Atomic and electronic structures ofPd13andPt13clusters

The electronic structures of ${\mathrm{Pd}}_{13}$ and ${\mathrm{Pt}}_{13}$ clusters of cuboctahedral and icosahedral symmetries are analyzed by the self-consistent spin-polarized density-functional scheme using the norm-conserving pseudopotential in the linear combination of atomic orbitals method. The electronic structure is discussed in relation to the shell structure of the giant atom. The stable atomic structure is discussed, considering the effects of the generalized gradient approximation of the exchange-correlation potential, the spin-orbit splitting, and the Jahn-Teller effect. The spin-orbit coupling effect depends on the symmetry of the whole cluster. It is the largest of these effects for Pt, and it is as large as the spin polarization effect for Pd. The electronic structure of Pd and Pt clusters of 13 atoms is comprehended as a complex of the shell structure and the localized Pd-$4d$ or Pt-$5d$ orbitals. The Jahn-Teller effect seems to be small to keep the shell structure. For both Pd and Pt metals the cuboctahedron clusters are more stable and have small spin polarization, $S=3\mathrm{}$ for the Pd cluster and $S=4\mathrm{}$ for the Pt cluster.