Ground states of large icosahedral fullerenes

The ground states for large icosahedral fullerenes and for ${\mathrm{C}}_{60}^{\mathit{n}}$ molecular ions (-6≤n≤+1) are treated starting from full rotational symmetry and the use of Hund’s rule. Treating the icosahedral symmetry as a subgroup of the full rotational group, the icosahedral symmetry of these molecular states is introduced. A method to calculate the electronic structures for the icosahedral molecules and ions is formulated for large fullerenes using a spherical harmonic expansion on a sphere, and the calculated results for ${\mathrm{C}}_{60}$ are compared with molecular orbital calculations.