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Aquilante F, Gagliardi L, Pedersen TB, et al. Atomic Cholesky decompositions: a route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency. J Chem Phys. 2009;130(15):154107doi: 10.1063/1.3116784.
Aquilante, F., Gagliardi, L., Pedersen, T. B., & Lindh, R. (2009). Atomic Cholesky decompositions: a route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency. The Journal of chemical physics, 130(15), 154107. https://doi.org/10.1063/1.3116784
Aquilante, Francesco, et al. "Atomic Cholesky decompositions: a route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency." The Journal of chemical physics vol. 130,15 (2009): 154107. doi: https://doi.org/10.1063/1.3116784
Aquilante F, Gagliardi L, Pedersen TB, Lindh R. Atomic Cholesky decompositions: a route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency. J Chem Phys. 2009 Apr 21;130(15):154107. doi: 10.1063/1.3116784. PMID: 19388736.
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J Chem Phys. 2009 Apr 21;130(15):154107. doi: 10.1063/1.3116784.

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

The Journal of chemical physics

Francesco Aquilante, Laura Gagliardi, Thomas Bondo Pedersen, Roland Lindh

Affiliations

  1. Department of Physical Chemistry, Université de Genève-Science II, 30 quai Ernest-Ansermet, CH-1211 Geneva 4, Switzerland. [email protected]

PMID: 19388736 DOI: 10.1063/1.3116784

Abstract

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 et al., 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.

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