Calculations predict a novel desired compound containing eight catenated nitrogen atoms: 1-amino-tetrazolo-[4,5-b]tetrazole

Abstract

A novel 8-N conjoined energetic compound 1-amino-tetrazolo-[4,5-b]tetrazole has been designed and investigated at the DFT-B3LYP/6-311++G** level of theory. The optimized geometry, vibration analysis, including thermochemistry and IR spectrum, NMR data, natural bond orbital and charges, HOMO–LUMO orbitals as well as electrostatic potential were calculated for inspecting the electronic structure properties and interactions of chemical bonds. Properties such as density, enthalpy of formation considering the enthalpy of phase transition and detonation performance have also been predicted. As a result, the detonation velocity and pressure of this compound are 8.90 km s⁻¹ and 33.83 GPa, respectively. The planar double rings (stable) with high-nitrogen structure (energetic), the high positive heat of formation (792.38 kJ mol⁻¹) and the eminent performance, lead 1-amino-tetrazolo-[4,5-b]tetrazole to be a potentially very promising powerful energetic insensitive compound. In addition, the azido-cyclization kinetics of 1-amino-5-azidotetrazole forming the target compound have been investigated. In the gaseous state, the reaction barrier is 30.34 kcal mol⁻¹ and the reaction is endothermic as well as non-spontaneous under general conditions. The rate constants are evaluated over a wide temperature region from 200 to 1000 K using the transition state theory (TST) and the Arrhenius experience formula has been fitted as well. The theoretical researches on extended nitrogen chains could improve the synthesis of new high-nitrogen materials in the foreseeable future.

---

Introduction

The development of energetic compounds from the fundamental research to their application is an exciting and challenging area of chemistry. Considering the numerous applications of energetic compounds as explosives or propellants, it is important to discover new representatives with significant advantages over compounds currently used not only for military but also for civilian purposes. Several new energetic compounds have emerged recently in order to meet the challenging requirements of improving the performance of existing products. The key requirements include performance, insensitivity, stability, vulnerability, and environmental safety.^1–5 Over the past decade, energetic heterocyclic compounds have been investigated extensively. Higher energetic performance has always been a primary requirement for research and development of explosives and propellants.⁶ The azido group is often used as a highly energetic ligand in energetic compounds to increase the enthalpy of formation to about +364 kJ mol⁻¹ along with an increase in the nitrogen content.⁷ 5-Azidotetrazole with a nitrogen content of 88.28% was synthesized in 1939, and many studies have dealt with the synthesis and characterization of these compounds since then.^8–10

Since 5-azidotetrazoles are very sensitive towards shock and friction, numerous attempts have been made to desensitize these materials by the introduction of aryl and alkyl groups,¹¹ which also negatively affects the corresponding detonation performance. Tetrazoles offer a good backbone for the development of energetic compounds together with their high thermal stability (due to aromaticity) and the high heat of formation of +237 kJ mol⁻¹ (5H-1,2,3,4-tetrazole).¹² Recently, many energetic compounds, which contain the tetrazole moiety have been investigated and synthesized.^13–24 Consequently, the isomeric tetrazoles,²⁵ which are formed by an 1,5-dipolar cyclization²⁶ of the polyazides, are potential replacements for the hazardous polyazides.

When the azido group is attached to a C atom adjacent to a nitrogen in a heterocyclic azide, it may spontaneously cyclize to give a tetrazole ring,²⁷ namely, azido–tetrazole chain–ring isomerization, which has been the subject of several studies.^28–36 In this work, we design a new high-nitrogen compound with double tetrazole rings, containing eight catenated nitrogens, which provide high-energy performance. Here, 1-amino-tetrazolo-[4,5-b]tetrazole is first studied in detail by high-level ab initio calculations. We report the electronic structure, thermochemical properties, enthalpy of formation, density, and detonation performance. On the basis of 1-amino-5-azidotetrazole,³⁷ it's the kinetics of azido-cyclization for 1-(amino)-tetrazolo-[4,5-b]tetrazole have been investigated in this paper. The construction of new high-nitrogen structures with highly catenated nitrogen chains³⁸ and the present theoretical study may promote further experimental studies on this new energetic material with high performance.

Computational methods

The geometry of 1-amino-tetrazolo-[4,5-b]tetrazole has been optimized using the hybrid DFT-B3LYP method with the 6-311++G** basis set. Thermochemical properties and IR spectrum were obtained by harmonic vibrational frequencies at the same level of theory. Meanwhile, natural bond orbital (NBO) charges, the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbital (LUMO) orbitals as well as the electrostatic potential of the title compound were calculated on the B3LYP/6-311++G** level of theory based on the optimized gas-phase structure, whereas NMR spectroscopy has been carried out using the 6-311++G(2df, 2pd) basis set for better estimates of chemical shift calculations.

