The dipole polarizabilities of two families of low-lying structures, cage, and space filling, of the medium-sized ${\mathrm{Au}}_N$ $(N=32,38,44,50,56)$ clusters are studied using gradient-corrected density functional theory and finite field method. Both dipole moments and polarizabilities exhibit clear shape-dependent features and the cage structures have systematically smaller dipole moments and larger polarizabilities than the space-filling isomers. The mean polarizability per atom increases with cluster size for the cage structures, but it decreases slowly and tends to approach a constant for the space-filling structures. A linearly correlation between polarizability and cluster volume is noted, complying with the jellium model prediction for spherical metal clusters. The electronic effects including HOMO-LUMO gap and ionization energy on polarizabilities are also explored. The geometric effects play a dominant role on the determination of the polarizability of the cluster over the electronic effects.

• Received 27 April 2006

DOI:https://doi.org/10.1103/PhysRevA.74.023202