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. 2026 Jul 20;17(35):17066–17079. doi: 10.1039/d6sc02343f

Defying antiaromaticity – the curious case of pentalenopentalenes

Amrita Gogoi a, Renana Gershoni-Poranne a,✉
PMCID: PMC13404374  PMID: 42517002

Abstract

Antiaromatic molecules offer attractive electronic properties but are intrinsically unstable. Annelation with arenes can stabilize antiaromatic cores, yet often suppresses the very properties of interest. Here, we investigate the (anti)aromatic character of two families of pentalenopentalene-based polycyclic hydrocarbons, bisbenzannelated and biscycloheptatriene-annelated, in both the S0 and T1 states. Despite exhibiting markedly different symmetry, open-shell character, and magnetic response, all systems follow a single unifying principle: a persistent preference for preserving local aromatic subunits. In T1, the same behavior emerges through localization of spin density, maintaining local aromaticity and inducing a local reversal of aromatic character. Resonance structure analysis combined with the Randić conjugated circuit model provides a general framework for rationalization and a direct connection between behavior and topology. These findings underscore that neither Hückel nor Baird rules can be naïvely applied to polycyclic (anti)aromatic systems and offer design principles for persistent antiaromatic molecules.

Local aromaticity wins. In extended pentalenopentalenses, molecular topology governs aromatic and antiaromatic behavior.graphic file with name d6sc02343f-ga.webp

Introduction

Aromaticity remains one of the most widely invoked yet ambiguously defined concepts in chemistry, closely linked to molecular stability,1,2 (opto)electronic properties,3 and reactivity.4 While aromatic systems are generally well understood and broadly exploited, the chemical space of antiaromatic molecules remains largely uncharted, as their inherent instability—often manifested in small HOMO–LUMO energy gaps and non-negligible diradical character—renders them difficult to prepare and isolate. Yet, it is these exact properties that make antiaromatic systems promising for various functionalities, such as field effect transistors5–8 and photoredox catalysts.9

Extending the conjugated system with arene annelation is a common strategy for stabilizing antiaromatic cores and rendering them isolable and persistent. However, this introduces a fundamental trade-off: while annelation enhances thermodynamic stability, it often suppresses the very antiaromatic character that underlies the desired electronic properties. Thus, to successfully harness the advantageous properties of antiaromatic molecules, it is imperative to understand the effects of extended annelation on antiaromatic cores. Several experimental and computational investigations into the effects of extended conjugation on the s-indacene,8,10–17 pentalene,18–26 and indenofluorene27,28 cores have been reported.

This raises a fundamental and general question: what determines whether antiaromatic character is preserved or suppressed upon annelation? To probe this question, we investigate two families of pentalenopentalene derivatives formed via bisannelation with benzene (alternant) and cycloheptatriene (non-alternant) rings. These systems provide a controlled platform to disentangle the roles of topology and π-electron count type in governing (anti)aromatic character. We show that the behavior of these systems is determined by a simple yet general principle: polycyclic (anti)aromatic systems preferentially preserve local aromatic subunits, even at the cost of incurring local antiaromaticity and diradical character. This principle explains the seemingly disparate structural, magnetic, and electronic behavior across the entire dataset, in the ground (S0) and the first excited triplet (T1) states. Moreover, by incorporating simple and intuitive concepts from chemical graph theory, we provide a unifying framework for understanding this behavior and how it is directly related to topology. These findings establish a topology-driven framework for understanding (anti)aromaticity in extended systems and provide actionable design principles for stabilizing and exploiting antiaromatic motifs.

Computational methods

The reliable description of antiaromatic systems is non-trivial, as these molecules often exhibit small HOMO–LUMO gaps, partial open-shell character, and sensitivity to bond localization. Thus, we elected to use the UM11 functional, based on prior benchmarking demonstrating its ability to reproduce both geometric and magnetic properties of notably challenging antiaromatic systems,29 and performed further validations against newly available experimental structural and 1H NMR data from ref. 30 (see Section S2 of the SI).

