Linear-scaling implementation of exact exchange using localized numerical orbitals and contraction reduction integrals

Lionel A. Truflandier; Tsuyoshi Miyazaki; David R. Bowler

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arXiv · 1112.5989

Linear-scaling implementation of exact exchange using localized numerical orbitals and contraction reduction integrals

Lionel A. Truflandier·Tsuyoshi Miyazaki·David R. Bowler

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Abstract

We present enhancements to the computational efficiency of exact exchange calculations using the density matrix and local support functions. We introduce a numerical method which avoids the explicit calculation the four-center two-electron repulsion integrals and reduces the prefactor scaling by a factor N, where N is the number of atoms within the range of the exact exchange Hamiltonian. This approach is based on a contraction-reduction scheme, and takes advantage of the discretization space which enables the direct summation over the support functions in a localized space. Using the sparsity property of the density matrix, the scaling of the prefactor can be further reduced to reach asymptotically O(N).

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Lionel A. Truflandier, Tsuyoshi Miyazaki, David R. Bowler. 2011-12-27. Linear-scaling implementation of exact exchange using localized numerical orbitals and contraction reduction integrals. https://arxiv.org/abs/1112.5989

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