Excited states via coupled cluster theory without equation-of-motion methods: Seeking higher roots with application to doubly excited states and double core hole states
Abstract
In this work, we revisited the idea of using the coupled-cluster (CC) ground state formalism to target excited states. Our main focus was targeting doubly excited states and double core hole states. Typical equation-of-motion (EOM) approaches for obtaining these states struggle without higher-order excitations than doubles. We showed that by using a non-Aufbau determinant optimized via the maximum overlap method, the CC ground state solver can target higher energy states. Furthermore, just with singles and doubles (i.e., CCSD), we demonstrated that the accuracy of ΔCCSD and ΔCCSD(T) (triples) far surpasses that of EOM-CCSD for doubly excited states. The accuracy of ΔCCSD(T) is nearly exact for doubly excited states considered in this work. For double core hole states, we used an improved ansatz for greater numerical stability by freezing core hole orbitals. The improved methods, core valence separation (CVS)-ΔCCSD and CVS-ΔCCSD(T), were applied to the calculation of the double ionization potential of small molecules. Even without relativistic corrections, we observed qualitatively accurate results with CVS-ΔCCSD and CVS-ΔCCSD(T). Remaining challenges in ΔCC include the description of open-shell singlet excited states with the single-reference CC ground state formalism as well as excited states with genuine multireference character. The tools and intuition developed inmore »
- Authors:
-
- Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). Chemical Sciences Division
- Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). Chemical Sciences Division
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1975812
- Alternate Identifier(s):
- OSTI ID: 1576805
- Grant/Contract Number:
- AC02-05CH11231; ACO2-05CH11231
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 151; Journal Issue: 21; 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; coupled-cluster methods; excitation energies; equations of motion
Citation Formats
Lee, Joonho, Small, David W., and Head-Gordon, Martin. Excited states via coupled cluster theory without equation-of-motion methods: Seeking higher roots with application to doubly excited states and double core hole states. United States: N. p., 2019.
Web. doi:10.1063/1.5128795.
Lee, Joonho, Small, David W., & Head-Gordon, Martin. Excited states via coupled cluster theory without equation-of-motion methods: Seeking higher roots with application to doubly excited states and double core hole states. United States. https://doi.org/10.1063/1.5128795
Lee, Joonho, Small, David W., and Head-Gordon, Martin. Mon .
"Excited states via coupled cluster theory without equation-of-motion methods: Seeking higher roots with application to doubly excited states and double core hole states". United States. https://doi.org/10.1063/1.5128795. https://www.osti.gov/servlets/purl/1975812.
@article{osti_1975812,
title = {Excited states via coupled cluster theory without equation-of-motion methods: Seeking higher roots with application to doubly excited states and double core hole states},
author = {Lee, Joonho and Small, David W. and Head-Gordon, Martin},
abstractNote = {In this work, we revisited the idea of using the coupled-cluster (CC) ground state formalism to target excited states. Our main focus was targeting doubly excited states and double core hole states. Typical equation-of-motion (EOM) approaches for obtaining these states struggle without higher-order excitations than doubles. We showed that by using a non-Aufbau determinant optimized via the maximum overlap method, the CC ground state solver can target higher energy states. Furthermore, just with singles and doubles (i.e., CCSD), we demonstrated that the accuracy of ΔCCSD and ΔCCSD(T) (triples) far surpasses that of EOM-CCSD for doubly excited states. The accuracy of ΔCCSD(T) is nearly exact for doubly excited states considered in this work. For double core hole states, we used an improved ansatz for greater numerical stability by freezing core hole orbitals. The improved methods, core valence separation (CVS)-ΔCCSD and CVS-ΔCCSD(T), were applied to the calculation of the double ionization potential of small molecules. Even without relativistic corrections, we observed qualitatively accurate results with CVS-ΔCCSD and CVS-ΔCCSD(T). Remaining challenges in ΔCC include the description of open-shell singlet excited states with the single-reference CC ground state formalism as well as excited states with genuine multireference character. The tools and intuition developed in this work may serve as a stepping stone toward directly targeting arbitrary excited states using ground state CC methods.},
doi = {10.1063/1.5128795},
journal = {Journal of Chemical Physics},
number = 21,
volume = 151,
place = {United States},
year = {Mon Dec 02 00:00:00 EST 2019},
month = {Mon Dec 02 00:00:00 EST 2019}
}
Web of Science
Works referenced in this record:
New and Efficient Equation-of-Motion Coupled-Cluster Framework for Core-Excited and Core-Ionized States
journal, April 2019
- Vidal, Marta L.; Feng, Xintian; Epifanovsky, Evgeny
- Journal of Chemical Theory and Computation, Vol. 15, Issue 5
Simulation of X-ray absorption spectra with orthogonality constrained density functional theory
journal, January 2015
- Derricotte, Wallace D.; Evangelista, Francesco A.
