Electronic properties, stability, and length scales of clusters

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Abstract
Three basically different models of clusters are studied, partly in order to explore the limitations of each model and partly in order to study general ground-state properties of the clusters. One model is based on the spherical-jellium model within the density-functional formalism, another is a semi-empirical tight-binding model obtained by parametrizing band structures for an infinite crystal, and the third model is a spherical-well model for non-interacting particles. Particularly stable clusters are found for systems with only completely filled electronic shells, although this result is somewhat obscured by surface effects for the tight-binding model. For the density of states as a function of N the tight-binding model is the one providing the most accurate information, especially for the features closest to the Fermi level. Only this model gives the proper description of those in the limit . Finally, we examine the electron density for different clusters and explore how Friedel oscillations occur. In particular the jellium model predicts very regular density oscillations, which can be ascribed to electron-electron interactions. We study both the pure clusters and ones with a void at the centre, where the latter represents a simple model for Cs-covered molecules. The two systems show many similarities - in particular it is demonstrated that the stable clusters occur with the same spacing of the radius of the system. The cluster sizes range up to values of N of about 10 000 for the jellium and the tight-binding models and to over 30 000 for the spherical-well model. In total the study shows that although many properties are well described by all of the models, it is important to be aware of their limitations, and it would be desirable to incorporate more experimental information in order to be able to evaluate the quality of the different models. To this end the `magic numbers' are less convenient.
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