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Welcome to the GW and BSE (and RPA) tutorial!

In this tutorial, you will learn about three methods that go beyond DFT: the many-body perturbation theory in the GW approach, the random-phase approximation (RPA), and the Bethe-Salpeter equation (BSE). These methods help to improve the predictive power of the numerical simulations, but at the expense of much higher computational costs.

This tutorial was updated to reflect the state of FHI-aims version 240507. This tutorial was a joint work by (in alphabetical order) Volker Blum, Saeed Bohloul, Dorothea Golze, James Green, Levi Keller, Sebastian Kokott, Mohammad Nakhaee, Xinguo Ren, Andrei Sobolev and Yi Yao.

Older versions of this tutorial

FHI-aims version 210716_2

The objective

This tutorial introduces several methods that go beyond the DFT level. The following points will be addressed:

  • How to run GW and BSE calculations for solids and molecules, as well as RPA for molecules, with FHI-aims.
  • How to interpret the results of the simulations and their meaning in the context of theoretical spectroscopy (e.g. photoemission and core level spectroscopy)


Users of this tutorial should have a sufficiently good understanding:

  • About the basics of running FHI-aims. If this is not the case, please consider to study the Basics of Running FHI-aims tutorial first.
  • Some of the exercises are computationally very demanding and may require a node or a whole bunch of nodes from computer clusters. Those parts cannot be run on a laptop and are specifically marked. Nevertheless, we still recommend to go through these expensive exercises. We provide the complete input and output files, which you can use to familiarize with these methods. To download all solutions, it is easiest to clone this repository:
    git clone


  1. GW and BSE calculations for molecules
    1. GW eigenvalues and Photoemission
    2. Counterpoise Correction
    3. Core levels
    4. BSE
    5. Multiple GW solutions
  2. GW for solids