Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: Solving Coupled Cluster Equations by the Newton Krylov Method

Abstract

We describe using the Newton Krylov method to solve the coupled cluster equation. The method uses a Krylov iterative method to compute the Newton correction to the approximate coupled cluster amplitude. The multiplication of the Jacobian with a vector, which is required in each step of a Krylov iterative method such as the Generalized Minimum Residual (GMRES) method, is carried out through a finite difference approximation, and requires an additional residual evaluation. The overall cost of the method is determined by the sum of the inner Krylov and outer Newton iterations. We discuss the termination criterion used for the inner iteration and show how to apply pre-conditioners to accelerate convergence. We will also examine the use of regularization technique to improve the stability of convergence and compare the method with the widely used direct inversion of iterative subspace (DIIS) methods through numerical examples.

Authors:
; ; ; ;
Publication Date:
Research Org.:
Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE Office of Science (SC); USDOE National Nuclear Security Administration (NNSA); Czech Science Foundation
OSTI Identifier:
1734948
Alternate Identifier(s):
OSTI ID: 1755915
Report Number(s):
PNNL-SA-155068
Journal ID: ISSN 2296-2646; 590184
Grant/Contract Number:  
AC05-76RL01830; AC05-00OR22725; 17-SC-20-SC; 19-13126Y
Resource Type:
Published Article
Journal Name:
Frontiers in Chemistry
Additional Journal Information:
Journal Name: Frontiers in Chemistry Journal Volume: 8; Journal ID: ISSN 2296-2646
Publisher:
Frontiers Research Foundation
Country of Publication:
Switzerland
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; couple cluster approximation; Newton-Krylov method; DIIS; precondition; nonlinear solver; coupled cluster; applied math; solvers

Citation Formats

Yang, Chao, Brabec, Jiri, Veis, Libor, Williams-Young, David B., and Kowalski, Karol. Solving Coupled Cluster Equations by the Newton Krylov Method. Switzerland: N. p., 2020. Web. doi:10.3389/fchem.2020.590184.
Copy to clipboard
Yang, Chao, Brabec, Jiri, Veis, Libor, Williams-Young, David B., & Kowalski, Karol. Solving Coupled Cluster Equations by the Newton Krylov Method. Switzerland. https://doi.org/10.3389/fchem.2020.590184
Copy to clipboard
Yang, Chao, Brabec, Jiri, Veis, Libor, Williams-Young, David B., and Kowalski, Karol. Thu . "Solving Coupled Cluster Equations by the Newton Krylov Method". Switzerland. https://doi.org/10.3389/fchem.2020.590184.
Copy to clipboard
@article{osti_1734948,
title = {Solving Coupled Cluster Equations by the Newton Krylov Method},
author = {Yang, Chao and Brabec, Jiri and Veis, Libor and Williams-Young, David B. and Kowalski, Karol},
abstractNote = {We describe using the Newton Krylov method to solve the coupled cluster equation. The method uses a Krylov iterative method to compute the Newton correction to the approximate coupled cluster amplitude. The multiplication of the Jacobian with a vector, which is required in each step of a Krylov iterative method such as the Generalized Minimum Residual (GMRES) method, is carried out through a finite difference approximation, and requires an additional residual evaluation. The overall cost of the method is determined by the sum of the inner Krylov and outer Newton iterations. We discuss the termination criterion used for the inner iteration and show how to apply pre-conditioners to accelerate convergence. We will also examine the use of regularization technique to improve the stability of convergence and compare the method with the widely used direct inversion of iterative subspace (DIIS) methods through numerical examples.},
doi = {10.3389/fchem.2020.590184},
journal = {Frontiers in Chemistry},
number = ,
volume = 8,
place = {Switzerland},
year = {2020},
month = {12}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.3389/fchem.2020.590184
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Convergence acceleration of iterative sequences. the case of scf iteration
journal, July 1980

Multireference Nature of Chemistry: The Coupled-Cluster View
journal, December 2011

  • Lyakh, Dmitry I.; Musiał, Monika; Lotrich, Victor F.
  • Chemical Reviews, Vol. 112, Issue 1
  • DOI: 10.1021/cr2001417

Enantioselective epoxidation of unfunctionalized olefins catalyzed by salen manganese complexes
journal, March 1990

  • Zhang, Wei; Loebach, Jennifer L.; Wilson, Scott R.
  • Journal of the American Chemical Society, Vol. 112, Issue 7
  • DOI: 10.1021/ja00163a052

Developing a Computational Chemistry Framework for the Exascale Era
journal, March 2019

  • Richard, Ryan M.; Bertoni, Colleen; Boschen, Jeffery S.
  • Computing in Science & Engineering, Vol. 21, Issue 2
  • DOI: 10.1109/MCSE.2018.2884921

