Pyridylpentazole and its derivatives: a new source of N₅⁻?

Abstract

Pyridylpentazole (PyN₅) and its derivatives with 1–2 electron withdrawing groups (–NO₂, –CN, –CF₃ and –NF₂) were studied using density functional theory to assess their potentials as the source of pentazole anion N₅⁻ for replacement of phenylpentazole (PhN₅). N₅⁻ can be produced more easily from PyN₅s because the activation energies (E_a,1 = 364.7–387.1 kJ mol⁻¹) for the cleavage of the central C–N bonds of PyN₅s are lower than that of PhN₅ (395.3 kJ mol⁻¹) and the C–N bond decomposition reactions of the former are faster than that of the latter. The energies (E_a,2) required for dissociation of the N₅ ring of PyN₅s (67.6–84.1 kJ mol⁻¹) are smaller than that of PhN₅ (88.7 kJ mol⁻¹), and the rates of the former are faster than that of the latter. Comparing the stabilities of the C–N bond and the N₅ ring of PyN₅s and PhN₅, the decrement in the C–N bond stability (2.1–7.8%) caused by the pyridine ring and substituents is less obvious than that of the N₅ ring (12.7–23.7%). Although N₅⁻ can be obtained more easily and faster from PyN₅s than PhN₅, the smaller E_a,2 makes PyN₅s less stable than PhN₅, so pyridylpentazoles may not be a better source of N₅⁻ than phenylpentazole.

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1. Introduction

In recent years, poly-nitrogen and nitrogen-rich compounds have received copious attention due to their chemical interest and potential as high energy density materials (HEDMs) that are environmentally friendly.^1–9 However, the highly positive heats of formation make safe synthesis and processing of poly-nitrogen and nitrogen-rich compounds a major challenge.¹⁰ The detection of N₅⁻ (ref. 11 and 12) brings hope for the syntheses of stable nitrogen-rich compounds, since a theoretical study showed that N₅⁻ has an acceptable stability (pyrolysis activation energy E_a = 113.0 kJ mol⁻¹).¹³ Lein et al.¹⁴ and Tang et al.¹⁵ pointed out that metals can stabilize N₅⁻. Significant interest has been shown in finding suitable metal cations and the various properties of a great deal of metal complexes of N₅⁻ have been investigated, e.g., the stability;^5,16–19 the bonding interactions of Fe(η⁵-N₅)₂ with D_5d symmetry; the most stable conformation of MN₅ (M = Li⁺, Na⁺, K⁺, Rb⁺);²⁰ the structures, dissociation enthalpies and aromaticities of M₂(ηⁿ-N₅)₂ (M = Be, Mg; n = 1, 2) and Ca₂(ηⁿ-N₅)₂ (n = 2, 5);¹⁸ equilibrium geometry, thermochemistry, and bonding interactions of Ir₂(N₅)₄.^15,21 These investigations reveal that N₅⁻ salts have high kinetic stability and high energy content, which means that metal complexes of N₅⁻ have immense potentials as HEDMs.¹⁰ However, syntheses of these complexes face a major challenge of preparation of N₅⁻, so discovering the good source of N₅⁻ should be the key issue for preparation of potential energetic materials with N₅⁻.

Previous study⁵ proposed that phenylpentazole (PhN₅) can be used as the N₅⁻ source. This suggestion is supported by the experiments of Ostmark et al.¹² and Vij et al.¹¹ who detected that the central C–N bond linking the phenyl and pentazole rings could break and N₅⁻ exists in gas phase from high-energy mass spectrometric degradation of phenylpentazole. In addition, our recent study has shown that HN₅ can be produced by breaking of the C–N bond of PhN₅ and its derivatives with electron donating group.²² And the acidity of HN₅ was estimated to be stronger than that of HNO₃.²³ Hence, once HN₅ is generated by dissociation of the C–N bond of phenylpentazoles in the aqueous solution of nitrate, N₅⁻ will be easily produced and its metallic complexes can be formed.²⁴ These experimental and theoretical researches show that N₅⁻ can be produced by PhN₅.

