Structure and Stability of Aromatic Nitrogen Heterocycles Used in the Field of Energetic Materials

Understanding the stabilization of nitrogen heterocycles is critical in the field of energetic materials and calls for innovative knowledge of nitrogen aromatics. Herewith, we report for the first time that nitrogen lone pair electron (NLPE) delocalization in five-membered nitrogen heterocycles creates a second σ-aromaticity in addition to the prototypical π-aromaticity. The NLPE delocalization and the attendant dual-aromaticity are enhanced as more carbon atoms in the ring are substituted by unsaturated nitrogen atoms. The presence of adjacent nitrogen atoms in the ring can enhance the aromaticity of the nitrogen heterocycles and improve in-crystal intermolecular binding strength but will decrease the firmness of the individual molecular architecture. Notably, such σ-aromaticity is not present in six-membered nitrogen heterocycles, probably due to the longer bonds and broader regions of their rings; therefore, six-membered heterocycles present overall lower aromaticity than five-membered heterocycles. This work brings new knowledge to nitrogen aromatics and is expected to inspire broad interest in the chemistry community.


MO min-σ(LP)
Structure NH3 Structure NH3 Structure NH3 Structure NH3 Structure NH3 Structure NH3 Structure NH3 Structure NH3 Structure NH3 The nitrogen in 1 (ammonia) was sp 3 hybridized, and the carbon and nitrogen in all the cyclic compounds  were sp 2 hybridized. The σ NLPE delocalization, as well as the π electron delocalization of the 22 systems, was visualized by the isosurfaces of each lowest molecular orbital (MO), as shown in Table 1. The quantities with min-π/min-σ(LP) subscripts were the components contributed by the lowest energy level of π-electrons/σ-NLPEs.

Label
We first studied the cases with a single unsaturated nitrogen atom (1, 3, 16, and 17), with each of these systems presenting only one pair of σ-NLPEs. For example, ammonia (1) has one pair of NLPEs at the top of the trigonal pyramidal of the structure; 3 has one pair of NLPEs in the ring; for 16 and 17, the NLPEs of the saturated nitrogen join the lower-energy π MO, so there is only one pair of σ-NLPEs affiliated with the unsaturated nitrogen in each heterocycle. As shown by the shapes of their MO min-σ(LP) in Table 1, these σ-NLPEs were highly localized in the region of the unsaturated nitrogen atom. The high localization of the σ-NLPEs makes these systems basic and attractive to electrophiles, which is consistent with traditional organic/inorganic chemistry knowledge [7].
However, the presence of more than two unsaturated nitrogen atoms in the ring, partially in the ortho positions, made the NLPEs delocalized in a broader region. For example, 4, 7, 10-12, and 18-21 had the isosurfaces of their MO min-σ(LP) continuously distributed in the region between the unsaturated nitrogen atoms, as shown in Table 1. Notably, although 8 and 13 had adjacent unsaturated nitrogen atoms in the ring, some of these nitrogen atoms contributed their NLPEs to the relative lower energy π orbital instead of the σ orbital. Therefore, these two compounds did not have ortho-NLPEs, but showed para-and para-NLPEs in each MO min-σ(LP) . Table 1 indicates that the σ-NLPEs in 5, 6, 8, 9, and 13, which had para or meta position in each ring, were generally more localized compared to those NLPEs in the ortho positions.
In extreme cases, when all carbon atoms were substituted by unsaturated nitrogen atoms in the ring, the delocalization of the NLPEs formed into a circle and achieved a maximum. For example, the MO min-σ(LP) of 14 and 22 spread out over each molecule into a flower shape in the equatorial plane, as shown in Table 1. This is consistent with our previous study on pentazolate anion [11,12].
In brief summary, the substitution of carbon atoms by unsaturated nitrogen atoms in the heterocycles improved the extent of the delocalization of NLPEs. More unsaturated nitrogen atoms led to a higher extent of NLPE delocalization, and the preferable order of the NLPE positions that contributed to such delocalization was ortho > meta > para.

Quantification of the NLPE Delocalization
In order to quantify the delocalization extent of the NLPEs, we calculated the electron-based aromaticity LI [13,14]. The LI quantitatively measured how many electrons were localized in a region; a higher LI value suggested stronger localization, but weaker delocalization of the NLPEs. The LI of the unsaturated nitrogen atoms projected in MO min-σ(LP) for each of the 22 studied compounds is shown in Figure 1.

