Article

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Analytical Study of Superaromaticity in Cycloarenes and Related Coronoid Jun-ichi Aihara,*,†,‡ Masakazu Makino,‡ Toshimasa Ishida,§ and Jerry R. Dias∥

† 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 § Fukui Institute for Fundamental Chemistry, Kyoto University, Takano-Nishibirakicho, Kyoto 606-8103, Japan ∥ Department of Chemistry, University of Missouri, Kansas City, Missouri 64110-2499, United States

*S Supporting Information

ABSTRACT: Recently synthesized septulene is a unique cycloarene molecule in that no macrocyclic conjugation circuits can be chosen from the π-system. This molecule has essentially no superaromatic stabilization energy (SSE) and can be viewed as an ideal nonsuperaromatic macrocycle. SSEs for kekulene and other cycloarenes are also very small. In these hydrocarbons, a macrocycle formed by fused rings effectively suppresses not only the aromaticity inherent in macrocyclic (4n+2)-site conjugation circuits but also the antiaromaticity inherent in macrocyclic (4n±1)-site circuits. Comparative study of superaromaticity in multilayered coronoid hydro- carbons revealed that not only SSE but also the HOMO contribution to SSE is minimized in odd-layered coronoids.

■ INTRODUCTION superaromaticity of many different macrocycles, such as fi cycloarenes, cyclacenes, carbon nanotubes, and porphyr- Cycloarenes are de ned as comprising many annelated benzene 14,25−38 rings that form a macrocycle with inward-pointing C−H ins. For this purpose, we devised some analytical − ff bonds.12 Since before the synthesis of kekulene (1),3 5 the theories of superaromaticity applicable to many di erent π 14,28−31,37,38 ́ prototypical cycloarene, electronic structure of cycloarenes has macrocyclic -systems. Hajgato et al. noticed − been a target of many theoretical and computational oscillatory behaviors of the HOMO LUMO gap and the 6−20 π macrocyclic -circulation in D6h-symmetric coronoid hydro- studies. Kekulene had been viewed as a closed cycle of 19−21 angularly annelated benzene rings and also as a combination of carbons including D6h-symmetric cycloarenes. Here, a two interacting [4n+2]. The synthesis and character- coronoid is a planar polycyclic benzenoid − 39−41 ization of kekulene (1)3 5 in 1978 answered a fundamental hydrocarbons with a central cavity. In this paper, we question about the nature of macrocyclic conjugation. Proton explore some novel aspects of superaromaticity in typical chemical shifts suggest that ring currents are induced primarily cycloarenes and related coronoid hydrocarbons using our own in individual benzene rings.21,22 Such a π-circulation pattern is theories of superaromaticity. Comparative study of super- not compatible with the -within-an-annulene aromaticity in multilayered coronoid hydrocarbons is useful to model.21,22 Recently, Kumar et al. reported the synthesis and seeking for the proper location of cycloarenes in the coronoid properties of kekulene’s nonalternant cousin septulene (2) and family. found that its properties reinforce this conclusion.21 In fact, electronic and magnetic properties of 2 are remarkably similar ■ THEORETICAL BACKGROUNDS to those of 1. It seemed likely that both are composed of fi Our theories of aromaticity and superaromaticity were benzenoid and ole nic benzene rings. This picture is also ̈ supported by their nucleus independent chemical shift (NICS) constructed within the framework of simple Huckel molecular − values.16,22 24 orbital (HMO) theory. In these theories, circuits stand for all The next question to be answered may be whether possible cyclic or closed paths that can be chosen from a cyclic π cycloarenes, such as 1 and 2, are superaromatic or not. -system. Two types of circuits can be chosen from macrocyclic π 14 Superaromaticity, or macrocyclic aromaticity, represents extra -systems: local and macrocyclic circuits. Local circuits are thermodynamic stabilization due to macrocyclic conjugation. those enclosing one or more benzene rings but not enclosing Cioslowski et al. first attempted to estimate the degree of the central cavity, while macrocyclic circuits are those enclosing superaromaticity in 1 using their own homodesmotic reaction scheme.13 Subsequently, Jiao and Schleyer concluded from Received: February 16, 2013 their computational studies that 1 was only a superbenzene Revised: May 15, 2013 from an aesthetic point of view.16 We have been studying Published: May 15, 2013

