Dimerization and fusion of two C60 molecules

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Chemical Physics 344 (2008) 176–184

Dimerization and fusion of two C60 molecules

Narinder Kaur a, K. Dharamvir b, V.K. Jindal b,*

a Department of Applied Sciences, Chandigarh College of Engineering and Technology, Chandigarh 160026, Indiab Department of Physics, Sector 14, Panjab University, Chandigarh 160014, India

Received 12 November 2006; accepted 21 December 2007Available online 4 January 2008

Abstract

We investigate the dimerization and fusion of C60 molecules to form various C60 dimers when pushed against each other at severalintermolecular distances. We study the stability of this dimerized C60 molecule based on its binding strength provided by intramolecularinteractions. Tersoff potential, which is considered to represent intramolecular interactions well, has been used to calculate potentialenergy at these distances of separation and for all possible orientations of the molecules. We observe that several minimum energy con-figurations exist at various distances between the C60 molecules. Our calculation shows that apart from the dumbbell structures, manyinteresting composite phases also result, such as fused, peanut and carbon nanotubes of geometry (5,5) of length 11.84 A and (10,0) oflength 12.30 A.� 2008 Elsevier B.V. All rights reserved.

Keywords: C60; Fullerene; Dimer C60; Bucky ball; Carbon nanotube; Tersoff potential

1. Introduction

The icosahedral 60-atom carbon clusters popularlyknown as bucky balls, have been subjected to much inves-tigation for the past two decades. They form molecularcrystals with weak intermolecular bonding, adequately rep-resented by Van der Waals interactions [1,2]. In this crys-talline state, at ambient temperature, the bucky balls arefree to change their mutual orientation or even to rotatearound the molecular centers while preserving a perfectcrystalline lattice order. At temperature below 260 K how-ever, the orientational freedom gets frozen. A gentle push,hydrostatic pressure, excitation by light or other factorscan promote a stronger covalent bonding between theC60 molecules thus allowing them to share some of theirelectrons [3,4]. This process leads to formation of dimers,polymer like chains (pearl necklaces) or rigid two- andthree-dimensional networks and may dramatically changethe electronic and optical properties of the bulk material.

0301-0104/$ - see front matter � 2008 Elsevier B.V. All rights reserved.

doi:10.1016/j.chemphys.2007.12.023

* Corresponding author. Tel.: +91 172 253 4458; fax: +91 172 278 3336.E-mail address: [email protected] (V.K. Jindal).

Numerous fascinating properties of a collective natureare also expected to be displayed by these formations.

It has been known for some time now [4] that on apply-ing high pressure and temperature new phases appear inwhich equilibrium distance between nearest neighbor C60

molecules get shortened from 9.9 A (in the crystalline stateof individual bucky ball molecules) to about 9.0 A. Oneobtains a dimer phase when C60 solid is cooled rapidlyfrom 450 to 77 K [5]. Similarly, chain and layered polymerphases have been produced by cooling the C60 solid slowlyfrom 450 to 77 K. The phase purity has been checked by X-ray diffraction. The dimer phase is metastable and changesgradually to chain polymer phase.

Dimerization and polymerization of C60 has also beenobserved under ion irradiated thin film samples of C60 onSi and quartz substrates studied at controlled fluences,when exposed to swift heavy ions of hundreds of MeV[6]. Iijima and coworkers [7,8] while heating nano-peapods(rows of bucky balls inside single-walled carbon nano-tubes) observed that inside the nanotube, the bucky ballsstarted to coalesce at 800 �C and, finally, completely trans-formed to a single-wall nanotube at 1200 �C.

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N. Kaur et al. / Chemical Physics 344 (2008) 176–184 177

The bond between two adjacent bucky ball monomers indimers or polymers is either sp3 like bond (single bond [9]or a 2 + 2 cycloaddition bond) [10,11] or sp2 like bond[8]. These types of bonds have been experimentally identi-fied. X-ray powder diffraction studies established [12] thatin the dimer molecule formed through a single C–C inter-fullerene bond the center to center distance d, betweentwo bucky balls is 9.1 A while that in a cyclo-added dimeris 9.3 A. sp2 like bonding is seen during the coalescence oftwo bucky balls giving rise to very strong intercage bondingwith d � 8.53 A. First principles molecular dynamicalrelaxation has been performed to study seven different con-figurations of a C60 dimer by Adams et al. [10]. Theyshowed the cyclo-added dimer to be the most stable dimerphase whereas other considered dimer structures wereshown as unbound structures. Menon et al. [11] have usedgeneralized tight-binding molecular dynamics technique tostudy various C60 dimer geometries and have suggested thecyclo-added dimer structure to be the minimum energydimer structure.

