12 March 1999

Ž .Chemical Physics Letters 302 1999 108–112

Capping C through C : studying the relative stability of the five72 6

C fullerene isomers78

Ying-Ting Lin, Rama K. Mishra 1, Shyi-Long Lee )

Department of Chemistry, National Chung-Cheng UniÕersity, Ming-Hsiung, Chai-Yi 62117, Taiwan

Received 10 September 1998; in final form 4 January 1999

Abstract

The penultimate step of the circumscribe algorithm proposed on Graph Theoretical footings is analyzed by an involvedquantum–chemical AM1 method. The five C isomers generated through the different base excised internal structures are72

Ž .subjected to a relative stability study. Finally a relationship between the C isomers with their corresponding five C IPR72 78

fullerenes has been used to establish a relative stability trend. The most unstable C isomer is found to generate the most72Ž .stable C IPR isomer through the capping technique used in the circumscribing algorithm. Further, the least spherical78

isomer attains the most spherical geometry after capping. q 1999 Elsevier Science B.V. All rights reserved.

w xAfter the seminal contribution of Kroto et al. 1in 1985 there has been an explosive growth in thearea of fullerene chemistry. There are sporadic ex-perimental reports of the fullerenes beyond C and60

w x w xC 2–5 . Certain preparative methods 6,7 have70

also indicated the existence of higher fullerenes likeC , C , C , C and C . Varying the experimen-76 78 84 90 94

tal conditions to maximize the yield of the higherfullerenes can also allow several others to be iso-

w xlated. Kratschmer et al. 8 have prepared buckmin-sterfullerene C on a macroscopic scale by resistive60

heating of graphite and the resulting soot containsC , C , C , and C which have been separated70 76 78 84

Ž .by high-performance liquid chromatography HPLC

) Corresponding author. Fax: q886 5 272 1040; e-mail:chesll@ccunix.ccu.edu.tw

1 On leave from the Department of Chemistry, SambalpurUniversity, 768019 India.

of the toluene-soluble soot extract and finally charac-terized by 13C NMR. This analysis yields pure C76w x w x w x9 , two C isomers 10 and two C isomers 11 .78 84

Further, a third C isomer has also been detected by78w xHPLC 12 .

The C fullerene has attracted the attention of78

many workers as it has five topologically distinctstructures satisfying the isolated pentagonal ruleŽ .IPR which stipulates that most stable fullerenesshould have isolated pentagons. The five isomers

Ž .with isolated pentagonal ring IPR structures can beŽ . Ž . Ž . Ž .described as 1 D , 2 D , 3 D , 4 C and3h 3h 3 2v

Ž . w x5 C . Balasubramanian 13 has pointed out the2v

non-availability of any unambiguous results for therelative stability trend for all the above five isomers.

w x w xSlanina et al. 14 and Bakowies et al. 15 havecarried out semi-empirical and ab-initio calculationsfor all the five IPR structures and have tried toestablish a relative stability trend.

0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0009-2614 99 00063-9

( )Y.-T. Lin et al.rChemical Physics Letters 302 1999 108–112 109

Here in this report, we have made an attempt toanalyze the relative stability trend by considering aC and capping it with a C to get C as demanded72 6 78

w xby the well-known circumscribing algorithm 16–23 .w xLiu et. al. 24 have pointed out that the C can72

have only one preferable and favorable cage struc-ture. Further, it has also been mentioned that this C72

w xisomer is closely related to buckminsterfullerene 25and hence, deserves a more detailed investigation.But, here all the five C isomers are having the72

dangling bonds. These isomers are being the prod-ucts of the successive circumscribing constructionprocess from their respective base excised internal

Ž .structures EIS . In this work, we have tried to makeone comparative analysis of C concerning C72 78Ž .IPR .

