Size evolution study of “molecular” and “atom-in-cluster” polarizabilities of medium-size gold clusters

A study on static polarizabilities for a family of gold clusters (Aun, n = 6, 12, 20, 34, 54) is presented. For each cluster, a density functional theory perturbation theory calculation was performed to compute the cluster polarizability and the polarizability of each atom in the cluster using Bader´s “quantum theory of atoms in molecules” formalism. The cluster polarizability tensor, $\mathord{\buildrel{\lower3pt\hbox{\scriptscriptstyle\leftrightarrow}}\over \alpha } _{\it cluster}$α↔cluster, is expressed as a sum of the atom-in-molecule tensors, $\mathord{\buildrel{\lower3pt\hbox{\scriptscriptstyle\leftrightarrow}}\over \alpha } _{\it cluster} = \sum_\Omega {\mathord{\buildrel{\lower3pt\hbox{\scriptscriptstyle\leftrightarrow}}\over \alpha} (\Omega)}$α↔cluster=∑Ωα↔(Ω). A strong quadratic correlation (R2 = 0.98) in the isotropic polarizability of atoms in the cluster and their distance to the cluster center of mass was observed. The cluster polarizabilities are in agreement with previous calculations.