Sodium clusters electronic shell structures

Knight W D, Clemenger K, de Heer W A, Saunders W A, Chou M Y and Cohen M L 1984 Electron shell structure and abundances of sodium clusters Phys. Rev. Lett. 52 2141... 

Knight WD, Clemenger K, de Heer WA, Saunders WA, Chou MY, Cohen ML. Electronic Shell Structure and Abundances of Sodium Clusters. Phys Rev Lett. 1984 52(24) 2141-2143. 

Within the shell-model of the electronic structure of clusters of monovalent metals, the ionization potential drops to a low value between sizes and N(, -I-1, where N. indicates a closed-shells cluster. The electron affinity, on the other hand, drops between Nj — 1 and Nc, since the cluster with size N — 1 easily accepts an extra electron to close its nearly-filled external shell. Consequently, the cluster of size N has a large ionization potential and a low electron affinity and will be inert towards reaction. One then expects peaks in a plot of 1 — A versus N for closed shell clusters. The shell effects arc clearly displayed in a Kohn-Sham density functional calculation. Figure 10 shows the results of such a calculation for jellium-like Sodium clusters using the non-local WDA description of exchange and correlation. This calculation employed the Przybylski-Borstel version of the WDA see reference 30 for details). The peaks in I — A occur at the familiar magic clusters with N = 2, 8,18, 20,34,40 and 58. It is well... 

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. 

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... 

Sodium is a simple metal with one 3s valence electron. As predicted by the shell model, a metal cluster with closed electronic shell should possess 8, 20, 40, 58... valence electrons. Therefore, Na clusters with closed electronic shells at n = 9, 21, 41, and 59 were studied by Zhao s group using GA combined with DFT. Several open-shell Na clusters at n = 15, 26, 31, 36, and 50 whose sizes lie between the magic numbers were also investigated. The lowest energy structures of these Na clusters are displayed in Fig. 2. The simulated photoabsorption spectra of Na clusters from time-dependent DFT (TDDFT) simulations shown in Fig. 3 agree excellently with experimental data, confirming the reliability of the theoretical approaches. 

As mentioned in Section 33.2, the many-body expansion cannot be expected to work for metals. One reason is that most atoms forming metals have open-shell ground states of symmetry other than S, therefore it is difficult to determine quantum states of the subsystems needed in the definition of the expansion, cf. Section 33.10. The second reason is that the complete delocalization of the conduction electrons results in the electronic structure of a metal that is very far from that of monomers. The first problem does not occur for alkaline-earth metals or for high-spin alkali-metal clusters, and the many-body expansion can be defined for such clusters. However, this expansion appears to be very slowly convergent [106-108]. For some specific information about the spin-polarized sodium trimer, see Section 33.10.2. 

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