1. Circumscribing algorithm and generation ofC72

When a polycyclic conjugated hydrocarbon is en-circled by a ring of carbon atoms and incrementedby additional hydrogens in such a way to form onlyhexagonal ring, then this process is termed as cir-

w xcumscribing with hexagonal rings 16 . Reversion of

this process generates EIS that is devoid of adjacentw xbay regions on its perimeter 16,17 . Successive cir-

cumscribing of qualified conjugated hydrocarbonswith a combination of pentagonal and hexagonalrings terminates at fullerenes when the number ofpentagonal rings reaches 12 or terminates at systemsthat can be capped to give fullerenes with 12 pentag-

w xonal rings 26a,26b . There are five elementary car-bon fragments such as benzenehexyl, cyclopentadi-enylpentyl, ethynylene, carbon and an edge throughwhich the last step of the circumscribing construc-tion could be complete resulting essentially in theformation of hexagonal or non-adjacent pentagonal

w xrings 23 at the outer most tier. Here our idea is notto broach an analysis of the circumscribing proce-dure but to concentrate on the generation of the five

Ž .C IPR isomers from the different base EISs and78

to pay particular attention to the last step of thealgorithm. The successive circumscribing can be vi-sualized from Fig. 1 for different IPRs.

Analyzing the Fig. 1 one can easily notice that inall the five IPRs formation C is the last but one72

product and finally this is capped with a C to give6

different C . Hence, we have tried to do the compu-78

tation of C and C by the well-established AM172 78

method.

Fig. 1. Generation of C through circumscribing the base EISs and are capped to obtain C .72 78

( )Y.-T. Lin et al.rChemical Physics Letters 302 1999 108–112110

2. Results and discussions

Semi-empirical closed-shell SCF calculations areperformed using standard AM1 hamiltonian withinthe MOPAC program for the least studied C iso-72

mers along with the five C IPRs isomers. The78

molecular geometries are completely optimizedwithin a given point group. The heat of formationsŽ . Ž .D H , HOMO–LUMO gaps D E , maximum,f g

Ž .minimum, average r , r , r bond lengths andmax min avw xmaximum, minimum, average POAV 27 angles

Ž .Q , Q , Q along with the over all curvaturesmax min av

ÝQ 2 are presented in Table 1.While tying to judge the relative stability of the

w xfive IPRs of C78, Slanina et al. 14 and Bakowies etw xal. 15 have pointed out the inconsistent results

obtained from the theoretical calculations. They havenoticed that Huckel calculations with curvature cor-

Žrections, tight binding, MNDO and MNDO mod-.ified along with AM1 have produced one relative

stability scale as 5)2)4)3)1. But, PM3 calcu-lations have given a relative scale to be 5)4)2)

w x3)1 28 . At the same time MM3, SCFrSTO-3G,SCFrDZ and SCFr3-21G calculations suggest thescale to be 5)4)3)2)1. While the SCFr6-31G ) produces the relative stability scale to be

w x5)3)4)2)1. Earlier, Fowler et al. 29 haveŽ .suggested that 2 D3h should have the highest stabil-

ity by considering the simple Huckel model and itsdelocalization energy along with the HOMO–LUMOgap. Unfortunately, this qualitative MO result did notcorroborate the experimental findings and this has

been found to be the least stable one through somew xtheoretical calculations 15 .

Here, in order to judge the relative stability weŽ X X.have calculated the DH f of the five C 1 –5 and72

Ž .five C 1–5 isomers. All five IPRs of C are78 78

being generated from the C following the capping72

process by the same C . We have calculated the6

difference in the D H between the C and itsf 78Ž Ž ..corresponding C D D H . A relative stability72 f

scale is obtained as 5–5X)2–2X

)3–3X;1–1X

)4–4X. When we try to judge the instabilities for the fiveC s, we have obtained the order 5X

-2X-3X

-1X-72

4X. From this result one can easily say that thestability scale for the formation of the C correlates78

with the instability scale of the five C isomers.72

Further the most stable 5 has been found to beproduced from the most unstable 5X possessing 10pentagonal rings. While trying to compare the r forav

the C and C we observed some interesting re-78 72

sults. The difference in the r for C and C for 5av 78 72

and 5X is the most minimum, suggesting a minimumeffort being required for the transformation of C to72

C through capping. Further, D r also follows a78 av

similar trend as 5–5X-2–2X

-3–3X;1–1X

-4–4X.This analysis duly supports the trend obtained through

Ž .the D D H results.f

Hence, making use of this qualitative circumscrib-ing construction, we can confirm that 5 is the moststable isomer of the five IPRs of C . Although there78

is a difference in the stability order lower down thescale obtained from the AM1 and MNDO results,this study certainly confirms the most stable IPRs of

Table 1Structural and thermodynamic data for the five C and corresponding C72 78

2Ž .Isomers D H D D H D E r r r D r Q Q Q ÝQf f g max min av av max min av2˚ ˚ ˚ ˚Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž .kcalrmol kcalrmol eV A A A A deg. deg. deg. rad