However, the N₅ ring decomposes easily.^12,24,25 And our investigation²² showed that the C–N bond is much more stable than the N₅ ring for PhN₅, which is not good for generating N₅⁻. If one wants to find a good source of N₅⁻ from the analogues of PhN₅, improving the stability of the N₅ ring and lowering the strength of the central C–N bond should be the crucial keys. Our study²² revealed that introducing electron donating groups into PhN₅ slightly improves the stability of the N₅ ring, while strengthens the C–N bond, too. This implies that introduction of electron donating groups is not a good strategy for producing the excellent source of N₅⁻. Peter et al. found that electron withdrawing groups slightly weaken the N₅ ring of PhN₅.⁵ This discovery inspires us to think that the electron withdrawing groups may bring hope for finding the good source of N₅⁻ when the strength of the C–N bond is significantly lowered while the stability of the N₅ ring is little affected by the electron withdrawing substituents. In addition, the pyridine ring has similar planar conjugated structure and the same number of electrons to the benzene ring, while the pyridylpentazole (PyN₅) has been rarely researched. According to our exploratory computations on pentazole derivatives, we found that the central C–N bond of PyN₅ is less stable than that of PhN₅, which implies that PyN₅ more easily provides N₅⁻ than PhN₅ does. In this paper, PyN₅ and its derivatives (IA–IVD, cf. Fig. 1) with the electron withdrawing groups –NO₂, –CN, –CF₃ and –NF₂ were studied for searching the potential N₅⁻ source. A–D represent the groups –NO₂, –CN, –CF₃ and –NF₂, respectively. Series I and II are pyridine substituted with one group on the ortho-position and meta-position, III and IV are pyridine substituted with two groups on the ortho-position and meta-position. IA–ID are the isomers of the corresponding ones of IIA–IID, and the same is true for series III and IV.

Fig. 1 Structures of PyN₅ and its derivatives.

2. Computational details

Geometry optimizations of PhN₅, PyN₅ and the derivatives of PyN₅ were carried out using the restricted Kohn–Sham formalism at the RM06-2X/6-311++G** level. The optimized structures were verified as local minima on the potential hypersurface by only positive frequencies.

The relaxed potential energy surface scans along the stretching of the central C–N bond and the N–N bonds of the N₅ ring were carried out at the RB3LYP/6-31G* level for searching transition states (TSs). The TSs were then optimized at the RM06-2X/6-311++G** level which is reliable for computation of transition state.^26–29 The optimized TSs were confirmed by the presence of only one imaginary frequency.

Geometry optimizations of the radicals produced by the central C–N bond breaking were carried out at the UM06-2X/6-311++G** level. All geometry optimizations and the relaxed potential energy surface scans were finished with the Gaussian program package.³⁰

The bond dissociation energy (BDE), the energy difference between the parent molecule and the corresponding radical products in the unimolecular bond dissociation,^31–34 was calculated using the following equation:

BDE = E_R1˙ + E_R2˙ − E (1)

where E represents the zero-point-corrected total energy of title molecules obtained at the RM06-2X/6-311++G** level, E_R1˙ and E_R2˙ stand for the zero-point-corrected total energies of two radicals obtained at the UM06-2X/6-311++G** 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 CSC-MP2/cc-pvtz//RM06-2X/6-311++G** level.

The density of electron at the bond critical point of the central C–N bond (ρ_BCP) was analyzed using the Multiwfn³⁵ 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)³⁶ analyses.

3. Results and discussion

3.1 Structure

For PhN₅, the N₅ ring and the central C–N bond linking the phenyl and pentazole rings can decompose^{11,12,22–27} and the stabilities of this bond and the N₅ ring are the crucial factors determining the possibility of providing N₅⁻. Due to the similar conformations of PyN₅ and its derivatives to that of PhN₅, the stabilities of the C–N bond and N₅ ring of pyridylpentazoles should be the essential indexes reflecting the molecular stability and the feasibility of providing N₅⁻. Therefore, the C–N and N–N bond lengths of PyN₅ and its derivatives were measured for preliminarily acquainting these bond stabilities, as well as that of PhN₅ for comparison. Since title molecules have the similar atomic arrangements, only the labeled atoms and the broken bonds of PyN₅ are shown in Fig. 2. The C1–N1, N1–N2, N1–N3 and N4–N5 bond lengths (L_C1–N1, L_N1–N2, L_N1–N3 and L_N4–N5) are summarized in Table 1. Since only one of N1–N2 and N1–N3 bonds breaks during dissociation of the N₅ ring, the maximum bond length (L_max) of N1–N2 and N1–N3 is listed in Table 1 too.

