Theoretical studies on the stability of phenylpentazole and its substituted derivatives of –OH, –OCH₃, –OC₂H₅ and –N(CH₃)₂

Abstract

Phenylpentazole (PhN₅) and its derivatives with 1–3 electron donating substituents (–OH, –OCH₃, –OC₂H₅ and –N(CH₃)₂) were studied using density functional theory. The pyrolysis mechanism and effects of substituents on stabilities were discussed. The activation energies (E_as, 362–402 kJ mol⁻¹) for the cleavage of the C–N bonds linking the aryl and the pentazole are far larger than those (109–117 kJ mol⁻¹) for the breaking of the N–N bonds in the pentazole ring. Decomposition of the pentazole ring should be the initial step of pyrolysis of arylpentazole and its derivatives. The pentazole ring in PhN₅ is stabilized by substituents which increase the electron density and strengthen the delocalization of the N₅ ring. The abilities of these substituents to improve E_a and to decrease the frontier orbital energy gap (E_g) have the same order: –N(CH₃)₂ > –OC₂H₅ > –OCH₃ > –OH.

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1. Introduction

Nitrogen-rich compounds, such as triazole, tetrazole and pentazole, are important azole-ring compounds. They are extensively found in purine, pyrimidine and natural products,¹ and many synthetic drugs also contain these nitrogen-rich azole rings.² In addition, azole compounds have high nitrogen contents, high heats of formation (HOFs), high solid-state densities^3–8 and more environmentally benign decomposition products. Hence, they are widely used in medicinal chemistry and the military,^2,9,10 and have been attracting significant interest in recent years.

Many triazole and tetrazole derivatives have been synthesized and studied.^11–21 Great progresses have been made in developing compounds based on triazole or tetrazole. On the other hand, researches on pentazole, which has an all-nitrogen five-membered ring and possesses strong aromaticity and high HOF (107.5 kcal mol⁻¹),²² have not yielded fruitful results. In 1903, Hantzsch et al. tried to prepare arylpentazole (PhN₅, A) but they failed.²³ Until 1956, PhN₅ was synthesized at low temperature by Huisgen and Ugi.²⁴ 4-Hydroxyphenylpentazole (A11, Fig. 1) was synthesized through cycloaddition reaction in 2002 by Benin et al.²⁵ Although this reaction is very fast, many by-products appear. 4-Dimethylaminophenylpentazole (A14) and anisylpentazole (A12) were produced in 2003 and 2008, respectively.^26,27 In addition, Frison et al. proposed that syntheses of some mono- and di-oxidized pentazole derivatives seem to be realistic.²⁸ Although some other pentazole derivatives have also been studied,^29–33 the development of pentazole derivatives is much slower in comparison with that of triazole and tetrazole derivatives. This is mainly because the N₅ ring easily decomposes.^25–27 In recent years, several photochemistry experimental investigations reveal that the N₅ rings of arylpentazole derivatives such as p-(dimethylamino)phenyl pentazole (DMAP) and p-oxidophenylpentazole easily decompose into N₂ and the corresponding phenyl azides.^34–36 Hence, the low stability of the N₅ ring should be the crucial factor in preventing the development of the pentazole derivatives.

Fig. 1 Structures of the title compounds.

In addition, the central C–N bond connecting the aryl and the pentazole may break. This is supported by the experiments of Östmark et al.²⁶ and Vij et al.³⁷ which have detected N₅⁻ in gas phase from high-energy mass spectrometric degradation of arylpentazoles. So, which can take place more easily and is the initial step of pyrolysis of arylpentazoles, breaking of the central C–N bond or the N₅ ring? Furthermore, we find that the synthesized PhN₅ compounds are mainly the substituted derivatives with –OH, –OCH₃ and –N(CH₃)₂, which seems to show that the electron donating groups may stabilize PhN₅. If this is the case, why can they stabilize PhN₅ and what's the difference in effects of different substituents? In view of the facts that the synthesized PhN₅ derivatives are limited and have low stabilities, above questions can not be answered by experiment at present. Fortunately, with the rapid development of computer technology, structures and properties of nitrogen-rich compounds can be accurately predicted.^{27–29,38–47} In this paper, the stabilities and pyrolysis mechanisms of PhN₅ and its derivatives were theoretically studied, and the effects of different substituents (–OH, –OCH₃, –OC₂H₅ and –N(CH₃)₂) on the stability of PhN₅ were investigated to answer the above questions. The structures of the title molecules are plotted in Fig. 1.

