Mitsuho Yoshida

Molecular Mechanics Calculations of Giant- and Hyperfullerenes with Eicosahedral Symmetry

Abstract Structures and energies of the first few members of giant- and hyperfullerenes with Ih symmetry have been calculated by using MM3.

Validity of the weighted HOMO–LUMO energy separation as an index of kinetic stability for fullerenes with up to 120 carbon atoms

The T value, a general index of kinetic stability defined as a HOMO–LUMO energy separation multiplied by the number of conjugated atoms, can be evaluated meaningfully for isolated-pentagon isomers of fullerenes with up to 120 carbon atoms. Fullerenes with 60+6k carbon atoms have one or more isolated-pentagon isomers with very large T values. Here, k is zero or any integer larger than unity.

Further test of the isolated pentagon rule: Thermodynamic and kinetic stabilities of C84 fullerene isomers

Thermodynamic and kinetic stabilities of 73 C84 fullerene isomers were estimated from the MM3 heats of formation and the recently defined bond resonance energies (BREs), respectively. The BRE represents the contribution of a given π bond in a molecule to the topological resonance energy (TRE). All π bonds shared by two pentagons turned out to be highly reactive without exceptions. C84 fullerene isomers with such π bonds must be incapable of survival during harsh synthetic processes. Thus, the isolated pentagon rule (IPR) proved to be applicable to such large fullerene cages. For sufficiently large fullerenes like C84, some isolated‐pentagon isomers are also predicted to be very unstable with highly antiaromatic π bonds.

Shape and Fantasy of Fullerenes

One of the many wonders that fullerenes have brought to us during the past few years is the variety of their shapes. When the elusive C 60 finally showed up in 1990, the perfect symmetry and astounding beauty of its molecular structure touched the hearts of scientists before they could consider the molecules vast technical possibilities. Already much has been said about the unique shape of C 60 and its potentialities. C 70 and higher fullerenes have simultaneously been found in the same soot that produced C 60 and were quickly revealed to be shaped like rugby balls or oblong eggs. Hence we were aware that there had to be an extensive series of roundish polyhedral clusters of carbon atoms. Then, in the following year, multilayered tubular fullerenes (Figures 1a and 1b) were discovered by Iijima and were named buckytubes (see the article by Iijima in this issue). Iijima also observed similarly huge and multilayered carbon balls, before C 60 was discovered. Soon after, buckyonions were recognized as an important class of fullerene (Figure 1c, see article by Ugarte in this issue). So, in the early days of fullerene research, we already knew three forms of fullerene: sphere, tube, and particle. At that time, however, nobody anticipated that this was only the beginning of a big show of stunning variations in the shapes of fullerenes. This article introduces current developments in the study of these fullerene styles.

Computations on nineteen isolated-pentagon-rule isomers of C86

Abstract The complete set of nineteen isolated-pentagon-rule isomers of C 86 is described by the SAM1 (semi-ab-initio model 1) quantum-chemical method, and their energetics are checked by ab initio SCF computations. Considerable temperature effects on the relative stabilities in the system are found. The ground state structure is a C 2 isomer but at elevated temperatures other structures also become significant.

Non-bonding orbitals in graphite, carbon tubules, toroids andfullerenes

It is shown that the non-bonding orbitals of many graphite-derived carbon frameworks can be understood in terms of the four non-bonding orbitals of the graphite sheet. Several infinite series of fullerenes with non-bonding orbitals are identified, and the frontier orbitals of icosahedral fullerenes rationalised, by considering fullerenes as cut and folded graphite. The leapfrog construction, which produces only closed-shells when acting on fullerenes, is shown in contrast to produce exactly the metallic tubules and the open-shell polyhex toroids when acting within these families.

Dihedral fullerenes of threefold symmetry with and without face spirals

A general geometrical construction for fullerenes of threefold dihedral (D 3 , D 3h , D 3d ) symmetry is reported and used to find those examples of this symmetry that are without face spirals. The smallest, a D 3 384-atom cage, has its twelve pentagons arranged in three separate crosses of four fully fused rings and has four atoms more than the smallest known non-spirallable fullerene. Another D 3 structure, a 672-atom cage, is the smallest example of an isolated-pentagon fullerene without a spiral, improving on the previous upper bound by 128 atoms. Altogether, 61 new enantiomeric pairs of nonspirallable fullerenes with less than 1000 atoms belonging to four different classes, all of D 3 symmetry, are identified.

Analysis of the Growth Mechanism of Carbon Nanotubes by C2 Ingestion

Abstract Cap structures capable of sustaining infinite growth by ingestion of C2 fragments to give a carbon nanotube were screened systematically. For this purpose a total of 23,296 IPR cap structures having characteristic tubule vectors of (5∼20, 0∼10) were generated by the use of net algorithm. Eighteen recurring patterns were found which involve 50 cap structures having tubule vectors (6∼11, 5).

Systematic relationships between fullerenes without spirals

Generalised truncations of the isolated-pentagon-triple fullerenes without face spirals lead to the construction of twelve new series of non-spirallable fullerenes of low (C3, C2, C1) symmetry and with a mixture of fused and isolated pentagons; the smallest of the new counterexamples to the fullerene face spiral conjecture has 610 atoms.

Polymorphism of Extended Fullerene Networks: Geometrical Parameters and Electronic Structures

Abstract The morphology of fullerene networks can be widely extended by introducing heptagonal or octagonal rings, which produce a Gaussian negative curvature. Their presence makes it possible to form donut-, coil- and sponge-shaped networks of carbon atoms. We discuss the geometry of the polymorphous forms based on the net diagram method relative to a honeycomb lattice, and further study the electronic structures constructed by the network of electrons system. Special emphasis is put on how the geometrical paramateres, which specify the relative arrangement of polygonal ring, control the electronic structures in the various extended-fullerene networks. In addition, we mention that the presence of a certain type of edge in fullerene network derives critical localized edge stages at the Fermi level.