  Contrary to recent experimental evidence suggesting that the monocyclic ring
is the most stable 20-atom carbon species, highly accurate calculations
convincingly predict that the smallest fullerene, the dodecahedron C$_{20}$,
has the lowest energy. A related corannulene-like bowl is nearly degenerate in
energy to the fullerene. Thermodynamic considerations suggest that at formation
temperatures of around 700 K the bowl should be the dominant species. The
recent application of gradient corrections to LDA which supported the ring
structure is qualitatively in error. (RK-94-02)
