Thermochemistry, Tautomerism, and Thermal Stability of 5,7-Dinitrobenzotriazoles

Abstract

Nitro derivatives of benzotriazoles are safe energetic materials with remarkable thermal stability. In the present study, we report on the kinetics and mechanism of thermal decomposition for 5,7-dinitrobenzotriazole (DBT) and 4-amino-5,7-dinitrobenzotriazole (ADBT). The pressure differential scanning calorimetry was employed to study the decomposition kinetics of DBT experimentally because the measurements under atmospheric pressure are disturbed by competing evaporation. The thermolysis of DBT in the melt is described by a kinetic scheme with two global reactions. The first stage is a strong autocatalytic process that includes the first-order reaction (E_a1^I = 173.9 ± 0.9 kJ mol⁻¹, log(A₁^I/s⁻¹) = 12.82 ± 0.09) and the catalytic reaction of the second order with E_a2^I = 136.5 ± 0.8 kJ mol⁻¹, log(A₂^I/s⁻¹) = 11.04 ± 0.07. The experimental study was complemented by predictive quantum chemical calculations (DLPNO-CCSD(T)). The calculations reveal that the 1H tautomer is the most energetically preferable form for both DBT and ADBT. Theory suggests the same decomposition mechanisms for DBT and ADBT, with the most favorable channels being nitro-nitrite isomerization and C–NO₂ bond cleavage. The former channel has lower activation barriers (267 and 276 kJ mol⁻¹ for DBT and ADBT, respectively) and dominates at lower temperatures. At the same time, due to the higher preexponential factor, the radical bond cleavage, with reaction enthalpies of 298 and 320 kJ mol⁻¹, dominates in the experimental temperature range for both DBT and ADBT. In line with the theoretical predictions of C–NO₂ bond energies, ADBT is more thermally stable than DBT. We also determined a reliable and mutually consistent set of thermochemical values for DBT and ADBT by combining the theoretically calculated (W1-F12 multilevel procedure) gas-phase enthalpies of formation and experimentally measured sublimation enthalpies.

1. Introduction

Benzotriazoles are an important class of heterocyclic compounds with a wide range of applications. For instance, they are employed as important intermediates in organic synthesis [1,2], biologically active agents in medicine and agriculture [3,4,5], and inhibitors of metal corrosion [6,7,8]. Nitro derivatives of benzotriazoles are also considered as promising energetic materials with generally low sensitivity to mechanical stimuli and high thermal stability [9,10,11]. Two representative benzotriazoles, namely, 5,7-dinitrobenzotriazole (DBT) and 4-amino-5,7-dinitrobenzotriazole (ADBT), are studied in the present work (Figure 1). While the first reports on DBT date back to 1897 [12] and several new synthetical procedures have been proposed since that time [13,14,15], ADBT has been synthesized for the first time only recently [16]. Both compounds have a moderate density of ~1.66 g cm⁻³ and, consequently, mediocre energetic performance (calculated detonation velocities ~7.3 km s⁻¹ [16]). However, these materials have remarkably high thermal stability, as confirmed in linear heating tests by differential scanning calorimetry (DSC). DBT melts at 466 K (193 °C) and then decomposes with the extrapolated onset of 564 K (291 °C), while ADBT melts with a subsequent decomposition at 610 K (337 °C) [16]. These values are the only available information on the thermal behavior of DBT and ADBT. At the same time, benzotriazoles with various non-explosophoric moieties have been extensively studied, and their pyrolysis and photolysis were proposed to occur via N₂ elimination [17,18,19,20]. In order to obtain a deeper insight into the possible decomposition mechanisms of dinitrobenzotriazoles, we also considered the structurally similar dinitrotriazolopyridines 3 and 4, and simpler species with the dinitrobenzotriazoles skeleton, viz., 1,3-nitrobenzene (5) and 1,2,3-triazole (6, Figure 1). Recently, we have studied the thermal stability of the similar compounds 3 and 4 using pressure DSC and quantum chemical calculations at the DLPNO-CCSD(T) level [21]. We found that the thermolysis of 3 occurs in the melt and is described by a kinetic scheme with two autocatalytic independent parallel reactions, whereas the decomposition kinetics of 4 is more complex due to its overlap with the melting. Theoretical calculations revealed the initial decomposition channel to change from the nitro-nitrite rearrangement (E_a~240 kJ mol⁻¹) to the C–NO₂ bond cleavage with an activation barrier of ~280 kJ mol⁻¹ at temperatures around 500 K.

The thermolysis of the prototypical 1,3-dinitrobenzene (5) was investigated in the gas phase by the manometry technique [22] and laser-powered homogeneous pyrolysis [23]. In both studies, the thermolysis kinetics of 5 was described as a first-order process with similar values of the Arrhenius parameters E_a = 285 kJ mol⁻¹, log(A/s⁻¹) = 16.9 [22] and E_a = 293 kJ mol⁻¹, log(A/s⁻¹) = 14.5 [23]. The radical C–NO₂ bond cleavage was hypothesized to be a rate-limiting process. Shao et al. [24] reported the theoretical estimations of the C-NO₂ bond dissociation energy for 5 to be 267–285 kJ mol⁻¹ at various DFT levels of theory. For the related nitro-amino compounds, a wider set of possible primary decomposition pathways has been proposed. For instance, in the case of TATB (1,3,5-triaminotrinitrobenzene) several particular initial pathways were discussed in the literature. Apart from the conventional C–NO₂ bond scission and nitro-nitrite isomerization, DFT calculations were used to consider intra- and intermolecular hydrogen transfers and intramolecular cyclization forming benzofurazan or benzofuroxan derivatives [25,26].

