Graph theoretical study of stabilization of some IPR fullerenes by cage closure

Fullerene structures can be built up step by step by adding C₂-fragments to pentagons and hexagons of sp²-carbon atoms systematically; if in this building process fusion of pentagons are avoided and the Euler formula is obeyed, structures of car-bon cages corresponding to the IPR fullerenes are obtained. Graph theoretical method involving 5- and 6-fold rotational symmetry can be used to obtain the π-MO energies of the sub-structures and also of the complete cage structure. This has been done in the present work and it has been shown that the total π-electron energy per atom gradually decreases as the sub-structures grow with addition of C₂-fragments and in the last step when the cage closure is complete, the stabilization is very much appreciable. The method has been shown with the IPR fullerenes C₆₀, C₇₀, C₇₂ and C₈₄. (author)