Chemical Physics Letters 461 (2008) 87–92

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Chemical Physics Letters

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Host–guest interaction in endohedral fullerenes

C.N. Ramachandran a, Debmalya Roy b, N. Sathyamurthy a,c,*

a Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur 208016, Indiab Defence Materials and Stores Research and Development Establishment (DMSRDE), Kanpur 208013, Indiac Indian Institute of Science Education and Research (IISER) Mohali, Chandigarh 160019, India

a r t i c l e i n f o a b s t r a c t

Article history:Received 8 May 2008In final form 24 June 2008Available online 28 June 2008

0009-2614/$ - see front matter � 2008 Elsevier B.V. Adoi:10.1016/j.cplett.2008.06.073

* Corresponding author. Address: Department of CTechnology Kanpur, Kanpur 208016, India. Fax: +91 1

E-mail address: nsath@iitk.ac.in (N. Sathyamurthy

Ab initio calculations using Hartree–Fock (HF) and second order Møller–Plesset perturbation (MP2) the-oretic methods using the 6-31G basis set have been used to study the interaction between H+, H�, He, Li+

and H2 with C60 fullerene. The barrier for penetration of the guest species through the center of thehexagon of the cage is reported. There is a substantial change in the HOMO–LUMO energy gap for theendohedral complex of C60 fullerene when the proton or hydride ion is encapsulated. The calculatedHOMO–LUMO energy gap for the endohedral complex is correlated with the orbital energy of the guestspecies. The interaction of the guest species with the host is examined by a critical point analysis usingBader’s theory of atoms in molecules. The effect of the guest species on the electrostatic potential insideand outside of the C60 cage is also discussed.

� 2008 Elsevier B.V. All rights reserved.

1. Introduction

The discovery of fullerene in 1985 as a stable allotrope of car-bon, with a closed cage structure attracted a lot of attention [1]Fullerenes are capable of encapsulating small guest species suchas atoms, ions and molecules inside their cavities. Soon after thediscovery of C60, the first such endohedral complex was reportedwith a lanthanum atom as the guest species [2]. Properties of theencapsulated fullerenes are expected to differ much from the freefullerenes and different methods have been developed in the pastto produce endohedral fullerene complexes with different guestspecies. This involves laser vaporization of graphite sheets interca-lated with metal salts or high energy bimolecular collision be-tween the guest species and the host fullerene cage [2,3].Recently, a new method called ‘molecular surgery method’ has alsobeen developed to encapsulate molecules inside the cage [4–7].The structure and stability of endohedral fullerenes has beeninvestigated theoretically. Maheshwari et al. studied the possibilityof a proton motion through C60 [8]. Their studies using Hartree–Fock method (HF) with the 4-21G basis set showed that a protoncould easily pass through the center of a pentagon or a hexagonforming an endohedral complex and rattle inside the cage. Thebinding energy and equilibrium constant for the formation of theendohedral He@C60 were computed by Patchkovski and Thiel usingsecond order Møller–Plesset perturbation (MP2) theory withTZP(C) + cc-pVQZ (He) basis set [9]. They found He@C60 to be sta-ble, with a stabilization energy of �2.0 kcal/mol. Buckingham

ll rights reserved.

hemistry, Indian Institute of72 2790188.).

and Read studied the Li@C60 and reported the stabilization of theeccentric position of Li due to the loss of degeneracy of orbitals[10]. Cioslowski’s group has done pioneering theoretical researchon the endohedral complexes of fullerene [11–13]. Their studieson the iso-electronic F-, Ne, Na+, Mg2+ and Al3+ species on encapsu-lation inside the fullerene cage have shown that these ionic speciesare located at the center of the cage and that the endohedral fuller-ene is stable. They have also reported a slight expansion of the cagein the presence of the cationic guest species and contraction due toanionic species. Ab initio HF calculations using the 4-31G basis setshowed that the C60 cage could act as a polarizable sphere and thatcages containing polar molecules were stable, while cages contain-ing nonpolar molecules were unstable. Williams et al. [14] studiedthe interaction and dynamics of some endohedral gas moleculesinside C60 using semi-empirical atom–atom potentials and foundthat only the complexes in which the gas molecules and fullerenecavities have minimum van der Waals overlap were stable. Dunlapet al. [15] investigated the interaction of alkali metals and ionswith fullerenes and reported the stabilization of these guest spe-cies at the off-center position inside the cage. Kim et al. [16] stud-ied the endohedral complexes of paramagnetic atoms inside C60

