Deterministic and Faster GW Calculations with a Reduced Number of Valence States: <i>O</i>(<i>N</i>² ln <i>N</i>) 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 <i>W</i> in <i>GW</i> calculations. In this way, denoting with <i>N</i> the generic size of a system, the computational cost is brought from the typical <i>O</i>(<i>N</i>⁴) to the more favorable <i>O</i>(<i>N</i>² ln <i>N</i>). The method becomes effective for large model structures. For enhancing the potentialities of our scheme, we combined it with a linear-response <i>GW</i> 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.