© 2013 American Chemical Society 4688 dx.doi.org/10.1021/jp4016678 | J. Phys. Chem. A 2013, 117, 4688−4697 The Journal of Physical Chemistry A Article β π the cavity. All species are assumed to be in a singlet electronic where 0 is the standard integral for a CC -bond and i is the state.42 square root of −1. This superaromaticity-free reference is The choice of reference structures is of central importance to nothing other than the reference structure used to calculate the the evaluation of aromaticity and superaromaticity. Our bond resonance energy (BRE).45,46 BRE for each π-bond references are graph-theoretically exact ones. Topological represents the extra stabilization energy due to the circuits that resonance energy (TRE) is calculated relative to the energy pass through the π-bond. of the aromaticity-free reference defined by the polynomial Note that all macrocyclic circuits in 3 pass through either the obtained by deleting the contribution of all circuits from the C C bond or the C C bond, where such a pair of π-bonds − c d e f coefficients in the HMO characteristic polynomial.14,43 45 must belong to the same ring. The superaromaticity-free Percentage TRE (%TRE) is defined as 100 times the TRE, reference for 3 can then be constructed by modifying the divided by the total π-binding energy of the polyene resonance integrals for these bonds in the following reference.14,45 This quantity is useful when one wants to manner:28,34,37 compare the degrees of aromaticity in different π-systems. β ==ββiiand ββ ==− β Superaromatic stabilization energy (SSE) is calculated relative c,d e,f 0 d,c f,e 0 (2) to the energy of the superaromaticity-free (i.e., nonsuperar- Both methods for constructing the superaromaticity-free omatic) reference, which is defined by the polynomial obtained reference bring about exactly the same superaromaticity-free by deleting the contribution of all macrocyclic circuits from the reference energy and necessarily the same SSE. coefficients in the HMO characteristic polynomial.28,37 Two Likewise, the superaromaticity-free reference for 8 in Figure methods have been developed for constructing such super- 2 can be constructed by modifying the resonance integrals for aromaticity-free references. 28,34,37 three bonds in the following manner: The first method is applicable to macrocycles with one or − more π-bonds through which all macrocyclic circuits pass.30 33 β ===ββii βand β ===− ββ β π a,b c,d e,f 0 b,a d,c f,e 0 For example, the -system 3 in Figure 1 has 66 local circuits (3) and 2048 macrocyclic circuits; all macrocyclic circuits pass through the CaCb bond. The superaromaticity-free reference for All macrocyclic circuits in 8 pass through one or three of the 3 can be constructed simply by modifying the resonance CaCb,CcCd, and CeCf bonds. Since kekulene (1) and septulene integrals for this π-bond in the manner (2) have no π-bond shared by all macrocyclic circuits, the first method cannot be applied to them. The second method is π βa,b==−iiβββ 0and b,a 0 (1) applicable to all possible macrocyclic -systems. For the details of this method, see ref 28. ■ RESULTS AND DISCUSSION We first study global aromaticity and superaromaticity of kekulene (1), septulene (2), and related species (3−15)in Figures 1 and 2. If a polycyclic benzenoid hydrocarbon (PBH) with a central cavity is cut out of a graphene sheet, it may be − called a coronoid hydrocarbon.39 41 The central cavity has been called an antidot.20 Coronoids 7−15 have been objects of − recent theoretical studies.18 20 Coronoids studied are classified into single-layered (1, 7, 9, and 12), double-layered (8, 10, and 13), triple-layered (11 and 14), and quadruple-layered (15) coronoids.39 Exactly speaking, 2 is not a coronoid hydrocarbon but a semibenzenoid analogue with a central cavity. TREs and SSEs for these species are listed in Tables 1 and 2. In fact, most of the coronoids studied are too large to calculate TREs. Global Aromaticity of Kekulene and Septulene. Kekulene (1) and septulene (2) are only two cycloarenes of their kind so far prepared. Both 1 and 2 are aromatic with positive %TREs of 2.340 and 2.336, respectively. As can be seen from Table 3, they are slightly less aromatic than most PBH molecules45 but are more aromatic than higher members of the polyacene series.47,48 Structural formulas of PBHs cited in this table are given in the Supporting Information, Figure S1. The difference between the total π-binding energy and the SSE may be called the superaromaticity-free π-binding energy of the π- system. Quite interestingly, the superaromaticity-free π-binding energy per unit structure for 1 is very close to that for 2; both values are ca. 11.43 445 |β|. Note that the numbers of unit structures are six for 1 and seven for 2. We previously showed that the distribution of π-bonds with large BREs within a PBH π-system is closely associated with the locations of aromatic or benzenoid sextets in the Clar Figure 1. Kekuléstructures of cycloarenes and related species studied. structure.45 BREs in units of |β| for nonidentical π-bonds in 1