and reported the importance of dispersive interaction in such com-plexes. Recently Pyykkö et al. [17] examined the dispersion inter-action between the endohedral noble gas species and the hostC60 cage. Cross [18] studied the rotational motion of the encapsu-lated H2 and reported a free motion of H2 inside C60. Erkoc and Tur-ker [19] studied the encapsulation of ammonia molecules insidethe fullerene cage by performing semi-empirical (PM3) calcula-tions and reported that (NH3)n@C60, where n = 1–6 were kineticallystable, but thermodynamically unstable. Dodziuk [20] modeledthe endohedral complexes of an H2 molecule in fullerenes and

88 C.N. Ramachandran et al. / Chemical Physics Letters 461 (2008) 87–92

emphasized the need for a high level of theory for the analysis ofsuch supramolecular systems in which non-bonded interactionsplay a decisive role. Shameema et al. [21] studied the encapsula-tion of iso-electronic molecules HF, H2O, NH3 and CH4. TheirMP2/6-31G calculations showed that these molecules are stable in-side the cage. Frequency calculations using the HF/6-31G methodhave shown an increase in the X–H (X = F, O, N and C) stretchingfrequency inside the cage. The effect of nonpolar confinement onwater clusters by encapsulating them in a fullerene cage was alsoreported [22]. It was found that the fullerene cage containing 1–6water molecules was intact and that the water clusters assumedstructures drastically different from those in the gas phase. Severalother studies have also been carried out in the past on endohedralcomplexes of higher fullerenes [23].

The motivation for the present study resulted from an attemptto understand in detail the interaction between fullerene cage andvarious guest species including a cation, an anion, an atom and amolecular species. A set of calculations have also been done forproton encapsulation and compared with the complexes of abovespecies.

As a first step to study the host–guest interaction in endohedralfullerenes, two electron systems He, H�, Li+ and H2 have been se-lected as the guest species. This set of iso-electronic species repre-sent an atomic, ionic (anionic and cationic), and a molecule asguest species. Properties like the stabilization energy, energy gapbetween the highest occupied molecular orbital (HOMO) and thelowest unoccupied molecular orbital (LUMO), effect of the guestspecies on the size and electrostatic potential behavior of C60 cageare studied and discussed below.

2. Computational methods

Geometry optimization for all systems under investigation wascarried out using GAUSSIAN 03 suite of programs [24]. Hartree–Fockmethod was used for geometry optimization using the 6-31G basisset. Frequency calculations were carried out to differentiate theminimum energy structure from the saddle points among the dif-ferent locations of the guest species. Single point energy calcula-tions using MP2 theory with the 6-31G basis set were carried outfor the HF/6-31G optimized geometries to study the effect of elec-

Fig. 1. The ground state interaction potential for the guest species (H

tron correlation. The stabilization energy (DEstab) of the endohedralcomplexes were calculated by the supermolecule approach asfollows;

DEstab ¼ Ecomplex � ðEcage þ EguestÞ

The wave functions for these complexes were generated fromthe HF/6-31G optimized geometries and the critical points werecalculated using AIM 2000 package [25].