A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples
journal, February 1982

  • Purvis, George D.; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 76, Issue 4
  • DOI: 10.1063/1.443164

The reduced linear equation method in coupled cluster theory.
journal, August 1981

  • Purvis, George D.; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 75, Issue 3
  • DOI: 10.1063/1.442131

Many – Body Methods in Chemistry and Physics
book, January 2009

Jacobian-free Newton–Krylov methods: a survey of approaches and applications
journal, January 2004

Catalytic asymmetric epoxidation of unfunctionalized olefins
journal, January 1990

The ‘tailored’ CCSD(T) description of the automerization of cyclobutadiene
journal, January 2011

Toward the efficient local tailored coupled cluster approximation and the peculiar case of oxo-Mn(Salen)
journal, August 2019

  • Antalík, Andrej; Veis, Libor; Brabec, Jiří
  • The Journal of Chemical Physics, Vol. 151, Issue 8
  • DOI: 10.1063/1.5110477

Reduced multireference CCSD method: An effective approach to quasidegenerate states
journal, October 1997

  • Li, Xiangzhu; Paldus, Josef
  • The Journal of Chemical Physics, Vol. 107, Issue 16
  • DOI: 10.1063/1.474289

Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation
journal, January 1997

  • Curtiss, Larry A.; Raghavachari, Krishnan; Redfern, Paul C.
  • The Journal of Chemical Physics, Vol. 106, Issue 3
  • DOI: 10.1063/1.473182

A fifth-order perturbation comparison of electron correlation theories
journal, May 1989

GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
journal, July 1986

  • Saad, Youcef; Schultz, Martin H.
  • SIAM Journal on Scientific and Statistical Computing, Vol. 7, Issue 3
  • DOI: 10.1137/0907058

An analysis for the DIIS acceleration method used in quantum chemistry calculations
journal, August 2011

  • Rohwedder, Thorsten; Schneider, Reinhold
  • Journal of Mathematical Chemistry, Vol. 49, Issue 9
  • DOI: 10.1007/s10910-011-9863-y

A ?Level-Shifting? method for converging closed shell Hartree-Fock wave functions
journal, July 1973

  • Saunders, V. R.; Hillier, I. H.
  • International Journal of Quantum Chemistry, Vol. 7, Issue 4
  • DOI: 10.1002/qua.560070407

Discarding Information from Previous Iterations in an Optimal Way To Solve the Coupled Cluster Amplitude Equations
journal, March 2015

  • Ettenhuber, Patrick; Jørgensen, Poul
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 4
  • DOI: 10.1021/ct501114q

NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations
journal, September 2010

  • Valiev, M.; Bylaska, E. J.; Govind, N.
  • Computer Physics Communications, Vol. 181, Issue 9, p. 1477-1489
  • DOI: 10.1016/j.cpc.2010.04.018

Globally Convergent Inexact Newton Methods
journal, May 1994

  • Eisenstat, Stanley C.; Walker, Homer F.
  • SIAM Journal on Optimization, Vol. 4, Issue 2
  • DOI: 10.1137/0804022

Solving the single‐reference coupled‐cluster equations involving highly excited clusters in quasidegenerate situations
journal, April 1994

  • Piecuch, Piotr; Adamowicz, Ludwik
  • The Journal of Chemical Physics, Vol. 100, Issue 8
  • DOI: 10.1063/1.467149

Coupled-cluster theory in quantum chemistry
journal, February 2007

Krylov subspace accelerated inexact Newton method for linear and nonlinear equations
journal, January 2003

  • Harrison, Robert J.
  • Journal of Computational Chemistry, Vol. 25, Issue 3
  • DOI: 10.1002/jcc.10108

Coupled-cluster method tailored by configuration interaction
journal, August 2005

  • Kinoshita, Tomoko; Hino, Osamu; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 123, Issue 7
  • DOI: 10.1063/1.2000251

Anderson Acceleration for Fixed-Point Iterations
journal, January 2011

  • Walker, Homer F.; Ni, Peng
  • SIAM Journal on Numerical Analysis, Vol. 49, Issue 4
  • DOI: 10.1137/10078356X

Accelerated multimodel Newton-type algorithms for faster convergence of ground and excited state coupled cluster equations
journal, July 2020

  • Kjønstad, Eirik F.; Folkestad, Sarai D.; Koch, Henrik
  • The Journal of Chemical Physics, Vol. 153, Issue 1
  • DOI: 10.1063/5.0010989
    Sort by:
    [ × clear filter / sort ]

    Similar Records in DOE PAGES and OSTI.GOV collections: