Orbital spaces in the divide-expand-consolidate coupled cluster method

Ettenhuber, Patrick; Baudin, Pablo; Kjærgaard, Thomas; Jørgensen, Poul; Kristensen, Kasper

doi:10.1063/1.4947019

Title: Orbital spaces in the divide-expand-consolidate coupled cluster method

Abstract

The theoretical foundation for solving coupled cluster singles and doubles (CCSD) amplitude equations to a desired precision in terms of independent fragment calculations using restricted local orbital spaces is reinvestigated with focus on the individual error sources. Four different error sources are identified theoretically and numerically and it is demonstrated that, for practical purposes, local orbital spaces for CCSD calculations can be identified from calculations at the MP2 level. The development establishes a solid theoretical foundation for local CCSD calculations for the independent fragments, and thus for divide–expand–consolidate coupled cluster calculations for large molecular systems with rigorous error control. Based on this theoretical foundation, we have developed an algorithm for determining the orbital spaces needed for obtaining the single fragment energies to a requested precision and numerically demonstrated the robustness and precision of this algorithm.

Authors:

Ettenhuber, Patrick ^[1];

^[1]; Kjærgaard, Thomas ^[1]; Jørgensen, Poul ^[1]; Kristensen, Kasper ^[1]

Aarhus Univ. (Denmark). qLEAP Center for Theoretical Chemistry, Dept. of Chemistry

Publication Date:: Thu Apr 28 00:00:00 EDT 2016

Research Org.:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1565471

Alternate Identifier(s):: OSTI ID: 1421168

Grant/Contract Number:: AC05-00OR22725

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 144; Journal Issue: 16; 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; Chemistry; Physics

Citation Formats


                    Ettenhuber, Patrick, Baudin, Pablo, Kjærgaard, Thomas, Jørgensen, Poul, and Kristensen, Kasper. Orbital spaces in the divide-expand-consolidate coupled cluster method.  United States: N. p., 2016. 
Web.  doi:10.1063/1.4947019.

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                    Ettenhuber, Patrick, Baudin, Pablo, Kjærgaard, Thomas, Jørgensen, Poul, & Kristensen, Kasper. Orbital spaces in the divide-expand-consolidate coupled cluster method.  United States.  https://doi.org/10.1063/1.4947019

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                    Ettenhuber, Patrick, Baudin, Pablo, Kjærgaard, Thomas, Jørgensen, Poul, and Kristensen, Kasper. Thu .  
"Orbital spaces in the divide-expand-consolidate coupled cluster method".  United States.  https://doi.org/10.1063/1.4947019.  https://www.osti.gov/servlets/purl/1565471.

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@article{osti_1565471,

  title        = {Orbital spaces in the divide-expand-consolidate coupled cluster method},

  author       = {Ettenhuber, Patrick and Baudin, Pablo and Kjærgaard, Thomas and Jørgensen, Poul and Kristensen, Kasper},

  abstractNote = {The theoretical foundation for solving coupled cluster singles and doubles (CCSD) amplitude equations to a desired precision in terms of independent fragment calculations using restricted local orbital spaces is reinvestigated with focus on the individual error sources. Four different error sources are identified theoretically and numerically and it is demonstrated that, for practical purposes, local orbital spaces for CCSD calculations can be identified from calculations at the MP2 level. The development establishes a solid theoretical foundation for local CCSD calculations for the independent fragments, and thus for divide–expand–consolidate coupled cluster calculations for large molecular systems with rigorous error control. Based on this theoretical foundation, we have developed an algorithm for determining the orbital spaces needed for obtaining the single fragment energies to a requested precision and numerically demonstrated the robustness and precision of this algorithm.},

  doi          = {10.1063/1.4947019},

  journal      = {Journal of Chemical Physics},

  number       = 16,

  volume       = 144,

  place        = {United States},

  year         = {Thu Apr 28 00:00:00 EDT 2016},

  month        = {Thu Apr 28 00:00:00 EDT 2016}

}

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Works referenced in this record:

Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method
journal, March 2009

Neese, Frank; Wennmohs, Frank; Hansen, Andreas
The Journal of Chemical Physics, Vol. 130, Issue 11
DOI: 10.1063/1.3086717

A perspective on the localizability of Hartree–Fock orbitals
journal, November 2013

Høyvik, Ida-Marie; Kristensen, Kasper; Kjærgaard, Thomas
Theoretical Chemistry Accounts, Vol. 133, Issue 1
DOI: 10.1007/s00214-013-1417-x

Fully automated implementation of the incremental scheme: Application to CCSD energies for hydrocarbons and transition metal compounds
journal, April 2007

