Isomers of Fullerenes C58 to C60

Abstract

We have designed possible structures of isomers of fullerenes from C58 to C60. The fullerenes studied refer to four-, five- and six-fold symmetry, they being divided into two classes, perfect (basic) having ordinary symmetry and intermediate having topological symmetry. We have used three the most natural mechanisms of their formation, namely, fusion of carbon cupolas having the same symmetry; fusion of fullerenes having compatible symmetry and embedding carbon dimers into the hexagons with a specific surrounding of initial fullerenes. The energies of the fullerenes calculated through the use of molecular mechanics are presented together with their graphs. We have separated fragments of curvature and put into accordance with their centers the centers of principal stresses. The arrangement of both centers for the five observed experimentally isomers of fullerene C60 corresponds to five geometric figures: icosahedron, pentagonal, hexagonal, deformed hexagonal bipyramids and cube. As a result the binding energy of isomers can be considered not only as a global quantity, but as a surface distribution.