Magic triangular and tetrahedral clusters

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Abstract
Using the methods of density functional theory and the jellium model we show that clusters with triangular [in two dimensions (2D)] or tetrahedral [in three dimensions (3D)] shapes have a strong shell structure and enhanced stability. Moreover, the shell closings correspond to the lowest magic numbers of a 2D and 3D harmonic oscillator and at the same time to the number of divalent atoms in close-packed triangles and tetrahedrons. Ab initio molecular dynamics simulations for Na and Mg clusters support the results of the jellium model.