Acidic Stabilization of the Dual-Aromatic Heterocyclic Anions

Abstract

Recently, we discovered that the delocalization of nitrogen lone-pair electrons (NLPEs) in five-membered nitrogen heterocycles created a second σ-aromaticity in addition to the prototypical π-aromaticity. Such dual-aromatic compounds, such as the pentazole anion, were proved to have distinct chemistry in comparison to traditional π-aromatics, such as benzene, and were surprisingly unstable, susceptible to electrophilic attack, and relatively difficult to obtain. The dual-aromatics are basic in nature, but prefer not to be protonated when confronting more than three hydronium/ammonium ions, which violates common sense understanding of acid−base neutralization for a reason that is unclear. Here, we carried out 63 test simulations to explore the stability and reactivity of three basic heterocycle anions (pentazole anion N₅¯, tetrazole anion N₄C₁H₁¯, and 1,2,4-triazole anion N₃C₂H₂¯) in four types of solvents (acidic ions, H₃O⁺ and NH₄⁺, polar organics, THF, and neutral organics, benzene) with different acidities and concentrations. By quantum mechanical calculations of the electron density, atomistic structure, interatomic interactions, molecular orbital, magnetic shielding, and energetics, we confirmed the presence of dual aromaticity in the heterocyclic anions, and discovered their reactivity to be a competition between their basicity and dual aromaticity. Interestingly, when the acidic ions H₃O⁺/NH₄⁺ are three times more in number than the basic heterocyclic anions, the anions turn to violate acid−base neutralization and remain unprotonated, and the surrounding acidic ions start to show a significant stabilization effect on the studied heterocyclic anions. This work brings new knowledge to nitrogen aromatics and the finding is expected to be adaptable for other pnictogen five-membered ring systems.

1. Introduction

Nitrogen-rich, high-energy-density materials (HEDMs), in which the nitrogen weight is higher than 50% [1], are known to generate a large amount of heat when exothermically decomposing into molecular dinitrogen [2]. In addition, a considerable amount of nitrogen-rich HEDMs also show low-shock sensitivity, improved burning rate, and other advanced advantages [3]. Therefore, nitrogen-rich HEDMs are very promising candidates to address the long-standing, high-energy density and low-sensitivity contradiction of HEDMs, and can potentially be utilized to safely conduct space exploration, explore ultra-deep mineral deposits on Earth, and so forth [4,5,6,7,8,9]. For example, 3-nitro-1,2,4-triazole-5-one (NTO) has a high-energy density (comparable to RDX) and low sensitivity (lower than HMX), and has become a very important ingredient in the polymer-bonded explosive (PBX) formulations for insensitive munitions (IMs) [1,10,11]. Triaminoguanidinium azotetrazolate (TAGzT) can increase the heat generation and burning rates of propellants over a wide pressure range [3]. 5,5′-hydrazinebistetrazole (HBT) and bis (3,4,5-triamino-1,2,4-triazolium) 5,5′-azotetrazolate (G₂ZT) contain up to ~80% of nitrogen weight and present a relatively high combustion heat (−2396 cal/g for HBT and −2775 cal/g for G₂ZT) [12]. In particular, the pentazole anion has a nitrogen weight of 100% and its reaction product consists only of molecular dinitrogen. Therefore, the pentazole anion is considered the ultimate in the pursuit of energetic material that is green, non-polluting, and ultra-high energetic [1].

