The dependence of the properties of small copper clusters on their size, and their relationships to the properties of the bulk metal have been studied throughabinitioSCF calculations (with the emphasis on the clusters Cu8and Cu13). The basis set used is of doublehyphen;zeta quality for the valence shells 3dand 4s. The analysis focuses on the following properties of the clusters: geometrical structure, binding energy, and distribution of energy levels. For the 13hyphen;atom cluster, the icosahedron is found more stable than the cubohyphen;octahedron corresponding to the fcc structure of the bulk metal. The binding energy per atom increases almost linearly with the number of atoms of the cluster. From the orbital energy values, the sets of 3dand 4slevels are well separated for Cu8and just begin to overlap for Cu13. This situation looks rather different from the one for the bulk metal where thesband totally overlaps thedband. The relationship between the orbital energies from theabinitioSCF calculations and the ionization potentials is discussed. For the 13hyphen;atom cluster, the relaxation effect is probably small enough that the above conclusions, based on Koopmansrsquo; theorem and the use of orbital energies, should not be altered by including it. On the whole, theabinitioresults contradict the conclusion of the SCFndash;Xagr;ndash;SW calculations that the electronic structure of small metal clusters and of the bulk metal are not fundamentally different and that not many atoms are needed in a cluster to have a resemblance to the bulk. This idea was based on the analysis of the orbital energy values from theXagr; calculations, which showed that the rsquo;rsquo;dbandrsquo;rsquo; was completely overlapped by the rsquo;rsquo;sband.rsquo;rsquo; However, this represents probably a spurious effect, since theXagr; eigenvalue differs from the corresponding ionization potential by a rsquo;rsquo;selfhyphen;interaction term,rsquo;rsquo; with rather different values for the orbitals of the 3dtype and of the 4stype.
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