J. CHEM. SOC. FARADAY TRANS., 1994, 90(18), 2791-2797 Single-crystal Structure of C,, at 300 K Evidence for the Presence of Oxygen in a Statically Disordered Model W. Bensch, H. Werner, H. Bartlt and R. Schlogl*$ lnstitut fur Anorganische Chemie University of Frankfurt, Marie-Curie Str. II,60439 Frankfurt, Germany The structure of solvent-free single crystals of sublimed c6, has been analysed at 300 K by X-ray diffraction. A unique solution of atom coordinates gave a satisfactory agreement with the intensity data. This indicates that the c60 balls exhibit a time-averaged preferred position in the crystals which are, however, heavily affected by rotational disorder. The structure reveals the truncated icosahedral molecular shape with two sets of carbon- carbon bond distances.Contour plots indicate the anisotropic distribution of electron density within the almost perfectly spherical shell of the molecule. The analytically pure crystals contained an impurity of molecular oxygen located statistically over some hexagons of each 'buckyball ' resulting in a limiting stoichiometry of c60 O2. Based on NMR,'.' X-ray diffraction studies3v4 and neutron diffraction data5 it is frequently assumed that within the molecular crystals of c60 the highly symmetric buckyballs rotate freely at 300 K. This would preclude structure analysis by diffraction methods at atomic resolution. The high molec- ular symmetry of the buckyball allows for such molecular dynamics, the detailed explanation of which, in terms of the nature of the intermolecular interaction potential, has led to considerable and controversial theoretical effort^.^.^ Very recently, the NMR interpretation of isotropic rotation with a high rotation frequency close to the value of free rotation was stated again in a study of the orientational ordering of c60.' One way to suppress the adverse influence of the molecular dynamics of the free molecules is to use low-symmetric deriv- atives of c60 either as metal-organic complexes9-" or cla- thrate c~mpounds.'~-'' A significant body of detailed structural information has now emerged from such studies confirming our general picture about the molecule but differ- ing in numerical details relevant for e.g.theoretical studies. This may be related to a certain distorting effect of the inter- acting ligands on the pristine structure. Another method to analyse the atomic structure of ful-lerenes is their analysis at very low temperatures where molecular dynamics is frozen out. Such studies carried out on powders5 and on single crystals4 yielded both structural details and information about the restricted molecular dynamics at intermediate temperatures.One study16 using precision intensity data measured as function of temperature found a first-order transition at 259 K followed by a complex evolution of orientational ordering with two anomalies at 165 K and 85 K. In addition, time-dependent effects of heating and cooling on diffracted X-ray intensities were noted. The numerous studies on the solid-state dynamics below the first- order phase transition with diffraction techniques, thermal methods and spectroscopy are summarised in a detailed review.17 In there it is pointed out that disorder is an intrin- sic property of a high-symmetry crystal made from molecules with non-crystallographic symmetry elements.The single-crystal structure of the OsO, derivative of c60 yielded a football made up from flat pentagons and hexagons in the expected topology with a radius of 351.2(3) pm and two types of bonds of length 138.8(9) and 143.2(5) pm. The t Institut fur Kristallographie der Universitat Frankfurt. $ Present address: Fritz Haber Institut der Max-Planck Gesell- schaft, Faradayweg 4, D-14195 Berlin, Germany. synchrotron powder diffraction study of pure c6, at 300 K was analysed with a model of freely rotating carbon atoms describing a sphere of homogeneous electron density with a radius of 352(1) pm.Numerous st~dies~-',~' have reported a phase transition at ca. 250 K associated with a change of the lattice type from centred F into simple cubic P.A phase tran- sition was also observed in NMR which con- cluded that in the high-temperature form the molecular carbon resonance is motionally narrowed by either free rota- tion or a rapid jump rotation. The transition temperature was, however, significantly lower as observed by diffraction and by thermal In a more detailed analysis21 the longitudinal relaxation time was found to exhibit, at 250 K, an anomaly which was interpreted as an indication of a