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

Abstract

In this letter, we introduce the reverse Cuthill-McKee (RCM) algorithm, which is often used for the bandwidth reduction of sparse tensors, to transform the two-electron integral tensors to their block diagonal forms. By further applying the pivoted 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 the low-rank factorization of the high-dimensional tensor contractions that are usually encountered in post-Hartree-Fock calculations. In this letter, we discuss the second-order Møller-Plesset (MP2) method and linear coupled- cluster model with doubles (L-CCD) as two simple examples to demonstrate the efficiency of the RCM-CD technique in representing two-electron integrals in a compact form.

Authors:
;
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1353329
Report Number(s):
PNNL-SA-122607
Journal ID: ISSN 0009-2614
DOE Contract Number:
AC05-76RL01830
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chemical Physics Letters; Journal Volume: 672
Country of Publication:
United States
Language:
English
Subject:
electronic structure theory; two-electron integral tensor; tensor contraction; low-rank factorization; reverse Cuthill-McKee

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.
Peng, Bo, & Kowalski, Karol. Low-rank factorization of electron integral tensors and its application in electronic structure theory. United States. doi:10.1016/j.cplett.2017.01.056.
Peng, Bo, and Kowalski, Karol. Wed . "Low-rank factorization of electron integral tensors and its application in electronic structure theory". United States. doi:10.1016/j.cplett.2017.01.056.
@article{osti_1353329,
title = {Low-rank factorization of electron integral tensors and its application in electronic structure theory},
author = {Peng, Bo and Kowalski, Karol},
abstractNote = {In this letter, we introduce the reverse Cuthill-McKee (RCM) algorithm, which is often used for the bandwidth reduction of sparse tensors, to transform the two-electron integral tensors to their block diagonal forms. By further applying the pivoted 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 the low-rank factorization of the high-dimensional tensor contractions that are usually encountered in post-Hartree-Fock calculations. In this letter, we discuss the second-order Møller-Plesset (MP2) method and linear coupled- cluster model with doubles (L-CCD) as two simple examples to demonstrate the efficiency of the RCM-CD technique in representing 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 Mar 01 00:00:00 EST 2017},
month = {Wed Mar 01 00:00:00 EST 2017}
}