3. Results and discussion

Before investigating in detail the interaction of two electronguest species with the fullerene cage, a study of the possibility ofencapsulation of these guest species through the hexagonal ringsin the fullerene cage was undertaken. Maheshwari et al. [8] re-ported earlier that there was not much difference between the bar-rier for penetration through the center of the pentagons and thehexagons. Therefore, in the present study, we have limited our cal-culations to the guest species penetrating through the center of ahexagon only. For H2, different orientations with respect to theC3 axis (passing through the center of the diametrically oppositehexagons) are possible for penetration into the C60 fullerene cage.Moreover, the encapsulation of H2 inside C60 has been reported re-cently by ‘molecular surgery method’ by widening the size of theorifice of the fullerene cage using chemical reactions [4]. To deter-mine the barrier for penetration for other guest species, singlepoint energy calculations were carried out at the HF/6-31G levelfor different positions of the guest species. Keeping C60 in its opti-mized geometry, the guest species was moved from a distance of10 Å from the center of the cage to the center along the C3 axis.The resulting interaction potentials are plotted in Fig. 1.

It is clear from the figure that except H+, all other guest speciesface a considerable barrier for penetration into the cage. For He andLi+, the barrier is more than 200 kcal/mol. It is worth mentioningthat for a noble gas encapsulation, a ‘window mechanism’ was pro-posed earlier [26,27], in which one or more of the carbon–carbonbonds of the cage is broken for facilitating encapsulation. AlthoughH+ and Li+ form stable exohedral complexes, only H+ forms a stableendohedral complex with C60. Near the center of the cage, the po-tential energy surface is very shallow for both the species. H- and

+, H�, Li+, He) approaching C60 through the center of a hexagon.

C.N. Ramachandran et al. / Chemical Physics Letters 461 (2008) 87–92 89

He do not form stable complexes near the surface of the cage. ButH� forms a stable endohedral complex when it is located at thecenter of the cage. The complex formed by locating He at the centerof the cage is a local minimum in the potential energy surface andit is higher in energy than the isolated He and C60. We must hastento add here that earlier MP2/TZP(C) + cc-pVQZ (He) calculationshad shown He@C60 to be stable [9].

For the purpose of geometry optimization, the center of mass ofH2 was fixed at the center of the cage, with the H–H bond pointingtoward the center of two opposite pentagons, keeping D5d symme-try for the system. Frequency calculations at the same level of the-ory showed all positive frequencies for all the systems except forH+@C60 and Li+@C60, suggesting that the optimized geometries cor-respond to true minima on the potential energy surface.

In the case of H+ and Li+, the presence of one negative frequencysuggested the center-of-the-cage geometries to be first order sad-dle points. Further geometry optimization studies for H+ and Li+ intheir off-center positions inside the cage showed that the true min-imum energy structure corresponded to a distance of 1.1258 Å and2.4221 Å, respectively, for H+ and Li+ from the nearest carbon of theC60 cage.

The stabilization energy of the endohedral complexes obtainedat the HF/6-31G and MP2/6-31G levels are listed in Table 1. TheMP2/6-31G level of calculation shows all the complexes exceptHe@C60 to be stable. The stabilization energy of He@C60 was re-ported earlier to be �2.0 kcal/mol at the MP2/TZP(C) +cc-pVQZ(He) level of calculation [9]. In the case of H2@C60, HF cal-culations showed the complex to be unstable, but MP2 calculationsusing the 6-31G basis set yielded a stabilization energy of�2.1 kcal/mol. This shows the importance of electron correlationeffect in the stabilization of guest species inside the fullerene cage.For H+ and Li+ encapsulation, the stabilization energies are calcu-lated both for the center and the off-center positions inside thecage. As was mentioned earlier, the off-center positions are morefavored for these guest species.

The Mulliken charges on the guest species inside the cage arealso listed in Table 1. In the case of H+@C60 the proton does not re-main a bare proton inside C60. The ionization potential of H and C60

are 13.6 and 7.54 eV, respectively [28].Thus energy considerations suggest that

Hþ þ C60 ! Hþ Cþ60 þ 6:06 eV: ðR1Þ

Thus it could be considered notionally as a hydrogen atom inthe vicinity of the positively charged cage.

