Aromatic Character of Nanographene Model Compounds - The

Article pubs.acs.org/JPCA

Aromatic Character of Nanographene Model Compounds Kenkichi Sakamoto,† Naoko Nishina,† Toshiaki Enoki,‡ and Jun-ichi Aihara*,† †

Department of Chemistry, Faculty of Science, Shizuoka University, Oya, Shizuoka 422-8529, Japan Department of Chemistry, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152-8551, Japan

‡

S Supporting Information *

ABSTRACT: Superaromatic stabilization energy (SSE) defined to estimate the degree of macrocyclic aromaticity can be used as a local aromaticity index for individual benzene rings in very large polycyclic aromatic hydrocarbons (PAHs) and finite-length graphene nanoribbons. Aromaticity patterns estimated using SSEs indicate that the locations of both highly aromatic and reactive rings in such carbon materials are determined primarily by the edge structures. Aromatic sextets are first placed on the jutting benzene rings on armchair edges, if any, and then on inner nonadjacent benzene rings. In all types of nanographene model compounds, the degree of local aromaticity varies markedly near the edges.

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INTRODUCTION A graphene sheet consists of innumerable benzene rings,1,2 all of which are equivalent with the same degree of local aromaticity. Nanographenes are large flakes of graphene, in which benzene rings are no longer equivalent to each other.3,4 Large polycyclic aromatic hydrocarbons (PAHs) can be regarded as molecular subunits of graphene. Many large PAHs have so far been designed to explore possible electronic and other physical properties of nanographenes.3−14 Müllen’s research group established the procedure for the rational synthesis of extremely large PAHs based on the cyclodehydrogenation of branched polyphenylenes.15,16 Nanographene sheets are characterized primarily by the presence of two types of edges, that is, armchair and zigzag edges.17,18 It is well-known that the electronic structure of nanographene model compounds depends crucially on the geometry of edges.19,20 Further structure−property relationships for nanographenes, if found, would serve to promote the design of practical nanographenes. Work in this field often starts by applying Clar’s aromatic sextet theory21,22 or various local aromaticity indices23,24 to graphene nanostructures. As comprehensively reviewed by Bultinck,23,24 many indices have been proposed to estimate the degree of local aromaticity in individual benzene rings of PAHs. Different local aromaticity indices, however, make different predictions. We recently found that the superaromatic stabilization energy (SSE) defined by us25,26 can be used as a physically sound local aromaticity index for large PAHs.27,28 SSE was originally defined as an extra stabilization energy due to macrocyclic conjugation or to a set of macrocyclic circuits in a macrocyclic π-system.25−27 When SSE is used as a local aromaticity index for a peripheral benzene ring, it is identical to the bond resonance energy (BRE) for peripheral π-bonds that belong to the ring.28−30 In fact, SSE is the first index that reflects the degree of local aromaticity straightforwardly;28 this index is not obscured by the aromaticity arising from adjacent six-site circuits. In this paper, we apply the SSE concept to a wide variety of nanographene model compounds and explore the aromatic character of these large carbon-based materials. © 2014 American Chemical Society

COMPUTATIONAL PROCEDURES BRE and SSE are defined within the framework of simple Hückel molecular orbital theory,25,28−31 which is equivalent to the tightbinding model employed in physical papers. For simplicity, naked nanographenes will not be distinguished from hydrogenterminated ones, in which dangling bonds are passivated by hydrogen atoms. The resulting hydrocarbons are nothing other than large closed-shell PAH molecules. They are assumed to have equilateral geometries. First, we briefly describe how to calculate BRE for a peripheral π-bond that belongs to ring B in coronene (1 in Figure 1).30,31 All

Figure 1. Nonidentical benzene rings in coronene (1) and dodecabenzocoronene (2).

circuits that surround or encompass this ring pass through the peripheral CaCb bond. Here, a circuit stands for any of the cyclic or closed paths that can be chosen from a cyclic π-system. We modify the resonance integrals for this π-bond in the following manner βa,b = iβ0