Friedrich, Joachim; Hanrath, Michael; Dolg, Michael
The Journal of Chemical Physics, Vol. 126, Issue 15
DOI: 10.1063/1.2721538

Maximum locality in occupied and virtual orbital spaces using a least-change strategy
journal, September 2009

Ziółkowski, Marcin; Jansík, Branislav; Jørgensen, Poul
The Journal of Chemical Physics, Vol. 131, Issue 12
DOI: 10.1063/1.3230604

Low-order scaling local electron correlation methods. I. Linear scaling local MP2
journal, October 1999

Schütz, Martin; Hetzer, Georg; Werner, Hans-Joachim
The Journal of Chemical Physics, Vol. 111, Issue 13
DOI: 10.1063/1.479957

The divide–expand–consolidate MP2 scheme goes massively parallel
journal, April 2013

Kristensen, Kasper; Kjærgaard, Thomas; Høyvik, Ida-Marie
Molecular Physics, Vol. 111, Issue 9-11
DOI: 10.1080/00268976.2013.783941

Molecular Electronic-Structure Theory
book, August 2000

Helgaker, Trygve; Jørgensen, Poul; Olsen, Jeppe
DOI: 10.1002/9781119019572

A natural linear scaling coupled-cluster method
journal, January 2004

Flocke, N.; Bartlett, Rodney J.
The Journal of Chemical Physics, Vol. 121, Issue 22
DOI: 10.1063/1.1811606

Efficient and accurate approximations to the local coupled cluster singles doubles method using a truncated pair natural orbital basis
journal, January 2009

Neese, Frank; Hansen, Andreas; Liakos, Dimitrios G.
The Journal of Chemical Physics, Vol. 131, Issue 6
DOI: 10.1063/1.3173827

Localizability of dynamic electron correlation
journal, September 1983

Pulay, Peter
Chemical Physics Letters, Vol. 100, Issue 2
DOI: 10.1016/0009-2614(83)80703-9

A general-order local coupled-cluster method based on the cluster-in-molecule approach
journal, September 2011

Rolik, Zoltán; Kállay, Mihály
The Journal of Chemical Physics, Vol. 135, Issue 10
DOI: 10.1063/1.3632085

A refined cluster-in-molecule local correlation approach for predicting the relative energies of large systems
journal, January 2012

Li, Wei; Guo, Yang; Li, Shuhua
Physical Chemistry Chemical Physics, Vol. 14, Issue 21
DOI: 10.1039/c2cp23916g

Exploring chemistry with the fragment molecular orbital method
journal, January 2012

Fedorov, Dmitri G.; Nagata, Takeshi; Kitaura, Kazuo
Physical Chemistry Chemical Physics, Vol. 14, Issue 21
DOI: 10.1039/c2cp23784a

Divide-and-conquer local correlation approach to the correlation energy of large molecules
journal, October 2004

Li, Wei; Li, Shuhua
The Journal of Chemical Physics, Vol. 121, Issue 14
DOI: 10.1063/1.1792051

MP2 energy and density for large molecular systems with internal error control using the Divide-Expand-Consolidate scheme
journal, January 2012

Kristensen, Kasper; Høyvik, Ida-Marie; Jansik, Branislav
Physical Chemistry Chemical Physics, Vol. 14, Issue 45
DOI: 10.1039/c2cp41958k

Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
journal, January 1989

Dunning, Thom H.
The Journal of Chemical Physics, Vol. 90, Issue 2
DOI: 10.1063/1.456153

General biorthogonal projected bases as applied to second-order Møller-Plesset perturbation theory
journal, August 2007

Weijo, Ville; Manninen, Pekka; Jørgensen, Poul
The Journal of Chemical Physics, Vol. 127, Issue 7
DOI: 10.1063/1.2752813

The Dalton quantum chemistry program system: The Dalton program
journal, September 2013

Aidas, Kestutis; Angeli, Celestino; Bak, Keld L.
Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 4, Issue 3
DOI: 10.1002/wcms.1172

An atomic orbital-based reformulation of energy gradients in second-order Møller–Plesset perturbation theory
journal, April 2008

Schweizer, Sabine; Doser, Bernd; Ochsenfeld, Christian
The Journal of Chemical Physics, Vol. 128, Issue 15
DOI: 10.1063/1.2906127

Molecular gradient for second-order Møller-Plesset perturbation theory using the divide-expand-consolidate (DEC) scheme
journal, September 2012

Kristensen, Kasper; Jørgensen, Poul; Jansík, Branislav
The Journal of Chemical Physics, Vol. 137, Issue 11
DOI: 10.1063/1.4752432