To obtain more insight into the nature of the interaction be-tween the guest species and the C60 cage, the molecular orbitalswere examined. Fig. 2 shows some of the molecular orbitals stud-ied along with their energy level diagrams.

The energy gap between the HOMO and the LUMO is 173.8 kcal/mol for C60 at the HF/6-31G level. This remains the same for theendohedral complexes of He, Li+ and H2 inside C60. The correspond-

Table 1Calculated properties for different endohedral complexes of C60 at the HF/6-31G andMP2/6-31G level of theory

System Stabilization energy (kcal/mol) DEHOMO–LUMO

(kcal/mol)Charge on theguest

HF/6-31G MP2/6-31G//HF/6-31G

C60 – – 173.8 –H+@C60 �143.4 (�71.0)a �148.8 154.2 �0.1H-@C60 �41.7 �50.5 96.8 �0.9He@C60 +0.2 +0.1 173.8 0.0Li+@C60 �10.8 (�3.6)a �18.8 171.2 0.8H2@C60 +1.6 �2.1 173.8 –

a Stabilization energy corresponding to the saddle point at the center of the cage.

ing molecular orbitals are also similar in all these cases. However,in the case of Li+ and H+ in their off-center position inside the cage,the energy gap between HOMO and LUMO is decreased to169.1 kcal/mol and 154.2 kcal/mol, respectively. For He, Li+ andH2 encapsulation inside C60, the molecular orbitals, which areformed mainly by the contribution of the guest species, are verylow in energy compared to that of the Frontier orbitals. But inthe case of H�@C60, the HOMO is mainly contributed by the guestorbital. As a result, the energy gap between HOMO and LUMO ishighly reduced to 96.8 kcal/mol compared to that for free C60.

A critical point analysis using the theory of atoms-in-molecules(AIM) has proved to be a valuable tool to understand the nature ofinteraction including van der Waals, hydrogen bonding and covalentinteractions [29–31]. Fig. 3 shows the molecular topography of theelectron density of H+@C60 and Li+@C60. In the case of the former, a(3, �1) bond critical point is located between the hydrogen atomand the nearest carbon atom of the cage. The electron density of thisbond critical point is 0:230e=a3

0 and the Laplacian of the electron den-sity is �0:129e=a5

0, which suggests that the interaction is covalent.The distance between the nearest C and H is 1.126 Å, which is a typ-ical C–H covalent bond distance. As a result of this interaction thecage is distorted and the carbon atoms near this site are pushed out-side by a dihedral angle of�30�. Earlier, Mauser et al. [32] studied theinteraction of H, F and methyl radical with C60 using semi-empiricaland density functional theoretical method (PM3 and UB3LYP/D95*)and reported that the interior of the cage is inert. The present resultsshow that it depends on the guest species.

Unlike proton, Li+ forms a p-complex with the cage. In the opti-mized minimum energy structure of Li+@C60, Li+ is found to be equi-distant from carbon atoms of one of the hexagons in the cage. Thedistance between the lithium and the nearest carbon atoms is2.422 Å. Three (3,�1) bond critical points are located with the elec-tron density 0:013e=a3

0 and the Laplacian of the electron density0:019e=a5

0 between the Li atom and one of the hexagons of the cage.The radius of free C60 cage is 3.530 Å at the HF/6-31G level of

calculations. The change in the radius for H+, Li+ and H- encapsu-lated endohedral complexes of fullerenes are +0.001 Å, +0.004 Åand �0.004 Å, respectively. There is practically no such change inthe radius of the cage due to He encapsulation. Although thechange in the size of the cage due to encapsulation of these guestspecies is negligible, it can be seen that the change is dependent onthe charge of the guest species. Cioslowskii and Fleischmann [11]also observed similar changes in their studies of encapsulation ofiso-electronic F�, Ne, Na+, Mg2+ and Al3+ species inside the C60 cage.Due to the strain involved in the fullerenes compared to planargraphite sheets, the p orbitals are more diffused outward than in-side, resulting in a positive potential inside the cage [32,33]. Hence,the presence of a cation inside C60 increases the size of the cage andthe presence of an anion decreases the size.

