Fullerenes Cn36 �n � 0; 2�; 2ÿ� and their B- and

N-doped analogues

Zhongfang Chen a,b, Haijun Jiao a, Andreas Hirsch a,*, Walter Thiel b

a Institut f�ur Organische Chemie, Universit�at Erlangen-N�urnberg, D-91054 Erlangen, Germanyb Max-Planck-Institut f�ur Kohlenforschung, 45466 M�ulheim an der Ruhr, Germany

Received 27 June 2000; received in ®nal form 2 August 2000

Abstract

The small fullerenes, Cn36 �n � 0; 2�; 2ÿ� and their heteroanalogues (C30N6, C30B6, C24N12 and C24B12) have been

investigated at the density functional B3LYP/6-31G* level of theory. The aromaticity of these systems was charac-

terized systematically by using the computed nucleus independent chemical shifts values at the cage center and also at

the center of individual rings. The hydrogenation product, C36H36, may be experimentally observable considering the

calculated strain energy. Ó 2000 Elsevier Science B.V.

1. Introduction

The proposed synthesis of the fullerene C36 byZettl [1] in 1998 has attracted considerable atten-tion, since fullerenes smaller than C60 are consid-ered to be highly strained due to the presence offused ®ve-membered rings. The pronounced strainenergy will give rise to high reactivity, low stabil-ity, and will make the determination and charac-terization di�cult. The synthesis, puri®cation andidenti®cation of C36H6 and C36H6O has been re-ported by Koshio et al. [2]. However, the questionremained open whether these compounds arefullerenes or not.

In addition to these experimental investigations,a series of theoretical papers on the structures and

energies [3±7], the unique bonding properties [8±10], and vibrational frequencies of the neutral andthe charged C36 species [11] have been published.Both ab initio and DFT calculations [7] show thatthe most stable isomer of C36 has D6h symmetrywith a triplet ground state.

In this Letter, systematic calculations on thestructures and electronic prop erties of both neu-tral and charged C36 species with D6h symmetry,their hydrogenation products and their B- and N-doped analogues are presented. In addition, thedegree of electron delocalization is evaluated byusing the computed nucleus independent chemicalshifts (NICS) [12] at the cage center and the indi-vidual ring centers of interest. NICS has beendemonstrated to be a useful criterion for aroma-ticity or anti-aromaticity of a molecule [12,13]. TheNICS at the cage center has essentially the samevalue as the 3He endohedral shift which is avaluable experimental tool for characterizingfullerenes and their derivatives [14,15].

13 October 2000

Chemical Physics Letters 329 (2000) 47±51

www.elsevier.nl/locate/cplett

* Corresponding author. Fax: +49-9131-85-26864.

E-mail address: andreas.hirsch@organik.uni-erlangen.de

(A. Hirsch).

0009-2614/00/$ - see front matter Ó 2000 Elsevier Science B.V.

PII: S 0 0 0 9 - 2 6 1 4 ( 0 0 ) 0 0 9 1 6 - 7

2. Computational details

Geometries were fully optimized in the givensymmetry at the density-functional B3LYP/6-31G* level, and frequency analyses were per-formed at the HF/3-21G level on optimized HF/3-21G structures using GAUSSIAN 98GAUSSIAN 98 [16]. The NICSvalues of the individual ring centers were com-puted at the GIAO-SCF/6-31G* level with theB3LYP/6-31G* geometries. This approach is wellestablished for closed-shell singlets, and has alsobeen applied and justi®ed for open-shell triplets[17]. The calculated zero-point energies (ZPE) andtotal electronic energies are summarized in Table 1.

3. Results and discussion

The D6h triplet ground state (1) and the corre-sponding D6h singlet state (2) are the two moststable structures in C36 [7]. Due to the high sym-metry, they have only four independent bondlengths. As shown in Fig. 1, there are no signi®cantgeometrical di�erences between 1 and 2. As notedby Tanaka et al. [18], only little changes are ob-served on going from C36 to the dianion C2ÿ

36 (3),and we ®nd the same to hold also for the dication

C2�36 (4). Hence, there is a close structural similarity

between neutral and charged species.The electronic changes of the C36 cages upon

oxidation and reduction can be studied e�cientlyby using the NICS values. Indeed, Tanaka et al.[18] assigned the local aromaticity of the individualrings of the C36; Cáÿ

36 and C2ÿ36 cages on this basis.