Trust Region Minimization of Orbital Localization Functions
journal, August 2012

Høyvik, Ida-Marie; Jansik, Branislav; Jørgensen, Poul
Journal of Chemical Theory and Computation, Vol. 8, Issue 9
DOI: 10.1021/ct300473g

Comparison of the boys and Pipek-Mezey localizations in the local correlation approach and automatic virtual basis selection
journal, June 1993

Boughton, James W.; Pulay, Peter
Journal of Computational Chemistry, Vol. 14, Issue 6
DOI: 10.1002/jcc.540140615

Laplace transform techniques in Mo/ller–Plesset perturbation theory
journal, January 1992

Häser, Marco; Almlöf, Jan
The Journal of Chemical Physics, Vol. 96, Issue 1
DOI: 10.1063/1.462485

Tighter multipole-based integral estimates and parallel implementation of linear-scaling AO–MP2 theory
journal, January 2008

Doser, Bernd; Lambrecht, Daniel S.; Ochsenfeld, Christian
Physical Chemistry Chemical Physics, Vol. 10, Issue 23
DOI: 10.1039/b804110e

Linear-Scaling Coupled Cluster with Perturbative Triple Excitations: The Divide–Expand–Consolidate CCSD(T) Model
journal, June 2015

Eriksen, Janus J.; Baudin, Pablo; Ettenhuber, Patrick
Journal of Chemical Theory and Computation, Vol. 11, Issue 7
DOI: 10.1021/acs.jctc.5b00086

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

The correlation energy of crystalline silicon
journal, April 1992

Stoll, Hermann
Chemical Physics Letters, Vol. 191, Issue 6
DOI: 10.1016/0009-2614(92)85587-Z

A Locality Analysis of the Divide–Expand–Consolidate Coupled Cluster Amplitude Equations
journal, May 2011

Kristensen, Kasper; Ziółkowski, Marcin; Jansík, Branislav
Journal of Chemical Theory and Computation, Vol. 7, Issue 6
DOI: 10.1021/ct200114k

Local Treatment of Electron Correlation
journal, October 1993

Saebo, S.; Pulay, P.
Annual Review of Physical Chemistry, Vol. 44, Issue 1
DOI: 10.1146/annurev.pc.44.100193.001241

Local treatment of electron correlation in coupled cluster theory
journal, April 1996

Hampel, Claudia; Werner, Hans‐Joachim
The Journal of Chemical Physics, Vol. 104, Issue 16
DOI: 10.1063/1.471289

Extension of linear-scaling divide-and-conquer-based correlation method to coupled cluster theory with singles and doubles excitations
journal, July 2008

Kobayashi, Masato; Nakai, Hiromi
The Journal of Chemical Physics, Vol. 129, Issue 4
DOI: 10.1063/1.2956490

The divide-expand-consolidate family of coupled cluster methods: Numerical illustrations using second order Møller-Plesset perturbation theory
journal, January 2012

Høyvik, Ida-Marie; Kristensen, Kasper; Jansik, Branislav
The Journal of Chemical Physics, Vol. 136, Issue 1
DOI: 10.1063/1.3667266

An efficient algorithm for solving nonlinear equations with a minimal number of trial vectors: Applications to atomic-orbital based coupled-cluster theory
journal, May 2008

Ziółkowski, Marcin; Weijo, Ville; Jørgensen, Poul
The Journal of Chemical Physics, Vol. 128, Issue 20
DOI: 10.1063/1.2928803

Efficient evaluation of Coulomb integrals in a mixed Gaussian and plane-wave basis using the density fitting and Cholesky decomposition
journal, March 2012

Čársky, Petr; Čurík, Roman; Varga, Štefan
The Journal of Chemical Physics, Vol. 136, Issue 11
DOI: 10.1063/1.3693411

Linear scaling local correlation approach for solving the coupled cluster equations of large systems
journal, December 2001

Li, Shuhua; Ma, Jing; Jiang, Yuansheng
Journal of Computational Chemistry, Vol. 23, Issue 2
DOI: 10.1002/jcc.10003

Linear scaling coupled cluster method with correlation energy based error control
journal, July 2010

Ziółkowski, Marcin; Jansík, Branislav; Kjærgaard, Thomas
The Journal of Chemical Physics, Vol. 133, Issue 1
DOI: 10.1063/1.3456535

Coupled-cluster theory based upon the fragment molecular-orbital method
journal, October 2005

Fedorov, Dmitri G.; Kitaura, Kazuo
The Journal of Chemical Physics, Vol. 123, Issue 13
DOI: 10.1063/1.2007588

An efficient and near linear scaling pair natural orbital based local coupled cluster method
journal, January 2013