Porezag et al. [13] have used density function based non-orthogonal tight-binding method to study the structure,energetics and vibrational properties of five different(C60)n oligomers (n = 2, 3 and 4). For various values of d,the C120 molecule was minimized by allowing 118 atomsto move and keeping the two atoms making dimer bond,fixed. Cycloaddition bond has been suggested as the link-age style in a C60 dimer molecule with binding energy of1.20 eV.

Peapods have also been studied by way of moleculardynamics simulations and it has been shown that 22 succes-sive Stone–Wales (SW) transformations (90� bond rotationwithin the plane of a sp2-carbon network) are a topologi-cally acceptable pathway for the transformation of acyclo-added dimer molecule to a perfect C120 buckytube[14–17]. However, the ordinary molecular dynamics studyfor the process was not applicable. For the whole coales-cence process, the energy barrier has been estimated to be8–12 eV [8]. Marcos et al. [18] find in their calculations thata thermal road to the annealing process requires much lessexpenditure of energy and have proposed 24 stable C120

isomers in SW pathway including the initial [2 + 2] andfinal state C120 nanotube.

Another approach is to study the collisions between twoC60 molecules [19]. By using molecular dynamics simula-tions it has been shown that dumbbell-shaped (C60)2 dimerwith almost intact cages could be formed at low collisionenergy (�21.5 eV) and coalesced dimer with symmetricallydistorted cages at higher incident energy (�52 eV) andwhen the collision energy was high enough (�400 eV) toovercome the fusion barrier, the two colliding C60 mole-cules fused to form one large cage-cluster, the C120

molecule.Solids formed out of dimerized C60 molecules have also

been studied theoretically using model potential approach[20,21]. These solids can have orthorhombic, tetragonalor monoclinic structures. The pressure and temperature

dependent properties such as bulk modulus, lattice and ori-entational structure, phonon dispersion relations, Grunei-sen parameters, heat capacity and entropy have beenstudied by us, considering the rigid dimer molecule to besingly bonded [20]. The possible crystal packings of dimer-ized C60 molecules were studied by minimizing the latticeenergy with a bond charge intermolecular potential model,when the two C60 monomers are cycloadded [21]. Thestudy on the C120 cluster produced by Laser desorptionof fullerene films, to measure ion mobility proposed severalC120 fullerene cages with different gross shapes [22].

On the basis of theoretical and experimental work doneup till now it emerges that several results have beenreported in literature which are based on different tech-niques. A comprehensive and systematic study of thedimerization process of two bucky balls has not beenreported by a single approach. The detailed study on therequisite conditions and the types of bonds formed betweentwo C60 molecules when brought closer to each other isdesirable.

In this paper we study the various possible structures ofC120 (henceforth a ‘‘bonded double C60” will be calleddimer molecule) obtained by bringing together two C60

cages. The structures obtained have been analyzed toobtain the number of intercage bonds, bond energies,lengths and several other characteristics. We have used atheoretical model in which the interaction between bondedcarbon atoms is governed by the Tersoff potential [23]. InSection 2, the form of this potential is given, which hasbeen used to calculate the binding energy of two buckyballs at various intercage distances for all possible orienta-tions. In Section 3, the numerical results for the dimerstructures obtained by using our theoretical model are pre-sented. The structures are discussed individually in Section4. Conclusions have been drawn about several stable dimerstructures in the last section of the paper.

2. Theoretical procedure

The form of the Tersoff potential for calculating poten-tial energy between ith and jth bonded carbon atoms at rij

distance apart is described below in Section 2.1. In Section2.2 we discuss the potential parameters. The procedure forobtaining different structures of the dimer molecule is dis-cussed in Section 2.3.

2.1. The model potential

The Tersoff potential has been successfully used for themodeling of intramolecular chemical bonding in a widerange of hydrocarbon molecules [24], diamond and graph-ite lattices as well as carbon nanotubes [25]. The resultsobtained for elastic constants and phonon dispersion, werein good agreement with experiments and with ab initio cal-culations (for defect energies). The potential is able to dis-tinguish among different carbon environments, fourfold sp3

bond as well as threefold sp2 bond.