- Physical Chemistry Chemical Physics, Vol. 17, Issue 22
Equation-of-Motion Coupled-Cluster Methods for Open-Shell and Electronically Excited Species: The Hitchhiker's Guide to Fock Space
journal, May 2008
- Krylov, Anna I.
- Annual Review of Physical Chemistry, Vol. 59, Issue 1
Self-Consistent Field Calculations of Excited States Using the Maximum Overlap Method (MOM) †
journal, December 2008
- Gilbert, Andrew T. B.; Besley, Nicholas A.; Gill, Peter M. W.
- The Journal of Physical Chemistry A, Vol. 112, Issue 50
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
Structure sensitivity of double inner-shell holes in sulfur-containing molecules
journal, February 2011
- Linusson, P.; Takahashi, O.; Ueda, K.
- Physical Review A, Vol. 83, Issue 2
Communication: The distinguishable cluster approximation
journal, July 2013
- Kats, Daniel; Manby, Frederick R.
- The Journal of Chemical Physics, Vol. 139, Issue 2
Excitation energies from the coupled cluster singles and doubles linear response function (CCSDLR). Applications to Be, CH + , CO, and H 2 O
journal, September 1990
- Koch, Henrik; Jensen, Hans Jo/rgen Aa.; Jo/rgensen, Poul
- The Journal of Chemical Physics, Vol. 93, Issue 5
Equation of motion coupled cluster theory calculations of the X-ray emission spectroscopy of water
journal, July 2012
- Besley, Nicholas A.
- Chemical Physics Letters, Vol. 542
Double vacancies in the core of benzene
journal, February 1987
- Cederbaum, L. S.; Tarantelli, F.; Sgamellotti, A.
- The Journal of Chemical Physics, Vol. 86, Issue 4
Structure sensitivity of double inner-shell holes in sulfur-containing molecules
journal, February 2011
- Linusson, P.; Takahashi, O.; Ueda, K.
- Physical Review A, Vol. 83, Issue 2
Coupled-cluster theory for excited electronic states: The full equation-of-motion coupled-cluster single, double, and triple excitation method
journal, November 2001
- Kucharski, Stanisław A.; Włoch, Marta; Musiał, Monika
- The Journal of Chemical Physics, Vol. 115, Issue 18
Analytic energy derivatives for ionized states described by the equation‐of‐motion coupled cluster method
journal, November 1994
- Stanton, John F.; Gauss, Jürgen
- The Journal of Chemical Physics, Vol. 101, Issue 10
Coupled-Cluster Valence-Bond Singles and Doubles for Strongly Correlated Systems: Block-Tensor Based Implementation and Application to Oligoacenes
journal, January 2017
- Lee, Joonho; Small, David W.; Epifanovsky, Evgeny
- Journal of Chemical Theory and Computation, Vol. 13, Issue 2
Molecular double core hole electron spectroscopy for chemical analysis
journal, May 2010
- Tashiro, Motomichi; Ehara, Masahiro; Fukuzawa, Hironobu
- The Journal of Chemical Physics, Vol. 132, Issue 18
Perturbative triple excitation corrections to coupled cluster singles and doubles excitation energies
journal, July 1996
- Christiansen, Ove; Koch, Henrik; Jo/rgensen, Poul
- The Journal of Chemical Physics, Vol. 105, Issue 4
Communication: X-ray absorption spectra and core-ionization potentials within a core-valence separated coupled cluster framework
journal, November 2015
- Coriani, Sonia; Koch, Henrik
- The Journal of Chemical Physics, Vol. 143, Issue 18
Many – Body Methods in Chemistry and Physics
book, January 2009
- Shavitt, Isaiah; Bartlett, Rodney J.
