Magic numbers, metal-cluster results

In quite another area of physics, the discovery of magic numbers in alkali and other metallic clusters [7] has provided a fresh example of the significance of electronic shell closure. These much larger shells have been shown to oscillate collectively, and the resulting oscillations are of great significance as an example of a many-body resonance. They are discussed at some length in chapter 12. 

Structural and magnetic studies on [Co3(CO)(7t-Cp)3S], [Co3(7t-Cp)3S2] and [Co3(7t-Cp)3S2] have been reported by Frisch and DahF and the results have been used as a test case for the apparent correlation between metal-metal bond lengths in cluster compounds and the number of extra d-electrons over the magic number for each metal atom, which has recently been extensively studied by Dahl and co-workers (see Vol. 2 p. 207). The first two of the cobalt-sulphur clusters have been reported previously and the cation was prepared by addition of iodine to the neutral analogue and was isolated as the iodide. The structures of the three compounds substantiate the predictions concerning the dominant influence of anti-bonding valence electrons on the metal-metal bond lengths of the cluster system and also provide evidence that the presence of these electrons can induce a dramatic Jahn-Teller distortion of the cluster. The results are evidenced by the data presented in Table 1. ... 

Main experimental findings both for the ground state (magic numbers for the stability of clusters [3] and the existence of supershells [4]) and for excited states (the dominance of collective states in the photoabsorption of metal clusters MeA with N > S) were predicted [5] before their experimental confirmation. Recently we were able to explain the temperature dependence of the absorption of small metal clusters as observed by Haber-land s group [6]. If the model is complemented by pseudopotential perturbation theory [7] the results obtained match qualitatively those obtained by demanding quantum-chemical methods (e.g. the photoabsorption spectra of Na6). Further improvement of the model includes the removal of self-interaction effects, the so-called SIC [8-10] (a consequence of using the local density approximation (LDA) to general density functional theory (DFT)). 

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