Highly Efficient and Scalable Compound Decomposition of Two-Electron Integral Tensor and Its Application in Coupled Cluster Calculations

Peng, Bo; Kowalski, Karol

doi:10.1021/acs.jctc.7b00605

Title: Highly Efficient and Scalable Compound Decomposition of Two-Electron Integral Tensor and Its Application in Coupled Cluster Calculations

Full Record
Other Related Research

Abstract

The representation and storage of two-electron integral tensors are vital in large- scale applications of accurate electronic structure methods. Low-rank representation and efficient storage strategy of integral tensors can significantly reduce the numerical overhead and consequently time-to-solution of these methods. In this paper, by combining pivoted incomplete Cholesky decomposition (CD) with a follow-up truncated singular vector decomposition (SVD), we develop a decomposition strategy to approximately represent the two-electron integral tensor in terms of low-rank vectors. A systematic benchmark test on a series of 1-D, 2-D, and 3-D carbon-hydrogen systems demonstrates high efficiency and scalability of the compound two-step decomposition of the two-electron integral tensor in our implementation. For the size of atomic basis set N_b ranging from ~ 100 up to ~ 2, 000, the observed numerical scaling of our implementation shows O(N_b^{2.5~3}) versus O(N_b^{3~4}) of single CD in most of other implementations. More importantly, this decomposition strategy can significantly reduce the storage requirement of the atomic-orbital (AO) two-electron integral tensor from O(N_b^4) to O(N_b^2 log_{10}(N_b)) with moderate decomposition thresholds. The accuracy tests have been performed using ground- and excited-state formulations of coupled- cluster formalism employing single and double excitations (CCSD) on several bench- mark systems including the C_{60} moleculemore »« less

Authors:

^[1];

^[1]

William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P. O. Box 999, Richland, Washington 99352, United States

Publication Date:: Fri Aug 11 00:00:00 EDT 2017

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

Sponsoring Org.:: USDOE

OSTI Identifier:: 1414535

Report Number(s):: PNNL-SA-126829
Journal ID: ISSN 1549-9618; 49220

DOE Contract Number:: AC05-76RL01830

Resource Type:: Journal Article

Journal Name:: Journal of Chemical Theory and Computation

Additional Journal Information:: Journal Volume: 13; Journal Issue: 9; Journal ID: ISSN 1549-9618

Publisher:: American Chemical Society

Country of Publication:: United States

Language:: English

Subject:: 54 ENVIRONMENTAL SCIENCES; Environmental Molecular Sciences Laboratory

Citation Formats


                    Peng, Bo, and Kowalski, Karol. Highly Efficient and Scalable Compound Decomposition of Two-Electron Integral Tensor and Its Application in Coupled Cluster Calculations.  United States: N. p., 2017. 
        Web.  doi:10.1021/acs.jctc.7b00605.

Copy to clipboard


                    Peng, Bo, & Kowalski, Karol. Highly Efficient and Scalable Compound Decomposition of Two-Electron Integral Tensor and Its Application in Coupled Cluster Calculations.  United States.  https://doi.org/10.1021/acs.jctc.7b00605

Copy to clipboard


                    Peng, Bo, and Kowalski, Karol. 2017.  
        "Highly Efficient and Scalable Compound Decomposition of Two-Electron Integral Tensor and Its Application in Coupled Cluster Calculations".  United States.  https://doi.org/10.1021/acs.jctc.7b00605.

Copy to clipboard


                    
@article{osti_1414535,

  title        = {Highly Efficient and Scalable Compound Decomposition of Two-Electron Integral Tensor and Its Application in Coupled Cluster Calculations},

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

  abstractNote = {The representation and storage of two-electron integral tensors are vital in large- scale applications of accurate electronic structure methods. Low-rank representation and efficient storage strategy of integral tensors can significantly reduce the numerical overhead and consequently time-to-solution of these methods. In this paper, by combining pivoted incomplete Cholesky decomposition (CD) with a follow-up truncated singular vector decomposition (SVD), we develop a decomposition strategy to approximately represent the two-electron integral tensor in terms of low-rank vectors. A systematic benchmark test on a series of 1-D, 2-D, and 3-D carbon-hydrogen systems demonstrates high efficiency and scalability of the compound two-step decomposition of the two-electron integral tensor in our implementation. For the size of atomic basis set N_b ranging from ~ 100 up to ~ 2, 000, the observed numerical scaling of our implementation shows O(N_b^{2.5~3}) versus O(N_b^{3~4}) of single CD in most of other implementations. More importantly, this decomposition strategy can significantly reduce the storage requirement of the atomic-orbital (AO) two-electron integral tensor from O(N_b^4) to O(N_b^2 log_{10}(N_b)) with moderate decomposition thresholds. The accuracy tests have been performed using ground- and excited-state formulations of coupled- cluster formalism employing single and double excitations (CCSD) on several bench- mark systems including the C_{60} molecule described by nearly 1,400 basis functions. The results show that the decomposition thresholds can be generally set to 10^{-4} to 10^{-3} to give acceptable compromise between efficiency and accuracy.},

