Stable structures and electronic properties of 6-atom noble metal clusters using density functional theory

The 6-atom clusters of group IB noble metals have been investigated theoretically using the density functional calculation with a plane-wave basis (CASTEP). We have calculated their optimized structures, relative cluster’s energies, atomic and bonding populations, spectra of the vibrational frequencies, energy gaps between the highest occupied and the lowest unoccupied molecular orbitals, and average polarizabilities per atom. The stable structures we found are planar triangular, pentagonal pyramid, and capped trigonal bipyramid. For the Cu₆ and Ag₆ cluster, the planar structure energetically competes with the pyramid structure for the ground state. According to the population analyses, the s–d orbital hybridization is explicitly shown to be in association with the corner atoms of the planar structure. We found that the vibrational spectra of the clusters are structural dependent. The average polarizabilities for the planar structure of the Cu₆ and Ag₆ cluster are quite different from their other stable isomers. In contrast, the polarizabilities are about the same for all stable gold hexamers. Our calculations benefit a reliable geometry identification of the 6-atom noble metal clusters.