All calculations were performed with the Gaussian 16 suite of programs.31 Structures were optimized at the UM11/def2-TZVP level of theory,32–38 and confirmed to be true minima on the potential energy surface (Nimag = 0). To ensure a reliable electronic description, all wavefunctions were checked for stability. Yamaguchi y0 values39 were calculated for all molecules with both UKS and UHF formalisms, to verify closed/open shell character. Almost all of the molecules have some open-shell character according to yUHF0, however none exceed 0.50. Thus, despite the small ΔES–T values of some molecules, we conclude that all molecules have a singlet ground state and are predominantly single-configuration.

Magnetic aromaticity was evaluated using Nucleus Independent Chemical Shifts (NICS);40–43 NICS(1)πzz values were computed with the gauge-including atomic orbitals (GIAO) method,44–47 with input generation via Aroma,48 and dissection to π-contributions using Stanger's σ-only model.49 Current density plots for the π-currents were obtained with the SYSMOIC package50 and with the ACID software51,52 using the continuous set of gauge transformations (CSGT) method53 (see Section S3.5 of the SI for the list of π-orbitals). All reported spin densities are Hirshfeld spin densities.54–56

Results and discussion

Molecular scaffolds and energies

Our dataset consists of 15 molecular scaffolds: pentalene, two isomeric pentalenopentalenes, six bisbenzannelated pentalenopentalenes, and six biscycloheptatriene-annelated pentalenopentalenes (the BEN and CHT sets, respectively). Fig. 1 details all structures in our data set, including their respective notations, relative energies (i.e., the difference in energy to the lowest-energy isomer, in kcal mol−1), optical gaps (i.e., vertical S0–S1 gaps, ΔEOG, in eV) and adiabatic S0–T1 energy gaps (ΔES–T, eV).

Fig. 1. All structures included in the dataset: (A) pentalene, (B) pentalenopentalene isomers, (C) BEN set, (D) CHT set. Molecule notations and relative energies (kcal mol−1), as well as optical and S0–T1 gaps (eV) are detailed. Blue and purple circles denote a- and b-annelation, respectively.

Fig. 1

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For conciseness and clarity, we defined a naming scheme for all molecules in the current study, based on the apical carbons of the 5MRs in the various scaffolds. The pentalenopentalenes are distinguished by the apical carbons in the second and third rings. The term a-annelation indicates that the two apical carbons are oriented in opposite directions, and b-annelation means they are oriented in the same direction. The a-annelated pentalenopentalene is denoted as Core A, and the b-annelated pentalenopentalene is denoted as Core B (Fig. 1B). In the bisannelated extended systems, we used the relative orientation in each of the two pentalene moieties. Accordingly, each derivative is named after its core pentalenopentalene, the orientation within each pentalene, and the type of moiety it is annelated with, e.g., AaaBen refers to the bisbenzannelated Core A, in which both pentalenes have apical carbons in opposite orientations.

In contrast to the rich experimental literature of the parent pentalene (vide supra), the majority of molecules in our dataset have never been synthetically achieved. To the best of our knowledge, only three have been prepared synthetically (in all cases, with additional substituents): Core A,57,58 AaaBen,59 and, very recently, AaaCHT.30

All structures were studied in two electronic states, S0 and T1. Three of the molecules were found to have some open-shell character in S0: Core B, AbbBen and BbbBen (see Section S3.4 of the SI for the spin density and open-shell metrics for these molecules). Nevertheless, all molecules were confirmed by wavefunction stability check to have singlet ground states (see Sections S3.2 and S3.3 of the SI for additional details).

Some general trends can be seen in both the relative energies and the ΔES–T values: the BEN isomers show similarities in pairs according to their annelation patterns, while the CHT isomers show similarities in trios, according to their core structure. Notably, the [a, a] and [b, b] BEN isomers and the Core A-CHT isomers have smaller ΔES–T than the parent pentalenopentalenes and pentalene. The extremely small ΔES–T of the [b, b] BEN isomers (0.02 and 0.09 eV) suggests that they may be good candidates for singlet fission.

