Optical excitations in organic molecules, clusters, and defects studied by first-principles Green's function methods

Spectroscopic and optical properties of nanosystems and point defects are discussed within the framework of Green's function methods. We use an approach based on evaluating the self-energy in the so-called GW approximation and solving the Bethe-Salpeter equation in the space of single-particle transitions. Plasmon-pole models or numerical energy integration, which have been used in most of the previous GW calculations, are not used. Fourier transforms of the dielectric function are also avoided. This approach is applied to benzene, naphthalene, passivated silicon clusters (containing more than one hundred atoms), and the $F$ center in LiCl. In the latter, excitonic effects and the $1s\ensuremath{\rightarrow}2p$ defect line are identified in the energy-resolved dielectric function. We also compare optical spectra obtained by solving the Bethe-Salpeter equation and by using time-dependent density-functional theory in the local, adiabatic approximation. From this comparison, we conclude that both methods give similar predictions for optical excitations in benzene and naphthalene, but they differ in the spectra of small silicon clusters. As cluster size increases, both methods predict very low cross section for photoabsorption in the optical and near ultraviolet ranges. For the larger clusters, the computed cross section shows a slow increase as a function of photon frequency. Ionization potentials and electron affinities of molecules and clusters are also calculated.