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Magoulas I, Shen J, Piecuch P. Addressing strong correlation by approximate coupled-pair methods with active-space and full treatments of three-body clusters. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2057365] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Ilias Magoulas
- Department of Chemistry, Michigan State University, East Lansing, MI, USA
| | - Jun Shen
- Department of Chemistry, Michigan State University, East Lansing, MI, USA
| | - Piotr Piecuch
- Department of Chemistry, Michigan State University, East Lansing, MI, USA
- Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA
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Deustua JE, Shen J, Piecuch P. High-level coupled-cluster energetics by Monte Carlo sampling and moment expansions: Further details and comparisons. J Chem Phys 2021; 154:124103. [PMID: 33810702 DOI: 10.1063/5.0045468] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
We recently proposed a novel approach to converging electronic energies equivalent to high-level coupled-cluster (CC) computations by combining the deterministic CC(P;Q) formalism with the stochastic configuration interaction (CI) and CC Quantum Monte Carlo (QMC) propagations. This article extends our initial study [J. E. Deustua, J. Shen, and P. Piecuch, Phys. Rev. Lett. 119, 223003 (2017)], which focused on recovering the energies obtained with the CC method with singles, doubles, and triples (CCSDT) using the information extracted from full CI QMC and CCSDT-MC, to the CIQMC approaches truncated at triples and quadruples. It also reports our first semi-stochastic CC(P;Q) calculations aimed at converging the energies that correspond to the CC method with singles, doubles, triples, and quadruples (CCSDTQ). The ability of the semi-stochastic CC(P;Q) formalism to recover the CCSDT and CCSDTQ energies, even when electronic quasi-degeneracies and triply and quadruply excited clusters become substantial, is illustrated by a few numerical examples, including the F-F bond breaking in F2, the automerization of cyclobutadiene, and the double dissociation of the water molecule.
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Affiliation(s)
- J Emiliano Deustua
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - Jun Shen
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - Piotr Piecuch
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
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Aroeira GJR, Davis MM, Turney JM, Schaefer HF. Coupled Cluster Externally Corrected by Adaptive Configuration Interaction. J Chem Theory Comput 2021; 17:182-190. [PMID: 33274920 DOI: 10.1021/acs.jctc.0c00888] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
An externally corrected coupled cluster (CC) method, where an adaptive configuration interaction (ACI) wave function provides the external cluster amplitudes, named ACI-CC, is presented. By exploiting the connection between configuration interaction and CC through cluster analysis, the higher-order T3 and T4 terms obtained from ACI are used to augment the T1 and T2 amplitude equations from traditional CC. These higher-order contributions are kept frozen during the CC iterations and do not contribute to an increased cost with respect to coupled cluster including the single and double excitations (CCSD). We have benchmarked this method on three closed-shell systems: beryllium dimer, carbonyl oxide, and cyclobutadiene, with good results compared to other corrected CC methods. In all cases, the inclusion of these external corrections improved upon the "gold standard" CCSD(T) results, indicating that ACI-CCSD(T) can be used to assess strong correlation effects in a system and as an inexpensive starting point for more complex external corrections.
