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Title: Properties of coupled-cluster equations originating in excitation sub-algebras

Abstract

In this paper we discuss properties of single-reference coupled cluster (CC) equations associated with the existence of nilpotent sub-algebras of excitations that allow one to represent CC equations in a hybrid fashion where the cluster amplitudes associated with these sub-algebras can be obtained by solving corresponding eigenvalue problem. For closed-shell formulations analyzed in this paper, the hybrid representation of CC equations provides a natural way for extending concepts behind actives-spaces and seniority numbers to provide more accurate description of electron correlation effects. Moreover, new representation can be utilized to re-define iterative algorithms used to solve CC equations, especially for though cases defined by the presence of strong static and dynamic correlation effects. We will also explore invariance properties associated with the nilpotent sub-algebras to define a new class of CC approximations referred in this paper to as the nilpotent-flow-based CC methods. We illustrate the performance of these methods on the example of ground- and excited-state calculations for commonly used small benchmark systems.

Authors:
 [1]
  1. William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1494313
Report Number(s):
PNNL-SA-130129
Journal ID: ISSN 0021-9606
DOE Contract Number:  
AC05-76RL01830
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 148; Journal Issue: 9; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English

Citation Formats

Kowalski, Karol. Properties of coupled-cluster equations originating in excitation sub-algebras. United States: N. p., 2018. Web. doi:10.1063/1.5010693.
Kowalski, Karol. Properties of coupled-cluster equations originating in excitation sub-algebras. United States. doi:10.1063/1.5010693.
Kowalski, Karol. Wed . "Properties of coupled-cluster equations originating in excitation sub-algebras". United States. doi:10.1063/1.5010693.
@article{osti_1494313,
title = {Properties of coupled-cluster equations originating in excitation sub-algebras},
author = {Kowalski, Karol},
abstractNote = {In this paper we discuss properties of single-reference coupled cluster (CC) equations associated with the existence of nilpotent sub-algebras of excitations that allow one to represent CC equations in a hybrid fashion where the cluster amplitudes associated with these sub-algebras can be obtained by solving corresponding eigenvalue problem. For closed-shell formulations analyzed in this paper, the hybrid representation of CC equations provides a natural way for extending concepts behind actives-spaces and seniority numbers to provide more accurate description of electron correlation effects. Moreover, new representation can be utilized to re-define iterative algorithms used to solve CC equations, especially for though cases defined by the presence of strong static and dynamic correlation effects. We will also explore invariance properties associated with the nilpotent sub-algebras to define a new class of CC approximations referred in this paper to as the nilpotent-flow-based CC methods. We illustrate the performance of these methods on the example of ground- and excited-state calculations for commonly used small benchmark systems.},
doi = {10.1063/1.5010693},
journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 9,
volume = 148,
place = {United States},
year = {2018},
month = {3}
}

Works referenced in this record:

Parallel Implementation of Multireference Coupled-Cluster Theories Based on the Reference-Level Parallelism
journal, February 2012

  • Brabec, Jiří; Pittner, Jiří; van Dam, Hubertus J. J.
  • Journal of Chemical Theory and Computation, Vol. 8, Issue 2
  • DOI: 10.1021/ct200809m

Physical and mathematical content of coupled–cluster equations: Correspondence between coupled–cluster and configuration–interaction solutions
journal, February 1999

  • Jankowski, K.; Kowalski, K.
  • The Journal of Chemical Physics, Vol. 110, Issue 8
  • DOI: 10.1063/1.478262

New coupled-cluster methods with singles, doubles, and noniterative triples for high accuracy calculations of excited electronic states
journal, January 2004

  • Kowalski, Karol; Piecuch, Piotr
  • The Journal of Chemical Physics, Vol. 120, Issue 4
  • DOI: 10.1063/1.1632474

The full CCSDT model for molecular electronic structure
journal, June 1987

  • Noga, Jozef; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 86, Issue 12
  • DOI: 10.1063/1.452353

An adaptive coupled-cluster theory: @CC approach
journal, December 2010

  • Lyakh, Dmitry I.; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 133, Issue 24
  • DOI: 10.1063/1.3515476

Erratum: The full CCSDT model for molecular electronic structure [J. Chem. Phys. 8 6 , 7041 (1987)]
journal, September 1988

  • Noga, J.; Bartlett, R. J.
  • The Journal of Chemical Physics, Vol. 89, Issue 5
  • DOI: 10.1063/1.455742

Communication: The distinguishable cluster approximation
journal, July 2013

  • Kats, Daniel; Manby, Frederick R.
  • The Journal of Chemical Physics, Vol. 139, Issue 2
  • DOI: 10.1063/1.4813481

