Therefore we will address several non-standard applications of the GW method like the calculation of the electronic lifetimes or total-energies. In addition the numerical procedures that define the basis of a successful GW calculation will be extensively discusses. We will dedicate specific lectures to choice of an accurate sampling of the Brillouin Zone, especially in low-dimensional systems like nano-structures that represent an important class of systems studied in the scientific community. We will also discuss the impact of the used basis (plane-waves versus localized basis) and the impact of pseudo-potentials versus all-electrons calculations.

More specific lectures will be developed to the problem of self-consistency, vertex corrections and total-energies evaluation in the GW method. These theoretical aspects will provide the students a more general view on the formal justifications, as well on the most up-to-date developments of the GW theory.

Besides theoretical and technical lectures (preferably in the morning) the tutorial will characterized by long hands-on sessions (in the afternoon) where the students will perform calculations on realistic materials following pre-organized tutorials[14]. During and after these hands-on sessions the students will have the possibility of discussing with the teachers about any aspect of the tutorial. These interactions will be particularly meaningful as the teachers of the hands-on sessions will be the main developers of the code used. We also plan to encourage the students, after the completion of the proposed hands-on exercises, to initiate small projects from their own.

Indeed a particularly valuable aspect of this tutorial is that two out of the four organizers (A. Marini and P. Umari) are the developers of two of the code used: Yambo7 and GWL6. These codes adopt a starting formalism based on plane-waves and pseudopotentials, used to describe the core and valence electrons. Moreover, both codes can perform MBPT calculations starting from DFT calculations performed using the Quantum-Espresso package [4] that we will use to to calculate the ground-state wave-functions using Density-functional Theory.

Yambo is a widely used GW code. Based on a plane-have expansion for wave-functions and operators, it offers a large range of capabilities. It is freely available through the GNU license. GWL is a more recent code which is based on optimized basis sets for representing operators in order to accelerate calculations in particular for isolated and non-crystalline systems. Within 2011 it will be fully available through the GNU license.

In addition to Yambo and GWL we will also use the FHI-aims[11] code.