Discovery of Additional σ-Aromaticity in Five-Membered Nitrogen Heterocycles
To determine how aromaticity (including prototypical π-aromaticity, newly proposed σaromaticity, and total aromaticity) varies in these heterocycles, we further calculated the magnetic index of aromaticity-NICSzz(r), which is the NICS value along the z axis, by far the most widely used method for diagnosing aromaticity [15,16]. The indices with π/σ subscripts were the components contributed by all the π-electrons/σ-electrons. The more negative the NICS values, the more aromatic were the rings.
Taking 2, 14, 15, and 22 as examples, we showed the NICSzz(r)total, as well as the π and σ orbital components (NICSzz(r)π and NICSzz(r)σ) in Figure 2A. As the vertical distance relative to the ring critical point varied from r = 0.0 to 5.0 Å , NICSzz(r)π was always negative for 2, 14, 15, and 22, suggesting the presence of π-aromaticity in these systems. NICSzz(r)σ was always negative in 22, whereas it was positive or close to zero in 2; the situations of 14 and 15 were between 2 and 22. This indicated the presence of σ-aromaticity in the all-nitrogen compound 22, whereas benzene 2 lacked such σ-aromaticity; 14 and 15 had only weak σ-aromaticity.
The order of the σ-aromaticity of the four compounds could be quantified by the absolute values of NICSzz(1)σ: 22 > 14 > 15 > 2. Here NICSzz(1) was the NICSzz value when the vertical distance relative to the ring critical point was 1 Å . Due to the significant contribution of σ-aromaticity in the four compounds, their overall aromaticity presented an identical order to the σ-aromaticity, with the order of the absolute values of NICSzz(1)total being 22 > 14 > 15 > 2. To determine how aromaticity (including prototypical π-aromaticity, newly proposed σ-aromaticity, and total aromaticity) varies in these heterocycles, we further calculated the magnetic index of aromaticity-NICS zz (r), which is the NICS value along the z axis, by far the most widely used method for diagnosing aromaticity [15,16]. The indices with π/σ subscripts were the components contributed by all the π-electrons/σ-electrons. The more negative the NICS values, the more aromatic were the rings.
Taking 2, 14, 15, and 22 as examples, we showed the NICS zz (r) total , as well as the π and σ orbital components (NICS zz (r) π and NICS zz (r) σ ) in Figure 2A. As the vertical distance relative to the ring critical point varied from r = 0.0 to 5.0 Å, NICS zz (r) π was always negative for 2, 14, 15, and 22, suggesting the presence of π-aromaticity in these systems. NICS zz (r) σ was always negative in 22, whereas it was positive or close to zero in 2; the situations of 14 and 15 were between 2 and 22. This indicated the presence of σ-aromaticity in the all-nitrogen compound 22, whereas benzene 2 lacked such σ-aromaticity; 14 and 15 had only weak σ-aromaticity.
The order of the σ-aromaticity of the four compounds could be quantified by the absolute values of NICS zz (1) σ : 22 > 14 > 15 > 2. Here NICS zz (1) was the NICS zz value when the vertical distance relative to the ring critical point was 1 Å. Due to the significant contribution of σ-aromaticity in the four compounds, their overall aromaticity presented an identical order to the σ-aromaticity, with the order of the absolute values of NICS zz (1) total being 22 > 14 > 15 > 2.