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Affiliation(s)
- Gustavo J R Aroeira
- Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States
| | - Madeline M Davis
- Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States
| | - Justin M Turney
- Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States
| | - Henry F Schaefer
- Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States
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Yuwono SH, Magoulas I, Shen J, Piecuch P. Application of the coupled-cluster CC(P;Q) approaches to the magnesium dimer. Mol Phys 2019. [DOI: 10.1080/00268976.2018.1564847] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Stephen H. Yuwono
- Department of Chemistry, Michigan State University, East Lansing, MI, USA
| | - Ilias Magoulas
- Department of Chemistry, Michigan State University, East Lansing, MI, USA
| | - Jun Shen
- Department of Chemistry, Michigan State University, East Lansing, MI, USA
| | - Piotr Piecuch
- Department of Chemistry, Michigan State University, East Lansing, MI, USA
- Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA
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Kowalski K. Properties of coupled-cluster equations originating in excitation sub-algebras. J Chem Phys 2018. [DOI: 10.1063/1.5010693] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
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Magoulas I, Bauman NP, Shen J, Piecuch P. Application of the CC(P;Q) Hierarchy of Coupled-Cluster Methods to the Beryllium Dimer. J Phys Chem A 2018; 122:1350-1368. [DOI: 10.1021/acs.jpca.7b10892] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Ilias Magoulas
- Department
of Chemistry, Michigan State University, East Lansing, Michigan 48824, United States
| | - Nicholas P. Bauman
- Department
of Chemistry, Michigan State University, East Lansing, Michigan 48824, United States
| | - Jun Shen
- Department
of Chemistry, Michigan State University, East Lansing, Michigan 48824, United States
| | - Piotr Piecuch
- Department
of Chemistry, Michigan State University, East Lansing, Michigan 48824, United States
- Department
of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, United States
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Ajala AO, Shen J, Piecuch P. Economical Doubly Electron-Attached Equation-of-Motion Coupled-Cluster Methods with an Active-Space Treatment of Three-Particle–One-Hole and Four-Particle–Two-Hole Excitations. J Phys Chem A 2017; 121:3469-3485. [DOI: 10.1021/acs.jpca.6b11393] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Adeayo O. Ajala
- Department
of Chemistry and ‡Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, United States
| | - Jun Shen
- Department
of Chemistry and ‡Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, United States
| | - Piotr Piecuch
- Department
of Chemistry and ‡Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, United States
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Hansen JA, Bauman NP, Shen J, Borden WT, Piecuch P. Ab initiocoupled-cluster and multi-reference configuration interaction studies of the low-lying electronic states of 1,2,3,4-cyclobutanetetraone. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1112926] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Tishchenko O, Zheng J, Truhlar DG. Multireference Model Chemistries for Thermochemical Kinetics. J Chem Theory Comput 2015; 4:1208-19. [PMID: 26631697 DOI: 10.1021/ct800077r] [Citation(s) in RCA: 119] [Impact Index Per Article: 13.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
By combining the generalized valence bond ansatz of correlated participating orbitals (CPO) with the complete-active-space prescription for selecting configurations and with the use of multireference second order perturbation theory (MRMP2) for including dynamical correlation, we define three levels of multireference (MR) theoretical model chemistries for electronic structure calculations of chemical reaction energies and barrier heights. The three levels differ in their choice of which orbitals are considered to be participating; the choices are called nominal (nom-CPO), moderate (mod-CPO), and extended (ext-CPO). Combining any of these three choices with a method for treatment of dynamical correlation energy and a one-electron basis set yields a theoretical model chemistry. Unlike the full-valence choice of active orbitals, the CPO choices lead to active spaces that contain the orbitals needed to include important static correlation effects on chemical reactions but do not increase with the size of the nonparticipating portion of the system, and hence they remain viable computational options even for many large and complex reacting systems. The accuracies of the new levels, combined with the MG3S basis set (a partially augmented, multiply polarized valence triple-ζ basis with appropriately tight d functions for 3p-block elements) and with the fully augmented correlation-consistent aug-cc-pVTZ basis set, are assessed against a previously presented database of barrier heights for diverse reaction types. We find that nom-CPO level captures the bulk of the static correlation energy, and MRMP2/nom-CPO calculations have an average error of only 1.4 kcal/mol in barrier heights, which may be compared to 5.0 kcal/mol for single-reference MP2 theory, 2.5 kcal/mol for CCSD, and 4.1 and 1.0 kcal/mol for the B3LYP and M06-2X density functionals, respectively. The accuracy of MRMP2/CPO for transition structure bond lengths and donor-acceptor distances is excellent, with a mean unsigned error of only 0.007 Å as compared to 0.018 Å for CCSD, 0.019 Å for M06-2X, and 0.039 Å for MP2 and B3LYP. We also introduce a new multireference diagnostic, called the M diagnostic, that allows one to measure the importance of static correlation in a given reagent or transition state.