transition from an almost free rotation to a jump rotation with a change in rotational barrier from the high-temperature value of 50 meV to a low-temperature value of 250 meV.Details of this analysis can be found in the review17 on the ordering transition. The recent DTA study" detected two high-temperature transitions at 250 and 310 K and con-cluded that structural and molecular-ordering transitions may be independent phenomena in the complex molecular dynamics of fullerenes. The transition temperature for the structural phase transition from fcc (face-centred cubic) to sc (simple cubic) varies in the literature between 249 and 260 K.22 This discrepancy in the detection of a first-order tran- sition which should exhibit a sharp change in the ordering parameter arises from different techniques of observation (diffracted intensities, thermal conductivity, electrical conductivity) and different definitions of the transition tem- perature (onset, inflection or completion of the anomaly) but implies further that details of the crystal quality may influ- ence the solid-state dynamic properties.The structural analysis of solvated varieties has clearly shown how important the sample purity is for an analysis of this solid, being affected by extraordinary rotational disorder effects arising from the highly symmetric shape of the molecu- lar units. It is often assumed that c60, after sublimation in high vacuum, is pure and air stable at ambient conditions.It could be shown, however, that purified c60 does take up molecules from its gaseous environment and intercalates them into its void ~ystem.~~-~~ The kinetics of gas uptake is severely affected by the stacking defect density of the solidz4 and may vary from crystal to crystal as has been recently illustrated by high-pressure studies27 which gave clear evi- dence of the dependence of the phase-transition temperature on the structural and chemical integrity of the c60 material. For this reason special attention is given to the possible pres- ence of molecular oxygen in the crystals. The importance of lattice defects for the solid-state proper- ties was also highlighted in a study2' of c60 by low-temperature high-resolution electron diffraction crystal-lography. Superlattice structures which were not detectable by integral X-ray diffraction methods,' were clearly apparent in the spatially high resolving electron diffraction patterns.The presence of such ordered defects in addition to stacking order defects will affect the structural dynamics directly and indirectly oia a modified rea~tivity~~,~,towards various gases. The purpose of the present single-crystal diffraction study using conventional crystallographic tools is to test the possi- bility of obtaining structural data at atomic resolution of nominally pure c60 at ambient temperature. First results were reported previously30 showing the phase transition to occur in our crystals at 255 K by the criterion of non-zero reflections forbidden in the fcc phase which is fully in agree- ment with later literature reports.,, Most of the diffraction studies published so far used either sub-ambient tem-peratures, derivatives of c60 or unconventional diffraction techniques and focused on the structural dynamics of the material.The present study is intended to serve as a reference for structural investigations of molecular adducts of fullerenes with single-crystal techniques. In addition, the effect of molec- ular oxygen, unavoidably present in fullerenes handled in air, on the crystal properties will be explored. Finally, as the importance of lattice defects as an essential property of highly symmetric fullerene solids was already stressed in the liter- ature,I7 it seems justified to address a possible discrimination between intrinsic structural properties occurring in all indi- viduals of solid C,, and extrinsic properties which may differ in each crystal of this molecular solid.Results The Material Home-made c60 was highly purified23 and sublimed. Single crystals of 0.1 mm length suitable for structural analysis were grown from the purified powder using the sublimation tech- nique. Several batches were investigated with growth times between 1 and 20 days. A total of 25 crystals were investi- gated with rotation photographs showing frequent twinning of equally large crystals. Only crystals without this twinning were further studied3' at 300 K, at 255 5 K and at 100 K.The present study focuses on the room-temperature structure of c60 and is complementary to structure determinations at low temperatures4v3 below the structural phase transition. FTIR measurements showed that the samples of purified c60 were clean to the standard discussed in a recent vibra- tional study of the structural phase tran~ition.