Molecular structure of the C70 fullerene

17 June 1994

CHEMICAL PHVSICS ELSEVIER

Chemical Physics Letters 223 (1994) 143-148

Molecular structure of the CT0fullerene Alexander V. Nikolaev a, T. John S. Dennis a, Kosmas Prassides a**,Alan K. Soper b ’ School of Chemistry andMolecularSciences, University of Sussex, Brighton BNI 9QJ, UK b RutherfordAppletonLaboratory,Didcot,Oxon OXI 1 OQX, UK Received 2 1 March

1993;in final form 20 April 1994

The molecular structure of C,e has been studied between 20 and 300 K using high-Q pulsed powder neutron difYraction of solid (&. The intra- and inter-molecular pair correlation functions were decoupled, allowing accurate determination of the intramolecular structure of CT,,.The C-C bond lengths range between R 1.38 and 1.48 A with no evidence of pinching in the equatorial region. There is essentially no change in the intermolecular structure on cooling, in contrast to the severe changes in the intermolecular pair correlation function that accompany orientational ordering.

Following the discovery of a method for preparing fullerenes [ 11, the predicted molecular structures [ 21 of C6,, (truncated-icosahedral) and CT0 (ellipsoidal) were quickly confirmed [ 3 1. The high-symmetry (I,) of the Cao molecule allowed facile experimental determination [ 4,5 ] of accurate values for the two types of C-C bond lengths (hexagon-hexagon fusions: 1.40 A, hexagon-pentagon fusions: 1.45 A). C& has also been structurally characterised, in this case all C-C bond lengths being equal within the experimental error (1.43( 1) A) [6]. The lower symmetry (DSh) of the CT0molecule (five symmetry-independent C atoms giving rise to eight inequivalent C-C bonds) has so far precluded a similar accurate determination of its molecular structure, with information coming at present from theoretical calculations [ 71, structural studies of its derivatives [ 8 J and a low-resolution electron diffraction [9] study. Here we present the results of a high-Q pulsed neutron powder diffraction study of the intra- and inter-molecular structures of pristine CT0between 20 and 300 K using a novel pair* Corresponding author.

correlation function analysis. Employing a DSh molecular model for the intramolecular structure and a free-form Monte Carlo solution for the intermolecular pair-correlation function, we extract values for the eight symmetry-inequivalent C-C bond lengths, ranging between 1.38 and 1.48 A. No pinching exists in the equatorial region of the molecule whose long and short axes are of length 7.96 and 7.12 A, respectively and show little temperature variation. In contrast, a drastic change in intermolecular distance is evident on passing through the order-disorder transition of the solid. Pure CT0 was prepared by standard procedures [ 10 1. 500 mg of sublimed solid with a face-centredcubic structure were loaded in a 5 mm diameter thinwalled vanadium can. Neutron powder diffraction data were measured by the time-of-flight technique using the small angle neutron diffractometer for amorphous and liquid samples (SANDALS) at the ISIS facility, Rutherford Appleton Laboratory, at 20, 100,200 and 300 K. The small scattering angles used ( 11”< 28~ 21”) minimised the effects of nuclear recoil in corrupting the diffraction data. The resulting

0009-2614/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDIOOO9-2614(94)00432-P

A. K Nikolaevet al. /Chemical PhysicsLetters223 (1994) 143-148

144

diffraction patterns after vanadium calibration are shown in Fig. 1. Despite the low scattering angles, the data are recorded to Q values as high as 50 A-‘. This large Q range is crucial in obtaining accurate information on the intramolecular structure of CrO.Sharp Bragg peaks are present at low Q values. The measured structure factor, S(Q), shown in Fig. 1 is related to the pair distribution function, g(r) by a Fourier-transform equation, s(a)-l=n,ijr’[g(r)-l]~dr,

ular one. In this way, the intermolecular part was allowed to take an arbitrary shape, subject only to the structure factor data, S(Q) and to the restriction that the ‘noise’, defined in terms of the second derivative of g( r), (@g(r) /ar2)2, was kept below a predetined limit, which was chosen by trial-and-error at the beginning of the simulation. The g(r) solutions were then generated by the simultaneous refinement of the intramolecular structure and the Monte Carlo optimisation of the intermolecular structure. In general, 3 x 70 - 6 = 204 independent coordinates are needed to describe the CT0molecular structure. Assuming D5,, symmetry for the molecule reduces the number of internal coordinates needed to 12 (five inequivalent C atoms) [ 7 1. However, these coordinates represent the centre of mass of the atomic positions which normally shift as a result of static and thermal disorder. While these disorder effects are complicated and correlated motion results from individual normal modes, averaging over a large number of ‘snapshots’ essentially leads to an effective decorrelation of the normal mode motion. We thus assume, as we have done before [ 5 ] for Cho,that each interatomic distance is broadened by convolution

