Verification of the 2(N + 1)2 rule for fullerenes

In general, a neutral or charged fullerene with 2(N + 1)2 π-electrons exhibits a large negative NICS (nucleus-independent chemical shift) at the center of the carbon cage, where N is an arbitrarily chosen positive integer. This rule was verified on the basis of the fact that a fullerene π-system can be viewed as an electron gas bound on the spherical surface. Diamagnetic susceptibility was derived for this electron gas. Van Vleck paramagnetism is presumably minimized for fullerenes with 2(N + 1)2 π-electrons. It turned out that the NICS value at the cage center is not related to the global or local aromaticity in the cage.