A study of the aromaticity and ring currents of azulene and azaazulenes

Abstract

The global aromaticity of azaazulenes has been investigated using topological resonance energy (TRE), percentage topological resonance energy (% TRE), and magnetic resonance energy (MRE) methods. The impact of nitrogen atoms on the aromaticity of azazulenes is discussed. The aromaticity results obtained by the TRE and % TRE methods were compared with the nucleus independent chemical shift (NICS(0)) values at the cage center. We found discrepancies between the NICS(0) predictions and our results. We have found that the aromaticity of the azaazulenes depends strongly on the substituted position of the nitrogen atoms on the ring. The local aromaticity was studied using bond resonance energy (BRE) and circuit resonance energy (CRE) indices. The BRE and CRE results show that the 10π-electron peripheral rings play an important role in both the global and local aromaticity of these compounds. Ring current (RC) results show that all the azaazulenes sustain diamagnetic currents regardless of any predicted antiaromaticity.

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1. Introduction

The concept of aromaticity is the most fundamental and widely studied subject in physical organic chemistry. Many experimental and theoretical probes have been developed to identify aromatic species, and to evaluate the degree of aromaticity. Since different criteria may cause different trends in aromaticity,¹ it is necessary to investigate various indices when performing an aromaticity study.

The aromatic character is generally evaluated on the basis of magnetic, energetic, and geometric criteria.² In 1996, Schleyer et al.^3,4 proposed a new magnetic criterion for aromaticity: nucleus-independent chemical shift (NICS). This is defined as the negative value of the absolute shielding computed either at the ring center or at various other points in the system. A negative NICS value (diatropic) implies aromaticity; a positive value (paratropic) implies antiaromaticity; a value close to zero implies a lack of aromaticity.

Azulenes is one of the few non-benzenoids that appears to have significant aromatic stabilization. Azaazulenes are interesting compounds, particularly in comparison with azulene.^5–8 In this study, we applied the graph theory of aromaticity and magnetotropicity^9–13 to investigate both the global and local aromaticity of azulene and azaazulenes. The impact of nitrogen atoms on the global and local aromaticity of the azaazulenes are also discussed. Our results are compared to those NICS(0) indices in the literature, as well. The origin of the discrepancies between the our results and NICS(0) results are analyzed.

2. Methods of calculation

TRE is a kind of energetic criterion of global aromaticity.^9–13 Positive and negative TREs are associated with aromaticity and antiaromaticity, respectively. The % TRE is useful when the degrees of aromaticity of different species are compared. The bond resonance energy (BRE) represents the contribution of a given π-bond to the TRE.¹⁴ The BRE for a peripheral π-bond can be used as an indicator of local aromaticity for the ring to which that π-bond belongs.^15–17 The circuit resonance energy (CRE), circuit current (CC) and the ring current (RC) concept has been introduced and applied in numerous studies.^12,16–19 It is not necessary to repeat this work here. All the calculations of TRE, % TRE, BRE, CRE, and RCs are performed within the framework of simple Hückel molecular orbital theory. In this paper, Van-Catledge's set of Hückel parameters for nitrogen²⁰ has been used. When computed in an aromatic ring, the more positive the BRE and CRE values, the larger the aromaticity.

