Structure of Fullerenes

Fullerenes are another exotic nanostructure of carbon. Initially, considering C60, fullerenes were usually thought to have a shape of regular sphere. Along with the in-depth research on fullerenes, other types have been discovered, such as cone shape and tube shape. Here the structures of some new fullerenes will be introduced.

11.4.1 Structure of C48 Fullerenes

A recent research has constructed 27 isomers for the C48 cage and these are shown in Fig. 11.12 (Wu et al. 2004). It is found that the most stable C48 structure has the smallest number of shared pentagonal bond (N55) and no squares and deltas, and all the reported structures are higher in energy. In comparison with the available isomers from literature, C48 isomer (1) with the least number of shared pentagonal C-C bonds (N55 = 6) is the most stable structure and has the largest vertical ionization potential. However, the low-lying isomers 2-4 are very close in energy, and the most stable triplet state is structure 2.

11.4.2 Toroidal Fullerenes

In finding structural conditions for preferable fullerenes, scientists investigated a variety of covering patterns, e.g., combinations of C5, C6, C7, and polygons, arranged in different ways, in view of lowering the total energy of possible molecular structures. Toroidal structure was first identified (Diudea et al. 2003). A toroidal surface can be covered with hexagons by cutting out a parallelogram from a graphite sheet, rolling it up to form a tube and finally gluing its two ends to form a torus. A 4-valent square-tiled toroid is transformed into 3-valent hexagonal (and other polygonal) lattices either by simple cutting procedures or by some more elaborated operations, such as leapfrog and related transformations (Fig. 11.13).

11.4.3 Structure of C60, C59, C58, C57

Recently, Hu and Ruckenstein studied the structures and stabilities of several defect fullerene clusters—C59, C58, and C57—formed by removing one, two, and three adjacent carbon atoms from a C60 cluster (Hu et al 2003). A more advanced structures and stabilities for all possible isomers of the defect fullerene clusters of

C60, C59, C58, and C57 have been investigated by Lee SU and Han YK. When one atom is removed from C60 cluster, one 5-membered ring and two 6-membered rings are destroyed and replaced with 5- and 8-membered rings, denoted as the C59_5-8 isomer, or 4- and 9-membered rings, the C59_4-9 isomer (Fig. 11.14). It is noteworthy that there are obvious relationships between structure and stability of the defect fullerene clusters. First, the unsaturated carbon atom favors being located at a 6-membered ring rather than a 5-membered ring. Second, the most stable isomers prefer to have newly-formed 5-membered rings, rather than newly-formed 4-membered rings.

11.4.4 The Smaller Fullerene C50

The smaller non-IPR fullerenes, predicted to have unusual properties because of their adjacent pentagons and high curvature, are so labile that their properties and reactivity have only been studied in gas phases. Fullerenes smaller than C60 are predicted to have unusual electronic, magnetic, and mechanical properties that arise mainly from the high curvature of their molecular surface (Xie et al. 2004). Fig. 11.15 describes the typical structure of C50Cl10 capturing C50. Similar element may be applied to produce C54Cl8 and C56Cl10 (Chen 2004).

Fig. 11.12: B3LYP/6-31G* C48 isomers
Fig. 11.13: Leapfrog transforms of two 4-valent tori: C4 (8, 32) andRC4 (8, 32)
Fig. 11.14: Optimized C59, C58, and C57 clusters
Fig. 11.15: The B3LYP/6-31G* optimized structure of C50Cl10 (D5h)

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