Evaluation of aromaticity

To obtain a comprehensive picture of (anti)aromaticity, we combined several complementary descriptors that probe distinct physical aspects. Magnetic behavior was evaluated with NICS(1)πzz for local quantitative measures of the induced magnetic field and with current density plots (generated with SYSMOIC and ACID) for global, topology-resolved visualization of the magnetically induced ring currents. In addition the Harmonic Oscillator model of Aromaticity (HOMA)60–62 and its excited-state version, HOMER,63 were used to study the geometric criterion. The Aromatic Fluctuation Index (FLU),64 the Normalized Multi-Center Bond Order (MCBO)65,66 and the Electron Density of Delocalized Bonds (EDDB)67 methods were used to study the electron delocalization criterion. Notably, good quantitative agreement was found between all metrics only for the terminal rings (6MRs and 7MRs), which are mostly aromatic in our molecules; for the 5MRs, the agreement is much poorer, likely because these metrics struggle with antiaromatic systems (see Section S4 of the SI for additional details and discussion).

The computed results were corroborated with an independent approach, based on resonance structures (RSs) and chemical graph theory concepts, including the Randić conjugated circuit model,68–70 Clar sextets,71 and Mandado analysis,72 taking into consideration optimized geometries and spin densities. Only the magnetic criteria showed a robust agreement with the graph-theoretical analysis, supporting the conclusion that the other metrics are less adequate for analysis of such systems. Therefore, only the magnetic aromaticity results are discussed herein.

As we show below, the diverse behavior of these systems can be rationalized by a single overarching principle: polycyclic systems preferentially preserve local aromatic subunits, even at the expense of global aromaticity or antiaromaticity. Although this idea underlies several established frameworks for understanding polycyclic aromaticity, including those of Platt,73 Clar,71 and Glidewell–Lloyd,74 its implications for non-alternant and antiaromatic polycycles remain comparatively unexplored. This preference governs bond localization, magnetic response, and spin distribution in both S0 and T1, and provides a unifying framework for understanding when extended conjugation stabilizes or suppresses antiaromatic character.

The S0 state

Pentalene and pentalenopentalenes

We began by characterizing the core compound, pentalene. Pentalene is a bicyclic conjugated molecule comprising two fused 5MRs and containing 8πe−. In the ground state (S0), pentalene is highly antiaromatic and sustains strong paratropic induced currents, as indicated by the current density plot and the high positive NICS(1)πzz = 51 ppm (Fig. 2A).

Fig. 2. Optimized geometries, current density plots, NICS(1)πzz, resonance structures (RS), and conjugated circuits (CCs) for (A) pentalene, (B) Core A, and (C) Core B. CCs are color-coded blue for 4n + 2 circuits and red for 4n circuits. NICS(1)πzz values are color-coded blue for diatropic and red for paratropic; the strength of the color correlates to the magnitude of the value. For Core B, spin density is depicted at the isosurface value of α = 0.02.

Fig. 2

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The two pentalenopentalene isomers, Core A and Core B, are almost isoenergetic—Core A is slightly more thermodynamically stable, ΔE = 1.2 kcal mol−1. This aligns with their almost identical ΔEOG and ΔES–T values (Fig. 1). Despite these similarities, they display significant differences: Core A is closed-shell, while Core B has some open-shell character in the singlet ground state (yUHF0 = 0.36). Core A is not symmetric with respect to the short axis of the molecule (the fused bond between the two pentalene moieties) and shows distinct bond localization. Toyota and Nakajimi predicted this Cs-symmetric ground state structure on the basis of second-order Jahn–Teller theory.75 They predicted a similar reduction from C2v to Cs symmetry for Core B, but our optimized geometry is symmetric and shows much less pronounced bond localization. In both isomers, the fused bonds elongate, compared to the parent pentalene, reminiscent of a ‘bridged annulene’ structure.

