Semi-fullerene structures

Ideally, a SWCNT is made of a single perfect graphene sheet rolled up into a cylinder and closed by two caps (semi-fullerenes). Considering that there are different ways to roll up a section of a two-dimensional graphene sheet, the structure of SWCNTs is characterized by a roll-up vector, also called a helicity vector [11 and Chapter 14]. The diameter of these structures can vary between 0.4 and 2.5 nm and the length between a few micrometers and several millimeters. 

The aromaticity of [10]cyclophenacene was evaluated with the percentage resonance energy (%RE) [12] as 2.573, which indicates that [10]cyclophenacene is much more aromatic than [60]fullerene (%RE = 1.795) and less aromatic than benzene (%RE = 3.528). Tinker also theoretically investigated the stability and electronic structure (UV/Vis band) of [n]cyclophenacenes with semi-empirical calculations (AMI and ZINDO/S) and proposed that [n]cyclophenacenes with medium size (n = 8 and 10) can be synthesized [13]. Thus, based on the theoretical... 

Abstract. Geometrical parameters, total energy, heat of formation, energies of HOMO and LUMO orbitals, density of one-electron states (DOS) are determined by using of semi-empirical quantum chemistry PM3-method for isolated molecules Cn, dimers (Cn)2 and cuban-like clusters (Cn)8 for n = 20, 24, 28, 32. The results of calculations allow assuming the existence of polymerized cubic crystal structure on base of all considered small fullerenes. 

Clearly, if any such quantitative explanation is to be found, it must take account of the fact that there can be a large number of distinct fullerene isomers for each given C . There are, for example, at least 1812 distinct fullerene isomers for Cso alone (vide infra). Icosahedral C o, which was first discovered by intuition [2], does indeed happen to be the most stable of these. However, since the majority of carbon clusters do not admit such remarkably symmetric closed-shell structures, the most stable C fullerene isomer is generally more difficult to find. Section 2 describes a practical solution to this problem, which amounts to no more than a direct computer search of all possible fullmne structures for each given C . Section 3 then ofTeit a semi-quantitative explanation for fig. 1, based on the relative kinetic stabilities of the fullerenes C34 to C70. 

FIG. 3 Planar monocyclic, bicycllc and tricyclic C40 ions form fullerene plus C2 when collisionally heated above the isomerization barrier for fullerene formation (see Fig. 2b). All structures shown are minima on the potential energy surface, according to semi-empirical PM3 electronic structure calculations. The bicycllc and tricyclic rings have lower isomerization barriers to fullerene formation than the monocyclic ring. 

Structural changes in C70 caused by He+ bombardment were monitored by FTIR and Raman spectra. There was no evidence for oligomer formation simply direct degradation to amorphous carbon.212 Ab initio calculations have been made of the vibrational wavenumbers for Cn5, a coplanar double-C6o cage.213 Semi-empirical AMI calculations have been reported for the vibrational wavenumbers of the peanut-shaped fullerenes Ci20.214... 

The addition of photochemically-generated phosphoryl radicals to [76] fullerene has been studied by EPR. Seven of the nineteen possible radical adducts were observed, six of which are stable. The study was supported by semi-empirical MNDO/PM3 calculations. Two new, cyclic phosphinylhydrazyl radicals, (393) and (394), have been generated by the oxidation of the corresponding hydrazines and their structures, and their interactions as guests in cyclodex-trins, studied by EPR. ... 

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. 

Huckel theory was extended to cover various other systems, including those with heteroatoms, but it was not particularly successful and has largely been superseded by other semi-empirical methods. Nevertheless, for appropriate problems Huckel theory can be very useful. One example is the calculations of P W Fowler and colleagues, who studied the relationship between geometry and electronic structure for a range of buckminster-fullerenes (the parent molecule of which, C50, was discovered in 1985) [Fowler 1993] The fullerenes (or buckyballs ) are excellent candidates for Hiickel theory as they are composed of carbon and have extensive tt systems three examples are shown in Figure 2.22. 

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. 

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