Geometric shells

When building clusters by coating the fullerenes with metal, features similar to the electronic and geometric shells found in pure metal clusters[9] are observed in the mass spectra. In the case of fullerene molecules coated with alkaline earth metals (section 3), we find that a particularly stable structure is formed... 

Before leaving the jellium model, it seems appropriate to mention some results for sodium clusters of up to 22000 atoms. The abundances observed can be explained in terms of the extra stability associated with both completed jellium shells (for less than about 3000 atoms) and with completed icosahedral or cuboctahedral geometric shells for larger sizes. The results are especially interesting because of the observation of supershells that occur because of an interference effect, which has been explained using semiclassical arguments. ... 

A. Clusters of noble gas atoms give geometrical shell structure... 

The number of atoms, N, required to form a cluster with L geometric shells is given by... 

Another consideration required to describe the electronic structure of metal clusters is the emergence of electronic shells. The closure of electronic shells, similar to the closure of geometric shells, bequeath special stability to specific nuclearities and is manifest best in the variation of ionization energies with cluster nuclearity [29,52]. The total number of electrons required to... 

Experimental evidence for electronic shells is foimd in the plot of cluster abundance vs. nuclearity and in the variation of the ionization energies of clusters (see Fig. 1.12). Electronic shell effects dominate the properties of alkali metal clusters. They are also broadly apphcable to p-block metals. The properties of transition and nobel metal nanoparticles, however, are influenced more by the formation of geometric shells. In fact, a transition from shells of electrons to shells of atoms is seen in the case of A1 [29,53]. It appears that the abundance of available oxidation states and the directional nature of the d- and f-orbitals (and to a limited extent, of the p-orbital) play a role in determining the shell that governs the property of a particular cluster. 

---