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Affiliation(s)
- Oksana Tishchenko
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431
| | - Jingjing Zheng
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431
| | - Donald G Truhlar
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431
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Erturk M, Meissner L. A posteriori corrections to the configuration interaction method: a single-reference and multi-reference study. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1066040] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Shen J, Piecuch P. Doubly electron-attached and doubly ionised equation-of-motion coupled-cluster methods with full and active-space treatments of 4-particle–2-hole and 4-hole–2-particle excitations: the role of orbital choices. Mol Phys 2014. [DOI: 10.1080/00268976.2014.886397] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Search of truncation of ( N−1) electron basis containing full connected triple excitations in computing main and satellite ionization potentials via Fock-space coupled cluster approach. J Comput Chem 2013; 34:1291-310. [DOI: 10.1002/jcc.23255] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2012] [Revised: 12/17/2012] [Accepted: 01/21/2013] [Indexed: 01/23/2023]
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Shen J, Piecuch P. Doubly electron-attached and doubly ionized equation-of-motion coupled-cluster methods with 4-particle–2-hole and 4-hole–2-particle excitations and their active-space extensions. J Chem Phys 2013; 138:194102. [DOI: 10.1063/1.4803883] [Citation(s) in RCA: 62] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Melnichuk A, Bartlett RJ. Relaxed active space: Fixing tailored-CC with high order coupled cluster. I. J Chem Phys 2012; 137:214103. [DOI: 10.1063/1.4767900] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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Shen J, Piecuch P. Merging Active-Space and Renormalized Coupled-Cluster Methods via the CC(P;Q) Formalism, with Benchmark Calculations for Singlet–Triplet Gaps in Biradical Systems. J Chem Theory Comput 2012; 8:4968-88. [DOI: 10.1021/ct300762m] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jun Shen
- Department of Chemistry, Michigan State University,
East Lansing, Michigan 48824, United States
| | - Piotr Piecuch
- Department of Chemistry, Michigan State University,
East Lansing, Michigan 48824, United States
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Shen J, Piecuch P. Biorthogonal moment expansions in coupled-cluster theory: Review of key concepts and merging the renormalized and active-space coupled-cluster methods. Chem Phys 2012. [DOI: 10.1016/j.chemphys.2011.11.033] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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18
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The coupled cluster approach with a hybrid treatment of connected triple excitations: Spectroscopic constants in open-shell diatomic molecules, and bond-breaking or twisting potential energy surfaces. Chem Phys 2012. [DOI: 10.1016/j.chemphys.2011.10.023] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Kou Z, Shen J, Xu E, Li S. Hybrid coupled cluster methods: Combining active space coupled cluster methods with coupled cluster singles, doubles, and perturbative triples. J Chem Phys 2012; 136:194105. [DOI: 10.1063/1.4716185] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
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20
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Shen J, Kou Z, Xu E, Li S. The coupled cluster singles, doubles, and a hybrid treatment of connected triples based on the split virtual orbitals. J Chem Phys 2012; 136:044101. [PMID: 22299855 DOI: 10.1063/1.3678008] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
We have proposed a simple strategy for splitting the virtual orbitals with a large basis set into two subgroups (active and inactive) by taking a smaller basis set as an auxiliary basis set. With the split virtual orbitals (SVOs), triple or higher excitations can be partitioned into active and inactive subgroups (according to the number of active virtual orbitals involved), which can be treated with different electron correlation methods. In this work, the coupled cluster (CC) singles, doubles, and a hybrid treatment of connected triples based on the SVO [denoted as SVO-CCSD(T)-h], has been implemented. The present approach has been applied to study the bond breaking potential energy surfaces in three molecules (HF, F(2), and N(2)), and the equilibrium properties in a number of open-shell diatomic molecules. For all systems under study, the SVO-CCSD(T)-h method based on the unrestricted Hartree-Fock (UHF) reference is an excellent approximation to the corresponding CCSDT (CC singles, doubles, and triples), and much better than the UHF-based CCSD(T) (CC singles, doubles, and perturbative triples). On the other hand, the SVO-CCSD(T)-h method based on the restricted HF (RHF) reference can also provide considerable improvement over the RHF-based CCSD(T).
