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The geometric and electronic structures of NaN, CuN, and AgN metal clustersare systematically studied based on the density functional theory over a widerange of cluster sizes 2=<N=<75. A remarkable similarity is observed betweenthe optimized geometric structures of alkali and noble metal clusters over allof the calculated cluster sizes N. The most stable structures are the same forthe three different metal clusters for approximately half the cluster sizes Nconsidered in this study. Even if the most stable structures are different, thesame types of structures are obtained when the meta-stable structures are alsoconsidered. For all of the three different metal clusters, the cluster shapeschange in the order of linear, planar, opened, and closed structures withincreasing N. This structural type transition leads to a deviation from themonotonic increase in the volume with N. A remarkable similarity is alsoobserved for the N dependence of the cluster energy E(N) for the most stablegeometric structures. The amplitude of this energy difference is larger in thetwo noble metal clusters than in the alkali metal cluster. This is attributedto the contribution of $d$ electrons to the bonds. The magic number is definedin the framework of total energy calculations for the first time. In the caseof NaN, a semi-quantitative comparison between the experimental abundancespectra (Knight et al., Phys. Rev. Lett., 52, 2141 (1984)) and the total energycalculations is carried out. The changing aspect of the Kohn-Sham eigenvaluesfrom N=2 to N=75 is presented for the three different metal clusters. Thefeature of the bulk density of states already appears at N=75 for all of threeclusters. With increasing N, the HOMO-LUMO gap clearly exhibits an odd-evenalternation and converges to 0.

Comprehensive study of sodium, copper, and silver clusters over a wide range of sizes 2=