2. Computational details

Geometry optimizations of A and its derivatives were carried out using the restricted Kohn–Sham formalism at the RB3LYP/6-31G* and RM06-2X/6-311G** levels. The optimized structures were confirmed to be local minima without imaginary frequencies.

The relaxed potential energy surface scans along the stretching of the C–N bond and the N–N bonds were carried out at the RB3LYP/6-31G* level for searching transition states (TSs). Then, the structures of the discovered TSs were optimized at the RM06-2X/6-311G** level, which is reliable for computation of transition state.^48–51 The optimized TSs were confirmed by only one imaginary frequency.

The optimized structures of A, its derivatives and TSs are shown in Fig. S1.† After optimization, the pentazole and benzene rings in A and its derivatives are coplanar. The HN₅ and benzyne (C₆H₄) and its derivatives (C₆H₃R) in the optimized structures of TS1 are coplanar, too. The N₂, azide group and the benzene ring are not coplanar in the optimized conformations of TS2.

The methyl groups in A12, A16, and A22 are all coplanar with the benzene ring. One methyl group in A32 is coplanar with the benzene ring. All ethyl groups in A13, A17, A23, A26 and A36 are coplanar with the benzene ring. One of 2–3 ethyl groups in A33 and A35 is coplanar with the benzene ring. No ethyl group in A25 is coplanar with the benzene ring.

The OH group in all molecules is coplanar with the benzene ring. The N(CH₃)₂ groups in A14, A18 and A24 are essentially coplanar with the benzene ring, while in A26 and A36 are almost perpendicular to the benzene ring.

One and two hydrogen bonds are found in A25 and A36, respectively. The hydrogen bond energies are 13.6 kJ mol⁻¹ for A25 and 41.0 kJ mol⁻¹ for A36, respectively. There is no hydrogen bond in A31. The conformations of A25 and A36 with hydrogen bond paths are shown in Fig. S2.†

Geometry optimizations of the radicals produced in breaking of the central C–N bond were carried out at the UM06-2X/6-311G** level. All geometry optimizations and relaxed potential energy surface scans were computed with the Gaussian program package.⁵²

The bond dissociation energy (BDE), the energy difference between the parent molecule and the corresponding radical products in the unimolecular bond dissociation,^53–56 was calculated using the following equation:

BDE = E_R1˙ + E_R2˙ − E (1)

where E represents the zero-point-corrected total energy of A and its derivatives obtained at the RM06-2X/6-311G** level, E_R1˙ and E_R2˙ stand for the zero-point-corrected total energies of two radicals obtained at the UM06-2X/6-311G** level. In this paper, only BDE for breaking of the central C–N bond was computed.

The activation energy (E_a) was obtained by eqn (2):

E_a = E_TS − E_R (2)

E_TS and E_R respectively represent the total energies of TS and reactant obtained at the RM06-2X/6-311G** level.

The density of electron at the bond critical point of the central C–N bond (ρ_BCP) was analyzed using the Multiwfn⁵⁷ program. The wavefunction files (.wfn) obtained from the Gaussian package were used as inputs for Multiwfn to perform these quantum theory of atoms in molecules (QTAIM)⁵⁸ analyses.

3. Results and discussion

3.1 Stability of the central C–N bond

Density of electron at the bond critical point (ρ_BCP) is tightly related to the bond strength, the increase in ρ_BCP is usually consistent with the increment in the bond strength. ρ_BCP of the central C–N bond connecting the benzene and pentazole rings and the differences in ρ_BCP (Δρ_BCPs) between derivatives and A are tabulated in Table 1. The positive Δρ_BCPs of A11–A14 suggest that the para-substitution strengthens the C–N bond. While the negative Δρ_BCPs of A12′–A14′ and A22–A24 reflect that the meta-substitution weakens the C–N bond. Δρ_BCPs of A25–A26, A31–A32 and A35 are positive, which suggests that the effects on the C–N bond strengths caused by the para-substitution are stronger than by the meta-substitution.