We further performed NICS zz (r) total , NICS zz (r) π , and NICS zz (r) σ calculations for all other cyclic systems when r varied from 0.0 to 5.0 Å. The highest absolute value of the NICS zz (r) total for 13 and 15 was r extreme = 1.0 Å vertically above the ring critical point; for 14 and 16-20, r extreme = 0.8 Å; for 21 and 22, r extreme shifted to 0.6 Å, identical to the P 2 N 3 − anion [17]. In order to evaluate the aromaticity of all 21 cyclic systems in identical conditions, we uniformly took the NICS zz (r) values at r = 1 Å to compare their aromaticity, as shown in Figure 2B.   We further performed NICSzz(r)total, NICSzz(r)π, and NICSzz(r)σ calculations for all other cyclic systems when r varied from 0.0 to 5.0 Å . The highest absolute value of the NICSzz(r)total for 13 and 15 was rextreme = 1.0 Å vertically above the ring critical point; for 14 and 16-20, rextreme = 0.8 Å ; for 21 and 22, rextreme shifted to 0.6 Å , identical to the P2N3 − anion [17]. In order to evaluate the aromaticity of all 21 cyclic systems in identical conditions, we uniformly took the NICSzz(r) values at r = 1 Å to compare their aromaticity, as shown in Figure 2B. Figure 2B clearly indicates that σ-aromaticity was present in all five-membered rings, and it was gradually enhanced as the number of nitrogen atoms in the ring increased; σ-aromaticity reached a maximum in 22, in which all carbon atoms were substituted by unsaturated nitrogen atoms. In addition, we found a significant influence of bond length in the ring on the aromaticity of the compound; longer bonds in the ring led to weaker aromaticity. For example, 16 and 17 were isomers;  Figure 2B clearly indicates that σ-aromaticity was present in all five-membered rings, and it was gradually enhanced as the number of nitrogen atoms in the ring increased; σ-aromaticity reached a maximum in 22, in which all carbon atoms were substituted by unsaturated nitrogen atoms. In addition, we found a significant influence of bond length in the ring on the aromaticity of the compound; longer bonds in the ring led to weaker aromaticity. For example, 16 and 17 were isomers; the latter had longer bonds in the ring ( Figure 3) and thereby had smaller π-aromaticity, σ-aromaticity, and total aromaticity. Similar phenomena occurred also in isomeric 18 and 19. Interestingly, except for 14, no obvious σ-aromaticity was present in the six-membered rings, probably due to the longer bonds and broader regions of their rings compared to the five-membered rings.   Table 1. DI [14], also called fuzzy bond order [25,26], measures the number of shared electrons between two atoms. Figure 3A clearly indicates that the average DI of the ring, namely the electron delocalization over the cyclic backbone, was enhanced as the number of unsaturated nitrogen atoms increased.  Table 1.
Due to the contribution of the NLPE delocalization, the five-membered rings showed dual-aromaticity, namely πand σ-aromaticity. Figure 2B indicates that dual-aromaticity of the five-membered rings, with NICS zz (1) total in the range of −43.77 to −30.99, was significantly higher than the prototypical aromaticity of the six-membered rings, which had their NICS zz (1) total in the range of −29.07 to −25.53.
We note that the dual aromaticity in five-membered nitrogen heterocycles is very different from the double aromaticity of metallic compounds. The dual aromaticity of, for example, Al 4 2− dianion means that four σ electrons and two π electrons together form a single aromatic system due to the electron deficiency of the dianion [18][19][20]. However, the dual aromaticity of five-membered nitrogen heterocycles was derived from two separate aromatic systems, with independently delocalized π-electrons and σ(LP)-electrons, like those present in 3,5-dehydrophenyl cation [21], saturated inorganic rings [22], and probably in pnictogen five-membered rings like P 5 − and As 5 − anion [23,24]. Therefore, the "dual" aromaticity in five-membered nitrogen heterocycles means two types of electrons and two separate aromatic systems. As we declared in one of our previous works, the two aromatic systems are independent in real space but are coupled in energy space. The competition between the nonbonding interactions in both aromatic systems and the LP-LP repulsive interactions in the σ aromatic system makes the dual-aromatics show different reactivity to electrophilic attack in different acidic solutions [11].

