CLOSED-SHELL CARBON FRAMEWORKS - LEAPFROG FULLERENES AND DECORATED SPHERIPHANE HYDROCARBONS

Two geometrical constructions generate structures with closed pi shells from an arbitrary fullerene graph. In the first, closed-shell fullerenes are given by the leapfrog transformation. The starting fullerene is capped on every face and then dualized, producing a new cage of the same symmetry with three times as many atoms, isolated pentagons, and a guaranteed closed shell. Leapfrog fullerenes have n = 60 + 6k (k not-equal 1) atoms, and together with the cylinder series (70 + 30k and 84 + 36k (all k)) they exhaust the known properly closed-shell fullerenes up to C100. In the second, decoration of a fullerence skeleton replacing each vertex by a (1, 3, 5)-linked C6H3 hexagon produces the spheriphane hydrocarbon series C2mH(m) where m is 60 + 6k (k not-equal 1). Each molecule has a closed pi system, a fixed HOMO-LUMO gap, and a pi energy that is independent of the starting isomer.