Enthalpy of formation is the most important parameter for energetic compounds. The gas-phase enthalpies of formation at 0 K and 298.15 K were calculated straightforwardly using the atomization energies method.³⁹ Often the standard state of the material of interest corresponds to the condensed phase. Thus, the condensed-phase heats of formation can be determined using the gas-phase enthalpy of formation and enthalpy of phase transition (either sublimation or vaporization) according to the Hess' law of constant heat summation:⁴⁰

ΔH(solid) = ΔH(gas) − ΔH(sublimation) (1)

ΔH(liquid) = ΔH(gas) − ΔH(vaporization) (2)

Based on the electrostatic potential of a molecule by quantum mechanical prediction, the heat of either sublimation or vaporization can be represented as:^41,42

where, (SA) is the molecular surface area for this structure, σ_Tot² is described as an indicator of the variability of the electrostatic potential on the molecular surface, υ is interpreted as showing the degree of balance between the positive and negative potentials on the molecular surface and a, b, and c are the fitting parameters. We further followed the approach of Politzer to predict the heats of sublimation and vaporization of energetic materials, and then combined these with eqn (1) or (2) to predict the solid and liquid enthalpies of formation.

Besides the enthalpy of formation, another critical parameter for energetic materials is the crystal packing density, which requires the datum of the molecular volume. The volume was defined as inside a contour of 0.001 electrons per bohr³ density, which was evaluated using a MonteCarlo integration. This method has been successfully applied to high-nitrogen compounds.⁴³ 100 single-point calculations were performed for each optimized structure to obtain an average volume at the B3LYP/6-311++G** level of theory.

The empirical Kamlet–Jacob equations⁴⁴ widely employed to evaluate the energy performance of energetic compounds were used to estimate the detonation velocity and detonation pressure of the title compound. Empirical Kamlet–Jacobs equations can be written as follows:

where, D is the detonation velocity (km s⁻¹); P is the detonation pressure (GPa); N is the moles of detonation gases per gram explosive; M̄ is the average molecular weight of these gases; Q is the heat of detonation (J g⁻¹); and ρ is the loaded density of explosives (g cm⁻³). In practice, the loading density can only be approximated to a value less than the theoretical density; thus, the D and P values obtained from eqn (5) and (6) can be regarded as their upper limits.

In order to investigate the feasibility of synthesis of the designed target compound, we studied the azido-cyclization kinetics of 1-amino-5-azidotetrazole. The geometries of the relevant stationary points along the reaction pathways were optimized at the B3LYP/6-311++G**level of theory. All the stationary points were characterized by their harmonic vibrational frequencies as minima (no imaginary frequency) or saddle points (only one imaginary frequency). The intrinsic reaction coordinate (IRC) was calculated to confirm whether the reaction transition state (TS) is connecting the reactant and product as two minimum points. The thermodynamic energy parameters and potential energy curve were determined from the vibrational frequencies, which were calculated at the same level. Moreover, the rate constants as well as the Arrhenius empirical formula were evaluated over a wide temperature range from 200 to 1000 K based on the traditional transition theory (TST).

All the ab initio calculations involved in this work were carried out using the Gaussian 09 program package.⁴⁵ The related kinetics of the azido-cyclization reaction including rate constant were performed using the VKLab⁴⁶ and POLYRATE 8.2 program package.⁴⁷

Results and discussion

Molecular structure

The optimized structure of 1-amino-tetrazolo-[4,5-b]tetrazole (as shown in Fig. 1) corresponds to at least a local energy minimum on the potential energy surface without imaginary frequency at the B3LYP/6-311++G** level of theory. The selected geometry parameters of the optimized molecule are listed in Table 1.

Fig. 1 The optimized geometry and NBO charges (e as unit) of 1-amino-tetrazolo-[4,5-b]tetrazole.

Table 1 Selected parameters of the optimized geometry for 1-amino-tetrazolo-[4,5-b]tetrazole

Bond lengths	Å	Bond angles	(°)	Dihedral angles	(°)
N1–N2	1.377	N1–N2–N3	110.1	N1–N2–N3–N4	−0.07
N2–N3	1.277	N2–N3–N4	105.6	N2–N3–N4–C5	0.05
N3–N4	1.362	N3–N4–C5	112.6	C5–N6–N7–N8	−0.03
N4–C5	1.347	N1–C5–N4	103.0	N9–N1–N2–C5	179.98
C5–N1	1.359	C5–N6–N7	102.9	N2–N1–N9–H10	60.81
C5–N6	1.316	N6–N7–N8	114.3	N2–N1–N9–H11	−60.80
N6–N7	1.372	C5–N1–N9	127.7	C5–N6–N7–N4	−0.01
N7–N8	1.298	N1–N9–H10	109.8	C5–N3–N4–N8	179.98
N8–N4	1.357	N7–N8–N4	103.6
N9–N1	1.379

---

It is evident that all the N and C atoms are in the same plane, and 8 N atoms are conjoined directly. The length of the bonds is averaged as a result of the π electron delocalization over the ring structure. The bonding angle of the ring atoms is approximately 108°, which illustrates that the molecule favors a five-membered ring structure. C and N atoms in the molecule are sp² hybridized, forming an approximate planar structure. Such a characteristic is very helpful for molecular stability. However, there is a certain deviation on the angles as a result of the lone pair electrons on the N atoms, leading to larger repulsive forces when the N atoms are close to each other. The entire molecule shows a stable five-membered structure as well as plane double rings without any symmetric properties.

