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

Department of Chemistry, Durgapur Government College, J. N. Avenue, Durgapur-713 214, West Bengal, India

E-mail: bankimghosh@yahoo.co.in

Manuscript received online 09 November 2019, accepted 18 November 2019

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 carbon 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 substructures 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.