Fig. 2 Dissociated bonds (labeled with pink line) and the atom numbering of PyN₅.

Table 1 Bond lengths and dihedral angles between the pyridine ring and pentazole ring

Compound	LC1–N1 (Å)	LN1–N2 (Å)	LN1–N3 (Å)	Lmax (Å)	LN4–N5 (Å)	D (°)
PhN5	1.430	1.317	1.317	1.317	1.337	0
PyN5	1.424	1.319	1.319	1.319	1.342	0
IA	1.416	1.321	1.321	1.321	1.346	42
IB	1.419	1.321	1.325	1.325	1.347	0
IC	1.423	1.322	1.320	1.322	1.345	44
ID	1.417	1.322	1.323	1.323	1.346	38
IIA	1.420	1.321	1.321	1.321	1.345	0
IIB	1.420	1.320	1.320	1.320	1.345	0
IIC	1.421	1.320	1.320	1.320	1.344	0
IID	1.420	1.320	1.320	1.320	1.345	0
IIIA	1.411	1.320	1.320	1.320	1.347	58
IIIB	1.415	1.325	1.325	1.325	1.349	50
IIIC	1.424	1.321	1.321	1.321	1.345	67
IIID	1.413	1.324	1.324	1.324	1.349	52
IVA	1.415	1.323	1.323	1.323	1.349	0
IVB	1.417	1.322	1.322	1.322	1.347	0
IVC	1.418	1.321	1.321	1.321	1.346	0
IVD	1.416	1.321	1.322	1.322	1.348	0

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Data in Table 1 show that L_C1–N1 of PyN₅ is smaller than that of PhN₅, that is, the pyridine ring shortens the C–N bond in comparison with the benzene ring. L_C1–N1s of derivatives are generally smaller than that of PyN₅, i.e., these electron withdrawing groups reduce the C–N bond of PyN₅. Increasing number of substituents shortens the C–N bond, which is reflected by the smaller L_C1–N1s of series III–IV in comparison with that of series I–II. The ortho-substituted derivative with the –NO₂, –CN or –NF₂ group has smaller L_C1–N1s than the meta-substituted isomer. L_C1–N1s of series I–IV increase in the order of A ≤ D ≤ B < C, –CF₃ is the most effective in reducing the C–N bond, –NO₂ is the least effective one. Generally, the smaller bond length corresponds to the higher bond stability. Are the C–N bonds of the PyN₅ derivatives with smaller bond length more stable than that of PhN₅? This question will be answered in the following studies.

L_max and L_N4–N5 have the same order of derivatives > PyN₅ > PhN₅, this shows that the pyridine ring and electron withdrawing groups elongate the N–N bonds of the N₅ ring. For series II and IV, increasing number of the substituted groups elongates the N–N bonds of the N₅ ring which can be reflected by the larger L_max and L_N4–N5 of series IV. For N4–N5 bonds of series I and III, introducing more substituents also elongates this bond. However, the opposite situation is found in L_maxs of series I and III. L_maxs of IA–ID are comparable to or even larger than the corresponding ones of IIIA–IIID. This diverse case can be explained by the remarkably different dihedral angles between the pyridine ring and the pentazole ring of series I and III. Unlike series II and IV, the pyridine ring and the pentazole ring of series I and III but IB are not coplanar. The obvious tortuosities may be caused by the strong electronic and steric repulsion between the substituted pyridine ring and the N₅ ring. The dihedral angles of series III are larger than the corresponding ones of series I because of the stronger repulsion of the formers caused by more substituents, the larger dihedral angles make the effects of substituents on the N₅ ring be weaker. Generally speaking, the N–N bonds of the meta-substituted series II and IV are shorter than that of series I and III. For L_max and L_N4–N5 of the derivatives with the same substituted position and number, the maximum differences caused by different groups are only 0.004 Å, that is, the different substituents do not significantly affect the N–N bond lengths.