They found that both the six- and ®ve-memberedrings are aromatic in 1 and 2, the former being lessaromatic than the latter. This is con®rmed by our

Table 1

Computed zero-point energies (ZPE, kcal/mol) and total elec-

tronic energies (Etot, a.u.)

Species Symmetry ZPEa Etotb

C36 (T), 1 D6h 139.8 )1371.26297

C36 (S), 2 D6h 141.5 )1371.25704

C2ÿ36 , 3 D6h 141.5 )1371.30657

C2�36 , 4 D6h 146.9 )1370.62668

C36H6, 5 C6v 195.7 )1375.01810

C36H6, 6 D3h 195.4 )1375.06571

C36H12, 7 D6h 243.6 )1378.74778

C36H12, 8 D6h 243.6 )1378.74807

C36H36, 9 D6h 444.4 )1393.35545

C30N6, 10 D3h 147.5 )1471.20278

C30B6, 11 D3h 140.0 )1291.89510

C24N12, 12 D6h 143.1 )1570.91955

C24B12, 13 D6h 126.6 )1212.35253

HC�CH3�3 Td 88.6 )158.45881

C2H6 D3d 50.2 )79.83040

C8H8 Oh 91.2 )309.46047

a At HF/3-21G.b At B3LYP/6-31G*.

Fig. 1. B3LYP/6-31G* bond lengths (�A) and GIAO-SCF/6-

31G* NICS values (ppm).

48 Z. Chen et al. / Chemical Physics Letters 329 (2000) 47±51

computed NICS values at the cage centers, i.e.,ÿ27:1 for 1 and ÿ38:2 ppm for 2, and they areeven more aromatic than C60 which has aromaticsix-membered-rings and anti-aromatic ®ve-mem-bered rings and therefore is weak aromatic. Ac-cording to this magnetic criterion, the more stabletriplet state is less aromatic than the singlet state.It should be kept in mind, however, that bothstates are energetically close (triplet favored by 3.7kcal/mol at B3LYP/6-31G* level) and that theirenergetic order has not yet been ®rmly established.

Tanaka et al. [18] also found that 3 exhibitsreduced aromaticity within the six-memberedrings, while the ®ve-membered rings become anti-aromatic (Fig. 1). This is consistent with the cal-culated NICS (ÿ8:1 ppm) value at the cage center,which is lower than that of C36. Compared to 2,the dication 4 also has reduced aromatic characterwith a calculated NICS value of ÿ28:3 at the cagecenter. In contrast to 3, both the ®ve- and six-membered rings in 4 are aromatic. It is interestingto note that all NICS values for 4 are comparableto those of 1. Moreover, the six-membered rings�NICS � ÿ21:5� along the sixfold axis in 1, 2

and 4 are even more aromatic than benzene�NICS � ÿ11:5� itself at the same level, while theNICS value for parallel six-membered ring arecomparable to the benzene value [12].

Inspired by the work of Koshio et al. [2], wehave also computed some of the hydrogena-tion products, C36H6 �5; 6�; C36H12 �7; 8� andC36H36 �9� for the evaluation of the experimentalwork. The optimized bond lengths and computedNICS values for the cage center and individualrings are shown in Fig. 2. For C36H6, two productswere considered, one of them originates from thehydrogenation of the six-membered ring aroundthe sixfold axis (5;C6v) and the other from that ofthe three six-membered rings forming a 1,4-cyclo-hexadiene substructures parallel to the sixfold axis(6, D3h). The latter one is 29.8 kcal/mol morestable than the former, and therefore hydrogena-tion of the three inner double bonds is energeti-cally more favorable.

We have also investigated two C36H12 species aspossible further hydrogenation products in similarway. The ®rst isomer (7;D6h) with two hydroge-nated six-membered rings at the both ends con-

Fig. 2. B3LYP/6-31G* bond lengths (�A) and GIAO-SCF/6-

31G* NICS values (ppm).

Z. Chen et al. / Chemical Physics Letters 329 (2000) 47±51 49

tains a closed hexacene belt in which all the p-orbitals point towards the cage center. The secondisomer (8, D6h) has six 1,4-cyclohexadiene moietiesand six parallel double bonds as well as two ben-zene ring at both ends. These two C36H12 isomershave nearly the same energy, within 0.2 kcal/mol.

