Thermochemistry, Tautomerism, and Thermal Decomposition of 1,5

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A: Molecular Structure, Quantum Chemistry, and General Theory

Thermochemistry, Tautomerism, and Thermal Decomposition of 1,5-Diaminotetrazole: A High-Level Ab Initio Study Margarita Shakhova, Nikita V. Muravyev, Nina P. Gritsan, and Vitaly G. Kiselev J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b01608 • Publication Date (Web): 27 Mar 2018 Downloaded from http://pubs.acs.org on March 30, 2018

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The Journal of Physical Chemistry

Thermochemistry, Tautomerism, and Thermal Decomposition of 1,5-Diaminotetrazole: a High-Level ab initio Study Margarita V. Shakhova,a,b Nikita V. Muravyev,c Nina P. Gritsan,a,b and Vitaly G. Kiseleva,b,c,* a b

Novosibirsk State University, 2 Pirogova Str., Novosibirsk, 630090 Russia

Institute of Chemical Kinetics and Combustion SB RAS, 3 Institutskaya Str., Novosibirsk, 630090 Russia c

Semenov Institute of Chemical Physics RAS, 4 Kosygina Str., Moscow, 119991 Russia

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ABSTRACT. Thermochemistry, kinetics, and mechanism of thermal decomposition of 1,5diaminotetrazole (DAT), a widely used “building block” of nitrogen-rich energetic compounds, were studied theoretically at a high reliable level of theory (viz., using the explicitly correlated CCSD(T)F12/aug-cc-pVTZ procedure). Quantum chemical calculations provided detailed insight into the thermolysis mechanism of DAT missing in the existing literature. Moreover, several existing contradictory assumptions on the mechanism and key intermediates of thermolysis were resolved. The unimolecular primary decomposition reactions of the seven isomers of DAT were studied in the gas phase and in the melt using a simplified model of the latter. The two-step reaction of N2 elimination from the diamino tautomer was found to be the primary decomposition process of DAT in the gas phase and melt. The effective Arrhenius parameters of this process were calculated to be Ea = 43.4 kcal mol-1 and log (A/s-1) = 15.2 in a good agreement with the experimental values. Contrary to the existing literature data, all other decomposition channels of DAT isomers turned out to be kinetically unimportant. Apart from this, a new primary decomposition channel yielding N2, cyanamide, and 1,1-diazene was found for some H-bonded dimers of DAT. We also determined a 0 reliable and mutually consistent set of thermochemical values for DAT ( ∆ f H solid = 74.5 ± 1.5

kcal·mol-1) by combining theoretically calculated (W1 multilevel procedure along with an isodesmic 0 reaction) gas phase enthalpy of formation ( ∆ f H gas = 100.7 ± 1.0 kcal·mol-1) and experimentally

measured sublimation enthalpy ( ∆ sub H 0 = 26.2 ± 0.5 kcal·mol-1).


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Introduction Nitrogen-rich heterocyclic compounds are promising components of environmental friendly energetic compositions.1-9 Among them, 1,5-diaminotetrazole (DAT, 1) is prominent due to its good thermal stability and high nitrogen content (~84 wt%).10-12 Besides that, DAT is widely used as a building block for a huge variety of novel high-energy compounds.13-21 Similarly to other tetrazoles, tautomerism is very typical of DAT (Scheme 1).22 However, despite notable experimental and theoretical efforts,22,23 the details of tautomeric equilibria in DAT yet remain unclear. Furthermore, tautomeric transformations are known to play an important role in the mechanism of thermolysis of tetrazole (TZ) and 5-aminotetrazole (5-ATZ).24,25 It is therefore reasonable to expect the same issues in the case of DAT. The standard state of DAT is crystalline with a melting point of 460 K.22 Several tautomeric forms of DAT have been discussed in the literature. In the crystalline state, X-ray diffraction data indicate that DAT exists as an amino-form (1 or 1,5-DAT, Scheme 1).26 He et al.23 performed CCSD(T)/6-311G(d,p) calculations and considered 1 along with its isomer 2,5-diaminotetrazole (2,5-DAT, Scheme 1), which was predicted to lie close to 1 on the enthalpic scale. The authors also calculated activation barriers of the monomolecular interconversion between hypothetical isomers 1, 2, and 2,5-DAT. The H-transfer reaction 1 → 2 has a thermally inaccessible activation barrier of ~62 kcal mol-1, moreover, even higher activation barrier (~75 kcal mol-1)23 was predicted for the sigmatropic shift of amino group in 1 yielding 2,5-DAT (Scheme 1). Thus, monomolecular reactions cannot lead to equilibribration of isomers.

