Energetic Preferences in Cyclic π-Conjugated Systems: Aromaticity Localizes and Antiaromaticity Spreads

Abstract

Cyclic π-conjugated organic species are classical examples of (anti)aromatic compounds. Two key features that characterize their (anti)aromatic behavior are the aromatic stabilization (or destabilization) energy and the degree of bond-length equalization or alternation. Both properties depend strongly on the size of the π-conjugated ring. In small rings, systems with 4n + 2 π electrons exhibit substantial aromatic stabilization and pronounced bond-length equalization, whereas those with 4n π electrons show significant antiaromatic destabilization accompanied by clear bond-length alternation. As the ring size increases, however, the differences in aromatic stabilization energy and bond-length patterns become progressively less distinct.

1. Introduction

The series of monocyclic π-conjugated hydrocarbons with the formula C_NH_N when N is even and C_NH_N+1 when N is odd constitutes the family of [N]annulenes [1,2,3,4]. Annulenes possessing 4n + 2 π electrons (n = 0, 1, 2, …) like benzene ([6]annulene, n = 1) or cyclodecapentaene ([10]annulene, n = 2) are classified as aromatic, whereas those with 4n π electrons, such as cyclobutadiene ([4]annulene, n = 1) or cyclooctatetraene ([8]annulene, n = 2), are considered antiaromatic [5]. Despite the destabilization of antiaromatic annulenes, all even-membered [N]annulenes up to N = 30 have been successfully synthesized, with the only exceptions being the N = 26 and N = 28 species [3,6]. The pivotal importance of annulenes for advancing our understanding of aromaticity has inspired extensive research. Early work by Longuet-Higgins and Salem [7] theoretically predicted that [30]annulene would be nonaromatic, whereas, in 1962, Jackman and co-workers [8] used NMR to conclude that [18]annulene is aromatic, but [24]annulene is nonaromatic. Later on, Dewar and Gleicher’s [9] calculations revealed that [N]annulenes up to and including N = 22 are aromatic, while Čížek and Paldus [10] concluded that delocalized [N]annulenes are unstable when N ≥ 14. Using the MNDOC approach, Yoshizawa and colleagues [11] found that the structure with localized double bonds is more stable for [30]annulene, while the delocalized/aromatic structure is more stable for [18]annulene. According to research by Choi and Kertesz [6], annulenes stop becoming aromatic at 30 π electrons. As a whole, it is widely accepted that the aromatic character of [N]annulenes decreases with the size of the annulene. However, the exact N value from which [N]annulenes are no longer aromatic is subjective and depending on the authors changes from N = 14 to N = 30.

2. Aromatic Stabilization Energy

The fact that aromatic compounds are more stable than their linear counterparts is probably their most significant feature. Perhaps the most accurate way to assess a molecule’s (anti)aromaticity is to compute its aromatic stabilization energy (ASE) [12,13]. The calculation of ASE requires a reference system, which might be either an acyclic polyene or a cyclic nonaromatic structure. It should be highlighted, nonetheless, that the ASE outcome is heavily influenced by the chosen reaction scheme and reference system [12]. Determining the ASE of annulenes can be achieved by employing one of the two isomerization stabilization energy (ISE) methods proposed by Schleyer and Pühlhofer [14]. The methyl–methylene method (ISE_I) utilizes the energy difference between a methylene (nonaromatic) and a methyl (aromatic) derivative of the annulene, whereas in the indene–isoindene method (ISE_II), the energy difference between isomers in which a cyclopentadiene ring fused to the annulene ring is used (Figure 1). To determine the ASE of [N]annulenes with the hyperhomodesmotic ISE_II method, the enthalpies of the (anti)aromatic structure A and the nonaromatic structure C are compared. This energetic difference needs to be adjusted in order to offset the anti-syn mismatch. Typically, this is accomplished by including two additional reference structures where a bond is saturated (structures B and D in Figure 1). The convention we use is that aromatic structures have positive ASE values, whereas antiaromatic compounds have negative ones.

Schleyer and co-workers [16,17] computed the ASE of 4n + 2 π [N]annulenes (N = 6 to 66) in their neutral closed-shell singlet state by employing the ISE_I approach and that of the 4n π [N]annulenes (N = 4 to 24) with the ISE_II method, showing that, from an energetic point of view, the (anti)aromaticity of annulenes decreases with the size and for large N values, it nearly vanishes. More recently, Jirásek and co-workers [15] reinvestigated the ASE of [N]annulenes (N = 12 to 66) in their neutral closed-shell singlet state (S₀) by employing the ISE_II approach. The results obtained by the authors at the B3LYP/6-31G(d) level of theory are summarized in Figure 1. As expected from the Hückel rule, annulenes with 4n + 2 π-electrons have positive ASE values, while those with 4n display negative ASEs. The ASE was found to be inversely proportional to the size of the rings even approaching zero for very large annulenes, which is in line with previous findings and also with Casademont-Reig et al.’s [18] observations that the Hückel rule disappears (differences between aromatic and antiaromatic species are lost) as the annulene ring size increases. Finally, van Nyvel and co-workers [19] extended these results to the lowest-lying triplet state (T₁) of neutral [N]annulenes and their dications in the S₀ and T₁ states. Interestingly, the authors found that the ASE of the T₁ is more or less half that of S₀ for annulenes of a similar size.

The main conclusion drawn from these studies is that the most important property of (anti)aromatic species, which is energetic (de)stabilization, disappears in large annulenes and that the ASE is large in absolute value only for small rings. Therefore, the smaller the ring size, the larger the stabilization of aromatic and destabilization of antiaromatic compounds. These results are in line with the Glidewell–Lloyd extension [20] of Clar’s π-sextet model [21,22] to non-benzenoid polycyclic conjugated hydrocarbons (PCHs), which states that the population of π-electrons in PCHs tends to form the smallest 4n + 2 groups and to avoid the formation of the smallest 4n groups. This is not unexpected, since the smallest 4n + 2 groups are the most stabilizing and the smallest 4n groups are the most destabilizing (see Scheme 1).

3. Bond-Length Alternation

Planarity and bond-length equalization (BLE) are two structural features of benzene that are connected to its aromatic character. Among the different distortions that a benzene ring can suffer, the Kekulean or bond-length alternation (BLA) distortion of in-plane b_2u symmetry that changes the D_6h symmetry of benzene into a Kekulé-like D_3h symmetry structure has an interesting property, namely upon excitation to the first ¹B_2u excited state of benzene, there is an important (and unexpected) upshift of this b_2u frequency mode from 1309 to 1570 cm⁻¹ [23,24,25]. This result is surprising in the context of a π*←π transition from the 1¹A_1g ground state to the 1¹B_2u excited state [26]. The physical basis for the large increase in the frequency of this b_2u mode when going from the 1¹A_1g to the 1¹B_2u states of benzene is based on the pseudo-Jahn-Teller (PJT) effect [6,27,28]. For a totally symmetric electronic ground state, the PJT effect couples the ground and the excited state along a non-totally symmetric mode of the same symmetry as the excited state, lowering the force constant of the ground state and increasing that of the excited state [29]. But the upshift can also be related to the fact that the π-electrons of benzene possess a distortive tendency away from the D_6h symmetry structure [30,31,32,33,34,35]. Moving to the 1¹B_2u excited state reduces the π-distortive tendency of the 1¹A_1g ground state, and, consequently, increases the frequency of the in-plane b_2u vibration in benzene.

The origin of the symmetric structure of benzene is the same as that of cyclohexane, namely the σ-electron framework. By contrast, the distortive tendency of the π electrons can be rationalized within both valence-bond [30,31,32,33,34] and molecular orbital (MO) [35] theories. In the MO description [35], in benzene, the propensity of the π system toward localization arises from a subtle balance of competing overlap effects being too weak to overcome the delocalizing influence of the σ framework. In cyclobutadiene, however, the π-overlap effects act cooperatively to favor double-bond localization and, consequently, are strong enough to override the σ framework.