The mechanism of 1,2,3-triazole thermolysis has been reported in several theoretical studies. Da Silva et al. [27] showed at the G3B3 level that the ring opening with the subsequent N₂ elimination with the activation energy of 222 kJ mol⁻¹ dominates the thermolysis of 1,2,3-triazole. Recently, Lu et al. [28] has refined the activation barrier of this reaction using the DLPNO-CCSD(T) procedure and obtained the value of ~189 kJ mol⁻¹.

It is also worth mentioning that DBT and ADBT are prone to annular tautomerism. The molecular structure of N-unsubstituted benzotriazole has been the subject of numerous structural studies [29,30,31]. Recently, Santa Maria et al. [32] used X-ray diffraction, NMR spectroscopy, and DFT calculations to demonstrate that the 5,6-dinitrobenzotriazole exists in the solid state as the 1H tautomer (7, Figure 1), while the 2H tautomer (8, Figure 1) is energetically more favorable in the gas phase. In the DMSO solution, the mixture of both tautomers coexists. Similarly, for a long time, the molecular structure of DBT was attributed to that of 4,6-dinitrobenzotriazole (denoted as 1H-4,6-tautomer henceforth) [12,13,14]. However, Graham et al. [15] employed B3LYP calculations to show that the 5,7-dinitro-1H-benzotriazole (1H-5,7-tautomer) isomer is ~35 kJ mol⁻¹ more favorable than the 1H-4,6 isomer in the gas phase. Then, Ehler et al. [16] experimentally confirmed the molecular structure of DBT using X-ray diffraction data. Moreover, the authors reported the structure of ADBT, which was also attributed to 1H-5,7-tautomer. At the same time, the role of tautomeric interconversions of benzotriazoles in their decomposition mechanism remains unclear.

The literature survey reveals that the thermal behavior and decomposition mechanisms of nitro-substituted benzotriazoles are not well understood. Thus, in the present contribution, we address the thermochemistry, tautomerism, and thermal stability (kinetics and decomposition mechanism) of DBT using thermal analysis techniques and quantum chemical calculations. To avoid evaporation, the experiments were performed using pressure differential scanning calorimetry (DSC), and then the kinetic data were fitted with advanced thermokinetic methods, e.g., isoconversional and model-fitting approaches. The experiment was complemented by high-level reliable quantum chemical calculations of the primary decomposition mechanism of DBT at the DLPNO-CCSD(T) level of theory. By analogy with the well-known energetic materials bearing similar fragments, we suggest that the primary decomposition mechanism of the dinitrobenzotriazoles involves the C–NO₂ radical bond cleavage and the molecular isomerizations, either nitro-nitrite or H-transfers yielding the aci-form. Moreover, we studied the influence of the amino group on the thermal stability of the dinitrobenzotriazole skeleton by considering the primary decomposition pathways of ADBT.

2. Results and Discussion

2.1. Thermal Behaviour of DBT under Atmospheric Pressure

Simultaneous thermal analysis data for DBT heated at a 1 K min⁻¹ rate at atmospheric pressure are shown in Figure 2. The DSC curve (blue trace, Figure 2) shows two endothermic effects. The first corresponds to the melting of a sample. The melting temperature determined as the extrapolated peak onset is 475.0 K. Note that this value is remarkably higher than those reported previously, viz., 466, 471, and 469–470 K [12,13,15,16]. These discrepancies can be attributed to higher sample purity in the present study or insufficient temperature control in the previous experiments. The second endothermic effect corresponds to evaporation, which is accompanied by the complete mass loss of the sample (red trace, Figure 2). Hence, to observe the exothermic effect of the thermal decomposition, we applied pressure to be DSC (PDSC), which is under elevated external pressure. This approach allowed us to shift the evaporation to higher temperatures and very often observe the sole decomposition kinetics of a compound under study [33,34].

2.2. Thermal Kinetics of DBT under Elevated Pressure

The pressure DSC experiments were performed under an elevated external pressure of 2.0 MPa and at heating rates varying from 0.5 to 10 K min⁻¹. Thermal decomposition of DBT occurs in the melt, and the PDSC curves have the characteristic shape with the two exothermic peaks (Figure 3). The first peak (I) has a sharp form, whereas the second (II) has a lower amplitude without a visible maximum and apparently corresponds to the heat released in secondary reactions. Note that peak II exhibits a broad and gradual decrease to the baseline. This effect can introduce inaccuracies in determining the total heat effect and subsequent thermokinetic modeling. It is worth mentioning that DBT exhibits very similar thermal behavior to its structural analog, 6,8-dinitrotriazolopyridine (3) [21]. The decomposition heat effect and residual sample mass dependences on the heating rate can be found in the Supporting Information (Figure S1).

The rough estimations of DBT decomposition kinetics were performed by the Kissinger method applied to peak I of the DSC data (Figure 3 and Figure 4). The Kissinger method yields the activation energy and the preexponential factor to be E_a = 157 ± 1 kJ mol⁻¹ and log(A/s⁻¹) = 11.8 ± 0.1. These values were used as an initial guess for the first reaction in the model-fitting analysis. At the same time, the second exothermic peak II does not exhibit a clear maximum within the range of heating rates applied. Thus, the Kissinger method is not directly applicable in this case.