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Affiliation(s)
- Jun Shen
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210093, People's Republic of China
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Shen J, Kou Z, Xu E, Li S. The coupled cluster approach with a hybrid treatment of connected triple excitations based on the restricted Hartree–Fock reference. J Chem Phys 2011; 134:044134. [DOI: 10.1063/1.3541250] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
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Shen J, Xu E, Kou Z, Li S. New coupled cluster approaches based on the unrestricted Hartree–Fock reference for treating molecules with multireference character. Phys Chem Chem Phys 2011; 13:8795-804. [DOI: 10.1039/c0cp01103g] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
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23
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Shen J, Kou Z, Xu E, Li S. A coupled cluster approach with a hybrid treatment of connected triple excitations: Implementation and applications for open-shell systems. J Chem Phys 2010; 133:234106. [DOI: 10.1063/1.3518100] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
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PIECUCH PIOTR, SPIRKO VLADIMIR, KONDO ANNEE, PALDUS JOSEF. Vibrational dependence of the dipole moment and radiative transition probabilities in the X1Sigma + state of HF: a linear-response coupled-cluster study. Mol Phys 2010. [DOI: 10.1080/002689798168349] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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25
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ADAMOWICZ LUDWIK, PIECUCH PIOTR, GHOSE KEYAB. The state-selective coupled cluster method for quasi-degenerate electronic states. Mol Phys 2010. [DOI: 10.1080/002689798168510] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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Piecuch P, Kowalski K, Pimienta ISO, Mcguire MJ. Recent advances in electronic structure theory: Method of moments of coupled-cluster equations and renormalized coupled-cluster approaches. INT REV PHYS CHEM 2010. [DOI: 10.1080/0144235021000053811] [Citation(s) in RCA: 210] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Shen J, Xu E, Kou Z, Li S. A coupled cluster approach with a hybrid treatment of connected triple excitations for bond-breaking potential energy surfaces. J Chem Phys 2010; 132:114115. [DOI: 10.1063/1.3359851] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
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Das S, Mukherjee D, Kállay M. Full implementation and benchmark studies of Mukherjee’s state-specific multireference coupled-cluster ansatz. J Chem Phys 2010; 132:074103. [DOI: 10.1063/1.3310288] [Citation(s) in RCA: 106] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Datta D, Mukherjee D. An explicitly spin-free compact open-shell coupled cluster theory using a multireference combinatoric exponential ansatz: Formal development and pilot applications. J Chem Phys 2009; 131:044124. [DOI: 10.1063/1.3185356] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Mahapatra US, Chattopadhyay S, Chaudhuri RK. Molecular applications of state-specific multireference perturbation theory to HF, H2O, H2S, C2, and N2 molecules. J Chem Phys 2008; 129:024108. [DOI: 10.1063/1.2952666] [Citation(s) in RCA: 50] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Shen J, Fang T, Hua W, Li S. Spectroscopic Constants of Single-Bond Diatomic Molecules and Singlet−Triplet Gaps of Diradicals by the Block-Correlated Coupled Cluster Theory. J Phys Chem A 2008; 112:4703-9. [DOI: 10.1021/jp7118907] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Affiliation(s)
- Jun Shen
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing, 210093, Peopleʼs Republic of China
| | - Tao Fang
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing, 210093, Peopleʼs Republic of China
| | - Weijie Hua
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing, 210093, Peopleʼs Republic of China
| | - Shuhua Li
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing, 210093, Peopleʼs Republic of China
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Piecuch P, Włoch M, Varandas AJC. Application of renormalized coupled-cluster methods to potential function of water. Theor Chem Acc 2007. [DOI: 10.1007/s00214-007-0297-3] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Ohtsuka Y, Piecuch P, Gour JR, Ehara M, Nakatsuji H. Active-space symmetry-adapted-cluster configuration-interaction and equation-of-motion coupled-cluster methods for high accuracy calculations of potential energy surfaces of radicals. J Chem Phys 2007; 126:164111. [PMID: 17477593 DOI: 10.1063/1.2723121] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
The electron-attached (EA) and ionized (IP) symmetry-adapted-cluster configuration-interaction (SAC-CI) methods and their equation-of-motion coupled-cluster (EOMCC) analogs provide an elegant framework for studying open-shell systems. As shown in this study, these schemes require the presence of higher-order excitations, such as the four-particle-three-hole (4p-3h) or four-hole-three-particle (4h-3p) terms, in the electron attaching or ionizing operator R in order to produce accurate ground- and excited-state potential energy surfaces of radicals along bond breaking coordinates. The full inclusion of the 4p-3h/4h-3p excitations in the EA/IP SAC-CI and EOMCC methods leads to schemes which are far too expensive for calculations involving larger radicals and realistic basis sets. In order to reduce the large costs of such schemes without sacrificing accuracy, the active-space EA/IP EOMCC methodology [J. R. Gour et al., J. Chem. Phys. 123, 134113 (2005)] is extended to the EA/IP SAC-CI approaches with 4p-3h/4h-3p excitations. The resulting methods, which use a physically motivated set of active orbitals to pick out the most important 3p-2h/3h-2p and 4p-3h/4h-3p excitations, represent practical computational approaches for high-accuracy calculations of potential energy surfaces of radicals. To illustrate the potential offered by the active-space EA/IP SAC-CI approaches with up to 4p-3h/4h-3p excitations, the results of benchmark calculations for the potential energy surfaces of the low-lying doublet states of CH and OH are presented and compared with other SAC-CI and EOMCC methods, and full CI results.