Natural bond orbital and charges

Natural Bond Orbital (NBO) charges are considered more reasonable for discussion, as shown in Fig. 1. The majority of the tetrazole ring's negative charge is localized on the nitrogen atoms in NBO, whereas the positive charge is located on the only carbon atom because of the stronger electronegativity of N compared with C. Almost all the N atoms display a negative charge, especially N9 with most negative charge (with a value of −0.596e), which may due to the inductive effect of –NH₂ as an electron-withdrawing group. In addition, N6 also displays a higher magnitude of negative charge (with a value of −0.331e), while N1 exhibited less negative charge (with a value of −0.0.098e) as a result of the same effect. Overall, both positive and negative charges in NBO support the contributing nature of delocalization of electrons on the tetrazole ring.

The Wiberg bond index was obtained from the NBO calculation. The corresponding results are listed in Table 2. The Wiberg bond indices of all the N–N bonds in the double tetrazole ring in the title compound are from 1.044 to 1.678 across the entire system. Comparing with the bonds between N1, N2, N3 and N4, the values of the bonds between N6, N7, N8 and N4 are a little larger from an overall perspective, which may be attributed to the conjugative effect of the right tetrazole ring. The only C5 atom connected close to the N1, N4 and N6 atoms indicates a strong covalent character with each other, promoting the stability of the molecular structure.

Table 2 The Wiberg bond index of 1-amino-tetrazolo-[4,5-b]tetrazole

Chemical bonds	Wiberg bond order	Chemical bonds	Wiberg bond order
C5–N4	1.130	N1–N9	1.044
C5–N1	1.120	N9–H10	0.840
C5–N6	1.445	N9–H11	0.840
N2–N1	1.151	N6–N7	1.309
N2–N3	1.678	N7–N8	1.610
N3–N4	1.137	N8–N4	1.147

---

Frontier molecular orbitals (FMOs)

The highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) are known as frontier molecular orbitals (FMOs). The HOMO represents the ability to donate an electron, and the LUMO as an electron acceptor represents the ability to obtain an electron. The energy gap between HOMO and LUMO, which determines the kinetic stability, chemical reactivity and optical polarizability and chemical hardness–softness of a molecule,⁴⁸ was calculated at the B3LYP/6-311++G** level.⁴⁹

As can be seen in Fig. 2, the orbital loops located on the HOMO and LUMO overlap; the positive phase is red and the negative phase is shown as green. It is clear from the figure that the HOMO is localized approximately on the right tetrazole ring, while the LUMO is localized on the left, which implies that the nitrogen atoms of the right tetrazole become the main electron donating group and may be attacked by the electron accepting group. The HOMO → LUMO transition implies an electron density transfer to nitrogen atoms on the left tetrazole because of the electrophilic nature of –NH₂. The calculated energy value of the HOMO is about −8.2899 eV and that of the LUMO is −2.5347 eV in the gaseous phase. The energy separation between the HOMO and LUMO is 5.7552 eV.

Fig. 2 The HOMO and LUMO orbitals of 1-amino-tetrazolo-[4,5-b]tetrazole.

Electrostatic potential

On the molecular surface, the contribution of the electronic and nuclear potential reaches to some extent a counterbalance, while a non-homogeneous distribution of the electron density leads to a positive or negative electrostatic potential.

By using the Multiwfn program⁵⁰ based on quantitative molecular surface analysis, the extreme value points of electrostatic potential on the molecular surface are visualized in Fig. 3. First, the positive and negative potentials are delocalized inside and outside the rings, respectively. It is evident that there are six surface minimum values of negative potential (shown as the blue points in Fig. 3), which are mostly distributed close to the nitrogen atoms because of their higher electronegativity. On the other hand, these positions displayed negative potential, especially near N6 (−33.68 kcal mol⁻¹), N7 (−35.67 kcal mol⁻¹) and N8 (−28.43 kcal mol⁻¹), and may react with electrophiles such as metal atoms easily. The four surface maximum values of positive potential (shown as the red points in Fig. 3) are located close to the carbon and hydrogen atoms, which illustrates that the electrostatic potential is dominated by nuclear charge. Among them, the electrostatic potential near the hydrogen atoms is the highest (55.32 kcal mol⁻¹) because of its low electronegativity in contrast to the carbon and nitrogen atoms. The positions with the most positive potential may be easily attacked by nucleophiles.