3.2 Stability of the central C–N bond

The difficulty of breaking of the central C–N bond is pivotal for assessing the easiness and possibility of producing N₅⁻. In order to have a deep understanding on the dissociation of the C–N bond, the breaking processes of this bond of title molecules were simulated. Since the breaking processes of series I and III are similar, and those of series II and IV are analogous, only that of IIB and IIIB are shown in Fig. 3.

Fig. 3 Variation of energy with the C–N bond length of IIB (left) and IIIB (right).

Fig. 3 shows that H rearrangement happens and one transition state appears during decomposition of the C–N bond of IIB, the final products are HN₅ and cyanopyridyne (C₅H₃N(CN)). For IIIB, breaking of the C–N bond produces two radicals (N₅ radical and cyanopyridine radical), and no TS presents in this process. Since there is one H atom adjoining the N₅ ring of series I, H rearrangement may occur, i.e., TS may exist too when their C–N bonds dissociate. In addition, decompositions of the C–N bonds of series II and IV may proceed without TS and finally produce two radicals, too. It can be concluded that there are two possible C–N breaking patterns for series I, II and IV: (1) no TS appears and products are two radicals, the required energy for this process is the difference between total energies of two radicals and parent molecule, i.e., BDE; (2) C–N bond breaks through a TS and two ground state molecules are final products (HN₅ and pyridyne (C₅H₃N) derivatives), the needed energy for this process is activation energy (E_a,1). Two decomposition paths of IB are shown in Fig. 4 for more intuitively comparing these decomposition paths. BDEs and E_a,1s of series I, II and IV were calculated and are listed in Table 2 to figure out the most possible pyrolysis mechanism.

Fig. 4 Two dissociation paths of IB.

Table 2 BDEs for path1, E_a,1s and ks for path 2 and electron densities (ρs) at the C–N bond critical points

Compound	BDE (kJ mol^−1)	Ea,1^a (kJ mol^−1)	Ea,1^b (kJ mol^−1)	k (s^−1)	ρ (kJ mol^−1)
a Results obtained at the M06-2X/6-311++G** level.b Results obtained at the CSC-MP2/cc-pvtz level.
PhN5	535.8	376.3	395.5	3.53 × 10^−53	683.2
PyN5	525.6	368.7	387.1	9.02 × 10^−52	695.0
IA	493.7	356.2	368.1	2.45 × 10^−49	721.1
IB	504.6	355.7	367.3	1.42 × 10^−49	711.0
IC	502.9	352.3	364.7	1.00 × 10^−48	707.0
ID	506.1	356.0	367.7	2.68 × 10^−49	715.5
IIA	516.7	368.7	384.7	3.03 × 10^−52	707.8
IIB	517.8	359.1	376.3	7.31 × 10^−50	705.3
IIC	523.5	361.1	379.4	1.72 × 10^−50	703.2
IID	519.2	368.5	384.3	2.56 × 10^−51	705.9
IIIA	473.6				741.6
IIIB	494.5				727.9
IIIC	488.9				714.8
IIID	496.4				731.5
IVA	508.6	358.1	367.5	1.20 × 10^−48	720.0
IVB	510.8	357.5	371.0	2.48 × 10^−49	714.6
IVC	514.9	359.7	374.3	4.29 × 10^−50	711.0
IVD	513.5	350.7	367.3	4.12 × 10^−49	715.7

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BDEs of series III are quite large, which implies that breaking of the C–N bond of this series is very hard. As is evident from Table 2, E_a,1s of PhN₅, PyN₅, series I, II and IV are considerably smaller than the corresponding BDEs by 137.5–162.8 kJ mol⁻¹, which reveals that breaking of their central C–N bonds is more likely to follow the path 2 rather than path 1. Therefore, PyN₅, series I, II and IV can provide HN₅ and N₅⁻. E_a,1 of PyN₅ is smaller than that of PhN₅, so HN₅ is more easily produced from PyN₅. Compared with PyN₅, derivatives have smaller E_a,1s. E_a,1s have the order of derivatives < PyN₅ < PhN₅. According to these results, the strategies of introducing pyridine and the electron withdrawing groups are effective in weakening the C–N bond and improving the easiness of producing HN₅. E_a,1s of derivatives with the same substituent generally have the order of I < IV < II. Obtaining N₅⁻ from series I is the easiest, followed by series IV. N₅⁻ is more easily produced by the ortho-substituted derivatives than the para-substituted derivatives.

