Constrained Clar Formulas of Coronoid Hydrocarbons - American

Article pubs.acs.org/JPCA

Constrained Clar Formulas of Coronoid Hydrocarbons Jun-ichi Aihara*,†,‡ and Masakazu Makino‡ †

Department of Chemistry, Faculty of Science, Shizuoka University, Oya, Shizuoka 422-8529, Japan Institute for Environmental Sciences, University of Shizuoka, Yada, Shizuoka 422-8526, Japan

‡

S Supporting Information *

ABSTRACT: Aromatic character of coronoid hydrocarbons is greatly influenced by the shapes of outer and inner peripheries. The most aromatic rings in coronoids are jutting benzene rings on the armchair edges, if any. Clar formulas of many coronoids conform to the aromaticity patterns. However, placement of all aromatic sextets on highly aromatic rings is sometimes forbidden by the presence of the central cavity. The magnitude of aromatic stabilization energy due to macrocyclic conjugation [SSE(mc)] and the NICS(1) value at the center of the cavity strongly depend on the structure of the superposed Clar formula. Localization of π-electrons in fixed aromatic sextets effectively suppresses macrocyclic conjugation. The sign of SSE(mc) is determined by the number of carbon atoms that form the hub cycle.

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INTRODUCTION In Clar’s aromatic sextet theory,1,2 an aromatic sextet is defined as six π-electrons localized in a single benzene ring, which must be separated from adjacent sextet rings by formal single or formal single and double bonds. Clar’s sextet formula (or a Clar formula) with a maximum number of disjoint aromatic sextets has been used to characterize the chemistry of polycyclic aromatic hydrocarbons (PAHs).1,2 For many PAHs, more than one Clar formula can be drawn. For example, two Clar formulas can be drawn for circumcircumcoronene (1 in Figure 1), each

number of aromatic sextets than anticipated from the Clar formulas.11 As shown in Figure 2, four Clar formulas can be written for 2, each with a maximum of nine aromatic sextets. However, these Clar formulas are not fully consistent with the local aromaticity patterns predicted from the CC bond lengths and HOMA (harmonic oscillator model of aromaticity) values;12−14 some aromatic sextets are assigned to the least aromatic benzene rings.11 Here, a local aromaticity pattern (or an aromaticity pattern for short) signifies a structural formula with the degree of local aromaticity11,14 in each benzene ring. It represents the density of aromaticity in a PAH π-system. In this paper, we systematically examine the local aromaticity patterns of different coronoid PAHs to see whether or not their Clar formulas conform to their respective local aromaticity patterns.

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Using the concepts of bond resonance energy (BRE)15−17 and superaromatic stabilization energy (SSE),18,19 we calculate the degrees of local aromaticity in individual benzene rings of PAHs. Remember that topological resonance energy (TRE)20,21 is the extra stabilization energy arising from all possible circuits in the π-system. Here, a circuit stands for any of the closed cycles that can be chosen from a cyclic π-system. As shown in Figure 3, circuits in coronoids can be classified into two groups: local and macrocyclic circuits.18,22 Macrocyclic circuits surround a central cavity, whereas local circuits do not surround it. BRE for a given π-bond is the extra stabilization energy arising from all circuits that pass through the bond.15−17 Original SSE was the extra stabilization energy arising from all macrocyclic circuits in a coronoid π-system.18,19

Figure 1. Two Clar formulas of circumcircumcoronene (1).

with 12 aromatic sextets; no more sextets can be assigned to the π-system. In general, the stability of isomeric PAHs increases with the increasing number of sextets.1,2 Fully benzenoid hydrocarbons, i.e., PAHs in which all carbon atoms belong to fixed sextet rings, are not only thermodynamically but also kinetically very stable.1,2 These empirical facts indicate that each ring in a PAH molecule must have a different degree of aromatic character.1−5 Dias called fully benzenoid hydrocarbons total resonant sextet (TRS) benzenoids.6 A coronoid hydrocarbon is a planar PAH with a central cavity.7−10 Circumkekulene (2) in Figure 2 is one of the typical coronoids. The coronoid cavities can serve as models of Schottky-type defects in graphene and graphene nanoflakes.9,10 We recently noticed that 2 might possibly have a smaller © 2014 American Chemical Society

EXPERIMENTAL SECTION

Received: November 10, 2013 Revised: January 28, 2014 Published: January 31, 2014 1258

dx.doi.org/10.1021/jp411046z | J. Phys. Chem. A 2014, 118, 1258−1266

The Journal of Physical Chemistry A

Article

Figure 2. Four Clar formulas of circumkekulene (2). Red circles indicate aromatic sextets assigned to the least aromatic rings.