Effect of Enhanced Aromaticity of Heterocycles on Structure Stability
In this section, we investigate the effect of enhanced aromaticity of nitrogen heterocycles on their structure stability, at both the molecular and crystal levels. Notably, the calculation method for crystal systems considers periodic boundary condition and intermolecular interactions and thereby can reflect the effect of aromaticity on the energetics of solid-state systems.

Reduced Molecular Structure Firmness
Structure stability of nitrogen heterocycles is closely related to the firmness of their backbone bonds. Herewith, we quantified the firmness of the bonds in the ring by their DI, bond length, and bond strength, as shown in Figure 3.
DI [14], also called fuzzy bond order [25,26], measures the number of shared electrons between two atoms. Figure 3A clearly indicates that the average DI of the ring, namely the electron delocalization over the cyclic backbone, was enhanced as the number of unsaturated nitrogen atoms increased.
The characteristics of each individual bond in the rings of the 21 cyclic compounds, including DI, length, and strength, are shown in Figure 3B,C. Bond length was calculated using the HASEM application [11,27]. Figure 3 indicates that higher DI and smaller bond length generally corresponded to higher bond strength. However, we found that N−N bonds presented significantly lower strength as compared to C−C or C−N bonds, even when they had higher bond orders (applicable when DI ≤ 2); this finding is consistent with a previous report [28].
When more carbons are substituted by nitrogen atoms, the attendant phenomenon is that more N−N bonds, which have low strength and are very likely to rupture, will be present. Therefore, although NLPEs are more delocalized in the ring and even create additional σ-aromaticity, the firmness of the entire molecular architecture is reduced once adjacent nitrogen atoms are present in the ring. For example, bond 4 and 5 in compound 7 (7-4 and 7-5) in Figure 3B; bond 4 in compound 10 (10-4) in Figure 3B; bond 3 in compound 20 (20-3) and so on. These mentioned N-N bonds have much lower strength compared to C−C or C−N bonds in the rings.
The very low N-N bond strength of cyclo-pentazolate anion (22) is the reason that 22 is difficult to productively separate, because these N-N bonds easily break prior to the C−N bond cleavage in the precursor 3,5-dimethyl-4-hydroxyphenylpentazole [3]. One practical way, as reported in our recent work [11], is to introduce an appropriate concentration of hydronium or ammonium in the solution, which strengthens all the N-N bonds in 22 with the aid of the electron delocalization of the formed hydrogen bonds.

Improved In-Crystal Intermolecular Binding Strength
Crystal structure stability depends significantly on the interspecies binding strength of the constitution components. Therefore, the stability of the crystals composed of nitrogen heterocycles is closely related to one of the important intermolecular-aromatic interactions.
Herewith, we collected 32 crystal structures composed of ammonia and various homocyclic and nitrogen heterocyclic molecules ( Table 2). Lattice energy (LE), the energy difference between total energy of constituent molecules in the free state and total energy of the crystal, was employed to quantify the in-crystal binding strength, as shown in Figure 4. The number of hydrogen atoms in each molecule was also plotted to evaluate the effect of hydrogen bonding on LE. application [11,27]. Figure 3 indicates that higher DI and smaller bond length generally corresponded to higher bond strength. However, we found that N−N bonds presented significantly lower strength as compared to C−C or C−N bonds, even when they had higher bond orders (applicable when DI ≤ 2); this finding is consistent with a previous report [28]. When more carbons are substituted by nitrogen atoms, the attendant phenomenon is that more N−N bonds, which have low strength and are very likely to rupture, will be present. Therefore, although NLPEs are more delocalized in the ring and even create additional σ-aromaticity, the firmness of the entire molecular architecture is reduced once adjacent nitrogen atoms are present in the ring. For example, bond 4 and 5 in compound 7 (7-4 and 7-5) in Figure 3B; bond 4 in compound 10 (10-4) in Figure 3B; bond 3 in compound 20  and so on. These mentioned N-N bonds have much lower strength compared to C−C or C−N bonds in the rings.
The very low N-N bond strength of cyclo-pentazolate anion (22) is the reason that 22 is difficult to productively separate, because these N-N bonds easily break prior to the C−N bond cleavage in the precursor 3,5-dimethyl-4-hydroxyphenylpentazole [3]. One practical way, as reported in our recent work [11], is to introduce an appropriate concentration of hydronium or ammonium in the solution, which strengthens all the N-N bonds in 22 with the aid of the electron delocalization of the formed hydrogen bonds. application [11,27]. Figure 3 indicates that higher DI and smaller bond length generally corresponded to higher bond strength. However, we found that N−N bonds presented significantly lower strength as compared to C−C or C−N bonds, even when they had higher bond orders (applicable when DI ≤ 2); this finding is consistent with a previous report [28]. When more carbons are substituted by nitrogen atoms, the attendant phenomenon is that more N−N bonds, which have low strength and are very likely to rupture, will be present. Therefore, although NLPEs are more delocalized in the ring and even create additional σ-aromaticity, the firmness of the entire molecular architecture is reduced once adjacent nitrogen atoms are present in the ring. For example, bond 4 and 5 in compound 7 (7-4 and 7-5) in Figure 3B; bond 4 in compound 10  in Figure 3B; bond 3 in compound 20  and so on. These mentioned N-N bonds have much lower strength compared to C−C or C−N bonds in the rings.

