Icosahedral shell-closings

An interesting case, and a step forward from the isolated molecule toward more extended systems, is when an icosahedron of 12 spheres about a central sphere is surrounded by a second icosahedral shell exactly twice the size of the first [9-31]. This shell will contain 42 spheres and will lie over the first so that spheres will be in contact along the fivefold axes. Further layers can be added in the same fashion. The third layer is shown in Figure 9-30 as an example of icosahedral packing of equal spheres. The layers of spheres succeed each other in cubic close-packing sequence on each triangular face. Each sphere which is... 

Pyykkd, P. and Runeberg, N. (2002) Icosahedral WAU]2 A Predicted Closed-Shell Species, Stabilized by Aurophilic Attraction and Relativity and in Accord with the 18-Electron Rule. Angewandte... 

It was discovered, however, that the spherical aromaticity of the icosahedral fullerenes C20, Cjq and CgQ depends on the filling of the Jt-sheUs with electrons [107]. As pointed out in Section 14.3.1 no distortion of the cage structure is expected in these fullerenes if their shells are fully filled. Closed-shell situations are realized if the fullerene contains 2(N -1-1) Jt electrons. This is closely related to the stable noble-gas configuration of atoms or atomic ions [108]. In this case the electron distribution is spherical and all angular momenta are symmetrically distributed. Correlation of the aromatic character determined by the magnetic properties is shown in Table 14.3. 

Icosahedral fullerenes that contain 2(N + 1) re-electrons are closed shell systems and are spherically aromatic. 

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