Is coronene better described by Clar's aromatic π‐sextet model or by the AdNDP representation?

The bonding patterns in coronene are complicated and controversial as denoted by the lack of consensus of how its electronic structure should be described. Among the different proposed descriptions, the two most representative are those generated by Clar's aromatic π‐sextet and adaptative natural density partitioning (AdNDP) models. Quantum‐chemical calculations at the density functional theory level are performed to evaluate the model that gives a better representation of coronene. To this end, we analyse the molecular structure of coronene, we estimate the aromaticity of its inner and outer rings using various local aromaticity descriptors, and we assess its chemical reactivity from the study of the Diels–Alder reaction with cyclopentadiene. Results obtained are compared with those computed for naphthalene and phenanthrene. Our conclusion is that Clar's π‐sextet model provides the representation of coronene that better describes the physicochemical behavior of this molecule. © 2017 Wiley Periodicals, Inc.


Introduction
Aromaticity is one of the most distinguished concepts in physical organic chemistry. It is crucial for understanding the geometry, stability, spectroscopy, and chemical reactivity of a considerable number of molecules. [1][2][3][4][5][6] In 1931, H€ uckel laid the stepping stone by proposing the acclaimed H€ uckel's 4n 1 2 rule to identify aromaticity in annulenes. [7][8][9][10] Since the applications of H€ uckel's 4n 1 2 rule were limited to monocyclic conjugated systems, several trials were performed to generalize this rule to polycyclic systems. Amidst them, one of the most prominent model was Clar's aromatic p-sextet rule, [11,12] which claims that the Kekul e structure with the largest number of disjoint aromatic p-sextets, that is, the so-called Clar valence structure, is the one that offers the best description of benzenoid polycyclic aromatic hydrocarbons (PAHs). This model was extended by Glidewell and Lloyd [13] to polycyclic conjugated hydrocarbons having rings with any even number of carbon atoms in their structure. [14] Several studies among the years provided support to Clar's p-sextet model. [15][16][17][18][19][20][21] More recently, Zubarev and Boldyrev [22] developed the adaptative natural density partitioning (AdNDP) method as an improvement of the natural bond orbital (NBO) [23,24] analysis. In the AdNDP approach, the charge density is partitioned into n-center 2electron bonds (nc-2e) with the highest possible degree of localization of electron pairs. In this manner, AdNDP recovers both Lewis bonding elements (1c-2e and 2c-2e objects, corresponding to the core electrons and lone pairs, and 2c-2e bonds) and delocalized bonding elements, which are associated with the concepts of multicenter bonding and aromaticity. AdNDP is a very efficient and visual method to analyse molecular orbital-based wave functions. This method has successfully described the chemical bonding patterns in several molecular clusters with many delocalized bonds providing interesting information and deep insight. [25][26][27][28][29] Interestingly, for PAHs that can be described with a unique Clar valence structure (for instance, phenanthrene, triphenylene, or circumcoronene), the description of the chemical bonding given by Clar's p-sextet model and the AdNDP approach coincide. [30,31] On the contrary, for PAHs described by a combination of several Clar valence structures (for instance, naphthalene, anthracene, or coronene), the two representations disagree. The discrepancy is attributed to the fact that the AdNDP analysis looks for the most compact single structure that can be used to define chemical bonding in a certain compound whereas Clar's psextet model uses a resonant description of the chemical bond. [30] Hexabenzobenzene or coronene (C 24 H 12 ) is one of the PAHs in which the chemical bonding pattern described by Clar and AdNDP models [31] differ. This benzenoid PAH with applications in materials chemistry, [32][33][34][35] comprises six benzene rings annelated to a benzene core and represents a basic graphene fragment. It is found naturally as a mineral called carpathite and is produced in hydrocracking petroleum-refining process. [36] Although initially it was considered coronene as a superaromatic compound, [37] it is now widely accepted that it is not. [19,[38][39][40][41][42][43][44][45][46] In fact, the aromatic stabilization energy (ASE) of coronene per p-electron was found to be significantly lower than that of pyrene that, in turn, is much lower than that of benzene. [45,46] Coronene structure can be represented by 20 covalent resonance structures, two of them having three psextets and D 3h symmetry (structures 1 and 2 in Scheme 1). The Clar valence structure, which is a combination of the two D 3h resonant structures with three p-sextets, has D 6h symmetry with three p-sextets that can migrate into the adjacent rings (structure I, Scheme 1). Therefore, one can consider that each outer ring of coronene has half a p-sextet, whereas no psextet is located in the inner "empty ring." Conversely, according to the AdNDP model, [30,31] the 108 valence electrons of coronene are distributed in 30 2c-2e CAC r bonds, 12 2c-2e CAH bonds, six 2c-2e p bonds, three 6c-2e p bonds, and three 24c-2e p bonds (structure II, Scheme 1). In the AdNDP representation, the p-system coronene is reminiscent to that of the B 2 19 species, [47] an aromatic Wankel motor [48] with double paromaticity in two concentric p-systems.
The estimated local properties of coronene differ considerably depending on which representation one considers. For instance, bond C1AC2 should be in between intermediate and double bond somewhat closer to double bond in Clar's representation, whereas it should have slightly more than double bond character in the AdNDP model. Similarly, the aromaticity of the outer ring A (Scheme 1) should be larger than that of the inner ring B in the Clar model and the other way round according to the AdNDP representation. In the present work, we investigate the best-suited model between Clar s aromatic p-sextet and AdNDP forms for representing coronene. To this end, we have analysed the molecular structure, aromaticity, and reactivity of coronene as compared to that of naphthalene and phenanthrene. We agree with Kutzelnigg who said: [49] "Understanding without models is impossible. However, a model is useful, only if one understands its scope and limitations." In this sense, we think it is worth to look for possible shortages of these models keeping in mind that models are just intrinsically deficient approximations to reality and that there is no perfect model. However, when comparing different models the degree of approximation to reality can be different and it is relevant to know which is the model that better approaches it and, consequently, is more useful. As Dewar wrote: [50] "the only criterion of a model is usefulness, not its 'truth' ."