Table 1 Predicted ρ_BCP and Δρ_BCP of C–N bond^a

		n = 1	n = 2	n = 3	n = 4	n = 5	n = 6
a ρBCP of A is 0.269916 a.u.
A1n	ρBCP (a.u.)	0.270719	0.270477	0.270352	0.270585
	ΔρBCP (a.u.)	0.000803	0.000561	0.000436	0.000669
A1n′	ρBCP (a.u.)	0.270285	0.269348	0.269190	0.267478
	ΔρBCP (a.u.)	0.000369	−0.000570	−0.000730	−0.002440
A2n	ρBCP (a.u.)	0.270546	0.269066	0.268735	0.265553	0.270899	0.270333
	ΔρBCP (a.u.)	0.000630	−0.000850	−0.001180	−0.004360	0.000983	0.000417
A3n	ρBCP (a.u.)	0.271165	0.270117	0.269728	0.269123	0.270474	0.269290
	ΔρBCP (a.u.)	0.001249	0.000201	−0.000190	−0.000790	0.000558	−0.000630

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Experimental researches show that N₅⁻ can be detected in gas phase from high-energy mass spectrometric degradation of arylpentazoles.^26,37 This means that the C–N linkage connecting the aryl and pentazole breaks. Cleavages of the C–N bonds of A and its derivatives were simulated using a relaxed potential energy surface scan for studying the thermal and kinetic stabilities of this bond. The simulated energy variation with breaking of the C–N bond of A is shown in Fig. 2 (left). Since the energy variation curves of derivatives are similar, only that of A21 is presented in Fig. 2 (right).

Fig. 2 Variation of energy with the length of C–N bond of A (left) and A21 (right).

The energy of A increases with the elongation of the C–N bond, and the slope of the curve decreases gradually. The energy will finally reach a constant and no TS exists in this decomposition process. The products are two radicals, i.e., pentazole radical (N₅˙) and benzene radical (Ph˙) (cf. Fig. 3). The energy of A21 increases first and then decreases, finally reaches a constant. The maximum point indicates that a TS exists in this decomposition process due to the H transfer and structural rearrangement. In fact, we found that the C–N bond of A may also break via a TS to produce molecules, not radicals, and that of A21 may also break without through a TS to produce radicals rather than molecules. So there are two possible pyrolysis processes of the central C–N bond: (1) C–N bond breaks without a TS and finally produces two radicals. The energy (BDE) needed for this path is the energy difference between two radicals and parent molecule; (2) C–N bond breaks through a TS and produces two ground state molecules (HN₅ and benzyne (C₆H₄) derivatives). The minimum energy required for this path is the activation energy (E_a,1), i.e., the energy difference between the total energies of TS and reactant. In order to figure out the more preferred breaking process of the C–N bond, two pyrolysis paths of all derivatives were studied. Taking A as example, these two paths are shown in Fig. 3. The calculated BDE and E_a,1 are listed in Table 2.

Fig. 3 Two possible pyrolysis paths of the C–N bond of A.

Table 2 Predicted BDE and E_a,1 at the M06-2X/6-311G** level^a

		n = 1	n = 2	n = 3	n = 4	n = 5	n = 6
a BDE and Ea,1 of A are 534.9 and 375.6 kJ mol^−1, respectively.
A1n	BDE (kJ mol^−1)	540.4	541.2	541.9	548.2
	Ea,1 (kJ mol^−1)	391.8	396.9	397.1	401.8
A1n′	BDE (kJ mol^−1)	534.0	535.6	536.1	539.5
	Ea,1 (kJ mol^−1)	362.5	367.1	367.9	373.9
A2n	BDE (kJ mol^−1)	533.7	536.5	537.3	543.9	538.1	535.8
	Ea,1 (kJ mol^−1)	371.8	373.7	374.8	382.2	367.2	367.4
A3n	BDE (kJ mol^−1)	537.6	536.6	540.8	544.9	538.2	537.7
	Ea,1 (kJ mol^−1)	371.2	369.6	374.2	382.4	355.8	370.7

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For path 1, BDEs are all higher than 533 kJ mol⁻¹. In view of these large values, pyrolysis through path 1 should be difficult. Compared with the corresponding BDEs, E_a,1s are lower by 144–172 kJ mol⁻¹. Therefore, path 2 is easier to proceed than path 1, which means that breaking of the C–N bond is more likely to follow the path 2 rather than 1, with the products of HN₅ and derivatives of C₆H₄. In addition, the acidity of HN₅ was estimated to be stronger than that of HNO₃.⁵⁹ This explains why N₅⁻ appears in the gaseous state of PhN₅.^26,37

E_a,1s have the order of A11 < A12 < A13 < A14, A11′ < A12′ < A13′ < A14′, A21 < A22 < A23 < A24, and A32 < A31 < A33 < A34. E_a,1 of A32 is smaller than that of A31, which may be because the steric repulsion is stronger in the former than in the latter. Generally speaking, the C–N bonds of the molecules with –N(CH₃)₂ are most stable, and those of the molecules with –OCH₃ and –OC₂H₅ have comparable stabilities. This conclusion is in accordance with the variation trends of BDEs.

