Density fitting of two-electron integrals in extended systems with translational periodicity: The Coulomb problem

Abstract

Density fitting approach to Coulomb integrals for infinite systems with translational periodicity is reformulated in direct space. Despite of the Coulomb infinite decay of some integrals, direct-space calculation is shown to be feasible. Moreover, we show that the direct-space ansatz is completely equivalent to our previous formulation in reciprocal space. Computational demands scale linearly with the number of unit cells. In addition, direct-space treatment has some practical advantages over the reciprocal-space formulation. The efficiency of our scheme is demonstrated on systems with translational periodicity in one dimension. Computation time takes only a small fraction of the conventional calculation with exact integrals. We show that for infinite systems auxiliary basis sets of equally good quality as for molecules can be constructed in a systematic way.