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Figure 2. D6h-symmetric coronoid hydrocarbons. Formal double bonds are omitted for clarity. D Table 1. TREs and SSEs for Kekulene, Septulene, and Table 2. SSEs for 6h-Symmetric Coronoids Related Species species total π-binding energy/β SSE/|β| NICS(1)a/ppm π total -binding C H (1) 68.610210 0.003483 2.7 species energy/β TRE/|β| % TRE SSE/|β| 48 24 C72H36 (7) 102.486088 0.000357 1.6 kekulene C48H24 68.610210 1.5688 2.340 0.003483 C H (8) 132.513299 0.048368 −11.6 (1) 90 30 C96H48 (9) 136.248163 0.000060 1.0 septulene C56H28 80.041176 1.8268 2.336 0.000002 − (2) C126H42 (10) 185.085176 0.028038 11.9 C H (11) 215.463454 0.007936 4.4 C48H20-I (3) 68.071702 1.5260 0.001839 144 36 C H (12) 169.959117 0.000014 0.7 C48H20-II (4) 68.018002 1.5212 0.002119 120 60 C H (13) 237.558707 0.018135 −11.1 C56H30-I (5) 79.504311 1.7855 +0.000000 162 54 C H (14) 286.872173 0.001440 3.1 C56H30-II (6) 79.450331 1.7804 +0.000000 192 48 − [18]annulene 0.0877 0.382 C210H42 (15) 317.142129 0.031855 10.1 [30]annulene 0.0524 0.137 aNICS(1) values, calculated 1 Å above the center of the cavity at the [21]annulene −0.0746 <0 GIAO-B3LYP/6-31G level of theory, were taken from ref 19. [35]annulene −0.0448 <0 circles in Figure 4. Thus, Clar’s intuition of aromatic sextets22 and 2 are presented in Figure 3; the upper side of each can be rationalized in terms of energetic quantities related to molecular fragment points to the inner cavity of the molecule. aromatic stabilization. Comparison of Figures 3 and 4 reveals that aromatic sextets are TREs for 1, 2, and their molecular ions are graphically located on the benzene rings formed by π-bonds with large summarized in Figure 5 as sequential line plots (i.e., sequential BREs (i.e., benzenoid benzene rings). These π-bonds are line graphs) of TRE against the number of π-electrons 36,49 depicted in bold in Figure 3. They contribute much to global (Nπ). Each plot represents the Nπ dependence of global aromaticity. Aromatic sextets in 1 and 2 are indicated using aromaticity, where Nπ corresponds to the neutral or charged

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Table 3. TREs and % TREs for Typical PBHs

species TRE/|β| % TRE species TRE/|β| % TRE benzene 0.273 3.53 terrylene 1.091 2.61 0.739 3.01 peropyrene 0.942 2.61 0.389 2.92 0.475 2.52 0.546 2.89 0.766 2.51 0.947 2.82 bisanthene 0.968 2.48 0.688 2.81 0.780 2.36 0.835 2.77 kekulene (1) 1.569 2.34 0.598 2.73 septulene (2) 1.827 2.34 1.224 2.70 naphthacene 0.553 2.27 0.740 2.69 0.630 2.11

Figure 3. BREs in units of |β| for nonidentical CC π-bonds in kekulene (1) and septulene (2).

Figure 5. Plots of TRE against the number of π-electrons (Nπ) for two cycloarenes and benzene. Neutral species are denoted by asterisks. Figure 4. Clar structures of two cycloarenes.

