Fast, efficient, and accurate dielectric screening using a local, real-space approach

Various many-body perturbation theory techniques for calculating electron behavior rely on {\it W}, the screened Coulomb interaction. Computing {\it W} 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 for screening core-level excitations [Ultramicroscopy {\bf 106}, 986 (2006)]. We extend this method to valence-level excitations. 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.