Superaromatic Stabilization Energy. The method for calculating SSE for a coronoid macrocycle is outlined below.18,19 All macrocyclic circuits in circumkekulene (2) pass through either the CaCb bond, the CdCe bond, or the CfCg bond in Figure 4. A hypothetical reference π-system for calculating SSE for the macrocyclic conjugation can then be constructed by modifying the resonance integrals for these three π-bonds in the following manner:18,19 βa,b = βd,e = βf,g = iβ0

and

βb,a = βe,d = βg,f = −iβ0 (2)

Circuits that pass through any two of the three π-bonds are not excluded from the resulting reference π-system; these circuits are local ones and so do not contribute to the macrocyclic aromaticity of the π-system.18,19 SSE for a benzene ring in a PAH π-system (e.g., ring B in 2) can in principle be calculated in the same manner.11 In this case, not cavity A but ring B is viewed as a cavity of the πsystem. All circuits that surround ring B pass through either the CdCe bond or the CfCg bond in Figure 4. Therefore, a hypothetical reference π-system for calculating SSE for the ring can be constructed by modifying the resonance integrals for these two π-bonds in the following manner:11

Figure 3. Examples of local (c1−c4) and macrocyclic (c5−c8) circuits in circumkekulene (2). Circuits c1, c4, c5, and c6 are conjugation circuits.

Bond Resonance Energy. Coronoid hydrocarbons have outer and inner peripheries, which may be compared to the rim and hub of a wheel, respectively. All nonidentical rings and some nonidentical π-bonds in circumkekulene (2) are labeled as in Figure 4. A hypothetical reference π-system for evaluating

βd,e = βf,g = iβ0

BRE for a π-bond on the rim of 2 (e.g., a CfCg bond) is given simply by modifying a pair of resonance integrals for the πbond in the manner:15,16 and

βg,f = −iβ0

βe,d = βg,f = −iβ0

(3)

Circuits that pass through the two π-bonds are not excluded from the resulting reference π-system, because they are local circuits. We showed that SSE for an inner benzene ring, surrounded by six other benzene rings, represents well the degree of local aromaticity for the ring.11 In this case, the inner benzene ring is regarded as a cavity of the π-system. Since BRE for a peripheral π-bond can likewise be interpreted as a local aromaticity index for the ring to which the bond belongs,17 both BRE for a peripheral π-bond and SSE for a benzene ring will hereafter be referred to simply as SSE.11 When SSE is used as an original superaromatic stabilization energy due to macrocyclic conjugation (mc),18,19 the symbol SSE(mc) will be used instead of SSE. General characteristics of the SSE concept have previously been described in some detail.11 We later noticed that the sum of SSEs for all rings (ΣSSE) in a PAH molecule is approximate to the TRE20,21 and the Hess-Schaad resonance energy (HSRE).24,25 In fact, ΣSSE is consistently 10−20% larger than TRE, probably because circuits larger than six-site ones are counted doubly or multiply (see the Supporting Information).11 However, it is interesting to note that ΣSSE is a much better approximation of TRE than HSRE is. This fact supports the view that our SSE concept is not only theoretically but also numerically reasonable as a local aromaticity index for PAHs. Electronic Structure of Coronoids. This study deals with coronoids 2−22 presented in Figures 5, 7, 9, and 11. According to Hajgató et al.,26,27 most of coronoids of D6h symmetry are planar in shape at the B3LYP/6-31G level of theory.28

Figure 4. Nonidentical π-bonds and rings in 2.

βf,g = iβ0

and

(1)

where β0 is the standard resonance integral for a CC π-bond, and i is the square root of −1. This procedure excludes contributions of all circuits that pass through the CfCg bond from the coefficients of the characteristic polynomial. That is, this procedure eliminates contributions of all circuits that surround ring D from the global aromaticity. Note that BRE for the CfCg bond is exactly the same as that for CgCh bond, because they belong to the same arc of the same ring. We previously pointed out that BRE for a π-bond on the rim can be interpreted as a local aromaticity index for the ring to which the bond belongs.11,17 In the present case, BRE for the CfCg bond represents the degree of local aromaticity in ring D. A detailed procedure for calculating BRE has already been described in ref 23. 1259