A spin correction procedure for unrestricted Hartree-Fock and Møller-Plesset wavefunctions for singlet diradicals and polyradicals
journal, September 1988
- Yamaguchi, K.; Jensen, F.; Dorigo, A.
- Chemical Physics Letters, Vol. 149, Issue 5-6
Non-orthogonal configuration interaction with single substitutions for the calculation of core-excited states
journal, July 2018
- Oosterbaan, Katherine J.; White, Alec F.; Head-Gordon, Martin
- The Journal of Chemical Physics, Vol. 149, Issue 4
Physical and mathematical content of coupled-cluster equations. II. On the origin of irregular solutions and their elimination via symmetry adaptation
journal, May 1999
- Jankowski, K.; Kowalski, K.
- The Journal of Chemical Physics, Vol. 110, Issue 19
Double vacancies in the cores of silane and tetrafluorosilane
journal, July 1991
- Ohrendorf, E. M. -L.; Cederbaum, L. S.; Tarantelli, F.
- Physical Review A, Vol. 44, Issue 1
Multiple solutions of the single-reference coupled-cluster equations. I. H4 model revisited
journal, May 1994
- Jankowski, K.; Kowalski, K.; Jankowski, P.
- International Journal of Quantum Chemistry, Vol. 50, Issue 5
Auger Electron Angular Distribution of Double Core-Hole States in the Molecular Reference Frame
journal, August 2010
- Cryan, James P.; Glownia, J. M.; Andreasson, J.
- Physical Review Letters, Vol. 105, Issue 8
Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications
journal, December 2011
- Szalay, Péter G.; Müller, Thomas; Gidofalvi, Gergely
- Chemical Reviews, Vol. 112, Issue 1
Theoretical core-level excitation spectra of N 2 and CO by a new polarisation propagator method
journal, March 1985
- Barth, A.; Schirmer, J.
- Journal of Physics B: Atomic and Molecular Physics, Vol. 18, Issue 5
Double Core-Hole Production in : Beating the Auger Clock
journal, August 2010
- Fang, L.; Hoener, M.; Gessner, O.
- Physical Review Letters, Vol. 105, Issue 8
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
Non-orthogonal configuration interaction for the calculation of multielectron excited states
journal, March 2014
- Sundstrom, Eric J.; Head-Gordon, Martin
- The Journal of Chemical Physics, Vol. 140, Issue 11
Evidence of Single-Photon Two-Site Core Double Ionization of Molecules
journal, November 2011
- Lablanquie, P.; Grozdanov, T. P.; Žitnik, M.
- Physical Review Letters, Vol. 107, Issue 19
Calculating core-level excitations and x-ray absorption spectra of medium-sized closed-shell molecules with the algebraic-diagrammatic construction scheme for the polarization propagator
journal, August 2014
- Wenzel, Jan; Wormit, Michael; Dreuw, Andreas
- Journal of Computational Chemistry, Vol. 35, Issue 26
On double vacancies in the core
journal, December 1986
- Cederbaum, L. S.; Tarantelli, F.; Sgamellotti, A.
- The Journal of Chemical Physics, Vol. 85, Issue 11
Applicability of single-reference coupled-cluster methods to excited states. A model study
journal, June 1994
- Jankowski, J.; Kowalski, K.; Jankowski, P.