Due to the above satisfactory comprehensive properties, nitrogen-rich HEDMs, such as triazoles, tetrazoles, and pentazoles, are extensively used as building blocks for the design of advanced, new HEDMs [1,13,14,15,16,17,18,19,20,21]. However, the stabilization mechanism of nitrogen heterocycles, which is essential for the rational design and large-scale production of advanced HEDMs, remains unclear. The problem is mainly focused on the distributions and states of the nitrogen lone-pair electrons (NLPEs), and their influence on the structural stability and chemical reactivity of heterocycles. For example, the valence shell electron pair repulsion (VSEPR) theory suggests that the NLPEs are localized in the vicinity of each separate nitrogen atom. Therefore, the NLPEs in a cyclic system should repel the adjacent C−N bonds and other lone pairs in the ring [22,23,24], thereby destabilizing the system. However, this derivation contradicts the fact that the presence of nitrogen in the ring can actually impart a higher degree of stability to these molecules compared to their hydrocarbon analogs [22,25]. To interpret this “aza-stabilization” anomaly, some researchers have proposed that the NLPEs are delocalized over the cyclic systems instead of being localized on separate nitrogen atoms [25,26]. However, this proposition is again challenged by the elusive chemistry of the pentazole anion. The pentazole anion has five nitrogen atoms and one π-electron aromatic system and, theoretically, it should be very stable. However, the pentazole anion has been proved to be surprisingly unstable, difficult to obtain, and susceptible to electrophilic attack [26,27,28,29,30,31,32]. The pentazole anion is basic in nature, but prefers not to be protonated when facing more than three hydronium/ammonium ions [28,33], which violates the acid−base neutralization rule for reasons that are unclear. Therefore, a better understanding of the stabilization and reactivity of nitrogen heterocyclic species requires new knowledge of nitrogen chemistry.

Recently, we discovered that the delocalization of NLPEs in five-membered nitrogen heterocycles creates a second σ-aromaticity, in addition to the prototypical π-aromaticity [34,35]. Taking the pentazole anion as an example, it has five nitrogen atoms in a planar ring and all the nitrogen atoms are sp² hybridized. Six electrons at the 2p_z π molecular orbital (MO) constitute a complete π aromatic system, and ten NLPEs at the 2sp² σ MO give rise to an additional σ aromatic system. The dual-aromatic system features a simultaneous delocalization of the π electrons above/below the plane and the σ lone-pair electrons in the equatorial plane, which is very different from the multi-aromaticity of all-metal systems caused by an electron deficiency. Such dual-aromatic heterocyclic compounds were proved to have distinct chemistry in comparison to traditional π-aromatics, such as benzene. In vacuums, solutions, and crystals, the pentazole anion is protonated when facing less than three H₃O⁺/NH₄⁺ ions, and prefers not to be protonated when the number of H₃O⁺/NH₄⁺ ions is more than three. It is the compatible coexistence of the inter-lone-pair repulsion and inter-lone-pair attraction within the σ-aromatic system that makes the stability and reactivity of these dual-aromatics vary according to their environments [34].

In this work, we designed and conducted a series of quantum mechanical calculations to explore the structural stability and chemical reactivity of three heterocyclic anions in four types of solvents with different acidity and concentrations. Interestingly, when the acidic H₃O⁺/NH₄⁺ ions are three times more in number than the heterocyclic anions, they start to show a stabilization effect on the structural stability of the studied heterocycles. The detailed calculation results and proposed mechanism are shown below.

2. Results and Discussion

2.1. Presence of Dual Aromaticity in the Heterocyclic Anions Studied

From the atomic orbital diagrams in Figure 1, all the carbon and nitrogen atoms in N₅¯, N₄C₁H₁¯, and N₃C₂H₂¯ were sp² hybridized. Taking into account the net foreign electron, which resided at the p orbital, each of the three heterocyclic anions obtained six π electrons, respectively, forming a complete π-aromatic system. The isosurface of the lowest π MO (MO_min-π) presented a shape spreading out over the entire molecule above and below each molecular plane. The delocalization index DI_min-π was calculated to be 0.16 between any two atoms (nearest neighbors and second nearest neighbors) in the ring, thus confirming the full delocalization of the electrons at this minimum π orbital. As shown at the bottom of Figure 1, NICS_zz(r)_π was always negative when the vertical distance relative to each ring critical point (r) varied from 0.0 to 5.0 Å, thereby confirming the presence of π-aromaticity in the three heterocyclic anions. By comparing the calculated NICS_zz(1)_π of the three anions, the order of their π-aromaticity was N₅¯ (−26.1) > N₄C₁H₁¯ (−25.8) > N₃C₂H₂¯ (−25.2). Compared with benzene, which had DI_min-π = 0.11 and NICS_zz(1)_π = −28.96, the three heterocyclic anions presented a higher level of electron delocalization, but a weaker π-aromaticity.