Fig. 3 The electrostatic potential distributions of 1-amino-tetrazolo-[4,5-b]tetrazole.

Vibration analysis and NMR

All the frequency values of the molecule are positive, which suggests that they are stable stationary points on the surface of the potential energy. IR spectrum is an effective tool to investigate the basic properties of compounds and identify the substances. Moreover, it is closely related to the thermodynamics properties. The simulated infrared spectra of 1-amino-5-azidotetrazole^a and 1-(amino)-tetrazolo-[4,5-b]tetrazole are shown in Fig. 4.

Fig. 4 The IR spectrum of 1-amino-5-azidotetrazole and 1-(amino)-tetrazolo-[4,5-b]tetrazole. ^a The experimental IR data³⁷ for 1-amino-5-azidotetrazole (cm⁻¹): 3332 (m), 3228 (m), 3162 (w), 2150 (vs), 1635 (m), 1531 (s), 1472 (m), 1404 (w),1301 (m), 1272 (w), 1191 (m), 1118 (w), 1079 (w), 992 (w), 926 (w), 816(w), 783 (w), 725 (w), 678 (m).

The calculated IR results (unscaled) show that 1-amino-5-azidotetrazole has two strongest IR peaks at 1573 cm⁻¹ and 2287 cm⁻¹, which are the asymmetrical stretching modes in the ring C–N and N–N of the azido group, respectively. In addition, the amine group vibration modes were observed along with four characteristic peaks in the IR spectrum. The stronger peaks at 903 cm⁻¹ and 227 cm⁻¹ refer to the N–H bending and out-of-plane deforming, respectively, and the weaker peaks around 3572 cm⁻¹ and 3489 cm⁻¹ are the asymmetrical and symmetrical stretching of the N–H bonds on the amine group, respectively. The fact that the calculated IR data is in good agreement with the experiment facilitates us to investigate the title compound. For 1-amino-tetrazolo-[4,5-b]tetrazole, the strongest IR peak at 836 cm⁻¹ corresponds to the N–H symmetrical bending and out-of-plane deforming, while the medium peaks at 1077 cm⁻¹ and 953 cm⁻¹ are mainly dominated by the stretching vibration of the N–N and C–N bonds of the tetrazole skeleton. The region in 1614 cm⁻¹ is attributed to the stretching of tetrazoles as well as the scissor vibration mode of the amine. It is interesting that the N–H bonds of the amine have different torsional vibration modes at 1707 cm⁻¹ and 240 cm⁻¹, and the peaks at 3496 and 3585 cm⁻¹ refer to symmetrical and asymmetrical stretching vibrations, respectively. It is worth noting that the disappearance of peaks at 2287 cm⁻¹ on the azido group and variances on the other main peaks predict the azido–tetrazolo tautomerization by comparison with two primary compounds.

On the basis of vibrational analysis and statistic thermodynamic method, thermodynamic functions, such as thermal correction to internal energy (U), enthalpy (H), free energy (G), standard molar heat capacity (C_v) and standard molar thermal entropy (S), as well as the zero-point energy (ZPE) of the two major compounds are evaluated and tabulated in Table 3. All these values are at 298.25 K, 1.00 atm and with kcal mol⁻¹ as unit (kca/(mol K) for S and C_v). All kinds of energy are approximately equal, while the heat capacity and entropy of the title compound are smaller than those of 1-amino-5-azidotetrazole, which may confirm the stability of 1-amino-tetrazolo-[4,5-b]tetrazole to some extent.

Table 3 Thermochemical parameters of the two major compounds

Species	ZPE	U	H	G	S	Cv
1-Amino-tetrazolo-[4,5-b]tetrazole	42.390	46.441	47.034	22.956	80.756	23.553
1-Amino-5-azidotetrazole	41.802	46.455	47.047	21.409	85.993	25.679