Improved In-Crystal Intermolecular Binding Strength
The very low N-N bond strength of cyclo-pentazolate anion (22) is the reason that 22 is difficult to productively separate, because these N-N bonds easily break prior to the C−N bond cleavage in the precursor 3,5-dimethyl-4-hydroxyphenylpentazole [3]. One practical way, as reported in our recent work [11], is to introduce an appropriate concentration of hydronium or ammonium in the solution, which strengthens all the N-N bonds in 22 with the aid of the electron delocalization of the formed hydrogen bonds. application [11,27]. Figure 3 indicates that higher DI and smaller bond length generally corresponded to higher bond strength. However, we found that N−N bonds presented significantly lower strength as compared to C−C or C−N bonds, even when they had higher bond orders (applicable when DI ≤ 2); this finding is consistent with a previous report [28]. When more carbons are substituted by nitrogen atoms, the attendant phenomenon is that more N−N bonds, which have low strength and are very likely to rupture, will be present. Therefore, although NLPEs are more delocalized in the ring and even create additional σ-aromaticity, the firmness of the entire molecular architecture is reduced once adjacent nitrogen atoms are present in the ring. For example, bond 4 and 5 in compound 7 (7-4 and 7-5) in Figure 3B; bond 4 in compound 10  in Figure 3B; bond 3 in compound 20  and so on. These mentioned N-N bonds have much lower strength compared to C−C or C−N bonds in the rings.

Improved In-Crystal Intermolecular Binding Strength
The very low N-N bond strength of cyclo-pentazolate anion (22) is the reason that 22 is difficult to productively separate, because these N-N bonds easily break prior to the C−N bond cleavage in the precursor 3,5-dimethyl-4-hydroxyphenylpentazole [3]. One practical way, as reported in our recent work [11], is to introduce an appropriate concentration of hydronium or ammonium in the solution, which strengthens all the N-N bonds in 22 with the aid of the electron delocalization of the formed hydrogen bonds. DI, length, and strength, are shown in Figure 3B,C. Bond length was calculated using the HASEM application [11,27]. Figure 3 indicates that higher DI and smaller bond length generally corresponded to higher bond strength. However, we found that N−N bonds presented significantly lower strength as compared to C−C or C−N bonds, even when they had higher bond orders (applicable when DI ≤ 2); this finding is consistent with a previous report [28]. When more carbons are substituted by nitrogen atoms, the attendant phenomenon is that more N−N bonds, which have low strength and are very likely to rupture, will be present. Therefore, although NLPEs are more delocalized in the ring and even create additional σ-aromaticity, the firmness of the entire molecular architecture is reduced once adjacent nitrogen atoms are present in the ring. For example, bond 4 and 5 in compound 7 (7-4 and 7-5) in Figure 3B; bond 4 in compound 10  in Figure 3B; bond 3 in compound 20  and so on. These mentioned N-N bonds have much lower strength compared to C−C or C−N bonds in the rings.

Improved In-Crystal Intermolecular Binding Strength
The very low N-N bond strength of cyclo-pentazolate anion (22) is the reason that 22 is difficult to productively separate, because these N-N bonds easily break prior to the C−N bond cleavage in the precursor 3,5-dimethyl-4-hydroxyphenylpentazole [3]. One practical way, as reported in our recent work [11], is to introduce an appropriate concentration of hydronium or ammonium in the solution, which strengthens all the N-N bonds in 22 with the aid of the electron delocalization of the formed hydrogen bonds. DI, length, and strength, are shown in Figure 3B,C. Bond length was calculated using the HASEM application [11,27]. Figure 3 indicates that higher DI and smaller bond length generally corresponded to higher bond strength. However, we found that N−N bonds presented significantly lower strength as compared to C−C or C−N bonds, even when they had higher bond orders (applicable when DI ≤ 2); this finding is consistent with a previous report [28]. When more carbons are substituted by nitrogen atoms, the attendant phenomenon is that more N−N bonds, which have low strength and are very likely to rupture, will be present. Therefore, although NLPEs are more delocalized in the ring and even create additional σ-aromaticity, the firmness of the entire molecular architecture is reduced once adjacent nitrogen atoms are present in the ring. For example, bond 4 and 5 in compound 7 (7-4 and 7-5) in Figure 3B; bond 4 in compound 10  in Figure 3B; bond 3 in compound 20  and so on. These mentioned N-N bonds have much lower strength compared to C−C or C−N bonds in the rings.

