Bulk properties or not: The electronic structure of small metal clusters

Abstract

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 through ab initio SCF calculations (with the emphasis on the clusters Cu8 and Cu13). The basis set used is of double-zeta quality for the valence shells 3d and 4s. The analysis focuses on the following properties of the clusters: geometrical structure, binding energy, and distribution of energy levels. For the 13-atom cluster, the icosahedron is found more stable than the cubo-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 3d and 4s levels are well separated for Cu8 and just begin to overlap for Cu13. This situation looks rather different from the one for the bulk metal where the s band totally overlaps the d band. The relationship between the orbital energies from the ab initio SCF calculations and the ionization potentials is discussed. For the 13-atom cluster, the relaxation effect is probably small enough that the above conclusions, based on Koopmans’ theorem and the use of orbital energies, should not be altered by including it. On the whole, the ab initio results contradict the conclusion of the SCF–Xα–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 the Xα calculations, which showed that the ’’d band’’ was completely overlapped by the ’’s band.’’ However, this represents probably a spurious effect, since the Xα eigenvalue differs from the corresponding ionization potential by a ’’self-interaction term,’’ with rather different values for the orbitals of the 3d type and of the 4s type.