---

Highly accurate calculations of molecular properties play an important role, especially if they complement experiments, which only yield indirect information regarding molecular and electronic structure as is the case in NMR spectroscopy. Large, systematic theoretical investigations only allow for reliable error estimates if appropriate experimental studies such as gas-phase NMR measurements on smaller molecular systems are available.⁵¹ In order to assess the quality of results from DFT methods and the performance of different theoretical basis, the calculated shifts of the ¹³C NMR and ¹⁵N NMR for 1-amino-5-azidotetrazole were investigated in detail. The chemical shift of only carbon atom in ¹³C NMR was calculated to be about 158.17 ppm, which is good agreement with the experimental shift† (150.60 ppm). What holds true in chemical applications – in ¹⁵N NMR spectroscopy progress often stems from the successful interplay between theory and experiment – is also valid for benchmark studies, especially for high-nitrogen compounds. The calculated chemical shifts of all the atoms are N3 (27.68), N2 (−0.95), N4 (−66.05), N8 (−142.23), N7 (−154.75), N1 (−167.43), N6 (−320.07) and N9 (−336.99), which are in near quantitative agreement with the experimental values for the ¹⁵N NMR chemical shifts† (0.81, −8.38, −77.26, −141.91, −145.73, −155.13, −300.60, −309.93 ppm). Therefore, the predicted chemical shift for 1-amino-tetrazolo-[4,5-b]tetrazole is 157.15 ppm in ¹³C NMR and those for ¹⁵N NMR are 61.91, 8.32, −35.77, −42.98, −72.64, −100.57, −191.27, −334.18 ppm, respectively. We included the calculated IR, thermochemical parameters and NMR for the easier assignment and positive identification of the target compound.

Predicted density and detonation performances

To evaluate the utility of new energetic materials, usually their performance characteristics should be calculated. The detonation velocity (V_D) and detonation pressure (P_D) have been evaluated by the empirical Kamlet–Jacobs equations with the above mentioned predicted theoretical density and enthalpy of formation in the solid phase. Full details of the detonation parameters are listed in Table 4.

Table 4 Detonation parameters for common HEDMs and two major compounds

Species^a	ΔfH298K(s)/kJ mol^−1	ρ/g cm^−3	VD/km s^−1	PD/GPa
a TNT, trinitrotoluene; RDX, cyclotrimethylenetrinitramine; TATB, (2,4,6-trinitro-1,3,5-benzenetriamine); FOX-7, 1,1-diamino-2,2-dinitroethene.b When the experimental data are not available the corresponding data have been calculated using the method in the references (as marked with b).
1-Amino-tetrazolo-[4,5-b]tetrazole	792.38	1.69	8.90	33.83
1-Amino-5-azidotetrazole	721.98	1.62	8.30	28.63
TNT^52	−63.12	1.64	6.95	19.00
RDX^52	79.00	1.80	8.75	34.70
TATB^52	−74.61	1.89	7.86	31.50
FOX-7^52	−133.7	1.89	8.87	34.00^b

---

As is evident in Table 4, the title compound 1-amino-tetrazolo-[4,5-b]tetrazole shows remarkable detonation parameters in comparison with the known compound 1-amino-5-azidotetrazole, which indicates the improvement in high-energy performance. Although the density of this compound is smaller than that of common HEMDs, the detonation velocity (8.90 km s⁻¹) and detonation pressure(33.83 GPa) are much greater than those of TNT, RDX and TATB, while they are almost equal to that of FOX-7 (V_D = 8.87 km s⁻¹, P_D = 34.0 GPa). It is worth noting that 1-amino-tetrazolo-[4,5-b]tetrazole has a perfect character of higher positive enthalpy of formation (792.38 kJ mol⁻¹), which contributes eminent performance. It suggests that this compound might be the most promising powerful energetic material among the CHNO-containing organic compounds.

Reaction pathways of azido-cyclization

Based on above mentioned research, we also investigated the azido-cyclization kinetics of 1-amino-5-azidotetrazole, and Fig. 5 shows the pathways of circulation for 1-amino-tetrazolo-[4,5-b]tetrazole.

Fig. 5 The synthesis reaction pathways of 1-(amino)-tetrazolo-[4,5-b]tetrazole.

All the geometries of stable points along the reaction paths have approximately plane configurations, except that the amine group is lifted out of the ring plane with a dihedral angle of about 69°. Other structural parameters are listed in Table 5. From the reactant, through the transition state to the product 1-amino-tetrazolo-[4,5-b]tetrazole, the most relevant changes upon cyclization concern the bonds N6–N7 and N7–N8, which increase by around 0.13 Å and 0.17 Å, while the lengths of the other bonds on the main ring slightly change to maintain a relatively stable structure. Meanwhile, most bond angles such as N4–C5–N6, C5–N6–N7 and N6–N7–N8 decrease to 110.1°, 102.9° and 114.3°, respectively, while N7–N8–N4 increases to 103.6°, which is close to 108° forming a five-membered ring. The bond angle C5–N1–N9 of the amine reduces by around 1° compared with the reactant, which remains unchanged from the overall. All the preceding analysis indicates that the obvious ring cyclization occurs mainly in the conversion of azido to tetrazole, in which the molecular and electronic structures change significantly.