Then, a more detailed description of the decomposition kinetics of DBT was obtained by isoconversional Friedman analysis, which tracks the change of activation energy E_a against a conversion degree α. The isoconversional plot in Figure 5 shows the considerable variation of activation energy throughout the process, with the two regions with relatively constant activation energy, which may indicate the activation barriers for contributing reaction steps [35]. At the beginning of decomposition (α < 0.2), the activation energy stabilizes around 146 ± 2 kJ mol⁻¹ (Figure 5), which slightly differs from the output of the Kissinger approach for peak I (cf. Figure 4). The reason for this is that the maximum of the DSC peak corresponds to larger conversion degree values α = 0.25 ± 0.02. Upon the reaction’s progress, the activation energy decreases and reaches the minimum value ~96 kJ mol⁻¹ at α = 0.34, possibly due to competition between the different reactions. Next, at the conversion degrees 0.55 < α < 0.75, the isoconversional plot shows the second region with the constant activation energy, which approximately coincides with the low conversion degree value E_a = 146 ± 1 kJ mol⁻¹. After that, the activation energy rises to 169 kJ mol⁻¹ at the end of the process (Figure 5).

Next, we applied the model-fitting approach to analyze the complex decomposition behavior of DBT. From the shape of DSC curves and results of isoconversional analysis, we considered several two-step kinetic schemes, viz., independent parallel, consecutive, and competitive parallel processes. These reactions obey a model of the extended Prout-Tompkins Equation (6). According to the Bayesian information criteria (the lower values correspond to a better model), among the two-step models, the best fit of the experimental data offers the kinetic scheme with two consecutive reactions (Figure S2, Supporting Information). The first reaction has the following kinetic parameters in Equations (3) and (6): E_a1 = 153.7 ± 0.3 kJ mol⁻¹, log(A₁/s⁻¹) = 12.56 ± 0.02, n₁ = 0.99 ± 0.03, m₁ = 1.95 ± 0.02, and q₁ = 0.9. The optimized values of the exponents n₁ and m₁ are close to integer numbers. Hence, the first reaction model is close to the autocatalytic process with a second order by the autocatalyst. The second global reaction is more complex in terms of the effective kinetic parameters: E_a2 = 90.9 ± 2.0 kJ mol⁻¹, log(A₂/s⁻¹) = 5.6 ± 0.2, n₂ = 1.28 ± 0.05, m₂= –0.31 ± 0.01, and q₂ = 0.9 (

Table 1. The kinetic parameters calculated using the different approaches for the non-isothermal PDSC data of DBT decomposition.

Model Name	A	B	C	D	E
Analysis method	Kissinger	model-fitting	model-fitting	model-fitting	model-fitting
Kinetic model	–	ePT + ePT a	ePT → ePT	AC b → ePT	AC → ePT
log (A1/s−1)	11.8 ± 0.1	12.61 ± 0.02	12.56 ± 0.02	18.0 ± 0.4/ 11.15 ± 0.07	12.82 ± 0.09/ 11.04 ± 0.07
Ea1, kJ mol−1	157 ± 1	155.8 ± 0.2	153.7 ± 0.3	241.9 ± 4.8/ 141.2 ± 0.8	173.9 ± 0.9/ 136.5 ± 0.8
n1	–	1.26 ± 0.03	0.99 ± 0.03	1/1	1/1
m1	–	1.046 ± 0.006	1.95 ± 0.02	0/1	0/2
q1	–	0.999 c	0.9	–	–
log (A2/s−1)	–	8.6 ± 0.1	5.6 ± 0.2	9.7 ± 0.2	8.7 ± 0.2
Ea2, kJ mol−1	–	126.7 ± 1.6	90.9 ± 2.0	144.4 ± 2.3	134.5 ± 1.8
n2	–	3.00 ± 0.07	1.28 ± 0.05	2.50 ± 0.07	1.98 ± 0.05
m2	–	0.35 ± 0.02	−0.31 ± 0.01	−0.25 ± 0.04	−0.78 ± 0.06
w1 d	–	0.300 ± 0.003	0.284 ± 0.004	0.347 ± 0.005	0.274 ± 0.007
q2	–	0.999 c	0.9	0.999	0.999
BICe	–	−40,489.3	−43,590.5	−41,524.4	−45,643.4

^a The kinetic model denoted “ePT” corresponds to the extended Prout-Tompkins Equation (6) with the different connections between reactions, viz., “+”—independent parallel reactions and “→”—the consecutive reactions. ^b The kinetic model denoted “AC” corresponds to the conventional autocatalytic model with an m-th order by autocatalyst according to Equation (1). ^c These values were fixed during kinetic modeling. ^d The contribution of the first reaction to the total heat released is denoted as w. ^e The Bayesian informational criteria (BIC) values.

, model C).

Since the first reaction of DBT thermolysis in the melt exhibits an autocatalytic nature, it is also reasonable to probe the conventional autocatalytic model [36]. Thus, the final formal scheme includes the first global reaction step, which is, in turn, comprised of two parallel reactions, namely, the first-order process and an m-th order autocatalytic reaction (AC):

$$\frac{d\alpha }{dt}=k_1\left(1-\alpha \right)+k_2{\alpha }^m\left(1-\alpha \right),$$

(1)

while the second global step model remains in the ePT form of Equation (6). Actually, Equation (1) is a particular case of the model with two parallel reactions in the ePT form (6) with q₁ = q₂ = 1 and m₁ = 0. In the present case, we employed the integer values of m = 1 and 2.

The model optimization revealed that the modified kinetic scheme with m = 2 improves the fit quality and its statistical performance (Table 1, Model E, and Figure 6). Note that the reaction rate of the autocatalytic part of the first global reaction is two orders of magnitude faster than its non-catalytic counterpart ($k_1/k_2\approx 59$, Figure 6). The final kinetic parameters for the noncatalytic decomposition reaction in the melt are: E_a1^I = 173.9 ± 0.9 kJ mol⁻¹, log(A₁^I/s⁻¹) = 12.82 ± 0.09.