Molecular electrostatic potential (MESP) has proved to be aneffective tool to understand the nature of interaction between mol-ecules [34]. Fig. 4 shows the MESP-textured planes of C60 and otherendohedral complexes of C60 for different positions of the guestspecies generated by UNIVIS 2000 [35]. As reported earlier, C60 hasa positive electrostatic potential inside the cage and a negative po-tential outside the cage as shown in the figure. There is a signifi-cant change in the value of MESP due to the encapsulation of theguest species inside C60. In the case of H� encapsulation, a highlynegative potential is observed inside the cage compared to the po-sitive potential in the case of C60. Due to the different charges ofguest species, a uniform color code was not informative. A carefulanalysis of the figure suggests the presence of a negative potentialoutside the cage which is higher than that in the case of free C60. Asexpected, there was no change in the electrostatic potential due toencapsulation of He inside the cage. Encapsulation of H+ and Li+ in-duces positive potential both inside and outside the cage. When

H-@C60 He@C60 Li+@C60 H2@C60C60

HOMO

LUMO

MO:61MO:91 MO:134

H+@C60

125

0

-125

-250

-375

-500

-625

-750

173.

8 kc

al/m

ol

169.

1 (1

73.8

) kc

al/m

ol

96.8

kca

l/mol

154.

2 (9

5.1)

kca

l/mol

173.

8 kc

al/m

ol

173.

8 kc

al/m

ol

H2@C60

Li+@C60

H-@C60H+@C60

H+ He@C60

He

C60

AO/M

O E

nerg

y/(k

cal/m

ol)

-875

a

b

Fig. 2. (a) Comparison of the Frontier molecular orbitals of the endohedral complexes along with the relevant orbitals of the guest species and (b) schematic representation ofthe molecular energy levels calculated at HF/6-31G level in their minimum energy geometries. Values in brackets correspond to the energy when the guest species are locatedat the center of the cage.

Fig. 3. Molecular topography of H+ and Li+ encapsulated endohedral fullerene complexes. Small red colored filled circle represents the (3, �1) bond critical point between twoatoms and the grey colored filled circle represents the guest species.

90 C.N. Ramachandran et al. / Chemical Physics Letters 461 (2008) 87–92

Fig. 4. MESP-textured planes for C60 and the endohedral species

C.N. Ramachandran et al. / Chemical Physics Letters 461 (2008) 87–92 91

these ions are at the center of the cage, there is a uniform distribu-tion of the potential. However, when the guest species is in an off-centered position, the potential is more localized inside the cage.This shows the polarization developed and it contributes to thestability of the system compared to the guest species located atthe center of the cage.

In conclusion, we have shown that the host–guest interaction inendohedral fullerene is dependent on the guest species. The orbitalenergy of the guest species plays a significant role in deciding the

HOMO–LUMO energy gap of the complex. Critical point analysisshows that covalent bonds can be formed from the inner side ofthe cage by the encapsulation of guest species like the proton.The guest species also alter the electrostatic properties of C60 cage.

Acknowledgements

This study was supported in part by a grant from Defence Mate-rials and Stores Research and Development Establishment

92 C.N. Ramachandran et al. / Chemical Physics Letters 461 (2008) 87–92

(DMSRDE), Kanpur. One of us (CNR) thanks the University GrantsCommission, New Delhi for a senior research fellowship and NSthanks the Department of Science and Technology, New Delhi fora J.C. Bose fellowship. N.S. is an Honorary Professor at the Jaw-aharlal Nehru Centre for Advanced Scientific Research, Bangalore.

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