  doi          = {10.1021/acs.jctc.7b00605},

  url          = {https://www.osti.gov/biblio/1414535},
  journal      = {Journal of Chemical Theory and Computation},

  issn         = {1549-9618},

  number       = 9,

  volume       = 13,

  place        = {United States},

  year         = {Fri Aug 11 00:00:00 EDT 2017},

  month        = {Fri Aug 11 00:00:00 EDT 2017}

}

Copy to clipboard

Journal Article:

https://doi.org/10.1021/acs.jctc.7b00605

Other availability

Find in Google Scholar

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Similar records in OSTI.GOV collections:

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

Journal Article Peng, Bo; Kowalski, Karol - Chemical Physics Letters

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 doublesmore »« less
https://doi.org/10.1016/j.cplett.2017.01.056
Low-rank factorization of electron integral tensors and its application in electronic structure theory

Journal Article Peng, Bo; Kowalski, Karol - Chemical Physics Letters

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.
Cited by 4
https://doi.org/10.1016/j.cplett.2017.01.056

Full Text Available
Tensor decomposition in electronic structure calculations on 3D Cartesian grids

Journal Article Khoromskaia, V; Chinnamsetty, S; Flad, H - Journal of Computational Physics

In this paper, we investigate a novel approach based on the combination of Tucker-type and canonical tensor decomposition techniques for the efficient numerical approximation of functions and operators in electronic structure calculations. In particular, we study applicability of tensor approximations for the numerical solution of Hartree-Fock and Kohn-Sham equations on 3D Cartesian grids. We show that the orthogonal Tucker-type tensor approximation of electron density and Hartree potential of simple molecules leads to low tensor rank representations. This enables an efficient tensor-product convolution scheme for the computation of the Hartree potential using a collocation-type approximation via piecewise constant basis functions onmore »« less
https://doi.org/10.1016/j.jcp.2009.04.043
GPU acceleration of rank-reduced coupled-cluster singles and doubles

Journal Article Hohenstein, Edward; Martínez, Todd - Journal of Chemical Physics

Here, we have developed a graphical processing unit (GPU) accelerated implementation of our recently introduced rank-reduced coupled-cluster singles and doubles (RR-CCSD) method. RR-CCSD introduces a low-rank approximation of the doubles amplitudes. This is combined with a low-rank approximation of the electron repulsion integrals via Cholesky decomposition. The result of these two low-rank approximations is the replacement of the usual fourth-order CCSD tensors with products of second- and third-order tensors. In our implementation, only a single fourth-order tensor must be constructed as an intermediate during the solution of the amplitude equations. Owing in large part to the compression of the doubles amplitudes, themore »« less
https://doi.org/10.1063/5.0063467

Full Text Available
Implementation of analytic gradients for CCSD and EOM-CCSD using Cholesky decomposition of the electron-repulsion integrals and their derivatives: Theory and benchmarks

Journal Article Feng, Xintian; Epifanovsky, Evgeny; Gauss, Jürgen; ... - Journal of Chemical Physics

We present a general formulation of analytic nuclear gradients for the coupled-cluster with single and double substitution (CCSD) and equation-of-motion (EOM) CCSD energies computed using Cholesky decomposition (CD) representations of the electron repulsion integrals. By rewriting the correlated energy and response equations such that the storage of the largest four-index intermediates is eliminated, CD leads to a significant reduction in disk storage requirements, reduced I/O penalties, and an improved parallel performance. CD thus extends the scope of the systems that can be treated by (EOM-)CCSD methods, although analytic gradients in the framework of CD are needed to extend the applicabilitymore »« less
Cited by 19
https://doi.org/10.1063/1.5100022

Full Text Available

Similar Records