New perspectives on unitary coupled-cluster theory
journal, January 2006

  • Taube, Andrew G.; Bartlett, Rodney J.
  • International Journal of Quantum Chemistry, Vol. 106, Issue 15
  • DOI: 10.1002/qua.21198

Coupled cluster response functions
journal, September 1990

  • Koch, Henrik; Jo/rgensen, Poul
  • The Journal of Chemical Physics, Vol. 93, Issue 5
  • DOI: 10.1063/1.458814

Molpro: a general-purpose quantum chemistry program package: Molpro
journal, July 2011

  • Werner, Hans-Joachim; Knowles, Peter J.; Knizia, Gerald
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 2, Issue 2
  • DOI: 10.1002/wcms.82

Tailored coupled cluster singles and doubles method applied to calculations on molecular structure and harmonic vibrational frequencies of ozone
journal, March 2006

  • Hino, Osamu; Kinoshita, Tomoko; Chan, Garnet Kin-Lic
  • The Journal of Chemical Physics, Vol. 124, Issue 11
  • DOI: 10.1063/1.2180775

Applicability of coupled-pair theories to quasidegenerate electronic states: A model study
journal, November 1980

  • Jankowski, K.; Paldus, J.
  • International Journal of Quantum Chemistry, Vol. 18, Issue 5
  • DOI: 10.1002/qua.560180511

Coupled Cluster Method with Single and Double Excitations Tailored by Matrix Product State Wave Functions
journal, October 2016

  • Veis, Libor; Antalík, Andrej; Brabec, Jiří
  • The Journal of Physical Chemistry Letters, Vol. 7, Issue 20
  • DOI: 10.1021/acs.jpclett.6b01908

Improved computational strategy for the state‐selective coupled‐cluster theory with semi‐internal triexcited clusters: Potential energy surface of the HF molecule
journal, December 1995

  • Ghose, Keya B.; Piecuch, Piotr; Adamowicz, Ludwik
  • The Journal of Chemical Physics, Vol. 103, Issue 21
  • DOI: 10.1063/1.469993

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 active-space equation-of-motion coupled-cluster methods for excited electronic states: Full EOMCCSDt
journal, July 2001

  • Kowalski, Karol; Piecuch, Piotr
  • The Journal of Chemical Physics, Vol. 115, Issue 2
  • DOI: 10.1063/1.1378323

A universal state-selective approach to multireference coupled-cluster non-iterative corrections
journal, May 2011

  • Kowalski, Karol
  • The Journal of Chemical Physics, Vol. 134, Issue 19
  • DOI: 10.1063/1.3589896

Externally and internally corrected coupled cluster approaches: an overview
journal, September 2016


Higher excitations in coupled-cluster theory
journal, August 2001

  • Kállay, Mihály; Surján, Péter R.
  • The Journal of Chemical Physics, Vol. 115, Issue 7
  • DOI: 10.1063/1.1383290

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

Seniority-based coupled cluster theory
journal, December 2014

  • Henderson, Thomas M.; Bulik, Ireneusz W.; Stein, Tamar
  • The Journal of Chemical Physics, Vol. 141, Issue 24
  • DOI: 10.1063/1.4904384

Seniority number description of potential energy surfaces: Symmetric dissociation of water, N 2 , C 2 , and Be 2
journal, September 2015

  • Bytautas, Laimutis; Scuseria, Gustavo E.; Ruedenberg, Klaus
  • The Journal of Chemical Physics, Vol. 143, Issue 9
  • DOI: 10.1063/1.4929904

The implementation of the multireference coupled‐cluster method based on the single‐reference formalism
journal, March 1992

  • Oliphant, Nevin; Adamowicz, Ludwik
  • The Journal of Chemical Physics, Vol. 96, Issue 5
  • DOI: 10.1063/1.461878

Combining active-space coupled-cluster approaches with moment energy corrections via the CC( P ; Q ) methodology: connected quadruple excitations
journal, January 2017


Communication: Projected Hartree Fock theory as a polynomial similarity transformation theory of single excitations
journal, September 2016

  • Qiu, Yiheng; Henderson, Thomas M.; Scuseria, Gustavo E.
  • The Journal of Chemical Physics, Vol. 145, Issue 11
  • DOI: 10.1063/1.4963082

The quadratic coupled cluster doubles model
journal, November 2000


Pair extended coupled cluster doubles
journal, June 2015

  • Henderson, Thomas M.; Bulik, Ireneusz W.; Scuseria, Gustavo E.
  • The Journal of Chemical Physics, Vol. 142, Issue 21
  • DOI: 10.1063/1.4921986

