Theoretical analysis of the optical excitation spectra of silver and gold nanowires

The excitation spectra of linear atomic chains of silver and gold with various sizes have been calculated using time-dependent density functional theory. Silver chains show longitudinal and transverse peaks as well as a low-intensity d-band. The longitudinal peak, corresponding to the HOMO-LUMO transition (along the main axis of the chain), shifts linearly to the red as the length of the system increases, consistent with the particle-in-a-box model. The transverse peak remains at approximately constant energy for all systems studied and corresponds to Sigma(m) -> Pi(m) transitions in the xy plane perpendicular to the chain. As the chain grows, transitions arising from d orbitals contribute to the transverse peak, which affects its oscillator strength. Contrary to silver, gold chains display a strong d-band that converges to a distinct pattern at a chain length of about twelve atoms. The transitions involved in the d-band originate from localized d-orbitals with a d(z2) character since they have the right symmetry to give transitions into the LUMO, LUMO + 1, ..., which have Sigma symmetry. Transitions arising from these localized d-orbitals also affect the position of the longitudinal peak and generate a wide transverse band. Although the majority of the transitions involved in the transverse band have a d Sigma -> Pi or d Pi -> Sigma character, they are hidden by much stronger excitations of d Pi -> Pi character in gold nanowires.