ENERGETICS OF C-20 AND C-22 FULLERENE AND NEAR-FULLERENE CARBON CAGES

Model semiempirical studies using quantum consistent force field/pi (Q CFF/PI) arid density functional tight binding (DFTB) methods show the C-20 dodecahedral fullerene to have the lowest energy of all 7595 math ematically possible 20-vertex trivalent polyhedral cages by a substant ial margin (estimated at 521 (QCFF/ PI) or 125 (DFTB) kJ mol(-1)). A t opological invariant based on the distribution of face sizes is used t o 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 po lyhedral rival.