- Chemical Physics Letters, Vol. 222, Issue 6
Reference Energies for Double Excitations
journal, January 2019
- Loos, Pierre-François; Boggio-Pasqua, Martial; Scemama, Anthony
- Journal of Chemical Theory and Computation, Vol. 15, Issue 3
Inner-shell ionizations and satellites studied by the open-shell reference symmetry-adapted cluster/symmetry-adapted cluster configuration-interaction method
journal, February 2006
- Ohtsuka, Yuhki; Nakatsuji, Hiroshi
- The Journal of Chemical Physics, Vol. 124, Issue 5
Third-Order Møller–Plesset Perturbation Theory Made Useful? Choice of Orbitals and Scaling Greatly Improves Accuracy for Thermochemistry, Kinetics, and Intermolecular Interactions
journal, July 2019
- Bertels, Luke W.; Lee, Joonho; Head-Gordon, Martin
- The Journal of Physical Chemistry Letters, Vol. 10, Issue 15
Description of core‐excitation spectra by the open‐shell electron‐attachment equation‐of‐motion coupled cluster method
journal, May 1995
- Nooijen, Marcel; Bartlett, Rodney J.
- The Journal of Chemical Physics, Vol. 102, Issue 17
Multiple solutions of coupled-cluster doubles equations for the Pariser?Parr?Pople model of benzene
journal, July 2003
- Podeszwa, Rafal; Stolarczyk, Leszek. Z.; Jankowski, Karol
- Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 109, Issue 6
Experimental Verification of the Chemical Sensitivity of Two-Site Double Core-Hole States Formed by an X-Ray Free-Electron Laser
journal, April 2012
- Salén, P.; van der Meulen, P.; Schmidt, H. T.
- Physical Review Letters, Vol. 108, Issue 15
Double core hole spectroscopy with synchrotron radiation
journal, October 2015
- Penent, F.; Nakano, M.; Tashiro, M.
- Journal of Electron Spectroscopy and Related Phenomena, Vol. 204
On the molecular mechanism of non-radiative decay of nitrobenzene and the unforeseen challenges this simple molecule holds for electronic structure theory
journal, January 2014
- Mewes, Jan-M.; Jovanović, Vladimir; Marian, Christel M.
- Phys. Chem. Chem. Phys., Vol. 16, Issue 24
Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections
journal, January 2008
- Chai, Jeng-Da; Head-Gordon, Martin
- Physical Chemistry Chemical Physics, Vol. 10, Issue 44
Orthogonality Constrained Density Functional Theory for Electronic Excited States
journal, May 2013
- Evangelista, Francesco A.; Shushkov, Philip; Tully, John C.
- The Journal of Physical Chemistry A, Vol. 117, Issue 32
Physical and mathematical content of coupled-cluster equations. III. Model studies of dissociation processes for various reference states
journal, August 1999
- Jankowski, K.; Kowalski, K.
- The Journal of Chemical Physics, Vol. 111, Issue 7
Two single-reference approaches to singlet biradicaloid problems: Complex, restricted orbitals and approximate spin-projection combined with regularized orbital-optimized Møller-Plesset perturbation theory
journal, June 2019
- Lee, Joonho; Head-Gordon, Martin
- The Journal of Chemical Physics, Vol. 150, Issue 24
Convergence acceleration of iterative sequences. the case of scf iteration
journal, July 1980
- Pulay, Péter
- Chemical Physics Letters, Vol. 73, Issue 2
Orthogonality Constrained Density Functional Theory for Electronic Excited States
journal, May 2013
- Evangelista, Francesco A.; Shushkov, Philip; Tully, John C.
