Robust Periodic Fock Exchange with Atom-Centered Gaussian Basis Sets

In this work, we present a robust implementation of the periodic Fock exchange for atom-centered Gaussian-type orbitals (GTOs). We discuss the divergence, appearing in the formulation of the periodic Fock exchange in the case of a finite number of k-points, and compare two schemes that remove it. These are the minimum image convention (MIC) and the truncated Coulomb interaction (TCI) that we use here in combination with k-meshes. We observe artifacts in four-center integrals of GTOs, when evaluated in the TCI scheme. They carry over to the exchange and density matrices of Hartree-Fock calculations for TCI but are absent in MIC. At semiconducting and insulating systems, we show that both MIC and TCI yield the same energies for a sufficiently large supercell or k-mesh, but the self-consistent field algorithm is more stable for MIC. We therefore conclude that the MIC is superior to TCI and validate our implementation by comparing not only to other GTO-based calculations but also by demonstrating excellent agreement with results of plane-wave codes for sufficiently large Gaussian basis sets.