Scheme 1. The Isomers of Diaminotetrazole Considered in the Literature. Brill et al.27 studied thermolysis of four amino-derivatives of tetrazole, including DAT and 2,5DAT. The authors detected the gas decomposition products using rapid-scan FTIR/temperature profiling technique. For both DAT and 2,5-DAT, the two competitive global decomposition pathways were proposed: the one leads to the formation of HCN, NH3, and N2, and another yields NH2CN, NH3, and N2. On the basis of the measured ratio [NH3]/[HCN], the authors estimated the relative contributions of these competitive channels to be approximately 1:1 and 2:1 for DAT and 2,5-DAT, respectively. ACS Paragon Plus Environment

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Levchik et al.28 emphasized an important role of tautomeric transformations (e.g., 1 ↔ 2, Scheme 1) in the mechanism of thermal decomposition of amino-substituted tetrazoles. DAT was proposed to coexist in amino 1 and imino 2 forms in both the solid state and melt, while evaporation shifts the equilibrium to the amino form 1.28 The authors proposed a reversible interconversion 1 ↔ 2 upon evaporation, condensation, and crystallization. Differential scanning calorimetry (DSC) and termogravimetric analysis (TGA) demonstrated that the decomposition of DAT occurred in the melt in the temperature range of 470-540 K. The two main channels of decomposition were proposed for DAT, viz., the imino form 2 decomposes via elimination of HN3 (Scheme 2), which is the predominant process at the early stage of thermolysis, and the amino form 1 decomposes via elimination of N2 leading to formation of a nitrene.28 The latter process was also supposed to dominate at the late stage of thermolysis (Scheme 3). Apart from this, mass-spectrometry indicated that N2 is the predominant gaseous product of DAT thermolysis.28

Scheme 2. The Dominating Decomposition Channel of 1-Imino-5-Amino-Teterazole (2) Proposed in the Literature.

Scheme 3. The Dominating Decomposition Channel of 1,5-DAT (1) Proposed in the Literature. Lesnikovich et al.22 studied thermal decomposition of a series of 1-substituted 5-aminotetrazoles (1-R,5-AT, R = H, CH3, NH2) using experimental techniques (DCS, TGA, analysis of gas products) and quantum chemical calculations at a low level of theory (MP2). HCN, NH3, HN3, and N2 were detected among the most abundant gas products using FTIR and mass-spectrometry. As in the previous study,27 all experimental data for 5-substituted aminotetrazoles were interpreted in terms of the two main channels presented in Schemes 2 and 3. An increase of temperature initiates the decomposition of 1 via the N2 elimination (Scheme 3).22 The authors22 also derived the Arrhenius parameters of mass-loss kinetics of the DAT samples using the non-isothermal TGA data. The activation energy (Ea) and the preexponential factor (A) calculated using different thermokinetic ACS Paragon Plus Environment

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approaches (viz., Ozawa, Coats-Redfern, and Flynn methods) were found to be Ea = 41.8–43.7 kcal mol-1 and log (A/s-1) = 15.9–16.6, respectively. The use of quantum chemical calculations is a very effective way to complement the experiment in the study of elementary reactions of DAT thermolysis. In a recent paper,29 the authors considered solely the gas-phase primary reaction 1 → NH2N3 + NH2CN and predicted the activation energy in the temperature range 200 – 2500 K to be 48.0 kcal mol-1 at the CCSD(T)/6-311G(d,p)//MP2/6311G(d,p) level of theory. To the best of our knowledge, other elementary reactions of the DAT decomposition have never been scrutinized, and tautomeric transformations have not been studied in detail as well. Moreover, the reactions in the H-bonded dimers of DAT have not been considered at all. The main goals of our paper are to investigate the thermodynamic properties of different isomers of DAT and their mutual interconversion, to identify the intermediates of their primary reactions, and to give an insight into the overall mechanism of the DAT thermal decomposition. To this end, we measured thermal properties of DAT including its sublimation enthalpy and calculated the activation barriers of the primary reactions in the gas phase and in the melt using the simplified model of the latter. For the purpose of comparison, the decomposition reactions of 2,5-DAT were considered as well. We also revealed previously unexplored reactions proceeding in the H-bonded dimers of DAT, and demonstrated their importance for equilibration of isomers in the gas phase and melt. Experimental and computational details 1. Quantum chemical calculations Electronic structure calculations were carried out using the Gaussian 0930 and Molpro 201031 program packages. The geometries of each structure corresponding to the stationary point on the potential energy surface (PES) for the DAT decomposition were fully optimized using density functional theory (DFT) at the M06-2X/6-311++G(2df,p) level.32 Zero-point energies and thermal corrections to enthalpy and Gibbs free energy were computed at the same level of theory. Singlepoint electronic energies were afterward refined using an explicitly correlated coupled-cluster formalism CCSD(T)-F12b in conjunction with the correlation consistent basis set aug-cc-pVTZ.33,34 In the case of dimers of DAT and its isomers, the cc-pVDZ-F12 basis set was employed.35 For the sake of brevity, these basis sets are denoted hereafter as aVTZ and VDZ-F12, respectively. Note that the explicitly correlated F12 procedure accelerates the slow basis set convergence of conventional CCSD(T) techniques.36 The moderate size of DAT (7 non-H atoms) renders various coupled-cluster methods feasible in the present case. The extensive benchmarking on a series of related heterocyclic ACS Paragon Plus Environment

