystal structure using a Dreiding force field.

The strength of bonding plays an important role in predicting the thermal stability of an energetic material. Generally, an X–NO₂ (X = C or N) bond is the easiest to break for an energetic compound with an X–NO₂ bond. Therefore, the bond dissociation energy (BDE)^31–33 was used to evaluate the strength of X–NO₂ bonds as follows:

X–NO₂(g) → X˙(g) + ˙NO₂(g) (4)

BDE(X–NO₂) = ΔH(X˙) + ΔH(˙NO₂) − ΔH(X–NO₂) − BSSE (5)

where X–NO₂ stands for the neutral molecule, and X˙ and ˙NO₂ for the corresponding product radicals after bond dissociation; BDE(X–NO₂) is the BDE of the X–NO₂ bond; ΔH(X–NO₂), ΔH(X˙) and ΔH(˙NO₂) are the enthalpies of the parent compound and corresponding radicals, respectively. All the BDEs were corrected with the basis set superposition errors (BSSEs).

The detonation velocities and pressures of these compounds were predicted using empirical Kamlet–Jacobs formulas³⁴ as follows:

P = 1.558NM̄^0.5Q^0.5ρ² (6)

D = 1.01(NM̄^0.5Q^0.5)^0.5(1 + 1.30ρ) (7)

where P is the detonation pressure (GPa); D is the detonation velocity (km s⁻¹); N is the number of moles of detonation gases per gram of explosive (mol g⁻¹); M̄ is the average molecular weight of these gases (g mol⁻¹); Q is the detonation heat (cal g⁻¹); and ρ is the density of the explosive (g cm⁻³).

All quantum chemistry calculations were performed with a Gaussian 09 package.³⁵ The crystal prediction was carried out using only the above-mentioned space groups with a Dreiding force field and a polymorph program.³⁶

Results and discussions

1 Molecular structure

The four backbones were designed based on four five-membered nitrogen-containing aromatic heterocycles. Two of the same rings were used to construct a planar conjugated polycyclic structure with a common bond as shown in Fig. 1. These structures present good electron delocalization (see Fig. S1 in ESI†). Actually, compounds based on backbone 2 (B2), DNPP, LLM-11 9 (B2-1) and LLM-121, have been previously studied^1,37 and backbone 4 (B4) has been paid attention to within many studies on energetic materials.^37,38 After the incorporation of –NH₂ and –NO₂ groups, a series of compounds (shown in Fig. S2†) developed from the backbones were investigated. Seven exhibit planar structures although the structures of the backbones were little changed as shown in Fig. 2. Moreover, almost all the –NO₂ groups connected with carbon atoms are located on the plane of the backbones. However, due to the strong electron-withdrawing characteristics of –NO₂, the conjugation with the lone-pair on the nitrogen atom can be broken, which means that the NO₂ group bonding to a nitrogen atom is not in the plane. Table 1 lists several selected geometry parameters of the optimized molecules. The intramolecular distances between a hydrogen atom on –NH₂ and an oxygen atom on –NO₂ are noteworthy, as presented in Table 1. Obviously, the distances are less than the average van der Waals radius of O and H of 2.62 Å.³⁹ For example, the distances are 2.241 and 2.381 Å for compounds B4-1 and B3-1, respectively. This means that the compounds should have intramolecular hydrogen-bonds.

Fig. 2 The structures of the heterocyclic compounds optimized at the M06-2X/6-311+G(p) level.

Table 1 The bond-lengths of X–NO₂ and the HBs (Å) for the compounds

	N–NO2	C–NO2	N–NO2⋯H2N	C–NO2⋯H2N
B1-1	1.423	1.408	2.072	2.068
B1-2	—	1.403	—	2.157
B2-1	—	1.445	—	2.760
B2-2	1.388	—	2.184	—
B3-1	—	1.455	—	2.381
B4-1	—	1.434	—	2.241
B4-2	—	1.400	—	2.221

