The electronic structure of the C20 cluster in monocyclic ring, bowl and
fullerene isomers has been calculated using the tight-binding scheme
developed by Harrison, starting in particular from the
sp2.803-hybrids for the fullerene structure. The study of energetics predicts
the fullerene to be the ground state with the bowl and ring lying over 1.32
and 3.35 eV higher in energy. The total energies will be lowered by Peierls
or Jahn-Teller distortion, but the energetic ordering remains unchanged. It
is also shown that the range of valence electron, the level difference
between the highest occupied molecular orbital and the lowest unoccupied
molecular orbital as well as the σ-π gap, which are less
sensitive to the exact geometry, vary in the ring, bowl and fullerene
sequence.