Shell structure of electronic states of Cu clusters

Electronic states of icosahedral Cu₁₃ and Cu₁₂ clusters were calculated by the DV-Xα method which took into account of many-electron effects. The valence 3d orbitals are localized within atom and isolated from the valence 4s orbitals extended over the whole cluster. The characteristic feature of the states ofs valence electrons of Cu₁₃ cluster well corresponds to that of one-electron picture i.e. the shell model of the 3-dimensional isotropic harmonic oscillator potential. Electronic states of valence levels of Cu₁₂ cluster which have no central atom fairly well correspond to those of a combined potential of the harmonic oscillator and a 3-dimensional Gaussian potential barrier at the center of the cluster.