~~ We note that in our spectra and in all literature data the intensity ratio of the spurious doublet at ca. 2327 cm-' did not change with the intensity ratios of the four main fullerene lines. This is taken as indication that a trace of CO, is present in the crys- tals. The densities of several single crystals were determined by the flotation method and found to be on average 1.765 g cm-over seven crystals of batch c with values ranging from 1.74 to 1.77 g ~m-~.Analysis of these crystals with energy- dispersive X-ray spectroscopy gave no detectable impurities of alkali metal or silicon. All handling of the material was done under purified Ar and structure determinations were carried out with the crystals sealed under Ar in Lindemann capillaries. A systematic investigation of the sample density with subli- mation parameters revealed a clear dependence of the density on the velocity of material deposition in the hot zone. The J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 20 15 10 5 r-:10 Q)CI.c 5 0 15 10 5- 0- I I a 10 12 28/degrees Fig. 1 Section of powder diffraction patterns around the (111) reflection (Cu-Ka transmission geometry, samples in Lindemann tubes) of three batches (a, b, c) of sublimed C6*.The asymmetric 'foot' superimposed on the normal Bragg reflection arises from stacking defects.averaged density varies from 1.765 g cm-3 (batch c) for 20 days to 1.720 g (batch b) after 2 days to 1.694 g (batch a) for rapid sublimation within 1 day. The calculated density of pure c6, is 1.689 g cm-3 with four molecules in the unit cell (lattice parameter 1415.2 pm). Note that the measured density is significantly above this value despite the diluting effect of lattice defects present in real crystals. High-resolution powder diffraction data of the three sample batches indeed revealed differences in stacking order.Fig. 1 shows the enlarged portion of the diffractograms around the (111) reflection revealing a varying degree of stacking disorder indicated by the wedge-shaped wide 'foot' of the main peak.33 These findings suggest strongly the presence of a light-element impurity in varying amounts. The impurity was iden- tified by several analytical methods including tempera-ture-programmed desorption (TPD), FTIR measurements, isotope labelling experiments and EPR spectroscopy. There is no doubt that the crystals contained extra oxygen present at 300 K as molecules. Heating above 450 K in inert atmo- sphere or vacuum removes most of the oxygen. Exposure to oxygen at elevated temperatures leads to the formation of epoxides and eventually to fullerene decomposition with evolution of CO and CO,.Details of the reaction analysis can be found el~ewhere.,~-,~ The identification of intercalated oxygen in single crystals of C,, showing no signs of structural disorder or defects in X-ray photographs but exhibiting a too high density is regarded as a significant finding and will be illustrated by an experiment carried out with batch c of the material used in the present study. Note that the crystals were optically smooth and exhibited a dark lustre in the microscope. Such material was heated in ultra-high vacuum to the sublimation temperature of ca. 700 K and exposed, after cooling to 300 K, to an atmosphere of 1802 and I6O2. After evacuation at 300 K the crystals were exposed to lo-, mbar I6O2 and heated at a rate of 0.25 K s-' to 650 K.The mass spectrometric response recorded with parallel detection is displayed in Fig. 2. The desorption of molecular oxygen of masses 32 (l6O,) J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Fig. 2 Temperature-programmed desorption of 180,-labelled oxygen from C,, . The desorption intensities (measured with a quad- rupole mass spectrometer equipped with a multichannel option from Hiden Analytical and processed for background contributions) were observed during a linear heating experiment of ca. 10 mg material of batch b under a vacuum of 1 x mbar. Dosing was done in situ at 450 mbar. The fragments chosen illustrate the (isotope labelled) evolution of CO (m/z 28, 29), 0, (m/z 32, 34, 36) and CO, (m/z 44,46, 48).The intensity scale is equal for all fragments and indicates the ion current in A. and 36 (1802) is clearly evident. No scrambling products at m/z 34 were observed indicating the molecular nature of the intercalate. Above 