Ž . Chemical Physics Letters 315 1999 181–186
www.elsevier.nlrlocatercplett
Possibility of proton motion through buckminsterfullerene
S. Maheshwari, Debashis Chakraborty, N. Sathyamurthy
)Department of Chemistry, Indian Institute of Technology, Kanpur 208 016 India Received 20 April 1999; in final form 1 October 1999
Abstract
The possibility of a proton entering a fullerene cage without breaking any C–C bond and undergoing oscillations through the cage is considered. A detailed understanding of the interaction of a proton with the five- and six-membered rings is obtained by examining proton–corannulene interaction, as a prototype.q1999 Elsevier Science B.V. All rights reserved.
1. Introduction
Following the synthesis of fullerenes and the de- w x
velopment of fullerene chemistry 1–5 , considerable effort has gone into the production of endohedral fullerenes – represented as M@C , where M is an60 atomrion trapped inside the cage of C , for exam-60 ple. This has opened up new ways of making materi- als with specific properties at the molecular level.
One way to make metallo-endohedral fullerenes is to vaporize graphite doped with the appropriate metal
w x
oxide or salt 6,7 . An alternative and more specific way is to repeatedly expose monolayers of C60 to an intense beam of alkali ions at an energy such that they penetrate the cage but not destroy it 8 . Saun-w x ders et al. 9 have been able to produce Rg@Cw x 60 ŽRgsHe, Ne, Ar, Kr and Xe by heating C. 60 to
Ž .
6508C under a high pressure 3500 atm of the rare gas for a few hours. These workers have proposed a
‘window’ mechanism for the formation of endohe- dral fullerenes. It is envisaged that one C–C bond is
) Corresponding author. Fax: q91-512-597436; e-mail:
broken, the rare gas enters through the resulting window and the cage closes by itself. Jimenez-´
w x
Vazquez et al. 10 have found evidence for trapping´ of tritium inside the C60 cage, when the latter was exposed to moderated tritium coming from a nuclear reaction. But, to the best of our knowledge, the interaction of protons with fullerenes has not been examined so far, either theoretically or experimen- tally. Therefore, we have undertaken a study of proton–fullerene interactions and found that a proton can easily enter the fullerene cage through either the five-or six-membered ring and that it can oscillate through the cage and also ‘rattle’ inside the cage.
w x
Recently we have pointed out 11 the possibility of a proton oscillating through the benzene ring and also through other aromatic rings such as naphtha- lene and anthracene. Therefore, it is not unreason- able to expect such a possibility to also exist in the case of fullerenes.
Traditionally, it is believed that protons form a s-complex with aromatic hydrocarbons like benzene ŽBz but Mason et al. 12 have found mass spectral. w x evidence for the formation of a Bz–Hq p-complex.
Ab initio calculations performed in our laboratory
0009-2614r99r$ - see front matterq1999 Elsevier Science B.V. All rights reserved.
Ž .
PII: S 0 0 0 9 - 2 6 1 4 9 9 0 1 2 2 9 - 4
w x
showed 11 that there is a potential minimum, corre- sponding to thep-complex formation, on either side of the benzene ring and that the proton can actually go through the ring without facing any barrier. More
w x
refined calculations 13 have reiterated our findings.
w x
Although Glukhovtsev et al. 14 have pointed out that the p-complex corresponds to a second-order saddle point, 2.06 eV higher in energy than the s-complex, there is no reason why the p-complex cannot be formed and the proton cannot oscillate
Ž . Ž .
Fig. 1. a Frontal and b side views of the corannulene structure. C indicates the position of the C axis. The numbers 1–3 refer to the5 5
particular sites referred to in the text and in Fig. 2b. The s-complex and p-complex formations are also indicated schematically. The distance of the proton approaching the hexagonrpentagon along a perpendicular direction is labelled Z, with Zs0 referring to the centre of
Ž . q
the hexagonrpentagon. c The ground state interaction potential, V, for H –C20H10as a function of the approach coordinate, Z, with the zero of energy corresponding to the asymptotically separated Hq and C20H10 in its equilibrium geometry. The solid line corresponds to motion through the centre of the hexagon, and the dashed line, motion through the centre of the pentagon. The break in the curves implies that the calculations have been carried out only for a limited range of Z values and an extrapolation is made to the asymptote.
through the ring, if the incoming proton has suffi- cient momentum in the direction orthogonal to the plane of the ring.
Before investigating the interaction of a proton with C , we studied the interaction potential be-60 tween a proton and corannulene which has a bowl
Ž .
shape see Fig. 1a and b and for which the carbon framework constitutes the polar cap of buckminster- fullerene and the results are summarized below.
2. Results and discussion
Ž .