Table 1Original and modified parameters of the Tersoff potential

Tersoff parameters Original [26] Modified

A (eV) 1393.6 1380.0B (eV) 346.7 349.491k1 (A�1) 3.4879 3.5679k2 (A�1) 2.2119 2.2564k3 (A�3) 0a 0b 1.57 � 10�7

n 0.72751c 38049.d 4.3484h �0.57058R (A) 1.95D (A) 0.15

178 N. Kaur et al. / Chemical Physics 344 (2008) 176–184

The potential consists of a pair of Morse-type exponen-tial functions with a cut-off function fc(r).

V ij ¼ fcðrijÞ½aijV RðrijÞ þ bijV AðrijÞ�; ð1Þwhere VR(r) and VA(r) are repulsive and attractive forceterms, respectively.

V RðrijÞ ¼ Ae�k1rij ; ð2ÞV AðrijÞ ¼ �Be�k2rij : ð3Þ

fc(r) is a function used to smooth the cutoff distance. It var-ies from 1 to 0 in sine form between R � D and R + D, Dbeing a short distance around the range R of the potential

fcðrÞ ¼1; r < R� D12� 1

2sin p

2ðr � RÞ=D

� �; R� D < r < Rþ D

0; r > Rþ D

8><>:

ð4ÞThe other functions in Eq. (1) are,

bij ¼1

ð1þ bnnnijÞ

12n

; ð5Þ

where; nij ¼Xk 6¼i;j

fcðrikÞgðhijkÞe½k33ðrij�rikÞ3� ð6Þ

Here hijk is the bond angle between ij and ik bonds asshown in Fig. 1. The state of the bonding is expressedthrough the term bij as the function of angle between bondi–j and each neighboring bond i–k and

gðhÞ ¼ 1þ c2

d2� c2

½d2 þ ðh� cos hÞ2�ð7Þ

Further,

aij ¼ ð1þ angijÞ� 1

2nð Þ ð8Þ

gij ¼X

fcðrikÞeðk33ðrij�rikÞ3Þ ð9Þ

Using this potential, composite energy Eb of all the atomsof the system is calculated as

Eb ¼1

2

Xij

V ij ð10Þ

The sum in Eq. (10) includes all the atoms in the system.For the intermolecular interactions between the non

bonded ith and jth carbon atoms, Van der Waals interac-tion potential can be used which is given by the expression

V Lij ¼ �

A

r6ij

þB expð�aLrijÞ ð11Þ

Fig. 1. The angles between ij and ik bonds as used in Eq. (6).

where A;B and aL are the interaction parameters. Theseparameters have been tabulated for carbon–carbon interac-tions in the literature [20]. However in comparison to theTersoff potential, at the distances of consideration, theintermolecular interaction potential generated by Eq. (11)is numerically insignificant so it has not been included inthe present calculation.

2.2. Potential parameters

All the parameters appearing in the expressions forpotential have been tabulated in Table 1.

Two types of bond lengths determine the coordinates of60 carbon atoms in C60 molecule. Single bond b1, joining ahexagon and a pentagon is of length 1.45 A and doublebond b2 joining two hexagons is shorter, having length1.40 A [27]. By using the parameters given by Tersoff, thebinding energy of a C60 molecule was minimized usingthe potential model as given in the earlier section. In thisway, the atomic coordinates of the 60 atoms are adjustedone by one to obtain a configuration with lower energy.The cycle is repeated many times till minimum energy isobtained. By doing this, b1 and b2 were obtained to be1.46 A and 1.42 A with binding energy 6.72 eV/atom asgiven in Table 2.

In order to reproduce the bond lengths and the bindingenergy of a C60 molecule in closer agreement with theexperimental results of Dresselhaus et al. [27], the potentialparameters given by Tersoff [26] had to be modified. It isfound that the first four Tersoff parameters A, B, k1, k2

are the effective parameters to get appropriate binding

Table 2Comparison between the calculated and experimental binding energy andbond lengths of a C60 molecule with original and modified parameters

Calculated Experimental[27]With Tersoff

parameterPresentwork

Binding energy (eV/atom) �6.73 �7.17 �7.04Bond lengths (A) 1.46, 1.42 1.45, 1.41 1.45, 1.40

Fig. 2. Binding energy of two approaching bucky balls with DB–DB and PF–PF orientation at various intercage distances.


energy and bond lengths so only these were modified. InTable 1 we presented the modified parameters as well asthe original potential parameters. The new bond lengthsand energies have been given in Table 2. The modifiedparameters have been used by us to obtain minimumenergy configurations of the dimer molecule.

