Diameter Dependence of the Excitation Spectra of Silver and Gold Nanorods

An analysis of the excitation spectra of silver and gold nanorods with different cross sections, lengths, and diameters was performed using time-dependent density functional theory at the LB94/DZ level. Silver nanorods show a strong longitudinal peak, corresponding to excitations along the main axis (z axis) of the nanorods, and a smaller transverse peak, corresponding to excitations in the xy plane of the nanorods. For systems with a large cross-section (star-shaped and large pentagonal nanorods), the single transverse peak is split into a wide band. The orbitals involved in these transitions are delocalized cylindrical orbitals. Constructive addition of the dipole moments of these transitions is observed for the strong longitudinal and transverse peaks, which is likely at the origin of the surface plasmon resonance phenomenon. The wavelength of the longitudinal peak increases linearly with increasing length, crossing over the transverse peak or transverse band, which remains at nearly constant energy and intensity. The intensity of the longitudinal peak increases with increasing system length due to the increasing number of electrons being collectively excited. The energy of the longitudinal peak for systems of identical length also tends to increase as the diameter of the system increases, which can be correlated to a decreasing aspect ratio. Gold nanorods display more complex excitation spectra due to the presence of transitions originating from the d-band. Such transitions may also mix with cylindrical orbital-based transitions, especially for systems with low aspect ratios, splitting the longitudinal peak into several peaks of lower intensity. As the aspect ratio increases, the energy of the longitudinal peak decreases, and its intensity increases. It then becomes separated from the d-band transitions which remain approximately constant in intensity and energy. Consequently, the amount of d-band coupling to the main cylindrical orbital-based excitations decreases, which leads to a strong isolated longitudinal peak similar to the silver case. No strong transverse peak is observed for gold nanorods at this level of theory. Instead, the transverse excitations are hidden by the d-band transitions.