---

2 Electronic structure and stability

The highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) can be called frontier molecular orbitals (FMOs). The energy gap (E_gap) between the HOMO and LUMO determines many molecular properties including the kinetic stability and chemical reactivity.⁴⁰ The E_gap values of B1, B2, B3, and B4 are predicted to be 6.55, 7.99, 7.41 and 7.46 eV. The E_gap values of the target compounds were evaluated to be lower than those of the corresponding backbones. They are 5.36, 5.21, 7.038, 6.01, 6.11, 4.88 and 5.84 eV for compounds B1-1 to B4-2, respectively. As mentioned above, these backbones are characterized by 10π-electron delocalization in the two five-membered rings, which significantly satisfies the 4n + 2 rule of aromaticity. Fig. 3 shows typical π bonding orbitals, HOMOs and LUMOs, for B3-1 and B4-1. Obviously, as the molecules lie in the xy plane, the π-electron delocalization involves almost all the p_z orbitals of the compounds, including those of the nitro-groups and lone pairs of the amino-groups. The HOMOs also consist of π orbitals, while the LUMOs mainly represent the lone pairs in the backbones and substituent groups.

Fig. 3 Typical π bonding orbitals, HOMOs and LUMOs for B3-1 and B4-1.

The molecular electrostatic potential (MEP) is always considered to be related to intermolecular interactions and the impact sensitivity of energetic compounds.^41,42 Fig. 4 illustrates the MEPs for compounds B3-1, B4-1 and B4-2. The MEPs are presented using a colour scale, ranging from −18.82 kcal mol⁻¹ to 18.82 kcal mol⁻¹, with red denoting the most negative potential and blue denoting the most positive potential. Obviously, as the aromatic conjugated structures, the four backbones act mainly as bridges and play an important role in charge transfer between the amino- and nitro-groups, because the MEPs are close to zero kcal mol⁻¹ at them. For the three compounds, the minima of the MEPs appear near the oxygen atoms in the nitro-groups, as the electron-withdrawing groups, while the maxima tend to occur at hydrogen atoms in the amino-groups, as the electron donating groups. The global maxima of the MEPs for B3-1, B4-1 and B4-2 are +49.36, +51.88 and +52.50 kcal mol⁻¹, corresponding to the hydrogens, while the minima are −31.36, −27.08 and −30.34 kcal mol⁻¹, corresponding to the oxygens. For B4-1 and B4-2 with the same backbone, the second maxima of about +31 kcal mol⁻¹ are distributed near the N–N bonds at the center of the backbone in spite of the different substituent sites. The area for each MEP range in Fig. 4 can provide more information. For the three compounds, the values of the MEPs are mainly distributed in the range from −30 to +50 kcal mol⁻¹. The largest areas have values of about −20 kcal mol⁻¹, corresponding to the nitro-groups, while the second largest areas have values located near to +20 kcal mol⁻¹, corresponding to the backbones. The areas with values larger than +30 kcal mol⁻¹ should consist of the hydrogens in amino-groups. Among them, B4-2 has the most areas with values of about 20 kcal mol⁻¹ and less than −20 kcal mol⁻¹. Compared with B3-1, more areas in B4-1 and B4-2 range from −20 to +20 kcal mol⁻¹. More MEP information for the other compounds is given in Fig. S2.†

Fig. 4 MEPs for compounds B3-1, B4-1 and B4-2, and the surface areas for each MEP range.

Hydrogen atoms with the positive MEP and oxygen atoms with the negative MEP will attract each other to form intermolecular hydrogen bonds. Fig. 5 shows the hydrogen bonds represented with an interaction surface around the critical point and the graphs of the reduced electron density gradient vs. sign(λ₂)ρ⁴³ for compounds B1-1, B2-1, and B3-1. From the sign(λ₂)ρ values, it was found that the strength of the intramolecular HBs in these compounds is not strong (Fig. S3 in ESI†). There are two types of sign(λ₂)ρ values for the compounds. One type is where sign(λ₂)ρ is about 0.02 a.u., representing a mid-strength hydrogen bond with more electrostatic attraction, whereas the other shows characteristics of a more dispersive interaction (sign(λ₂)ρ ≈ 0.01 a.u.). The HBs in B3-1 belong to the former type, while those in B2-1 are obviously the latter. Compound B1-1 displays the two types of HBs.

Fig. 5 The hydrogen bonds (depicted by an interaction surface around the critical point) and the graphs of the reduced electron density gradient vs. sign(λ₂)ρ for B1-1, B2-1, and B3-1.