580 K oxidation of the fullerene caused the evolution of CO and CO, . The significant amounts of l80 incorporated indicate that the intercalated molecular oxygen acted as a precursor in the oxidation reaction. The small amount of CO being desorbed with the molecular oxygen was caused by incomplete reversibility of the intercalation : purification of c60 from oxygen in high vacuum always leads to a small amount of gasification products which are co- intercalated into the fullerene crystal.Single-crystal Data Collection and Data Reduction X-Ray studies were performed on a CAD-4 instrument at 300 K (Cu radiation) and on a STOE AED I1 instrument in the temperature range 100-300 K with Mo radiation. The known structural phase transition at ca. 250 K was found3' with all crystals at 256 & 3 K. The change of the lattice type was fol- lowed by the intensity changes of several reflections of the P system not allowed in F symmetry which occur irrespective of the heating/cooling rate (between 1 and 20 K h-') reversibly and in a narrow temperature range of a few K. An integral investigation of the transition with oriented oscil- lation photographs (orientation [ 1001, 30" oscillation angle, cooling rate 8 K h-I) showed that at 254 K the expected additional P-allowed reflections3' begin to occur.Further cooling to 100 K caused a significant gain in intensity of the sharp reflections besides partial disintegration of the crystal into micro-domains as seen from rings of diffracted intensity. Warming to 300 K for 24 h restored the initial crystal quality (reflection profiles). The volume of the unit cell changed from 2.8344 x lo3 pm3 at 300 K to 2.7976 x lo3 pm3 at 200 K and to 2.7759 x lo3pm3 at 100 K. The crystal structure at 300 K was determined from a crystal of batch c using a data set collected with Cu radiation in the 28 range from 2" to 148" yielding 1532 observations. The density of the crystals as well as the volume of the unit cell require four c60 molecules per translation unit.The point symmetry of the molecule is m35 of which m3 is a subgroup satisfying the crystallographic translational requirements. It is plausible to adopt this symmetry for the crystal structure model of a face-centred cubic closed-packed arrangement of the buckyballs. The resulting space group in accordance with the point symmetry is Fm-3. With this assumption the mea- sured intensities reduce into 281 unique data with an internal R value of 2.55%. The lattice constant was at 300 K 1415.2(1) pm, at 200 K 1409.1(2) pm and at 100 K 1405.4(3)pm. The alternative space group Fm-3m requires an additional four-fold symmetry axis which would in a non-twinned crystal only be possible with a special packing of two pairs of molecules rotated by 90".Merging the intensities in space group Fm-3m leads to 187 unique data with an internal R value of 3.22%. The difference in the internal R values between the two Laue groups amounts to 0.67% which is too small as a single indication for a clear distinction of the correct space group. In Laue group m3 the intensities are only cyclically permutable whereas in m3m the intensities are permutable. The sensitive intensities I(hkZ) and Z(khl) were thus extracted from the measured data set and averaged in the two Laue groups. This procedure yields an internal R value of 4.30% for m3 and 5.93% for m3m. These results together with the observation that the least-squares refine- ments in the space group Fm-3 lead consistently to a better model, led us to conclude that Fm-3 is the correct space group for the present crystal.Single-crystal diffraction data sets collected from various crystals grown from batches a and b as starting material yielded similar but non-identical lattice parameters and inten- sity distributions in the scattering law. Some examples are listed in Table 1. Using the described method for distinction of the space group the difference in R value between the two possibilities varied significantly with one example yielding even better R value for the space group Fm-3m. The scattering law for the crystal of batch c, i.e. the total scattered intensity as a function of the scattering angle is dis- played in Fig. 3. This unusual representation of a single-crystal data set shows that the total scattered intensity decays rapidly with the scattering angle indicating significant dis- order within the crystal.The intensity shows in addition an unusual periodic modulation which is caused by the spherical shape of the buckyball molecule. Its description with a homo- geneous