2.3. Theoretical Calculations

As seen from the previous section, the non-isothermal thermoanalytical experiment yielded only the effective kinetic parameters of the thermal decomposition of DBT without any mechanistic assumptions. It is impossible to separate the contributions from primary and secondary elementary chemical reactions. In such cases, quantum chemical calculations often complement the experiment in a very effective way. We applied modern quantitative quantum chemistry approaches to calculating the activation barriers and rate constants of the primary decomposition reactions of DBT. Furthermore, we investigated the influence of the introduction of the amino group in the benzotriazole skeleton on thermal stability, considering the primary decomposition reactions of the ADBT compound as well.

2.3.1. Mutual Interconversions of DBT and ADBT Tautomers

We started with the analysis of the molecular structure of benzotriazoles. We considered three different annular tautomeric forms, viz., 1H-5,7-tautomer, 2H-4,6-tautomer, and 1H-4,6-tautomer (Figure 7). The single unimolecular hydrogen transfer via _xTS1 (where x corresponds to DBT and ADBT, respectively) leads to 2H-4,6-tautomer with a high activation barrier ~235 kJ mol⁻¹, whereas the subsequent hydrogen transfer via _xTS2 with a similar barrier ~240 kJ mol⁻¹ gives the 1H-4,6-tautomer (Figure 7). Note that the 1H-5,7-form lies significantly lower on the PES, viz., by ~25–30 kJ mol⁻¹ than 2H-4,6 and by ~30–56 kJ mol⁻¹ compared to the 1H-4,6-tautomer. Thus, the 1H-5,7-tautomer of DBT and ADBT is the most energetically preferable one. These results agree well with previous DFT calculations for DBT [15] and also with the crystalline structures for both compounds from X-ray diffraction experiments [16]. Therefore, for all following calculations of decomposition pathways, the 1H-5,7-form was chosen as a reference species.

The tautomeric interconversions can also proceed via bimolecular reactions in the dimers. As shown in our previous works, the concerted double hydrogen transfer in the dimers often occurs with lower activation barriers than the corresponding unimolecular reactions [37,38]. In the present case, we considered the concerted double hydrogen transfer in the dimers from the 1H-5,7-tautomer yielding the 2H-4,6 and 1H-4,6 forms (Figure 8). It was found that the activation barriers of _xTS_D12 and _xTS_D34 are significantly lower than those for unimolecular processes. Consequently, if the tautomeric interconversions are faster than the unimolecular decomposition pathways, then the tautomeric forms are in equilibrium during the thermolysis of DBT and ADBT. Therefore, the 2H-4,6 and 1H-4,6 forms can also contribute to the primary decomposition mechanism. Thus, we consider next the monomolecular decomposition reactions of the DBT and ADBT tautomers.

2.3.2. Mechanisms of the Primary Decomposition Reactions of DBT and ADBT

We examined the primary decomposition mechanisms proposed in the literature for structurally similar nitroaromatic compounds [25,26,39]: the radical C–NO₂ bond cleavage, nitro-nitrite rearrangement, the reactions involving the aci intermediate, and the triazole ring opening channel, which is widely discussed for 1, 2, 3-triazole and benzotriazoles [18,19,27,28]. For these channels, all non-equivalent positions of NO₂ groups and hydrogen atoms were considered.

Let us start with the decomposition mechanisms for the 1H-5,7-tautomers of DBT and ADBT. The barrierless radical C-NO₂ bond cleavage yields heterocyclic radicals •_xR6 and •NO₂ (Figure 9). The corresponding reaction enthalpies are 299.2 and 318.7 kJ mol⁻¹ for DBT and ADBT, respectively. These enthalpies agree well with the typical values for nitroaromatic compounds, including 1,3-dinitrobenzene (5) [22,23,40,41].

The activation barriers of a competitive nitro-nitrite rearrangement _xTS7 are 32 and 42 kJ mol⁻¹ lower than the corresponding radical asymptotes, •_xR6 + •NO₂ (Figure 9), respectively. The nitrite species _xP7, formed in primary reactions, are prone to very fast elimination of the •NO radical, with reaction enthalpies of 80 and 58 kJ mol⁻¹ for DBT and ADBT, respectively (Figure 9).

The N₂ elimination channel proceeds via two subsequent elementary reactions. The triazole ring opening occurs first (xTS8), yielding the diazo intermediate xP8, which has a low activation barrier of reverse reaction E_a~10 kJ mol⁻¹, whereas the second xTS8a leads to the release of N₂ and the formation of xP8a (Figure 9). Since the reaction via the transition state xTS8 is reversible, the kinetics of the N₂ elimination is determined by the effective activation barrier of xTS8a. The corresponding values of 281.4 and 286.4 kJ mol⁻¹ for DBT and ADBT, respectively, are slightly higher (in 10–15 kJ mol⁻¹) than those for the nitro-nitrite rearrangement _xTS7 and lower than the enthalpy of C-NO₂ bond cleavage by 32 and 18 kJ mol⁻¹ (Figure 9). Note that these values largely exceed their counterparts for unsubstituted 1,2,3-triazole (6) by 60 [27] and 100 kJ mol⁻¹ [28].

In addition, we considered the reactions of intramolecular isomerization to aci-form via xTS3 and xTS4 and the hydrogen transfer from the benzene ring to a triazole moiety via xTS5 (Figures S3 and S4, supporting information). The aci-isomerizations xTS3 and _ADBTTS4 have activation barriers 40–80 kJ mol⁻¹ lower than those of tautomeric interconversions. However, the activation barriers of the reverse reactions Ea~10–25 kJ mol⁻¹ indicate that the intermediates xP3 and xP4 should rearrange fast to the initial reagent. Furthermore, the hydrogen transfer xTS5 with the activation barriers of 394 kJ mol⁻¹ for DBT and 196 kJ mol⁻¹ for ADBT is the least favorable process among the isomerization pathways (Figures S3 and S4, Supporting Information). Among the considered unimolecular isomerizations, only the aci-form xP3 and _ADBTP4 can take part in the subsequent decomposition. We considered the radical elimination of •NO₂, •OH, and the molecular elimination of HONO. These channels have effective activation barriers higher than 320 kJ mol⁻¹ (the details can be found in the Supporting Information, Section S3); therefore, they are kinetically unimportant.