Usually a and k3 are taken 0 for the carbon systems [26]so that we have aij = 1 (see Eq. (8)). However for siliconsystem finite values of these parameters have been pro-posed [23] to better understand the system. Initially coordi-nation number of each atom (say ith) is 3 (k1, k2, k3) in aC60 molecule, but when two neighboring bucky balls comeclose to each other for intermolecular bonding this numberincreases, for the contacting atoms, depending upon theintermolecular distance. It is generally believed that a finitevalue of parameter k3 plays a major role in controlling theattractive forces between the contacting carbon atoms,when coordination number increases from 3 to 5 or more.We made several runs of relaxation with nonzero k3, andfound that, during the application of pressure on a C60 ball,when coordination number changes as a result of signifi-cant alteration in the distances, k3 makes a major differencein the binding energy calculations and this work is reportedelsewhere [28]. However, its finite value does not alter theresults significantly during dimerization reaction. There-fore, in this work, we have presented our results usingthe value of this parameter as zero. Rest of the parametersin Table 1 are taken to be the same as given by Tersoff.

2.3. Application to dimer structure

We adopt a procedure (relaxation) where the initial con-figuration consists of two bucky balls with a certain mutualorientation at a certain distance apart such that the buckyballs are within chemical bonding range. The initial config-uration was fixed by the following criteria. We identify 16different configurations of two C60 molecules on the basisof orientational differences, which lead to distinct dimerstructures. Various combinations of single bond SB, dou-ble bond DB, corner atom, hexagonal face HF and pentag-onal face PF with each other, make different starting

configurations of the two facing molecules, such as singlebond of one molecule facing single bond of the other mol-ecule (SB–SB) or single bond of one molecule facing doublebond of the other molecule (SB–DB) and so on. Atomicpositions of all the 120 atoms were now varied to obtainthe minimum energy dimer structure for a particularorientation.

The binding energy of two bucky balls w.r.t. intercagedistance d has been shown in Fig. 2 for two orientationsi.e. DB–DB, in which double bonds of the two balls faceeach other and PF–PF, in which pentagonal faces of thetwo balls face each other anti-parallel. Incase of DB–DBorientation dimer phase starts from 9.0 A at which weobtained a minimum energy dimer structure with singlecovalent bond as the intercage bond as shown in Fig. 3.Another dimer structure is obtained at 8.6 A with cycload-dition bond as the intercage bond. We have been able toobtain one more stable new dimer structure at 7.9 A withfive covalent bonds as the intercage bonds giving rise to afused structure. However for the PF–PF orientation weobtained single minimum at 8.3 A which give rise to struc-ture 7 as shown in Fig. 3.

Similar plots for other possible orientations were studiedand it was found that initial intercage distances are usuallyfrom 7.9 to 9.1 A and yield the dimer structures. Severalother minimum energy configurations are possible toobtain using distorted C60 molecules (i.e. by opening someof the on-cage bonds). Within our treatment, this is theonly way to arrive at the final states of carbon nanotubeC120 and the peanut. The cage opening represents thermalactivation as has also been described by Marcos et al. [18].

3. Numerical results

The dimers obtained were categorized depending upontheir bonding schemes and are shown in Fig. 3. we find thatthe possible three classes are (a) structures with very fewbonds, not significantly disturbing carbon atoms otherthan those involved in intercage bonding; (b) fused struc-tures – those in which contact atoms have some of the ori-ginal C60 bonds broken and new bonds formed – mixture

Fig. 3. Various structures obtained after relaxation under Tersoff potential. The set of diagrams in category (a) shows sp3 like intercage bonding, (b) showsa mixture of sp3 and sp2 like intercage bonding and (c) shows pure sp2 like intercage bonding.


of sp2–sp3; (c) coalesced structures – those with all of thecarbon atoms finally attaining sp2. Further features ofthese structures are discussed in the next section. Thenumerical results are summarized in Table 3.