sphere of electrons represented by a higher-order Bessel function3 (in the shape of the envelope of the intensity distribution) is, however, for small scattering angles a poor representation of the scattering law. Structural Model In the early stages of refinement attempts were made to fit the observations with three unique C atoms with isotropic Table 1 Structural parameters of several single crystals of C,, crystaldesignation (batch lattice parameter and number) symmetry IPm b5 cubic 1416.6 (30) b7 cubic 1405.4 (20)" 1417.9 (2) b 11 cubic 1406.9 (l0)ll 1415.8 (2) a1 cubic 1418.2 a2 cubic 1415.5 (1 1) a3 cubic 1417.7 a7 cubic 1419.9 (5) hexagonal 1003, 1003, 2456 " Determined at 100 K.2794 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 'Oo0 1 0.1 0.2 0.3 0.4 0.5 0.6 sin Of2 Fig. 3 Scattering law of C6, at 300 K. The integrated intensity dis- tribution is shown for an average in space group Fm-3. thermal parameters. Only one set of parameters and a restrained variation of the bond lengths [C(l)-C(2): 142.0(5) pm, C(2)-C(3): 134.q5) pm, C(1)-C(3): 243.q5) pm] led uniquely to the truncated icosahedral shape of the molecule with a diameter of 348 pm.This model yielded R values between 30% and 40% depending on the constraints and the number of observations used. In the following steps starting values for the main axes and orientations of the probability ellipsoids were applied such as to simulate the spherical average surface of the buckyball. In this stage of refinement it is essential to assign the correct signs to the different U,, whereas the magnitude of the Uii and U, displacement parameters is of minor importance. No further constraints were applied to the anisotropic displace- ment parameters during the refinement. Different disorder models were considered with split sites for the three carbon atoms to account for possible static rota- tional disorder.The main problem of such models was, as expected, to find the correct site occupation factors (sof) for the splitted carbon atom sites as the sof are highly correlated with the displacement factors. Several disorder models gave better R values which may be due to the enlarged number of parameters. In all cases, however, the anisotropically refined carbon atoms were not defined positively. Therefore, we decided to refine the structural model with only three carbon atoms with the disadvantage of high values for the U, com-ponen ts. The final refinement of the three carbon atom model resulted in an R value of 14.3%using 270 observations and 24 parameters. The highest residual electron density of 0.375 x e pm3 was located above 8 of the 20 hexagons at a distance to carbon of 147 pm.This relatively low electron density must be compared with the electron density of a carbon atom found in a difference Fourier synthesis using only two carbon atoms in the refinement procedure. The refinement with C(2) and C(3) (80% total scattering power from the C atoms) exhibited a difference peak with a height of 0.59 x e pm3 for the missing C(l) atom. It needs to be considered that the residual electron density pointing to an additional atomic site above some of the six-membered rings may be an artefact from series termination effects. The only selective occurrence and the high overall temperature factor of the structure render this explanation highly unlikely.Keeping in mind the proven presence of molecular oxygen and noting that the (hOO) reflections were non-zero in intensity we concluded that the additional atomic site marks one atom of the oxygen molecules attached to the buckyballs. Fig. 4 Average structure of the C,, molecule with its oxygen adduct in the crystal at 300 K. The three unique carbon atoms are labelled. The oxygen molecules occur with detectable electron density only for the bonding atom, the free arom has too many inequivalent locations in the void of the crystal packing (see text). The position of each oxygen atom is only partly occupied. An oxygen atom Cjustified by non-crystallographic arguments) on a partially occupied special position was included in the refinement.The sof of the oxygen atom was refined to 0.029(4) [U,,= 0.05(1)]. This complies with eight atoms per unit cell (maximum stoichiometry C,,O,) resulting in a perfect match between calculated and measured densities. The R value reduced finally to 11.20% (270 observations, 29 parameters) with the weighted R value coming down to 5.18%. This value needs to be compared with the literature data from powder profile refinements of 8-10%17 and with the internal