In the case of tautomers 2H-4,6 and 1H-4,6, we examined the most competitive decomposition pathways, i.e., the C-NO₂ bond cleavage and the nitro-nitrite rearrangement (Figures S5 and S6, Supporting Information). We found that the relative reaction enthalpy for radical bond cleavage exceeds 15–30 kJ mol⁻¹ for 1H-5,7-tautomers. The nitro-nitrite rearrangements have closer activation barriers to the 1H-5,7-tautomer for DBT (difference ~1–3 kJ mol⁻¹), but for ADBT the difference is still large. Overall, the lowest activation barriers correspond to 1H-5,7-form (_xTS7 and •_xR6 + •NO₂, Figure 9). These results suggest that thermolysis of dinitrobenzotriazoles occurs via 1H-5,7-tautomer.

The initial decomposition reactions of DBT and ADBT comprise the same channels (C-NO₂ bond cleavage, nitro-nitrite rearrangement, and N₂ elimination). As seen in Figure 9, the activation barriers for amino-substituted dinitrobenzotriazole are noticeably higher, which implies its higher thermal stability as compared to DBT. Therefore, the introduction of the amino group to the benzotriazole moiety increases its thermal stability. This fact is in line with our previous results for dinitrotriazolopyridines 3 and 4 [21].

In the experiment, the thermolysis of DBT proceeds in a melt. According to the literature [16], the thermal decomposition of ADBT also occurs in the melt at heating rates higher than 5 K min⁻¹. To estimate the influence of the media on the primary decomposition reactions of DBT and ADBT, we used the PCM model. Several model solutions, viz., the isotropic media with ε = 1.96 (cyclopentane), ε = 19.26 (2-propanol), and ε = 46.83 (dimethyl sulfoxide), were used in the PCM calculations. The latter value is exceptionally high and was used to demonstrate the insensitivity of the thermolysis mechanisms of DBT and ADBT to the dielectric properties of the melt. Indeed, the results of PCM calculations show only marginal changes for important decomposition channels (further details can be found in the Supporting Information, Figures S7 and S8). Note that the tautomers 2H-4,6 and 1H-4,6 become more thermally accessible in the solutions with high polarity (2-propanol and DMSO); however, the dominant role of the 1H-5,7-tautomer persists. Thus, we believe the C-NO₂ bond cleavage, nitro-nitrite rearrangement, and N₂ elimination remain competitive processes in the melt.

To determine the dominant channel among the primary decomposition pathways, we calculated the rate constants of the elementary reactions of DBT and ADBT using the transition state theory (Equation (7)). In the case of barrierless reactions, the phase space theory (Equation (9)) was employed to localize the transition state. Note that for the decomposition pathways with a reversible first step, e.g., the xTS8, the effective rate constant was calculated as $k_{eff}\cong \frac{k_1}{k_{-1}}{k}_{lim}$, where $\frac{k_1}{k_{-1}}$ is the equilibrium constant of the first step (k₁ is the rate constant of a direct reaction, k_-1-the rate constant of the reversion), and k_lim is the rate constant of the limiting process occurring via xTS8a. The Arrhenius parameters for all decomposition channels are given in the supporting information (Section S6 in Supporting Information, Table S1). The rate constants for the most important primary decomposition pathways are summarized in

Table 2. The calculated kinetic parameters of the primary gas-phase decomposition reactions for DBT and ADBT. The rate-limiting transition state is shown in parentheses.

Reaction	ΔH°, kJ mol−1	Ea, kJ mol−1	log(A/s−1)
DBT→•DBTR6+•NO2	299.2 a	297.6	18.10
DBT→ DBTP7 (DBTTS7)	267.1	271.2	13.61
DBT→ DBTP8 (DBTTS8a)	281.4	289.4	21.10
ADBT→•ADBTR6+•NO2	318.7 a	319.8	19.11
ADBT→ ADBTP7 (ADBTTS7)	276.2	280.3	13.88
ADBT→ ADBTP8 (ADBTTS8a)	286.4	293.3	20.14

^a In the case of barrierless reactions, the reaction enthalpies are shown.

and Figure 10.

From the energetic point of view, the nitro-nitrite rearrangements _xTS7 are the most favorable primary channels, followed by the two-step N₂ elimination via _xTS8, and by the (least energetically preferred of three) C-NO₂ bond cleavage yielding •_xR6 + •NO₂ (Figure 9). On the other hand, the radical channels have the largest preexponential factors (Table 2) typical of barrierless reactions [40,41]. The latter values exceed by two and five orders of magnitude the more energetically favorable channels, _xTS8 and _xTS7, respectively (Table 2). Figure 10 compares the rate constants for the competitive primary channels extrapolated by the Arrhenius equation (Equation 6). As seen from Figure 10, the N₂ elimination via _xTS8 is overall the least favorable process, while the nitro-nitrite rearrangement and C-NO₂ bond cleavage have the closest rate constants. Moreover, the high reaction enthalpy of •_xR6 + •NO₂ pathway is compensated by a greater preexponential factor (or, equivalently, the activation entropy), which leads to the change of the dominant channel at relatively low temperatures (viz., 307 K for DBT and 395 K for ADBT) from the nitro-nitrite isomerization (red lines, Figure 10) to the radical C-NO₂ bond cleavage (blue graphs, Figure 10). Taking into account the temperature range where the decomposition was observed experimentally (Figure 2 and Figure 3), and the results of PCM calculations, we propose that the thermolysis of both DBT and ADBT in the melt occurs via the radical C-NO₂ bond cleavage.