These differences extend to the magnetic aromatic character of the isomers. Both molecules are formally 14πe− (i.e., 4n + 2) systems, thus one may naïvely expect both to be aromatic, and therefore globally diatropic. However, as famously written by Breslow, “two wrongs don't make a right”,76 meaning that the antiaromaticity of the two pentalene systems is not necessarily canceled out by fusing them together. Instead, annelation can redistribute, localize, or even reinforce antiaromatic character, depending on which new conjugation pathways are formed. Indeed, the current density plots for the two pentalenopentalenes show that, although both isomers do sustain global diatropic currents, as expected from their 14πe− count and consistent with the elongated fused bonds, Core A sustains in addition a local paratropic current in one of the pentalene moieties (Fig. 2B and C). NICS(1)πzz values provide a more quantitative view of the current density visualizations, showing that Core B has overall global diatropic behavior (NICS(1)πzz = −12 to −13 ppm) and Core A has two distinct regions—a paratropic pentalene (NICS(1)πzz = 13 ppm) and a diatropic one (NICS(1)πzz = −15 to −17 ppm). For comparison, for benzene at the same level of theory NICS(1)πzz = −33 ppm.

To better understand the origins of these differences, we drew RSs, using the optimized geometries to identify single/double bond placement. Our analysis focused on the RSs that best match the computed bond lengths, as these are the most contributing RSs. Following Randić’s conjugated circuit model,68–70 for each RS, we identified all possible 4n (paratropic) and 4n + 2 (diatropic) circuits formed by following alternating single and double bonds.

The dominant RS structure of Core A (Fig. 2B) contains the expected global 14πe− circuit as well as a 8πe− circuit (in the left pentalene), in agreement with the observed ‘duality’ of aromatic character described above. In contrast, the bond-equalized geometry of Core B is consistent with a superposition of two RSs, each sustaining a global 14πe− circuit and an 8πe− circuit in one of the pentalene moieties (Fig. 2C), in agreement with the overall modest diatropic character.

The substantial differences in structure and aromatic character between these two cores underline the dramatic impact that annelation topology can have on molecular properties. This reinforces Breslow's studies on fused non-benzenoid systems, which established that antiaromaticity is a global, topology-dependent property, and also aligns with our recent work on bisborole-annelated antiaromatic cores, showing the same dependency.77

The BEN set

Just as with the ΔES–T values, the six isomers of the BEN set divide into pairs with similar magnetic response, depending on their annelation pattern (Fig. 3).

Fig. 3. (A) Current density plots and (B) NICS(1)πzz for the six BEN isomers. NICS(1)πzz values are color-coded blue for diatropic and red for paratropic; the strength of the color correlates to the magnitude of the value.

Fig. 3

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Although all isomers contain 22πe− and are potentially Hückel aromatic, current density plots show global diatropic currents only in some of them. All isomers show clear local diatropicity in the flanking 6MRs (benzenes) and differ mainly in the magnitude of the diatropicity and in the behavior of the pentalenopentalene cores. The [a, a] pair have moderately diatropic 6MRs (NICS(1)πzz = −19 ppm) and moderately paratropic cores (NICS(1)πzz = 31 ppm; compare to 51 ppm for the parent pentalene). The [a, b] pair have more strongly diatropic 6MRs (NICS(1)πzz = −21 to −35 ppm) and their cores show a ‘duality’ whereby the b-annelated pentalene is moderately paratropic (NICS(1)πzz = 18 to 20 ppm) while the a-annelated pentalene has no tropicity. The [b, b] pair have diatropic 6MRs (NICS(1)πzz = −24 ppm) and their cores have essentially no tropicity (NICS(1)πzz = −5 to 3 ppm), despite being the only two isomers to show a global diatropic current.

To identify the dominant RSs we invoked Clar's rule,71,78 which states that the most contributing RS is the one that maximizes the number of disjoint π-sextets. Notably, Solà and coworkers recently showed that the Clar rule predicts the ground state of indenofluorene-type systems.79 For conciseness, we show in Fig. 4 only one representative of each isomer pair (see Section S4.1 of the SI for all isomers).

Fig. 4. Optimized geometries, current density plots, NICS(1)πzz, resonance structures (RS), and conjugated circuits (CCs) for representative examples of (A) [a, a]-BEN, (B) [a, b]-BEN, and (C) [b, b]-BEN. CCs are color-coded blue for 4n + 2 circuits and red for 4n circuits. NICS(1)πzz values are color-coded blue for diatropic and red for paratropic; the strength of the color correlates to the magnitude of the value.

