A study on static polarizabilities for a family of gold clusters (Au(n), 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, α(cluster), is expressed as a sum of the atom-in-molecule tensors, α(cluster)=∑(Ω)α(Ω). A strong quadratic correlation (R(2) = 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.

We introduce relativistic density functional theory (DFT) calculations on the gold cluster complexes (cluster-molecule-cluster) Au4-S-CnH2n-S'-Au4' (n=2-5). The structural, electronic and relativistic (ZORA) Bader's quantum theory of atoms in molecules (QTAIM) properties of the two lowest-energy complex isomers were computed as a function of the alkanedithiol size (n). The lowest-energy isomer is a triplet spin state independently of the complex size. According to QTAIM, the Au-Au and S-Au bonds are classified as closed shell (non-covalent) type. The HOMO-LUMO gap of the cluster complexes shows a zigzag behavior typical of gold nanoclusters with respect to the size of the alkanedithiol chain (n).

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