Table 5 Bond lengths (Å) and angles (°) for the reactant, transition state and product

	N1–N2	N2–N3	N3–N4	N4–C5	C5–N6	C5–N1	N6–N7	N7–N8	N1–N9
R	1.364	1.284	1.363	1.317	1.379	1.351	1.245	1.124	1.385
TS	1.383	1.278	1.352	1.327	1.349	1.346	1.340	1.194	1.381
P	1.377	1.277	1.362	1.347	1.316	1.359	1.372	1.298	1.379

---

	N4–C5–N6	C5–N6–N7	N6–N7–N8	N7–N8–N4	C5–N1–N9
R	129.2	115.5	171.4	38.9	127.8
TS	119.0	101.9	127.5	95.3	127.7
P	110.1	102.9	114.3	103.6	127.7

---

To gain insight into the electron redistribution in the cyclization, the net charge in the studied compounds was calculated by the natural bond orbital (NBO) method. The calculated results are listed in Table 6. The results indicate that most of the electron redistribution occurs mainly in the azido group, and the shift of electrons along the cyclization is highly asynchronous. For example, the net charges of the terminal N8 atom of the azido group increase by 0.03e for the process of reactant to TS, while it decreases by about 0.13e for the process of TS to product. The difference of the net charges residing on the middle N7 atom of the azido group has always decreased by about 0.19e and 0.10e for the two processes, respectively. In addition, the charges on the N3 and N4 atoms of the tetrazole ring have been found to increase to −0.013e and −0.079e as a result of electron delocalization. In the whole cyclization process, the electrons transfer rapidly from the tetrazole ring into the azido group, which makes the two closer nitrogen atoms (the terminal atom of azido group and the nearest nitrogen atom in the tetrazole ring) possess the stronger Coulombic interaction.

Table 6 NBO net charges for all atoms along the reaction path (e as unit)

	N1	N2	N3	N4	C5	N6	N7	N8	N9	H10
R	−0.095	−0.080	−0.054	−0.352	+0.500	−0.346	+0.256	+0.033	−0.604	+0.371
TS	−0.096	−0.054	−0.015	−0.253	+0.517	−0.376	+0.064	+0.066	−0.598	+0.372
P	−0.098	−0.028	−0.013	−0.079	+0.498	−0.331	−0.035	−0.067	−0.596	+0.374

---

Energy parameters and rate constant

The transition state with only one virtual frequency (value of −261.05 cm⁻¹) connects the reactant and the product through the IRC calculation. Fig. 6 depicts the entire reaction potential energy curve.

Fig. 6 The potential energy curve and rate constant of azido-cyclization reaction.

The energy parameters, including the reaction energy (Δ_rE), reaction enthalpy (Δ_rH^Θ_298K) and reaction Gibbs free energy (Δ_rG^Θ_298K) have been obtained by calculating vibration frequency. These results show that the total energy of reaction (Δ_rE = 20.75 kcal mol⁻¹) is positive, implying that the energy of the product is higher. Both the reaction enthalpy change (Δ_rH^Θ_298K = 20.15 kcal mol⁻¹) and the Gibbs free energy of reaction (Δ_rG^Θ_298K = 21.71 kcal mol⁻¹) are positive, which implies that the reaction is endothermic and not spontaneous in general conditions, while the calculated theoretical reaction barrier is only 30.34 kcal mol⁻¹, indicating that the synthesis of 1-amino-tetrazolo-[4,5-b]tetrazole through the azido-cyclization of 1-amino-5-azidotetrazole is theoretically feasible. In actual synthesis, some methods such as solvent polarity and electrochemical methods may be used to enhance the reaction conditions, which is conducive to the synthesis of the target compound.

Using the traditional transition state theory, the rate constant of the azido-cyclization reaction has been evaluated between 200–1000 K temperature regions. Fig. 6 displays that the reaction rate constant ln (k) changes linearly with the reciprocal of temperature. As can be seen, the higher temperature accelerates the cyclization reaction, and at about 500 K the reaction would proceed quickly. In addition, the reaction rate constant's relationship with the temperature meets the Arrhenius equation. The modified equation of three parameters to be corrected and fitted to the rate constant is as follows:

k(T) = 9.28 × 10¹¹ × T^0.02568 × e^{−(1.49×104/T)}s⁻¹

Conclusions

A novel desired compound 1-amino-tetrazolo-[4,5-b]tetrazole containing eight catenated nitrogen atoms has been proposed and investigated by the DFT methods for the first time. The optimized geometry, NBO charges, Wiberg bond index, HOMO–LUMO orbital, electrostatic potential, IR spectrum and NMR data as well as thermochemical parameters were calculated for inspecting the electronic structure properties and interactions of chemical bonds with the B3LYP/6-311++G** and B3LYP/6-311++G(2df, 2pd) levels of theory.

The entire molecule shows a stable five-membered ring structure as well as plane double rings without any symmetrical properties. Both positive and negative charges in NBO support the contributing nature of electron delocalization on the tetrazole ring. On the other hand, these positions displayed negative electrostatic potential, especially near N6, N7 and N8, and may react with electrophiles such as metal atoms. The thermochemical parameters, IR and NMR spectrum data have been calculated for the easier assignment and positive identification of the target compound.