E_a,1s of A11–A14 are larger than that of A, i.e., C–N bonds of A11–A14 are stronger than that of A, which is consistent with the fact that ρ_BCPs of A11–A14 are larger than that of A. E_a,1s of A11′–A14′ are smaller than that of A. These suggest that the para-substituents improve the thermal stability of the C–N bond, while the meta-substituents decrease the stability. E_a,1s of A31–A34 are close to the corresponding ones of A21–A24 while smaller than those of A11–A14, because steric repulsions are stronger in A21–A24 and A31–A34 than in A11–A14. The lower symmetries and stronger repulsion interactions of A25 and A26 result in the fact that E_a,1s of them are lower than that of A21–A24.

E_a,1 or the stability of the C–N bond, is affected by the different substituents and substitution positions which lead to different symmetries and steric repulsions. BDE and E_a,1 obtained at the B3LYP/6-31G* level (in Table S1†) lead to similar conclusions.

3.2 Stability of the pentazole ring

According to experimental investigations,^{25–27,34–36,60} A and its derivatives easily decompose into N₂ and azido compounds. This suggests that breaking of the N–N bonds of the N₅ ring may take place. Hence, a relaxed potential energy surface scan along stretching of two N–N bonds (labelled as SC1 and SC2) was carried out to simulate the decomposition of the pentazole ring. The simulated energy surface of A24 is plotted in Fig. 4. After geometry optimizations of possible TS structures, one TS was found and shown in Fig. 4, too.

Fig. 4 Potential energy surface with breaking of N–N bonds of A24.

Fig. 5 shows the TSs and products of decompositions of the N₅ ring of A and A11. For other molecules, the processes are similar. In the pyrolysis processes, TSs appear when SC1 and SC2 elongate respectively to about 1.70 and 1.75 Å, N₂ and azido benzene derivatives finally emerge as products. Conversion of the reactant into TS is the key step in decomposition of the N₅ ring, the activation energy (E_a,2) of this step is listed in Table 3.

Fig. 5 Decompositions of the N₅ ring of A and A11.

Table 3 Predicted E_a,2s and Q_ts of all derivatives at the M06-2X/6-311G** level^a

		n = 1	n = 2	n = 3	n = 4	n = 5	n = 6
a Ea,2 and Qt of A is 112.6 kJ mol^−1 and −0.471e, respectively.
A1n	Ea,2 (kJ mol^−1)	114.5	114.9	114.9	116.7
	Qt (e)	−0.486	−0.487	−0.489	−0.506
A1n′	Ea,2 (kJ mol^−1)	111.6	113.9	114.0	115.2
	Qt (e)	−0.471	−0.475	−0.476	−0.479
A2n	Ea,2 (kJ mol^−1)	111.6	114.2	114.4	116.8	113.7	109.2
	Qt (e)	−0.475	−0.479	−0.482	−0.484	−0.486	−0.484
A3n	Ea,2 (kJ mol^−1)	114.2	114.0	113.4	117.4	114.9	113.4
	Qt (e)	−0.484	−0.484	−0.488	−0.493	−0.493	−0.483

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E_a,2s required for breaking the N₅ rings of A and its derivatives are 109–118 kJ mol⁻¹, which are far smaller than E_a,1s for breaking the C–N bonds through path 2 (>355 kJ mol⁻¹). Obviously, decomposition of the N₅ ring is much easier than breaking of the C–N bond, so decomposition of the N₅ ring may be the initial step of pyrolysis of these molecules. This conclusion is consistent with the experimental results.^{25,27,34–36}

E_a,2s of derivatives are generally larger than that of A. Although the increases in E_a,2 caused by introduction of electron donating groups are not significant, these groups generally do improve the stability of the pentazole. The total charges (Q_ts) of five N atoms in the N₅ ring were calculated and are listed in Table 3, too. Q_ts of all molecules but A11′ are more negative than that of A, that is, these substituents increase the electron density of N₅ in A which may strengthen the delocalization of the N₅ ring and stabilize this ring. Inspections of E_a,2s and Q_ts of A11–A14, A11′–A14′ and A21–A24 reveal that the increments in stability and electron density of the N₅ ring caused by these substituents generally have the order of –N(CH₃)₂ > –OC₂H₅ > –OCH₃ > –OH. This reveals that the abilities of these functional groups to improve the stability of A have the order of –N(CH₃)₂ > –OC₂H₅ > –OCH₃ > –OH. Q_ts of A31 and A32 are the same, E_a,2 of the former is larger than that of the latter, which is benefit from the weaker steric repulsion of the former in comparison with the latter. E_a,2s and the absolute values of Q_ts of A11′–A14′ are smaller than the corresponding ones of A11–A14, so the pentazoles of the para-substituted molecules are more stable than those of the meta-substituted molecules. E_a,2s and Q_ts calculated at the B3LYP/6-31G* level (Table S2†) lead to similar conclusions.

