In practice, implementing the GW approximation involves several steps. First, a ground-state calculation is performed using DFT to obtain the initial electronic structure. Then, the Green's function and the screened Coulomb interaction are calculated and iteratively updated. This process requires significant computational resources and is often performed using specialized software packages such as Quantum ESPRESSO, VASP, or YAMBO. These tools provide the necessary algorithms to perform GW calculations and often include optimizations to reduce computational cost.