It seems contradictory that the aromaticity of benzene is attributed to the delocalization of the six π-electrons, while at the same time, these electrons exhibit a distortive tendency, favoring BLA instead of BLE, the latter being a fingerprint of aromaticity. This apparent paradox can be solved by considering that the BLA favored by the π-electrons is counteracted by the preference of σ-electrons for the BLE and the additional stabilization of the BLE structure by resonance (aromatic stabilization). For the antiaromatic species, such as cyclobutadiene, a BLA structure is favored by the distortive nature of π-electrons despite the σ-electrons, which prefer BLE structures. Is this result extrapolatable to all [N]annulenes?

Table 1. The bond-length alternation (BLA, in Å) for the neutral closed-shell [N]annulenes (N = 12–66) computed at the B3LYP/6-31G(d) level of theory. Data extracted from ref. [19].

N	12	16	20	24	28	32	36	40	44	48	52	56	60	64
	0.104	0.101	0.086	0.073	0.068	0.065	0.063	0.061	0.060	0.059	0.058	0.058	0.057	0.057
N	14	18	22	26	30	34	38	42	46	50	54	58	62	66
	0.008	0.011	0.008	0.006	0.034	0.044	0.048	0.051	0.053	0.054	0.055	0.055	0.055	0.055

gathers the results for the BLA in neutral closed-shell [N]annulenes (N = 12–66) computed with the following formula:

$$\mathrm{BLA}={\displaystyle \frac{1}{2n}}{\sum }_{\mathrm{i}=1}^n\left|{\mathrm{r}}_{{\mathrm{A}}_{\mathrm{i}},{\mathrm{A}}_{\mathrm{i}+1}}-{\mathrm{r}}_{{\mathrm{A}}_{\mathrm{i}+1},{\mathrm{A}}_{\mathrm{i}+2}}\right|,$$

(1)

where n is the total number of bonds within the ring. The presence of large BLA values is indicative of antiaromatic structures with π-localization, whereas values close to zero are suggestive of aromatic species with delocalized π-electrons. As can be seen in Table 1, the BLA in 4n antiaromatic [N]annulenes is large for small rings and is reduced when the size of the ring increases [17]. For the 4n + 2 aromatic [N]annulenes, it is the other way around [6]. For values of N > 40, the BLA in 4n and 4n + 2 systems of similar size is almost the same and there is negligible difference between the molecular structure of Hückel aromatic and antiaromatic [N]annulenes.

These results show that bond-length equalized structures are obtained only in small aromatic [N]annulenes (N < 30). In these systems, the preference of the π-electrons for the BLA is opposed by the resonance energy and the preference of σ-electrons for the BLE, with the final result being structures with BLE or minor BLA. For large N, the resonance energy is much lower, and the distortive force of the π-electrons prevails over the BLE structure favored by the σ framework. For antiaromatic systems, the resonance energy is less stabilizing. In these cases, the π-distortivity outweighs the σ-preference for BLE structures.

4. Some Examples

In this section, we address some implications for specific examples of the features covered in the preceding sections.

