Auxiliary basis expansions for large-scale electronic structure calculations

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One way to reduce the computational cost of electronic structure calculations is to employ auxiliary basis expansions to approximate 4 center integrals in terms of 2 and 3-center integrals, usually using the variationally optimum Coulomb metric to determine the expansion coefficients. However the long-range decay behavior of the auxiliary basis expansion coefficients has not been characterized. We find that this decay can be surprisingly slow. Numerical experiments on linear alkanes and a toy model both show that the decay can be as slow as 1/r in the distance between the auxiliary function and the fitted charge distribution. The Coulomb metric ... continued below

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Jung, Yousung; Sodt, Alexander; Gill, Peter W.M. & Head-Gordon, Martin April 4, 2005.

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One way to reduce the computational cost of electronic structure calculations is to employ auxiliary basis expansions to approximate 4 center integrals in terms of 2 and 3-center integrals, usually using the variationally optimum Coulomb metric to determine the expansion coefficients. However the long-range decay behavior of the auxiliary basis expansion coefficients has not been characterized. We find that this decay can be surprisingly slow. Numerical experiments on linear alkanes and a toy model both show that the decay can be as slow as 1/r in the distance between the auxiliary function and the fitted charge distribution. The Coulomb metric fitting equations also involve divergent matrix elements for extended systems treated with periodic boundary conditions. An attenuated Coulomb metric that is short-range can eliminate these oddities without substantially degrading calculated relative energies. The sparsity of the fit coefficients is assessed on simple hydrocarbon molecules, and shows quite early onset of linear growth in the number of significant coefficients with system size using the attenuated Coulomb metric. This means it is possible to design linear scaling auxiliary basis methods without additional approximations to treat large systems.

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  • Other Information: Journal Publication Date: 05/10/2005

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  • Report No.: LBNL--57454
  • Grant Number: AC03-76SF00098
  • Office of Scientific & Technical Information Report Number: 843011
  • Archival Resource Key: ark:/67531/metadc781259

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  • April 4, 2005

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  • Dec. 3, 2015, 9:30 a.m.

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  • April 4, 2016, 12:19 p.m.

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Jung, Yousung; Sodt, Alexander; Gill, Peter W.M. & Head-Gordon, Martin. Auxiliary basis expansions for large-scale electronic structure calculations, article, April 4, 2005; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc781259/: accessed October 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.