species with Nπ π-electrons. For reference, the analogous line aromaticity in 1, 2, and their molecular ions is benzene rings. plot for benzene is added in Figure 5. Within the Hückel This geometric aspect of aromaticity, together with their proton framework, Nπ varies in the 0 to 2NC range, where NC is the chemical shifts, is not consistent with the annulene-within-an- number of carbon atoms. It is interesting to see that the first annulene model for cycloarenes. In fact, 1 is an alternant two plots in this figure are very similar in appearance to each hydrocarbon, but 2 is not. Therefore, the line plot for 1 is fi other. Both plots have ve major extrema in common (i.e., symmetric with respect to Nπ = NC. That for 2 is not exactly three maxima and two minima). These maxima and minima symmetric but still is roughly symmetric with five extrema. represent molecular ions with maximum and minimum TREs, We recently examined the line plots of TRE against Nπ for respectively. Remember that such a variation of TRE is a many porphyrinoid species and found that these plots are very notable characteristic of PBHs formed by fusion of two or more similar in appearance to that for [5]annulene.36 All plots have benzene rings.49 four major extrema (i.e., two maxima and two minima). Such a Cycloarenes 1 and 2 consist of benzene rings alone and so resemblance between the plots strongly suggests that the main the line plots of TRE against Nπ for these species are similar to origin of global aromaticity in porphyrinoids is five-membered that for benzene. The plot for benzene likewise has three rings (or five-site circuits). Although many porphyrin chemists maxima and two minima.49 The central sharp peaks in the three identify macrocyclic aromaticity as global aromaticity,50,51 this plots correspond to the neutral species, indicating that the proved not to be true. Macrocyclic circuits contribute modestly neutral species exhibit the highest degree of aromaticity. to the global aromaticity of porphyrins.32,33 Just in the same Therefore, we can presume that the main origin of global manner, we presume that macrocyclic circuits in kekulene (1)

4691 dx.doi.org/10.1021/jp4016678 | J. Phys. Chem. A 2013, 117, 4688−4697 The Journal of Physical Chemistry A Article and septulene (2) never contribute much to their global aromaticity. Superaromaticity of Kekulene and Septulene. One should note that marked benzenoid character of 1 and 2 never means that these cycloarenes are not superaromatic at all, because they have innumerable macrocyclic circuits; numbers of macrocyclic circuits are 212 = 4096 for 1 and 214 = 16 384 for 2. These macrocyclic circuits are the origin of possible superaromaticity. Therefore, it is disappointing to see that SSEs for 1 and 2 are as small as 0.003 483 and 0.000 002 |β|, respectively. In particular, SSE for 2 is vanishingly small. It follows that most part of the TRE for a cycloarene molecule indeed arises from local (i.e., nonmacrocyclic) circuits. It is generally true that small conjugation circuits (or conjugated circuits in Randic’́s terminology)52,53 make a major contribution at least to the global aromaticity of the neutral − species.52 57 All local circuits in 1 and 2 are conjugation circuits. In this sense, local circuits in these two species play essentially the same role in the determination of global aromaticity. Macrocyclic circuits in cycloarenes, however, are all very large. Macrocyclic circuits in 2 are in quite a different situation from those in 1. Many of the macrocyclic circuits in 1 are conjugation circuits but 2 has no macrocyclic conjugation circuits. It is obvious that both aromaticity of [4n+2]annulenes and antiaromaticity of [4n±1]annulenes are heavily suppressed when they are incorporated in the cycloarene π-systems as macrocyclic (4n+2)- and (4n±1)-site circuits, respectively. For example, the inner and outer peripheries of 1 correspond to Figure 6. Plots of SSE against the number of π-electrons (Nπ) for two [18]annulene and [30]annulene, respectively, whereas