βb,a = −iβ0

(1)

where β0 is the standard resonance integral for a CC π-bond and i is the square root of −1. The hypothetical π-system thus defined is Received: February 17, 2014 Revised: April 1, 2014 Published: April 1, 2014 3014

dx.doi.org/10.1021/jp5017032 | J. Phys. Chem. A 2014, 118, 3014−3025

The Journal of Physical Chemistry A

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devoid of the contributions of all circuits that encompass ring B to global aromaticity, thus defining the reference π-system for estimating the local aromaticity of ring B.30,31 In another viewpoint, the BRE for a peripheral π-bond represents the aromaticity arising from all circuits that encompass the benzene ring to which the πbond belongs.32 This is why the BRE for the peripheral CaCb bond can be interpreted as a local aromaticity index for the peripheral ring B. Our method for calculating SSE25 can be used to estimate the degree of local aromaticity in all constituent benzene rings.28,29 In this case, a given benzene ring is viewed as a cavity in a macrocyclic π-system. The reference π-system that is devoid of macrocyclic aromaticity around the central benzene ring (ring A) of 1 is designed by modifying the resonance integrals for the CaCb and CcCd bonds in the following manner25,28,29 βa,b = βc,d = iβ0

βb,a = βd,c = −iβ0

Figure 2. Superposed Clar formula of coronene (1).

formula can be written for a PAH molecule, we will use the superposition of all possible Clar formulas instead of individual Clar formulas;7,28,29 the superposed Clar formula then reflects the symmetry of the SSE pattern in the π-system properly. In general, a Clar formula is closely associated with the partial π-electron density due to high-lying molecular orbitals.36 We recently noticed that Clar formulas of some coronoid hydrocarbons are exceptional in that placement of some aromatic sextets on highly aromatic rings is forbidden by the presence of the central cavity.29

(2)

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All circuits that encompass ring A pass through either the CaCb bond or the CcCd bond. Therefore, eq 2 excludes the contributions of these circuits from the coefficients of the characteristic polynomial, thus defining the reference π-system for estimating the local aromaticity of ring A. A detailed procedure for calculating the BRE is found in ref 33, and that for calculating SSE will readily be imagined by analogy. Because the BRE for a π-bond on the rim can likewise be interpreted as a local aromaticity index for the ring to which the π-bond belongs, it will also be referred to as the SSE. A comparative study of the SSE and typical local aromaticity indices has already been made in some detail.28 The same approach can be applied to any inner benzene ring in larger PAHs.28,29 For example, the reference π-system needed to evaluate the SSE for the central benzene ring A of dodecabenzocoronene (2 in Figure 1) can be constructed by modifying the resonance integrals for the CaCb, CcCd, and CeCf bonds in the following manner βa,b = βc,d = βe,f = iβ0

βb,a = βd,c = βf,e = −iβ0

RESULTS AND DISCUSSION The aromatic character of nanographenes is explored below by analyzing the aromaticity patterns of many different model compounds, such as large PAHs and rectangular nanoribbons. Numerical values of the SSE for benzene rings in these species, used to draw their aromaticity patterns, are given in the Supporting Information. Zigzag-Edged D6h-PAHs. The electronic structure of large D6h-symmetric PAHs has been studied systematically by many researchers, including Stein and Brown,5 Dias,6 Watson et al.,15,16 Moran et al.,7 Hajgato et al.,9 and Steiner et al.10 The first group of D6h-PAHs (1−55,6 in Figure 3) are those rimmed primarily by zigzag edges, in which six zigzag edges constitute six sides of each hexagonal molecule. For this type of molecules, the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) rapidly decreases with the molecular size (Table 1).5 This aspect of electronic structure is closely associated with the presence of a so-called edge state. Nanographene sheets rimmed with zigzag edges have a large local density of states around the edge regions.5,17 Large zigzag-edged PAHs, such as 2−5, have not been prepared yet, partly because they are predicted to be kinetically unstable and partly because there have been no appropriate synthetic routes to these species. One can distinguish clearly between highly aromatic and less aromatic rings in the first three members (1−3), although very highly aromatic rings with SSEs > 1.8 |β| are lacking. In larger members, such as 5 and 6, even aromatic rings with SSEs > 1.4 |β| are missing. Thus, the π-system of a zigzag-edged nanographene sheet rapidly approaches that of an infinite-sized graphene sheet with a homogeneous density of local aromaticity. As shown in Figure 4, more than one Clar formula can be written for 3 and 5, indicating that aromaticity is not concentrated on a small number of rings. Only one Clar formula can be written for 2 and 4. Many formal double bonds remain in the Clar formulas of all zigzagedged D6h-PAHs. Zigzag-edged nanographenes are similar in a sense to linear polyacenes. As in the case of polyacenes, only one sextet can be placed on the benzene rings arranged along each zigzag edge and is necessarily accompanied by mobile and reactive double bonds. Aromatic sextets cannot be placed on benzene rings at the six corners if one wants to secure the maximum number of aromatic sextets (Figure 4). The numbers of aromatic sextets in the Clar formulas of all species studied are summarized in Table 1. In general, the aromaticity patterns of zigzag-edged PAHs in Figure 3