Due to the aromatic backbones and intra-molecular hydrogen bonds, the compounds tend to possess high stability. The BDE provides useful information for understanding the stability of energetic materials. Generally, the stronger the weakest bonds are, the more stable the energetic materials are; that is, the sensitivity and stability of the energetic materials are directly related to bond strength, which is commonly described using the BDE. Because the backbones are aromatic, Table 2 just lists the BDEs for the breaking of the C–NO₂ and N–NO₂ bonds. Obviously, the compounds with only C–NO₂ should exhibit good stability at the molecular level. For insensitive TNT and TATB, the BDEs were predicted to be 63.88 and 70.65 kcal mol⁻¹ at the same level, respectively, in agreement with other calculations for TNT (61.7 kcal mol⁻¹)⁴⁴ and TATB (69.4 kcal mol⁻¹).⁴⁴ Compounds B1-2, B2-1, B3-1, B4-1 and B4-2 have great BDEs due to the breaking of C–NO₂ bonds, which are 75.44, 72.93, 68.51, 66.95, and 62.72 kcal mol⁻¹, higher than or close to those of TNT and TATB. While the BDEs of B2-2 and B1-1, with breaking of N–NO₂ bonds, are low at 26.14 and 4.84 kcal mol⁻¹.

Table 2 The HOMO–LUMO gap, bond dissociation energy without and with BSSE correction, molecular volume, degree of balance between the positive and the negative potentials, and total variance of the electrostatic potential for the target compounds

	Egap (eV)	BDE (kcal mol^−1)	BDE(BSSE) (kcal mol^−1)	V (Å^3)	v	σtot^2 ((kcal mol^−1)^2)
B1-1	5.37	7.62	4.84	281.93	0.22	8.95
B1-2	5.21	77.70	75.44	227.32	0.20	7.37
B2-1	7.04	75.37	72.93	218.84	0.19	8.78
B2-2	6.01	29.25	26.14	216.51	0.21	8.61
B3-1	6.11	70.90	68.51	217.50	0.19	8.52
B4-1	4.88	69.39	66.95	218.32	0.20	9.58
B4-2	5.84	65.20	62.73	217.31	0.22	9.74

---

3 Crystal packing structure

Table 3 summarizes the predicted crystal packing parameters of the compounds. Three space groups were chosen for all the compounds, namely, P2₁, P1̄, and P2₁2₁2₁, according to their energy orders. These compounds tend to form layered crystal packing through intermolecular HB-aided π–π stacking. From Fig. 6, compounds B1-2, B2-2, B3-1 and B4-1 chose this packing style. From the prediction, both B2-2 and B3-1 use two molecules and P1̄ symmetry to form triclinic cells, respectively. Two molecules of compound B1-2 construct a monoclinic cell with P2₁ symmetry, while four molecules of compound B4-1 pack to form an orthogonal cell with P2₁2₁2₁ symmetry. The compounds with layered structures should possess good sensitivity at the crystal level.^19,20,45 For the other compounds, the predicted cell structures are presented in Fig. S4.† Based on the predicted cell structures, the lattice energies can be obtained using force directly. As listed in Table 3, the compounds possess great E_latt because of the participation of HBs and π–π stacking. For B1-2, B2-2, B3-1 and B4-1, the magnitude of the E_latt is predicted to be −43.37, −34.78, −40.92, and −12.79 kcal mol⁻¹.

Table 3 The predicted crystal packing parameters of the compounds, density, and lattice energy

	Symmetry	Z	a (Å)	b (Å)	c (Å)	α (°)	β (°)	γ (°)	ρ (g cm^−3)	Elatt (kcal mol^−1)
B1-1	P212121	4	12.281	8.253	10.270	90.00	90.00	90.00	2.017	−62.27
B1-2	P21	2	5.047	13.432	6.702	90.00	118.78	90.00	1.886	−43.37
B2-1	P21	2	4.828	6.680	12.589	90.00	76.67	90.00	1.917	−36.34
B2-2	P1̄	2	6.989	18.294	7.342	38.47	49.64	73.43	1.926	−34.78
B3-1	P1̄	2	7.124	12.723	10.362	140.90	56.98	137.29	1.889	−40.92
B4-1	P212121	4	9.049	8.897	8.587	90.00	90.00	90.00	2.192	−12.79
B4-2	P21	2	6.932	8.802	5.538	90.00	82.12	90.00	2.263	−13.45

---

Fig. 6 The cell structures of B1-2, B2-2, B3-1 and B4-1.

