Atomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency

Research output: Contribution to journalArticle


Cholesky decomposition of the atomic two-electron integral matrix has recently been proposed as a procedure for automated generation of auxiliary basis sets for the density fitting approximation [F. Aquilante , J. Chem. Phys. 127, 114107 (2007)]. In order to increase computational performance while maintaining accuracy, we propose here to reduce the number of primitive Gaussian functions of the contracted auxiliary basis functions by means of a second Cholesky decomposition. Test calculations show that this procedure is most beneficial in conjunction with highly contracted atomic orbital basis sets such as atomic natural orbitals, and that the error resulting from the second decomposition is negligible. We also demonstrate theoretically as well as computationally that the locality of the fitting coefficients can be controlled by means of the decomposition threshold even with the long-ranged Coulomb metric. Cholesky decomposition-based auxiliary basis sets are thus ideally suited for local density fitting approximations.


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

Subject classification (UKÄ) – MANDATORY

  • Theoretical Chemistry


  • Gaussian processes, ab initio calculations, density functional theory, orbital calculations
Original languageEnglish
JournalJournal of Chemical Physics
Issue number15
Publication statusPublished - 2009
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)