We next turned to the NLPE in the three heterocyclic anions. As shown by the isosurface of MO_min-σ(LP) at the top of Figure 1, the NLPE presented an obvious delocalization over the rings of N₅¯, N₄C₁H₁¯, and N₃C₂H₂¯, and the delocalization region expanded when more nitrogen atoms were present in the ring. Interestingly, the delocalization of the NLPE spreads out over the interior and exterior of the ring (Figure S4 of the Supplementary Materials). In N₄C₁H₁¯ and N₃C₂H₂¯, the presence of the CH bonds destroys the NLPE delocalization in the exterior of the ring, but their delocalization in the interior of the ring is not much influenced. In N₅¯, the NLPE delocalization fulfills both the interior and exterior of the ring. Correspondingly, the DI_min-σ(LP) values of N₅¯, N₄C₁H₁¯, and N₃C₂H₂¯ were all calculated to be 0.16, thereby confirming the NLPE delocalization at each minimum σ orbital. As shown at the bottom of Figure 1, the highest absolute value of the NICS_zz(r)_σ of N₅¯ was r_extreme = 0.6 Å vertically above the ring critical point, which is the same as the P₂N₃ˉ anion [27]; for N₄C₁H₁¯, r_extreme = 0.8 Å; for N₃C₂H₂¯, r_extreme shifted to 1.0 Å. As shown in

Table 1. Magnetic index of aromaticity and electron delocalization index of N₅¯, N₄C₁H₁¯ and N₃C₂H₂¯ [37].

Indices		N5¯	N4C1H1¯	N3C2H2¯	Benzene
Total	NICSzz(1)total	−45.16	−40.24	−35.78	−29.07
	NICSzz(rextreme)total	−51.81	−43.44	−37.53	-
π	DI min-π	0.16	0.16	0.16	0.11
	NICSzz(1)π	−26.09	−25.81	−25.23	−28.96
σ	DI min-σ(LP)	0.16	0.16	0.16	-
	NICSzz(1)σ	−19.06	−14.42	−10.55	−0.11
	NICSzz(rextreme)σ	−19.87	−14.42	−10.55	-

, the values of NICS_zz(1)_σ and NICS_zz(r_extreme)_σ were both negative, indicating the presence of an additional σ-aromaticity in the three heterocyclic anions; the order of their σ-aromaticity was N₅¯ > N₄C₁H₁¯ > N₃C₂H₂¯. The contributions of the NLPE delocalization to σ-aromaticity was also discovered in the (NH)_n (n = 3–6) systems [36].

We next evaluated the total aromaticity of the three heterocyclic anions and compared them with the prototypical benzene. As shown in Table 1, the NICS_zz(1)_total and NICS_zz(r_extreme)_total values both showed the order of N₅¯ > N₄C₁H₁¯ > N₃C₂H₂¯, and all three heterocyclic anions presented a stronger aromaticity than benzene. Therefore, as more nitrogen atoms are present in the heterocycles, the NLPE are more delocalized, and the σ-aromaticity and overall aromaticity increases.

2.2. Basicity of Heterocyclic Anions and Acidity of Solvents Studied

The PA defined by Equation (1) was employed to evaluate the basicity of the nitrogen heterocyclic anions studied; a higher PA corresponds to a stronger basicity. As shown in Figure 2, the value of the PA increased with the decrease in nitrogen atoms in the heterocyclic anion. Therefore, the sequence of their basicity was N₅¯ < N₄C₁H₁¯ < N₃C₂H₂¯, which is consistent with the order obtained from experimental pH tests (pK_b = 9.1 for N₄C₁H₁¯ and pK_b = 4.0 for N₃C₂H₂¯) [28,38].

When the PA is used to characterize the acidity of the solvents, a higher PA corresponds to a weaker acidity. As shown in

Table 2. Basicity of heterocyclic anions and acidity of solvents studied.

