Geometric structure of the magic number clusters Li n Na 8-n,Na n K 8-n,and K n Li 8-n

The mixed alkali clusters Li_nNa_8-n, Li_nK_8-n, and Na_nK_8-n were studied by Kohn-Sham theory with a gradient corrected (PBE) exchange-correlation functional. Geometry optimization was done with a Tabu Search algorithm to find possible global minima, followed by local optimization with a quasi-Newton method. For the pure clusters and all Na_nK_m mixed clusters, the predicted global minimum is a dodecahedron having D_2d symmetry in its ideal form. There are various structures among the predicted global minima of Li_nNa_m and Li_nK_m: they all have in common that the Li_n subunit achieves maximal coordination and forms a compact core at, or near, the center of the cluster. The clusters Li_nNa_m and Li_nK_m all have near zero asphericity, in line with the prediction of the ellipsoidal jellium model for 8 electrons, and the asphericity in nonzero but small in all other clusters. The clusters Li₄Na₄, Na₄K₄, and K₄Na₄ each have the four atoms of the lighter element near the center of mass and these clusters are more stable than those of other compositions. Calculated ionization potentials and static dipole polarizabilities agree rather well with experimental values but do not allow a structure assignment to be made.