Fig. 4

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For the [a, a] pair (Fig. 4A), it is possible to draw RSs that place Clar sextets in both 6MRs and the resulting placement of the remaining single/double bonds aligns with the optimized bond lengths. Using Randić’s conjugated circuit model, we identify that these RSs also sustain 4n circuits (either an 8πe− pentalene circuit in each of the pentalene moieties or a 12πe− circuit in half of the molecule).

For the [a, b] pair (Fig. 4B), it is also possible to draw RSs that place Clar sextets in each of the 6MRs, and the resulting bond alternation aligns with the computed bond lengths. In these RSs, we identify a global 22πe− circuit, a 14πe− circuit in the pentalenopentalene core, and a single 8πe− circuit, located within the b-annelation pentalene—in perfect agreement with the magnetic aromaticity. We note, also, that the NICS(1)πzz values in the 6MRs are slightly more negative in this pair, consistent with a summation of local and global diatropic currents.

For the [b, b] pair (Fig. 4C), it is only possible to obtain Clar sextets in both 6MRs if an open-shell RSs is adopted. Indeed, these two latter isomers are the only two to show open-shell character in the ground state and also have the smallest ΔES–T values (AbbBen: yUHF0 = 0.19, ΔES–T = 0.02 eV; BbbBen: yUHF0 = 0.49, ΔES–T = 0.09 eV). The corresponding RSs host global diatropic 22πe− circuits and paratropic 12πe− semi-global circuits, consistent with the current density plots of both isomers and the lack of diatropicity in the core, based on NICS(1)πzz. The adoption of the open-shell solution suggests that the associated energetic cost is offset by the stabilization afforded by forming two distinct Clar sextets.

Thus, the RS analysis not only explains the similarity between pairs of isomers, but also the origin of the seemingly anomalous paratropicity in formally 4n + 2 systems. It highlights the complexity of the magnetic behavior in polycyclic (anti)aromatic molecules, while also providing an intuitive way to understand that complexity.

The CHT set

In the current study, the CHT set serves as a representative of non-alternant annelation. However, it is worth noting that the unique characteristics of molecules containing seven-membered rings (7MRs) fused to five-membered rings (5MRs) have been of interest for several decades,57,58,80–94 and several recent reports have reiterated their potential for various (opto)electronic uses.95–97

Similarly to their ΔES–T values, the magnetic response of the six isomers of the CHT set also divides them into two groups of three, according to their pentalenopentalene core (Fig. 5). Though all isomers are formally 24πe−-systems, they defy the naïve expectation and none show global paratropic behavior.

Fig. 5. (A) Current density plots and (B) NICS(1)πzz for the six CHT isomers. NICS(1)πzz values are color-coded blue for diatropic and red for paratropic; the strength of the color correlates to the magnitude of the value.

Fig. 5

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The Core A-based isomers all show a moderately paratropic pentalene core (NICS(1)πzz = 21 to 26 ppm), flanked by two strongly diatropic 5MRs (NICS(1)πzz = −36 to −39 ppm) and modestly diatropic 7MRs (NICS(1)πzz = −9 to −15 ppm). In other words, the central pentalene core is flanked by two azulenes (for comparison, NICS(1)πzz = −48 and −27 ppm, for the 5MR and 7MR of azulene, respectively). We note that our results for AaaCHT agree with those recently reported by Chi and coworkers, who synthesized this scaffold.30 The Core B-based isomers all show a moderately-to-strongly paratropic central pentalene core (NICS(1)πzz = 35 to 42 ppm), flanked on one side by a strongly diatropic 5MR (NICS(1)πzz = −27 to −32 ppm) and on the other by a 7MR with modest paratropicity (NICS(1)πzz = 13 to 17 ppm); the other rings show negligible tropicity.

RSs provide explanations for these observations. Importantly, because the CHT set do not contain 6MRs, we invoke the Glidewell–Lloyd rule74 rather than the Clar rule, which states that the preference will be to form the smallest possible 4n + 2 circuit, which, for these isomers, is an azulene 10πe− moiety. For conciseness, we show in Fig. 6 only one representative for each trio; the data for all isomers is provided in Section S4.1 of the SI.

Fig. 6. Optimized geometries, NICS(1)πzz, resonance structures (RS), and conjugated circuits (CCs) for representative examples of (A) Core A-CHT (B) and Core B-CHT. CCs are color-coded blue for 4n + 2 circuits and red for 4n circuits. NICS(1)πzz values are color-coded blue for diatropic and red for paratropic; the strength of the color correlates to the magnitude of the value.

Fig. 6

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For all Core A-based isomers (Fig. 6A), it is possible to form two disjoint 10πe− circuits in the azulene moieties, concurrent with an 8πe− circuit in the central pentalene moiety, a 16πe− semi-global circuit, and a 24πe− global circuit. The superposition of these circuits matches the observed magnetic behavior.

For the Core B-based isomers (Fig. 6B), it is impossible to draw closed-shell RSs that contain two disjoint 10πe− circuits. As opposed to the analogous cases of AbbBen and BbbBen, which adopt an open-shell structure to enable two simultaneous 4n + 2 circuits, the CHT isomers retain a closed-shell structure, ‘sacrificing’ one of the azulene moieties, as is apparent in the lack of symmetry of the optimized geometries and in the magnetic behavior. For AabCHT, in which the two azulene moieties are not equivalent, the dominant diatropic circuit is formed in the a-annelated one. Despite its lack of symmetric connectivity, the magnetic behavior in this isomer is almost identical to the other two isomers in this group (Fig. 5). The dominant RSs also give rise to a global 24πe− circuit, a local 8πe− circuit in the central pentalene, and a semi-global 16πe− circuit. Importantly, the preference for one azulene over the other is not absolute, as can be seen from the current density plots and NICS(1)πzz values in all three isomers. The modest paratropicities of the ‘sacrificial’ azulene moiety suggest that there are also diatropic circuits in this side of the molecule, stemming from other non-dominant RSs.

Altogether, the superposition of circuits in all isomers is in excellent agreement with their respective observed magnetic aromatic behavior. Moreover, it is clear from the behavior of the isomers that the smaller circuits have greater impact than the larger ones, in accordance with the Glidewell–Lloyd rule.74 Therefore, it is generally sufficient to draw the Clar RS (the two Kekulé structures of the benzenes can be drawn with a circle) and then identify the smallest 4n and 4n + 2 circuits that co-exist in that RS. For example, in AaaBen (Fig. 4), the overall behavior of the molecule is described by the RS that contains the two 6πe− and two 8πe− circuits.

In other words, fusion of the pentalenopentalene cores to alternant rings (e.g., benzene) affords two pentalene moieties, whereas fusion to a non-alternant ring (e.g., cycloheptatriene) affords one central pentalene moiety. This is the reason the BEN set divides into three distinct groups and the CHT set divides into two groups: there are three ways to combine two singly-annelated pentalenes and only two ways to annelate a pentalene. This gives important insight for guiding molecular design.

The T1 state

For cyclically conjugated molecules in T1, it is common to invoke Baird's rule,98,99 which states that the aromatic character flips upon excitation to T1. However, just as the Hückel 4n + 2 rule cannot be trivially generalized for polycyclic molecules in S0, so should Baird's rule not be misused in the excited state. Application of this rule relies on the location of the unpaired electrons; the aromatic character flips only if the unpaired electrons are located within it.100 In polycyclic molecules, spin often localizes on one part of the molecule, leaving the remaining part ‘S0-like’. We previously showed this type of behavior in both T1 and S1 polybenzenoid hydrocarbons.101,102 In the current work, we explored whether similar principles could be found for non-benzenoid molecules. To enable RS-based analysis on the T1-systems, we used the Mandado analysis,72 which is a generalization of the Hückel rule to open-shell cases; it separates the α and β electrons and assigns 2n circuits as paratropic and 2n + 1 circuits as diatropic.

In T1, pentalene shows global diatropicity (NICS(1)πzz = −28 ppm) and the two pentalenopentalenes both display mild global paratropicity (NICS(1)πzz = 9 to 15 ppm), which current density plots reveal as stemming from the superposition of diatropic and paratropic currents, all rationalized by the local and global circuits identified with Mandado analysis. We demonstrate this analysis on these three molecules in Fig. 7.

