Fast construction of the exchange operator in an atom-centred basis with concentric atomic density fitting

Abstract

ABSTRACTAn algorithm is presented for computing the Hartree–Fock exchange matrix using concentric atomic density fitting with data and instruction count complexities. The algorithm exploits the asymptotic distance dependence of the three-centre Coulomb integrals along with the rapid decay of the density matrix to accelerate the construction of the exchange matrix. The new algorithm is tested with computations on systems with up to 1536 atoms and a quadruple-zeta basis set (up to 15585 basis functions). Our method handles screening of high angular momentum contributions in a particularly efficient manner, allowing the use of larger basis sets for large molecules without a prohibitive increase in cost.