Electron repulsion integrals and their associated operations pose a fundamental computational barrier in quantum chemistry, as both the storage and evaluation of the 4-center integrals naively scale as O(N4). Density-fitting reduces these integrals to a 3-center form that allows for storage scaling of O(N3) while the Coulomb and exchange matrices can be formally built in O(N3) and O(N4) operations, respectively. For intermediate-sized systems, density fitting provides substantial speedups for many quantum chemistry methods. Still, the exchange build remains a major bottleneck for Hartree-Fock calculations. Exploiting sparsity in the 3-center integrals enables exchange matrix builds in O(N3-4)operations. However, poor implementation of sparsity-screened exchange builds can hinder parallel scalability. Since both sparsity screening and parallel scaling are essential to high performance computing, it is critical to formulate software which utilizes both aspects maximally. We have identified a sparse memory layout which optimizes parallel scaling when using the 3-center integral tensors. The resulting algorithms were implemented in the Psi4 electronic structure package. Parallel scaling was first optimized on multi-core architectures. After, we optimized the method for use on the manycore architecture, Intel’s Knights Landing. We show that our data layout maximizes parallel scaling for sparsity-screened density-fitting operations.

Strong parallel scaling for sparsity-screened density-fitted integrals on Knights Landing

255th National Meeting (2018)

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