(1)

0

where p is the atomic number density. In the present work, the inversion procedure to obtain g(r) involved the simulation of an ensemble of solutions which were both consistent with the data and optimally smooth. Analysis of the CT0radial distribution function thus proceeded by decoupling and treating separately the inter- and intra-molecular parts. While the intramolecular structure of CT0was always constrained to be consistent with ellipsoidal DSh symmetry, the intermolecular structure was treated in a model-independent manner, with the only assumption that it was much smoother than the intramolec-

I

I

I

20.

I

20 K

15.

100K

I a_ “, 10. 200K

5,

0. 15

10

25

cd',

Fig. 1. Structure factor data, S(Q) - 1, for Cl0 at 20, 100,200 and 300 K. The data are the summed results from 360 detectors situated at angles in the range 11”to 21”using neutron energies up to 35 eV.

A. K Nikolaev et al. /Chemical Physics Letters 223 (1994) 143-148

with a Gaussian profile of root-mean-square deviation, a, o(&-c)=o,

+a* @E

(2)

3

where dc= is the interatomic separation. In the present refinement procedure, the broadening parameters rrI and a2 were varied together with the internal coordinates and a weighted R-factor, Rf defined as Rf=

CQw(Q) t~(Q)ob-Z(Q)dcl 2 & m(Q) [Z(QYb”12

J

(3)

was minimised. Z(Q)* represents the data, Z(Q)“‘” is the sum of intra- and inter-molecular structure factors, and w(Q) is a weight function. The results of the refinements at 20 and 300 K are collected in Table 1. The calculated C-C bond distances are shown in Table 2 together with the dimensions of the long d1 (distance between the planes of the two pentagonal end faces) and the short d2 (diameter of the circle passing through the ten equatorial atoms) axes of the

145

Table 2 C-C bond distances (in A) in Cru at 20 and 300 K. d, is the distance between the planes of the two pentagonal end faces and d2 is the diameter of the equatorial circle. The bold numbers in parentheses refer to the C-C bond types shown in Fig. 2 from the equator towards the poles of the Cr,, molecule Bond type

20K

300K

hexagon-hexagon ( 1) hexagon-pentagon (2) within pentagon (3) within pentagon (4) pentagon-pentagon (5) within pentagon (6) pentagon-pentagon (7) within pentagon (8 )

1.479(7) 1.417(6) 1.438(4) 1.46( 1) 1.376(7) 1.449(6) 1.385(7) 1.459(4)

1.477(6) 1.415(5) 1.420(4) 1.464(7) 1.396(6) l&49(5) 1.382(6) 1.460(4)

4

7.960(6) 7.123(7)

7.968(4) 7.125(5)

dz

Table 1 The optimised coordinates (in A) of the five inequivalent atoms in Cm(DR, symmetry) at 20 and 300 K. The molecule is oriented with its five-fold symmetry axis along the z direction. The broadening parameters u1 and q and the R-factors are also included coordinates

atom 1

20K

300K

3.253(3) 1.450(2) 0.0

3.254(2) 1.451(2) 0.0

3.390(3) 0.719(2) 1.206(4)

3.394(2) 0.710(2) 1.197(3)

2.779(2) 1.169(3) 2.452(3)

2.786(2) 1.161(2) 2.450(2)

Z

2.398(3) 0.0 3.219(2)

2.394(2) 0.0 3.223(2)

x Y I

1.241(2) 0.0 3.980(3)

1.242(2) 0.0 3.987(2)

4.6 0.012 0.030

2.2 0.013 0.032

x Y Z

atom 2

x Y Z

atom 3

X

Y Z

atom 4

X

Y atom 5

R-factor (%) 01 (A) uz (A”*)

Temperature

Fig. 2. The CT0molecule with the eight symmetry-inequivalent C-C bonds consecutively numbered from the equator towards the poles.