the cycloarenes. Neutral species are denoted by asterisks. inner and outer peripheries of 2 correspond to [21]annulene and [35]annulene, respectively. As shown in Table 1, all these nonalternant hydrocarbon. It is noteworthy that SSE changes annulenes have small positive or negative TREs when they are appreciably when 1 and 2 form molecular ions. It follows that isolated molecules. very small SSEs found for 1 and 2 with Nπ = NC is a All macrocyclic circuits in cycloarenes pass through the outer characteristic of the neutral-state species only. Their molecular or inner π-bonds of each benzene ring; half of the macrocyclic ions exhibit enhanced positive or negative SSEs, suggesting that circuits pass through the outer bonds of each ring (e.g., the macrocyclic circuits contribute more to superaromaticity. CaCb bonds in 1 and 2) and the remaining half through the Superaromaticity of Larger Coronoids. In order to inner bond(s) of the same ring (e.g., the CcCd bonds in 1 and further characterize the superaromaticity of cycloarenes, we 2).14 With this fact in mind, we estimated the SSEs for next examine superaromaticity of multilayered coronoid incomplete kekulene molecules 3 and 4, in which the CaCb and hydrocarbons. Among nine D6h-symmetric coronoids presented CcCd bonds in kekulene (1) are missing, respectively. This may in Figure 2 are three larger cycloarenes (7, 9, and 12). Like 1 be a coincidence, but SSEs for 3 and 4 were found to be about a and 2, these cycloarenes are slightly superaromatic with very half that for 1. SSEs for incomplete septulene molecules 5 and small positive SSEs (Table 2). BREs for nonidentical π-bonds 6, in which the CaCb and CcCd bonds in septulene (2) are in 7 are graphically summarized in Figure 7. Since SSE for 7 is missing, respectively, are essentially zero, corresponding to very small like 1 and 2, BRE for an outer π-bond of each essentially zero SSE for 2. benzene ring is very close to that for an inner π-bond of the Close examination of BREs for 1 reveals that BREs for outer same ring. The situation must be essentially the same for 9 and π-bonds of each benzene ring are slightly smaller that for the 12, because they are also marginally superaromatic. For all that, inner π-bond(s) of the same ring. For example, BRE for the extremely small SSE for the septulene π-system (2)is CaCb bond is slightly smaller than that for the CcCd bond. Such impressive, which must be closely associated with the fact a small BRE difference is associated with the nonzero SSE of that this molecule has no macrocyclic even-carbon conjugation the macrocycle, reflecting the difference between the average circuits. sizes of macrocyclic circuits that pass through the outer and As can be seen from Table 2, all coronoids studied are more inner π-bonds of a given ring. On the average, smaller circuits or less superaromatic with positive SSEs. Interestingly, the must contribute more to superaromaticity.56,57 Essentially zero magnitude of SSE alternates on going from single- to multiple- SSE for 2 is fully consistent with the fact that BRE for the CaCb layered species. SSEs for odd-layered coronoids (1, 7, 9, 11, 12, bond is essentially the same as that for CcCd bond. Even for this and 14) are very small, whereas those for even-layered ones (8, π-system, BRE for an outer π-bond of each benzene ring is only 10, 13, and 15) are more than 1 order of magnitude larger. This slightly smaller than that for an inner π-bond of the same ring. aspect of SSEs cannot be explained simply in terms of the A sequential line plot of SSE against Nπ may reveals another number of macrocyclic circuits, which does not oscillate but feature of superaromaticity.36 Figure 6 shows the plots of SSE increases rapidly on going from single- to multilayered species. against Nπ for 1 and 2. The plot for 1 is symmetric with respect We can say at the present stage that cycloarenes are not highly to Nπ = NC, However, the plot for 2 is not so, because it is a superaromatic because they are single-layered coronoids.