R value of our data set of 4.30%. The resulting molecular shape of the oxygen adduct with C,, is displayed in Fig. 4. The parameters of this model are given in Table 2. The dashed oxygen atom positions indicate one atom of an oxygen molecule chemisorbed to the surface of a buckyball molecule.This coordination is not to be mis-taken for a covalent bond, as an increase in temperature of less than 100 K is suficient to remove the interaction (see Fig. 2). The short distance of 30 pm between the molecule and the carbon surface is indicative of a significant dipolar intera~tion~~between the molecules giving rise to the EPR23 signal of the adduct. The low binding energy of the adduct despite the significant orbital interaction is in line with the electron-poor character of the C,, molecule. The other atom of the oxygen molecule has many locations owing to the lack of spatial constraints in the voids of the fullerene crystal so that it does not show up as a clear maximum in the difference Fourier map. For the buckball two sets of bond lengths of ca.134 and 142 pm were obtained. These values are artificially shortened by the rotational disorder as discussed by Bur@ et aL4 and no meaningful correction is possible in the present model without data about the details of the disorder. The model Table 2 Parameters of the unique structural elements for c6, at 300 K atom X Y z U C(1) C(2) C(3) 0(1) 0.2349 (5) 0.2015 (5) 0.1722 (4) 0.1379 (5) 0.0 0.0845 (4) 0.1599 (2) 0.1379 (5) 0.0517 (7) 0.0946 (4) 0.0469 (7) 0.1379 (5) 0.358 (4) 0.482 (4) 0.430 (4) 0.150 (4) J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 requires, however, two sets of bond lengths with a difference of ca. 5 pm in order to yield a buckyball as solution. It was noted that the other models which do not expand into even- shaped balls lead to bond lengths in better agreement with gas-phase data34 and lead also to better R values but are considered as chemically meaningless.The carbon atoms exhibit large anisotropic displacement parameters (ADP) indicating significant intermolecular dis- order (projection of different rotamers). The overall effect of such high ADP on the calculated structure factors is their faster decay with increasing scattering angle compared to a well ordered situation. Exactly this is observed experimen- tally, as illustrated in Fig. 3. A significant improvement of the R value towards the internal R value may thus be achieved artificially by omitting suitable observations or in a physi- cally meaningful manner by considering different rotamers in the model. This latter procedure was successfully applied to the low-temperature structure which was explained by the superposition of two unequally populated rotamer~.~By assigning the phase transition of 250 K to an order-disorder transition it may be seen as an increase in the number of rotamers from two to a finite larger number at high tem- perature.Their small difference in energy renders it, however, inadequate to model these high-temperature rotamers con- sidering the other types of influences on the orientational dis- tribution as there are stacking defects and impurities. It is, further, quite likely that their population is different from crystal to crystal. The finite number of rotamers differs from the picture of free rotation and requires an averaged uneven electron dis- tribution on the buckyball surface.This is demonstrated by electron-density maps within and perpendicular to the least- squares plane of one hexagon of the buckyball. Results at various temperatures are shown in Fig. 5. It is evident that the electron density in the high-temperature form is smeared out but not uniform. Lowering the temperature through the t t Fig. 5 Electron density distribution, s, calculated from the measured scattering law for one six-membered ring at various temperatures (top 300 K, centre 248 K, bottom 100 K). The electron density maximum (at the calculated atom positions denoted by dots) is 3.5 x lop3e ~m-~.The length scale is in units of 5 pm. Fig. 6 Electron contour plot of a section through the equator of two C,, molecules at 300 K. The dots represent the atom positions of the six-membered ring used for the electron contour plots in Fig. 5. The contours range from 0.5 x to 3.5 x e pm-’. phase transition reduces the number of rotamers and clearly improves the localisation of the electron density at the ring corners. This must not be mistaken for a change in the intra- molecular electron density distribution as it is only a conse- quence of the