Linear scaling computation of the Hartree–Fock exchange matrix

Thresholding criteria are introduced that enforce locality of exchange interactions in Cartesian Gaussian-based Hartree–Fock calculations. These criteria are obtained from an asymptotic form of the density matrix valid for insulating systems, and lead to a linear scaling algorithm for computation of the Hartree–Fock exchange matrix. Restricted Hartree–Fock/3-21G calculations on a series of water clusters and polyglycine α-helices are used to demonstrate the 𝒪(N) complexity of the algorithm, its competitiveness with standard direct self-consistent field methods, and a systematic control of error in converged total energies.