(3)

All circuits that encompass ring A pass through one or all of the three π-bonds. Equation 3 then excludes the contributions of these circuits from the coefficients of the characteristic polynomial, thus defining the reference π-system for estimating the local aromaticity of the central ring. Circuits that pass through any two of the three π-bonds are not excluded from the characteristic polynomial because they are not macrocyclic but local circuits. For SSEs thus calculated for all rings in 1 and 2, see the Supporting Information. We noticed that the sum of SSEs for all benzene rings (∑ SSE) in a PAH molecule29 is approximate to the topological resonance energy (TRE)34 and the Hess− Schaad resonance energy.35 This fact supports the view that our SSE concept is not only theoretically but also numerically reasonable as a local aromaticity index for PAHs. Clar’s sextet formula (or a Clar formula for short) with a maximum number of disjoint aromatic sextets has been used to account for many properties of PAHs.21,22 An aromatic sextet or a sextet ring is defined as six π-electrons localized in a single benzene ring, which is separated from adjacent sextet rings by formal single or formal single and double bonds. Clar formulas will be used to see the reasonableness of the aromaticity patterns drawn for PAHs. In this paper, structural formulas with a SSE value in each benzene ring are employed as aromaticity patterns.28,29 As can be seen from Figure 2, two Clar formulas can be written for 1. When, like this PAH, more than one Clar 3015



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Figure 3. Aromaticity patterns of D6h-PAHs with zigzag edges. Filled blue and gray circles indicate rings with SSEs larger than 1.4 and 1.2 |β|, respectively. There are no benzene rings with SSEs ≥ 1.8 |β|.

Figure 4. Superposed Clar formulas of PAHs 2−5.

large HOMO−LUMO gaps, together with a fairly uniform distribution of the HOMO state.5 One can see from Table 1 that the HOMO−LUMO gap of armchair-edged 8 (C222H42) is twice as large as that of zigzag-edged 5 (C216H36). In general, armchair-edged nanographenes have more sextet rings with fewer formal double bonds than zigzag-edged ones of a similar size (e.g., 37 for 8 versus 27 for 5). PAHs 6−8 have so far been prepared and characterized.5,6,15 They are totally resonant PAHs, that is, PAHs in which all carbon atoms belong to fixed sextet rings. They are nothing other than fully benzenoid hydrocarbons

resemble their respective superposed Clar formulas. Whether or not more than one Clar formula can be written, the difference in local aromaticity between sextet rings and others is relatively small. Therefore, the inner part of a sufficiently large zigzagedged PAH can be employed as a model of a graphene sheet with a fairly uniform density of aromaticity. Armchair-Edged D6h-PAHs. The second group of D6hsymmetric PAHs (6−10 in Figure 5) are those rimmed primarily by armchair edges, in which armchair edges constitute six sides of each hexagonal molecule. Armchair-edged nanographenes have 3016



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Figure 5. Aromaticity patterns of D6h-PAHs with armchair edges. Filled indigo, blue, and gray circles indicate rings with SSEs larger than 1.8, 1.4, and 1.2 |β|, respectively.