reduction in the number of projected rotamers. In addition, we found that the variation of the observed structure amplitudes with increasing scattering angle is aniso- tropic for different directions (the plot in Fig.3 is the spatial average). Such a modulation is not in agreement with the expected scattering factor for a freely rotating buckyball. The cross-section through the electron density distribution at the equator of one buckyball at 300 K in Fig. 6 shows the expected hollow structure of the buckyball and the empty void space between the molecules. A thin shell of electrons in an inhomogeneous internal distribution forms the wall of the molecules. It becomes apparent that the representation of a C6, molecule as a giant atom is a poor approximation of its spatial electron distribution. A group scattering factor for a c60 ball was calculated using the program NORMAL with the MULTAN package. In agreement with the observed electron-density distribution and the progress of the observed structure factors (see Fig.3) this calculated structure factor exhibits strong modulations in contrast to the shape of a scattering factor derived from a hollow sphere of electrons distributed on the surface of a c60 ball. Discussion The successful analysis of the diffracted X-ray intensity dis- tribution in terms of an atomically resolved molecular struc- ture with a clear minimum between observed and calculated intensities for one set of atomic parameters excludes the model for the molecular dynamics of free isotropic rotation of independent buckyballs in the crystal at 300 K. The present study confirms the shape of the c60 molecule in its crystal at 300 K and illustrates the dominating influence of the rotational disorder on the crystal structure.The time- and space-averaging X-ray diffraction experiment cannot dis- tinguish between a hopping rotation dynamic disorder at 300 K and a static rotational disorder. Time-resolved structural clearly reveal the dynamic nature of the dis- J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 order. It may be described as a tumbling motion of the mol- ecules between several orientationally inequivalent states. The 2D NMR observation^",^^ and the neutron scattering studies5 imply that, indeed, a complex motional system with more than two states is present. These observations let us hesitate to try to fit our observations to a two-state rotation- al disorder system as was done by Bur@ et d4Such models yield good agreements between calculated and experimental scattering laws but overestimate the physical content of the static X-ray diffraction experiment.The measured scattering law is, however, satisfactorily described with a conventional model of a perfect buckyball with the well known point sym- metry of the c6, molecule expanding from one set of three unique carbon atoms. There is no necessity to invoke a special des~ription~,~~*~~,~~ of the crystal structure in terms of a modulated spherical electron distribution which ends at a picture with the same physical content as the present analysis. If the aim of a structural study is the determination of atomically resolved dimensional parameters, then the concept of using sets of derivatives of c60 with large ligands symmetrically bonded to the balls may be more successful than building complicated models of the disorder of the free fullerene molecule which may fall short of physical justification’ within a diffraction experiment.These findings have implications for the solutions of struc- tures of fullerene derivatives in which the buckyballs retain their shape. There is no a priori reason to assume the absence of rotational disorder in compounds without the phase tran- sition at 250 K. In such cases, as represented by intercalation compounds, the fullerene molecules may either be statically disordered (frozen state of the dynamic structure of the pris- tine molecule, ‘glassy’) or slowed in their dynamics resulting in a different phase-transition temperature.Incorporation of neutral molecules such as pentane or noble gases in the void system of c60 does modify the molecular dynamics of such crystals as has been shown by high-pressure treatments fol- lowed by DTA analy~is.’