To comprehensively assess the potentials of these molecules as the source of N₅⁻, the reaction rate constants (ks) of path 2 were calculated at 300–1500 K with the KiSThelP program³⁷ according to the transition state theory (TST). In this paper, only ks at 300 K are shown in Table 2, results at other temperatures are supplied in Table S1.† As we expected, ks sharply increase with the improving temperature, this reveals that high temperature is good for producing HN₅. ks have the order of I > IV (IV > I) > II > PyN₅ > PhN₅, decomposition reactions of pyridylpentazoles are about 9–33 994 times (k_PyN5s/k_PhN5) faster than that of PhN₅. Based on the lower E_a,1 (ΔE_a,1 = E_a,1(PhN₅) − E_a,1(PyN₅s) = 8.4–30.8 kJ mol⁻¹, ΔE_a,1/E_a,1(PhN5) = 2.1–7.8%) and larger ks of PyN₅ and its derivatives, especially series I and IV, N₅⁻ can be more easily derived from pyridylpentazoles in comparison with PhN₅.

The above mentioned L_C1–N1s have the order of PhN₅ > PyN₅ > II > IV > I which is in agreement with the C–N bond stability. This result is not consistent with the common viewpoint that the longer bond links with the lower bond stability. In addition, electron density at the C–N bond critical point (ρ, Table 2) related to bond strength was evaluated, too. The variation trend of ρs is contrary to that of L_C1–N1, i.e., the larger ρ generally corresponds to the shorter C–N bond. The relationship between ρ and L_C1–N1 is in line with chemical intuition. However, the smaller ρ corresponds to the larger E_a,1 and higher bond stability, which is contrary to the common situation. How do these “abnormal phenomena” happen? Since the bond length and electron density at the bond critical point are all the properties of the static molecule, if the decomposition of bond directly proceeds by breaking the bond (path 1), they can be the indexes reflecting the bond stability. But when the deformation presents in the bond breaking process (path 2), they are no longer directly related with the bond stability, as was observed in series I, II, and IV.

3.3 Stability of the pentazole ring

Previous investigations^{12,24,25,38–41} reported that the N–N bonds of the N₅ ring of PhN₅ and its derivatives break much easier than other bonds. Therefore, the stability of the N₅ ring determines the molecular stability, and consequently affects application and storage of molecules with this ring. The good source of N₅⁻ should have the N₅ ring with high stability to ensure safe synthesis, convenient handling and easy acquisition of N₅⁻ rather than N₂ and azide derivatives. To assess the stability of the N₅ ring of title molecules, a relaxed potential energy surface scan along stretching of two N–N bonds (labeled as SC1 and SC2) was carried out to simulate the decomposition of the N₅ ring. The simulated energy surface of IA is plotted in Fig. 5. One TS (TS2) was found and is shown in Fig. 5, too.

Fig. 5 Potential energy surface with breaking of N–N bonds of IA.

The decomposition path of the N₅ ring of PyN₅ (path 3) is presented in Fig. 6 for clearly describing the pyrolysis process. When SC1 and SC2 respectively elongate to about 1.695–1.712 Å and 1.712–1.743 Å, TS2s of title molecules emerge. The final products are N₂ and azido pyridine or its derivatives. The activation energy (E_a,2) needed for path 3 and reaction rate constant, the essential factors determining the decomposition reaction, are tabulated in Table 3.

Fig. 6 Decomposition process of the N₅ ring of PyN₅.

Table 3 Predicted E_a,2s and ks of path 3^a

Compound	Ea,2 (kJ mol^−1)	k (s^−1)
a Ea,2 and k of PyN5 (PhN5) are 84.1 (88.7) kJ mol^−1 and 4.90 × 10^−4 (2.23 × 10^−5) s^−1, respectively.
IA	77.1	3.47 × 10^−2
IB	72.1	1.10 × 10^−1
IC	77.4	2.51 × 10^−2
ID	76.0	5.16 × 10^−2
IIIA	74.4	3.04 × 10^−1
IIIB	67.6	1.47
IIIC	73.4	1.69 × 10^−1
IIID	70.6	6.99 × 10^−1
IIA	78.9	8.92 × 10^−4
IIB	79.7	2.57 × 10^−3
IIC	81.1	9.62 × 10^−4
IID	80.3	2.73 × 10^−3
IVA	73.8	7.59 × 10^−2
IVB	75.4	2.36 × 10^−2
IVC	78.1	9.16 × 10^−3
IVD	76.5	4.01 × 10^−3