Type	Compounds	PA (kcal/mol)		−Log of Dissociation Constant
		This Work	Exp.	Exp.
Heterocyclic anions	N5¯	323.2	-	-
	N4C1H1¯	336.7	-	pKb = 9.1
	N3C2H2¯	344.8	-	pKb = 4.0
Solvents	H3O+	176.3	165.0 [39]	pKa = −1.74 [40]
	NH4+	211.9	204.0 [39]	pKa = 9.3 [40]
	Benzene	409.7	-	pKa = 43 [40]
	THF	411.1	-	-
	H2O	396.1	390.3 [39]	pKa = 15.74 [40]

, the calculated values of the PA were 176.3 kcal/mol for H₃O⁺, 211.9 kcal/mol for NH₄⁺, 409.7 kcal/mol for THF, and 411.1 kcal/mol for benzene, respectively. Our results were very close to the experimental results of PA(H₃O⁺) = 165.0 kcal/mol and PA(NH₄⁺) = 204.0 kcal/mol [39]. We also conducted a PA calculation for H₂O for further verification. PA(H₂O) was calculated to be 396.1 kcal/mol, which was close to the experimental result of 390.3 kcal/mol [39]. The PA(H₂O) value was between PA(NH₄⁺) and PA(benzene), which was consistent with the experimental pK_a: 9.3 (NH₄⁺) < 15.74 (H₂O) < 43 (benzene). From the above calculations and for verification, the order of the acidity of the solvents was H₃O⁺ > NH₄⁺ > H₂O > benzene > THF, which was consistent with the pK_a sequence obtained from the experiments: −1.74 (H₃O⁺) < 9.3 (NH₄⁺) < 43 (benzene) [40].

2.3. Different Reactivity of Heterocyclic Anions Depending on Solvent Types and Concentrations

Taking the solvent NH₄⁺ as an example, Figure 3A presents the optimized structures of the N₃C₂H₂¯⋯cNH₄⁺, N₄C₁H₁¯⋯cNH₄⁺, and N₅¯⋯cNH₄⁺ complexes. When c < 3, the NH₄⁺ ions turned to be neutral NH₃ molecules after the reaction, and the heterocyclic anions were protonated. That is, acid and base underwent a neutralization process. Correspondingly, the BE values of the three heterocyclic complexes all increased to the maximum when the NH₄⁺ concentration increased from c = 1 to c = 2, as shown in Figure 3B–D. However, when c ≥ 3, the proton would stay near NH₄⁺, and the heterocyclic anions tended to remain unprotonated, as shown by the interaction strengths (distances) of the proton with the heterocyclic anion and with solvent species in Figures S5 and S6 of the Supplementary Materials. Namely, acid and base would not proceed neutralization. Besides, the BE value of the complex started to decrease with a further increase in c, as shown in Figure 3B–D.

The effect of the H₃O⁺ concentration on the reactivity of the three heterocyclic anions was similar to that of NH₄⁺, as shown in Figure S1 of the Supplementary Materials. However, the interactions between H₃O⁺ and the heterocyclic anion were about 60% stronger than those between NH₄⁺ and the heterocyclic anion. This resulted in H₃O⁺⋯heterocyclic complexes having higher BE values than the NH₄⁺⋯heterocyclic complexes by 28–79 kcal/mol. In benzene and THF solvents, when c varied from 1 to 5, the three heterocyclic anions were never protonated, as shown in Figures S2, S3, S5, and S6 of the Supplementary Materials. The interactions between benzene/THF and the heterocyclic anion were weak hydrogen bonds (HB, <10 kcal/mol), much weaker than the HB connected to H₃O⁺ or NH₄⁺, as shown in Figure S7 of the Supplementary Materials. Correspondingly, the BE values of the benzene/THF⋯heterocyclic complexes increased monotonously with the increase in c, but were much lower than the BE values of the H₃O⁺/NH₄⁺⋯heterocyclic complexes, as shown in Figure 3B–D.

The anomaly of the reactivity of the three heterocyclic anions is that they are basic, but they prefer to be unprotonated when encountering more than three H₃O⁺ or NH₄⁺ ions. This not only violates the common sense of acid−base neutralization, but also leads to an increase in the total energy of the complex, as shown in Figure 3B–D. This increase in energy is caused by the mutual repulsion between the adjacent H₃O⁺/NH₄⁺, because when c ≥ 3, the proton was in the vicinity of H₃O⁺/NH₄⁺ instead of near the heterocyclic anions. It is interesting that these H₃O⁺/NH₄⁺ ions would rather suffer mutual repulsion than diffuse away from the heterocyclic anion center. Although the protonation of N₅¯, N₄C₁H₁¯, and N₃C₂H₂¯ could eliminate this mutual electrostatic repulsion and convert intermolecular HBs into much lower energy H–N bonds to reduce the total energy of the complex, this process did not proceed as expected when c ≥ 3. There must be some unseen incentives to drive mutations in the reactivity of heterocyclic anions.

