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

Abstract

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 applicability of (EOM-)CCSD methods in the context of geometry optimizations. This paper presents a formulation of analytic (EOM-)CCSD gradient within the CD framework and reports on the salient details of the corresponding implementation. The accuracy and the capabilities of analytic CD-based (EOM-)CCSD gradients are illustrated by benchmark calculations and several illustrative examples.

Authors:
 [1];  [2]; ORCiD logo [3]; ORCiD logo [4]
+ Show Author Affiliations
  1. Q-Chem, Inc., Pleasanton, CA (United States); Univ. of Southern California, Los Angeles, CA (United States). Dept. of Chemistry
  2. Univ. of Southern California, Los Angeles, CA (United States). Dept. of Chemistry
  3. Johannes Gutenberg Univ., Mainz (Germany)
  4. Univ. of Southern California, Los Angeles, CA (United States). Dept. of Chemistry; Johannes Gutenberg Univ., Mainz (Germany)
Publication Date:
Research Org.:
Univ. of Southern California, Los Angeles, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1613023
Grant/Contract Number:  
SC0018910
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 151; Journal Issue: 1; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Chemistry; Physics; Excited states; Coupled-cluster methods

Citation Formats

Feng, Xintian, Epifanovsky, Evgeny, Gauss, Jürgen, and Krylov, Anna I. Implementation of analytic gradients for CCSD and EOM-CCSD using Cholesky decomposition of the electron-repulsion integrals and their derivatives: Theory and benchmarks. United States: N. p., 2019. Web. doi:10.1063/1.5100022.
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Feng, Xintian, Epifanovsky, Evgeny, Gauss, Jürgen, & Krylov, Anna I. Implementation of analytic gradients for CCSD and EOM-CCSD using Cholesky decomposition of the electron-repulsion integrals and their derivatives: Theory and benchmarks. United States. https://doi.org/10.1063/1.5100022
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Feng, Xintian, Epifanovsky, Evgeny, Gauss, Jürgen, and Krylov, Anna I. Sun . "Implementation of analytic gradients for CCSD and EOM-CCSD using Cholesky decomposition of the electron-repulsion integrals and their derivatives: Theory and benchmarks". United States. https://doi.org/10.1063/1.5100022. https://www.osti.gov/servlets/purl/1613023.
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@article{osti_1613023,
title = {Implementation of analytic gradients for CCSD and EOM-CCSD using Cholesky decomposition of the electron-repulsion integrals and their derivatives: Theory and benchmarks},
author = {Feng, Xintian and Epifanovsky, Evgeny and Gauss, Jürgen and Krylov, Anna I.},
abstractNote = {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 applicability of (EOM-)CCSD methods in the context of geometry optimizations. This paper presents a formulation of analytic (EOM-)CCSD gradient within the CD framework and reports on the salient details of the corresponding implementation. The accuracy and the capabilities of analytic CD-based (EOM-)CCSD gradients are illustrated by benchmark calculations and several illustrative examples.},
doi = {10.1063/1.5100022},
journal = {Journal of Chemical Physics},
number = 1,
volume = 151,
place = {United States},
year = {Sun Jul 07 00:00:00 EDT 2019},
month = {Sun Jul 07 00:00:00 EDT 2019}
}
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https://doi.org/10.1063/1.5100022
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Cited by: 24 works
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Figures / Tables:

TABLE I TABLE I: Norm of the errors (a.u.) between analytic CD-CCSD and standard CCSD forcesa for different CD thresholds, δ.
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  • Sattelmeyer, Kurt W.; Schaefer III, Henry F.; Stanton, John F.
  • Chemical Physics Letters, Vol. 378, Issue 1-2
  • DOI: 10.1016/s0009-2614(03)01181-3

Integral approximations for LCAO-SCF calculations
journal, October 1993

Analytic energy gradients for the coupled-cluster singles and doubles method with the density-fitting approximation
journal, May 2016

  • Bozkaya, Uğur; Sherrill, C. David
  • The Journal of Chemical Physics, Vol. 144, Issue 17
  • DOI: 10.1063/1.4948318

Gradient techniques for open‐shell restricted Hartree–Fock and multiconfiguration self‐consistent‐field methods
journal, August 1979

  • Goddard, John D.; Handy, Nicholas C.; Schaefer, Henry F.
  • The Journal of Chemical Physics, Vol. 71, Issue 4
  • DOI: 10.1063/1.438494

Energies and analytic gradients for a coupled-cluster doubles model using variational Brueckner orbitals: Application to symmetry breaking in O4+
journal, September 1998

  • Sherrill, C. David; Krylov, Anna I.; Byrd, Edward F. C.
  • The Journal of Chemical Physics, Vol. 109, Issue 11
  • DOI: 10.1063/1.477023

Linear-Scaling Techniques in Computational Chemistry and Physics: Methods and Applications
book, January 2011

  • Zalesny, Robert; Papadopoulos, Manthos G.; Mezey, Paul G.
  • Challenges and Advances in Computational Chemistry and Physics
  • DOI: 10.1007/978-90-481-2853-2
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    Works referencing / citing this record:

    NWChem: Past, Present, and Future
    text, January 2020

    Accurate reproduction of strongly repulsive interatomic potentials
    journal, March 2020

    Extension of frozen natural orbital approximation to open-shell references: Theory, implementation, and application to single-molecule magnets
    journal, January 2020

    • Pokhilko, Pavel; Izmodenov, Daniil; Krylov, Anna I.
    • The Journal of Chemical Physics, Vol. 152, Issue 3
    • DOI: 10.1063/1.5138643
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