In addition, we investigated the hydrogenationproduct, C36H36 (9), which should be highly strainedwith its planar six- and ®ve-membered rings, andthe eclipsed C±H bonds resulting angle and tor-sion strain. The strain energy of C36H36 �9;D6h�has been estimated from the following reactionusing ethane and iso-butane as references:

C36H36 �9� � 54C2H6 � 36HC�CH3�3: �1�At B3LYP/6-31G* + ZPE (HF/3-21G), the

computed strain energy for 9 is 170.3 kcal/mol. Thecontribution of each >CH± unit is only 4.7 kcal/mol, much less than in the case of cubane (17.3 kcal/mol)using the same approach as for C36H36 and19.3 kcal/mol according to Wiberg [19]. Therefore,from a thermodynamic perspective it should bepossible to detect C36H36 experimentally.

Fig. 2 also shows the NICS values for the hy-drogenation products 5±8. The values at the centerof the cage cover a wide range, between ÿ7:8 �8�and ÿ44:2 �7� ppm. It should thus be possible todistinguish these isomers on the basis of the cor-responding 3He endohedral shifts. On the otherhand, C36H36 �9� behaves like a normal saturatedhydrocarbon, as expected, with C±C bond lengthsof 1.555±1.561 �A and a NICS value at the cagecenter of 2 ppm, comparable to the value (ÿ1:1ppm) for adamantane [12].

The successful syntheses of heterofullerenesopened up the possibility of the ®ne tuning of theelectronic properties of the cage structures. Thus,in addition to the isocyclic C36 systems, we havecomputed some selected nitrogen and boron dopedderivatives, i.e., C30X6 �10; 11� and C24X12 �12; 13�.The C30X6 systems are D3h symmetric, whileC24X12 retains the D6h symmetry. The calculatedbond lengths and NICS values are shown in Fig. 3.

Compared with the carbon systems, the substi-tution by nitrogen results in large changes of thestructural parameters and therefore also the degreeof electron delocalization of the cage. With anincreased number of nitrogen atoms, the C±C

bond length s become localized. For example, theparallel C±C bonds, 1.443 �A in 2, are shorter in 10

(1.390 �A) and in 12 (1.334 �A), as found byGrossman et al. [3]. This localization is re¯ected bythe change of the computed NICS values at thecage center, which are ÿ38:2 in 2, and ÿ18:5 in 10,and only ÿ4:3 in 12. The same trend is seen forboth the ®ve- and six-membered rings.

Similar geometric changes are found for boronincorporation, but the changes of the computed

Fig. 3. B3LYP/6-31G* bond lengths (�A) and GIAO-SCF/6-

31G* NICS values (ppm).

50 Z. Chen et al. / Chemical Physics Letters 329 (2000) 47±51

NICS values are dramatic, especially for the six-membered rings around the C3 axis in 11 in whichthe corresponding NICS is only ÿ1:2! In addition,the NICS value for the cage center of 13 is thelargest found among those compounds, and allrings in 13 have larger NICS values than benzene.

4. Conclusion

The density functional B3LYP/6-31G* methodwas employed to compute the fullerenes Cn

36 �n �0; 2�; 2ÿ�, the heteroanalogues �C30N6, C30B6,C24N12 and C24B12) and some hydrogenationproducts. The NICS values at the center of thecages and the ®ve- and six-membered rings werecalculated to assess the global and local aroma-ticity of these systems.

According to NICS, the less stable singlet C36 ismore aromatic than the more stable triplet state,while reduction (C2ÿ

36 ) and oxidation (C2�36 ) result in

lower aromaticity relative to the neutral singletstate.

Incorporation of both nitrogen and boron leadsto large geometric changes. While C24N12 �12;D6h)with 48 p-electrons contains localized substruc-tures and NICS value of ÿ4:3 at cage center,C24B12 �13;D6h� with 24 p-electrons has a highlydelocalized substructure and the most negativeNICS value �ÿ44:6� at the cage center.

The hydrogenation product, C36H36, might beaccessible on the basis of the calculated strain en-ergy since the strain contribution of each >CHÿunit (4.7 kcal/mol) is rather small.

Acknowledgements

This work was ®nancially supported by theDeutsche Forschungsg emeinschaft (DFG). Chen

thanks the Alexander von Humboldt Foundationfor a fellowship. We thank Dr. M. B�uhl for helpfuldiscussions.

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