Figure 6. Superposed Clar formulas of PAHs 9−11, 15, and 27. Red circles indicate the least aromatic “sextet rings” with SSEs of 0.1069−0.1095 |β|.

in Clar’s terminology.21,22 In these PAHs, the migration of any aromatic sextet is prohibited. It is well-known that totally resonant PAHs are not only thermodynamically but also kinetically very stable.21,22

Figure 5 shows that jutting benzene rings arranged along the armchair edges in 6−8 are very highly aromatic with SSEs > 1.8 |β|. Note that the SSE for a benzene molecule, which is the same as the TRE for this hydrocarbon, is as large as 0.2726 |β|. 3017



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Figure 7. Aromaticity patterns of PAHs with o-phenylene moieties. Filled indigo, blue, and gray circles indicate rings with SSEs larger than 1.8, 1.4, and 1.2 |β|, respectively.

All sextet rings in 6−8 are highly aromatic with SSEs > 1.4 |β|, which is in marked contrast to those in zigzag-edged species 1−5. Inner sextet rings exhibit a bit smaller SSEs. Localization of aromatic sextets in hexa-peri-hexabenzocoronene (6) has been observed in the scanning tunneling (STM) and atomic force (AFM) microscopy images.37−40 For 9 and 10 in Figure 5, which have not been prepared yet, more than one Clar formula can be written, and therefore, the degrees of local aromaticity in sextet rings are more or less diluted. Their aromaticity patterns are similar in appearance to their respective superposed Clar formulas in Figure 6. Superposed Clar formulas of totally resonant PAHs are essentially the same as their respective aromaticity patterns and therefore are omitted from this figure. Other Large Compact PAHs. PAHs 11,15 12,15,37 13,16 14,5,15 and 155 in Figure 7 have two or more o-phenylene moieties. All but 15 have been prepared.15,16 Outstanding o-phenylene rings in these PAHs are highly aromatic with SSEs > 1.8 |β|. Superposed Clar formulas in Figure 6 suggest that PAHs with fjord regions, such as 11 and 15, have some formal double bonds in their Clar formulas. Thus, hexabenzo[a,d,g,j,m,p]coronene (11) has one fewer sextet in its Clar formula than hexa-peri-hexabenzocoronene (6), although the numbers of constituent benzene rings are the same. PAHs 12−14 are totally resonant ones. Müllen’s research group and some others prepared so-called super-PAHs using hexa-peri-hexabenzocoronene molecules (6) as building blocks.15,16,41 Among this type of PAHs are supernaphthalene (16),15 supertetracene (17),16 superphenalene (18),15 supertriphenylene (19),15 supertriangulene (20),41 and supercoronene (21)15 in Figure 8. These PAHs, together with 14 in Figure 7, are totally resonant PAHs with cave regions. As can be seen from Figure 8, the aromaticity patterns of super-PAHs are very similar in appearance to those of the other totally resonant PAHs, such as 6−8 in Figure 5 and 12−14 in Figure 7. Sextet rings located

at the innermosts of the coves exhibit a bit smaller SSEs than the other peripheral sextet rings, although they are placed on the rim. Some other PAHs studied (22−2615 and 27) are presented in Figure 9. They happen to be of D2h symmetry. Most of them are again totally resonant PAHs, the aromaticity patterns of which are consistent with the single Clar formulas for them. Still elusive PAH 27 is not a totally resonant PAH. Like 9 and 10, more than one Clar formula can be written for 27; its aromaticity pattern is more or less similar to the superposed Clar formula shown in Figure 6. However, this PAH is somewhat unusual in that sextet rings are placed in the least aromatic rings in the superposed Clar structure.28 Benzenoid dendrimer 28 in Figure 10 is not a PAH but a precursor for the synthesis of the largest totally resonant PAH 8.15 Constituent benzene rings in 28 are all substituted benzenes with large SSEs; the SSE of each benzene ring decreases depending on the number of substituents. Aromaticity patterns of all PAHs so far studied are generally consistent with the conjugation circuit model42−44 in that highly aromatic rings can be predicted properly. Antiaromatic benzene rings are absent in all PAHs, which corresponds to the absence of 4n-site conjugation circuits. Rectangular Graphene Nanoribbons. The aromatic character of long graphene nanoribbons has been studied extensively.11−14 We here focus on the aromaticity patterns of closed-shell rectangular graphene nanoribbons with two zigzag and two armchair edges.3,14,45,46 These nanoribbons can be obtained by cutting a two-dimensional graphene sheet along the armchair and zigzag directions. Among such finite-length nanoribbons are pentacene-, hexacene-, and heptacene-based ones in Figures 11, 12, and 13, respectively. These are different in width. In all of these rectangular nanoribbons, zigzag edges form shorter upper and lower sides, while longer right and left sides are formed by armchair edges. 3018



