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

Aquilante, Francesco LU ; Pedersen, Thomas LU and Lindh, Roland LU (2007) In Journal of Chemical Physics 126(19).
Abstract
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... (More)
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. (Less)
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author
organization
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type
Contribution to journal
publication status
published
subject
in
Journal of Chemical Physics
volume
126
issue
19
publisher
American Institute of Physics
external identifiers
  • wos:000246646600017
  • scopus:34249036762
ISSN
0021-9606
DOI
10.1063/1.2736701
language
English
LU publication?
yes
id
ddd2ec92-d749-489f-8bce-ce09cefb9b3b (old id 659457)
date added to LUP
2007-12-06 11:23:30
date last changed
2017-11-12 03:29:45
@article{ddd2ec92-d749-489f-8bce-ce09cefb9b3b,
  abstract     = {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.},
  author       = {Aquilante, Francesco and Pedersen, Thomas and Lindh, Roland},
  issn         = {0021-9606},
  language     = {eng},
  number       = {19},
  publisher    = {American Institute of Physics},
  series       = {Journal of Chemical Physics},
  title        = {Low-cost evaluation of the exchange Fock matrix from Cholesky and density fitting representations of the electron repulsion integrals},
  url          = {http://dx.doi.org/10.1063/1.2736701},
  volume       = {126},
  year         = {2007},
}