Formulation and implementation of the full coupled-cluster method through pentuple excitations
journal, March 2002

  • Musiał, M.; Kucharski, S. A.; Bartlett, R. J.
  • The Journal of Chemical Physics, Vol. 116, Issue 11
  • DOI: 10.1063/1.1445744

Communication: The distinguishable cluster approximation. II. The role of orbital relaxation
journal, August 2014

  • Kats, Daniel
  • The Journal of Chemical Physics, Vol. 141, Issue 6
  • DOI: 10.1063/1.4892792

Analytic connection between configuration–interaction and coupled‐cluster solutions
journal, May 1978

  • Živković, Tomislav P.; Monkhorst, Hendrik J.
  • Journal of Mathematical Physics, Vol. 19, Issue 5
  • DOI: 10.1063/1.523761

The Density Matrix Renormalization Group in Quantum Chemistry
journal, May 2011


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

Projected seniority-two orbital optimization of the antisymmetric product of one-reference orbital geminal
journal, June 2014

  • Boguslawski, Katharina; Tecmer, Paweł; Limacher, Peter A.
  • The Journal of Chemical Physics, Vol. 140, Issue 21
  • DOI: 10.1063/1.4880820

Clifford algebra and unitary group formulations of the many-electron problem
journal, January 1988

  • Paldus, Josef; Jeziorski, Bogumil
  • Theoretica Chimica Acta, Vol. 73, Issue 2-3
  • DOI: 10.1007/bf00528196

Can Single-Reference Coupled Cluster Theory Describe Static Correlation?
journal, June 2015

  • Bulik, Ireneusz W.; Henderson, Thomas M.; Scuseria, Gustavo E.
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 7
  • DOI: 10.1021/acs.jctc.5b00422

Size-consistent single-reference methods for electronic correlation: a unified formulation through intermediate hamiltonian theory
journal, April 1996

  • Sánchez-Marín, José; Nebot-Gil, Ignacio; Malrieu, Jean Paul
  • Theoretica Chimica Acta, Vol. 95, Issue 5-6
  • DOI: 10.1007/bf02335465

Configuration interaction calculations on the nitrogen molecule
journal, January 1974

  • Langhoff, Stephen R.; Davidson, Ernest R.
  • International Journal of Quantum Chemistry, Vol. 8, Issue 1
  • DOI: 10.1002/qua.560080106

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

A new implementation of the full CCSDT model for molecular electronic structure
journal, November 1988


Single-reference CCSD approach employing three- and four-body CAS SCF corrections: A preliminary study of a simple model
journal, January 1997


Reduced multireference coupled cluster method with singles and doubles: Perturbative corrections for triples
journal, May 2006

  • Li, Xiangzhu; Paldus, Josef
  • The Journal of Chemical Physics, Vol. 124, Issue 17
  • DOI: 10.1063/1.2194543

Canonical transformation theory from extended normal ordering
journal, September 2007

  • Yanai, Takeshi; Chan, Garnet Kin-Lic
  • The Journal of Chemical Physics, Vol. 127, Issue 10
  • DOI: 10.1063/1.2761870

Relaxed active space: Fixing tailored-CC with high order coupled cluster. II
journal, February 2014

  • Melnichuk, Ann; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 140, Issue 6
  • DOI: 10.1063/1.4862676

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

Addition by subtraction in coupled-cluster theory: A reconsideration of the CC and CI interface and the nCC hierarchy
journal, November 2006

  • Bartlett, Rodney J.; Musiał, Monika
  • The Journal of Chemical Physics, Vol. 125, Issue 20
  • DOI: 10.1063/1.2387952

Binding in transition metal complexes: Reduced multireference coupled-cluster study of the MCH2+ (M=Sc to Cu) compounds
journal, June 2007

  • Li, Xiangzhu; Paldus, Josef
  • The Journal of Chemical Physics, Vol. 126, Issue 23
  • DOI: 10.1063/1.2741265

Seniority zero pair coupled cluster doubles theory
journal, June 2014

  • Stein, Tamar; Henderson, Thomas M.; Scuseria, Gustavo E.
  • The Journal of Chemical Physics, Vol. 140, Issue 21
  • DOI: 10.1063/1.4880819

Bound states of a many-particle system
journal, June 1958


Bridging single and multireference coupled cluster theories with universal state selective formalism
journal, May 2013

  • Bhaskaran-Nair, Kiran; Kowalski, Karol
  • The Journal of Chemical Physics, Vol. 138, Issue 20
  • DOI: 10.1063/1.4806768