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We instead found that, for all coronoids studied, the SSEHOMO value correlates qualitatively with the magnitude of fi ff the SSE. SSEHOMO is de ned as twice the energy di erence between the HOMO of an actual π-system and that of the superaromaticity-free reference. Interestingly, for most of the coronoids studied, SSEHOMO is much larger than SSE itself. As can be seen from Table 4, both SSE and SSEHOMO are closely related to superaromaticity. For even-layered coronoids (8, 10, 13, and 15), the HOMO in an actual π-system is significantly lower in energy than that in the superaromaticity-free reference, whereas, for odd-layered coronoids (1, 7, 9, 11, 12, and 14), the energy of the HOMO in an actual π-system is rather close to that in the superaromaticity-free reference. This finding reminds us of the correlation between the ASE per π-electron and the HOMO−LUMO energy gap found for many 58,59 PAHs. For comparison, SSEHOMO for nonalternant septulene (2) is 0.0617 |β|, which is slightly larger than that |β| π for kekulene (1). Figure 7. BREs in units of for nonidentical CC -bonds in larger π coronoid hydrocarbons 7 and 8. Macrocyclic -Circulation in Coronoids. The NICS(1) values for 1 and 7−15, calculated by Hajgatóet al. at the 19 It is well-known that in general a highly aromatic PBH B3LYP/6-31G level of theory, are added in Table 2. In 2004, molecule has a large HOMO−LUMO energy gap.58,59 Total- they noticed an oscillatory variation of the NICS(1) value at the center of the cavity on going from a single- to multilayered resonant-sextet (TRS) isomers, if any, will have the largest 18 HOMO−LUMO gaps. In other words, the HOMO of a cyclic coronoids. That is, the NICS(1) values for even-layered π-system represents the essence of aromaticity and kinetic coronoids have large negative values, whereas those for odd- stability. We then examined whether or not any correlation is layered ones have small positive values. Such an oscillatory found between the SSE and the HOMO−LUMO energy gap behavior of NICS(1) values is essentially the same as that of the for all coronoids studied. Energies of the HOMOs for actual SSE values. A relatively large SSE value corresponds to a large coronoids and their superaromaticity-free references are listed negative NICS(1) value at the center of the cavity. As pointed ́ 18,19 in Table 4. Since these species are alternant hydrocarbons, the out by Hajgato and Ohno, large negative NICS(1) values must be associated with the induction of a strong diatropic D current around the central cavity. Table 4. Energies of the HOMOs for 6h-Symmetric Coronoids The direct way to actually feel the variation of SSE and NICS(1) at the center of the cavity then is to compare them energy of the HOMOa/β with the pattern of ring currents induced in the π-system. ̈ − π actual superaromaticity-free SSEHOMO/ Figure 8 shows the Huckel London -current maps for four species SSE/|β| systemb reference |β| representative macrocycles (1, 2, 7, and 8), where all current π 1 0.003483 0.4372 0.4107 0.0530 strengths are given in units of the benzene value (I0). These - 7 0.000357 0.3483 0.3370 0.0227 current strengths were calculated using a traditional Hückel− 60−62 8 0.048368 0.1775 0.0919 0.1714 London procedure. The benzene value was obtained for 9 0.000060 0.2739 0.2689 0.0100 the benzene molecule with all CC bond lengths being equal to 10 0.028038 0.1072 0.0546 0.1051 1.40 Å. In the same experimental condition, the current is 11 0.007936 0.1807 0.1746 0.0121 induced counterclockwise in the benzene π-system. Molecular 12 0.000014 0.2162 0.2138 0.0048 geometries of 1, 7, and 8 employed are those calculated at the 13 0.018135 0.0700 0.0355 0.0690 B3LYP/6-31G* level of theory;63 Cartesian coordinates of all 14 0.001440 0.1379 0.1388 −0.0019 atoms in these coronoids are presented in the Supporting − 15 0.031855 0.0917 0.0512 0.0810 Information, Table S1 S3. Those of D7h-septulene (2) at the aEnergies of the HOMO are given relative to the Coulomb integral α. same level of theory were taken from ref 21. Steiner et al. noted bHOMOs and LUMOs in these species are doubly degenerate. that the Hückel−London π-current map for 1 is in qualitative agreement with the ab initio π-current map.17 HOMO−LUMO gap energy is just twice the HOMO energy According to our graph theory of ring-current diamagnet- − given relative to the Coulomb integral α. We found that ism,64 66 a π-electron current is induced independently along coronoids with relatively large SSEs have relatively small each circuit. This is why local and macrocyclic currents can be HOMO−LUMO gaps (8, 10, 13, and 15) and that those with analyzed separately. Therefore, a π-current map is a super- relatively small SSEs have relatively large HOMO−LUMO gaps position of currents induced in all circuits. The strength of the (1, 7, 9, 11, 12, and 14). Both SSE and the HOMO−LUMO current induced in each circuit is proportional to the aromatic energy gap indeed oscillate on going to single- to multiple- stabilization energy (ASE) due to the circuit, multiplied by the − layered coronoids. However, this is opposite to the correlation area of the circuit.67 69 Because SSE is a rough sum of ASEs for we wanted to see, because the maximum and minimum SSEs all macrocyclic circuits, the areas of which are of the same order do not correspond to the maximum and minimum HOMO− of magnitude,31 the NICS(1) value at the center of the cavity LUMO gaps, respectively. We cannot understand why, but a must strongly reflect the magnitude of SSE. HOMO−LUMO gap may correlate not with superaromaticity As has been seen, SSEs for cycloarenes are very small and so but with global aromaticity. BRE for the outer π-bond of each benzene ring is very close to

