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A linear-scaling algorithm is presented for computing the Hartree-Fock (HF)exchange matrix using concentric atomic density fitting. The algorithm utilizesthe stronger distance dependence of the three-center electron repulsionintegrals along with the rapid decay of the density matrix to accelerate theconstruction of the exchange matrix. The new algorithm is tested withcomputations on systems with up to 1536 atoms and 15585 basis functions, thelatter of which represents, to our knowledge, the largest quadruple-zeta HFcomputation ever performed. Our method handles screening of high angularmomentum contributions in a particularly efficient manner, allowing the use oflarger basis sets for large molecules without a prohibitive increase in cost.

Fast construction of the exchange operator in an atom-centered basis with concentric atomic density fitting