Riplinger, Christoph; Neese, Frank
The Journal of Chemical Physics, Vol. 138, Issue 3
DOI: 10.1063/1.4773581

Efficient linear-scaling second-order Møller-Plesset perturbation theory: The divide–expand–consolidate RI-MP2 model
journal, February 2016

Baudin, Pablo; Ettenhuber, Patrick; Reine, Simen
The Journal of Chemical Physics, Vol. 144, Issue 5
DOI: 10.1063/1.4940732

Linear scaling second-order Moller–Plesset theory in the atomic orbital basis for large molecular systems
journal, February 1999

Ayala, Philippe Y.; Scuseria, Gustavo E.
The Journal of Chemical Physics, Vol. 110, Issue 8
DOI: 10.1063/1.478256

Works referencing / citing this record:

Explicitly correlated local coupled-cluster methods using pair natural orbitals
journal, July 2018

Ma, Qianli; Werner, Hans-Joachim
Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 6
DOI: 10.1002/wcms.1371

Divide–Expand–Consolidate Second-Order Møller–Plesset Theory with Periodic Boundary Conditions
journal, March 2018

Rebolini, Elisa; Baardsen, Gustav; Hansen, Audun Skau
Journal of Chemical Theory and Computation, Vol. 14, Issue 5
DOI: 10.1021/acs.jctc.8b00021

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Title: Orbital spaces in the divide-expand-consolidate coupled cluster method

Abstract

Citation Formats

Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method journal, March 2009

A perspective on the localizability of Hartree–Fock orbitals journal, November 2013

Fully automated implementation of the incremental scheme: Application to CCSD energies for hydrocarbons and transition metal compounds journal, April 2007

Maximum locality in occupied and virtual orbital spaces using a least-change strategy journal, September 2009

Low-order scaling local electron correlation methods. I. Linear scaling local MP2 journal, October 1999

The divide–expand–consolidate MP2 scheme goes massively parallel journal, April 2013

Molecular Electronic-Structure Theory book, August 2000

A natural linear scaling coupled-cluster method journal, January 2004

Efficient and accurate approximations to the local coupled cluster singles doubles method using a truncated pair natural orbital basis journal, January 2009

Localizability of dynamic electron correlation journal, September 1983

A general-order local coupled-cluster method based on the cluster-in-molecule approach journal, September 2011

A refined cluster-in-molecule local correlation approach for predicting the relative energies of large systems journal, January 2012

Exploring chemistry with the fragment molecular orbital method journal, January 2012

Divide-and-conquer local correlation approach to the correlation energy of large molecules journal, October 2004

MP2 energy and density for large molecular systems with internal error control using the Divide-Expand-Consolidate scheme journal, January 2012

Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen journal, January 1989

General biorthogonal projected bases as applied to second-order Møller-Plesset perturbation theory journal, August 2007

The Dalton quantum chemistry program system: The Dalton program journal, September 2013

An atomic orbital-based reformulation of energy gradients in second-order Møller–Plesset perturbation theory journal, April 2008

Molecular gradient for second-order Møller-Plesset perturbation theory using the divide-expand-consolidate (DEC) scheme journal, September 2012

Trust Region Minimization of Orbital Localization Functions journal, August 2012

Comparison of the boys and Pipek-Mezey localizations in the local correlation approach and automatic virtual basis selection journal, June 1993

Laplace transform techniques in Mo/ller–Plesset perturbation theory journal, January 1992

Tighter multipole-based integral estimates and parallel implementation of linear-scaling AO–MP2 theory journal, January 2008

Linear-Scaling Coupled Cluster with Perturbative Triple Excitations: The Divide–Expand–Consolidate CCSD(T) Model journal, June 2015

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

The correlation energy of crystalline silicon journal, April 1992

A Locality Analysis of the Divide–Expand–Consolidate Coupled Cluster Amplitude Equations journal, May 2011

Local Treatment of Electron Correlation journal, October 1993

Local treatment of electron correlation in coupled cluster theory journal, April 1996

Extension of linear-scaling divide-and-conquer-based correlation method to coupled cluster theory with singles and doubles excitations journal, July 2008

The divide-expand-consolidate family of coupled cluster methods: Numerical illustrations using second order Møller-Plesset perturbation theory journal, January 2012

An efficient algorithm for solving nonlinear equations with a minimal number of trial vectors: Applications to atomic-orbital based coupled-cluster theory journal, May 2008

Efficient evaluation of Coulomb integrals in a mixed Gaussian and plane-wave basis using the density fitting and Cholesky decomposition journal, March 2012

Linear scaling local correlation approach for solving the coupled cluster equations of large systems journal, December 2001