3. Results and discussion

3.1 Global aromaticity of azulene and azaazulenes

The replacement on the azulene molecule at one or more CH units with a nitrogen atom(s) will result in azazulenes. The structure of the resulting compounds is shown in Fig. 1. All azaazulenes (2–47) and also azulene (1) are isoelectronic and have 10π-electrons. The TRE and % TRE values calculated for these isomers are given in Table 1. As shown in Table 1, some of the azaazulenes are aromatic with positive TREs, while others are antiaromatic with negative TREs. By comparing the TRE and % TRE values of 1–47, we find that the number and positioning of the nitrogen atom(s) in the molecule is the most important factor in determining the global aromaticity of these molecules. For the convenience of discussion, all the isomers can be divided into three groups. The first group of isomers are those with nitrogen atom(s) substituted only at the five-membered ring of 1. The resulting structures (2–6) have significantly higher TRE values than that of 1. The second groups of isomers are those where nitrogen atom(s) are substituted both at the five-membered ring of 1 and where the seven-membered ring has one or two substituted nitrogen atom(s). This causes those structures (26–30, 32, 34, 36, and 39–45) to have slightly higher TRE values than that of 1. The third groups of isomers are those where one or two nitrogen atom(s) are substituted at the five-membered ring, and where three or four nitrogen atom(s) are substituted on the seven-membered ring. This causes those structures (7–25, 31, 33, 35, 37, 38, 46 and 47) to have TRE and % TRE values significantly lower than that of 1. As an increasing number of nitrogen atoms are substituted in the seven-membered rings, the global aromaticity of these molecules gradually decreases. We then tried to find the reason for such different aromaticity behavior of the isomers under analysis. According to the topological charge stabilization (TCS) rule,^21,22 the heteroatomic molecules are stabilized when more electronegative atoms are placed in those positions where the atoms in the uniform reference frame (URF) have the highest electron charge. Azulene (1) is the URF for 2–47. The π-electron density in 1 is presented in Fig. 2. In compounds 2 and 5, the nitrogen atoms are located at the sites of the highest charge density in the URF. The entire π-electron systems of 2 and 5 conform to the TCS rule. However, in compounds 7–47, the nitrogen atoms are located at the sites of appreciably lower charge density in the corresponding URF. These molecules must be destabilized by the presence of nitrogen atoms, as they do not obey the TCS rule. So far, some of the azaazulenes, such as 2 and 5, have been synthesized a long time ago.^23,24 Despite 4 having been prepared, it is sensitive to strong acids, and easily converts in nitrocompounds.²⁵ Although there are a few reports of the existence of 7, it rapidly decomposes in the presence of oxygen.²⁶ Isomer 8 is also generally less stable.²⁷ The structures of 3 and 9 and the other azaazulenes have not been reported. As shown in Table 1, anomaly TRE values are observed in the cases (4 and 6) where a N–N bond is formed. If the Hückel resonance integral for the N–N bond become much smaller, then the TRE values for 4 and 6 are close to the 1. According to the TCS rule and our TRE results, we can conclude that the systems with nitrogen at the 1- or 3-positions in the five-membered ring are stable, whereas their analogues bearing seven-membered-ring nitrogen are unstable and elusive.

Fig. 1 BREs in units of |β| for all π-bonds of azulene (1) and azaazulenes (2–47). Values in parentheses are the RCs, all in units of that for benzene (I₀).

Table 1 The TRE, % TRE, MRE, CRE, CC and NICS(0) values of compounds 1–47

Species	TRE	% TRE	MRE	CRE			CC			NICS-5	NICS-7
				c1	c2	c3	c1	c2	c3
1	0.151	1.144	0.126	0.013	−0.007	0.120	0.038	−0.043	1.111	−18.1	−5.5
2	0.223	1.611	0.175	0.040	0.037	0.099	0.118	0.233	0.916	−15.0	−6.9
3	0.171	1.236	0.141	0.038	−0.011	0.115	0.114	−0.067	1.070	−19.5	−3.8
4	0.247	1.704	0.191	0.063	0.033	0.098	0.189	0.205	0.911	−15.8	−6.1
5	0.273	1.887	0.211	0.059	0.069	0.082	0.176	0.432	0.760	−12.4	−7.7
6	0.301	1.985	0.229	0.083	0.063	0.085	0.246	0.395	0.784	−14.5	−7.2
7	0.072	0.523	0.066	−0.047	−0.026	0.139	−0.139	−0.165	1.286	−17.1	−5.7
8	0.142	1.028	0.117	0.019	−0.020	0.118	0.058	−0.124	1.091	−18.1	−4.1
9	0.080	0.578	0.073	−0.040	−0.025	0.138	−0.119	−0.159	1.280	−17.6	−6.1
10	0.068	0.468	0.060	−0.041	−0.041	0.141	−0.122	−0.256	1.309	−16.9	−4.3
11	−0.011	−0.073	−0.007	−0.116	−0.049	0.158	−0.347	−0.307	1.466	−16.2	−6.2
12	0.065	0.452	0.058	−0.040	−0.041	0.139	−0.119	−0.259	1.290	−17.3	−4.0
13	−0.022	−0.152	−0.019	−0.130	−0.050	0.162	−0.388	−0.317	1.498	−15.5	−5.9
14	0.077	0.529	0.068	−0.032	−0.040	0.140	−0.095	−0.251	1.296	−17.6	−4.1
15	0.130	0.901	0.107	0.026	−0.032	0.113	0.078	−0.200	1.048	−17.7	−2.7
16	−0.009	−0.061	−0.008	−0.107	−0.066	0.165	−0.318	−0.417	1.534	−17.6	−4.6
17	0.057	0.379	0.049	−0.034	−0.055	0.138	−0.100	−0.348	1.282	−16.0	−2.0
18	−0.021	−0.138	−0.019	−0.118	−0.068	0.166	−0.353	−0.425	1.544	−16.1	−4.1
19	−0.016	−0.109	−0.014	−0.111	−0.067	0.165	−0.332	−0.424	1.529	−15.2	−3.7
20	−0.114	−0.756	−0.121	−0.226	−0.078	0.183	−0.674	−0.488	1.694	−14.1	−6.3
21	0.070	0.460	0.060	−0.024	−0.054	0.138	−0.071	−0.341	1.283	−18.7	−3.2
22	−0.018	−0.116	−0.017	−0.101	−0.085	0.168	−0.301	−0.535	1.315	−14.4	−1.7
23	−0.111	−0.706	−0.117	−0.212	−0.100	0.195	−0.632	−0.628	1.806	−14.3	−4.4
24	−0.023	−0.143	−0.023	−0.106	−0.085	0.168	−0.315	−0.532	1.555	−15.7	−2.5
25	−0.111	−0.674	−0.116	−0.197	−0.123	0.203	−0.586	−0.772	1.882	−6.4	−2.1
26	0.156	1.082	0.130	−0.006	0.026	0.110	−0.019	0.162	1.023	—	—
27	0.218	1.507	0.169	0.046	0.025	0.098	0.136	0.160	0.912	—	—
28	0.164	1.131	0.136	−0.001	0.026	0.110	−0.002	0.166	1.023	—	—
29	0.217	1.504	0.169	0.045	0.025	0.098	0.135	0.160	0.911	—	—
30	0.157	1.087	0.130	−0.006	0.026	0.111	−0.017	0.161	1.026	—	—
31	0.085	0.561	0.076	−0.057	0.012	0.122	−0.171	0.078	1.128	—	—
32	0.153	1.014	0.124	−0.001	0.013	0.112	−0.004	0.083	1.039	—	—
33	0.074	0.494	0.067	−0.069	0.012	0.124	−0.204	0.074	1.150	—	—
34	0.154	1.022	0.125	−0.001	0.013	0.113	−0.002	0.082	1.045	—	—
35	0.085	0.563	0.077	−0.057	0.012	0.122	−0.169	0.075	1.129	—	—
36	0.208	1.380	0.161	0.052	0.013	0.096	0.154	0.083	0.889	—	—
37	−0.008	−0.052	−0.005	−0.136	−0.005	0.135	−0.404	−0.030	1.249	—	—
38	−0.004	−0.026	−0.006	−0.122	−0.038	0.154	−0.363	−0.236	1.425	—	—
39	0.219	1.449	0.174	0.023	0.062	0.089	0.070	0.389	0.825	—	—
40	0.272	1.805	0.206	0.065	0.059	0.082	0.193	0.372	0.760	—	—
41	0.224	1.488	0.179	0.028	0.063	0.089	0.082	0.393	0.825	—	—
42	0.158	1.004	0.133	−0.015	0.053	0.095	−0.045	0.334	0.882	—	—
43	0.220	1.404	0.171	0.028	0.052	0.091	0.084	0.330	0.842	—	—
44	0.149	0.949	0.126	−0.025	0.054	0.097	−0.073	0.337	0.897	—	—
45	0.266	1.700	0.200	0.071	0.048	0.080	0.212	0.304	0.746	—	—
46	0.077	0.471	0.071	−0.073	0.042	0.102	−0.218	0.266	0.943	—	—
47	0.089	0.519	0.075	−0.066	0.023	0.118	−0.197	0.144	1.094	—	—

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Fig. 2 Labeling of 1 and π-electron density in the URFs for compounds 2–47.

3.2 Local aromaticity of azaazulenes

In order to explain how nitrogen doping affects the global aromaticity, we use the (1) BRE and (2) CRE indices as a measure of local aromaticity in predicting this for these compounds.

3.2.1 BRE of azaazulenes. The BRE values for all the distinct π bonds in compounds 1–47 are shown in Fig. 1. As shown in Fig. 1, all the bonds in the 1, the first group (2–6) and the second group isomers (26–30, 32, 34, 36 and 39–45) exhibit large positive BRE values, indicating that they make aromatic contributions to the whole molecule. The peripheral bonds in 1 exhibit large positive BRE values, indicating that these bonds contribute significantly to aromaticity, whereas the BRE for the bond shared by the two rings is negligibly small, suggesting that peripheral bonds are the main origin of aromaticity in 1. The X-ray crystallography and electron-diffraction results show that peripheral bond lengths of 1 are in the aromatic range and show no regular alternation. The bond shared by the two rings is significantly longer (X-ray bond length is 1.498 Å; electron-diffraction bond length is 1.501 Å),^28,29 indicating that it predominantly has single-bond character, which indicates that the conjugated system more closely resembles¹⁰ annulene. A very small BRE for bond the shared by the two rings in 1 is fully consistent with its fairly long single-bond character. AM1 calculation results revealed that the bond length and bond angles of 2 and 5 are very similar to that of 1.³⁰ Calculated BREs for bond the shared by the two rings in 2 and 5 also support the interpretation that the character of these isomers as a peripheral 10π-system. Similar results can be found if compounds 3–5 and 6 and the second group isomers (26–30, 32, 34, 36 and 39–45) are analyzed. From this we can conclude that peripheral bonds are the main origin of aromaticity and these compounds are stabilized as 10π-peripheral systems. All π-bonds in 1, in first group isomers (2–6), and in second group isomers (26–30, 32, 34, 36 and 39–45) were found to have positive BREs, which is consistent with the view that all these molecules are aromatic with positive TREs. By comparing the BRE values of third group isomers (7–25, 31, 33, 35, 37, 38, 46 and 47), we found that the peripheral bonds have positive BRE values, whereas the bond shared by the two rings has a relatively large negative BRE value. As increasing numbers of nitrogen atoms are substituted in the seven-membered ring, the BRE values of the bond shared by the two rings tend to decrease and exhibit very large negative values. Thus, we can predict that the bond shared by the two rings destabilizes to a large extent the entire π-electron system and is the main source of low aromaticity or antiaromaticity in third group isomers (7–25, 31, 33, 35, 37, 38, 46 and 47).

3.2.2 CREs of azaazulenes. In order to clarify the origin of the aromaticity of compounds 1–47, we calculated their CREs. The π-electron ring system in azulene and azaazulenes consists of π-ring circuits, from c₁ to c₃, as shown in Fig. 3. The c₁ and the c₂ circuits values are related to the five-membered circuit and seven-membered circuit, respectively, while c₃ circuit values are related to the peripheral circuit. By comparing the CRE values as shown in Table 1, we find that in the case of 1–6, the c₁ and the c₂ circuits have small positive or small negative values. However, each c₃ circuit has a relatively larger positive values. We can predict that the ten-membered circuit is the main origin of aromaticity and these compounds are stabilized as 10π-peripheral systems. For compounds 7–47, we have also found the same trend of c₁, c₂ and c₃ circuit values. By increasing the number of nitrogen atoms in the seven-membered ring, the c₁ and the c₂ circuit values are decreased, however, the c₃ circuit values are increased. The presence of large antiaromatic bonds or antiaromatic circuits in the third group isomers (7–25, 31, 33, 35, 37, 38, 46 and 47) cause the TRE and % TRE values of to be smaller than that of 1–6. According to the BRE values in Fig. 1 and the CRE values in Table 1, we can predict that the aromaticity of 1–47 arises primarily from the peripheral ten-membered circuit. The nitrogen atom substitution to the azulene does not change its nature as mainly a 10π-peripheral electronic system. Namely, the aromaticity of 1 as well as of 2–47 conforms to Platt's perimeter model which states that peripheral conjugation is a determinant for the aromaticity of a polycyclic π-system.³¹ MREs of these species can be obtained by summing up the CRE values from c₁ to c₃ in Table 1. A high degree of correlation is found between the TRE and MRE, with a correlation coefficient of 0.9947. This outcome provides compelling evidence that MRE is a reliable indicator of global aromaticity. It also shows that global aromaticity arises from all possible circuits in the molecule. The trends in local aromaticity obtained by the BRE and CRE methods correspond consistently with the TRE, % TRE and MRE value changes for all the studied compounds.

Fig. 3 Circuits in azulene π-system.

4. Comparision of the aromaticity of 1–47 with that of other bicyclic systems

The question arises regarding the extent of aromaticity that azulene and azaazulenes possess. What are the differences in local aromaticity between the corresponding alternant hydrocarbons? To answer these questions we chose the bicyclic systems 48–51 for comparison with 1–47. These structural isomers are given in Fig. 4. These systems were obtained by connecting different places within compounds 1–3. The TRE, % TRE, and MRE results as calculated are reported in Table 2. In the case of 48–50, the TRE values are positive and predicted to be aromatic. However, 51 is predicted to be antiaromatic with a negative TRE value. The relative aromaticity of 48 and 49 has been analyzed in detail with the TRE method using different nitrogen atom parameters.³² In the nitrogen atom parameters we used, 48 and 49 almost give the same degree of aromaticity. Based on the TRE and % TRE results we can predict that 1 will be moderately aromatic with less than half the aromaticity of the highly aromatic 48–50. Based on the above TRE and % TRE analysis, we obtained the following order of aromaticity: 48 > 49 ≈ 50 > 1–47 > 51.

