Phenomenological shell model

With respect to Au TM+ cations, we have explained, from first principles calculations, the recently observed magic numbers °, without resorting to the phenomenological shell model. 

T. Holtzl, T. Veszpremi and P. Elevens and M. T. Nguyen. Phenomenological shell model and aromaticity in metal clusters. In Aromaticity and Metal Cluster. ed. P. K. Chattaraj, Taylor Francis FL, 2010. 

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... 

Phenomenological Shell Model and Aromaticity in Metal Clusters... 

FIGURE 14.1 Energy levels using the phenomenological shell model for spherical clusters (a) homogeneous background potential, (b) electronegative dopant atom in the center, and (c) electropositive dopant atom in the center. 

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. 

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