1 1154.50 178.69 6.16 1.4693 1.3532 1.4356 0.0031 12.1256 6.5688 10.364 2.65483X1 975.81 5.84 1.4874 1.3546 1.4325 12.0972 6.0512 9.5986 1.9422

2 1138.30 146.55 5.13 1.4813 1.3535 1.4349 0.0027 11.72975 8.5958 10.230 2.50866X2 991.75 5.22 1.4803 1.3521 1.4322 11.70814 7.1299 9.8170 1.97296

3 1140.30 177.65 5.123 1.4712 1.3713 1.4351 0.0031 12.006 6.5041 10.323 2.6063X3 962.65 5.00 1.4822 1.3642 1.4320 11.9884 6.6660 9.580 1.9092

4 1138.40 276.47 5.53 1.4690 1.3594 1.4352 0.0045 12.26101 6.4523 10.308 2.5942X4 861.93 5.53 1.5198 1.3622 1.4397 12.3294 5.2059 9.3002 1.8256

5 1133.20 138.12 5.15 1.4793 1.3571 1.4349 0.0002 12.2839 7.2786 10.263 2.5450X5 995.08 4.54 1.5251 1.3566 1.4351 12.2648 6.5342 9.7420 1.9740

( )Y.-T. Lin et al.rChemical Physics Letters 302 1999 108–112 111

C and reveals the relationship between the unstable78

C and the stable C . The curvature measurement72 78

happens to be an important structural parameter forall these isomers. For a particular atom this measure-ment can be done with the help of the p-orbital axis

Ž . w xvector POAV method 27 . This angle is theŽ .pyramidalization angle Q and is defined as, Qs

Ž .Q yPr2 , where Q is the angle between thes p s p

axis of the p-orbital and a s-bond. It may be notedthat Qs0 in the planar case. Here we have calcu-

Ž . Ž .lated the maximum Q , minimum Q , aver-max minŽ . Ž 2 .age Q and the overall curvature ÝQ of theav

five C and their corresponding five C IPRs. It72 78

may be mentioned that all the C isomers have six72

carbon centers with dangling bonds. Thus, the Q isav

calculated by considering the rest of the carbonvertices. Considering Q , spread POAV anglesavŽ . Ž 2 .Q y Q and overall curvatures ÝQ ,max min

w xBakowies et al. 15 have pointed out that the spheri-cal shape follows a scale 1-3-4-5-2 for thefive IPRs of C . This clearly indicates that 2 has the78

most spherical geometry followed by 5. However,when we tried to analyze the five isomers of C , we72

obtained a scale for the spherical geometry as 2X-5X

-1X-3X

-4X from the Q and ÝQ 2 results. Thisav

proves that the most non-spherical geometry attainsthe spherical geometry after capping with a C . In6

Ž .fact, the difference in Q , i.e. DQ in betweenav avŽ X. Ž X.2–2 and 5–5 are found to be minimum, whereas

Ž X.for 4–4 it is maximum. Hence, we can concludethat in this capping process a minimum effort isrequired for the least spherical isomer to attain themost spherical geometry. HOMO–LUMO gaps havebeen calculated for all the five IPRs of C and their78

w xcorresponding C s. However, Slanina et al. 1472

have pointed out that D E might not be a helpfulg

parameter to judge the chemical stability of theclusters having the same dimensions. The graphtheoretically formulated circumscribing algorithm has

Ž .been used to verify the generation of the five IPRstructures of C by using a more involved and78

well-studied AM1 semi-empirical calculations. Cap-ping of the five C isomers with C was analyzed72 6

and a relative stability scale has been proposed basedŽ .on this qualitative graph theoretical algorithm. Fur-

Ž .ther, this study confirms 5 C to be the most stable2v

C isomer which is generated from the most unsta-78XŽ .ble 5 C isomer through capping. Again, analyz-72

ing the curvatures of the five C and their corre-72

sponding C we have noticed that the least spherical78Ž .isomer of C gives the most spherical C IPR72 78

isomer when the former is capped with a C .6

Acknowledgements

Ž .We thank the National Science Council NSC ,Taiwan for the financial support through ContractNSC 87-2811-M-194-0009. Further, we would liketo acknowledge the help from Prof. J.R. Dias, Uni-versity of Missouri, Kansas City, Kansas, USA.