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species revealed a perfect agreement (within 0.5 kcal mol-1) between the activation barriers calculated using CCSD(T)-F12b/aVTZ and a multi-level procedure W137 (Fig. S1, Supporting Information). Apart from this, the earlier benchmarks also demonstrated a good agreement between complete basis set extrapolated CCSD(T) and CCSD(T)-F12 values calculated with various correlation consistent basis sets of a double- and triple-zeta quality.38,39 On the basis of these facts, we infer that the CCSD(T)-F12b/aVTZ procedure provides a good balance between computational cost and accuracy. The multireference character of the wave functions of the reagents, intermediates, and transition states considered in the present work was estimated using the T1 diagnostic for the CCSD calculations.40 The modest T1 values obtained in all cases (> k1b, Table 2). Thus, the effective rate constant of N2 formation reads as )*+,, ≅

./0

.1/0

)* (Table 3). It is

also worth mentioning that the activation energies of the elementary reactions )*2 , )3*2 and )* (Table 3) coincide well with the estimations proposed by Prokudin et al.51 for a series of 1,5substituted derivatives of tetrazole.

Scheme 4. Kinetic Scheme of the Primary Decomposition Channel of the Tautomer 1. Note that the computations do not support the formation of the nitrene intermediate (Scheme 3) proposed earlier.22,28 Moreover, contrary to the case of DAT (Scheme 4), the two-step N2 elimination in the case of tetrazole (TZ) and 5-ATZ yields the non-cyclic products as a result of a Curtius-like rearrangement.24,25 The activation barrier of the closest competing channel of 1 decomposition (TS2, Fig, 4, left side) is ~4 kcal mol-1 higher than that of Scheme 4. This reaction yields three products, viz., N2, cyanamide, and 1,1-diazine (Fig. 4). Note that such process is very specific for DAT in comparison with other 1-substituted tetrazoles due to enhanced stabilization of 1,1-diazine, which is a singlet aminonitrene, in comparison with similar simple singlet nitrenes (e.g., :NH or :N-CH3).52,53 The elimination of azide NH2N3 (TS3, Fig. 4, left side) is ~10 kcal mol-1 higher than the primary channel (Scheme 4). Although the former reaction has been scrutinized in detail in a recent computational work,29 it turned out to be entirely unimportant kinetically. Note that in a similar way, the N2 elimination dominates over the channels leading to corresponding azides for TZ and 5ATZ.24,25


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Apart from the above discussed main decomposition channel of 1 (Scheme 4), there are two other minor channels proceeding through the azide 1a (Fig. 5). Although being kinetically unimportant, they are worth to be discussed for particular reasons. First, the hydrogen atom transfer in the azide 1a followed by subsequent recyclization to 5-hydrazino-1H-tetrazole 1c (Fig. 5, left side) was already proposed as a plausible mechanism of DAT transformation upon thermolysis.22 However, Figure 5 demonstrates that the corresponding activation barriers (i.e., those of cis-trans isomerization of 1a, TSc-t, and of the H-transfer, TSH) are too high in comparison with the dominating N2 elimination (cf. TS1b, Fig. 4). Besides that, we found another isomeric form of the azide 1a, viz., a zwitterionic intermediate 1z (Fig. 5, right side). The activation barrier of the H-transfer between amino groups (TS1z, Fig. 5) is close to the endothermicity of reaction 1a → 1z, and the account of the zero-point energies even drops the enthalpy of TS1z slightly below that of 1z (Fig. 5). Under thermolysis conditions, the 1z is thermally accessible and could be an intermediate, provided the presence of a decomposition channel with low enough activation energy. However, the lowest one, viz., HN3 elimination, has an activation barrier (TS2z, Fig. 5), which is almost 15 kcal mol-1 higher than TS1b (Fig. 4), thus rendering this channel to be minor as well. The details of recyclization reactions of both conformers of 1a are given in the Supporting Information (Section 5, Fig. S6).

