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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 non-orthogonal basis sets. Our approach does not require the explicit calculation of unoccupied electronic states, only uses 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 planewaves calculations. We show that accuracy comparable to planewaves calculations can be achieved via a systematic optimization of the basis set.