Fig. 7. Optimized geometries with spin densities, current density plots (CD), NICS(1)πzz, and conjugated circuits (CCs) for (A) pentalene, (B) Core A, and (C) Core B. CCs are color-coded blue for 2n + 1 circuits and red for 2n circuits. NICS(1)πzz values are color-coded blue for diatropic and red for paratropic; the strength of the color correlates to the magnitude of the value. Spin density is shown in pink on the optimized geometries, isosurface value α = 0.02.

Fig. 7

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For all BEN isomers in T1, the spin-density is located on the 5MRs of the pentalenopentalene cores and the various isomers show the same tendency to form pairs as they did in S0, dividing according to the annelation patterns. The [a, a] pair both show strongly diatropic 6MRs (NICS(1)πzz = −27 ppm) and very weakly paratropic cores (NICS(1)πzz = 3 to 7 ppm). The [b, b] pair have a similar division of character, but show differences in magnitude: moderately diatropic 6MRs (NICS(1)πzz = −20 to −22 ppm) and more strongly paratropic cores (NICS(1)πzz = 17 to 21 ppm). For the [a, b] pair, the behavior is not symmetric—the a-annelated pentalene is paratropic (NICS(1)πzz = 23 to 41 ppm) and has a moderately diatropic annelated 6MR (NICS(1)πzz = −18 to −19 ppm), while the b-annelated pentalene is weakly diatropic (NICS(1)πzz = −4 to −12 ppm) and has a strongly diatropic annelated 6MR (NICS(1)πzz = −19 to −29 ppm).

In T1 as in S0, the CHT set separates into two groups based on the geometry of the pentalenopentalene core. The Core A-annelated isomers undergo substantial changes upon excitation. Whereas in the ground state, all three isomers are symmetric with respect to the fused bond between the two pentalene units, in T1 this symmetry is lost and one of the azulene moieties behaves like an S0-azulene (5MR: NICS(1)πzz = −28 to −26 ppm; 7MR: NICS(1)πzz = −17 to −23 ppm), while the remainder of the molecule shows varied behavior (Fig. 8). It appears that b-annelation allows for more delocalization of the spin density and extension of diatropicity beyond the azulene moiety.

Fig. 8. Left: (A) spin density and (B) NICS(1)πzz for the BEN set in T1. Right: (C) spin density and (D) NICS(1)πzz for the CHT set in T1.

Fig. 8

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The Core B-annelated isomers have the opposite trends: while in S0 these isomers show dramatically non-symmetric magnetic behavior, in T1 they all display symmetric magnetic behavior (even in AabCHT, which is not symmetric by connectivity). In all three, both azulene moieties are diatropic (5MR: NICS(1)πzz = −26 to −35 ppm; 7MR: NICS(1)πzz = −10 to −21 ppm), while the central pentalene moiety is at most weakly paratropic (NICS(1)πzz = −1 to 9 ppm).

Our findings show that all molecules tend to localize the unpaired electrons such that local aromaticity in the smallest 4n + 2 circuits is retained. For the BEN set, the preference is for maintaining Clar sextets in the 6MRs and, as a result, the consequences of excitation are manifested in the pentalenopentalene core. For the Core A-CHT set, the preference is to maintain azulene moieties, but since only one azulene can be formed, the consequences of excitation are manifested in the remaining 5MRs and 7MR. The rings that contain the unpaired electrons show, in essence, a local application of Baird's rule: rings that are strongly paratropic in S0 display attentuated paratropicity or even diatropicity in T1, rings that are diatropic or have no tropicity in S0 are paratropic in T1.

The retention of diatropicity in the 6MRs of the BEN set and in the azulene moieties of the CHT set highlights that the preference for local aromatic behavior persists in T1. In Section S4.1 of the SI, we provide the Mandado analysis for all isomers, which shows that the retention of the local 4n + 2 circuits, as well as what other circuits are formed as a result, depends on the topology of annelation. In addition, we show the quantitative relationship between spin density and tropicity.