4.1. The Lowest-Lying Triplet State of Hexabenzenoids

In a recent paper [36], the S₀ and T₁ states of the 37 different cata-condensed hexabenzenoids were investigated. The relative energies of the different isomers in these two states were compared to analyze the impact of topological features like bays, coves, fjords, and K-edges, as well as the number of Clar π-sextets on the stability of benzenoids in their S₀ and T₁ states. As expected, in the S₀ state, the most stabilizing factor was the number of Clar π-sextets, whereas the presence of coves and fjords was a destabilizing factor. The most stable system turns out to be dibenzo[f,k]tetraphene (Scheme 2a) with four π-sextets and the least stable was hexacene (Scheme 2b) with only one migrating π-sextet. For the T₁ state, the most stable is benzo[a]pentacene (Scheme 2c), with hexacene being the second most stable at just 1.8 kcal/mol and the least stable is hexahelicene (Scheme 2d). In T₁, the main stabilizing factors are again the number of Clar π-sextets, but also the number of rings involved in the antiaromatic region (the larger the number, the higher the stabilization), whereas topological regions such as K-edges, bays, coves, or fjords are destabilizing. The T₁ states in cata-condensed polycyclic aromatic hydrocarbons display some small aromatic islands in the form of Clar π-sextets and an antiaromatic region in which the spin density is concentrated. Hexacene has the second most stable T₁ state and is the least stable among the S₀ states, which results in a computed singlet–triplet energy gap of only 9.9 kcal/mol [36]. On the contrary, dibenzo[f,k]tetraphene, which is the most stable in the S₀ state, has a singlet–triplet energy gap of 57.6 kcal/mol.

One can rationalize the distribution of aromaticity in the T₁ states of cata-condensed polycyclic aromatic hydrocarbons by considering that the ASE becomes more stabilizing when aromaticity is concentrated in small regions (Clar π-sextets), and less destabilizing when the region with antiaromatic and unpaired electron character is delocalized over a larger number of rings, as shown in the case of [N]annulenes. In the T₁ state, cata-condensed hexabenzenoids maximize the number of Clar π-sextets and distribute the unpaired electrons over the largest possible region. In conclusion, aromaticity localizes and antiaromaticity spreads.

4.2. C₁₈

Cyclo[18]carbon (C₁₈) is a ring formed uniquely by carbon atoms [37]. For C₁₈, two symmetric geometries have been taken into consideration, namely, a D_18h BLE cumulenic form and a D_9h polyynic structure with alternating single and triple bonds or, preferably, alternating short and long bonds. Both structures have two π-conjugated (π_in and π_out) systems [38]. High-resolution atomic force microscopy (AFM), [39] high-level coupled cluster calculations [40,41], and DFT calculations with a high percentage of Hartree–Fock exchange [42] show that the most stable structure is the D_9h polyynic structure, with the D_18h structure being a transition state between two D_9h species with a barrier of ca. 10 kcal/mol [40]. The coupled cluster method predicts a polyynic structure of C₁₈ with bond lengths of 1.238 and 1.383 Å [40], and therefore a BLA of 0.148 Å, which is relatively high when compared to the values of Table 1, indicating a quite localized structure with alternating single and triple bonds [41], as shown in Scheme 3b. On the other hand, there is a perfect BLE in the cumulenic structure and, consequently, it can only be explained by the resonance hybrid form shown in Scheme 3a.

Calculations of the ring currents indicate that the D_9h polyynic and D_18h cumulenic structures of C₁₈ are both diatropic, and, consequently, aromatic [43,44,45,46,47,48]. However, the polyynic structure has the π_in and π_out systems localized in triple bonds, and therefore the polyynic structure cannot be aromatic. We have seen in the previous section that 4n + 2 [N]annulenes increase the BLA with the size, i.e., for large N, they localize the double bonds. For C₁₈H₁₈, the BLA is about 0.01 Å, ten times less than in cyclo[18]carbon. However, we have to consider that in [N]annulenes, BLA measures the difference between formal single and double bonds, while in cyclo[18]carbon, the BLA compares formal single and triple bonds. In addition, in C₁₈, we do not have 18 π-electrons but 36. When the number of π-electrons increases, the decrease in kinetic energy and Coulomb interaction due to delocalization is counteracted by the extra cost of the exchange correlation between electrons of the same spin, which is localizing in nature. As a result, for large rings, the localized structure is favored over the delocalized one. In C₁₈, this is translated into a polyynic structure being favored over the delocalized and aromatic cumulenic structure [41,49]. On the other hand, the ASE of C₁₈H₁₈, which has only one π-system, was computed to be 10.3 kcal/mol, and, therefore, for C₁₈ with two π-systems (π_in and π_out), one could expect an ASE of ca. 20.6 kcal/mol. Now, if we want to calculate the ASE of the cumulenic structure of C₁₈, we can consider the hyperhomodesmotic reaction [50] that transforms the cumulenic aromatic delocalized form into the polyynic nonaromatic structure (see Scheme 3c). The ASE for this is ca. −10 kcal/mol (depending on the level of calculation), showing that even the BLE cumulenic form should not be considered aromatic because it is not stabilized by electronic delocalization.

