Cluster model alkali-lead

Early interest in heteroatom clusters having alkali metals as the host was academic rather than dictated by precise observations. The main question regarded the extent to which the jellium-derived shell model retained its validity. However, this question was approached on the basis of oversimplified structural models in which the heteroatom (typically a closed-shell alkali-earth such as Mg) was located at the center of the cluster [235, 236]. In this hypothetical scheme, the perturbation of the electronic structure relative to that of the isoelectronic alkali cluster is somewhat trivial for instance, in the Na Mg system the presence of Mg would only alter the sequence of levels of the shell jellium model from Is, Ip, Is, 2s,. .. (appropriate to sodium clusters) to Is, Ip, 2s, Id,. .. (see also [236]). This would lead to the prediction that Na6Mg and NasMg are MNs. 

These results, still in a preliminary state, beautifully conform to the intuitive model of chemical bonding with alkali metal suboxides. The description of the characteristic clusters as quasi-free ionic units seems adequate. But in reality the / w sumrna) repulsive forces between the ions have to be compensated by a constraining field of free electrons to make the clusters stable. As a first approximation the constraining field is represented by a shielding effect of the electrons on the Rb ions leading to a reduction of the net charge of the clusters in the described calculations. 

In all the models discussed above, the spin-plus-orbital degeneracy ensures that there will be filled shell electronic configurations at certain sizes. Atoms that have filled shell elecfronic configurations tend to be more stable. Extending that idea to clusters, one can claim that clusters with filled elecfronic shells will be more stable. The exact number of valence electrons that leads to filled elecfronic shells depends on the model, but most of the major peaks in the abundance spectra of the alkali clusters are contained in all the models we have discussed so far. One can, therefore, conclude that the enhanced stability of small metal clusters at specific sizes is due to electronic shell closure effects. These extra-stable clusters have been termed magic clusters in the literature. 

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