It is also instructive to compare the thermal stability of the benzotriazoles compounds with their structural isomers 3 and 4. Since the experimental kinetics for all compounds is very complicated, we compared the results of theoretical calculations. Quantum chemical calculations of the effective rate constants for the C–NO₂ bond scission at the mean experimental temperature of 650 K are presented in

Table 3. Thermal stability of the dinitrobenzotriazoles and dinitrotriazolopyridines: the effective rate constants of C–NO₂ bond scission.

Species	DBT	ADBT	3	4
keff(650 K) a	1	0.1	18.3	5.5

^a The relative rate constants with respect to that of DBT are shown.

. These results indicate that the dinitrobenzotriazoles DBT and ADBT have higher thermal stability than the dinitrotriazolopyridines 3 and 4.

2.3.3. Thermochemistry of the Compounds Studied

The gas-phase enthalpy of formation (${\mathsf{\Delta }}_f{H}_m^{°}\left(g\right)$) for dinitrobenzotriazoles and their structural analogs, dinitrotriazolopyridines 3 and 4, were calculated using the high-level computational W1-F12 method. The sublimation enthalpies (${\mathsf{\Delta }}_s^g{H}_m^{°}$) are necessary to complement the gas-phase ${\mathsf{\Delta }}_f{H}_m^{°}\left(g\right)$ values to obtain the solid-state enthalpy of formation ${\mathsf{\Delta }}_f{H}_m^{°}\left(s\right)$. In the case of DBT, the sublimation enthalpy was determined experimentally using thermogravimetry at atmospheric pressure [42] (Figure S9, Supporting Information). The higher temperature of the region used to derive the vaporization data at every heating rate was smaller than the onset of the rise of PDSC curves at the same rate. Hence, the thermal decomposition was supposed to not influence the results. The evaporation enthalpy value corrected to room temperature (${\mathsf{\Delta }}_l^g{H}_m^{°}$= 94.6 ± 1.9 kJ mol⁻¹), was supplemented by the melting enthalpy from pressure DSC tests (${\mathsf{\Delta }}_s^l{H}_m^{°}$= 27.3 ± 1.3 kJ mol⁻¹) to give the final value ${\mathsf{\Delta }}_s^g{H}_m^{°}$= 121.8 ± 3.2 kJ mol⁻¹.

For ADBT and dinitrotriazolopyridines, the sublimation enthalpies were estimated using the recently suggested modified empirical Trouton-Williams rule for CHNO compounds [42]:

$${\Delta }_s^g{H}_m^0=0.15\cdot T_m+3.27\cdot \left[H\right]+5.30\cdot \left[N\right]+3.30\cdot \left[O\right].$$

(2)

Note that the outcome of Equation (2) matches the experimental result within the experimental error (

Table 4. The enthalpies of formation in the gas phase (${\mathsf{\Delta }}_f{H}_m^{°}\left(g\right)$) and solid state (${\mathsf{\Delta }}_f{H}_m^{°}\left(s\right)$) along with the sublimation enthalpies (${\mathsf{\Delta }}_s^g{H}_m^{°}$) for dinitrobenzotriazoles (DBT and ADBT) and relative dinitrotriazolopyridines (3 and 4).

Compound	${\mathsf{\Delta }}_{\mathit{f}}{\mathit{H}}_{\mathit{m}}^{°}\left(\mathit{g}\right)$, kJ/mol	${\mathsf{\Delta }}_{\mathit{s}}^{\mathit{g}}{\mathit{H}}_{\mathit{m}}^{°}$, kJ/mol	${\mathsf{\Delta }}_{\mathit{f}}{\mathit{H}}_{\mathit{m}}^{°}\left(\mathit{s}\right)$, kJ/mol
DBT	308.1 a	121.8 ± 3.2 120	187.3 179 c
ADBT	271.2 a	150	129.5 128 c
3	308.6 a 262.3 b	124	184.4 191.6 d
4	279.4 a	150	129.6 138.1 d

^a Calculated using the W1-F12 multi-level procedure and atomization energy approach. ^b The gas phase enthalpy of formation is calculated using the G3B3 multi-level procedure and atomization energy approach [43]. ^c Calculated as a combination of the gas-phase formation enthalpy from the CBS-4M multi-level procedure and the sublimation enthalpy estimated by the Trouton rule [16]. ^d Calculated as a combination of the gas-phase formation enthalpy from the G3B3 multi-level procedure and the sublimation enthalpy estimated by the Trouton rule [44].

). Then, the solid-state enthalpy of formation was calculated according to the Hess law, ${\mathsf{\Delta }}_f{H}_m^{°}\left(s\right)={\mathsf{\Delta }}_f{H}_m^{°}\left(g\right)-{\mathsf{\Delta }}_s^g{H}_m^{°}$. The obtained results are displayed in Table 4 against available literature data, which comprise only the theoretical estimates. Considered structural isomers pairwise (DBT–3 and ADBT–4) show very close thermochemistry parameters (Table 4). The calculated values of ${\mathsf{\Delta }}_f{H}_m^{°}\left(s\right)$ in the present study differ from the literature data. However, the methodology used in our work is generally more reliable.