Based on the gas-phase enthalpy of formation derived from the atomization energies method, it is more reasonable that the enthalpy of formation in solid was obtained by considering the enthalpy of phase transition. The detonation performance has also been predicted with the theoretical enthalpy of formation and density. It has been confirmed that 1-amino-tetrazolo-[4,5-b]tetrazole might be a very promising energetic (high nitrogen) and insensitive (stable tetrazole double rings) compound with high enthalpy of formation (792.38 kJ mol⁻¹) and exceptional detonation properties (V_D = 8.90 km s⁻¹, P_D = 33.83 GPa), equal to the that of FOX-7 to some extent.

In addition, we investigated the azido-cyclization kinetics of 1-amino-5-azidotetrazole forming the target compound based on the geometry and NBO charges analysis, indicating that the obvious ring cyclization occurs mainly in the conversion of azido to tetrazole, in which the molecular structures and electronic redistribution change significantly. Although the reaction is endothermic and not spontaneous in general conditions, the reaction barrier of only 30.34 kcal mol⁻¹ indicates theoretical feasibility. Finally, the rate constant of the azido-cyclization reaction has been evaluated between 200–1000 K temperature regions as well as the Arrhenius equation with the modified equation of three parameters. This synthesis of 1-amino-tetrazolo-[4,5-b]tetrazole through azido-cyclization of 1-amino-5-azidotetrazole may be practically feasible when using some methods such as high temperature, solvent polarity and electrochemical methods to enhance the reaction conditions.

Overall, in pursuit of new high-nitrogen structures, a fascinating novel compound containing eight catenated nitrogen atom chains has been reported for the first time. The relative theoretical work of such extended nitrogen chains may open new methods for the synthesis of new high-nitrogen materials in the foreseeable future.

Acknowledgements

The support of the National Natural Science Foundation of China (Grant no. 10776002) and the project of State Key Laboratory of Science and Technology (ZDKT12-03) are gratefully acknowledged.

