Archimedean structure of the carbon cluster C12: Alternation of bond lengths and aromaticity

We consider the possibility that the stability of the Archimedean structure C60 (a truncated icosahedron) is a consequence of the aromaticity of this nonalternant molecule. As the model, we used the structure of C12 in the form of a truncated tetrahedron — the first of the Archimedean solids, having triangular faces in addition to hexagonal faces (rather than the pentagonal faces in the analogous C60 molecule of symmetry Ih). On the basis of calculation of the topological resonance energy of the C12 molecule of Td symmetry, we conclude that the structure with different bond lengths is antiaromatic, while the C12 molecule (whose hexagonal faces are benzene rings of the Kekule type) has a slight degree of aromatic character. MNDO and AMl calculations have shown that these structures for C12 correspond to minima on the potential energy surface, but the structure with different bond lengths has lower energy. We also observe an isomer of C12 having benzene rings of the quinoid type, which corresponds to a minimum on the potential energy surface but is less stable than the structure with equal bonds. Aromatic stabilization is expected, as shown by the calculation for the tetracation C4+ 12 of Td symmetry with virtually equal lengths of all the carbon-carbon bonds.