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RESULTS AND DISCUSSION

Circumkekulene. Hajgató et al. classified coronoids of D6h symmetry into single-, double-, triple-, and quadruple-layered species.26 Circumkekulene (2) is one of the double-layered coronoids. The aromaticity pattern of circumcircumcoronene (1) predicted from the SSEs (1 in Figure 5) is fully consistent with the superposed Clar formula 1 in Figure 6. Clar formulas of many familiar PAHs likewise conform to Clar’s aromatic sextet theory.11 In most cases, sextet rings are highly aromatic. However, the aromaticity pattern of 2 is not consistent with the superposed Clar formula.11 Numerical values of SSEs for all nonidentical rings in 1 and all coronoids studied (2−22) are presented in the Supporting Information. Two pairs of Clar formulas (four in all) can be drawn intuitively for 2, in all of which the maximum of nine aromatic sextets are distributed (Figure 2). As can be seen from the superposed Clar formula 2 in Figure 6, aromatic sextets can be assigned to any of the benzene rings. Therefore, all these benzene rings are supposed to contribute significantly to global aromaticity. However, this superposed Clar formula is not compatible with the aromaticity pattern estimated from the SSEs (2′ in Figure 6). Note that benzene rings at the outer and inner corners of 2 exhibit the smallest SSEs in the π-system. These benzene rings correspond to rings D and B in Figure 4. It follows that three of the nine aromatic sextets in each Clar structure are assigned to these least aromatic rings.11 The smallest SSE for ring B in 2 is compatible with the optimized geometry of the molecule; the CaCb bond that belongs to this ring is the longest one in the π-system (1.451 Å at the B3LYP/6-31+G** level of theory28). Further, the smallest Hückel π-bond order of 0.455 is assigned to this longest π-bond. The HOMA values are relatively small for rings B and D.11 Therefore, it seems likely that, in marked contrast to most PAH molecules, every Clar formula of 2 contains fewer sextet rings than expected from the intuitively drawn Clar formulas. Ring C exhibits the largest SSE with the CbCc bond being as short as 1.393 Å.11 As the aromaticity pattern of 2 in Figure 5 suggests, the effective number of sextet rings in 2 may be six rather than nine. On the other hand, the least aromatic benzene rings at the outer corners of 1 are not counted as sextet rings in the superposed Clar formula, which conforms to the aromaticity pattern predicted from the SSEs. Cycloarenes. We then explore possible correlations between aromatic character of many different coronoids with their Clar formulas. Cycloarenes are single-layered coronoid hydrocarbons.31 The aromaticity patterns of typical cycloarenes 3−8 are shown in Figure 7. A rim of a cycloarene π-system consists of zigzag edges (Figure 8a), whereas the hub is partly formed by the variant of armchair edges (Figure 8c). As graphically summarized in Figure 8, the locations of highly

Figure 5. Aromaticity patterns of 1 and 2. Indigo, blue, and gray filled circles indicate benzene rings with SSEs larger than 1.8, 1.4, and 1.2 |β|, respectively.

Although some of them (14, 21, and 22) are relaxed into bowlshaped structures of C6v symmetry, the energy differences between the planar and bowl-shaped structures are marginally small, less than 0.10 kcal/mol and NICS(1) values for individual benzene rings remain almost unchanged.27 Here, NICS(1) signifies the nucleus-independent chemical shift at a point 1 Å above the cavity center.29 They also found that magnetism predicted to occur in hexagonal coronoids is quenched by nonlocal electron correlation.27 Therefore, we assumed that all species studied are planar in shape in the closed-shell singlet state. Superposed Clar Formula. The aromaticity patterns drawn using SSEs for circumcircumcoronene (1) and circumkekulene (2) are shown in Figure 5. These aromaticity patterns have the same symmetry as the actual π-systems. Clar’s aromatic sextet theory forbids adjacent aromatic rings even if degenerate Clar structures are conceivable.1,2 Therefore, each Clar formula is often less symmetric than the aromaticity pattern. In order to overcome this kind of inconsistency, we use the so-called superposed Clar formula obtained by superposing all possible Clar formulas.11,30 A superposed Clar formula necessarily has the same symmetry as the actual π-system and can be compared readily with the aromaticity pattern. The superposed Clar formulas of 1 and 2 are presented in Figure 6.

Figure 6. Superposed Clar formulas of 1 and 2. Red circles indicate aromatic sextets assigned to the least aromatic rings. For reference, 2′ is a superposed Clar formula of 2, predicted from the aromaticity pattern.

