A Catalogue of Isomerization Transformations of Fullerene Polyhedra.

Abstract

Computers in chemistryComputers in chemistry V 0380 A Catalogue of Isomerization Transformations of Fullerene Polyhedra. -(BRINKMANN, G.; FOWLER*, P. W.; JUSTUS, C.; J. Chem. Inf. Comput. Sci. 43 (2003) 3, 917-927; Sch. Chem., Univ. Exeter, Exeter, Devon EX4 4QD, UK; Eng.) -Lindner 35-189

A Catalogue of Growth Transformations of Fullerene Polyhedra

“…A systematic catalogue of isomerization transformations based on this approach has been constructed. 7 Similar reasoning is applied here to classify the transformations that lead from an isomer of a fullerene C n to an isomer of a fullerene C n+2m . A comprehensive catalogue of combinatorially distinct growth and carbon-loss mechanisms ordered by patch boundary and pentagon content is thereby made possible.…”

“…Much of the mathematical approach is common to isomerization and growth mechanisms, and only a brief summary of background and algorithmic considerations is given here before presenting the new catalogue. As with the previous catalogue of isomerization transformations, 7 step-by-step enumeration uncovers many possibilities that have not yet received attention in the chemical literature, and it gives a firm basis for future evaluation of hypothetical mechanisms using explicit quantum chemical calculations.…”

“…In our approach, a patch is defined as follows. 7 The surface of the starting fullerene polyhedron is partitioned into two parts by a closed boundary circuit of vertices and edges, drawn such that all changes necessary to the conversion of the initial into the final fullerene are confined to the interior of the disklike region enclosed by the boundary. Each vertex in the boundary is incident with two edges lying wholly in the boundary and one edge that points either inward to the interior or outward to the exterior region.…”

“…These cases of isomerization patches ((i)) and isomerization pairs ((ii)) have been considered previously. 7 The third possibility is that of the formal replacement involving a new patch with a different number of vertices. This corresponds to inflation or deflation of the fullerene (necessarily by an even number of vertices), and the two patches are said to form a growth pair or an inflation pair.…”

“…With isomerization processes, some care is needed to distinguish between real and null transformations. 7 Processes of type (iii) suffer from none of these difficulties, as the initial and final fullerenes are certain to have nonisomorphic graphs.…”