Introduction

Since the first 1,2,3,4-tetrazine-1,3-dioxide derivatives were introduced in 1990 [1], many of them have been reported theoretically and experimentally [2–10], and the studies before 2004 have been summarized by Churakov [11]. However, only [1,2,5] oxadiazolo [3,4-e] [1,2,3,4]-tetrazine-4,6-di-N-dioxide (FTDO) could be called high energetic density compounds (HEDCs) among the synthesized compounds, though several other ones with higher predicted properties have been designed, such as TTTO, DTTO, etc., and their structures and predicted properties are listed in Table 1 [10, 12]. From then on N-oxides have also been arousing great interest because of the high detonation performance [14–16].

Table 1 Designed 1,2,3,4-tetrazine-1,3-dioxide high energy density compounds by Russian scientists
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The first sample of FTDO was obtained by Aleksandr et al. [17] in 1995. Rezchikova et al. [18, 19] reported its IR and Raman spectra at the same year. Li et al. [20] designed a new synthetic route of FTDO with yield of 31 % in 2012, and its density and enthalpy of formation were measured in 2004 and 2011, with the value of 1.85 g cm−3 [5] and 160.9 kcal mol−1 [9] respectively. Security and combustion properties on this compound are studied. Teselkin et al. [8] reported the mechanical sensibility of FTDO in 2009. They found its mechanical sensibility was close to that of lead azide. In 2009 and 2011, Kalmykov et al. [21, 22] studied the combustibility of co-crystal of FTDO with 2,4-dinitro-2,4-diazapentane. They found it could combust stably at normal pressure, but unstably under several decades atmosphere pressure; and the higher the FTDO’s content is, the lower the critical pressure for stable combustion.

FTDO is not only a promising energetic molecule, but also an ideal intermediate for the synthesis of TTTO, one of the most desired high energetic density compounds. A procedure from FTDO to TTTO was proposed by Russian scientists about 10 years ago (see Scheme 1) [12]. However, there is no report on successful synthesis of TTTO up to now.

Scheme 1
scheme 1

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The stability of FTDO is essential for its applications in explosives or propellants. However, there are not systemic investigations on FTDO’s stability until now. The present work investigated the structure of FTDO further using density functional theory (DFT) method, and made systemic calculations on its stability by the method of potential energy surface scanning and structure interconverted thermodynamics under different temperatures. The synthesis feasibility of TTTO from FTDO was reconsidered.

Calculation details

DFT B3LYP method with cc-pvdz and 6-31G** basis set were carried out to investigate the structure of FTDO using Gaussian 09 program [23]. The geometries were fully optimized, and the frequency calculations were performed. The results indicated that these geometries correspond to be minima (no imaginary frequency) in the potential energy surfaces. FTDO’s dissociation barriers in different channels were calculated by the potential energy surface scanning for its dissociation routes and stability. The enthalpy change (ΔH), entropy change (ΔS), and Gibbs free energy change (ΔG) were calculated at different temperature (25-500 °C) to further confirm its stability.

Results and discussion

Structure

The optimized structure of FTDO with numbering atoms is presented in Fig. 1, and the bond lengths, bond angles, and dihedral angles are listed in Table 2.

Fig. 1
figure 1

Optimized geometric configuration of FTDO

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Table 2 Optimized geometric parameters of FTDO
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It could be seen that the values of geometric parameters optimized at cc-pvdz and 6-31G** basis sets were nearly consistent. All atoms of FTDO molecule are approximatively in one plane, and the lengths of the bonds are between a typical single bond and a typical double bond to come into being a π conjugate system, which makes it aromatic.

Stability

In our present work, the stability of FTDO was investigated according to its dissociation, and the dissociation process was calculated and analyzed by the means of potential energy surface scanning (see Fig. 2) and Gibbs free energy changes (see Table 3). The results indicate FTDO would isomerize spontaneously (channel b) at ambient condition, in which the O(10) atom transfers from the tetrazine ring to the furazan ring, and the stability decreases after the isomerization. The calculated dissociation energy of the isomer (channel f) is only 13.27 kcal mol−1 (cc-pvdz) or 14.08 kcal mol−1 (6-31G**), with 12.95 kcal mol−1 (cc-pvdz) or 12.38 kcal mol−1 (6-31G**) lower than the dissociation energy of FTDO (channel c), which is 26.22 kcal mol−1 (cc-pvdz) or 26.46 kcal mol−1 (6-31G**). That means the isomer is much easier to dissociate than FTDO. According to the calculation results, the dissociation would begin at the N(7)-N(8) bond in tetrazine ring (channel f), and then be followed by the rupture of N(3)-O(5) bond in furazan ring (channel k). The dissociation energy of this process is 7.88 kcal mol−1 (cc-pvdz) or 6.62 kcal mol−1 (6-31G**). Ultimately, the C(2)-N(6) bond and C(1)-N(9) bond would break at the same time to generate N2, N2O, and furoxan fragments (channels n and o). This result is consistent with the mass spectrum data of FTDO [20] and the result of some preliminary research works carried out by other groups [24–27].

Fig. 2
figure 2

Potential energy scanning results (the data in parentheses is calculated at B3LYP/cc-pvdz basis set, and that in square brackets is calculated at B3LYP/6-31G**, unit: kcal mol−1)

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Table 3 Enthalpy change (ΔH), entropy change (ΔS), and Gibbs free energy change (ΔG) for each channel
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The enthalpy change (ΔH), entropy change (ΔS), and Gibbs free energy change (ΔG) for all channels were calculated in the range of 25–500 °C to investigate the stability further (see Table 3). It could be concluded from the results that the data of Gibbs free energy change at room temperature for each channel is very nearly the energy calculated by potential energy surface scanning. The temperature has little effect on each channel, and the most difference of ΔG is only about 1 kcal mol−1. The conversion from FTDO to isomer 1 (channel b) is a spontaneous process, and the increasing temperature would make the process easier.

It could be seen from the above results that 1,2,3,4-tetrazine ring in FTDO would break first during its dissociation, which means the furazan ring in FTDO is more stable than the 1,2,3,4-tetrazine ring. As a result, the synthetic route from FTDO to TTTO designed by Russian scientist might be impracticable. The low energy barrier for the opening of 1,2,3,4-tetrazine in FTDO indicates its poor stability, and its application would be restricted under the specified conditions.

Conclusions

In the present work, the structure of FTDO was investigated using DFT method with cc-pvdz and 6-31G** basis sets. The results show that all atoms in FTDO are approximatively in one plane and the molecule is aromatic. The potential energy surface scanning and the thermodynamics calculation for FTDO were performed. The results indicated spontaneous conversion from FTDO to its isomer occurred and its stability was decreased, which would dissociate to N2, N2O, and furoxan fragments. So the stability of FTDO is poor, and its application would be restricted under specified conditions. The result also indicated the synthetic route from FTDO to TTTO might be infeasible because the furazan ring is more stable than the 1,2,3,4-tetrazine ring, and the tetrazine ring would open first during a reaction.