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Affiliation(s)
- Yuhki Ohtsuka
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan
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Chattopadhyay S, Mitra A, Sinha D. Explicitly intruder-free valence-universal multireference coupled cluster theory as applied to ionization spectroscopy. J Chem Phys 2007; 125:244111. [PMID: 17199344 DOI: 10.1063/1.2403858] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Although it is quite promising to compute the spectroscopic energies [say, ionization potential (IP)] via the traditional valence-universal multireference coupled cluster (VUMRCC) method based on the description of the complete model space being seriously plagued by the perennial intruder state problem, the eigenvalue independent partitioning (EIP) based VUMRCC (coined as EIP-MRCC) method is quite effective to predict the spectroscopic energies in an intruder-free manner. Hence, the EIP-MRCC method is suitable for generating both the principal IPs and the satellite IPs of the inner-valence region. An EIP strategy converts the nonlinear VUMRCC equations for M(m,n) dimensional model space of m hole and n particle to a non-Hermitian eigenproblem of larger dimension whose M(m,n) roots are only physically meaningful. To increase the quality of the computed energy differences in the sense of chemical accuracy and to locate the correct position of it in the spectrum, the inclusion of higher-body cluster operators on top of all the standard singles-doubles is not the only pivotal issue, the effect of the size of the basis set is also equally important. This paper illustrates these issues by calculating the principal and satellite IPs of HF and HCl molecules using various basis sets (viz., Dunning's cc-pVDZ, cc-pVTZ, and cc-pVQZ) via EIP-MRCC method with full inclusion of triples (abbreviated as EIP-MRCCSDT). The results seem quite encouraging in comparison with the experimental values. The controversial 2Pi satellite at 28.67 eV of HCl of Svensson et al. [J. Chem. Phys. 89, 7193 (1988)] is also reported.
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Affiliation(s)
- Sudip Chattopadhyay
- Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India.
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Crawford TD, Schaefer HF. An Introduction to Coupled Cluster Theory for Computational Chemists. REVIEWS IN COMPUTATIONAL CHEMISTRY 2007. [DOI: 10.1002/9780470125915.ch2] [Citation(s) in RCA: 372] [Impact Index Per Article: 21.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/05/2022]
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Piecuch P, Wloch M, Varandas AJC. Renormalized coupled-cluster methods: Theoretical foundations and application to the potential function of water. ACTA ACUST UNITED AC 2007. [DOI: 10.1007/978-1-4020-5460-0_3] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/07/2023]
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38
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Gour JR, Piecuch P. Efficient formulation and computer implementation of the active-space electron-attached and ionized equation-of-motion coupled-cluster methods. J Chem Phys 2006; 125:234107. [PMID: 17190547 DOI: 10.1063/1.2409289] [Citation(s) in RCA: 87] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
The efficient, general-purpose implementations of the active-space electron-attached (EA) and ionized (IP) equation-of-motion coupled-cluster (EOMCC) methods including up to 3p-2h and 3h-2p excitations, called EA-EOMCCSDt and IP-EOMCCSDt, respectively, are discussed. The details of the algorithm that enables one to achieve a high degree of code vectorization for the active-space methods and the factorized forms of the EA- and IP-EOMCCSDt equations that maximize the benefits of using active orbitals in the process of selecting the dominant 3p-2h and 3h-2p excitations are presented. The results of benchmark calculations for the low-lying doublet and quartet states of the CH and SH radicals reveal that the active-space EA-EOMCCSDt and IP-EOMCCSDt methods are capable of producing results for the electronic excitations in open-shell systems that match the high accuracy of EA- and IP-EOMCC calculations with a full treatment of 3p-2h and 3h-2p excitations, even when the excited states of interest display a manifestly multideterminantal nature, with the costs that can be on the same order of those characterizing the basic EOMCC singles and doubles approach.
