Revisiting a local, real-space approach to dielectric screening calculations

Various many-body perturbation theory techniques for calculating electron behavior rely on $W$, the screened Coulomb interaction. The screening requires complete knowledge of the dielectric response of the electronic system, and the fidelity of the calculated dielectric response limits the reliability of predicted electronic and structural properties. As a simplification, calculations often begin with the random phase approximation (RPA). However, even RPA calculations are costly and scale poorly, typically as $N^4$ ($N$ representing the system size). A local approach has been shown to be efficient while maintaining accuracy [Ultramicroscopy 106, 986 (2006)]. We present improvements to the accuracy and execution of this scheme, including reconstruction of the all-electron character of the pseudopotential-based wave functions, improved $N^2\log N$ scaling, and a parallelized implementation. We discuss applications to Bethe-Salpeter equation (BSE) calculations of core and valence spectroscopies.