Computational Details
All considered geometries were optimized using hybrid density functional theory (DFT) with the M06-2X [51] and B3LYP [52][53][54] methods in conjunction with the cc-pVTZ Dunning type basis set. [55] Grimme's-D3 dispersion correction [56] with the Becke-Johnson (BJ) damping [57][58][59] was included in all B3LYP calculations. These two functionals perform quite well for the predicting relative energies of polycyclic aromatic hydrocarbons. [60] Harmonic vibrational frequencies were performed to characterize the nature of stationary points and to obtain enthalpies and Gibbs energies. The reported minima and transition states structures exhibited zero and one imaginary frequencies, respectively. All geometry optimizations and frequency calculations were carried out using the Gaussian 09 set of programs. [61] Following previous recommendations, [62][63][64] the local aromaticity in the systems considered was studied using several aromaticity indices like the geometric-based [65,66] harmonic model of aromaticity (HOMA), [67,68] the electronic-based [69,70] para-delocalization index (PDI), [71] aromatic fluctuation index (FLU), [72] Giambiagi's index (I ring ), [73] and multicentre index (MCI), [43] and the magnetic-based [74][75][76][77] nucleus-independent chemical shift (NICS). [78,79] The NICS was evaluated using the regular GIAO method [80] on probing ghost atoms at the ring centres and to 1.0 Å away from the ring centre following the perpendicular of the molecular plane. We also performed NICS-XY-scans. [77,81] These scans can distinguish the global (current along the perimeter of whole molecule) and local (current inside each circuit) currents in p-conjugated polycyclics. The NICS-XY-scans were recorded using NICS zz values at 1.7 Å above the molecular plane at the M06-2X/cc-pVTZ computational level. As to the aromaticity indices calculated, the aromaticity of a given ring increases when HOMA, PDI, I ring , and MCI increase and FLU and NICS decrease. All electronic indices of aromaticity were obtained with the ESI-3D program [72,82] using overlaps of molecular orbitals generated by the AIMAll program [83] and calculated with the atoms-inmolecules atomic partition. [84,85] Results and Discussion  The latter PAH has a unique Clar valence structure and, therefore, it is likely that AdNDP provides the same description as the Clar model. Naphthalene, phenanthrene, and pyrene can be considered fragments of coronene with different bonding patterns. We will compare the molecular structure, aromaticity, and reactivity of these fragments with those of coronene to discuss whether coronene is better described by Clar or AdNDP representations. We will focus our comparisons on naphthalene and phenanthrene. The results of pyrene, having a similar bonding pattern as phenanthrene are given in the Supporting Information.
This section is organized as follows. First, we discuss the molecular structure of coronene, second, we analyse the local aromaticity of the inner and outer ring of coronene, and, finally, we study the reactivity of coronene in Diels-Alder reactions.
The molecular structure of coronene  that, geometrically, the outer rings of coronene are more similar to the rings of naphthalene than to the central ring of phenanthrene, thus favoring Clar s representation.