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the same strength as a paramagnetic current along the inner side of the same ring. In this sense, 2 can be regarded as an ideal nonsuperaromatic macrocycle. In fact, the strengths of net macrocyclic currents are 0.1984 for 1, 0.0003 for 2, and 0.0462 for 7, all in units of I0. Unlike single-layered coronoids, the presence or absence of superaromaticity in multiple-layered coronoids cannot be estimated from the BREs for individual π-bonds. The π-current map can again be used to estimate the degree of super- aromaticity. For example, double-layered coronoid 8 has a much larger positive SSE than those for single-layered coronoids and so must sustain a large diamagnetic current along the macrocycle. As shown in Figure 8, a fairly large diamagnetic current indeed is induced along the inner periphery. The strength of the net macrocyclic currents induced in 8 is as large as 3.5359 I0. This large macrocyclic current clearly indicates that a large diamagnetic current is induced along the macrocycle, overwhelming the apparent paramagnetic current induced by many local circuits. The overall diamagnetic current induced along the outer periphery of 8 is very strong as a result of the superposition of diamagnetic currents induced in many local circuits on strong diamagnetic currents induced in macrocyclic circuits. The same must be true for other even-layered coronoids. What is the origin of the difference in superaromaticity between even- and odd-layered coronoids? The NICS(1) values for all benzene rings in 1 and 7−15 may give us some clue to this problem. All π-systems studied are globally aromatic but consist of not only highly aromatic benzene rings with large negative NICS(1) values but also less aromatic ones with small − negative or positive NICS(1) values.18 20 As can be seen from Figure 1 in ref 19, the pattern of NICS(1) values in odd-layered Figure 8. π-Current maps for coronoids 1, 2, 7, and 8. Current coronoid molecules indicates that each highly aromatic benzene strengths are given in units of the benzene value (I0). ring and/or each group of highly aromatic benzene rings are separated from each other by less aromatic benzene rings. that for the inner π-bond of the same ring. However, the Therefore, the π-electrons might be rather difficult to flow contribution of macrocyclic circuits to ring currents must be freely throughout the π-system; that is, they must be more or larger than expected from the magnitude of the SSE, because less localized around the highly aromatic benzene rings. The macrocyclic circuits have much larger areas. In fact, for 1 and 7, pattern of NICS(1) values in even-layered coronoid molecules the diamagnetic current induced in the outer π-bonds of each is considerably different from that in odd-layered ones, in that benzene ring is appreciably stronger than the apparent many aromatic benzene rings are arranged side by side paramagnetic current induced in the inner π-bond(s) of the throughout the macrocycle.19 The π-electrons in these species same ring. Such a difference in current strength indicates that a must have a larger mobility in the macrocycle. This way of diamagnetic current is really induced along the macrocycle. reasoning may be helpful to explaining at least qualitatively the Note that the senses of diamagnetic currents induced in local relative magnitudes of SSEs and macrocyclic π-currents in and macrocyclic circuits are different along the inner periphery, different coronoid hydrocarbons of odd−even layers. It is but are the same along the outer periphery. If a macrocyclic noteworthy that all the electronic and magnetic values listed in current is absent, an apparent paramagnetic current induced Table 4 oscillate if one holds the cavity size fixed (e.g., the along the inner periphery must be as strong as that of the sequence 1, 8, 11, and 15) or the outer rim size fixed (e.g., the apparent diamagnetic current induced along the outer sequence 12, 13, 14, and 15). periphery. TRS coronoid hydrocarbons were first depicted by Cyvin et For cycloarenes 1, 2, and 7, most part of the apparent al.70 These coronoids must be the best examples in which paramagnetic current induced along the inner periphery is highly aromatic rings are isolated from each other and fixed as associated with diamagnetic currents induced in many local aromatic sextets. In order to see if the mobility of π-electrons circuits. Therefore, the reduced strength of the apparent really are limited in such species, SSEs for two typical TRS paramagnetic current induced along the inner periphery coronoids (16 and 17 in Figure 9) were calculated and are indicates the induction of a weak diamagnetic current along listed in Table 5. Coronoids 16 and 17 are hexabenzo the macrocycle. As the NICS(1) values for higher members of derivatives of 1 and 8, respectively. As predicted from the above the cycloarene series, such as 9 and 12, are also positive at the reasoning, SSEs for TRS coronoids 16 and 17 are much smaller center of the macrocycle,19 they must be in a similar situation than those for non-TRS species 1 and 8, respectively. In to 1, 2, and 7. However, it does not seem that an appreciable accordance with these SSEs, NICS(1) values at the centers of macrocyclic current is induced in 2, since a diamagnetic current these molecules, calculated at the GIAO-B3LYP/6-31G level of induced along the outer side of each ring still is of essentially theory, are positive in sign. This suggests that only a weak

