VALENCE POINTS AND SYMMETRY VIEWS OF THE STRUCTURES OF CARBON CLUSTERS, FULLERENES AND METALLOFULLERENES

Planar Schlegel diagrams of fullerene cages for the reaction mechanism s between open clusters and between metals and fullerenes are used to determine the qualitative symmetry properties. The detailed Schlegel d iagrams help to illustrate the subgroup symmetries of the cages that c ontain localized pi bondings with Dewar structure bondings plus free r adical pi electrons, positive and negative ions, metal locations, hydr ogen additions etc. Cluster interactions include C36H12, C36H18, C24H1 2, C20H20, C20H10. Free radical pi-electrons are shown inside C-88(D-3 ), C-82(C-3v), C-74(D-3h), C-60(I-h), C-36(D-3h), C-34(C-3v) along wit h their endohedral interaction, with single metals Sc, Y, La and Lu ha ving three top electrons s(2)d. Similarly, free-radical pi-electrons a re shown inside C-28(T-d) and C-56(T-d) along with their interaction w ith single metals Ti, Zr, Hf and Th having four-top electrons s(2)d(2) (plus metal U having f(3)d). The extra case of Ti@C28H4 (C-3v or D-2d ) is also considered. For dimetal interactions, we consider C-84(T-d) yielding Sc-2@C-84 and Lu-3@C-84 with subgroup symmetry D-2d and C-80( I-h) yielding Lu-2@C-80 with subgroup symmetry D-3d. For trimetal inte ractions, we consider C-82(C-3v) yielding Sc3C82 and La-3@C-82 with su bgroup symmetry C-3v and C-88(D-3) yielding La-3@C-88 with subgroup sy mmetry C-3. For exohedral interactions, we consider C-30(D-5h) yieldin g LaC29+ and C-34(C-3v) yielding LaC33+ with subgroup symmetry C-s.