Electrostatic interaction model for the calculation of the polarizability of large noble metal nanoclusters

In this work we have presented a capacitance-polarizability interaction model for describing the polarizability of large metal clusters. The model consists of interacting atomic capacitances and polarizabilities that are optimized to reproduce the full polarizability tensors of medium sized (N ≤ 68) gold and silver clusters. The reference polarizability tensors have been calculated using time-dependent density functional theory and shown good agreement with experimental results. We have shown that very good agreement between the model and the DFT results can be achieved both for the isotropic and anisotropic polarizability as a function of size, thus providing an accurate description of the polarizability of noble metal clusters. The model is computationally efficient and can easily handle cluster several nm in radius, thus, provides a natural bridge between the quantum mechanical methods and the macroscopic electrodynamic description. This allowed us to study the polarizability of silver and gold clusters having different shapes, i.e., spheres, rods, and disks, and sizes having diameters as large as 4.5 nm, thus, reaching the saturation of the polarizability. By partitioning the total polarizability into effective atomic polarizabilities that depend on the atomic position in the cluster, we provide a physical picture of the saturation of the polarizability of metal clusters as a function of size. This illustrates that the onset of the saturation occurs as the cluster starts to have a core of atoms showing bulk-like polarizabilities, surrounded by layers of atoms with surface-like polarizabilities. For larger clusters we see that the bulk core grows whereas the surface layers keep roughly the same thickness thus leading to a saturation of the polarizability as the size of the cluster increases.