Structure of the fullerenes

The total potential number of geometrie isomers inereases enormously with inerease in eluster size, being, for example, three for C30, 40 for C40, 271 for C50 and no fewer than 1812 for Ceo. However, the number beeomes mueh more manageable if one eonsiders only those isomers that have no eontiguous pentagons. The theoretieal justifieations for this 

C atoms are labelled a-e (see text), (b), (c) Line drawings of the two enantiomers of C76 viewed along the short C2 rotation axis and illustrating the chiral D2 symmetry of the molecule. 

Except for Ceo, lack of sufficient quantities of pure material has prevented more detailed structural characterization of the fullerenes by X-ray diffraction analysis, and even for Ceo problems of orientational disorder of the quasi-spherical molecules in the lattice have exacerbated the situation. At room temperature Cgo crystallizes in a face-centred cubic lattice (Fm3) but below 249 K the molecules become orientationally ordered and a simple cubic lattice (Po3) results. A neutron diffraction analysis of the ordered phase at 5K led to the structure shown in Fig. 8.7a this reveals that the ordering results from the fact that 

20a p Fowler and D. E. Manolopoulos, An Atlas of Fullerenes, Clarendon Press, Oxford, 1995, 392 pp. 

The structures of the black crystalline benzene solvate C6o-4C6H6, the black charge-transfer complex with bis(ethylenedithio)tetrathiafulvene, [C6o(BEDT-TTF)2], and the black ferrocene adduct [C6o Fe(Cp)2)2] (Fig. 8.7b) ) have also been solved and all feature the packing of Cso clusters. 

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C60 shows an extremely facile reduction profile and there is evidence for the addition of up to 12 electrons to the molecule. The prediction that C60 will exhibit an exceptionally high electron affinity and that the molecule will add up to 12 electrons under suitable conditions (Haddon et al. 1986a) seems to be borne out by the experimental results. Rehybridization plays an important role in determining the electronic structure of the fullerenes and it is the combination of topology and rehybridization which together account for the extraordinary ability of C60 to accept electrons. 

Haddon, R. C. Raghavachari, K. 1992 Electronic structure of the fullerenes carbon allotropes of intermediate hybridization, buckminsterfullerenes. VCH. (In the press.)... 

For carbon, it is of course also tempting to study clusters of clusters, namely aggregation of C60 fullerenes [67-69]. This is not really a molecular cluster application since the inner structure of the fullerene, leading to dependence of the particle interaction on relative particle orientation, is largely or completely ignored. The Pacheco-Ramalho empirical potential is used frequently, and fairly large clusters up to n=80 are studied. There appears to be agreement that small fullerene clusters are icosahedral in this model. In contrast to LJ clusters, however, the transition to decahedral clusters appears to occur as early as at n=17 the three-body term of the potential is found to be responsible for this [67]. 

Figure 8 Computer-generated cage structures of the //,-fullerenes...

Abstract. - High-resolution powder neutron diffraction has been used to study the crystal structure of the fullerene Cm in the temperature range 5 K to 320 K. Solid Cm adopts a cubic structure at all temperatures. The experimental data provide clear evidence of a continuous phase transition at ca. 90 K and confirm the existence of a first-order phase transition at 260 K. In the high-temperature face-centred-cubic phase (T > 260 K), the Cm molecules are completely orientation-ally disordered, undergoing continuous reorientation. Below 260 K, interpretation of the diffraction data is consistent with uniaxial jump reorientation principally about a single (111) direction. In the lowest-temperature phase (T < 90 K), rotational motion is frozen although a small amount of static disorder still persists. 

St92b P. W. Stephens et al, Lattice Structure of the Fullerene Ferromagnet TDAE-Cso, Nature 355, 331-332 (1992). 

Fig. 1. Left graph shows the chemical structure of the fullerene derivative - PCBM. Right graph shows a schematic cross section of the Al/p-Si/PCBM/Al hetero-junction with an sample photograph [2],...

The hollow cage structure of the fullerenes allows a spherical standing wave to be formed inside the cluster, and this has been advanced as the explanation for marked oscillations of the photoionisation cross section of Ceo which persist in both the gaseous and the solid phase [666]. 

For a first survey of the electronic structures of the fullerenes, we take the position that all variation in Huckel parameters and all implicit or explicit treatment of o electrons is to be relegated to the steric factor and that the crude version of Huckel theory is taken to describe the pure 7t effects. The advantages of this approach for searching for formal rules of fullerene electronic structure will be made apparent in the following sections. It is also clear that the steric factor defined as above must be taken into account if realistic energies and energetic trends are to be obtained. Indeed, the steric factor seems to dominate relative stabilities of both lower and higher fullerenes, as will also become apparent later. 

In order to evaluate the influence of the geometric and electronic properties of the educts on the observed product distributions a variety of experimental and calculated mono adduct structures were analyzed (Fig. 21, Table 5). For example, as can be seen from the X-ray crystal structure of 47 the average values of the [5,6] -bonds are 1.451 A and those of the [6,6] -bonds excluding the cyclo-propanated [6,6]-bond between C-1 and C-2 1.388 A [102]. This clearly shows that the [5]radialene-type structure of the fullerene cage is preserved. 

Almost immediately after the discovery of Cgo in the gas phase [8], it was suggested that atoms could be encapsulated into the hollow structure of this fullerene [9]. This concept was in fact used to probe whether the structure of the fullerenes are spherical as originally proposed [8], when no other methods other... 

FIGURE 8.4 Typical structure of the fullerene The double bindings are illustrated by double lines. In the nuclear case the Carbon atoms are replaced by a particles and the double bindings by the additional neutrons. Such a structure would immediately explain the semi-hollowness of that superheavy nucleus, which is revealed in the mean-field calculations within meson-field theories. For a colour reproduction of this figure see the colour plate section, near the end of this book. 

The electronic structure of the fullerene materials is determined by the tt electron system. In Ceo the highest occupied molecular orbital (HOMO) has a fivefold degenerate hu symmetry and the lowest unoccupied molecular orbital (LUMO) has a threefold degenerate ti symmetry. Thus, the lowest possible optical transition is symmetry forbidden. The first allowed transition is from HOMO to LUMO-fl with the initial and final orbital symmetries an d txg, respectively. Insertion of the fullerene into a... 

VA Fig. 14.5 (a) The structure of the fullerene C o the approximately spherical molecule is composed of fused 5- and 6-membered rings of carbon atoms. [X-ray diffraction at 173 K of the benzene solvate CgoAQHe, M.F. Meidine et al. (1992) J. Chem. Soc., Chem. Commun., p. 1534.] (b) A representation of C o, in the same orientation as is shown in (a), but showing only the upper surface and illustrating the localized single and double carbon-carbon bonds. 

According to the spiral conjecture the spiral of the polyhedron is represented by a one-dimensional sequence of 5s and 6s which give the positions of pentagons and heptagons. Thus the list of the 12 pentagon serial number describe the topological structure of the fullerenes (Fig. 6.1). 

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