Keeping corannulene C H20 10 in its equilibrium
Ž . Ž Ž .
geometry see Fig. 1a rC – C1 1 along the pentagon
˚ Ž . ˚
s1.41 A, rC – C2 3 along the periphery s1.45 A,
˚ ˚ ˚.
rC15C2s1.36 A, rC35C3s1.37A, rC – Hs1.07 A we varied the distance Z of Hq from the centre of a hexagonal ring and for each value of Z, we compute the ground state interaction potential using the 6- 31G) ) basis set and the GAUSSIAN 94 set of pro-
w x
grams 15 . It is clear from the potential-energy curve shown in the form of a solid line in Fig. 1c that there are two minima: one corresponding to an
Ž .
exohedral position convex side and another to an
Ž .
endohedral position concave side . It is also clear that the double-well potential is asymmetric, favor- ing the Hqto be on the endohedral side of corannu- lene. It should be emphasized that the barrier separat- ing the two minima is well below the zero of energy corresponding to the asymptotically separated proton and corannulene. This means that proton motion through the centre of any one of the hexagonal rings faces no barrier.
Proton interaction with the pentagonal ring alongŽ
. Ž .
the C axis5 see Fig. 1b is qualitatively similar to that with any of the hexagonal rings as can be seen from the results shown in the form of a dashed line in Fig. 1c. Although the barrier separating the two minima is larger in the case of the pentagon, it is still below the zero of energy, suggesting a free motion through the pentagon as well. In addition, it can be seen that the proton interaction with the pentagon is stronger than that with the hexagon, at the endohe- dral as well as the exohedral side of corannulene.
We have reported the potential energy curves for only a limited range of Z as one has to go beyond Hartree–Fock level calculations to get asymptoti- cally correct results.
We have examined the tendency of the proton to
Ž .
bind with one of the carbon atoms labelled 1 in Fig. 1a of the five-membered ring and so form a s-complex by plotting the interaction potential as a function of the approach coordinate Z distance alongŽ the line pointing towards the carbon atom and per- pendicular to the plane of the ring in the form of a. dashed line, as shown in Fig. 2a. It is clear that the s-complex at the 1-position is indeed more stable than the interaction along the C5 axis and that the exohedral C–H bond would be stronger than the endohedral bond.
The results shown in Fig. 1c represent the ground state adiabatic potential energy curves and therefore imply that a slow moving proton brought towards the pentagon would tend to form an exohedral C–H s-complex. However, a fast moving proton directed along the C axis can easily pass through the centre5 of the pentagon and preferentially form an endohe- dral complex. The barrier to penetration is lowest along the C axis and increases as the proton drifts5 towards one of the carbon atoms labelled 1 in Fig.
1a.
An examination of the interaction potential for the proton approaching any of the peripheral carbon
Ž .
atoms labelled 2 in Fig. 1b , in the form of a dashed line marked s in Fig. 2b reveals a minimum corre- sponding to an exohedral C–H s-complex. The pro- ton can also form a stable p-complex with any of the 1–2 or 3–3 C5C bonds as shown by the dashed lines labelled p1 – 2 and p3 – 3, respectively in Figs.
1b and 2b. However, this does not preclude the possibility of a proton passing through the center of the hexagon and forming an endohedral complex, as can be seen from the potential plotted in the form of a solid line in Fig. 2b.
Since a single point calculation using the 6-31G) )
Ž . q
basis set GAUSSIAN94 for C -H60 interactions takes nearly two days on our workstation, we have gener- ated potential energy curves for the fullerene–proton interaction using the 4-21G basis set. In any case, our studies on Hq–corannulene interaction have shown that calculations using the 4-21G basis set yield qualitatively the same result as do the ones using 6-31G) ).
We keep fullerene in its equilibrium geometry
˚ ˚
ŽrC – Cs1.45 A, rC5Cs1.36 A and vary the dis-. tance Z from the centre of a hexagonal ring as
Fig. 2. a The ground state interaction potential for a proton approaching one of the carbon atoms labelled 1 of the pentagon in CŽ . 20H10 ŽFig. 1a is plotted in the form of a dashed line. The interaction potential along the C axis is included as a solid line for comparison. b. 5 Ž . The dashed line markedsshows the interaction potential for the proton approaching carbon atoms labelled 2. The dashed lines marked p1 – 2andp3 – 3represent the interaction potential for proton approaching the 1–2 and 3–3p-bonds, respectively. The solid line represents the interaction potential for the proton approaching through the centre of a hexagonal ring, for comparison.
shown in Fig. 3a. For each value of Z we computed the ground state C60PPPHq interaction potential. It becomes clear from the results shown in the form of a soild line in Fig. 3b that there are two minima: one corresponding to Zs1.3 A and another to Z˚ s y0.9
˚ Ž
A, implying the formation of an exohedral outside
. Ž .
the cage and an endohedral inside the cage com- plex, respectively.
