Linear scaling computation of the Hartree–Fock exchange matrix
- 15 August 1996
- journal article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 105 (7) , 2726-2734
- https://doi.org/10.1063/1.472135
Abstract
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.Keywords
This publication has 47 references indexed in Scilit:
- Improvements on the direct SCF methodJournal of Computational Chemistry, 1989
- An unconventional scf method for calculations on large moleculesJournal of Computational Chemistry, 1986
- Principles for a direct SCF approach to LICAO–MOab‐initio calculationsJournal of Computational Chemistry, 1982
- Methods for efficient evaluation of integrals for Gaussian type basis setsTheoretical Chemistry Accounts, 1974
- No N 4-dependence in the calculation of large moleculesTheoretical Chemistry Accounts, 1973
- Perturbation Theory for the Fock-Dirac Density MatrixPhysical Review B, 1962
- Self-Consistent Orbitals for RadicalsThe Journal of Chemical Physics, 1954
- Approximate Formulas for Many-Center Integrals in the Theory of Molecules and CrystalsThe Journal of Chemical Physics, 1953
- New Developments in Molecular Orbital TheoryReviews of Modern Physics, 1951
- Electronic wave functions - I. A general method of calculation for the stationary states of any molecular systemProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1950