SYMMETRY AND ISOMERIC STRUCTURES OF GIANT FULLERENES AND POLYHEDRAL CLUSTERS

In order to illustrate the extension of cage cluster of given symmetry to a possible larger giant cluster of the same symmetry type, we have designed methods fbr drawing Schlegel (or quasi-Schlegel) diagrams th at show clearly all (or almost all) the faces, vertices and edges of a three-dimensional cluster in a two-dimensional plane. The symmetries and structural details were used to select unit cells which serve as ' 'abbreviations'' for huge (fullerene) clusters, and these unit cells w ere then used as basis to derive mathematical principles for extending the structures up to infinitely large clusters. Possible isomers and various fullerene clusters (up to C-150 of D-5h symmetry) of different point-group symmetries are presented (the point groups involved for d ifferent sizes are I-h, D-6d, D-5d D-3d, D-6h, D-5h, D-3h, D-3, T-d, C -3, C-3v and D-6). Simple illustrations are given to show how such cle arly visible detailed structures can be used to derive the possible ma gic numbers of (van der Waals) clusters and to formulate the mechanism and reaction coordinates of isomeric transformations. For mixed clust ers with different sets of atoms (molecules), the common (minimum) sub group symmetry is illustrated, which can be used to determine the tota l structures. An example of A(8)B(12) (e.g. Ti8C12+) is given to show the possibility of T-h or D-3d symmetry.