molecule (Fig. 2). The present results clearly discount the existence of a pinching in the waist of the molecule, as claimed in ref. [ 9 1. The five hexagonal faces around the equator comprise two types of bond lengths which are essentially equal ( x 1.42 A) and are joined together by the longest C-C bonds of the molecule ( x 1.48 A). This is consistent with the chemical inertness exhibited by the equatorial region of the molecule. On the other hand, the polar regions exhibit bond length patterns reminiscent of ChOand mimic its chemical behaviour, essentially acting as electron-deficient oletins. Little change in the intramolecular structure is evident between 20 and 300 K (Fig. 3 ) with the long and short molecular axes re-

146

A. V. Nikolaev et al. /Chemical Physics Letters 223 (1994) 143-148

5-

measurements and reported excellent agreement. The atomic displacements due to the zero-point motion are found to be %0.07 A [ 111 and in excellent agreement with the essentially temperature-independent thermal broadening factor ( x0.05-0.06 A) introduced in the present study. In contrast, the intermolecular radial distribution functions (Fig. 4) show significant changes between 200 and 300 K. This result can be understood in terms of molecular orientational ordering accompanying the phase transitions of solid CT0 [ 13,141. At 300 IS, the present sample adopts a face-centred-cubic structure [ 13,15 ] in which the C,,, molecules perform a diffusive type of motion, characterised only by a small anisotropy. On cooling below =270-280 K, orientational ordering is accompanied by the molecules aligning themselves along the unit cell diagonals and spinning about their long molecular axis, while at the same time there is some orientational disorder of the long axis itself [ 161. Fig. 5 shows an expanded view of the intermolecular g(r) between %3 and 7 A at 200 and 300 K. The room temperature data are very smooth, indicating the absence of significant intermolecular correlations and extend down to * 2.9 A. At 200 K, pronounced oscillations in the g(r) have appeared with the data extending to distances of x 3.05 A. A somewhat surprising feature of our results is the closer intermolecular contact which is evident at room temperature when compared to the 200

RT

O0

I

I

I

I

I

I

1

2

3

4

5

6

I 7

6

C-C distance (A)

Fig. 3. Calculated intrumolecular pair correlation function g(r) for CT0at 20,100,200 and 300 K.

maining essentially constant at 7.96 and 7.12 A, respectively. In general, our results are in excellent agreement with the various theoretical calculations as well as the CT0structure derived from X-ray crystal structure determinations of CT0derivatives. More specifically, Onida et al. [ 111 have recently performed a comparison of their ab initio molecular dynamics calculations of CT0with both the present experimental data and inelastic neutron scattering [ 12 ] 1

I

I

I

I

I

2.520 K

10

15

20

25

30

C-C distance (A)

Fig. 4. Calculated intermolecular pair correlation function g( r) for Cm at 20,100,200 and 300 K.

A. K Nik&ev et al. /Chemical PhysicsLetters 223 (1994) 143-148

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

147

8.0

C-C distance (A)

Fig. 5. Calculated intermolecularpair correlation function g(r) for Crc at (---) 200 and (--) 300 K in the range 2.9 to 8 A. orientational ordering is clearly seen at 200 K. The onset of intermolecular correlations increases from = 2.90 A at 300 K to = 3.05 200K. K data, despite the lattice contraction which has occurred. This may be understood in terms of simple geometrical considerations, taking into account the ellipsoidal shape of CT0and the change in the dynamics that accompanies the phase transition. The reorientational motion in the fee phase results in an enlarged quasi-spherical shape for the molecules, permitting closer intermolecular contact than in the low-temperature rhombohedral and monoclinic phases when the molecules have ordered with their long molecular axes essentially pointing along the unit cell diagonals. In conclusion, we have refined independently both the intra- and inter-molecular structures of CT0 between 20 and 300 K. The C-C bond lengths span a somewhat wider range than in Cso but still not large enough to result in well-separated peaks in the measured pair correlation function. We have established that the equatorial hexagons show little bond alternation and are joined by very long bonds, thus accounting for the lack of reactivity of CT0away from its polar regions. Orientational ordering effects are clearly seen in the intermolecular g(r), while the intramolecular part is barely affected with changes in temperature.

We thank C. Christides for help with the experiments and W. Andreoni and P.W. Fowler for useful

discussions. The work is supported by the Science and Engineering Research Council and the Royal Society. We also thank SERC for access to ISIS.