Improved In-Crystal Intermolecular Binding Strength
The very low N-N bond strength of cyclo-pentazolate anion (22) is the reason that 22 is difficult to productively separate, because these N-N bonds easily break prior to the C−N bond cleavage in the precursor 3,5-dimethyl-4-hydroxyphenylpentazole [3]. One practical way, as reported in our recent work [11], is to introduce an appropriate concentration of hydronium or ammonium in the solution, which strengthens all the N-N bonds in 22 with the aid of the electron delocalization of the formed hydrogen bonds. application [11,27]. Figure 3 indicates that higher DI and smaller bond length generally corresponded to higher bond strength. However, we found that N−N bonds presented significantly lower strength as compared to C−C or C−N bonds, even when they had higher bond orders (applicable when DI ≤ 2); this finding is consistent with a previous report [28]. When more carbons are substituted by nitrogen atoms, the attendant phenomenon is that more N−N bonds, which have low strength and are very likely to rupture, will be present. Therefore, although NLPEs are more delocalized in the ring and even create additional σ-aromaticity, the firmness of the entire molecular architecture is reduced once adjacent nitrogen atoms are present in the ring. For example, bond 4 and 5 in compound 7 (7-4 and 7-5) in Figure 3B; bond 4 in compound 10  in Figure 3B; bond 3 in compound 20  and so on. These mentioned N-N bonds have much lower strength compared to C−C or C−N bonds in the rings.

Improved In-Crystal Intermolecular Binding Strength
The very low N-N bond strength of cyclo-pentazolate anion (22) is the reason that 22 is difficult to productively separate, because these N-N bonds easily break prior to the C−N bond cleavage in the precursor 3,5-dimethyl-4-hydroxyphenylpentazole [3]. One practical way, as reported in our recent work [11], is to introduce an appropriate concentration of hydronium or ammonium in the solution, which strengthens all the N-N bonds in 22 with the aid of the electron delocalization of the formed hydrogen bonds. DI, length, and strength, are shown in Figure 3B,C. Bond length was calculated using the HASEM application [11,27]. Figure 3 indicates that higher DI and smaller bond length generally corresponded to higher bond strength. However, we found that N−N bonds presented significantly lower strength as compared to C−C or C−N bonds, even when they had higher bond orders (applicable when DI ≤ 2); this finding is consistent with a previous report [28]. When more carbons are substituted by nitrogen atoms, the attendant phenomenon is that more N−N bonds, which have low strength and are very likely to rupture, will be present. Therefore, although NLPEs are more delocalized in the ring and even create additional σ-aromaticity, the firmness of the entire molecular architecture is reduced once adjacent nitrogen atoms are present in the ring. For example, bond 4 and 5 in compound 7 (7-4 and 7-5) in Figure 3B; bond 4 in compound 10  in Figure 3B; bond 3 in compound 20  and so on. These mentioned N-N bonds have much lower strength compared to C−C or C−N bonds in the rings.

Improved In-Crystal Intermolecular Binding Strength
The very low N-N bond strength of cyclo-pentazolate anion (22) is the reason that 22 is difficult to productively separate, because these N-N bonds easily break prior to the C−N bond cleavage in the precursor 3,5-dimethyl-4-hydroxyphenylpentazole [3]. One practical way, as reported in our recent work [11], is to introduce an appropriate concentration of hydronium or ammonium in the solution, which strengthens all the N-N bonds in 22 with the aid of the electron delocalization of the formed hydrogen bonds. DI, length, and strength, are shown in Figure 3B,C. Bond length was calculated using the HASEM application [11,27]. Figure 3 indicates that higher DI and smaller bond length generally corresponded to higher bond strength. However, we found that N−N bonds presented significantly lower strength as compared to C−C or C−N bonds, even when they had higher bond orders (applicable when DI ≤ 2); this finding is consistent with a previous report [28]. When more carbons are substituted by nitrogen atoms, the attendant phenomenon is that more N−N bonds, which have low strength and are very likely to rupture, will be present. Therefore, although NLPEs are more delocalized in the ring and even create additional σ-aromaticity, the firmness of the entire molecular architecture is reduced once adjacent nitrogen atoms are present in the ring. For example, bond 4 and 5 in compound 7 (7-4 and 7-5) in Figure 3B; bond 4 in compound 10  in Figure 3B; bond 3 in compound 20  and so on. These mentioned N-N bonds have much lower strength compared to C−C or C−N bonds in the rings.

