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

Aquilante, Francesco LU ; Gagliardi, Laura; Pedersen, Thomas LU and Lindh, Roland LU (2009) In Journal of Chemical Physics 130(15).
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 , 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... (More)
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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Gaussian processes, ab initio calculations, density functional theory, orbital calculations
in
Journal of Chemical Physics
volume
130
issue
15
publisher
American Institute of Physics
external identifiers
  • wos:000265486300010
  • scopus:65449152949
ISSN
0021-9606
DOI
10.1063/1.3116784
language
English
LU publication?
yes
id
d09d4514-74b2-4007-84f1-245455036bb2 (old id 1427926)
date added to LUP
2009-06-25 13:29:02
date last changed
2017-11-12 03:24:16
@article{d09d4514-74b2-4007-84f1-245455036bb2,
  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 , 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.},
  author       = {Aquilante, Francesco and Gagliardi, Laura and Pedersen, Thomas and Lindh, Roland},
  issn         = {0021-9606},
  keyword      = {Gaussian processes,ab initio calculations,density functional theory,orbital calculations},
  language     = {eng},
  number       = {15},
  publisher    = {American Institute of Physics},
  series       = {Journal of Chemical Physics},
  title        = {Atomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency},
  url          = {http://dx.doi.org/10.1063/1.3116784},
  volume       = {130},
  year         = {2009},
}