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Figure 8. Aromaticity patterns of super-PAHs. Filled indigo and blue circles indicate rings with SSEs larger than 1.8 and 1.4 |β|, respectively.

Figure 13. Here, [n]acene stands for linear polyacene with n benzene rings. As for type-I nanoribbons, all benzene rings arising from [n−1]acenes are empty, in the sense that no aromatic sextets can be assigned to these rings. Type-II nanoribbons are formed by alternate fusion of 10 [n-1]acenes with 9 [n]acenes, as in the case of 30 (n = 5) in Figure 11, 33 (n = 6) in Figure 12, and 36 (n = 7) in Figure 13. Rectangular nanoribbons of types I and II may be called collectively twodimensional (2D) periacenes and circumacenes, respectively.47 Finally, type-III nanoribbons are formed by fusion of 18 [n]acenes, as in the case of 31 (n = 5) in Figure 11, 34 (n = 6) in Figure 12, and 37 (n = 7) in Figure 13. There are no empty rings in type-II and type-III nanoribbons. For each type of nanoribbon, the broad aspect of the aromaticity pattern varies with a period of three when the width or the n value is increased. That is, the aromaticity pattern of [n]acene-based nanoribbon is similar to that of the [n+3]acene-based one.8 Such a periodicity of three has been observed for carbon nanotubes.48,49 Figure 14 shows three examples of decacene-based nanoribbons with longer zigzag and shorter armchair edges; 38, 39, and 40 belong to type-I, -II, and -III nanoribbons, respectively. It seems that the marked difference in local aromaticity between adjacent rings fades away upon going from the armchair edges to the inner part of the nanoribbon sheet. Benzene rings located

Table 1. HOMO−LUMO Gaps in Large PAHs Studied speciesa

molecular formulab

1 2 3 4 5 6* 7* 8* 9 10 11 12* 13* 14*

C24H12 (3) C54H18 (7) C96H24 (12) C150H30 (19) C216H36 (27) C42H18 (7) C114H30 (19) C222H42 (37) C84H24 (9) C180H36 (27) C48H24 (6) C54H22 (9) C60H24 (10) C78H30 (13)

HOMO− molecular LUMO gap/|β| speciesa formulab 1.0784 0.6841 0.3972 0.3134 0.2142 0.9295 0.5822 0.4224 0.6355 0.4497 0.9010 0.7639 0.8316 0.7428

15 16* 17* 18* 19* 20* 21* 22* 23* 24* 25* 26 27 28*

C138H42 (19) C72H26 (12) C132H42 (22) C96H30 (16) C132H42 (22) C168H42 (28) C186H42 (31) C60H22 (10) C78H26 (13) C96H30 (16) C114H34 (19) C76H24 (10) C132H34 (22) C222H150 (37)

HOMO− LUMO gap/|β| 0.4817 0.7478 0.6433 0.6630 0.6461 0.5186 0.4777 0.7379 0.6328 0.5674 0.5234 0.4160 0.5195 0.7540

a

Species marked with asterisks are totally resonant PAHs. bValues in parentheses are the number of aromatic sextets in the Clar formula(s).

Rectangular nanoribbons in Figures 11−13 can be classified into three types. Type-I nanoribbons are formed by alternate fusion of 10 [n]acenes with 9 [n-1]acenes, as in the case of 29 (n = 5) in Figure 11, 32 (n = 6) in Figure 12, and 35 (n = 7) in 3019



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Figure 9. Aromaticity patterns of D2h-PAHs. Filled indigo and blue circles indicate rings with SSEs larger than 1.8 and 1.4 |β|, respectively.

