The degenerate Fermi gas of π electrons in fullerenes and the σ surface instabilities

The departure from perfect spherical symmetry in the case of fullerenes (C-60 being the sole exception) induces instabilities due to the stresses generated by the pentagonal protrusions in the or-bonded surfaces. By assuming sigma-pi separability and treating pi electrons as a degenerate Fermi gas in the two shells around the central a structure, the resulting degeneracy pressures can further enhance the a-surface initiated instabilities for non-icosahedral structures (especially for those < C-60) as well as the icosahedral fullerenes (> C-60) with large protrusions. Under certain circumstances the net degeneracy pressure across the or surface may have a structure stabilizing effect. The role of the pi-electron degeneracy in a broad range of fullerenes from C-20 to C-1500 and its effects on fullerene stability are investigated.