In Table 3 we defined the center to center distance,referred to as the intercage distance, as the distance betweenthe center of gravity of the first 60 atoms and that of theremaining 60 atoms, originally belonging to the two buckyballs as shown in Fig. 4. The dimer length is defined as theend to end axial distance between the two balls. The mini-mum energy represents the energy of the dimer moleculeby allowing all the 120 atoms to relax. In reality only afew atoms closer to the two molecules relax appreciably asshown in Fig. 3. The structures obtained after relaxationfrom open cages require, in addition to proximity, someextra energy, which could be provided by temperature.Out of the possible 16 initial orientations, some did not yielda stable dimer structure so in all we had eleven differentstructures of the stable dimer molecule as shown in Table 3.

We have not considered the energetically stable cages i.e.Cage-Td, Cage-C1H, Cage-C2 studied by Esfarjani et al. [29]or toroidal cage form of point group D5d of C120 structuresstudied by Ihara et al. [30], because our procedure ofobtaining a C120 structure was by compressing two C60

monomers for various possible orientations so that thetwo balls retain their individuality at least by 50%, afterthe dimer formation. For the above mentioned structuresthe two balls completely lose their identities, so these struc-tures were not studied.

4. Discussion of the obtained dimer structures

In this section, we discuss the results i.e. Fig. 3 andTable 3.

4.1. Single bonded or cyclo-added dimers

The dimer structures under this category are formedwhen the initial intercage distances are between 8 and9 A. For different orientations, different bonding schemesresult, as shown in Fig. 3a. In structure 1 the two ballsare placed in a manner that double bonds of each of thetwo balls face each other. A ring type intercage bondingis there called 2 + 2 cycloaddition. Intramolecular doublebond of each ball breaks and form parallel covalent inter-molecular bonds of length 1.54 A each, whereas the intra-molecular bonds of this ring are 1.47 A each. This typeof bonding is the most talked about bonding in the C60

dimers and polymers. The central C4 unit that connectsthe neighboring bucky balls can be viewed as a cyclobutanefragment where every carbon atom is connected to fourothers. Structure 2 is obtained when single bond of one ballfaces the double bond of the other ball placed at around8 A distance apart. It is more stable than structure 1 (seeTable 3) although their distortion at the inter-connectingsites is similar. Structure 3 is obtained when the carbonatoms of the balls face each other at around 8.4 A. Thistype of bonding has been observed in alkali doped C60 sol-ids. In structure 4 double bond of one ball face pentagonal

Tab

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Th

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rien

tati

on

and

min

imiz

eden

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eso

fth

eel

even

C60

dim

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s

St.

no

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tru

ctu

reas

sho

wn

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rien

tati

on

Init

ial

cen

ter

toce

nte

rd

ista

nce

(A)

Init

ial

ener

gy(e

V)

Min

imiz

eden

ergy

(eV

)N

o.

of

inte

rca

geb

on

ds

Inte

rcag

eb

on

dle

ngt

h(A

)F

inal

cen

ter

toce

nte

rd

ista

nce

(A)

Dim

erle

ngt

h(A

)

1D

um

bb

ell

DB

faci

ng

DB

8.6

.78

�1.

512

1.54

each

8.90

315

.95

2C

yclo

add

edS

Bfa

cin

gD

B8.

044

.59

�1.

862

1.53

,1.

548.

8215

.83

3S

ingl

eb

on

ded

-1C

-ato

ms

Fac

ing

8.4

3.41

�2.

165

11.

489.

0816

.196

4S

ingl

eb

on

ded

-2D

Bfa

cin

gP

F8.

57.

44�

1.07

11.

486

8.68

15.6

85

Sin

gle

bo

nd

ed-3

DB

faci

ng

DB

9.0

0.9

�1.

711

1.48

58.

975

16.0

166

Fu

sed

–1

DB

faci

ng

DB

7.9

88.6

3�

.14

51.

49,1

.49,

1.51

,1.

33,

1.56

7.87

14.9

27

Fu

sed

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faci

ng

PF

anti

-par

alle

l8.

322

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�2.

222

1.52

3ea

ch8.

381

15.2

7

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use

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21.

567e

ach

8.75

15.7

19

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pen

Hf

faci

ng

clo

sed

Hf

8.1

10.6

1�

16.3

61.

39ea

ch8.