- The Journal of Physical Chemistry A, Vol. 117, Issue 32
An efficient first principles method for molecular pump-probe NEXAFS spectra: Application to thymine and azobenzene
journal, October 2018
- Ehlert, Christopher; Gühr, Markus; Saalfrank, Peter
- The Journal of Chemical Physics, Vol. 149, Issue 14
Single-Reference ab Initio Methods for the Calculation of Excited States of Large Molecules
journal, November 2005
- Dreuw, Andreas; Head-Gordon, Martin
- Chemical Reviews, Vol. 105, Issue 11
In Search of the Relationship between Multiple Solutions Characterizing Coupled-Cluster Theories
book, October 2000
- Piecuch, Piotr; Kowalski, Karol
- Computational Chemistry: Reviews of Current Trends
Distinguishing artificial and essential symmetry breaking in a single determinant: approach and application to the C 60 , C 36 , and C 20 fullerenes
journal, January 2019
- Lee, Joonho; Head-Gordon, Martin
- Physical Chemistry Chemical Physics, Vol. 21, Issue 9
ImprovedSCF convergence acceleration
journal, January 1982
- Pulay, P.
- Journal of Computational Chemistry, Vol. 3, Issue 4
A Mountaineering Strategy to Excited States: Highly Accurate Reference Energies and Benchmarks
journal, June 2018
- Loos, Pierre-François; Scemama, Anthony; Blondel, Aymeric
- Journal of Chemical Theory and Computation, Vol. 14, Issue 8
Gaussian basis sets for use in correlated molecular calculations. V. Core‐valence basis sets for boron through neon
journal, September 1995
- Woon, David E.; Dunning, Thom H.
- The Journal of Chemical Physics, Vol. 103, Issue 11
Multiple Solutions to the Single-Reference CCSD Equations for NiH
journal, August 2010
- Mayhall, Nicholas J.; Raghavachari, Krishnan
- Journal of Chemical Theory and Computation, Vol. 6, Issue 9
Core-electron binding energies for gaseous atoms and molecules
journal, November 1984
- Jolly, W. L.; Bomben, K. D.; Eyermann, C. J.
- Atomic Data and Nuclear Data Tables, Vol. 31, Issue 3
Multiple solutions of coupled-cluster equations for PPP model of [10]annulene
journal, December 2002
- Podeszwa, Rafał; Stolarczyk, Leszek Z.
- Chemical Physics Letters, Vol. 366, Issue 3-4
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
Simple Models for Difficult Electronic Excitations
journal, February 2018
- Barca, Giuseppe M. J.; Gilbert, Andrew T. B.; Gill, Peter M. W.
- Journal of Chemical Theory and Computation, Vol. 14, Issue 3
Many-body theory of core holes
journal, July 1980
- Cederbaum, L. S.; Domcke, W.; Schirmer, J.
- Physical Review A, Vol. 22, Issue 1
Hartree–Fock solutions as a quasidiabatic basis for nonorthogonal configuration interaction
journal, September 2009
- Thom, Alex J. W.; Head-Gordon, Martin
- The Journal of Chemical Physics, Vol. 131, Issue 12
Performance of Delta-Coupled-Cluster Methods for Calculations of Core-Ionization Energies of First-Row Elements
journal, July 2019
- Zheng, Xuechen; Cheng, Lan
- Journal of Chemical Theory and Computation, Vol. 15, Issue 9
Analysis and comparison of CVS-ADC approaches up to third order for the calculation of core-excited states
journal, June 2015
- Wenzel, Jan; Holzer, Andre; Wormit, Michael
- The Journal of Chemical Physics, Vol. 142, Issue 21
Properties of Hollow Molecules Probed by Single-Photon Double Ionization
journal, February 2011
- Lablanquie, P.; Penent, F.; Palaudoux, J.
- Physical Review Letters, Vol. 106, Issue 6
Multiple solutions of the single-reference coupled-cluster equations. II. Alternative reference states
journal, March 1995
- Jankowski, K.; Kowalski, K.; Jankowski, P.
