A TDDFT study of the optical absorption spectra of gold and silver clusters

The absorption cross-section over the optical range of frequencies of gold and silver clusters of up to 171 atoms was calculated using time-dependent density functional theory. Calculations were performed using the package Octopus and used the explicit time propagation method. The wavefunctions were calculated over a real-space grid and exchange-correlation interactions were including using the local density approximation. Structures were cleaved from a bulk crystal and included high-symmetry structures as well as structures with lower levels of symmetry. The evolution of the absorption spectra over cluster size was investigated and several trends were identified. As cluster size increases the absorption spectra becomes smoother. For gold clusters with more than approximately 70 atoms, the absorption spectra have several common features, including an absorption peak at around 2.5-3.0 eV, commonly attributed to a plasmonic oscillation. Absorption spectra were compared to past calculations and experimental measurements where available. For gold clusters above approximately 150 atoms, the calculated absorption spectra are in reasonable agreement with Mie theory calculations and experimental measurements. The effect of different calculation methods and approximations on the calculated absorption cross-section was also identified. The inclusion of spin-polarisation and the use of an exchange-correlation potential using the generalised gradient approximation had minor impact on the calculated absorption spectra. A new method of analysing the nature of peaks in the absorption spectra was also investigated. This method entailed exciting the system at a single frequency, and analysing the evolution of the electron density over time. This initial investigation indicated a difference in the evolution of the system when it was oscillated at a frequency corresponding to a plasmonic response as compared to a frequency corresponding to an electron hole excitation. This possibly indicates a method for investigating the nature of a plasmonic response in clusters of this size. This thesis demonstrates that with current computing power the optical absorption spectra of metallic clusters can be calculated using time-dependent density functional theory over a continuous range of cluster sizes from several atoms up almost to the point at which classical calculations become accurate. It identifies what calculation parameters are important to the optical absorption spectra for future calculations to agree with classical calculations as more computing power becomes available.