Figure 5. The relative thermodynamic parameters of the stationary points on the PES corresponding to thermal decomposition of DAT via the intermediacy of the azide 1a. 1 was chosen as a reference compound for the calculations of the relative thermodynamic properties. The electronic energies were calculated at the CCSD(T)-F12b/aVTZ level of theory using the M06-2X/6-311++G(2df,p) optimized geometries. Zero-point energies and thermal corrections to thermodynamic potentials were computed at the same level of theory. All energy values are given in kcal mol-1. ACS Paragon Plus Environment

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For tautomer 2, the concerted elimination of N2 is indeed the most favorable decomposition channel (TS4, Fig. 4). The competing reactions of the azide elimination (HN3 and NH2N3) have notably higher activation barriers (TS5, TS6, Fig. 4). Therefore, our calculations do not confirm the literature assumption that 2 decomposes primarily to HN3 and P6 (Scheme 2).22 On the contrary, this channel is the least favorable kinetically among all counterparts (Fig. 4, lower part). Moreover, due to high values of effective activation barriers of all decomposition reactions (TS4-TS6, Fig. 4), the tautomer 2 does not play an important role as an intermediate of DAT thermolysis. It is also worth mentioning that DAT has another thermodynamically favorable isomer – 2,5-DAT (Fig. 2, Table 1). For the sake of comparison, we studied its decomposition as well. The most favourable channel of 2,5-DAT decomposition is the concerted reaction of N2 elimination (Fig. 6). The activation barrier of this reaction is more than 20 kcal mol-1 lower than that of competing elimination of azide NH2N3. Note that the effective activation barrier of 2,5-DAT decomposition is notably lower than that of its counterpart 1 (cf. Fig. 4 and 6). However, as was discussed above (Section 2), the interconversion of 1 and 2,5-DAT has a very high activation barrier (~73 kcal mol-1, Fig. 2). The 2,5-DAT isomer is not accessible from the PES region corresponding to 1 under thermolysis conditions. Thus, the reactions of 2,5-DAT are entirely unimportant for kinetic mechanism of DAT thermolysis, but provide insights for the mechanism of thermolysis of this particular species.

Figure 6. The relative thermodynamic parameters of the stationary points on the PES corresponding to thermal decomposition of 2,5-DAT. 1 was chosen as a reference compound for the calculations of the relative thermodynamic properties. The electronic energies were calculated at the CCSD(T)F12b/aVTZ level of theory using the M06-2X/6-311++G(2df,p) optimized geometries. Zero-point ACS Paragon Plus Environment

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energies and thermal corrections to thermodynamic potentials were computed at the same level of theory. All energy values are given in kcal mol-1. Table 3. The Arrhenius Parameters of the Rate Constants of 1, 2, and 2,5-DAT Decomposition. The Transition States are Denoted in Accordance with Figures 4 and 6. Rate constant

log (A/s-1)

Ea, kcal mol-1

1 → 1a (TS1a)

k1a

13.7

27.5

1a → 1 (TS1a)

k-1a

12.4

17.1

1a → P1 + N2 (TS1b)

k1b

13.7

28.0

1 → P1 + N2

k1eff

15.2

43.4

1 → NH2CN + N(NH2) + N2 (TS2)

k2

14.7

46.8

1 → NH2CN + NH2N3 (TS3)

k3

14.5

54.2

2 → P4 + N2 (TS4)

k4

13.7

39.6

2 → NH=C=NH + P2 (TS5)

k5

14.0

45.4

2 → P6 + HN3 (TS6)

k6

14.9

55.6

2,5-DAT → P7 + N2 (TS7)

k7

14.2

35.0

2,5-DAT → NH2CN + NH2N3 (TS8)

k8

14.3

57.3

Reaction

4. Influence of the environment on the decomposition reactions of DAT isomers All calculations discussed so far refer to the gas phase. However, the DAT decomposes at the temperatures above the melting point.22,28 Thus, for understanding and interpretation of experimental results we need a correct account for the melt. As a rough approximation, we can use the rate constants of elementary reactions calculated for a gas phase (Table 3). However, the next logical step is to estimate these elementary rate constants by representing the melt as an isotropic dielectric medium as implemented in the widely used PCM models.44,45 Note that such models allow for correct statistical averaging over all numerous local conformational minima, e.g., in the first coordination sphere of a particular molecule studied. We have already explicitly accounted for some effects of melt by considering the double H-transfer in the dimers of 1 and 2 (Section 2). The use of more sophisticated consistent models, e.g., explicit consideration of all molecules in the first coordination sphere (with a proper statistical averaging) placed in the isotropic medium, is unfortunately an intractable problem. Since the estimation of the dielectric properties of DAT is also