Linear scaling coupled cluster method with correlation energy based error control journal, July 2010

Coupled-cluster theory based upon the fragment molecular-orbital method journal, October 2005

An efficient and near linear scaling pair natural orbital based local coupled cluster method journal, January 2013

Efficient linear-scaling second-order Møller-Plesset perturbation theory: The divide–expand–consolidate RI-MP2 model journal, February 2016

Linear scaling second-order Moller–Plesset theory in the atomic orbital basis for large molecular systems journal, February 1999

Explicitly correlated local coupled-cluster methods using pair natural orbitals journal, July 2018

Divide–Expand–Consolidate Second-Order Møller–Plesset Theory with Periodic Boundary Conditions journal, March 2018

Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method
journal, March 2009

A perspective on the localizability of Hartree–Fock orbitals
journal, November 2013

Fully automated implementation of the incremental scheme: Application to CCSD energies for hydrocarbons and transition metal compounds
journal, April 2007

Maximum locality in occupied and virtual orbital spaces using a least-change strategy
journal, September 2009

Low-order scaling local electron correlation methods. I. Linear scaling local MP2
journal, October 1999

The divide–expand–consolidate MP2 scheme goes massively parallel
journal, April 2013

Molecular Electronic-Structure Theory
book, August 2000

A natural linear scaling coupled-cluster method
journal, January 2004

Efficient and accurate approximations to the local coupled cluster singles doubles method using a truncated pair natural orbital basis
journal, January 2009

Localizability of dynamic electron correlation
journal, September 1983

A general-order local coupled-cluster method based on the cluster-in-molecule approach
journal, September 2011

A refined cluster-in-molecule local correlation approach for predicting the relative energies of large systems
journal, January 2012

Exploring chemistry with the fragment molecular orbital method
journal, January 2012

Divide-and-conquer local correlation approach to the correlation energy of large molecules
journal, October 2004

MP2 energy and density for large molecular systems with internal error control using the Divide-Expand-Consolidate scheme
journal, January 2012

Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
journal, January 1989

General biorthogonal projected bases as applied to second-order Møller-Plesset perturbation theory
journal, August 2007

The Dalton quantum chemistry program system: The Dalton program
journal, September 2013

An atomic orbital-based reformulation of energy gradients in second-order Møller–Plesset perturbation theory
journal, April 2008

Molecular gradient for second-order Møller-Plesset perturbation theory using the divide-expand-consolidate (DEC) scheme
journal, September 2012

Trust Region Minimization of Orbital Localization Functions
journal, August 2012

Comparison of the boys and Pipek-Mezey localizations in the local correlation approach and automatic virtual basis selection
journal, June 1993

Laplace transform techniques in Mo/ller–Plesset perturbation theory
journal, January 1992

Tighter multipole-based integral estimates and parallel implementation of linear-scaling AO–MP2 theory
journal, January 2008

Linear-Scaling Coupled Cluster with Perturbative Triple Excitations: The Divide–Expand–Consolidate CCSD(T) Model
journal, June 2015

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

The correlation energy of crystalline silicon
journal, April 1992

A Locality Analysis of the Divide–Expand–Consolidate Coupled Cluster Amplitude Equations
journal, May 2011

Local Treatment of Electron Correlation
journal, October 1993

Local treatment of electron correlation in coupled cluster theory
journal, April 1996

Extension of linear-scaling divide-and-conquer-based correlation method to coupled cluster theory with singles and doubles excitations
journal, July 2008

The divide-expand-consolidate family of coupled cluster methods: Numerical illustrations using second order Møller-Plesset perturbation theory
journal, January 2012

An efficient algorithm for solving nonlinear equations with a minimal number of trial vectors: Applications to atomic-orbital based coupled-cluster theory
journal, May 2008

Efficient evaluation of Coulomb integrals in a mixed Gaussian and plane-wave basis using the density fitting and Cholesky decomposition
journal, March 2012

Linear scaling local correlation approach for solving the coupled cluster equations of large systems
journal, December 2001

Linear scaling coupled cluster method with correlation energy based error control
journal, July 2010

Coupled-cluster theory based upon the fragment molecular-orbital method
journal, October 2005

An efficient and near linear scaling pair natural orbital based local coupled cluster method
journal, January 2013

Efficient linear-scaling second-order Møller-Plesset perturbation theory: The divide–expand–consolidate RI-MP2 model
journal, February 2016

Linear scaling second-order Moller–Plesset theory in the atomic orbital basis for large molecular systems
journal, February 1999

Explicitly correlated local coupled-cluster methods using pair natural orbitals
journal, July 2018

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