Figure 7. Aromaticity patterns of cycloarenes. Values in blue are SSE(mc) values given in units of |β|. Indigo, blue, and gray filled circles indicate benzene rings with SSEs larger than 1.8, 1.4, and 1.2 |β|, respectively. 1260



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Figure 10. Aromaticity patterns near the armchair edges. Figure 8. Typical arrangements of highly aromatic rings near the edges.

be interpreted in terms of edge shapes. Locations of highly aromatic benzene rings predicted from the outer edges are consistent with those predicted from the inner edges. SSE(mc) values (i.e., the degrees of superaromaticity) are given in blue in Figure 7 and listed in Table 1. The sign of SSE(mc) for a cycloarene macrocycle depend on the number of carbon atoms that constitute the hub cycle; (4n + 2)- and 4nmembered hub cycles bring about positive and negative

aromatic benzene rings are determined primarily by the type of edge shapes; these types of edges are also found in the aromaticity patterns of many different coronoids in Figures 9 and 10. Benzene rings at the corners of the cycloarene macrocycle are least aromatic with the smallest SSEs. Thus, the aromaticity patterns of cycloarenes in Figure 7 can in principle

Figure 9. Aromaticity patterns of coronoids with a coronene-shaped cavity. Circumkekulene (2) in Figure 5 and kekulene (7) in Figure 7 also belong to this group. Indigo, blue, and gray filled circles indicate benzene rings with SSEs larger than 1.8, 1.4, and 1.2 |β|, respectively. NICS(1) values at the cavity centers are given thereat. 1261



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SSE(mc) values, respectively. Positive or negative SSE(mc) decreases on going to higher members of the cycloarene series. This strongly suggests that the circuit that corresponds to the hub cycle contributes predominantly to SSE(mc), because it is the smallest macrocyclic conjugation circuit.32 However, even this hub circuit is very large, so that SSE(mc) anyways is very small in magnitude.32 Coronoids in General. We go on to a series of coronoids with an 18-membered hub cycle (2, 7, and 9−16). These coronoid structures are formally generated from sufficiently large PAHs of D6h symmetry by excising out the benzene nucleus and attaching hydrogen atoms to the dangling bonds created within the resulting coronene-shaped cavity.9 The aromaticity patterns of 9−16, drawn with SSEs, are presented in Figure 9; values written in the cavities are NICS(1) values at the B3LYP/6-31G level of theory.28 Those for 2, 9, 11, and 15 were calculated by Hajgató et al. at the same level of theory.26 NICS(1) values for 3−6 and 8 were not calculated, because their cavity centers are crowded with hydrogens. Many PAHs have one or more zigzag edges, from each of which a polyacene-like substructure can be chosen. Since at most one aromatic sextet can be assigned to such a substructure, formal double bonds result in rings other than the sextet ring. Therefore, such PAHs are never fully benzenoid ones. Fully benzenoid hydrocarbon π-systems are always rimmed with armchair edges. For these PAHs, the locations of highly aromatic rings can be easily distinguished from others. As can be inferred from Figure 9, jutting benzene rings on outer

Table 1. Macrocyclic Aromaticity of Coronoids Studied species C90H30 (circumkekulene, 2) C32H16 (3) C36H18 (4) C40H20 (5) C44H22 (6) C48H24 (kekulene, 7) C52H26 (8) C90H30 (9) C144H36 (10) C144H36 (11) C144H36 (12) C144H36 (13) C210H42 (14) C108H36 (15) C108H36 (16) C72H36 (17) C126H42 (18) C192H48 (19) C96H48 (20) C162H54 (21) C120H60 (22)

number of aromatic sextets

SSE(mc)/|β|

NICS(1)a/ ppm

9

0.048 368

−11.6b

4 3 4 4 6 5 11 18 17 17 18 24 18 16 6 12 21 6 12 6

0.026 734 −0.014 328 0.009 603 −0.005 580 0.003 483 −0.002 319 0.009 485 0.007 936 0.025 776 0.021 195 0.006 592 0.031 855 0.001 143 0.018 756 0.000 357 0.028 038 0.001 440 0.000 060 0.018 135 0.000 014

− − − − 2.7b − 2.44 4.4b −3.39 −2.13 4.36 −10.1b 4.38 1.44 1.6b −11.9b 3.1b 1.0b −11.1b 0.7b

a

NICS(1) values calculated 1 Å above the center of the cavity at the B3LYP/6-31G level of theory. bTaken from ref 26.