2.4. Mechanism of Anomalous Reactivity of Heterocyclic Anions

In the following, we take N₄C₁H₁¯ in an NH₄⁺ solvent as an example to explore the mechanism of its anomalous reactivity. When N₄C₁H₁¯ was protonated at c = 1 and c = 2, compared with its naked state, the DI_min-σ(LP) in the ring was reduced by 0.08, and the values of NICS_zz(1)_total, NICS_zz(1)_π, and NICS_zz(1)_σ were reduced by 2.72, 1.17, and 1.55 ppm, respectively, as shown by the red curves in Figure 4C,D and Figure S8 of the Supplementary Materials. This implied that the formation of additional single bonds consumed the delocalization of electrons in the heterocycles, thereby reducing their dual aromaticity, whereas the formation of H–N bonds could substantially lower the total energy of the complex, as shown in Figure 3A. Therefore, the basicity of N₄C₁H₁¯ dominated the reactivity, and the anion underwent an additional reaction by scarifying the dual aromaticity.

If N₄C₁H₁¯ continued to be protonated by more NH₄⁺, the dual aromaticity would be further weakened, which provoked N₄C₁H₁¯ to balance the dual aromaticity and its basicity in another way when c ≥ 3. In order to keep the dual aromaticity intact, N₄C₁H₁¯ started to reduce the bonding states of electrons with nearby protons, tending to remain unprotonated and interact with all NH₄⁺ through intermolecular HB. In this way, the electron delocalization of HB helped increase the dual aromaticity of N₄C₁H₁¯ [41]. Compared with its protonation state, the DI_min-σ(LP) in the N₄C₁H₁¯⋯3NH₄⁺ complex increased by 0.03, and the aromaticity indices NICS_zz(1)_total, NICS_zz(1)_π, and NICS_zz(1)_σ increased by 1.01, 0.31, and 0.71, respectively, as shown in Figure 4C,D. Note that at c = 3, the interactions of the proton with N₄C₁H₁¯ and NH₃ were in a critical state of competition, and σ-aromaticity is apparently the lead in changing the reactivity of N₄C₁H₁¯.

When c = 4, N₄C₁H₁¯ interacted with the surrounding NH₄⁺ ions via typical intermolecular HBs, the DI_min-σ(LP) in the N₄C₁H₁¯⋯4NH₄⁺ complex further increased by 0.03, and the aromaticity indices NICS_zz(1)_total, NICS_zz(1)_π, and NICS_zz(1)_σ continued to increase by 0.55, 0.45, and 0.10, respectively, as shown in Figure 4C,D. That is, at c = 4, the dual aromaticity of N₄C₁H₁¯ totally defeated its basicity and totally dominated the N₄C₁H₁¯ to violate the acid–base neutralization.

The reaction mechanism of N₄C₁H₁¯ in H₃O⁺ was similar to that in NH₄⁺. Because H₃O⁺ (pK_a = −1.74 [39]) has a higher acidity than NH₄⁺ (pK_a = 9.3 [39]), the electron delocalization and aromaticity in N₄C₁H₁¯⋯cH₃O⁺ presented larger variations than that in N₄C₁H₁¯⋯cNH₄⁺ with the increase in c, as shown in Figure 4C,D.

The proposed mechanism of the anomalous reactivity of N₄C₁H₁¯ is also applicable to N₅¯ and N₃C₂H₂¯, as shown in Figure 3A. It is worth mentioning that N₃C₂H₂¯contains two hydrogen atoms, repelling nearby H₃O⁺/NH₄⁺ ions. Therefore, this anion could have up to three H₃O⁺/NH₄⁺ ions in its vicinity, and the fourth H₃O⁺/NH₄⁺ ion was not allowed to approach thermodynamically.