A suitable density is one of the most attractive properties for energetic materials. Based on the cell structures, the crystal densities were estimated for these compounds, as listed in Table 2. Obviously, these compounds have high densities. Among the compounds, B4-1 and B4-2 have the highest densities, 2.192 and 2.263 g cm⁻³, which are higher than 2.035 g cm⁻³, the density of ε-CL-20 (2,4,6,8,10,12-hexanitrohexaazaisowurtzitane). The density of B1-1 is 2.017 g cm⁻³, approaching that of CL-20. Compound B2-2 also has a higher density (1.926 g cm⁻³) 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 B1-2 and B3-1, the predicted densities are 1.886 and 1.884 g cm⁻³, respectively, higher than that of RDX. At the same time, density (ρ′) values were also predicted using eqn (1), which were much lower than those above, as shown in Table 4. For example, the ρ′ values of B4-1 and B4-2 are 1.750 and 1.773 g cm⁻³, respectively. Because of the hydrogen bonding interactions and layered stacking, the expression should not be suitable for these compounds (detailed explanation in Table S1 of the ESI†). Thus, the densities from the crystal packing were used for the following work.

Table 4 The calculated densities from eqn (1), the heat of formations, oxygen balance, and detonation performance for the target compounds

	ρ′ (g cm^−3)	HOFgas (kcal mol^−1)	HOFcon (kcal mol^−1)	OB%	D (km s^−1)	P (GPa)
B1-1	1.901	92.25	29.98	−35.22	8.95	37.89
B1-2	1.709	45.24	1.87	−77.86	7.37	24.79
B2-1	1.734	165.29	128.94	−55.81	8.78	35.47
B2-2	1.750	133.81	99.03	−55.81	8.61	34.18
B3-1	1.754	144.34	103.42	−55.81	8.52	33.12
B4-1	1.750	128.80	116.01	−55.81	9.58	45.48
B4-2	1.773	128.80	106.91	−55.81	9.74	47.79

---

4 Heat of formation

Based on the vibrational frequencies and statistical thermodynamic methods, the gaseous-phase HOFs of the compounds were estimated and are listed in Table 4. Using an atomization reaction at the G3B3 level, the HOFs of the 4 backbones were predicted firstly. Then, Δ_fH_gas values for all the target compounds were obtained according to the isodesmic reactions in Scheme S1.† All these compounds exhibit a high positive Δ_fH_gas in the range from 45.24 (B1-2) to 165.29 kcal mol⁻¹ (B2-1).

Together with E_latt obtained from the packing prediction, the condensed-phase HOFs (Δ_fH_con) were estimated according to eqn (3). Because of the high E_latt, the Δ_fH_con values are decreased greatly compared to Δ_fH_gas. Except for B1-2 with 1.87 kcal mol⁻¹, all the compounds in solid state have high HOFs ranging from 29.98 to 128.94 kcal mol⁻¹, greater than that of β-HMX (24.5 kcal mol⁻¹).⁴⁶ Among these compounds, B2-1 (LLM-119) possesses the highest HOF of 128.94 kcal mol⁻¹. Moreover, B3-1 and B2-2 exhibit positively large HOFs of 103.42 and 99.02 kcal mol⁻¹, respectively. The three compounds exhibit a larger Δ_fH_con than the 90.2 kcal mol⁻¹ of CL-20.⁴⁷

5 Detonation performance

The detonation parameters were evaluated using Kamlet–Jacobs equations and Table 4 also lists the D, P, and oxygen balance (OB) of the target molecules. Most of the compounds possess the same OB value of 55.81% as TATB with the presence of –NH₂. The detonation velocity (D) and the pressure (P) were evaluated, and D and P of all these compounds are much greater than those of TNT.⁴⁶ It is worth noting that most of the compounds exhibit better performances than the 9.1 km s⁻¹ and 39.0 GPa of HMX.⁴⁸ Among them, two compounds with the backbone B4 exhibit promising detonation performances. The D and P of B4-1 are predicted to be 9.59 km s⁻¹ and 45.48 GPa, and those of B4-2 are 9.74 km s⁻¹ and 49.79 GPa. Together with the discussion on the stability, the compounds with B2, B3, and B4 can be considered as novel candidates for insensitive highly energetic compounds.