Table 2. HOMO−LUMO Gaps for Rectangular Graphene Nanoribbons Studied species

molecular formula

29a 30b 31c 32a 33b 34c

C220H50 C216H48 C226H48 C260H52 C256H50 C264H50

a

HOMO− LUMO gap/|β| species 0.000 003 0.133 767 0.000 989 0.000 000 0.020 847 0.000 083

35a 36b 37c 38a 39b 40c

molecular formula

HOMO− LUMO gap/|β|

C300H54 C296H52 C302H52 C210H40 C206H38 C196H38

0.000 000 0.003 090 0.000 009 0.000 006 0.001 951 0.000 281

Type-I nanoribbon. bType-II nanoribbon. cType-III nanoribbon.

the largest SSE. This aspect of local aromaticity strongly suggests that aromatic sextets must first be placed on these benzene rings. As for our rectangular graphene nanoribbons (29−40), two of the four sides are armchair edges. Therefore, each of these armchair edges is a determinant of the locations of highly aromatic rings. The basic aromaticity pattern is that of totally resonant PAHs. Therefore, the aromaticity patterns of rectangular nanoribbons can basically be predicted in the following manner. As in the case of large compact PAHs, armchair edges primarily determine the locations of highly aromatic rings. Figure 15 indicates how highly aromatic rings can be arranged in 29 and 30 when one starts from the left or right armchair edge. Note that the central part of the aromaticity pattern of 29 is the same as that of 30. In this case, the aromaticity pattern predicted from the left edge is not in phase with that predicted from the right edge. It follows that the actual aromaticity patterns of 29 and 30 are a compromise between these two arrangements. On the other hand, the aromaticity pattern of 31 is in contrast to those of 29 and 30 in that aromaticity patterns predicted from left and right edges are exactly in phase with each other. In this case,

Figure 10. Aromaticity pattern of the precursor for the synthesis of 8. Filled indigo and blue circles indicate rings with SSEs larger than 1.8 and 1.4 |β|, respectively.

along the long zigzag edges are never highly aromatic. Therefore, it does not seem meaningful to assign aromatic sextets to interior benzene rings located far away from the armchair edges. Shi et al. noted that when a type-III nanoribbon reaches 16 × 16 rings or beyond, the average C−C binding energy becomes almost the same as that of the graphene sheet.46 As can be predicted from Clar formulas and aromaticity patterns of large compact PAHs, the locations of aromatic sextets in rectangular nanoribbons are primarily determined by the armchair edges. The most aromatic rings are jutting benzene rings located along the armchair edges. That is, a benzene ring flanked by three continuous benzene rings almost always exhibits 3020



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Figure 11. Aromaticity patterns of pentacene-based rectangular nanoribbons. Filled indigo, blue, and gray circles indicate rings with SSEs larger than 1.8, 1.4, and 1.2 |β|, respectively.

Figure 12. Aromaticity patterns of hexacene-based rectangular nanoribbons. Filled indigo, blue, and gray circles indicate rings with SSEs larger than 1.8, 1.4, and 1.2 |β|, respectively.

the actual aromaticity pattern becomes the one characteristic of a totally resonant PAH with all carbon atoms belonging to sextet rings or benzene rings that carry aromatic sextets. Clar formulas of most nanoribbons can in principle be predicted in this manner.

One should note that type-I nanoribbons (i.e., 2D periacenes) consist of many polyacene units linked by formal single bonds. Therefore, like higher members of a perylene/bisanthrene series, there are many empty rings. However, many of these empty rings are found to be fairly aromatized with large SSEs. We have 3021



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Figure 13. Aromaticity patterns of heptacene-based rectangular nanoribbons. Filled indigo, blue, and gray circles indicate rings with SSEs larger than 1.8, 1.4, and 1.2 |β|, respectively.

Figure 14. Aromaticity patterns of decacene-based rectangular nanoribbons. Filled indigo, blue, and gray circles indicate rings with SSEs larger than 1.8, 1.4, and 1.2 |β|, respectively.

