Density fitting of Coulomb integrals in electronic structure calculations of solids

A density fitting approach to Coulomb integrals is formulated for infinite systems with translational periodicity. Demands for Coulomb integrals scale linearly with regard to the number of unit cells, thereby opening the possibility of highly effective evaluation of the Coulomb part of electronic structure calculations in the solid state. The problem of the inverse of the Coulomb matrix in the Gamma point of the momentum space is solved analytically. As a byproduct, self-reproducibility of the overlap matrix (a feature not having a molecular analogue, with fundamental consequences for Coulomb tail cancellation) is revealed.