Conclusion

In this work, a series of conjugated backbones based on nitrogen-containing five-membered cyclic compounds was chosen for the design of insensitive highly energetic compounds. With the participation of both –NH₂ and –NO₂, seven derivatives exhibit the characteristics of aromaticity and intra-molecular hydrogen bonds. Through DFT calculations, their geometrical and electronic structure, and gas and condensed-phase heat of formation were evaluated. The crystal structures of these compounds were predicted with molecular packing calculations. All the compounds were estimated to possess large HOFs and high densities, which means that the compounds exhibit great detonation performances. Among them, the compounds with the B4 backbone possess great detonation properties (D = 9.59 km s⁻¹ and P = 45.48 GPa for B4-1, D = 9.74 km s⁻¹ and P = 49.79 GPa for B4-2). According to the estimation of the stability, including BDEs and crystal packing, the compounds with C–NO₂ bonds have good stability. Considering both the detonation properties and stabilities, the compounds with the backbones, particularly B4, are very promising candidates for energetic compounds with low sensitivity and high power. These results provide theoretical support for molecular design and experimental investigation of EMs.

Acknowledgements

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

References

1. L. E. Fried, M. R. Manaa, P. F. Pagoria and R. L. Simpson, Annu. Rev. Mater. Res., 2001, 31, 291.
2. P. F. Pagoria, G. S. Lee, A. R. Mitchell and R. D. Schmidt, Thermochim. Acta, 2002, 384, 187.
3. H. Wei, H. X. Gao and J. M. Shreeve, Chem.–Eur. J., 2014, 20, 16943.
4. P. Yin, D. A. Parrish and J. M. Shreeve, Angew. Chem., Int. Ed., 2014, 53, 12889.
5. P. He, J.-G. Zhang, K. Wang, X. Yin, X. Jin and T.-L. Zhang, Phys. Chem. Chem. Phys., 2015, 17, 5840.
6. Q. Zeng, Y.-Y. Qu, J.-S. Li and H. Huang, RSC Adv., 2016, 6, 5419.
7. P. Politzer and J. S. Murray, in Advances in Quantum Chemistry, ed. J. R. Sabin, 2014, vol. 69, pp. 1–30.
8. D. R. Miller, D. C. Swenson and E. G. Gillan, J. Am. Chem. Soc., 2004, 126, 5372.
9. T. M. Klapotke, F. A. Martin and J. Stierstorfer, Angew. Chem., Int. Ed., 2011, 50, 4227.
10. A. A. Dippold, D. Izsak and T. M. Klapotke, Chem.–Eur. J., 2013, 19, 12042.
11. J. H. Zhang, C. L. He, D. A. Parrish and J. M. Shreeve, Chem.–Eur. J., 2013, 19, 8929.
12. N. Fischer, K. Hull, T. M. Klapotke and J. Stierstorfer, J. Heterocycl. Chem., 2014, 51, 85.
13. N. Kommu, V. D. Ghule, A. S. Kumar and A. K. Sahoo, Chem.–Asian J., 2014, 9, 166.
14. M. Goebel, K. Karaghiosoff, T. M. Klapoetke, D. G. Piercey and J. Stierstorfer, J. Am. Chem. Soc., 2010, 132, 17216.
15. Y.-C. Li, C. Qi, S.-H. Li, H.-J. Zhang, C.-H. Sun, Y.-Z. Yu and S.-P. Pang, J. Am. Chem. Soc., 2010, 132, 12172.
16. B. Abarca and R. Ballesteros-Garrido, in Chemistry of 1,2,3-triazoles, ed. W. Dehaen and A. V. Bakulev, Springer International Publishing, Cham, 2015, pp. 325–378.
17. V. Thottempudi, F. Forohor, D. A. Parrish and J. M. Shreeve, Angew. Chem., Int. Ed., 2012, 51, 9881.
18. H. Gao and J. n. M. Shreeve, Chem. Rev., 2011, 111, 7377.
