Sodium clusters stabilization energies

The simple hard-wall boundary condition, eqn (5.1), does yield the correct ordering of the energy levels as shown in Fig. 5.1. The only exceptions are the 3s and lh states, which have their sequence reversed compared to that of the self-consistent jellium predictions. Experimentally, the most frequently occurring sodium clusters are indeed Na8 and Na20 as expected from their special stability in Fig. 5.3. 

The existence of discrete electronic states of electrons confined in a small metal cluster has been observed to influence the thermodynamic stability of the system, in particular during the production of sodium clusters in supersonic beams composed of the metal vapor and an inert gas. The statistics of the relative abundances of different particle sizes reveal the existence of magic numbers for the number of atoms in the cluster, A = 8, 20,40,58, 92,... [3.9]. This has been interpreted in terms of the existence of degenerate energy levels in a spherical well with infinite-potential walls. Particularly stable structures are obtained when the number of valence electrons is such that it leads to a closed-shell electronic structure, i. e. a structure with a completely filled energy level and an empty up-... 

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... 

Up to the saturation of the 5-atom ring, the energy gained by each argon atom addition corresponds to the addition of a new IT-like interaction with sodium, plus the formation of an extra weak ArAr dispersion bond (two in NaArs). Beyond this size, the addition of argon atoms mainly involves the formation of ArAr bonds, and the stabilization is found to be weaker. In this respect, the stability of Na(3p)Ars is enhanced with respect to its immediate size neighbors and this cluster can be considered as an excited magic size cluster. 

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