5015

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rmch

air

nan

otu

be

Op

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Ffa

cin

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8.0

130.

08�

33.6

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1.41

each

3.92

11.8

4

11Z

igza

gn

ano

tub

eaC

120

iso

mer

–26

.93a

�35

.10

61.

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ch6.

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acin

gp

enta

gon

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iso

mer

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ese

mo

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mer

sar

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ght

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ser.

We

hav

em

inim

ized

the

C120

iso

mer

wit

ho

ur

po

ten

tial

mo

del

,so

init

ial

ener

gyre

qu

ired

ism

uch

mo

reth

anq

uo

ted

her

e.

Fig. 4. Intercage distance and dimer length.


face of the other ball and in structure 5 again double bondsof the two balls face each other but at 9 A to form singlecovalent bond as the intercage bond. Structures 3 and 4

look similar but have different energies and initial orienta-tions. In fact 3, with lower energy has shorter route duringrelaxation. Given enough time to relax, structure 4 alsorelaxes to 3. In this category structure 5 needs special men-tion as the intercage distance is larger than that in the otherstructures but it relaxes to be a very stable dimer (see Table3).

4.2. Fused dimers

The dimer structures under this category are formedwhen the initial intercage distances are between 7.9 and8.5 A with sp2 like intermolecular bonding (see Fig. 3b).Structure 6 is obtained from DB–DB orientation with 5intercage bonds. Structure 7 has been obtained when thepentagonal faces of the two C60 molecules face each otheranti-parallely. Two intramolecular bonds from the ballsbreak and form two covalent intermolecular bonds. Struc-ture 8 is obtained when the single bond of one ball is facingpentagonal face of the second ball. An intramolecular bondbreak open the pentagon of one ball and the balls maketwo intermolecular bonds giving rise to a fused structure.

4.3. Coalesced dimers

The dimer structures under this category were formedwhen the initial intercage distances were less than 8.2 A.Different starting orientations; result in buckytube or pea-nut formation as shown in Fig. 3c. In the resulting threestructures all C-atoms are sp2 bonded. We discuss thesethree coalesced structures individually.

Structure 9 also referred as P66 [29] have been obtainedby bringing two C60 monomers in such a way that the hexa-gons of both the molecules are facing each other in whichone has three loose bonds (the erstwhile single bonds) asshown in Fig. 5. Pure sp2 type bonding can be seen at theinter-connecting sites. The balls fuse into each other mak-ing intermolecular sp2 bonds and give rise to a very stablestructure. The coalesced structure has been confirmed bylaser desorption mass spectroscopy and its structure wasassigned to a peanut shaped structure by comparison ofthe IR absorption spectrum, with theoretical spectra offive C120 isomers by Strout et al. [31]. Two more peanut

Fig. 5. Front and side view of opened cage for peanut formation.

Fig. 8. Binding energy of two bonded bucky balls as a function ofintercage distance.


structures have been studied by Esfarjani et al. [29] i.e. P55and P56. These structures have been observed to form inthe Electron Beam-irradiated C60 thin film as well as inthe photo-irradiated KxC60 film [32–34].

Other groups also found the coalesced dimers in aggre-gation following laser ablation of fullerene films, in colli-sion between fullerene ions and thin films of fullerenesand in fullerene–fullerene collisions [35]. The Bucky ballshave also been observed to coalesce during peapod forma-tion reactions.

Structure 10, the C120 molecule in the form of ArmchairBuckytube has been obtained by bringing together two C60

monomers approaching each other in such a way that par-tially open pentagons are facing each other. This ‘partialopening’ has been shown in Fig. 6. The contacting penta-gon has all its single bonds cut (all five C-atoms allowedto move away from each other) so that each of these hasonly one remaining bond. As the two cages are now openthey can fit into each other if brought very close, makingnew double bonds with other cage as shown in Fig. 7. Puresp2 type bonding can be seen at the inter-connecting sitesresulting in a nanocapsule of length 11.84 A. Theoreticallybreaking of the ten bonds of the two C60 molecules seemseasier way to open the cages, but it is believed that theisomerization mechanism is preferred as there is less expen-diture of energy for the SW transformations, which can be

Fig. 7. The seamless joining of two open

Fig. 6. Cage opening for bucky-tube formation.

viewed as bond rotations and require less energy than bondbreaking. A sequence of only five SW-type bond rotationstransforms a perfect C60 molecule to a capped segment of a(5,5) nanotube [18].

