Lowrank factorization of electron integral tensors and its application in electronic structure theory
In this paper, we apply reverse CuthillMcKee (RCM) algorithm to transform twoelectron 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 highdimensional twoelectron integral tensors in terms of permutation matrices and lowrank Cholesky vectors. This representation facilitates lowrank factorizations of highdimensional tensor contractions in postHartreeFock calculations. Finally, we discuss the secondorder MøllerPlesset (MP2) method and the linear coupledcluster model with doubles (LCCD) as examples to demonstrate the efficiency of this technique in representing the twoelectron integrals in a compact form.
 Authors:

^{[1]};
^{[1]}
 Pacific Northwest National Lab. (PNNL), Richland, WA (United States). William R. Wiley Environmental Molecular Sciences Lab.
 Publication Date:
 Report Number(s):
 PNNLSA122607
Journal ID: ISSN 00092614; PII: S0009261417300751; TRN: US1700935
 Grant/Contract Number:
 AC0576RL01830
 Type:
 Accepted Manuscript
 Journal Name:
 Chemical Physics Letters
 Additional Journal Information:
 Journal Volume: 672; Journal ID: ISSN 00092614
 Publisher:
 Elsevier
 Research Org:
 Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC23)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Electronic structure theory; Twoelectron integral tensor; Tensor contraction; Lowrank factorization; Reverse CuthillMcKee; Cholesky decomposition
 OSTI Identifier:
 1342758
 Alternate Identifier(s):
 OSTI ID: 1413350
Peng, Bo, and Kowalski, Karol. Lowrank factorization of electron integral tensors and its application in electronic structure theory. United States: N. p.,
Web. doi:10.1016/j.cplett.2017.01.056.
Peng, Bo, & Kowalski, Karol. Lowrank 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. 2017.
"Lowrank factorization of electron integral tensors and its application in electronic structure theory". United States.
doi:10.1016/j.cplett.2017.01.056. https://www.osti.gov/servlets/purl/1342758.
@article{osti_1342758,
title = {Lowrank 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 CuthillMcKee (RCM) algorithm to transform twoelectron 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 highdimensional twoelectron integral tensors in terms of permutation matrices and lowrank Cholesky vectors. This representation facilitates lowrank factorizations of highdimensional tensor contractions in postHartreeFock calculations. Finally, we discuss the secondorder MøllerPlesset (MP2) method and the linear coupledcluster model with doubles (LCCD) as examples to demonstrate the efficiency of this technique in representing the twoelectron integrals in a compact form.},
doi = {10.1016/j.cplett.2017.01.056},
journal = {Chemical Physics Letters},
number = ,
volume = 672,
place = {United States},
year = {2017},
month = {1}
}