The local aromaticity of coronene
In the AdNDP model, the inner ring of coronene is expected to be more aromatic than outer ring. On the contrary, Clar's psextet scheme suggests the local aromaticity of the outer ring to be larger than that of the inner ring. Table 1 collects FLU, PDI, MCI, I ring , NICS(1) zz , and HOMA values of the investigated PAHs. All indices agree indicating that the outer ring A is more aromatic than the inner ring B. HOMA is the index showing the smallest difference between the two rings. In addition, HOMA is the only index that considers ring B of coronene more aromatic than that of phenanthrene. These results seems to indicate that HOMA overestimates the aromaticity of ring B of coronene. Conversely, NICS(1) zz is the indicator providing the largest dissimilarity between rings A and B of coronene. As it is well-known, in fused polycyclic conjugated hydrocarbons, NICS measure is affected by the couplings between induced magnetic fields generated by adjacent rings. [89][90][91][92][93] In fact, it has been already suggested that the NICS value of the inner ring of coronene is underestimated and it should be more negative. [19,88] We also calculated the NICS-X-scan for the different species (see Fig. 1 for coronene and Supporting Information Fig. S2 for the rest of species studied). Results of the NICS-X-scan also points out that the outer ring is the most aromatic in coronene. Not only the indices used in this work, but also other indices used in previous works like NICS(0), [31,42,44,94] NICS (1), [16,19,31,42,44] NICS(0) zz , [31] NICS(0) pzz , [95] SSE, [19] BOIA, [19,43] and ATI [43] as well as FLU, PDI, and MCI calculated with the H€ uckel molecular orbital method [96] point in the same direction. In addition, the topography of the molecular electrostatic potential of coronene [86,97] strongly support the Clar's model that describes the innermost ring of coronene as an "empty ring." The only index that gives a large aromaticity for the central ring is the extra cyclic resonance energy (ECRE) that indicates the inner ring of coronene to have similar aromaticity than benzene. [95] In summary, the outer ring of coronene is more aromatic than the inner ring and this result is in accordance with Clar's model prediction. This conclusion agrees with scanning tunnelling microscope (STM) images that show coronene as a hollow ring like structure with a circular protrusion for the outer rings of coronene and a small depression for the central "empty ring." [98,99] Finally, all indices in Table 1 except NICS(1) zz , consider that the aromaticity of the outer ring of coronene is closer to that of the ring of naphthalene than to that of the outer ring of phenanthrene and that the aromaticity of the inner ring in coronene is similar (but somewhat lower except in the case of HOMA) to that of the central ring in phenanthrene. The ring currents of coronene were computed in previous works using different approximations. [19,[39][40][41]44,76,100,101] These studies showed the presence of a diamagnetic ring current in the [18]annulene periphery and a weak paramagnetic ring current in the central six-membered ring. This pattern of ring currents was interpreted as the result of a combination of diamagnetic local ring currents in all six-membered rings. [19,40,41] This combination also explains the lack of radial currents. Moreover, considering the intensity of the outer rings being two or three times stronger than that of the inner ring, the observed global pattern of counter-rotating strong rim and weak hub currents in coronene is perfectly reproduced. [19,40,41] A more intense diamagnetic local ring current in the outer rings concurs with the larger aromaticity attributed to these rings as compared to the inner ring by all indices of aromaticity. This picture of local ring currents is analogous to that derived from the Clar's model. In the AdNDP representation, we have a 6p (i.e., 4n 1 2) inner circuit with three 6c-2e p bonds and another 6p circuit in the periphery with three 24c-2e p bonds. Since the two circuits have 6p electrons, one should observe two (inner and outer) diamagnetic ring currents.
In summary, many descriptors of aromaticity points out that the outer rings of coronene are more aromatic than the central ring. In addition, the ring currents show a diamagnetic ring current in the [18]annulene rim and a weak paramagnetic ring current in the [6]annulene inner perimeter. These