3. Methods and Materials

3.1. Materials

5,7-Dinitrobenzotriazole (DBT) was synthesized according to the modified literature procedure [16]. A mixture of 70% HNO₃ (23 mL) and concentrated H₂SO₄ (23 mL) was added dropwise to the suspension of benzotriazole (20 g, 0.168 mol) in H₂SO₄ (80 mL) at 15–20 °C. After stirring for 24 h at 20 °C, the mixture was poured into ice water; a precipitate was filtered off, washed with water, and dried on air to give 4-nitrobenzotriazole (25.5 g, 92.5%), which was used without further purification. Crude 4-nitrobenzotriazole (10 g, 47.8 mmol) was suspended in concentrated H₂SO₄ (120 mL), cooled to 0 °C, and then fuming HNO₃ (20 mL, d 1.5 g/cm³) was added dropwise. A reaction mixture was stirred for 1 h at 20 °C and for 3 h at 120 °C. After cooling to 20 °C, it was poured into the crushed ice. The resulting precipitate was filtered off, thoroughly washed with H₂O, dried on air, and recrystallized from EtOH to give 5,7-dinitrobenzotriazole (7.7 g, 57%) as a white solid. ¹H NMR (DMSO-d₆): 9.00 (s, 1H); 9.50 (s, 1H). ¹³C NMR (DMSO-d₆): 118.9, 123.2, 129.9, 133.2, 143.6, 146.5. HRMS (ESI), found: m/z 210.0257 [M+H]; calculated for C₆H₃N₅O₄: 210.0258. Elemental analysis calculated (%) for C₆H₃N₅O₄: C, 34.46; H, 1.45; N, 33.49; found: C, 34.57; H, 1.39; N, 33.60.

3.2. Thermoanalytical Experiments

The thermal behavior of DBT was examined by the simultaneous thermal analyzer STA 449 F1 (Netzsch), which combines thermogravimetry (TG) and differential scanning calorimetry (DSC). The samples of ca. 1.8 mg weight were placed in open aluminum crucibles and heated at a rate β = 10 K min⁻¹ under an argon flow of 50 mL min⁻¹.

The thermal decomposition of DBT was assessed using the pressure differential scanning calorimeter DSC 204 HP (Netzsch). Samples were poured into closed aluminum crucibles with pierced lids and heated with the rates β of 0.5, 1, 2, 5, and 10 K min⁻¹ up to 500 °C. The instrument has been calibrated with respect to heat flow and temperature using highly-pure metal calibrants, and all measurements were performed under a nitrogen flow of 150 mL min⁻¹. The sample mass of DBT was varied from 0.2 to 3.9 mg with the heating rate to keep the DSC signal magnitude below 8 mW to minimize the detrimental self-heating phenomenon [45].

The thermokinetic analysis of DBT was performed using various kinetic techniques, from the conventional Kissinger method to modern isoconversional and model-fitting approaches. The basic equation of thermokinetics is

$$\frac{d\alpha }{dt}=k\left(T\right)f\left(\alpha \right),$$

(3)

where α is a conversion degree, $k\left(T\right)$ is an Arrhenius dependence of the rate constant against temperature, $f\left(\alpha \right)$—the kinetic model in a differential form. For the DSC data, the conversion degree is determined as the ratio of a partial area under the DSC curve with respect to the total heat release of the reaction. The initial evaluation of the kinetic parameters was performed using the Kissinger approach [45,46], which gives an apparent activation energy E_a and a preexponential factor A from the shift of the DSC peak temperature T_p against a heating rate β:

$$E_a=-R\frac{d\mathit{ln}(\beta /{T_p}^2)}{d\left(1/T_p\right)}.$$

(4)

More detailed information on the thermal kinetics can be obtained from the isoconversional Friedman analysis [47], which yields the Arrhenius parameters A and E_a against the conversion degree α:

$${\mathit{ln}\left(\frac{d\alpha }{dt}\right)}_{\alpha ,i}=\mathit{ln}\left[f\left(\alpha \right)\cdot A_{\alpha }\right]-\frac{E_a}{R{T}_{\alpha ,i}},$$

(5)

where a subscript i corresponds to a particular measurement. To determine the final kinetic model, we employed the model fitting analysis along with the “top-down” approach [48]. To this end, we optimized the reaction model in the flexible form of an extended Prout−Tompkins (ePT) equation [49]:

$$f\left(\alpha \right)={\left(1-\alpha \right)}^n{\left[1-q\left(1-\alpha \right)\right]}^m.$$

(6)

Equation (6) is referred to as ePT(n, m, q). Initially, the single reaction was probed, and if necessary, more reaction steps were added. Additionally, the exponents in Equation (6) were fixed to particular integer values to reduce the model to one of the ideal theoretical reaction types (e.g., a first-order reaction, a one-dimensional diffusion, etc.).

All thermokinetic calculations were carried out using self-developed open-source THINKS software [50] and under ICTAC recommendations [35,51].

3.3. Quantum Chemical Calculations

Electronic structure calculations were carried out using Gaussian 16 [52], ORCA 4.2.1 [53,54], and Molpro 2010 [55] quantum chemical programs. The density functional theory (DFT) calculations at the M06-2X/6-311++G(2df,p) [56] level were used for the geometry optimization of all considered species (reactants, products, and transition states), as well as for calculations of frequencies and thermal corrections to thermodynamic potentials. All the stationary point and transition state structures correspond to minima on the potential energy surfaces (PES). To confirm the nature of localized transition states, the intrinsic reaction coordinate (IRC) approach [57] was used. Gaussian 16 software was used to perform all the calculations at the DFT level of theory [52]. To get the desired “chemical” accuracy of ~4 kJ mol⁻¹ for the activation barriers, we refined the single-point electronic energies using the DLPNO-CCSD(T0) methodology (the “Normal PNO” truncation thresholds were used) [58] with the jun-cc-pVQZ “seasonally” augmented basis set [53]. Recent reports demonstrated that this technique can be used to obtain the accurate thermochemistry and activation barriers for the cage and heterocyclic nitramino energetic materials, such as hexanitrohexaazaisowurtzitane (CL-20) [59,60], at a reasonable computational cost. To accelerate the convergence of the SCF components of DLPNO-CCSD(T) energy, the RIJK density fitting (DF) approximation [61] was applied. For the calculations of corresponding integrals in the framework of the DF approximation, the auxiliary basis sets (aug-cc-pVQZ/JK and aug-cc-pVQZ/C in the ORCA nomenclature) [53] were used. The multireference character of the wave functions of the reagents, intermediates, and transition states was estimated using the T1 diagnostic during the DLPNO-CCSD(T) calculations [62]. Modest T1 values obtained in all cases (<0.020) indicate that a single reference-based electron correlation procedure is appropriate in the present case. All DLPNO-CCSD(T) calculations were performed using the ORCA 4.2.1 [53,54] set of programs.