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previously pointed out that empty rings are more or less aromatized in large PAH molecules.50−52 Thus, upon going far from the zigzag edges, the aromaticity patterns of type-I nanoribbons become very similar to those of type-II nanoribbons. As can be seen from Table 2, the type-II nanoribbon has a much larger HOMO−LUMO gap than the corresponding type-I species. This possibly reflects the fact that a circumacene molecule has a much larger HOMO−LUMO gap than a periacene molecule of a similar size.53,54

CONCLUDING REMARKS

In general, an aromaticity pattern depicted using SSEs is similar to the superposed Clar structure. However, the aromaticity pattern has some advantages over the superposed Clar formula. The aromaticity pattern, drawn with SSEs, shows a variation of local aromaticity quantitatively, so that the degrees of local aromaticity can be compared not only among different rings of a PAH molecule but also among those of different PAH molecules. 3022



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Figure 15. Aromaticity patterns of 29−31 as predicted from the edge structures. Filled indigo, blue, and gray circles indicate rings with SSEs larger than 1.8, 1.4, and 1.2 |β|, respectively.

HOMA value is fairly unchanged.28,32 Here, the HOMA value is a typical geometric index of aromaticity.57,58 Likewise, the ratio of the SCI to the SSE is larger for benzene rings with larger SSEs, but both indices indeed are still highly correlative with each other (see the Supporting Information). As demonstrated by Feixas et al.,59 even though different local aromaticity indices do not always give consistent results, most of them are consistent with superposed Clar formulas.

As illustrated by PAH 27 in Figure 6, sextet rings are not always highly aromatic. Aromatization of empty rings in large PAHs, such as those in 29, 32, and 35, cannot be predicted from a superposed Clar formula. Aromaticity patterns drawn by us are free from these difficulties, enabling us to assess the absolute degrees of local aromaticity in individual benzene rings. An arbitrarily shaped nanographene sheet and any large PAH molecule may be rimmed by a complicated combination of zigzag and armchair edges, with the edge states still being populated around the zigzag-edged region.17−20 In general, armchair edges are long and less defective in actual nanographenes, whereas zigzag edges tend to be defective and relatively short and are often embedded between armchair edges.19,55 These observations are fully consistent with our aromaticity patterns, indicating that local aromaticity is a determinant of kinetic stability and reactivity of edge structures. We repeatedly showed that jutting benzene rings located along the armchair edges exhibit the highest degree of aromaticity. It is impressive to see that all totally resonant PAHs studied in this paper have been prepared and fully characterized. Aromaticity patterns of finite-length nanoribbons studied are essentially the same in appearance as those for nanoribbons of infinite length obtained by Martı ́n-Martı ́nez et al.13 They drew aromaticity patterns using the six-center index (SCI) for every benzene ring; this index is based on diatomic delocalization indices between atoms, taking into account all possible resonance structures.23,24 The validity and limitations of this index were discussed previously by Bultinck et al.23,24,56 and then by Aihara et al.28 Bultinck found that the SCI value is rather proportional to the CRE (circuit resonance energy).28,56 For benzene rings in many PAHs, the ratio of the SCI to the harmonic oscillator model of aromaticity (HOMA) value is larger for benzene rings with larger HOMA values,23 whereas that of the SSE to the

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ASSOCIATED CONTENT

S Supporting Information *

Numerical values of superaromatic stabilization energy (SSE) for all nonidentical benzene rings in 40 nanographene model compounds and the plot of the six-center index (SCI) against SSE for benzene rings of 31 familiar PAHs. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Electric Field Effect in Atomically Thin Carbon Films. Science 2007, 306, 666−669. (2) Geim, A. K.; Novoselov, K. S. The Rise of Graphene. Nat. Mater. 2007, 6, 183−191. (3) Snook, I.; Barnard, A. Graphene Nano-Flakes and Nano-Dots: Theory, Experiment and Applications. In Physics and Applications of Graphene  Theory; Mikhailov, S., Ed.; InTech: Rijeka, Croatia, 2011; pp 277−302. The online version of this book is accessible free of charge

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