References

w x1 H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl, R.E.Ž .Smalley, Nature 218 1985 162.

w x Ž .2 K.C. Khemani, M. Prato, F. Wudl, J. Org. Chem. 57 19923254.

w x3 W.A. Scrivens, A.M. Cassell, B.L. North, J.M. Tour, J.Ž .Am. Chem. Soc. 116 1994 6939.

w x4 E.D. Jemmis, G.N. Sastry, G.N. Mehta, J. Chem. Soc.Ž .Perkin 2 1994 437.

w x5 L.T. Scott, M. Hashemi, D. Meyer, H. Warren, J. Am.Ž .Chem. Soc. 113 1991 7082.

w x6 F. Diederich, R. Ettl, Y. Rubin, R.L. Whetten, R. Beck, M.Alvarez, S. Anz, D. Sensharma, F. Wudl, K. Khemani, A.

Ž .Koch, Science 252 1991 548.w x7 D. Ben-Amotz, R.G. Cooks, L. Dejarme, J.C. Gunderson,

S.H. Hoke II, B. Kahr, G.L. Payne, J.M. Wood, Chem.Ž .Phys. Lett. 183 1991 149.

w x8 W. Kratschmer, L.D. Lamb, K. Fostiropoulos, D.R. Huff-Ž .man, Nature 347 1990 354.

w x9 E. Ettl, I. Chao, F. Diederich, R.L. Whetten, Nature 353Ž .1991 149.

w x10 F. Diederich, R.L. Whetten, C. Thilgen, R. Ettl, I. Chao,Ž .M.M. Alvarez, Science 254 1991 1768.

w x Ž .11 F. Diederich, R.L. Whetten, Accounts Chem. Res. 25 1992119.

w x12 K. Kikuchi, N. Nakahara, T. Wakabayashi, S. Suzuki, H.Shiromaru, Y. Miyake, K. Saito, I. Ikemoto, M. Kainosho,

Ž .Y. Achiba, Nature 357 1992 142.w x Ž .13 K. Balasubramanian, Chem. Phys. Lett. 206 1993 210.w x14 Z. Slanina, S.-L. Lee, C. Yu, in: K.B. Lipkowitz, D.B.

Ž .Boyd Eds. , Reviews in Computational Chemistry, Vol. 8,VCH Publ., New York, 1996, p. 37.

w x15 D. Bakowies, A. Gelessus, W. Thiel, Chem. Phys. Lett. 197Ž .1992 324.

w x Ž .16 J.R. Dias, J. Chem. Inf. Comput. Sci. 30 1990 61, 251.w x Ž .17 J.R. Dias, Theoret. Chim. Acta 77 1990 143.w x Ž .18 S.J. Cyvin, Chem. Phys. Lett. 176 1991 413.w x Ž .19 S.J. Cyvin, Theoret. Chim. Acta 81 1991 269.

( )Y.-T. Lin et al.rChemical Physics Letters 302 1999 108–112112

w x Ž .20 J.R. Dias, Chem. Phys. Lett. 185 1991 10.w x Ž .21 J.R. Dias, J. Chem. Inf. Comput. Sci. 32 1992 2.w x Ž . Ž .22 S.J. Cyvin, J. Mol. Struct. THEOCHEM 262 1992 219.w x Ž .23 J.R. Dias, Z. Naturforsch. 489 1993 1009.w x24 X. Liu, T.G. Schmalz, D.J. Klein, Chem. Phys. Lett. 188

Ž .1992 550.w x25 T.G. Schmalz, W.A. Seitz, D.J. Klein, G.E. Hite, J. Am.

Ž .Chem. Soc. 110 1988 1113.

w x Ž .26a J.R. Dias, J. Chem. Inf. Comput. Sci. 34 1994 248.w x Ž .26b J.R. Dias, J. Math. Chem. 4 1990 17.w x Ž .27 R.C. Haddon, L.T. Scott, Pure Appl. Chem. 58 1986 137.w x28 Z. Slanina, J.-P. Francois, D. Bakowies, W. Thiel, J. Mol.

Ž .Struct. 279 1992 213.w x29 P.W. Fowler, R.C. Batten, D.E. Manolopoulos, J. Chem.

Ž .Soc. Faraday Trans. 87 1991 3103.