~ Ordering of the c60 molecules with respect to each other would occur at finite temperatures if the undirected intermolecular interaction would be signifi- cantly amplified by spatially modulated charges on each mol- ecule. Such a situation will occur upon charge transfer from the guest species intercalated in the crystal and localisation of the extra charges within the c60 electronic structure. In this sense it may be possible that the space group of a given single crystal may depend on the abundance of polar- ising oxygen molecules which affect the intermolecular orien- tation (e.g.by forming pairs of buckyballs). The distribution of the rotamer population over a large but finite number of possibilities in the fcc phase varies, in the absence of a signifi-cant energy barrier,21 with the growth history of the crystal and seems thus not to be specific for the material c60. This was illustrated by the variation in structural properties of single crystals grown with varying rates of sublimation (see Fig. 1 and Table 1). The parameter variation reflects the dis- order of the molecular crystals. For this reason the choice of space groups which is only differentiated by the relative inter- molecular orientation is also affected by the rotational dis- order and may thus be either Fm-3 or Fm-3m depending on the rotamer population.The definitive statement about the correct choice of the space group for the material c60 which ‘does not adopt the Fm-3 space group at any temperat~re’~seems in the light of the present discussion overstated. The electron density contour plot of Fig. 6 shows clearly that the buckyballs naturally exhibit nodes in the potential distribution which may cause the energy barriers in the rota- tion process required for a jump mode. It is pointed out that the nodes appear even in the experimental electron distribu- J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 2797 tion which is the average over several rotamer orientations.6 K. H. Michel, J. R. D. Copley and D. A. Neumann, Phys. Rev. This result is fully in line with a synchrotron room-temperature single-crystal diffraction study3 arrived at after a different structure analysis with a modulated spherical elec- tron distribution and a spatial inhomogeniety of +lo% of the total electron density of the molecule. The density variation of many single crystals has shown 7 8 9 Lett., 1992,68, 2929. E. Burgos, E. Halac and H. Bonadeo, Phys. Rev. Lett., 1992, 68, 3598. R. Blinc, J. Seliger, J. Dolinsek and D. Arcon, Phys. Rev. B, 1994, 49,4993. J. M. Hawkins, A. Meyer, T. A. Lewis, S. Loren and F. J. Hol- lander, Science, 1991, 252, 312. the range of impurity doping. The identification of purified and cleanly handled c60 as oxygen adduct has implications beyond the possible effect of these additional molecules on the molecular dynamics of the crystals.The interaction between oxygen and c60 is much reduced as compared to 10 11 12 A. L. Balch, V. J. Catalan0 and J. W. Lee, Znorg. Chem., 1991, 30,3980. P. J. Fagan, J. C. Calabrese and B. Malone, Science, 1991, 252, 1160. B. Morosin, P. P. Newcomer, R. J. Baughman, E. L. Venturini, D. Loy and J. E. Schirber, Physica C, 1991,84,21. that in the epoxide C6,0. The epoxide exhibits, however, the same fcc structure as pristine c60 and undergoes a structural phase transition similar to that of pure c60 .38 This indicates that the presence of a single extra atom and thus the oxygen (and C02) impurities may exhibit only a limited influence on the rotational behaviour which is in contrast to the drastic 13 14 15 M.F. Meidine, P. B. Hitchcock, H. W. Kroto, R. Taylor and D. R. M. Walton, J. Chem. SOC.,Chem. Commun., 1992, 1534. S. M. Gorun, M. A. Greaney, V. W. Day, C. S. Day, R. M. Upton and C. E. Briant, in Fullerenes :Synthesis, Properties and Chemistry of Large Carbon Clusters, ed. G. S. Hammond and V. J. Kuck, American Chemical Society, Washington DC, 1992. P. R. Birkett, C. Christides, P. B. Hitchcock, H. W. Kroto, K. impurity effects on the transport properties3’ described recently. Nevertheless, care should be taken to consider puri- fied c60 even as single crystals after exposure to air as a clean material. The small effect of the attachment of an extra atom onto a hypothetically freely rotating buckyball is quite unex- pected as at least orientational preference of the free rotation 16 17 18 19 Prassides, R.Taylor and D. R. M. Walton, J. Chem. SOC., Perkin Trans. 2, 1993, 1407. R. Moret, Phys. Rev. B, 1993,48, 17619. P. A. Heiney, J. Phys. Chem. Solids, 1992,53, 1333. N. Yao, C F. Klein, S. K. Behal, M. M. Disko, R. D. Sherwood, K. M. Creegan and D. M. Cox, Phys. Rev. B, 1992,45, 11366. A. Dworkin, H. Szwarc, S. Leach, J. P. Hare, T. J. Dennis, H. W. should occur in the oxide adduct. Kroto, R. Taylor and D. R. M. Walton, C.R. Acad. Sci. 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