In this work, we apply the atomic resolution of the identity (ARI) fitting approximation to the computation of Hartree-Fock exchange. The ARI approximation is a local modification of the RI approximation that produces an energy which is differentiable with respect to nuclear motion, unlike other local applications of RI. We justify empirically the use of locality and present timing comparisons of ARI, RI, and exact computation for one-, two-, and three-dimensional carbon systems. ARI is found to reduce significantly the cost of RI for large systems, while retaining accuracy.
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