Plasmon resonances in linear noble-metal chains.

The electronic excitations of three noble-metall chains--copper, silver, and gold--have been investigated at the time-dependent density functional theory level. The reduced single-electron density matrix is propagated according to the Liouville-von Neumann equation in the real-time domain after an impulse excitation. The propagation in the real-time domain enables us to investigate the formation and size evolution of electronic excitations in these metallic chains with different number of atoms, up to a total of 26 atoms. The longitudinal oscillations at lower excitation energies are dominated by s → p transitions in these chains and have collective or central resonances, while the first peak involving d → p transitions in the longitudinal mode appears at a higher excitation energy and shows collective resonances. In the transverse oscillations, there are in most cases d → p transitions in each resonance, which can be attributed to either central or end resonances. Convergence of the oscillations, in particular those involving the collective and central resonances in the three noble-metal chains can only be observed for chains with 18 atoms or more. Different spectroscopic characteristics among these three metallic chains can be attributed to their different electronic structures, in particular the relativistic effects in the gold chains have a dramatic effect on their electronic structures and excitations.