Electronic structure of the fullerene

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 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. 

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... 

Apparently the formation of the fulleroids, as shown schematically above (Fig. 4.41) implies only subtle changes in the electronic structure of the fullerenes which are not enough for substantially changing their electronic spectrum and their electrochemistry. 

In comparison with pristine C6o and C70, the fullerene derivatives (Fig. 2) show partly different photophysical properties due to the pertubation of the fullerene s TT-electron system. The degree of variation is dependent on (1) the electronic structure of the functionalizing group, (2) the number of addends, and (3) in the case of multiple adducts on the addition pattern at the fullerene core [59-112],... 

In this chapter we have described the photophysics and photochemistry of C6o/C70 and of fullerene derivatives. On the one hand, C6o and C70 show quite similar photophysical properties. On the other hand, fullerene derivatives show partly different photophysical properties compared to pristine C6o and C70 caused by pertuba-tion of the fullerene s TT-electron system. These properties are influenced by (1) the electronic structure of the functionalizing group, (2) the number of addends, and (3) in case of multiple adducts by the addition pattern. As shown in the last part of this chapter, photochemical reactions of C60/C70 are very useful to obtain fullerene derivatives. In general, the photoinduced functionalization methods of C60/C70 are based on electron transfer activation leading to radical ions or energy transfer processes either by direct excitation of the fullerenes or the reaction partner. In the latter case, both singlet and triplet species are involved whereas most of the reactions of electronically excited fullerenes proceed via the triplet states due to their efficient intersystem crossing. 

The electronic structure of the hypothetical fulleroids also parallels that of the fullerenes in several significant respects. Properly closed n shells are found within the Hiickel approximation only for isolated p-gon isomers, and then only when the structure is either (a) leapfrogged from a smaller fulleroid of the same symmetry, or (b) a p-fold analogue of one of the fullerene carbon cylinder series (Fowler 1990). D1(l C84 is the smallest fulleroid with a properly closed shell (figure 3). 

Quite apart from their singular topology, the fullerenes are distinguished from other conjugated hydrocarbons by their non-planarity. The geometrical aspects of fullerene formation as it relates to pyramidalization of the constituent carbon atoms has been recognized for some time (Haddon et al. 1986 Haddon 1988). Here we consider the effect of non-planarity on the electronic structure of the carbon atoms as it arises in the fullerenes (Haddon et al. 1986 Haddon 1992). 

In the case of metal clusters, for example, valence electrons show the shell structure which is characteristic of the system consisting of a finite number of fermions confined in a spherical potential well [2]. This electronic shell structure, in turn, motivated some theorists to study clusters as atomlike building blocks of materials [3]. The electronic structure of the metallofullerenes La C60 [4] and K C60 [5] was investigated from this viewpoint. This theorists dream of using clusters as atomlike building blocks was first realized by the macroscopic production of C60 and simultaneous discovery of crystalline solid C60, where C60 fullerenes form a close-packed crystalline lattice [6]. 

Kietzmann H, Rochow R, Gantefor G, Eberhardt W (1998) Electronic Structure of Small Fullerenes Evidence for the High Stability of C32, Phy Rev Lett 81 5378-5381... 

The a values of fullerenes increase as the degree of fluorination increases and, consequently, the electronic structures of fluorinated fullerenes varies as a function of the number of fluorine atoms attached to the fullerene molecules. These results... 

Scandium metallofullerenes were also produced in macroscopic quantity and solvent-extracted by Shinohara et al. (1992b) and Yannoni et al. (1992). The Sc fullerenes exist in extracts as a variety of species (mono-, di-, tri-and even tetra-scandium fullerenes), typically as Sc Cs2/ Sc2 C74, Sc2 Cs2, Sc2 Cg4, Sc3 Cs2, and Sc4 C82- It was found that Scs C82 was also an ESR-active species whereas di-and tetra-scandium fullerenes like Sc2 C84 and Sc4 C82 were ESR-silent. (See Section 5 for the present correct assignment for some of the di- and tri-scandium metallofullerenes.) A detailed discussion on the electronic structures of the scandium fullerenes accrued from these ESR experiments is given in Section 6.1. 

Dunsch and co-workers (Bartl et al., 1996 Dunsch et al., 1995, 1997 Petra et al., 1996) studied electron transfers in metallofullerenes by CV coupled with in situ ESR experiments. The electron transfer fo fhe endo-hedral La Cg2 molecule studied by this method gives evidence of a charge in the electronic state of the fullerene the electrochemical reaction in the anodic scan causes the formation of La Cs2", and during the cathodic scan the spin concentration decreases as the La + C82 structure formed by reduction is not paramagnetic. 

Fullerenes. - Jonsson et al.234 have carried out analytical Hartree-Fock calculations, expected to be near the basis set limit, of a, and the magnetiz-ability for the C70 and C84 fullerenes. The results are compared with earlier calculations on ) and the electronic structures of the molecules discussed. Moore et al.235 have made semi-empirical AMI finite field calculations of the static y-hyperpolarizability of Qo, C70, five isomers of C78 and two isomers of C84. The results are interpreted in terms of bonding and structural features. 

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. 

The key in many of known reactions of fullerenes appears to be the pyra-cyclene moieties existing in this type of clusters. Figure 4.38 illustrates a representation of backminsterfullerene emphasizing the presence of such a moiety. The fact that in this structure each double bond is surrounded by four other electron-withdrawing groups is possibly related with the high electron affinity of the fullerenes already mentioned. 

Theoretical as well experimental studies show that although there are some differences in the electron structure of pure and alkali metal-doped fullerenes, the band structures of both type of compounds are fundamentally similar. Band width as well as the energy gap between the bands remain qualitatively unchanged after the fullerene doping. In other words, the molecular features of Ceo dominates the electronic structure of the solid phases. 

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