Efficient Implementation of Exact Exchange for Periodic Systems within Concentric Atomic Density Fitting Approximation*

Development of electronic structure theory methods for periodic systems has been hampered for decades due to the unaffordable scaling with system size. One of the obstacles is the computation of two-electron repulsion integrals, whose near-field interaction can only be computed exactly or approximated using density fitting (DF). In this work, a massively-parallel implementation of an efficient local DF algorithm is presented in which atomic orbital (AO) products are fitted using only auxiliary AOs on one of the nuclei in that product. We applied this approach on the exact exchange term in Hartree-Fock with periodic boundary conditions (periodic HF) based on linear combinations of Gaussian-type AOs. Our algorithm has shown a significant reduction of computational costs with an accuracy below millihartree per atom, and thus will be beneficial to both hybrid density functional theory and post-HF methods.

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