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 (C60 being the sole exception) induces instabilities due to the stresses generated by the pentagonal protrusions in the σ-bonded surfaces. By assuming σ-π separability and treating π electrons as a degenerate Fermi gas in the two shells around the central σ structure, the resulting degeneracy pressures can further enhance the σ-surface initiated instabilities for non-icosahedral structures (especially for those C60) with large protrusions. Under certain circumstances the net degeneracy pressure across the σ surface may have a structure stabilizing effect. The role of the π-electron degeneracy in a broad range of fullerenes from C20 to C1500 and its effects on fullerene stability are investigated.