Energetics of C20 and C22 Fullerene and Near-Fullerene Carbon Cages

Model semiempirical studies using quantum consistent force field/π (QCFF/PI) and density functional tight binding (DFTB) methods show the C 20 dodecahedral fullerene to have the lowest energy of all 7595 mathematically possible 20-vertex trivalent polyhedral cages by a substantial margin (estimated at 521 (QCFF/PI) or 125 (DFTB) kJ mol -1 ). A topological invariant based on the distribution of face sizes is used to correlate the energies and predict the best polyhedral structure for C 22, which must be a nonfullerene cage. With 1 square, 10 pentagonal, and 2 hexagonal faces, this structure is verified to be more stable (by 259 (QCFF/PI), 60 (DFTB) kJ mol -1 ) than its nearest trivalent polyhedral rival.