The geometry of small fullerene cages: C20 to C70

The ground-state structures of small fullerenes below C₇₀ were determined by tight-binding molecular-dynamics total energy optimization. An efficient simulated annealing scheme was used to generate closed, hollow, spheroidal cage structures for all even-numbered carbon clusters from C₂₀ to C₇₀. As a general trend, fullerenes prefer geometries which separate the pentagonal rings as far apart as possible. Except for C₆₀, C₇₀, and C₅₀, most fullerenes have relatively low symmetries.