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We can see that E_a,2s are far smaller than the corresponding E_a,1s and BDEs, so decomposition of the N₅ ring should be the first step on dissociation of title molecules. E_a,2 of PyN₅ is 4.6 kJ mol⁻¹ smaller than that of PhN₅. Electron withdrawing groups obviously lower the stability of the N₅ ring due to the smaller E_a,2s of derivatives. The differences (ΔE_a,2s) between E_a,2s of PhN₅ and pyridylpentazoles are 11.3–21.0 kJ mol⁻¹ (ΔE_a,2/E_a,2(PhN5) = 12.7–23.7%). The pyridine ring and these electron withdrawing groups both weaken the N₅ ring.

For the derivatives with the same functional groups, E_a,2 generally decreases in the order of II > IV > I > III. Ortho-substituted groups more obviously affect the stability of the N₅ ring than the meta-substituted groups, and the stability of the N₅ ring decreases with the increasing number of substituents. Compared with other groups, –NF₂ causes the tiniest decrements in E_a,2s. The maximum differences of E_a,2s caused by different groups are 5.2, 2.1, 6.7 and 4.4 kJ mol⁻¹ for series I–IV respectively. These results agree with the conclusions obtained from the N–N bond lengths, i.e., the larger N–N bond distance corresponds to the lower N₅ ring stability, because N₅ ring directly decomposes by breaking of N–N bonds.

The reaction rate constants of path 3 were assessed at 300–1500 K. Only results at 300 K are shown in this paper, the other data are listed in Table S2.† k values of all molecules but IIIB are smaller than 1, this implies that decomposition of the N₅ ring of title molecules is not very fast under the normal condition. k increases drastically with the improving temperature, i.e., elevating temperature speeds up breaking of the N₅ ring, so high temperature is not good for molecules with the N₅ ring. While high temperature is beneficial to dissociation of the C–N bond, so the appropriate temperature is important for molecules analogous to title molecules as the source of N₅⁻. Reaction rate constant decreases in the order of III > I > IV (IV > I) > II > PyN₅ > PhN₅, decompositions of the N₅ ring of pyridylpentazoles are 44–11 437 times (k_PyN5s/k_PhN5) faster than that of PhN₅. Dissociation of the N₅ ring of series III are the fastest, decomposition speeds of series I and IV are comparable. The smaller E_a,2s and the larger ks of these derivatives with the electron withdrawing groups show that the stability of the N₅ rings of PyN₅ is obviously lowered by the electron withdrawing groups, which is beyond our expectation that the stability of the N₅ ring is slightly affected.

4. Conclusion

The central C–N bond breakings of all molecules but series III follow path 2 to produce HN₅ and pyridyne or its derivatives, so PyN₅, series I, II and IV can provide N₅⁻ for complexes. Compared to PhN₅, pyridine ring and electron withdrawing groups lower E_a,1 (ΔE_a,1) by 8.4–30.8 kJ mol⁻¹ (2.1–7.8%), and accelerate path 2 by about 9–33 994 times. The decrement (ΔE_a,2) in stability of the N₅ ring caused by pyridine ring and substituents is 11.3–21.0 kJ mol⁻¹ (12.7–23.7%), and the speed of path 3 is improved by 44–11 437 times. The magnitude of ΔE_a,1 is close to that of ΔE_a,2, while the percentage of ΔE_a,1 is smaller than that of ΔE_a,2, which means that pyridine ring and substituents more obviously lower the stability of the N₅ ring than the C–N bond. Replacement of the phenyl ring in PhN₅ with pyridine or its derivatives of the electron withdrawing groups can lower the stability of the central C–N bond, as well as that of the N₅ ring. PyN₅ and its substituted derivatives with the electron withdrawing groups are not the better replacements for PhN₅ as the source of N₅⁻.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra00813a

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