References [ 1 ] W. Krizltschmer, L.D. Lamb, K. Fostiropoulos and D.R. Huffman, Nature 347 ( 1990) 354. [2] H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl and RR. Smalley, Nature 318 (1985) 162. [ 31 R. Taylor, J.P. Hare, AK. Abdul-Sada and H.W. Kroto, J. Chem. Sot. Chem. Commun. (1990) 1423. [4] R.D. Johnson, G. Meijer, J.R. Salem and D.S. Bethune, J. Am.Chem.Soc.113(1991)3619; W.I.F. David, R.M. Ibberson, J.C. Matthewman, K. Prassides, T.J.S. Dennis, J.P. Hare, H.W. Kroto, R. Taylor and D.R.M. Walton, Nature 353 (1991) 147; F. Li, D. Ramage, J.S. Lamin and J. Conceicao, Phys. Rev. B44(1991)13167; S. Liu, Y. Lu, M.M. Kappes and J.A. Ibers, Science 254 (1991) 408; H. Hedkg, L. Hedberg, D.S. Bethune, C.A. Brown, H.C. Dom, RD. Johnson and M. de Vries, Science 254 (1991) 410; H.B. Bth@, R. Blanc, D. Schwamenbach, S. Liu, Y. Lu, M.M. Kappes and J.A. Ibers, Angew. Chem. 31 ( 1992) 640. (5lA.K. Soper, W.I.F. David, D.S. Sivia, T.J.S. Dennis, J.P. Hare and K. Prassides, J. Phys. Condens. Matter 4 ( 1992) 6087.

148

A. K Nikdaev et al. /Chemical Physics Letters 223 (1994) 143-148

[6] K. Prassides, C. Christides, I.M. Thomas, J. Mizuki, K Tanigaki, I. Hirosawa and T.W. Ebbesen, Science 263 (1994) 950. [7] K Ra8havachari and C.M. Rohlfing, J. Phys. Chem. 95 (1991) 5768; F. Negri, G. Orlandi and F. Zerbetto, J. Am. Chem. Sot. 113 (1991) 6037; G.E. Scuseria, Chem. Phys. Letters 180 ( 199 1) 45 1; J. Baker, P.W. Fowler, P. Lazzaretti, M. Malagoli and R. Zanasi, Chem. Phys. Letters 184 ( 1991) 182; C.Z. Wang, C.H. Xu and LH. Ho, Phys. Rev. B 46 (1992) 9761; W. Andreoni, F. Gygi and M. Parrinello, Chem. Phys. Letters 189 (1992) 241. [8] A.L. Balch, V.J. Catalano, J.W. Lee, M.M. Olmstead and S.R. Parkin, J. Am.Chem.Soc. 113 (1991) 8953; G. Rothand P. Adelmann, J. Phys. I (Paris) 2 (1992) 1541. [ 9 ] D.R. McKenzie, C.A. Davis, D.J.H. Cockayne, D.A. Muller and A.M. Vassallo, Nature 355 (1992) 622. [lo] K Prassides, T.J.S. Dennis, C. Christides, E. Roduner, H.W. Kroto, R. Taylor and D.RM. Walton, J. Phys. Chem. 96 (1992) 10600.

[ 111 G. Onida, W. Andreoni, J. Kohanoff and M. Parrinello, Chem. Phys. Letters 219 (1994) 1. [ 121 C. Christides, A.V. Nikolaev, T.J.S. Dennis, K Prassides, F. Negri, G. Grlandi and F. Zerbetto, J. Phys. Chem. 97 (1993) 3641. [ 131 C. Christides, I.M. Thomas, TJ.S. Dennis and K Prassides, Europhys. Letters 22 ( 1993 ) 6 11. [ 141 G.B.M. Vaughan, P.A. Heiney,D.E. Cox, J.E. Fischer,A.R. McGhie, A.L. Smith, R.M. Strongin, M.A. Cichy and A.B. Smith, Chem. Phys. 178 (1993) 599. [ 151 C. Christides, T.J.S. Dennis, K Prassides, R.L. Cappelletti, D.A. Neumann and J.R.D. Copley, Phys. Rev. B 49 ( 1994) 2897. [ 161 T.J.S. Dennis, K. Prassides, E. Roduner, L. Cristofolini and R. DeRenzi, J. Phys. Chem. 97 (1993) 8553; R. Blinc, J. Dolinsek, J. Seliger and D. Arcon, Solid State Commun. 88 (1993) 9; R Tycko, G. Dabbagh, G.B.M. Vaughan, P.A. Heiney, R.M. Strongin, M.A. Cichy and A.B. Smith, J. Chem. Phys. 99 (1993) 7554.