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Aromaticity and Superaromaticity in Carbon Nanotoroids

Mitsuho Yoshida and Eiji Osawa Department of Knowledge-Based Information Engineering, Toyohashi University of Technology, Tempaku-cho, Toyohashi 441, Japan Jun-ichi Aihara* Department of Chemistry, Faculty of Science, Shizuoka University, Oya, Shizuoka 422, Japan

Percentage topological resonance energies (%E,,s) have been estimated for 15 hypothetical carbon nanotoroids composed of 240 carbon atoms. These carbon materials were predicted to be moderately aromatic with moder- ately large positive %E,,s. They are presumably less aromatic than graphite and carbon nanotubes, but must be appreciably more aromatic than fullerenes such as C,, and C,*. It seems that superaromaticity arising from torus-shaped super-ring structures is negligible.

Aromaticity arises from extra thermodynamic stabilization due to cyclic conjugation. The topological resonance energy (TRE, E,,) is known as one of the representative measures of aromatic stabilization. '-' We have been investigating aro- matic properties of carbon-based materials extensively using the TRE method.'-' This method can be applied easily to molecules with fewer than 60 conjugated atom^.'-^*^.^ The E,,s of C,, and C70 were evaluated successfully, which indi- cates that these fullerene molecules are moderately aro- ma ti^.'-^.^ However, the TRE method in its original form is not applicable to larger conjugated systems since a suitable polyene reference cannot be constructed by graph t h e ~ r y . ~ , ~ , '

The E,,s of graphite and graphitic tubules in a carbon nanotube cannot be evaluated because they have infinite n- electron systems. We previously reported that the polyene reference of a hypothetical 54carbon molecule, 1, can be used as a substitute for the polyene references of these carbon material^.^*^*^ All straight and curved lines in 1 represent C-C bonds. This carbon molecule resembles graphite in many respects: all carbon atoms are equivalent, forming an edge-less hexagonal network. The E,,s of graphite and carbon nanotubes can be estimated by referring to the polyene refer- ence of 1. These carbon materials then turned out to be as highly aromatic as fully benzenoid hydrocarbons, such as benzene, triphenylene and hexa[bc,ef,hi,kl,no,qr)benzocoron- ene?v6l7

1 In addition to diamond, graphite, fullerenes and carbon

nanotubes, many other structures are conceivable for elemen- tal carbon. A toroidal or doughnut-shaped network of carbon atoms may be formed as a variant of a carbon nano-

Such a carbon nanotoroid has not been synthe- sized yet, but it is far from being an unrealistic material. The electronic structure of the carbon nanotoroid has been inves- tigated by two research We have also been interested in conjugation and aromaticity in such hypotheti- cal carbon molecules. In this paper, the aromatic character of a typical carbon nanotoroid has been estimated using the polyene reference 1 and is compared with that of other carbon-based materials.

Theory Hundreds or thousands of carbon atoms are necessary to design a carbon nanotoroid of a realistic size. Dunlap and Ihara and co-workers presumed that a network on the surface of a carbon nanotoroid consists of hexagons, pentag- ons and heptagons.''-15 As a carbon nanotoroid is a kind of deformed carbon nanotube, it is reasonable to assume that most of the constituent rings are hexagons. Introduction of pentagons and heptagons is necessary for designing less- strained toroidal structures.

The TRE method is based on simple Huckel theory. A carbon nanotoroid is too large a molecule to construct the polyene reference using graph theory. Therefore, the polyene reference of 1 has been used as a substitute. Considering that most constituent rings in sizeable carbon nanotoroids are hexagons, we believe that this is a reasonable choice. The unit reference energy (E,,) of 1 was calculated to be 1.52784 I /3 14, which is the z-binding energy per carbon atom of the polyene re feren~e .~ '~ '~ The E,, of 1 has been used as an approximate E,, for carbon nanotoroids.

As in the case of graphite and carbon n a n ~ t u b e s , ~ * ~ * ~ the difference between the 7c-binding energy per carbon atom of a given carbon nanotoroid and the E,, of 1 can be interpreted as an approximate E,, per carbon atom of the nanotoroid. The %E,, is of practical use when one wants to compare aromaticity in different molecule^.'-^ The %E,, of a carbon nanotoroid is defined as 100 times the E,, per carbon atom, divided by the 7c-binding energy per carbon atom of l.le7 The n-binding energy per carbon atom of an actual molecule will be referred to as the unit n-binding energy (Eub).

