Dielectric screening in extended systems using the self-consistent Sternheimer equation and localized basis sets

We develop a first-principles computational method for investigating the dielectric screening in extended systems using the self-consistent Sternheimer equation and localized nonorthogonal basis sets. Our approach does not require the explicit calculation of unoccupied electronic states, uses only two-center integrals, and has a theoretical scaling of order O(N-3). We demonstrate this method by comparing our calculations for silicon, germanium, diamond, and LiCl with reference plane-wave calculations. We show that accuracy comparable to that of plane-wave calculations can be achieved via a systematic optimization of the basis set.