Lead electron-precise cluster

Electron-precise cluster systems can be seen to be a more complex version (three-connect units) of chains (one-connect units) and rings (two-connect units), leading up to an extended solid (four-connect units, e.g. the diamond structure). This is most easily appreciated for homonuclear examples, for example, (1) and (2). For the mixed systems like (3), two distinct descriptions are possible - as a 4-atom cluster or as a trinuclear metal complex with a /U.3-P cap. In many cases, the difference is of little consequence however, in others, proper choice of description can lead to analyses of significant conceptual value. 

Incomplete spherical clusters that require the addition of two fragments to be closed are called arachno-clusters (spider web-like). As the shape is based on a deltahedron of order n but with only n —2 vertices occupied, the number of cluster bonding electrons per cluster fragment is larger than that for closo- and mdo-clusters. It follows that a continuation of the closo-, nido-, arachno- progression eventually leads to electron precise rings or chains. 

These considerations lead one to suggest a modified cluster model that takes advantage of the fact that local density models admit partial occupation numbers (RSGK). We formally broaden in energy each levd by a and apply Fermi statistics to this continuous system. We add infinitesimal fractions of an electron to the broadened levels in order, until all the dectrons are used up, yidding a precise Fermi energy, f, and the various occupation numbers... 

It is instructive to study the vacant atomic orbital population in dimers and trimers. As mentioned in the Introduction, in the 80 s Bauschlicher et al. [10,11] came to the conclusion that the promotion of ns-electrons to np-orbitals leading to sp-hybridization is the main mechanism responsible for binding in alkaline-earth clusters. This conclusion was based on a study of the SCF Mulliken population analysis for tetramers, which are stable at the SCF level. At present, we can perform more precise analysis using the Natural Bond Orbital Analysis and calculate it at the electron correlation level. 

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. 

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