- International Journal of Quantum Chemistry, Vol. 53, Issue 5
A fusion of the closed-shell coupled cluster singles and doubles method and valence-bond theory for bond breaking
journal, September 2012
- Small, David W.; Head-Gordon, Martin
- The Journal of Chemical Physics, Vol. 137, Issue 11
Regularized Orbital-Optimized Second-Order Møller–Plesset Perturbation Theory: A Reliable Fifth-Order-Scaling Electron Correlation Model with Orbital Energy Dependent Regularizers
journal, August 2018
- Lee, Joonho; Head-Gordon, Martin
- Journal of Chemical Theory and Computation, Vol. 14, Issue 10
Reference Energies for Double Excitations
journal, January 2019
- Loos, Pierre-François; Boggio-Pasqua, Martial; Scemama, Anthony
- Journal of Chemical Theory and Computation, Vol. 15, Issue 3
Efficient Implementation of NOCI-MP2 Using the Resolution of the Identity Approximation with Application to Charged Dimers and Long C–C Bonds in Ethane Derivatives
journal, July 2018
- Yost, Shane R.; Head-Gordon, Martin
- Journal of Chemical Theory and Computation, Vol. 14, Issue 9
Non-orthogonal configuration interaction with single substitutions for the calculation of core-excited states
journal, July 2018
- Oosterbaan, Katherine J.; White, Alec F.; Head-Gordon, Martin
- The Journal of Chemical Physics, Vol. 149, Issue 4
New algorithms for iterative matrix-free eigensolvers in quantum chemistry
journal, December 2014
- Zuev, Dmitry; Vecharynski, Eugene; Yang, Chao
- Journal of Computational Chemistry, Vol. 36, Issue 5
Iterative and non-iterative triple excitation corrections in coupled-cluster methods for excited electronic states: the EOM-CCSDT-3 and EOM-CCSD(T̃) methods
journal, August 1996
- Watts, John D.; Bartlett, Rodney J.
- Chemical Physics Letters, Vol. 258, Issue 5-6
Core-electron binding energies for gaseous atoms and molecules
journal, November 1984
- Jolly, W. L.; Bomben, K. D.; Eyermann, C. J.
- Atomic Data and Nuclear Data Tables, Vol. 31, Issue 3
The inclusion of connected triple excitations in the equation‐of‐motion coupled‐cluster method
journal, August 1994
- Watts, John D.; Bartlett, Rodney J.
- The Journal of Chemical Physics, Vol. 101, Issue 4
Response functions in the CC3 iterative triple excitation model
journal, November 1995
- Christiansen, Ove; Koch, Henrik; Jo/rgensen, Poul
- The Journal of Chemical Physics, Vol. 103, Issue 17
Multiple solutions of the single-reference coupled-cluster method
journal, September 1993
- Meissner, Leszek; Balková, Anna; Bartlett, Rodney J.
- Chemical Physics Letters, Vol. 212, Issue 1-2
Double-core-hole spectroscopy for chemical analysis with an intense X-ray femtosecond laser
journal, October 2011
- Berrah, N.; Fang, L.; Murphy, B.
- Proceedings of the National Academy of Sciences, Vol. 108, Issue 41
Cheap and Near Exact CASSCF with Large Active Spaces
journal, October 2017
- Smith, James E. T.; Mussard, Bastien; Holmes, Adam A.
- Journal of Chemical Theory and Computation, Vol. 13, Issue 11
Use of 2h and 3h−p-like coupled-cluster Tamm–Dancoff approaches for the equilibrium properties of ozone
journal, August 2003
- Sattelmeyer, Kurt W.; Schaefer III, Henry F.; Stanton, John F.
- Chemical Physics Letters, Vol. 378, Issue 1-2
Equation of motion coupled cluster theory calculations of the X-ray emission spectroscopy of water
journal, July 2012
- Besley, Nicholas A.
- Chemical Physics Letters, Vol. 542
Multiple Solutions to the Single-Reference CCSD Equations for NiH
journal, August 2010
- Mayhall, Nicholas J.; Raghavachari, Krishnan
- Journal of Chemical Theory and Computation, Vol. 6, Issue 9
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
Accelerating the convergence of the coupled-cluster approach
journal, October 1986
- Scuseria, Gustavo E.; Lee, Timothy J.; Schaefer, Henry F.
- Chemical Physics Letters, Vol. 130, Issue 3
The distinguishable cluster approximation
text, January 2013
- Kats, Daniel; Manby, Frederick R.
- arXiv