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Affiliation(s)
- Jeffrey R Gour
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
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39
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Non-iterative coupled-cluster methods employing multi-reference perturbation theory wave functions. ACTA ACUST UNITED AC 2006. [DOI: 10.1016/j.theochem.2006.03.014] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Bochevarov AD, Temelso B, Sherrill CD. Hybrid correlation models based on active-space partitioning: Seeking accurate O(N5) ab initio methods for bond breaking. J Chem Phys 2006; 125:054109. [PMID: 16942205 DOI: 10.1063/1.2222350] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Moller-Plesset second-order (MP2) perturbation theory remains the least expensive standard ab initio method that includes electron correlation, scaling as O(N5) with the number of molecular orbitals N. Unfortunately, when restricted Hartree-Fock orbitals are employed, the potential energy curves calculated with this method are of little use at large interatomic separations because of the divergent behavior of MP2 in these regions. In our previous study [J. Chem. Phys. 122, 234110 (2005)] we combined the MP2 method with the singles and doubles coupled cluster (CCSD) method to produce a hybrid method that retains the computational scaling of MP2 and improves dramatically the shape of the MP2 curves. In this work we expand the hybrid methodology to several other schemes. We investigate a new, improved MP2-CCSD method as well as a few other O(N5) methods related to the Epstein-Nesbet pair correlation theory. Nonparallelity errors across the dissociation curve as well as several spectroscopic constants are computed for BH, HF, H2O, CH+, CH4, and Li2 molecules with the 6-31G* basis set and compared with the corresponding full configuration interaction results. We show that among the O(N5) methods considered, our new hybrid MP2-CCSD method is the most accurate and significantly outperforms MP2 not only at large interatomic separations, but also near equilibrium geometries.
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Affiliation(s)
- Arteum D Bochevarov
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA
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Łoch MW, Lodriguito MD, Piecuch† P, Gour JR. Two new classes of non-iterative coupled-cluster methods derived from the method of moments of coupled-cluster equations. Mol Phys 2006. [DOI: 10.1080/00268970600659586] [Citation(s) in RCA: 89] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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42
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Fan PD, Piecuch P. The Usefulness of Exponential Wave Function Expansions Employing One- and Two-Body Cluster Operators in Electronic Structure Theory: The Extended and Generalized Coupled-Cluster Methods. ADVANCES IN QUANTUM CHEMISTRY 2006. [DOI: 10.1016/s0065-3276(06)51001-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/07/2023]
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43
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Piecuch P, Włoch M. Renormalized coupled-cluster methods exploiting left eigenstates of the similarity-transformed Hamiltonian. J Chem Phys 2005; 123:224105. [PMID: 16375468 DOI: 10.1063/1.2137318] [Citation(s) in RCA: 324] [Impact Index Per Article: 17.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Completely renormalized (CR) coupled-cluster (CC) approaches, such as CR-CCSD(T), in which one corrects the standard CC singles and doubles (CCSD) energy for the effects of triply (T) and other higher-than-doubly excited clusters [K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 18 (2000)], are reformulated in terms of the left eigenstates Phimid R:L of the similarity-transformed Hamiltonian of CC theory. The resulting CR-CCSD(T)(L) or CR-CC(2,3) and other CR-CC(L) methods are derived from the new biorthogonal form of the method of moments of CC equations (MMCC) in which, in analogy to the original MMCC theory, one focuses on the noniterative corrections to standard CC energies that recover the exact, full configuration-interaction energies. One of the advantages of the biorthogonal MMCC theory, which will be further analyzed and extended to excited states in a separate paper, is a rigorous size extensivity of the basic ground-state CR-CC(L) approximations that result from it, which was slightly violated by the original CR-CCSD(T) and CR-CCSD(TQ) approaches. This includes the CR-CCSD(T)(L) or CR-CC(2,3) method discussed in this paper, in which one corrects the CCSD energy by the relatively inexpensive noniterative correction due to triples. Test calculations for bond breaking in HF, F(2), and H(2)O indicate that the noniterative CR-CCSD(T)(L) or CR-CC(2,3) approximation is very competitive with the standard CCSD(T) theory for nondegenerate closed-shell states, while being practically as accurate as the full CC approach with singles, doubles, and triples in the bond-breaking region. Calculations of the activation enthalpy for the thermal isomerizations of cyclopropane involving the trimethylene biradical as a transition state show that the noniterative CR-CCSD(T)(L) approximation is capable of providing activation enthalpies which perfectly agree with experiment.