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problematic, we performed PCM calculations for the typical model solutions with moderate (ε = 6.8, aniline was used as a model solvent) and high polarity (ε = 35.7, acetonitrile). Calculations demonstrate (SI, Section 6, Figures S7 and S8) that account for the plausible dielectric properties of melt has a marginal impact on the thermolysis mechanism. The differences in the solvation free energy of the rate-limiting transition states of the lowest energy decomposition channels (TS1b, TS2-TS4, Fig. 4) do not exceed 2 kcal mol-1 for the medium with ε = 6.8 and remain insignificant even for a very high ε = 35.7. Thus, we used the results of Figures 4-6 and Table 3 for subsequent mechanistic analysis. However, the specific interactions in the melt can make a serious impact on the decomposition mechanism of DAT. E.g., in the case of 5-ATZ, entirely new decomposition pathways appear in the H-bonded dimers.25 As the isomers 1 and 2 are also liable to forming H-bonded complexes, we analyzed their decomposition reactions in selected dimers D1 and D2 (Fig. 3). It should be noted that a vast number of complexes could be proposed even for the tautomers 1 and 2, and primary products of their decomposition. We studied in detail only some of them in order to show important distinctions from the conventional single-molecule consideration (e.g., Fig. 4, Scheme 4). As an example, Figure 7 demonstrates the two lowest decomposition channels for the dimer D1, which is comprised of two 1 moieties (cf. Fig. 3). All other minor channels of D1 and D2 decomposition are given in the Supporting Information (Section 7).

Figure 7. The relative enthalpies at 0 K ( ∆ ( ∆H

0K

) , black numbers), relative enthalpies at 298 K (

0 ∆ (∆H 0 ) , green numbers), and Gibbs free energies at 298 K ( ∆(∆G ) , red numbers) of the

stationary points on the PES corresponding to thermal decomposition of a hydrogen bonded dimer ACS Paragon Plus Environment

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D1 of 1,5-DAT (1) moieties. D1 was chosen as a reference for relative thermodynamic properties. The electronic energies were calculated at the CCSD(T)-F12b/VDZ-F12 level of theory energies using the M06-2X/6-311++G(2df,p) optimized geometries. Zero-point energies and thermal corrections to thermodynamic potentials were computed at the same level of theory. All energy values are given in kcal mol-1. Analysis of the decomposition channels in the dimers D1 and D2 (Supporting Information, Section 7) demonstrates that the main stable product of the dominating channel, viz., N2, remains the same for monomer and dimer reactions. Moreover, the Arrhenius parameters of the D1 decomposition via TSD2 are Ea = 42.5 kcal mol-1 and log (A/s-1) = 14.4, which are almost identical to those of k1eff (Ea = 43.4 kcal mol-1 and log (A/s-1) = 15.2, Table 3). Discussion Figures 4 and 5 and Figure S3 (SI) demonstrate that the decomposition of all DAT isomers lead preferentially to the formation of N2, the eliminations of azides (NH2N3 or HN3) are profoundly slower. In the TGA/GS-MS and T-jump/FTIR experiments, HCN, NH2CN, NH3, HN3, and N2 were detected as final products of DAT decomposition.22,27 The most intense bands in the IR spectra were assigned to HCN and NH3.27 It should be noted that the N3-stretching mode has very high intensity in the IR spectrum, and its detection does not rule out that HN3 is actually a minor, but not the most abundant product. Most likely, almost all identified simple decomposition products of DAT are formed in the secondary reactions (cf. Fig. 4 and 6). To get insight into the primary stage of DAT thermolysis, one should combine the results given in two previous sections. Figure 3 shows that the activation barrier of interconversion between 1 and 2 isomers in the dimer D1 is less than 20 kcal mol-1, which is noticeably lower than that of the monomolecular decomposition of 1 and 2 (Fig. 4). This implies that the mutual interconversion of 1 and 2 isomers in the dimer is significantly faster than the subsequent monomolecular reactions of N2 elimination. If to take into account the equilibrium between 1 and 2, the effective rate constant of DAT thermal decomposition reads as *

)+,, = *45

6/

)*+,, + )7 ∙ #8*

(8),

where #8* is the equilibrium constant: #8* = exp −

∆

Thermochemistry, Tautomerism, and Thermal Decomposition of 1,5

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