The reactivity of coronene
In this last section, we study the Diels-Alder (DA) reaction between the analysed PAHs and cyclopentadiene. We calculated the endo and exo approaches for the DA, although in Table  2 we gather only the results for the thermochemistry and kinetics of the exo approach, which is the most favorable approach for most of the systems studied. However, the results of the endo approach are also provided in the Supporting Information. The DA reaction has been studied on the C1AC2 bond of coronene, the C9AC10 bond of phenanthrene, and the C1AC2 bond of naphthalene. As before, we consider that the reactivity of the C1AC2 bond in coronene has to be more similar to that of C9AC10 bond in phenanthrene if the AdDNP representation is followed and to that of C1AC2 bond of naphthalene according to the Clar description. Values of Table 2 indicate that the most and least reactive bonds are those of phenanthrene and naphthalene, respectively. The reaction energy and energy barriers of the C1AC2 bond in coronene differ by less than 0.7 kcal mol 21 from those of the C1AC2 bond of naphthalene, whereas differences are larger than 2.5 kcal mol 21 when compared to those of the C9AC10 bond in phenanthrene. Hence, this reactivity analysis shows coronene being more "naphthalene-like" than "phenanthrene-like," thus emphasizing Clar's model as a prime representation of coronene. Finally, results in Table 2 clearly show that coronene cannot undergo Diels-Alder reactions in the C1AC2 bond because of the high barrier and endergonic nature of the reaction.
As a whole, analysis of the molecular structure, aromaticity, and reactivity indicates that the Clar representation of coronene describes better its bonding pattern than the AdNDP model. This view is also supported by ring currents calculations and STM images of coronene. We attribute the failure of AdNDP to provide a better representation of coronene to the fact that AdNDP by construction looks for the single most compact description avoiding a resonant description of the chemical bond. We argue that PAHs that are described in Clar's p-sextet model with Clar valence structures having p-migrating sextets, are not well-represented by a single structure. In fact, if threshold for acceptance of 2c-2e bonds in the AdNDP analysis is reduced to 1.55 e, the AdNDP method recovers a Kekul e structure like 1 in Scheme 1. [30] It is likely that if resonance were introduced in AdNDP analysis, the result would be a combination of structures 1 and 2 in Scheme 1, that is, the same representation given by Clar's theory. Finally, although we consider that, for coronene, the representation given by Clar's method is better than that provided by the AdNDP approach, it is important to emphasize that Clar's model is restricted to benzenoid PAHs, whereas AdNDP can be applied to any chemical system.

Conclusions
The representation of the bonding pattern in coronene is complicated and controversial. In the present work, we compare the descriptions of this molecule given by Clar's p-sextet model and the adaptative natural density partitioning (AdNDP) method, the aim being to find the best representation of the bonding in coronene. To this end, we analyse the molecular structure, the local aromaticity, and the local chemical reactivity of coronene as a dienophile in a Diels-Alder reaction with cyclopentadiene. Keeping in mind that any model of the bonding pattern is intrinsically deficient as it makes approximations, the results obtained favor the Clar representation as the best suited to describe the chemical bond in coronene. We attribute the possible origin of the shortcoming of AdNDP when applied to coronene to the need of including resonant structures in the description of this molecule.

Acknowledgments
MS is very grateful to Dr. A. A. Dyrda and her team for the surgery that allowed him to recover the vision of the right eye after retinal detachment. MS thanks his wife for postoperative care.

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