Electronic Structure and Stability of C₂₀ Isomers

The electronic structure of 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 sp^2.803-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 unoccapied 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.