Improved In-Crystal Intermolecular Binding Strength
The very low N-N bond strength of cyclo-pentazolate anion (22) is the reason that 22 is difficult to productively separate, because these N-N bonds easily break prior to the C−N bond cleavage in the precursor 3,5-dimethyl-4-hydroxyphenylpentazole [3]. One practical way, as reported in our recent work [11], is to introduce an appropriate concentration of hydronium or ammonium in the solution, which strengthens all the N-N bonds in 22 with the aid of the electron delocalization of the formed hydrogen bonds. DI, length, and strength, are shown in Figure 3B,C. Bond length was calculated using the HASEM application [11,27]. Figure 3 indicates that higher DI and smaller bond length generally corresponded to higher bond strength. However, we found that N−N bonds presented significantly lower strength as compared to C−C or C−N bonds, even when they had higher bond orders (applicable when DI ≤ 2); this finding is consistent with a previous report [28]. When more carbons are substituted by nitrogen atoms, the attendant phenomenon is that more N−N bonds, which have low strength and are very likely to rupture, will be present. Therefore, although NLPEs are more delocalized in the ring and even create additional σ-aromaticity, the firmness of the entire molecular architecture is reduced once adjacent nitrogen atoms are present in the ring. For example, bond 4 and 5 in compound 7 (7-4 and 7-5) in Figure 3B; bond 4 in compound 10  in Figure 3B; bond 3 in compound 20  and so on. These mentioned N-N bonds have much lower strength compared to C−C or C−N bonds in the rings.

Improved In-Crystal Intermolecular Binding Strength
The very low N-N bond strength of cyclo-pentazolate anion (22) is the reason that 22 is difficult to productively separate, because these N-N bonds easily break prior to the C−N bond cleavage in the precursor 3,5-dimethyl-4-hydroxyphenylpentazole [3]. One practical way, as reported in our recent work [11], is to introduce an appropriate concentration of hydronium or ammonium in the solution, which strengthens all the N-N bonds in 22 with the aid of the electron delocalization of the formed hydrogen bonds. DI, length, and strength, are shown in Figure 3B,C. Bond length was calculated using the HASEM application [11,27]. Figure 3 indicates that higher DI and smaller bond length generally corresponded to higher bond strength. However, we found that N−N bonds presented significantly lower strength as compared to C−C or C−N bonds, even when they had higher bond orders (applicable when DI ≤ 2); this finding is consistent with a previous report [28]. When more carbons are substituted by nitrogen atoms, the attendant phenomenon is that more N−N bonds, which have low strength and are very likely to rupture, will be present. Therefore, although NLPEs are more delocalized in the ring and even create additional σ-aromaticity, the firmness of the entire molecular architecture is reduced once adjacent nitrogen atoms are present in the ring. For example, bond 4 and 5 in compound 7 (7-4 and 7-5) in Figure 3B; bond 4 in compound 10  in Figure 3B; bond 3 in compound 20  and so on. These mentioned N-N bonds have much lower strength compared to C−C or C−N bonds in the rings.

Improved In-Crystal Intermolecular Binding Strength
The very low N-N bond strength of cyclo-pentazolate anion (22) is the reason that 22 is difficult to productively separate, because these N-N bonds easily break prior to the C−N bond cleavage in the precursor 3,5-dimethyl-4-hydroxyphenylpentazole [3]. One practical way, as reported in our recent work [11], is to introduce an appropriate concentration of hydronium or ammonium in the solution, which strengthens all the N-N bonds in 22 with the aid of the electron delocalization of the formed hydrogen bonds. DI, length, and strength, are shown in Figure 3B,C. Bond length was calculated using the HASEM application [11,27]. Figure 3 indicates that higher DI and smaller bond length generally corresponded to higher bond strength. However, we found that N−N bonds presented significantly lower strength as compared to C−C or C−N bonds, even when they had higher bond orders (applicable when DI ≤ 2); this finding is consistent with a previous report [28]. When more carbons are substituted by nitrogen atoms, the attendant phenomenon is that more N−N bonds, which have low strength and are very likely to rupture, will be present. Therefore, although NLPEs are more delocalized in the ring and even create additional σ-aromaticity, the firmness of the entire molecular architecture is reduced once adjacent nitrogen atoms are present in the ring. For example, bond 4 and 5 in compound 7 (7-4 and 7-5) in Figure 3B; bond 4 in compound 10  in Figure 3B; bond 3 in compound 20  and so on. These mentioned N-N bonds have much lower strength compared to C−C or C−N bonds in the rings.