Figure 11. Aromaticity patterns of coronoids with a larger cavity. Indigo, blue, and gray filled circles indicate benzene rings with SSEs larger than 1.8, 1.4, and 1.2 |β|, respectively. NICS(1) values at the cavity centers are given there. 1262



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Figure 12. Superposed Clar formulas of cycloarenes.

Figure 13. Superposed Clar formulas of coronoids with an coronene-shaped cavity. Red circles in 14 indicate aromatic sextets assigned to the second least aromatic rings, whereas red letters x in 16 indicate highly aromatic rings unrelated to aromatic sextets.

and inner armchair edges are usually highly aromatic (Figure 8, parts b and c). Highly aromatic rings in the inner part of a large π-system may be arranged like those in fully benzenoid hydrocarbons. Coronoids 9, 10, 13, and 15 belong to this group. Armchair edges in these species primarily determine the entire aromaticity patterns. In 11, 12, 14, and 16, however, highly aromatic rings are rather limited to either the inner or outer armchair edges. If a rim consists of zigzag edges alone, the degree of local aromaticity varies rather modestly along the polyacene-like substructures (Figure 8a). Benzene rings at the corners of the zigzag rim are least aromatic. Coronoids 15 and 16 in Figure 9 have armchair edges both along the hub and the rim. Therefore, both outer and inner

armchair edges must tend to determine the locations of highly aromatic rings. Figure 10 illustrates the typical arrangements of highly aromatic rings expected near the inner and outer armchair edges. As a result, 15 becomes a fully benzenoid hydrocarbon with all carbon atoms belonging to highly aromatic rings. However, highly aromatic rings in 16 are not arranged in this manner, because the locations of highly aromatic rings predicted from the outer armchair edges (Figure 10a) disagree halfway with those predicted by the inner armchair edges (Figure 10b). The outer armchair edges determines the locations of highly aromatic rings and so some of the jutting aromatic rings around the hub are made less aromatic. 1263



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Figure 14. Superposed Clar formulas of coronoids with a larger cavity. Red letters x in 18 indicate highly aromatic rings unrelated to aromatic sextets.

Superposed Clar Formulas of Coronoids. Figures 12−14 show superposed Clar formulas of all coronoids studied (9−22). Clar formulas of many coronoids straightforwardly reflect the aromaticity patterns presented in Figures 7, 9, and 11; most aromatic sextets are located in benzene rings of high local aromaticity. Only one Clar formula can be drawn for 3, 7, 9−13, 15, and 16. Clar formulas of all these species but 16 obviously resemble those of fully benzenoid hydrocarbons (Figure 15), which represent the two-dimensional closest

Aromaticity patterns of 17−22, each with a larger cavity, are presented in Figure 11. All these coronoids happen to have D6hsymmetry with zigzag-shaped rims. Since these coronoids have no armchair edges along the rim, their aromaticity patterns are determined primarily by the inner armchair edges. However, these species seem to have no highly aromatic rings due to the presence of many polyacene-like substructures along the rim and the hub. Benzene rings located at the inner and outer corners again are less aromatic than others. SSE(mc) and NICS(1) values at the cavity centers for 2 and 9−22 are added in Table 1. SSE(mc) values for these coronoids are all positive in sign, because they have (4n + 2)-membered hub cycles. Thus, the macrocycles of these species are aromatic in nature. In this context, we previously reported that the SSE(mc) values for coronoids with 4n-membered hub cycles are negative in sign.10 NICS(1) values at the cavity centers of 2 and 9−17 are also given in Figures 9 and 11. It is interesting to see that these NICS(1) values are not always negative at the cavity centers, even though SSE(mc) values are all positive. This never means that both quantities are not correlative with each other. Coronoids with large negative NICS(1) values exhibit relatively large SSE(mc) values, whereas those with positive NICS(1) values exhibit relatively small negative or positive SSE(mc) values. Thus, NICS(1) and SSE(mc) correlate well with each other, because both quantities are closely associated with the same set of macrocyclic circuits. In fact, SSE(mc) reflects aromaticity of all macrocyclic circuits, whereas NICS(1) reflects currents induced in all local and macrocyclic circuits to varying extents.