3.3 Chemical stability

Table 4 summarizes the highest occupied molecular orbital energy (E_HOMO), the lowest unoccupied molecular orbital energy (E_LUMO) and the energy gap (E_g) between the frontier orbitals. Variation trends of them are plotted in Fig. 6. This figure shows that the variation trends of E_HOMO and E_LUMO are the same, which are completely contrary to that of E_g. E_HOMOs and E_LUMOs of all derivatives are higher than that of A, while increases in E_LUMOs are smaller than that in E_HOMOs. Therefore, E_gs of derivatives are smaller than that of A, i.e., these electron donating substituents lower the chemical stability of PhN₅.

Table 4 Predicted E_HOMO, E_LUMO and E_g at the M06-2X/6-311G** level^a

		n = 1	n = 2	n = 3	n = 4	n = 5	n = 6
a EHOMO, ELUMO and Eg of A are −8.91, −1.11 and 7.80 eV, respectively.
A1n	EHOMO (eV)	−8.24	−8.10	−8.07	−7.09
	ELUMO (eV)	−0.89	−0.84	−0.82	−0.55
	Eg (eV)	7.35	7.26	7.25	6.54
A1n′	EHOMO (eV)	−8.42	−8.24	−8.20	−7.20
	ELUMO (eV)	−1.09	−1.08	−1.06	−0.83
	Eg (eV)	7.33	7.16	7.15	6.37
A2n	EHOMO (eV)	−8.28	−8.19	−8.13	−6.79	−7.98	−7.86
	ELUMO (eV)	−1.10	−1.05	−1.00	−0.58	−0.97	−0.99
	Eg (eV)	7.17	7.13	7.12	6.21	7.01	6.87
A3n	EHOMO (eV)	−7.92	−8.09	−7.91	−6.78	−7.21	−8.03
	ELUMO (eV)	−0.92	−0.99	−0.84	−0.69	−0.83	−0.94
	Eg (eV)	7.00	7.10	7.07	6.09	6.38	7.09

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Fig. 6 Variations of E_HOMOs, E_LUMOs and E_gs of title compounds.

E_gs of A11–A14 are larger than the corresponding ones of A11′–A14′, i.e., the para-substituted molecule is more stable than the meta-substituted molecule in chemical process with electron transfer. Inspections of the variations of E_gs of A11–A14, A11′–A14′ and A21–A24 show that E_gs of derivatives with different substituents have the order of –OH > –OCH₃ > –OC₂H₅ > –N(CH₃)₂. Effects on the chemical stability caused by these substituents are completely contrary to that on the thermal stability, i.e., the substituent that leads to the greater increment in thermal stability causes the larger decrease in the chemical stability. The E_gs of the derivatives with –OCH₃ and –OC₂H₅ are very close, which is similar to their comparable thermal stabilities. Comparisons of E_gs of A11–A14, A21–A24 and A31–A34 reveal that the chemical stability decreases with the increasing number of substituents. E_gs in Table S3† obtained at the B3LYP/6-31G* level have the same variation trends to those obtained at the M06-2X/6-311G** level.

4. Conclusion

Decomposition of the N₅ ring (E_a,2 = 109–117 kJ mol⁻¹) is much easier than breaking of the central C–N bond (E_a,1 = 362–402 kJ mol⁻¹), and should be the initial step of pyrolysis of PhN₅ and its derivatives with the products of N₂ and azido benzene derivatives. Substituents somewhat improve the thermal stability of the N₅ ring by increasing the electron density of the N₅ ring with the order of –N(CH₃)₂ > –OC₂H₅ > –OCH₃ > –OH. The para-substitution is more helpful for improving the thermal stability than the meta-substitution. Higher symmetry and weaker steric interactions are also helpful for improving thermal stability. Substituents lower the chemical stability of PhN₅ with the order of –OH > –OCH₃ > –OC₂H₅ > –N(CH₃)₂.

Acknowledgements

Thanks to the 086 Project for supporting this research.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4ra10669e

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