Clifford algebra unitary group approach to many‐electron correlation problem
journal, November 1985

  • Paldus, J.; Sarma, C. R.
  • The Journal of Chemical Physics, Vol. 83, Issue 10
  • DOI: 10.1063/1.449726

Renormalized coupled-cluster methods exploiting left eigenstates of the similarity-transformed Hamiltonian
journal, December 2005

  • Piecuch, Piotr; Włoch, Marta
  • The Journal of Chemical Physics, Vol. 123, Issue 22
  • DOI: 10.1063/1.2137318

Canonical transformation theory for multireference problems
journal, May 2006

  • Yanai, Takeshi; Chan, Garnet Kin-Lic
  • The Journal of Chemical Physics, Vol. 124, Issue 19
  • DOI: 10.1063/1.2196410

Computing coupled-cluster wave functions with arbitrary excitations
journal, July 2000

  • Kállay, Mihály; Surján, Péter R.
  • The Journal of Chemical Physics, Vol. 113, Issue 4
  • DOI: 10.1063/1.481925

Approximate variational coupled cluster theory
journal, July 2011

  • Robinson, James B.; Knowles, Peter J.
  • The Journal of Chemical Physics, Vol. 135, Issue 4
  • DOI: 10.1063/1.3615060

Gaussian Basis Functions for Use in Molecular Calculations. I. Contraction of (9s5p) Atomic Basis Sets for the First‐Row Atoms
journal, October 1970

  • Dunning, Thom H.
  • The Journal of Chemical Physics, Vol. 53, Issue 7
  • DOI: 10.1063/1.1674408

The method of moments of coupled-cluster equations and the renormalized CCSD[T], CCSD(T), CCSD(TQ), and CCSDT(Q) approaches
journal, July 2000

  • Kowalski, Karol; Piecuch, Piotr
  • The Journal of Chemical Physics, Vol. 113, Issue 1
  • DOI: 10.1063/1.481769

The equation-of-motion coupled-cluster method: Excitation energies of Be and CO
journal, December 1989


Calculation of properties with the coupled-cluster method
journal, January 1977

  • Monkhorst, Hendrik J.
  • International Journal of Quantum Chemistry, Vol. 12, Issue S11
  • DOI: 10.1002/qua.560120850

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


Coupled‐cluster method truncated at quadruples
journal, November 1991

  • Oliphant, Nevin; Adamowicz, Ludwik
  • The Journal of Chemical Physics, Vol. 95, Issue 9
  • DOI: 10.1063/1.461534

Full CI calculations on BH, H2O, NH3, and HF
journal, March 1983


Alternative coupled-cluster ansätze II. The unitary coupled-cluster method
journal, February 1989


Multireference state-specific coupled-cluster methods. State-of-the-art and perspectives
journal, January 2009

  • Ivanov, Vladimir V.; Lyakh, Dmitry I.; Adamowicz, Ludwik
  • Physical Chemistry Chemical Physics, Vol. 11, Issue 14
  • DOI: 10.1039/b818590p

Alternative ansätze in single reference coupled‐cluster theory. III. A critical analysis of different methods
journal, July 1995

  • Szalay, Péter G.; Nooijen, Marcel; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 103, Issue 1
  • DOI: 10.1063/1.469641

A state‐selective multireference coupled‐cluster theory employing the single‐reference formalism
journal, August 1993

  • Piecuch, Piotr; Oliphant, Nevin; Adamowicz, Ludwik
  • The Journal of Chemical Physics, Vol. 99, Issue 3
  • DOI: 10.1063/1.466179

Coupled-cluster methods with internal and semi-internal triply and quadruply excited clusters: CCSDt and CCSDtq approaches
journal, April 1999

  • Piecuch, Piotr; Kucharski, Stanisław A.; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 110, Issue 13
  • DOI: 10.1063/1.478517

Relaxed active space: Fixing tailored-CC with high order coupled cluster. I
journal, December 2012

  • Melnichuk, Anna; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 137, Issue 21
  • DOI: 10.1063/1.4767900

Multi-root configuration interaction calculations
journal, September 1980


Externally corrected singles and doubles coupled cluster methods for open-shell systems
journal, July 1997

  • Li, Xiangzhu; Peris, G.; Planelles, J.
  • The Journal of Chemical Physics, Vol. 107, Issue 1
  • DOI: 10.1063/1.474355

pCCSD: Parameterized coupled-cluster theory with single and double excitations
journal, November 2010

  • Huntington, Lee M. J.; Nooijen, Marcel
  • The Journal of Chemical Physics, Vol. 133, Issue 18
  • DOI: 10.1063/1.3494113