Figure 15. Partial Clar formula of fully benzenoid hydrocarbons.

packing of aromatic sextets. This fact again seems to support not only the general usefulness of Clar formulas but also the meaningfulness of our SSE concept as a local aromaticity index. Many coronoids with two or more Clar formulas, such as 4−6, 8, and 19−22, also have aromatic sextets on the rings with relatively large SSEs. We have pointed out that circumkekulene (2) is exceptional in that some aromatic sextets are placed on the least aromatic 1264



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rings.11 In this connection, double-layered coronoids 18 and 21 are higher homologues of 2. Benzene rings located at the outer and inner corners of 18 and 21 likewise exhibit relatively small SSEs, and so aromatic sextets cannot be assigned to the corner rings. Therefore, unlike 2, these coronoids are not exceptions. However, we found another circumkekulene-like exception. It is quadruple-layered coronoid 14, for which four Clar formulas can be drawn (Figure 16). In the first two of the Clar formulas,

cycle.33 As predicted by Hajgató et al.,26 double- and quadruplelayered coronoids (2, 18, and 21) exhibit large negative NICS(1) values at the cavity centers. Their superposed Clar formulas are not similar in appearance to those of fully benzenoid hydrocarbons, suggesting the large mobility of aromatic sextets.

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CONCLUDING REMARKS It is now obvious that aromatic character of coronoid hydrocarbons is strongly influenced by the shapes of outer and inner edges. The most aromatic rings in coronoids are jutting benzene rings in armchair edges, if any. We have seen that the Clar formulas of most coronoids conform to the aromaticity patterns. A Clar formula of a coronoid tends to imitate the Clar formula of a fully benzenoid hydrocarbon as it tends to maximize the number of aromatic sextets. This does not mean that all aromatic sextets in a Clar formula are never placed on the least aromatic rings. Some coronoids maximize the number of aromatic sextets at the expense of the conformity to the aromaticity pattern. Thus, the locations of aromatic sextets are constrained by the central cavity. The magnitude of aromatic stabilization energy due to macrocyclic conjugation [SSE(mc)] and the NICS(1) value at the cavity center strongly depend on the structure of the Clar formula. Localization of πelectrons in fixed sextet rings effectively suppresses macrocyclic conjugation. The sign of SSE(mc) is determined by the number of carbon atoms that form the hub cycle.

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Figure 16. Four Clar formulas of coronoid 14. Red circles indicate aromatic sextets assigned to the second least aromatic rings.

ASSOCIATED CONTENT

S Supporting Information *

Correlation among TRE, HSRE, and ΣSSE for familiar PAHs and numerical values of SSE for all nonidentical benzene rings in circumcircumcoronene (1) and 21 coronoid hydrocarbons (2−22). This material is available free of charge via the Internet at http://pubs.acs.org.

three aromatic sextets are placed on benzene rings at the corners of the cavity, although these rings exhibit relatively small SSEs. These two are obviously less important Clar formulas. The other two formulas are not exceptional in the arrangement of aromatic sextets. On the other hand, 16 is an exception in the opposite sense. In this coronoid, the locations of 16 aromatic sextets are determined by the outer armchair edges. If aromatic sextets are placed on all jutting rings of the rim and hub, the number of aromatic sextets cannot be maximized. Therefore, aromatic sextets cannot be placed on all jutting benzene rings located along the hub although they are highly aromatic rings. Thus, the Clar formula of this coronoid somewhat deviates from the aromaticity pattern. Likewise, the central ring in every zigzag edge of the rim in 18 (Figure 11) exhibit a moderately large SSE, but aromatic sextets cannot be assigned to them. The occurrence of such anomalous or constrained Clar formulas must be associated with the requirement that the number of aromatic sextets must be maximized even in macrocyclic coronoid π-systems.1,2 Placement of some aromatic sextets on the highly aromatic rings is sometimes forbidden by the presence of the central cavity. Such highly aromatic benzene rings in 16 and 18 are marked with letter x in Figures 13 and 14, respectively. Most coronoids with the Clar formulas similar in the arrangement of sextet rings to those of fully benzenoid hydrocarbons (Figure 15) exhibit small negative or positive NICS(1) values, suggesting that diamagnetic currents are localized in each sextet ring. Kekulene (7) is one of such examples, in which a macrocyclic diamagnetic current is weak22 and each benzene ring sustains a strong diamagnetic current. As a result, an apparent paramagnetic current flows along the hub

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AUTHOR INFORMATION

Corresponding Author

*E-mail: (J.A.) [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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Constrained Clar Formulas of Coronoid Hydrocarbons - American

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