Low-cost evaluation of the exchange Fock matrix from Cholesky and density fitting representations of the electron repulsion integrals

Research output: Contribution to journalArticle


The authors propose a new algorithm, "local K" (LK), for fast evaluation of the exchange Fock matrix in case the Cholesky decomposition of the electron repulsion integrals is used. The novelty lies in the fact that rigorous upper bounds to the contribution from each occupied orbital to the exchange Fock matrix are employed. By formulating these inequalities in terms of localized orbitals, the scaling of computing the exchange Fock matrix is reduced from quartic to quadratic with only negligible prescreening overhead and strict error control. Compared to the unscreened Cholesky algorithm, the computational saving is substantial for systems of medium and large sizes. By virtue of its general formulation, the LK algorithm can be used also within the class of methods that employ auxiliary basis set expansions for representing the electron repulsion integrals. (C) 2007 American Institute of Physics.


  • Francesco Aquilante
  • Thomas Pedersen
  • Roland Lindh
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Theoretical Chemistry
Original languageEnglish
JournalJournal of Chemical Physics
Issue number19
StatePublished - 2007
Publication categoryResearch

Bibliographic note

The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Theoretical Chemistry (S) (011001039)