2.5. Acidic Stablization of the Dual-Aromatics Studied

It is of interest to take advantage of the discovered anomalous reactivity to catalyze a generating rate and improve the production yield of heterocycles. Taking N₅¯ as an example, a successful preparation of N₅¯ from the solution is to keep all the N-N bonds intact before the rupture of the C–N bond in 3,5-dimethyl-4-hydroxyphenylpentazole (HPP). Although the synthesis of N₅¯ was successfully achieved with the aid of m-chloroperbenzoic acid (m-CPBA) and ferrous bisglycinate [Fe(Gly)₂] [42], the production yield as well as the generating rate of N₅¯ is still to be improved and accelerated.

One of the most important preconditions of the catalysis of these heterocyclic anions is to keep their structure stable in the preparation solution. Because the strength of the C–N and N–N bonds of a heterocycle is one of the most important factors for its structural stability, we calculated all the bond strengths in the rings of N₅¯, N₄C₁H₁¯, and N₃C₂H₂¯ under different solvent concentrations. For all three heterocycles in each solvent, the weakest bonds were all N–N bonds, and their strengths were plotted as a function of c, as shown in Figure 5 and Figure S9 of the Supplementary Materials. The calculation method of the bond strength is detailed in the Methodology Section.

Compared with naked N₅¯, N₄C₁H₁¯, and N₃C₂H₂¯, the bonds of heterocycles in H₃O⁺/NH₄⁺ solvents were significantly enhanced, and this enhancement increased with the increase in H₃O⁺/NH₄⁺ concentration. For example, the weakest bond in the N₅¯⋯4H₃O⁺ complex was 145.24 kcal/mol, which was improved by 54% than that of the naked N₅¯; the weakest bond in N₅¯⋯4NH₄⁺ was 140.54 kcal/mol and was improved by 48.7%. Similarly, the weakest bonds in the N₄C₁H₁¯⋯4H₃O⁺ and N₄C₁H₁¯⋯4NH₄⁺ were enhanced by 67% and 51%, respectively, compared with that of the naked N₄C₁H₁¯; the weakest bonds in N₃C₂H₂¯⋯3H₃O⁺ and N₃C₂H₂¯⋯3NH₄⁺ were enhanced by 44% and 37%, respectively, compared with the naked N₃C₂H₂¯. In contrast, the presence of benzene and THF surrounding N₅¯, N₄C₁H₁¯, and N₃C₂H₂¯ showed little influence on the strength of the bonds in the rings. Their influence on the weakest bond strength was in the range of −4.0–6.6%. Therefore, the H₃O⁺/NH₄⁺ ions showed a significant stabilization effect on the enhancement of the studied heterocyclic structures, in particular at a high concentration of H₃O⁺/NH₄⁺, implying a potential catalytic effect of the H₃O⁺/NH₄⁺ ions in the preparation of heterocyclic compounds.

The stabilization effect of the H₃O⁺/NH₄⁺ ions on the heterocyclic structures was caused by their HB interactions with the NLPE. Such HB interactions stretched the NLPE away from its original position, thereby reducing the inter-lone-pair repulsion within the σ-aromatic system. In contrast, since the HB interactions between the heterocycles and the benzene/THF were very weak, the location of the NLPE in the heterocycles was almost unaffected. Therefore, the two solvents showed little effect on the structural stability of the heterocycles.

3. Methodology

The heterocyclic anions studied here include the pentazole anion N₅¯, tetrazole anion N₄C₁H₁¯, and 1,2,4-triazole anion N₃C₂H₂¯. In order to evaluate the influence of the acidity and concentration of the solvent on the reactivity of heterocyclic anions, we built atomistic models for each heterocyclic anion by traversing the four solvents of H₃O⁺, NH₄⁺, benzene, and THF. For each type of solvent, the molar ratio of solvent to heterocyclic anion increased from c = 1 to c = 5. In addition, one naked anion laid in a vacuum was calculated for comparison. Therefore, 63 atomistic models were used for calculation and evaluation in total.