Fig. 4 BREs in units of |β| for all π-bonds of naphthalene (48), quinoline (49), iso-quinoline (50) and bicyclo(6.2.0)decapentaene (51). Values in parentheses are the RCs, all in units of that for benzene (I₀).

Table 2 The TRE, % TRE, MRE, CRE, and CC values of compounds 48–51

Species	TRE	% TRE	MRE	CRE			CC
				c1	c2	c3	c1	c2	c3
48	0.389	2.924	0.289	0.112	0.112	0.065	0.504	0.504	0.589
49	0.384	2.763	0.287	0.110	0.113	0.064	0.494	0.509	0.579
50	0.385	2.765	0.287	0.110	0.112	0.065	0.497	0.504	0.583
51	−0.461	−3.464	−0.642	−0.614	−0.368	0.341	−1.064	−3.080	3.439

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According to the BRE values shown in Fig. 2, all the bonds in 48–50 make a large aromatic contribution to the whole molecule. Among them, the C–C bond shared by the two rings have larger BRE values than the peripheral bonds. This is sharp in contrast with those of 1–47. In the case of 51, all the bonds make an antiaromatic contribution to the whole molecule, and the C–C bond shared by the two rings displays the largest negative BRE value. For 48 and 49, the left ring with no nitrogen atom substitutions exhibits larger BRE values than the right ring with one nitrogen atom substitution. Thus, we assume that these left, six-membered rings have larger local aromaticity than the right rings. Since nitrogen has larger electronegativity than carbon, it produces a strong attraction of the electrons around it and a smaller range of delocalization, resulting in a weaker degree of local aromaticity. As indicated in Fig. 5, three circuits can be chosen for the 48–51 system. By comparing the CRE values shown in Table 2, we find that in the case of 48–50, all the circuits make aromatic contribution to the whole molecule. Among them, the c₁ and the c₂ circuits have larger positive values than the c₃ circuit. Thus, we can predict that for 48–50, the six-membered circuit is the main origin of aromaticity and, as a six-membered 6π-electronic system, it is the main stabilizer. In the case of 51, the c₁ and c₂ circuits have large negative values because the two individual rings have 4π- and 8π-electrons, respectively. Thus, 51 is mainly destabilized by the 4π-electronic and the 8π-electronic circuits. Even so, the 10π-electronic peripheral c₃ circuit has a small positive CRE value. That is to say, the local aromaticity contribution of these circuits satisfies Hückel's (4n + 2) π-electronic rule of aromaticity. As can be seen, the aromaticity contribution of the 48–51 systems is quite different from those of 1–47. Thus, Platt's perimeter model³¹ cannot be applied to predict the aromaticity of 48–51.

Fig. 5 Circuits in naphthalene π-system.

