  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.
