Deterministic and Faster GW Calculations with a Reduced Number of Valence States: ( ln ) Scaling in the Plane-Waves Formalism.

We introduce a method for reducing the number of valence states entering the calculation of screened the Coulomb interaction in calculations. In this way, denoting with the generic size of a system, the computational cost is brought from the typical () to the more favorable ( ln ). The method becomes effective for large model structures. For enhancing the potentialities of our scheme, we combined it with a linear-response approach, which can exploit the symmetries of the simulation cell in direct space. We registered quadratic scaling up to more than thousand atoms with an almost 10-fold speed-up with respect to a standard implementation. Our scheme can be extended to any linear response calculation.