5. RCs of azulene and azaazulenes

We now examine the magnetic properties of 1–47. In general, monocyclic aromatic compounds support a diatropic current and monocyclic antiaromatic systems support a paratropic ring current under an external magnetic field. Three circuits can be chosen from azulene as shown in Fig. 3. The calculated CC values of 1–47 are given in Table 1. The positive and negative values therein represent diatropicity and paratropicity, respectively. The RC susceptibility is equal to the sum of the three circuit CC values. The intensity and direction of the currents can be observed in the maps depicted in Fig. 1. The counterclockwise and clockwise arrows indicate diamagnetic and paramagnetic currents, respectively. As shown in Fig. 1, all the compounds sustain a diatropic perimeter ring current. Analyses of the RCs of 1 were performed by three research groups, independently.^33–35 We have recalculated the RC result of 1. As for 1, a strong diamagnetic flow runs around the molecular periphery (1.150I₀ and 1.069I₀) and very small diatropic bond current (0.081I₀) vortices appear on the bond shared by the two rings. The bond current value in the bond shared by the two rings is the result of superposing between the RCs of the five-membered ring and the seven-membered ring. For 1, as shown in Table 1, the induced diatropic CC contribution to the RC arising from the c₃ circuit is a much larger than that of small diatropic contribution of c₁ and small paratropic contribution of c₂ circuits. Based on the CC results in Table 1, we can predict that for 2–47, a small paratropism or small diatropism will arise from the c₁ and c₂ circuits. However, a large diatropism will arise primarily from the 10π peripheral circuit. The magnitude of paratropic or diatropic contribution of c₁ and c₂ circuits will increase markedly with the increasing number of substituted nitrogen atoms in the seven-membered ring, it is much smaller than that of diatropic contribution of c₃ circuit. As a result, the CCs induced from the c₃ circuit cause diatropism in 2–47. As shown in Fig. 1, the diatropic or paratropic bond currents induced at the bond shared by the two rings have relatively very low intensities. That is to say, for all compounds the peripheral ten-membered 10π-electron circuit values (c₃) dominates the RCs. In all cases, comparative study further reveals that the BRE, CRE and the RC patterns are very similar in appearance to each other. The NICS(0) values at all ring centers of azulene and azaazulenes (1–25) are listed in Table 1. These values are those calculated by Gümüş⁸ at the B3LYP/6-31+G(d,p) level of theory. All the azaazulenes exhibit negative NICS(0) values at the two ring centers and show diatropic current environments in the two rings. Our RC calculation results are consistent with the diatropic prediction of NICS(0) values. However, our RC values show that the large diatropicity was mainly arises from the peripheral 10π-electron circuits. According to the original interpretation of the NICS(0) criterion, all 1–25 must be aromatic with negative NICS(0) values, and the aromaticity of 1 will be larger than that of 2–25. These results are inconsistent with our results and do not follow the TCS rule. Our results show that all possible circuits are responsible for aromaticity and magnetropicity. Thus, the NICS(0) values calculated for five- and seven-membered rings do not reveal the main source of diatropicity and aromaticity and are not directly related to their local aromatic character. In general, both the diatropicity and aromaticity are predicted to be similar only for monocyclic systems.³⁶ However, the diatropicity and antiaromaticity coexist in bicyclic compounds such as azaazulene systems. According to the results as shown in Table 1, we can predict that 1–10, 12, 14, 15, 17, 21, 26–36 and 39–47 are aromatic with positive TREs and diatropic compounds. However, the remaining azaazulenses are antiaromatic with negative TREs, even though they are diatropic compounds. For this reason we can conclude that not only an aromatic compound but an also polycyclic antiaromatic compound is sometimes diatropic and RCs are not always a reliable index of aromaticity for polycyclic systems. For all compounds, the peripheral large circuit makes a very large contribution both to the aromaticity and magnetropicity when compared to the five- and seven-membered rings.

As shown in Fig. 2, all the compounds sustain are diatropic currents along the peripheral π-system. In the case of 48–50, the c₁ and c₂ circuits make a smaller diatropic contribution than the c₃ circuit. In 51, the c₁ and c₂ circuits have paratropic currents. However, the peripheral c₃ circuit has a very large diatropic current. As a result, the bond currents induced in the peripheral c₃ circuit cause 51 to be diatropic. That is to say, like some of the azaazulene isomers mentioned above, 51 is antiaromatic, although it sustains a diatropic current.^37,38

6. Conclusions

A detailed study of the global aromaticities of the azaazulenes was performed using the TRE, % TRE, and MRE methods and compared with the parent structure 1. The local aromaticities were analyzed using the BRE and CRE indexes, while the magnetropicity was predicted by the RC method. The important findings in this study can be summarized as follows:

(1) The positions and the numbers of nitrogen atoms substituted in azulene can play an important role in both the global and local aromaticity of these molecules. Our global aromaticity results, which were predicted using TREs, % TREs, and MREs are fully consistent with the TCS rule. Discrepancies exist however between results based upon the NICS(0) index and the results we have obtained here. Various aspects of NICS-based indexes as an aromaticity criterion have been refined since its introduction in 1996.^3,4,39–41 It has been proposed that NICS(1)_zz be utilized as it is a good indicator of π-aromaticity.⁴¹ It may in fact be helpful to use the refined NICS(1)_zz index to predict the global and local aromaticity of azulene and azaazulenes.

(2) The large local aromaticity and diatropicity arising from the molecular perimeter has a significant effect on the global aromaticity and diatropicity. Despite many of the azaazulenes being antiaromatic compounds with negative TREs, azulene and the azaazulenes are diatropic compounds.

Acknowledgements

Financial support from the Chinese National Natural Science Foundation (No. 21262037) is gratefully acknowledged.

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