Low-rank factorization of electron integral tensors and its application in electronic structure theory

Peng, Bo; Kowalski, Karol

doi:10.1016/j.cplett.2017.01.056

Title: Low-rank factorization of electron integral tensors and its application in electronic structure theory

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Abstract

In this paper, we apply reverse Cuthill-McKee (RCM) algorithm to transform two-electron integral tensors to their block diagonal forms. By further applying Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates low-rank factorizations of high-dimensional tensor contractions in post-Hartree-Fock calculations. Finally, we discuss the second-order Møller-Plesset (MP2) method and the linear coupled-cluster model with doubles (L-CCD) as examples to demonstrate the efficiency of this technique in representing the two-electron integrals in a compact form.

Authors:

Peng, Bo ^[1]; Kowalski, Karol ^[1]

Pacific Northwest National Lab. (PNNL), Richland, WA (United States). William R. Wiley Environmental Molecular Sciences Lab.

Publication Date:: Wed Jan 25 00:00:00 EST 2017

Research Org.:: Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Biological and Environmental Research (BER)

OSTI Identifier:: 1342758

Alternate Identifier(s):: OSTI ID: 1413350

Report Number(s):: PNNL-SA-122607
Journal ID: ISSN 0009-2614; PII: S0009261417300751; TRN: US1700935

Grant/Contract Number:: AC05-76RL01830

Resource Type:: Accepted Manuscript

Journal Name:: Chemical Physics Letters

Additional Journal Information:: Journal Volume: 672; Journal ID: ISSN 0009-2614

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Electronic structure theory; Two-electron integral tensor; Tensor contraction; Low-rank factorization; Reverse Cuthill-McKee; Cholesky decomposition

Citation Formats


                    Peng, Bo, and Kowalski, Karol. Low-rank factorization of electron integral tensors and its application in electronic structure theory.  United States: N. p., 2017. 
Web.  doi:10.1016/j.cplett.2017.01.056.

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                    Peng, Bo, & Kowalski, Karol. Low-rank factorization of electron integral tensors and its application in electronic structure theory.  United States.  https://doi.org/10.1016/j.cplett.2017.01.056

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                    Peng, Bo, and Kowalski, Karol. Wed .  
"Low-rank factorization of electron integral tensors and its application in electronic structure theory".  United States.  https://doi.org/10.1016/j.cplett.2017.01.056.  https://www.osti.gov/servlets/purl/1342758.

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@article{osti_1342758,

  title        = {Low-rank factorization of electron integral tensors and its application in electronic structure theory},

  author       = {Peng, Bo and Kowalski, Karol},

  abstractNote = {In this paper, we apply reverse Cuthill-McKee (RCM) algorithm to transform two-electron integral tensors to their block diagonal forms. By further applying Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates low-rank factorizations of high-dimensional tensor contractions in post-Hartree-Fock calculations. Finally, we discuss the second-order Møller-Plesset (MP2) method and the linear coupled-cluster model with doubles (L-CCD) as examples to demonstrate the efficiency of this technique in representing the two-electron integrals in a compact form.},

  doi          = {10.1016/j.cplett.2017.01.056},

  journal      = {Chemical Physics Letters},

  number       = ,

  volume       = 672,

  place        = {United States},

  year         = {Wed Jan 25 00:00:00 EST 2017},

  month        = {Wed Jan 25 00:00:00 EST 2017}

}

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