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Physica E 40 (2007) 285–288

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Reactivities of C60 and C70

Yusuke Ueno�, Susumu Saito

Department of Physics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan

Available online 20 June 2007

Abstract

We study the reactivities of Ih C60 and D5h C70 fullerenes in the framework of the density-functional theory. To quantify the reactivities

of fullerenes, we calculate the total energies of the system consisting of a fullerene and a C atom as a function of the distance from each C

site on the fullerene surface to the C atom, and obtain the reaction energy defined as energy gain at the minimum-energy configuration

from the infinite distance configuration. Surprisingly, it is found that some of the C70 sites have larger reaction energies than that of C60,

although C70 is energetically more stable than C60. This result sheds new light on the formation process of fullerenes and the abundance

of C60 in soot.

r 2007 Elsevier B.V. All rights reserved.

PACS: 73.61.Wp; 36.40.Jn; 31.15.Ew

Keywords: Fullerene; C60; C70; Reactivity; Density-functional theory

1. Introduction

In 1985, the truncated-icosahedron structure of C60 wasproposed by Kroto et al. [1]. Since the macroscopicproduction of C60 fullerenes by arc-heating of graphite in1990 [2], the various interesting physical and chemicalproperties of C60 have been revealed. C60 clusters arecondensed into semiconducting fcc solid by van der Waalsforce [3]. Potassium-doped solid C60 shows the super-conductivity at 18K [4]. Under high pressure andtemperature, solid C60 transforms to one- or two-dimen-sional polymer [5,6]. In addition to C60, larger fullerenessuch as C70, C76, C78, C82, C84, etc., are extracted fromcarbon soot [7,8]. The amount of production of C70 issecond largest, which is much less than that of C60.Contrary to these successful studies of the properties offullerenes, the fundamental question, why C60 clusters areby far most abundant in carbon clusters, still remainsunsolved. C60 fullerene is not energetically most stable inall the fullerenes. Actually, C70 and C84 fullerenes, whichare larger than C60, have larger binding energies per atom

e front matter r 2007 Elsevier B.V. All rights reserved.

yse.2007.06.030

ing author.

ess: ueno@stat.phys.titech.ac.jp (Y. Ueno).

than C60 [9]. Nevertheless, C60 is much more abundantthan these two fullerenes in carbon soot. This implies thatthe binding energy is unimportant for the selectivity of theproduction of fullerenes. To solve the mystery on theabundance of C60, one has to reveal the microscopicformation process of C60.It is known that all the empty fullerenes extracted so far

satisfy the so-called isolated-pentagon-rule (IPR), whichmeans that two pentagons are not adjacent in theirgeometric structure. IPR-breaking fullerenes are expectedto be more reactive than IPR-satisfying ones because theyhave not only sp2-like but also sp3-like hybridized carbonatoms on the side shared by two or three pentagons. Themore reactive a cluster is, the less likely the cluster willsurvive in the cluster formation process. Therefore, the IPRindicates the high importance of reactivities in theformation process of fullerenes.In this paper, to clarify the origin of the large difference

between the abundance of C60 and that of C70, we study thereactivities of Ih C60 and D5h C70 obtained by the local-density-approximation (LDA) in the framework of thedensity-functional theory [10,11]. In addition, we also studyD5h C50 as a representative of IPR-breaking fullerenes and agraphene sheet, and compare them with C60 and C70.

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dG

G

A - E

D5h C70 D5h C70

G’

dC,Dd

Fig. 2. System consisting of a fullerene and a C atom, where d represents

the distance between the fullerene surface and the C atom. (a) System

consisting of a C60 and a C atom. The C atom is put on the half-straight

line from the center of gravity of the C60 through the surface C atom. (b)

System consisting of a C70 and a C atom. Case I: The C atom is put on the

half-straight line from the center of gravity of the C70 (G) through the

surface C atom. Case II: The C atom is put on the half-straight line from

the center of gravity of the hypothetical C60 in the C70 (G0) through the

surface C atom.

Y. Ueno, S. Saito / Physica E 40 (2007) 285–288286

2. Computational method

In the LDA, the Troullier–Martins norm-conservingpseudo-potential is used with Kleinman–Bylander approx-imation [12]. The wave functions are expanded in terms ofthe plane-wave basis set with a cutoff energy of 50Ry. Forthe exchange-correlation potential, we adopt the para-meterized Ceperley–Alder formula [13]. Both of theelectronic and geometric structure are optimized byconjugate-gradient method [14].

3. Reactivity of C60 and C70

Both Ih C60 and D5h C70 are IPR-satisfying fullerenes.While 60 atomic sites of C60 are all equivalent, the atomicsites of C70 can be classified into 5 sites (‘‘A’’–‘‘E’’)(Fig. 1(a)).

