On preconditioning the self-consistent field iteration in real-space Density Functional Theory

We present a real-space formulation for isotropic Fourier-space preconditioners used to accelerate the self-consistent field iteration in Density Functional Theory calculations. Specifically, after approximating the pre-conditioner in Fourier space using a rational function, we express its real-space application in terms of the solution of sparse Helmholtz-type systems. Using the truncated-Kerker and Resta preconditioners as representative examples, we show that the proposed real-space method is both accurate and efficient, requiring the solution of a single linear system, while accelerating self-consistency to the same extent as its exact Fourier-space counterpart.