All the calculations were performed using a quantum mechanical method based on the density functional theory (DFT). The quantities of electron density, atomistic structure, interatomic interactions, MO, magnetic shielding, and energetics were calculated based on the corresponding optimized structure, which was obtained using Gaussian 09 at the B3LYP/6-31G(d) level [43]. After the optimization of the 63 atomistic models, 55 presented with clustered structures, with 1 heterocyclic anion present in the middle and solvent species distributed nearby, as shown in Figures S1–S3 of the Supplementary Materials. For the other 8 models with c = [H₃O⁺ or NH₄⁺]/[N₅¯, N₄C₁H₁¯, or N₃C₂H₂¯] = 5 and c = [H₃O⁺ or NH₄⁺]/ [N₃C₂H₂¯] = 4, the H₃O⁺/NH₄⁺ ions diffused away from the vicinity of the heterocyclic anions.

The strengths of the relevant interatomic interactions, including bonding interactions, nonbonding interactions, and antibonding interactions, were evaluated by the integrated value of the crystal orbital Hamilton population (COHP) below the Fermi energy, using a recently developed High Accuracy Atomistic Simulation for Energetic Materials (HASEM) package [44,45]. The number of electrons shared between atoms was characterized by the delocalization index (DI); a higher DI value suggests a stronger delocalization of the NLPE [46]. The aromaticity was quantified by NICS_zz, namely nucleus-independent chemical shifts, along the z-direction [47]. A considerable negative NICS_zz value indicates the presence of aromaticity, and this method is by far one of the most widely used magnetic shielding indexes for diagnosing aromaticity. All DI and NICS values were calculated at the B3LYP/6-311++G(d, p) level. We further separated DI and NICS into individual components contributed solely by π-electrons/lone-pair electrons, using the natural bond orbital (NBO) [48,49,50] analysis and the quantum theory of atoms in molecules (QTAIM) [51,52] method that was implemented in the Multiwfn application [53]. The indices with π/σ subscripts are the components contributed by all the π-electrons/σ-electrons, whereas those with min-π/min-σ(LP) subscripts are the components contributed by the π-electrons/lone-pair σ-electrons at each lowest energy level.

The basicity of the nitrogen heterocyclic anions and the acidity of the solvents studied were evaluated by their proton affinity (PA) [54,55]:

PA = E_protonated – E_unprotonated

(1)

where E_protonated is the total energy of the protonated species and E_unprotonated is the total energy of the corresponding unprotonated species. The higher the PA, the stronger the base and the weaker the conjugate acid in the gas phase. Therefore, the heterocyclic anion with a higher PA is more basic, and the solvent with a lower PA is more acidic.

The energetics of the heterocyclic anion–solvent complexes were characterized by binding energy (BE):

$$BE=E_{anion}+{\displaystyle {\sum }_1^{\mathrm{c}}{E}_{solvent}-E_{complex}}$$

(2)

where $E_{anion}$ is the total energy of the naked heterocyclic anion, $E_{solvent}$ is the total energy of a separate solvent ion or molecule, and $E_{complex}$ is the total energy of the overall complex. A higher positive BE value implies that the interspecies interactions are more favorable and the complex is energetically more stable. Otherwise, the negative BE value indicates that the structure of the proposed complex is thermodynamically unstable.

4. Conclusions

We performed a series of quantum mechanical calculations to explore the stability and reactivity of the pentazole anion N₅¯, tetrazole anion N₄C₁H₁¯, and 1,2,4-triazole anion N₃C₂H₂¯ in four types of solvents with different acidities and concentrations. The main conclusions are as follows:

(1)

Through the analysis of electron density, atomistic structure, interatomic interactions, molecular orbital, magnetic shielding, and energetics, we confirmed the basicity of N₅¯, N₄C₁H₁¯, and N₃C₂H₂¯, and the presence of dual aromaticity in the three heterocyclic anions;

(2)

The three heterocyclic anions were found to violate the acid–base neutralization rule when confronting more than three H₃O⁺/NH₄⁺ ions. The mechanism of the anomalous reactivity of heterocyclic anions was found to be a competition between their basicity and dual aromaticity;

(3)

Due to the stretching effect of hydrogen bonding on the nitrogen lone-pair electrons, the H₃O⁺/NH₄⁺ ions showed a significant stabilization effect on the studied heterocyclic structures, in particular at a high concentration of H₃O⁺/NH₄⁺. In contrast, benzene and THF presented little influence on the structural stability of heterocyclic anions.