We study the reactivities of all the five sites of C70 as wellas that of C60. To quantify their reactivities, we calculatethe total energies of the system consisting of a fullerene anda C atom as a function of the distance (d) between thefullerene surface and the C atom (Fig. 2). In this work,geometries of both C60 and C70 fullerenes have beenoptimized, and the C atom is put along the straight linefrom the center of gravity of the fullerene through thesurface C atom (Case I, see Fig. 2(b)). We next define thereactivity of each site as an energy gain at the minimum-energy configuration from the infinite distance configura-tion. The larger the reaction energy is, the more reactive thesite should be.

In Fig. 3(a) and (b), the results on the reactivities of C60

and C70 are shown. It is interesting to note that the reactionenergies of C and D sites of C70 are larger than that of thesite of C60. However, the straight line from the center ofgravity of C70 through the B, C, D and E sites in C70 is notperpendicular to the C70 surface. For this reason, theaforementioned definition of d is not unique for these sites.

Therefore, for C and D sites, we also study another halfstraight line on which the C atom is put (Case II, seeFig. 2(b)). Here, we consider a hypothetical C60 in thestructure of C70. The half-straight line from the center ofgravity of the hypothetical C60 through the surface C atom

A

B

C

D

A

B

C

D

E

D5h C70 D5h C50

Fig. 1. (a) Structure of D5h C70. C70 has five different atomic sites

(‘‘A’’–‘‘E’’), and (b) structure of D5h C50. C50 has four different atomic

sites (‘‘A’’ –‘‘D’’).

of C70 becomes nearly perpendicular to the C70 surface.The choice of this line may give us more precise reactionenergies of these sites.In Fig. 3(c), we show the result on C and D sites in Case

II, where both C and D sites are again found to be morereactive than the site of C60. Now we can conclude that C70

is more reactive than C60. This result is in accord with theexperimental relative abundance of C60 and C70. Our resultthat C and D sites are most reactive sites of C70 is also ingood agreement with the experimental fact that at least oneof the C and D sites of C70 is involved in the intercagebridging bonds in all five identified isomers of C70 dimerðC70Þ2 [15].In addition to Ih C60 and D5h C70, we study the

reactivities of D5h C50 and graphene, which have beenoptimized by the LDA as in the case of C60 and C70. C50 isan IPR-breaking fullerene and its atomic sites are dividedinto four different sites (‘‘A’’–‘‘D’’) (Fig. 1(b)). Amongthese four sites in C50, A site is expected to be mostreactive, since A site is not sp2 but rather sp3-hybridizedsite with two adjacent pentagons. Therefore, we calculate

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-3

-1.5

0

1.5

3

4.5

1 1.5 2 2.5 3 3.5 4

En

erg

y[e

V]

d[Å]

-3.5

-3

-2.5

-2

-1.5

-1

1.2 1.4 1.6 1.8

En

erg

y[e

V]

d[Å]

C60C70 (A)C70 (B)C70 (C)C70 (D)C70 (E)

-3.1

-3

-2.9

-2.8

-2.7

-2.6

-2.5

1.3 1.4 1.5 1.6 1.7

En

erg

y[e

V]

d[Å]

-4.5

-3

-1.5

0

1.2 1.4 1.6 1.8

En

erg

y[e

V]

d[Å]

C60

C50 (A)

GrapheneC60

C70 (C)

C70 (D)

Fig. 3. Reaction energies of (a) C60, (b) five sites of C70 (‘‘C70 (A)–(E)’’) in Case I, (c) C and D sites of C70 (‘‘C70 (C), (D)’’) in Case II, and (d) A site of C50

(‘‘C50 (A)’’) and graphene (‘‘Graphene’’). From (b) to (d), the result for C60 is also shown for comparison.

Y. Ueno, S. Saito / Physica E 40 (2007) 285–288 287

the reaction energy of this A site for C50. In the case ofgraphene, on the other hand, it is expected to be lessreactive than C60 because of its planar structure. Theresults on C50 and graphene are shown in Fig. 3(d). Asexpected, the reaction energy of A site of C50 is much largerthan that of C60 while that of graphene is smaller.

4. Concluding remarks

From the total-energy electronic-structure study, it isfound that not only C50 but also C70 is more reactive thanC60 although C70 is energetically more stable than C60. Thisis consistent with the high abundance of C60 in soot, andfurther confirms that the reactivity is of high importance inconsidering the relative abundance of fullerenes. Thepresent work therefore sheds new light on the formationprocess of fullerenes presently unrevealed yet.

Acknowledgments

The authors would like to thank Professors A. Oshiya-ma, T. Nakayama, M. Saito, and O. Sugino for the LDAprogram used in the present study. Some of the numericalcalculations were performed on TSUBAME Grid Clusterat the Global Scientific Information and ComputingCenter of the Tokyo Institute of Technology.This workwas partially supported by Grant-in-Aid for Scientific

Research from the Ministry of Education, Science, andCulture of Japan.They also acknowledge the financialsupport from the Asahi Glass Foundation and the 21stCentury Center of Excellence Program by Ministry ofEducation, Science, and Culture of Japan through theNanometer-Scale Quantum Physics Project of the TokyoInstitute of Technology.

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