The rate constants of monomolecular reactions in the gas phase in the high-pressure limit were computed in accordance with the canonical transition state theory (TST):

$$k\left(T\right)=\alpha \frac{kT}{h}exp\left(-\frac{\mathsf{\Delta }{G}^{\ne }\left(T\right)}{kT}\right),$$

(7)

where α is a statistical factor (a number of equivalent reaction channels), and ΔG^≠(T) is the free energy of activation calculated using the DLPNO-CCSD(T)/jun-cc-VQZ electronic energies and corresponding M06-2X thermal corrections. The TST rate constants were calculated in the temperature range 300–1000 K with a step of 100 K and then approximated by the Arrhenius equation:

$$k=Aexp\left(-\frac{E_a}{RT}\right),$$

(8)

The rate constants of barrierless radical C–NO₂ bond cleavage were estimated using the phase space theory [63,64] implemented in the PAPR software [65]. In the framework of this theory, the interaction between the radical moieties is described with the potential:

$$U=-\frac{C_n}{r^n},$$

(9)

where parameters C_n = 6.0 and n = 5.0 were chosen to match the high-pressure limit of the rate constant of hexogen radical decomposition [66].

To understand the reactivity of DBT and ADBT in the melt, the polarized continuum model (PCM) [67,68] calculations at the M06-2X/6-311++G(2df,p) level of theory were performed. To this end, we calculated the free energy of solvation for all stationary points on the PES for a series of model isotropic solvents with varied polarities, including cyclopentane (ε = 1.96), 2-propanol (ε = 19.26), and dimethyl sulfoxide (ε = 46.83).

To calculate the standard state enthalpies of formation in the gas phase, Δ_fH_m⁰(g) (at p⁰ = 1 bar and T = 298.15 K), the explicitly correlated W1-F12 multi-level procedure [69] along with the atomization energy approach [69,70] was employed. Note that the conventional CCSD(T) calculations typically exhibit slow basis set convergence. This can be remarkably accelerated with the aid of the explicitly correlated F12 modifications [71]. Note that the W1-F12 approach used in this study has been slightly modified from the original version. More specifically, the B3LYP-D3BJ/def2-TZVPP optimized geometries were used (with the ZPE correction factor of 0.99) [72,73], and the diagonal Born-Oppenheimer corrections were omitted. The contributions from post-CCSD(T) excitations to the valence term of the atomization energies were controlled using the %TAE[(T)] diagnostics (viz., the percentage of the perturbative triples (T) in the CCSD(T) atomization energy) [74]. In the present study, these values did not exceed 5%, which supports the reliability of the CCSD(T)-F12 atomization energies calculated using the W1-F12 approach. The latter calculations were performed by the Molpro 2010 software [55]. The heats of formation at 0 K for the elements in the gas phase Δ_fH_m^0K(g) [H] = 216.04 kJ mol⁻¹, Δ_fH_m^0K(g) [C] = 711.19 kJ mol⁻¹, Δ_fH_m^0K(g) [N] = 470.82 kJ mol⁻¹, and Δ_fH_m^0K(g) [O] = 246.79 kJ mol⁻¹ were taken from the NIST-JANAF tables [75].

4. Conclusions

In the present work, we studied thermochemistry, tautomerism, and thermal stability of 5,7-dinitrobenzotriazole (DBT) and 4-amino-5,7-dinitrobenzotriazole (ADBT) using several complementary thermal analysis techniques and high-level quantum chemical calculations. Thermoanalytical experiments under elevated pressure allowed tracking of the thermolysis of DBT in the melt free of the concomitant vaporization. Model-fitting thermokinetic analysis shows that the kinetic scheme with two global consecutive steps provides the best fit for DBT decomposition. The first global stage (I) is a strong autocatalytic process that includes the noncatalytic (E_a1^I = 173.9 ± 0.9 kJ mol⁻¹, log(A₁^I/s⁻¹) = 12.82 ± 0.09) and catalytic reaction of the second order with E_a2^I = 136.5 ± 0.8 kJ mol⁻¹, log(A₂^I/s⁻¹) = 11.04 ± 0.07. The second global stage (II) is of non-integer order and corresponds to the secondary processes with the effective kinetic parameters E_a^II = 134.5 ± 1.8 kJ mol⁻¹, log(A^II/s⁻¹) = 8.7 ± 0.2.

Mechanistic insights into the decomposition process were obtained using quantum chemical calculations. We show that the 1H-5,7-tautomer is a preferable form for both benzotriazoles in the gas phase and solutions. Theoretical calculations reveal a similar primary decomposition mechanism for DBT and ADBT. Namely, the energetically preferable channel is the nitro-nitrite rearrangement, with barriers of 267 and 276 kJ mol⁻¹ for DBT and ADBT, respectively. However, due to significantly higher activation entropies (or, equivalently, preexponential factors), the C–NO₂ cleavage (with the reaction enthalpies of 298 and 320 kJ mol⁻¹, correspondingly) becomes the dominant channel at the experimental temperatures.