Notes and references

1. L. Türker and S. Variş, Polycyclic Aromat. Compd., 2009, 29, 228–266.
2. M. B. Talawar, R. Sivabalan, T. Mukundan, H. Muthurajan, A. K. Sikder, B. R. Gandhe and A. S. Rao, J. Hazard. Mater., 2009, 161, 589–607.
3. P. K. Swain, H. Singh and S. P. Tewari, J. Mol. Liq., 2010, 151, 87–96.
4. G. Steinhauser and T. M. Klapötke, Angew. Chem., Int. Ed., 2008, 47, 3330–3347.
5. T. M. Klapötke and J. Stierstorfer, Phys. Chem. Chem. Phys., 2008, 10, 4340–4346.
6. H. Gao and J. n. M. Shreeve, Chem. Rev., 2011, 111, 7377–7436.
7. E. S. Domalski and E. D. Hearing, J. Phys. Chem. Ref. Data, 1993, 22, 805–1159.
8. J. Stierstorfer, T. M. Klapötke, A. Hammerl and R. D. Chapman, Z. Anorg. Allg. Chem., 2008, 634, 1051–1057.
9. T. M. Klapötke and J. r. Stierstorfer, J. Am. Chem. Soc., 2009, 131, 1122–1134.
10. A. Hammerl, T. M. Klapötke, P. Mayer, J. J. Weigand and G. Holl, Propellants, Explos., Pyrotech., 2005, 30, 17–26.
11. J. C. Kauer and W. A. Sheppard, J. Org. Chem., 1967, 32, 3580–3592.
12. V. A. Ostrovskii, M. S. Pevzner, T. P. Kofman and I. V. Tselinskii, Targets Heterocycl. Syst., 1999, 3, 467–526.
13. Z. Liu, Q. Wu, W. Zhu and H. Xiao, J. Phys. Org. Chem., 2013, 26, 939–947.
14. Q.-H. Lin, Y.-C. Li, C. Qi, W. Liu, Y. Wang and S.-P. Pang, J. Mater. Chem. A, 2013, 1, 6776.
15. T. M. Klapötke, F. A. Martin and J. Stierstorfer, Chemistry, 2012, 18, 1487–1501.
16. T. M. Klapötke, B. Krumm, F. A. Martin and J. Stierstorfer, Chem.–Asian J., 2012, 7, 214–224.
17. N. Fischer, T. M. Klapötke, M. Reymann and J. Stierstorfer, Eur. J. Inorg. Chem., 2013, 2013, 2167–2180.
18. D. Fischer, T. M. Klapötke, D. G. Piercey and J. Stierstorfer, Chemistry, 2013, 19, 4602–4613.
19. R. P. Singh, R. D. Verma, D. T. Meshri and J. n. M. Shreeve, Angew. Chem., Int. Ed., 2006, 45, 3584–3601.
20. M. A. Hiskey, N. Goldman and J. R. Stine, J. Energ. Mater., 1998, 16, 119–127.
21. S. C. S. Bugalho, E. M. S. Macoas, M. L. S. Cristiano and R. Fausto, Phys. Chem. Chem. Phys., 2001, 3, 3541–3547.
22. T. Abe, G.-H. Tao, Y.-H. Joo, Y. Huang, B. Twamley and J. n. M. Shreeve, Angew. Chem., Int. Ed., 2008, 47, 7087–7090.
23. T. M. Klapötke, in High Energy Density Materials, Heidelberg, 2007.
24. J. F. Satchell and B. J. Smith, Phys. Chem. Chem. Phys., 2002, 4, 4314–4318.
25. A. F. Brigas, in Science of Synthesis, Stuttgart, 2004.
26. R. Huisgen, Angew. Chem., Int. Ed. Engl., 1968, 7, 321–328.
27. E. Kessenich, K. Polborn and A. Schulz, Inorg. Chem., 2001, 40, 1102–1109.
28. T. Lioux, G. Gosselin and C. Mathé, Eur. J. Org. Chem., 2003, 2003, 3997–4002.
29. M. K. Lakshman, M. K. Singh, D. Parrish, R. Balachandran and B. W. Day, J. Org. Chem., 2010, 75, 2461–2473.
30. A. Katrusiak, U. Skierska and A. Katrusiak, J. Mol. Struct., 2005, 751, 65–73.
31. M. Kanyalkar and E. C. Coutinho, Tetrahedron, 2000, 56, 8775–8777.
32. S. L. Deev, Z. O. Shenkarev, T. S. Shestakova, O. N. Chupakhin, V. L. Rusinov and A. S. Arseniev, J. Org. Chem., 2010, 75, 8487–8497.
33. H. A. Dabbagh and W. Lwowski, J. Org. Chem., 2000, 65, 7284–7290.
34. I. Alkorta, F. Blanco, J. Elguero and R. M. Claramunt, Tetrahedron, 2010, 66, 2863–2868.
35. I. Alkorta, F. Blanco and J. Elguero, Tetrahedron, 2010, 66, 5071–5081.
36. R. H. Abu-Eittah, F. Taha, M. M. Hamed and K. E. El-Kelany, J. Mol. Struct.: THEOCHEM, 2009, 895, 142–147.
37. T. M. Klapötke, B. Krumm, F. A. Martin and J. Stierstorfer, Chem.–Asian J., 2012, 7, 214–224.
38. Q. Zhang and J. M. Shreeve, Angew. Chem., Int. Ed., 2013, 52, 8792–8794.
39. L. A. Curtiss, K. Raghavachari, P. C. Redfern and J. A. Pople, J. Chem. Phys., 1997, 106, 1063–1066.
40. P. W. Atkins, Physical Chemistry, Oxford University Press, Oxford, 1982.
41. P. Politzer, J. S. Murray, T. Brinck and P. Lane, in Immunoanalysis of Agrochemicals, ACS Symp. Ser. 586, American Chemical Society, Washington, DC, 1994.
42. J. S. Murray and P. Politzer, in Quantitative Treatment of Solute/Solvent Interactions, Theoretical and Computational Chemistry, Amsterdam, 1994.
43. B. M. Rice, J. J. Hare and E. F. C. Byrd, J. Phys. Chem. A, 2007, 111, 10874–10879.
44. M. J. Kamlet and S. J. Jacobs, J. Chem. Phys., 1968, 48, 23–35.
45. G. W. Trucks, M. J. Frisch, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery Jr, T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, 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. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. iashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez and J. A. Pople, GAUSSIAN 9 (Revision A.01), Gaussian, Inc, 2009.
46. S. W. Zhang and T. N. Truong, VKLab version1.0 [CP/CD], Minneapolis: University of Minnesota, Utah: University of Utah, 2001.
47. Y. Y. Chuang, J. C. Corchado and P. L. Fast, POLYRATE, Program vision 8. 2 [CP/CD], University of Minnesota, Minneapolis, 1999.
48. B. Kosar and C. Albayrak, Spectrochim. Acta, Part A, 2011, 78, 160–167.
49. A. Suvitha, S. Periandy, S. Boomadevi and M. Govindarajan, Spectrochim. Acta, Part A, 2014, 117, 216–224.
50. T. Lu, Multiwfn, version 1.4, http://multiwfn.codeplex.com/.
51. A. A. Auer, Chem. Phys. Lett., 2009, 467, 230–232.
52. P. Politzer and J. S. Murray, Cent. Eur. J. Energ. Mater., 2011, 8, 209–220.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4ra03515a

---