Conclusions

We systematically investigated the (anti)aromatic character of two families of extended pentalenopentalenes—bisbenzannelated and biscycloheptatriene-annelated—in both S0 and T1. A recurring theme throughout this study is that neither the Hückel 4n + 2 rule nor Baird's rule can be straightforwardly applied to polycyclic systems, despite working well for monocyclic annulenes.103 This limitation has long been recognized in the context of polybenzenoid hydrocarbons through concepts such as Platt's perimeter model73 and Clar sextets, and in non-benzenoid polycyclic aromatic systems through the Glidewell–Lloyd rule. The present work extends these ideas into the substantially less explored chemical space of non-alternant and antiaromatic polycyclic systems. Already at the level of the pentalenopentalene cores, fusing two antiaromatic pentalene units does not simply cancel out their antiaromaticity, reinforcing Breslow's assertion that “two wrongs don't make a right.” We find that the molecular topology, and not the overall π-electron count, is the primary determinants of (anti)aromatic character.

Across the entire dataset, we observe a strong preference for local aromatic character (Clar sextets in benzannelated and azulene moieties in CHT-annelated systems), even at the cost of paratropic cores or open-shell ground states. In T1, this is achieved by localizing spin density in specific subsections, allowing local aromaticity to be preserved elsewhere. The rings hosting unpaired electrons follow a local application of Baird's rule, as confirmed by the correlation between spin density and NICS(1)πzz values on the central pentalene. Importantly, these conclusions are corroborated by independent resonance structure analysis combined with the Randić conjugated circuit model and Mandado analysis for open-shell molecules, overall providing a unified framework that successfully rationalizes the magnetic behavior of all isomers, including the pairing by annelation pattern (BEN set) and grouping by core type (CHT set).

In contrast, metrics based on other criteria (geometric and electronic) are inconsistent with RS-based analysis. Moreover, the agreement between these metrics and NICS(1)πzz is substantially improved when only the terminal (6MRs and 7MRs) are considered. This suggests that the underlying reason for these methods' failure to describe the extended pentalenopentalenes satisfactorily is that they are poorly suited for dealing with antiaromatic rings, a situation that is exacerbated when extending to polycyclic antiaromatic systems.

These results establish a general, topology-driven principle: the outcome of extending a π-system is dictated not by total electron count, but by the ability to sustain stabilizing local aromatic circuits. In the current context, alternant annelation preserves two distinct pentalene subunits, whereas non-alternant annelation enforces a single reorganized pentalene core. This framework is expected to extend broadly across polycyclic (anti)aromatic systems and provides a basis for the design of such molecules.

Author contributions

A. G.: data curation, formal analysis, investigation, resources, validation, writing – original draft. R. G. P.: conceptualization, formal analysis, funding acquisition, methodology, project administration, supervision, validation, visualization, writing – original draft, writing – review and editing.

Conflicts of interest

The authors declare no conflicts of interest.

Supplementary Material

SC-017-D6SC02343F-s001
SC-017-D6SC02343F-s002

Acknowledgments

This work was generously supported by the Israel Science Foundation (grant no. 1745/23 to R. G. P.). A. G. gratefully acknowledges financial support of the Margaret Kaplan Postdoctoral Fellowship in honor of Judith Kaplan. The authors thank Prof. Amnon Stanger, Prof. Michael Haley, Prof. Judy Wu, Dr Alexandra Tsybizova, and all members of the Poranne Group for fruitful discussions and helpful commentary on the manuscript.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information: additional details on computational methods, including input templates for all calculations, benchmarking, additional aromaticity metrics and comparison among them, RS analysis for all isomers in S0 and T1, xyz coordinates for all optimized structures. See DOI: https://doi.org/10.1039/d6sc02343f.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

SC-017-D6SC02343F-s001
SC-017-D6SC02343F-s001.pdf (48.2MB, pdf)
SC-017-D6SC02343F-s002
SC-017-D6SC02343F-s002.zip (11.2KB, zip)

Data Availability Statement

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information: additional details on computational methods, including input templates for all calculations, benchmarking, additional aromaticity metrics and comparison among them, RS analysis for all isomers in S0 and T1, xyz coordinates for all optimized structures. See DOI: https://doi.org/10.1039/d6sc02343f.

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