4.3. Porphyrins

The parent porphyrin (porphine, Scheme 4a) features a delocalized 26 π-electron system with its main conjugation pathway comprising 18 π-electrons according to the Vogel’s diaza[18]annulene model [51]. This electron count satisfies the Hückel rule for aromaticity and explains the global electronic delocalization inside the macrocyclic framework. Porphine adds a layer of complexity because it also has two pyrrole rings sharing a migrating Clar π-sextet that provides local aromaticity [52]. In general, the discussion of the aromaticity in porphyrins is carried out considering the diaza[18]annulene macrocyclic path [53,54]. Indeed, the delocalized ring currents have the largest intensity following this path [55]. However, in 2013, Schleyer and co-workers [56] concluded that the main source of ASE in porphyrins and porphyrinoids comes from the pyrrole rings. This conclusion is in line with the important reduction in ASE observed in large annulenes, as discussed in previous sections. It is also consistent with the fact that a number of Hückel antiaromatic porphyrinoids with macrocyclic conjugated paths of 4n π electrons have been synthesized [57,58,59,60,61,62,63], as noted by Schleyer et al. [56]. Moreover, calculations of the electron density of delocalized bonds (EDDBs) by Szczepanik [64,65] show a larger electron delocalization per atom in the pyrrole rings than in the diaza[18]annulene macrocyclic conjugated path [66]. We computed the ASE of the diaza[18]annulene macrocyclic conjugated path with the equation shown in Scheme 4b and that of the pyrrole rings with the equation in Scheme 4c. We included cis- and trans-butadiene in the equations to correct for the syn-anti mismatches [13]. The result, including zero-point energy correction at the ωB97XD/def2TZVP level of theory, was 20.3 kcal/mol for the reaction of Scheme 4b and 39.8 kcal/mol for that of Scheme 4c. The ASE of the pyrrole rings is almost twice that of the diaza[18]annulene macrocyclic pathway, confirming that the main source of ASE in porphyrins are the pyrrole rings.

5. Conclusions

From a chemical perspective, the most significant characteristic of (anti)aromatic compounds is the energetic (de)stabilization arising from cyclic electronic delocalization relative to appropriate nonaromatic reference species. This (de)stabilization strongly affects the stability of (anti)aromatic molecules and plays a crucial role in chemical reactions in which (anti)aromatic species appear as reactants, products, intermediates, or transition states.

Based on the analysis of [N]annulenes and the examples discussed herein, several general conclusions can be drawn:

(i)

Aromatic stabilization and antiaromatic destabilization are most pronounced in small rings and become increasingly marginal as the ring size grows.

(ii)

In small aromatic rings, the distortive tendency of the π electrons is compensated by the stabilization gained from resonance and by the intrinsic preference of σ-electrons for bond-length equalization.

(iii)

In large aromatic rings, as well as in antiaromatic systems, the tendency toward π-electron localization outweighs the stabilization provided by resonance and the preference of σ-electrons for bond-length equalization.

(iv)

Extended π-conjugated circuits may exhibit only marginal aromatic stabilization energies—suggesting a largely nonaromatic energetic character—while simultaneously sustaining diatropic ring currents and substantial electron delocalization typical of aromatic compounds.