Abstract
We use interlacing techniques to prove that carbon nanocones who have a Fries Kekule structure have closed Huckel shells, and that this result can be extended to all conjugated cones where each edge belongs to a hexagonal face and the configuration of the non-hexagonal faces are consistent with a Fries Kekule structure. Cones with Fries Kekule structure or substructure are topical—not only from a valence bond theoretical point of view—since a previous ab initioanalysis favored cones where the pentagons at the tip are configured as in a Fries Kekule structure. The question of interdependence will therefore be addressed.
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