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

TL;DR

This paper introduces a new numerical method that significantly improves the computational efficiency of exact exchange calculations in quantum chemistry by reducing the scaling to linear with system size.

Contribution

The paper presents a contraction-reduction scheme that avoids explicit four-center integral calculations, achieving asymptotic linear scaling for exact exchange computations.

Findings

Reduces computational prefactor by a factor of N

Achieves asymptotic O(N) scaling

Utilizes sparsity of the density matrix

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).