19. Y. Ma, A. B. Zhang, X. G. Xue, D. J. Jiang, Y. Q. Zhu and C. Y. Zhang, Cryst. Growth Des., 2014, 14, 6101.
20. Y. Ma, A. B. Zhang, C. H. Zhang, D. J. Jiang, Y. Q. Zhu and C. Y. Zhang, Cryst. Growth Des., 2014, 14, 4703.
21. N. V. Latypov, J. Bergman, A. Langlet, U. Wellmar and U. Bemm, Tetrahedron, 1998, 54, 11525.
22. N. Fischer, D. Fischer, T. M. Klapotke, D. G. Piercey and J. Stierstorfer, J. Mater. Chem., 2012, 22, 20418.
23. D. E. Chavez, J. C. Bottaro, M. Petrie and D. A. Parrish, Angew. Chem., Int. Ed., 2015, 54, 12973.
24. Y. Zhao and D. G. Truhlar, Theor. Chem. Acc., 2008, 120, 215.
25. N. Y. Chernikova, V. K. Bel’skii and P. M. Zorkii, J. Struct. Chem., 1990, 31, 661.
26. P. Politzer, J. Martinez, J. S. Murray, M. C. Concha and A. Toro-Labbé, Mol. Phys., 2009, 107, 2095.
27. B. M. Rice and E. F. C. Byrd, J. Comput. Chem., 2013, 34, 2146.
28. W. Hehre, L. Radom, P. Schleyer and J. Pople, Ab Initio Molecular Orbital Theory, Wiley, New York, 1986.
29. L. A. Curtiss, P. C. Redfern, K. Raghavachari and J. A. Pople, J. Chem. Phys., 2001, 114, 108.
30. P. W. Atkins, Physical Chemistry, Oxford University Press, Oxford, 2nd edn, 1982.
31. I. Mills, T. Cvitas, K. Homann, N. Kallay and Z. Kuchitsu, Quantities, Units and Symbols in Physical Chemistry, Blackwell Scientific Publications, Oxford, 1988.
32. F. J. Owens, J. Mol. Struct.: THEOCHEM, 1996, 370, 11.
33. N. J. Harris and K. Lammertsma, J. Am. Chem. Soc., 1997, 119, 6583.
34. M. J. Kamlet and S. J. Jacobs, J. Chem. Phys., 1968, 48, 23.
35. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. J. A. Montgomery, J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochtersk, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski and D. J. Fox, GAUSSIAN 09 A01, Gaussian, Inc., Wallingford CT, 2009.
36. Materials Studio 6.0, Accelrys, Inc., San Diego, CA, 2011.
37. L. Turker and S. Varis, Polycyclic Aromat. Compd., 2009, 29, 228.
38. M. H. V. Huynh, M. A. Hiskey, D. E. Chavez and R. D. Gilardi, Angew. Chem., Int. Ed., 2005, 44, 7089.
39. M. Mantina, A. C. Chamberlin, R. Valero, C. J. Cramer and D. G. Truhlar, J. Phys. Chem. A, 2009, 113, 5806.
40. W. H. Zhu and H. M. Xiao, Struct. Chem., 2010, 21, 657.
41. B. M. Rice and J. J. Hare, J. Phys. Chem. A, 2002, 106, 1770.
42. M. Pospisil, P. Vavra, M. C. Concha, J. S. Murray and P. Politzer, J. Mol. Model., 2010, 16, 895.
43. E. R. Johnson, S. Keinan, P. Mori-Sánchez, J. Contreras-García, A. J. Cohen and W. Yang, J. Am. Chem. Soc., 2010, 132, 6498.
44. D. Furman, R. Kosloff, F. Dubnikova, S. V. Zybin, W. A. Goddard, N. Rom, B. Hirshberg and Y. Zeiri, J. Am. Chem. Soc., 2014, 136, 4192.
45. C. Y. Zhang, X. C. Wang and H. Huang, J. Am. Chem. Soc., 2008, 130, 8359.
46. P. J. Linstrom and W. G. Mallard, NIST Chemistry WebBook, NIST, Gaithersburg, MD, 2005.
47. R. L. Simpson, P. A. Urtiew, D. L. Ornellas, G. L. Moody, K. J. Scribner and D. M. Hoffman, Propellants, Explos., Pyrotech., 1997, 22, 249.
48. P. Politzer and J. S. Murray, Cent. Eur. J. Energ. Mater., 2011, 8, 209.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra11624h

---