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the macrocyclic structure. The magnitude of SSE for a coronoid hydrocarbon depends primarily on the number of layers. Single-layered cycloarenes, such as 1 and 2, belong to the least superaromatic species with the weakest macrocyclic π-current. We noted that, for all benzenoid macrocycles so far studied, including cyclacenes,25,26,28,34 the sign of SSE is determined by the number of carbon atoms that form the inner periphery (i.e., the size of the smallest macrocyclic circuit). Dias referred to the inner cavity fringed with a 4n-membered periphery properly as an antiaromatic hole.34,71 All of coronoids 1 and 7−15 have a central cavity fringed with a [4n+2]-membered periphery, which is an aromatic hole in this sense. Clar structures proposed for 1 and 2 can be justified reasonably in terms of BREs.

■ ASSOCIATED CONTENT *S Supporting Information Structural formulas of PBHs cited in Table 3, molecular geometries of coronoids 1, 7, and 8, optimized at the B3LYP/6- 31G* level of theory, and the full description of ref 63. This material is available free of charge via the Internet at http:// pubs.acs.org.

■ AUTHOR INFORMATION Corresponding Author Figure 9. Clar structures of two TRS coronoids. *E-mail: [email protected]. Notes Table 5. SSEs for Two TRS Coronoids The authors declare no competing financial interest. π β |β| a species total -binding energy/ SSEHOMO/ NICS(1) /ppm

C72H36 (16) 103.636204 0.000837 3.1 ■ ACKNOWLEDGMENTS C108H36 (17) 160.165445 0.001143 4.4 Computations were carried out at the Information Processing aNICS(1) values at the centers of the cavities were calculated at the Center, Shizuoka University, and the Research Center for GIAO-B3LYP/6-31G level of theory. Computational Science, Okazaki National Research Institutes. π diamagnetic -current is induced along the macrocycle. Thus, it ■ REFERENCES seems quite likely that Clar’s aromatic sextets22 tend to more or less localize the motion of π-electrons and restrict the degree of (1) Staab, H. A.; Diederich, F. Cycloarenes, a New Class of Aromatic Compounds. I. Synthesis of Kekulene. Chem. Ber. 1983, 116, 3487− superaromaticity. 3503. ■ CONCLUDING REMARKS (2) Diederich, F.; Staab, H. A. Benzenoid versus Annulenoid Aromaticity: Synthesis and Properties of Kekulene. Angew. Chem., Homodesmotic reaction has so far been used to estimate the Int. Ed. Engl. 1978, 17, 372−374. SSE for kekulene.13,16 This approach employs relatively small (3) Schweitzer, D.; Hausser, K. H.; Vogler, H.; Diederich, F.; Staab, PBHs, such as anthracene and phenanthrene, as part of the H. A. Electronic Properties of Kekulene. Mol. Phys. 1982, 46, 1141− superaromaticity-free reference. However, SSEs for cycloarenes 1153. are very small in general and so the calculated homodesmotic (4) Staab, H. A.; Diederich, F.; Krieger, C.; Schweitzer, D. stabilization energy might lie within computational errors. Our Cycloarenes, a New Class of Aromatic Compounds. II. Molecular Structure and Spectroscopic Properties of Kekulene. Chem. Ber. 1983, analytical theories of superaromaticity overcame this kind of − ffi 116, 3504 3512. di culty and proved to be very useful for estimating and (5) McWeeny, R. The Diamagnetic Anisotropy of Large Aromatic discussing small quantities, such as SSE and the macrocyclic π- Systems: Structures with Hexagonal Symmetry. Proc. Phys. Soc., Sect. A current strength. This approach has a unique advantage in that 1951, 64, 921−930. ASEs arising from individual macrocyclic circuits can be taken (6) Ege, G.; Vogler, H. Zur Konjugation in Makrocyclischen − into account with equal weights.67 69 Note that NICS(1) Bindungssystemen [1] XX. Charakterordnung, Magnetische Suszepti- values and proton chemical shifts are strongly influenced not bilitaten̈ und Chemische Verschiebungen von Corrannulen. Theor. − only by the geometry of the π-system but also by the π-currents Chim. Acta 1972, 26,55 65. (7) Aihara, J. On the Number of Aromatic Sextets in a Benzenoid induced in nearby local and macrocyclic circuits that do not − belong to the ring concerned. Hydrocarbon. Bull. Chem. Soc. Jpn. 1976, 49, 1429 1430. (8) Randic,́ M. On the Role of KekuléValence Strucutres. Pure Appl. We established that kekulene (1), septulene (2), and other − fi Chem. 1983, 55, 347 354. cycloacenes (7, 9, and 12) cannot be viewed as signi cant (9) Vogler, H. Theoretical Study of Geometries and 1H-Chemical superaromatic species. In particular, SSE for 2 is essentially Shifts of Cycloarenes. J. Mol. Struct. (Theochem) 1985, 122, 333−341. zero. In cycloarenes, contributions of all macrocyclic circuits to (10) Vogler, H. Structures and 1H-Chemical Shifts of Conjugation global and macrocyclic aromaticity are effectively suppressed in Deficient Hydrocarbons. Int. J. Quantum Chem. 1986, 30,97−107.

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