Aromaticity in Carbon Nanotoroids As we are interested not only in aromaticity but also in pos- sible effects of the toroidal super-ring structure on aromati- city, we focus on 15 relatively small carbon nanotoroids (A-O), whose structures are given in Fig. 1. All of them are composed of 240 carbon atoms arranged in five-fold sym- metry. They consist of five unit structures, each of which is formed from 48 carbon atoms. There are 100 hexagons, 10 pentagons, and 10 heptagons in each carbon nanotoroid.

The %E,, of A-O are listed in Table 1 and lie in the rela- tively narrow range 2.23-2.57. As can be seen from Table 2, these carbon nanotoroids are appreciably more aromatic than fullerenes such as c60 and C70, but are less aromatic than graphite and carbon nanotubes. The intermediate aro- matic character of carbon nanotoroids can be explained in terms of conjugated circuit theory.16-' ' According to this

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1564 J. CHEM. SOC. FARADAY TRANS., 1995, VOL. 91

A B

D

G

3

E

H

C

F

I

K L

M N 0

Fig. 1 Carbon nanotoroids composed of 240 carbon atoms

Table 1 Percentage topological resonance energies (%E,,s) of carbon nanotoroids, A-O, composed of 240 carbon atoms

~ -~ ~ ~~

nanotoroid HOMO-LUMO gap/l PI Eub/l B 1 %E,,

A B C D E F G H I J K L M N 0

O.OO0 0.005 0.020 0.017 0.195 0.08 1 0.275 0.203 0.27 1 0.497 0.257 0.263 0.453 0.430 0.426

~~

74.970 75.0 15 75.038 75.049 75.059 75.092 75.094 75.099 75.1 14 75.1 55 75.168 75.169 75.202 75.209 75.2 18

2.228 2.290 2.321 2.335 2.349 2.394 2.397 2.404 2.424 2.480 2.498 2.498 2.544 2.554 2.566

Table 2 Percentage topological resonance energies (%E,,s) of typical carbon-based materials

HOMO-LUMO gap/lj?I %E,, species

benzene 2.000 3.528 naphthalene 1.236 2.924 anthracene 0.828 2.519 triphen ylene 1.368 3.012 pyrene 0.890 2.729 coronene 1.078 2.8 17 hexa[bc,ef,hi,kl,no,qr]benzo- 0.930 2.917

pyracy lene 0.414 0.551 corannulene 1.215 2.626 C60 0.757 1.795

graphitic t~bule(9,O)~ 0.000 3.011' graphitic t~bule(20,O)~ 0.184 3.062' graphite 0.000 3.061'

coronene

C70 0.529 1.906"

Ref. 9. For the nomenclature of graphitic tubules, see ref. 4 and 7. ' Estimated using the E,, of 1.

theory, hexagons or benzene rings are the main origin of aromaticity. Six-sided rings constitute highly aromatic conju- gated circuits. Pentagons and heptagons do not contribute significantly to aromaticity since they do not participate in the formation of relatively small conjugated circuits.

Graphite and graphitic tubules in a carbon nanotube consist entirely of a hexagonal network of carbon atoms. Therefore, they are highly aromatic in n a t ~ r e . ~ . ~ A carbon nanotoroid is composed of not only hexagons but also pen- tagons and heptagons. The presence of 10 pentagons and 10 heptagons, in place of 20 hexagons, in A - 0 makes the %E,, somewhat smaller than that of graphite. This is the primary reason why carbon nanotoroids are less aromatic than graphite. Since abutting pentagons are absent in A-0, these nanotoroids must be fairly stable against chemical reac- tions.20-22

Most polycyclic benzenoid hydrocarbons are slightly less aromatic than graphite and carbon nanotubes. However, it is noteworthy that the carbon nanotoroids with the largest %E,,s are slightly more aromatic than anthracene and higher polyacenes. Polyacenes are somewhat less aromatic than other types of polycyclic benzenoid hydrocarbons since there is only one aromatic sextet in the Clar structure.23 An aro- matic sextet is identical to a six-membered conjugated circuit. 16-'

Non-benzenoid hydrocarbons, such as pyracylene and corannulene, are appreciably less aromatic than graphite and carbon nanotubes since few six-membered conjugated circuits can be chosen from them. Fullerenes are also a kind of non- benzenoid hydrocarbon. The %E,, of fullerenes increases more or less monotonically from C,, to the graphite limit, reflec- ting the increased aromaticity associated with a larger pro- portion of six-membered ring^.^.^.^ Carbon nanotoroids are comparable in aromaticity with corannulene.

The highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) energy separation has been recognized as a crude indicator of kinetic ~tability.,~-,~ Table 1 indicates that there is a rough correlation between the HOMO-LUMO energy separations and the %E,,s of carbon nanotoroids. In general, a more aromatic nanotoroid has a slightly larger HOMO-LUMO gap. However, as in the case of carbon nanotubes? the %E,, of a carbon nanotoroid appears to be the sum of a large constant and a small fraction dependent on the HOMO-LUMO energy separation. Even those with no HOMO-LUMO energy gap are moderately aromatic. This seems to be an inherent property of tubular carbon.

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J. CHEM. SOC. FARADAY TRANS., 1995, VOL. 91 1565

Table 3 The %E,,s of carbon nanotoroids composed of five to ten unit structures (a) Carbon nanotoroids having the same unit structure as A

number of unit structures number of carbon atoms HOMO-LUMO energy gap/l p I E,d( fl I %E,,

5 6 7 8 9

10

240 288 336 384 432 480

O.OO0 O.OO0 O.OO0 O.OO0 O.OO0 O.OO0

74.970 2.228 74.961 2.2 16 74.974 2.233 74.978 2.238 74.978 2.238 74.978 2.238

(b) Carbon nanotoroids having the same unit structure as 0 ~-

number of unit structures number of carbon atoms HOMO-LUMO energy gap// fl I E,,J fl I %E,,

5 6 7 8 9

10

240 288 336 384 432 480

0.426 0.406 0.428 0.404 0.41 1 0.409

~ ~ ~ ~ ~ ~ _ _ _ _ ~

75.218 2.566 75.218 2.566 75.218 2.566 75.218 2.566 75.218 2.566 75.2 18 2.566

Superaromaticity in Carbon Nanotoroids Superaromaticity is additional aromaticity due to a super- ring structure that is associated with conjugated circuits chosen in such a manner that they enclose the inner cavity of the toroid.7,27-29 Therefore, there is a possibility that a carbon nanotoroid has some degree of superaromaticity.

The degree of superaromaticity can be estimated by evalu- ating %E,,s for a homologous series of carbon nanotoroids with different numbers of unit structures. If a carbon nanoto- roid with five unit structures is superaromatic, the %E,, will change monotonically or oscillate on going to higher members of the same series. It is reasonable to assume that a carbon nanotoroid with a sufficiently large inner cavity is non-superaromatic. %E,,s for two series of carbon nanoto- roids composed of five to ten unit structures are listed in Table 3.

We found that %E,, remains almost the same for all members of each series. Even if the number of unit structures is changed, E,, remains almost unchanged. It then follows that the superaromatic stabilization energy must be less than 1% of the E,, even for relatively small members of the series. This implies that superaromaticity or superantiaromaticity due to toroidal structure is negligibly small although very many conjugated circuits can be chosen in such a manner that they enclose the inner cavity. Thus, all carbon nano- toroids are predicted to be essentially non-superaromatic. The lack of superaromaticity is presumably due to the cancel- lation of superaromaticity and superantiaromaticity arising from many different circuits. For the carbon nanotoroids studied, the energies of the HOMO and the LUMO are not strongly dependent upon the number of unit structures.

Concluding Remarks Carbon nanotoroids were found to be aromatic with fairly large %E,,s, but are probably non-superaromatic even if they are relatively small. Since abutting pentagons and a periphery containing CH groups are absent, they must be fairly stable against chemical reaction. Very large carbon nanotoroids must be as highly aromatic as graphite because of their very large proportion of hexagonal rings.

The TRE model and its modifications are totally depen- dent upon Huckel theory. This theory provides a crude first- order description of n-electron structure. We made no attempt to correct for departures from perfect sp2 hybrid- ization caused by non-planarity. In the TRE method, however, a polyene reference is assumed to be strained to the

same degree as a real molecule. The %E,, is a dimensionless quantity, independent not only of strain but also of the mag- nitude of b. Therefore, the %E,,s reported here are meaning- ful enough to interpret various aspects of carbon nanotoroids. It should be stressed that there are no analytic methods for evaluating the degree of aromaticity in conju- gated systems as large as carbon nanotoroids.

Dr. D. BabiC at the Rugjer BoSkovii: Institute kindly informed us of the unpublished data on C7*. This work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, and Culture, Japan.

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Paper 4/06917J; Received 14th November, 1994

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