Metal clusters closed electronic structure

Here, as in other branches of inorganic chemistry, interatomic distances show a considerable variation and, although some correlation with bond order is possible, attempts to do so should be regarded with caution.For metals with close-packed structures, the coordination number of any atom is 12 for cubic or hexagonal structures, and 14 (8 plus 6 more neighbors at about 15% further away) for body-centered cubic structures. In general, this number exceeds the number of electrons per atom available for metal-metal bond formation and precludes the formation of localized, two-electron bonds between metal atoms. Bond orders of less than 1 are therefore commonly recorded. For metal clusters, it is necessary to consider the variety of ways in which valence electrons may be utilized in chemical bonding within the Mm... 

Then, a fundamental question arises how many metal atoms should be in a cluster, which exhibits a metallic nature Mercury is the most suitable element to examine such a question. Liquid mercury is a typical metal while two mercury atoms is weaJcly bonded by a dispersion force, because a mercury atom has a closed electronic structure, where all the orbitals... 

The study of pure and doped metal clusters has become an interesting and rapidly progressing research topic over the past decades. This is because of their structural richness, unexpected stability and reactivity patterns, the variation of these properties with respect to the number of the constituting atoms, and also because of the observed aromaticity in certain species. Similarly to an organic compound [1], the aromaticity of a metal cluster is showed by the coexistence of different properties such as equalized bond lengths and bond orders, the thermodynamic stability, specific reactivity, magnetic behavior, and the closed electronic structure. 

Electron configuration of metal clusters with itinerant electrons is represented in terms of the phenomenological shell model (PSM). The main assumption of this model is that the itinerant electrons are confined in a box according to the cluster shape, and these determine the properties of the given cluster to a great extent. This model was developed to explain the observed stability patterns of sodium clusters and has been successfully applied in other elements (such as Li, Al, Cu) and properties (such as ionization energy, electronaffinity). Furthermore, it was formulated for different cluster shapes and also for doped metal clusters. In this chapter, we aim to demonstrate that the aromaticity of metal clusters can be interpreted in terms of the PSM, which can be used to formulate the criteria to obtain a closed electronic structure in different cluster shapes. Therefore, the PSM provides the different electron... 

Thus a simple question arises Based on this model, at which size can we expect a stable alkaline-earth metal cluster As each alkaline-earth metal has two itinerant valence s electrons, stable clusters are expected for clusters constituting 4, 10, 20,... atoms, which was indeed confirmed by experiments. Although the configuration IS IP 1D ° corresponds to a closed electronic structure, 18 was not observed as a magic number in homogeneous clusters. This is because both ID and 2S levels... 

Some examples for 3D spherical aromaticity can be fonnd in different fullerenes. It is well known that the Ji orbitals of the carbon atoms in fullerenes are perpendicular to the surface and these electrons are itinerant, similarly to the benzene. Hence, the electronic structure of these compounds can be modeled using a Hiickel-type model, and the condition to obtain a closed electronic structure and aromaticity can also be formulated as previously done by Hirsch et al. Their rule is valid for icosahe-dral fullerenes. We will see that spherical aromaticity is a more common feature of metal clusters. 

The connection between the phenomenological shell model (PSM) and aromaticity of metal clusters is presented in this chapter. This model allows us to probe the aromaticity of metal clusters, and also organic compounds, in a general framework and context. The 4n + 2 rule of planar rings is shown to be a special case of this model. It can be applied to the cases of planar, spherical, and distorted (oblate and prolate) clusters. The different criteria (stability, symmetry, magnetic properties, electronic structure) are considered with the examples of different scandium-doped copper clusters Cu c and Cu c+. In summary, a closed electronic structure according to the PSM often results in an aromatic behavior. 

As to the number of atoms required to close the gap between insulator and metallic clusters, they vary from as few as 20 to several hundred atoms. Freund3 suggests that the precise numbers will vary from metal to metal, depending on the electronic structure of the metal. 

This behavior differs completely from the discrete one-electron absorptions of low-nuclearity metal cluster molecules [17]. Instead, it resembles the 5d - 6s,6p interband transition of colloidal gold. This demonstrates clearly that the AU55 cluster has electronic energy levels which are closely spaced in a developing band structure, quite similar to colloidal gold. On the other hand, these electrons do not seem to show a collective behavior which would give rise to the plasma resonance. 

It has been long known that for a given transition-metal cluster the open-shell and the closed-shell species may differ. Typically, metal-ligand bond lengths are elongated for the open-shell structures, where the metal centers carry local spins and electrons occupy antibonding orbitals, in comparison to their closed-shell... 

The metal clusters in HFeCo3(CO)g(P(OMe)3)3 and H3Ni4(Cp)4 contain different numbers of electrons. The former cluster is a closed-shell structure (60 electrons) while the latter contains 63 electrons and is paramagnetic with S... 

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