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Abstract. We present the first systematic study of potential energy curves and prolate-oblate shape transitions of sodium clusters with 8 < N< 40 atoms. The Kohn-Sham equations are solved in the local density approximation for the jellium model with spheroidal deformations. The ionic background density is taken to have a diffuse surface of Woods-Saxon type. The quadrupole and hexadecupole moments of the electron and jellium densities are investigated, revealing a strong hexadecupole dependence for selected clusters. Collective dipole resonances are described in the simple surface plasmon model. Shape transitions are found to occur at particle numbers 12-14 (prolate-oblate), 18 -20-22 (oblate-spherical-prolate) and 30-32 (prolate-oblate), which are in good agreement with experimental results; triaxiality is predicted for Na-36. Comparing our results with those of molecular dynamics calculations, we confirm the scheme of Kohn-Sham levels and the gross behaviour of potentials and densities.

We have calculated multidimensional BornOppenheimer energy surfaces of singly charged and neutral sodium clusters with quadrupole, octupole, and hexadecapole deformed shapes in a particle range from 8 ≤ N ≤ 58. We use the local-density approximation (LDA) and solve the Kohn-Sham equations on a cylindrical mesh for axially symmetric shapes. Employing the structure-averaged jellium model (SAJM), we ascertain that the correct empirical bulk properties and surface tension are reproduced. Besides a pronounced isomerism in the β 2 /β 4 plane we also find superdeformed shapes. We compare the PES data with shape transitions deduced from experimental splittings of the dipolephotoabsorption cross sections. The influence of large octupole moments reverts the scheme of prolate-oblate shape transitions above the filled 2p-shell (N = 42, 44) which is wrongly predicted in spheroidal models.

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Structure and electron dynamics of sodium clusters are investigated within the local-density approximation for the electrons. We compare results from detailed ionic structure with those from a structure averaged jellium model and find that the dominance of the electron cloud overlays most of the differences in the background. Ionic structure is indispensable, however, to compute the surface energy of clusters and to provide an unprejudiced picture of cluster fission. For all cases, we compute the resonance spectra associated with electron dynamics. In particular, the very strong deformations during fission deliver unusual resonance modes with a broad spectral fragmentation. 36.40.Gk; 36.40.Qv; 36.40.Mr PACS:The jellium model for sodium clusters was extremely successful in predicting the sizable electronic shell effects [1] and the collective electronic response [2], for a review see [3]. Nonetheless, the approach has been often questioned in view of the a priori more reliable quantum chemical ab initio methods [4]. In order to understand the differences and similarities of either model, we have investigated sodium clusters within the jellium model as well as with detailed ionic structure using the same level of description at the electronic side, namely the (time-dependent) local-density approximation (TDLDA) for the valence electrons. We present here in short several examples, covering ground state properties (shapes, surface energy), fission, position and width of plasmon resonances, highly excited electrons. To keep the space limits, we refer to previous publications for formal details and basic discussions. The presentation here concentrates on a few selected, typical and recent examples.The formal background is quickly summarized: In any case, we use the energy-density functional of [5] in the (timedependent) Kohn-Sham equations for the valence electrons. For the calculations with full ionic structure, we employ local pseudo potentials for the ionic cores exploiting the near axial symmetry of the system, for details of this Cylindrically Averaged Pseudo potential Scheme (CAPS) see [6]. Fig. 1. The binding energy per particle for sodium clusters in the SAJM (+) and with full ionic structure (o) drawn versus N −1/3 . The surface energy is the average slope through data. It is determined by the CAPS and used as input in SAJMThe ionic configurations are optimized by simulated annealing. The jellium model is enriched by structural information on the ionic structure energy and the ionic contribution to the surface energy, yielding the structure averaged jellium model (SAJM) [7]. A finite surface width of the jellium background, as it can be motivated from a pseudo potential folding [8], guarantees an appropriate frequency of the Mie plasmon resonance [9]. For a discussion of general trends and features of the plasmon, see [10].The most prevalent features of cluster structure are the sequence of magic clusters, measured by abundances [3,11], and the ground-state deformations, measured by the splitting of the plasm...