Although there is a barrier separating the exo- and endohedral complexes, the maximum of the barrier is still below the zero of energy corresponding to the proton asymptotically separated from C . This60
means that as a proton approaches C , it can easily60 go through any one of the hexagonal rings. As a matter of fact, it can easily come out on the other side of the cage as well. If it loses some of its energy to the cage, it can result in oscillations through the cage. It is quiet possible that a slow moving proton can form an exohedral s-complex with any of the carbon atoms but we would like to emphasize that a fast moving proton can easily pass through the cage and form an endohedral complex.
Results for proton motion through the pentagonal ring are qualitatively similar, as can be seen from the
Fig. 3. a Fullerene structure, with a proton approaching along aŽ . direction perpendicular to the hexagonrpentagon, with Zs0 representing the centre of the hexagonrpentagon. b The groundŽ . state interaction potential, V, for Hq–C60 as a function of the approach coordinate, Z, with the zero of energy corresponding to the asymptotically separated Hq and C60 in its equilibrium geometry. The solid line represents the interaction potential for motion through the centre of a hexagon, and the dashed line is for motion through the centre of a pentagon. The break in the curves implies that the calculations have been carried out only for a limited range of Z values and an extrapolation is made to the
Ž . q
asymptote. c Schematic representation of H –fullerene interac- tion along the radial distance r of the fullerene cage, with rs0 representing the centre of the fullerene cage.
dashed line in Fig. 3b. Understandably, the barrier separating the exo- and endohedral complexes is larger for the pentagonal face than for the hexagon.
Our calculations show that the C –H60 q interac- tion potential has a local minimum at the centre of the cage, that is higher in energy than the endohedral and exohedral minima. We have difficulty in getting convergence at some of the in-between positions.
Therefore, we represent the interaction potential schematically as a function of the radial distance, r through the pentagonal ring, in Fig. 3c. Considering the anisotropy of the fullerene cage, one can antici- pate that there might be significant hindered oscilla- tions and rattling of the proton inside the cage.
Although one could argue in favor of more exten- sive calculations using larger basis sets for determin- ing accurately the C –H60 q interaction, it is very unlikely that the qualitative findings of our work will change.
w x Interestingly, our ab initio calculations 16 for the interaction of Liq and He with C H6 6 show that there is a large barrier to penetration larger than theŽ C–C bond dissociation energy thus making the pen-. etration route accessible only to proton. Within the
w x local density approximation, Dunlap et al. 17 found Liq@C60 to be stable. A similar conclusion was
Ž .
arrived at for M@C60 MsLi, K and O by Li and w x
Tomanek 18 . It has also been found that the guest´ atomrion does not prefer the central position in the cage and it ‘rattles’ around, giving rise to a large
w x number of peaks in the infrared spectrum 19 .
w x
Buckingham and Read 20 , using a minimal basis set calculation, have explained how the eccentric position of Li in Li@C60 is stabilized. Hauser et al.
w21 have shown, using semiempirical and densityx functional theory calculations that the interior of the C60cage is inert and that the exterior is reactive with respect to H, F, and CH radicals.3
When it comes to the C –H60 q interaction, ener- getic considerations ionization potentials for H andŽ
w x. C60 are 13.6 and 7.54 eV, respectively 22 suggest that
HqqC60™ HqCq60q6.06 eV .
This would mean that a lot of energy could potentially be released as Hq approaches C60 and the proton may no longer remain a bare proton. It
could easily be considered to be a hydrogen atom while in the vicinity of the positively charged cage and it can still come out as a proton at the other end.
A similar mechanism has been invoked to explain the results of experiments involving high-energy Ž20–60 eV projectiles of He. q colliding with HCl
w x
targets 23 . We only wish to point out that a proton Žor a hydrogen atom could easily be trapped inside. or held outside the cage and that it can oscillate between the two minima. Furthermore, it should be pointed out that because of the differences in the interaction of Hqwith the hexagonal and pentagonal rings and the in-between positions, the proton or theŽ hydrogen atom would be expected not only to oscil-. late radially, but also ‘rattle’ around anisotropically Žsee above ..
It would be interesting to isolate C H60 qand other w x
protonated fullerenes in an ion trap 24 , for exam- ple, and study their spectroscopy.
Acknowledgements
The authors are grateful to Dr. S. Manogaran for his assistance and guidance at various stages of the work and to Dr. J. Chandrasekhar for pointing out the significance of our earlier results to fullerene chemistry. This study was supported in part by a Senior Research Fellowship to S.M. from the Coun- cil of Scientific and Industrial Research, New Delhi.
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