Structure 11 zigzag buckytube was not attainable by anykind of cage opening as a precursor. Instead, we fed theassumed structure to the program and let it minimize.The resulting zigzag tube has a length of 12.30 A, and isthe most stable of the dimerized C60 molecules found byus. Notice that the cap of zigzag nanotube is not the sameas half of C60 molecule. The terminating pentagon of thistube is surrounded by six hexagons as in the most stableC60. However these hexagons are surrounded by PHHPHHsequence (P-pentagon, H-hexagon), instead of PHPHPHsequence as in the most stable C60. This results in a capappropriate for zigzag nanotube as shown in Fig. 3c. Allthe ten relaxed structures as observed by us at variousintercage distances have been shown in Fig. 8. Structure11 is not included as it has been obtained by a differentmethod.

5. Summary and conclusion

We have studied various forms of dimer C60 obtainedafter squeezing together two bucky balls. In our calcula-tions we see that, if C60 molecules are considered rigid, thendimer structures 1, 3–5, 8 and 9 result in energies close tominima. The minima in energies are obtained by allowingthe atoms of the molecules to relax, thus including the

C60 molecules to form a bucky-tube.


non-rigidity in molecules (see column 5 in Table 3). Whennon-rigidity of C60 molecules is allowed then these struc-tures are the energetically favorable structures (see column6 in Table 3). Further, structures 2, 6 and 7 do not showany tendency to stabilize in rigid molecule model, they dostabilize when non-rigidity is considered (columns 5 and6 of Table 3). The binding energy of these structures comesout to be roughly of the order of 2 eV which is in closeagreement with the experimental estimate of 1.25 eV [36].However if opening of the cages in addition to non-rigidityis allowed then energetically most favorable structures arethe coalesced structures (structures 9–11) with bindingenergy of roughly of the order of 34 eV for the bucky tubesand 17 eV for the peanut structure.

Structures 2 and 5 were obtained by Kim et al. [37] asdianionic (C60)�2 dimer phase while investigating suddenchange in magnetic property of this phase in a rapidlycooled AC60 samples (A-alkali metal). Fullerene coales-cence, experimentally found in fullerene embedded single-walled carbon nanotubes under heat treatment, has beensimulated by minimizing the classical action for manyatom systems for structures 10 and 11 by Kim et al. [8].The initial state for the process has been taken as twoC60 molecules separated by 1 nm. The synthesized innertubes had their diameters ranging from 0.6 to 0.9 nm.Esfarjani et al. [29] performed total energy minimizationsfor structures 1, 3, 4, 9 and 10 of Fig. 3. Structure 7 and8 were also studied by Choi et al. [38] theoretically, usingnon local density functional theory while doing geometryoptimizations on C120. Structure 6 has never been reportedso far.

We have minimized the above discussed structures afterorientational positioning and partial opening of cages (asrequired for some dimer structures) have been done. Sothe calculated binding energies are lower than those quotedin the Refs. [8,29]. In Ref. [29] the most likely candidate forthe experimentally found dimer structure i.e. Dumbbellstructure has been reported as having positive bindingenergy, so their quoted energies are not in accordance withthe experimental data available.

The bond energy for sp3 like intercage bonding such asin structure 1 having intercage bond length 1.54 A and sp2

like bonding as in structure 9 having intercage bond length1.39 A have been estimated, which are of the order of3.15 eV/bond and 5 eV/bond, respectively. As bondstrength is directly proportional to the bond energy of thatbond so we conclude that the strength of sp2 like bond ismore than that of sp3 like bond.

Some of the dimer structures have not been experimen-tally identified. The reason could be that the crystallineorder restricts desired fusion or coalescence between twobucky balls when a C60 solid is compressed. These struc-tures can be formed by compressing C60 molecules in gasphase.

It is interesting to observe all the known structures ofdimerized and fused C60 by following a uniform theoreticalprocedure adopted here. In this way, the possibility of los-

ing any observable structure is very unlikely. Indeed, wefind an unreported structure (structure 6) also. The resultsand inferences of this work provide motivation for experi-mentation on the C60 dimer molecule forming the dimersolids. For the discussed dimer structures we propose toinvestigate the consequent structures of the dimer solids,in line with our earlier work [20].

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Dimerization and fusion of two C60 molecules