The solution of the many-body problem has been a challenging task form the burn of Quantum Chemistry till now. In this context, the development of the many-body perturbation theory and the GW approximation has built the tools to quantitatively describe electronic excitations. The GW approximation will be presented briefly, as well as the Bethe-Salpeter equation. GW gives the quasi-particle band structure and BSE gives the two particle excitonic spectrum. A particular accent will be put on implementation schemes and implementation differences between 3D, 2D, 1D or 0D systems. To illustrate the technique two examples will be shown, CO and SiH4.
Universita di Modena e Reggio Emilia, Italy