Improved In-Crystal Intermolecular Binding Strength
The very low N-N bond strength of cyclo-pentazolate anion (22) is the reason that 22 is difficult to productively separate, because these N-N bonds easily break prior to the C−N bond cleavage in the precursor 3,5-dimethyl-4-hydroxyphenylpentazole [3]. One practical way, as reported in our recent work [11], is to introduce an appropriate concentration of hydronium or ammonium in the solution, which strengthens all the N-N bonds in 22 with the aid of the electron delocalization of the formed hydrogen bonds. (benzene) has very low LE (12.83 kcal·mol −1 ) and is liquid at ambient condition. c3 (HNB explosive), with a low LE = 12.50 kcal·mol −1 , is very sensitive to light and easy to decompose. c12-c21 generally have abundant hydrogen bonding, whereas they have relatively lower LE than the crystals composed of heterocyclic molecules (like c22, c25, c26, c27, c29, c30, and c32) due to the absence of nitrogen atoms in their rings and therefore relatively weaker aromaticity.

Improved In-Crystal Intermolecular Binding Strength
In brief, we found that strong aromaticity of heterocyclic molecules is conducive to enhancing in-crystal intermolecular binding, and vice versa.  Crystal structure stability depends significantly on the interspecies binding strength of the constitution components. Therefore, the stability of the crystals composed of nitrogen heterocycles is closely related to one of the important intermolecular-aromatic interactions.
Herewith, we collected 32 crystal structures composed of ammonia and various homocyclic and nitrogen heterocyclic molecules (Table 2). Lattice energy (LE), the energy difference between total energy of constituent molecules in the free state and total energy of the crystal, was employed to quantify the in-crystal binding strength, as shown in Figure 4. The number of hydrogen atoms in each molecule was also plotted to evaluate the effect of hydrogen bonding on LE.
As shown in Figure 4, c1 (ammonia), which has no aromaticity, is gaseous at ambient condition and has the lowest LE of 13.01 kcal·mol −1 . As for the cyclic systems, Figure 4 indicates that the crystals composed of C-N heterocycles generally have higher stability as compared to those composed of all-C homocyclic molecules. One typical example is c9 and c11, which have one nitrogen atom in each heterocycle. Both have relatively less hydrogen bonding than c5-c7, but present higher LE (20.27 and 20.49 kcal·mol −1 for c9 and c11, respectively) than c5-c7 (LE in the range of 18.28-19.78 kcal·mol −1 ). Another typical example is c25 and c32, which have two nitrogen atoms in each heterocycle. Both have much less hydrogen bonding than c23 and c24, whereas they present higher LE (27.22 kcal·mol −1 for c25 and 32.67 kcal·mol −1 for c32, respectively) due to their relatively stronger aromaticity. In addition, the presence of nitro group is conducive to provoking dipole-dipole interactions, thereby further enlarging LE of the crystal.
c2-c8, on the other hand, have no nitrogen atoms in their rings, relatively less hydrogen bonding, and present very low LE (in the range of 12.83-19.91 kcal·mol −1 , respectively). For example, c2 (benzene) has very low LE (12.83 kcal·mol 1 ) and is liquid at ambient condition. c3 (HNB explosive), with a low LE = 12.50 kcal·mol −1 , is very sensitive to light and easy to decompose. c12-c21 generally have abundant hydrogen bonding, whereas they have relatively lower LE than the crystals composed of heterocyclic molecules (like c22, c25, c26, c27, c29, c30, and c32) due to the absence of nitrogen atoms in their rings and therefore relatively weaker aromaticity.
In brief, we found that strong aromaticity of heterocyclic molecules is conducive to enhancing in-crystal intermolecular binding, and vice versa.