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Affiliation(s)
- Piotr Piecuch
- Department of Chemistry, Michigan State University, East Lansing, MI 48824, USA.
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Gour JR, Piecuch P, Włoch M. Active-space equation-of-motion coupled-cluster methods for excited states of radicals and other open-shell systems: EA-EOMCCSDt and IP-EOMCCSDt. J Chem Phys 2005; 123:134113. [PMID: 16223281 DOI: 10.1063/1.2042452] [Citation(s) in RCA: 95] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The previously developed active-space coupled-cluster (CC) and equation-of-motion (EOM) CC methods are extended to radicals and other open-shell systems by combining them with the electron attached (EA) and ionized (IP) EOMCC approaches. As illustrated by the calculations for the CH and OH radicals, the resulting EA-EOMCCSDt and IP-EOMCCSDt theories are capable of providing a highly accurate description of the electronic spectra of radical systems, including excited states displaying a manifestly multideterminantal nature, with the low costs that are not much greater that those characterizing the standard EOMCC singles and doubles method.
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Affiliation(s)
- Jeffrey R Gour
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
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Kowalski K, Hirata S, Włoch M, Piecuch P, Windus TL. Active-space coupled-cluster study of electronic states of Be3. J Chem Phys 2005; 123:074319. [PMID: 16229582 DOI: 10.1063/1.2001656] [Citation(s) in RCA: 58] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The active-space coupled-cluster (CC) and equation-of-motion (EOM) CC methods with all single and double excitations with triple excitations defined via active orbitals (CCSDt, EOMCCSDt), as implemented with TENSOR CONTRACTION ENGINE, are applied to the challenging Be3 system, which is characterized by a large number of low-lying excited states dominated by two-electron transitions and significant high-order correlation effects in the ground electronic state. It is demonstrated that the CCSDt and EOMCCSDt methods provide an excellent description of complicated electronic quasidegeneracies present in the Be3 cluster. Different strategies for defining triple excitations within the CCSDtEOMCCSDt approach are discussed.
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Affiliation(s)
- Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, Richland, Washington 99352, USA.
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Fan PD, Kowalski K, Piecuch * P. Non-iterative corrections to extended coupled-cluster energies employing the generalized method of moments of coupled-cluster equations. Mol Phys 2005. [DOI: 10.1080/00268970500131595] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Meissner # L, GryniakÓw J, HubaČ I. The coupled-cluster corrections to multi-reference configuration interaction method: the HF and F2bond breaking description. Mol Phys 2005. [DOI: 10.1080/00268970500084059] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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48
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Chaudhuri RK, Freed KF, Hose G, Piecuch P, Kowalski K, Włoch M, Chattopadhyay S, Mukherjee D, Rolik Z, Szabados A, Tóth G, Surján PR. Comparison of low-order multireference many-body perturbation theories. J Chem Phys 2005; 122:134105. [PMID: 15847453 DOI: 10.1063/1.1863912] [Citation(s) in RCA: 57] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Tests have been made to benchmark and assess the relative accuracies of low-order multireference perturbation theories as compared to coupled cluster (CC) and full configuration interaction (FCI) methods. Test calculations include the ground and some excited states of the Be, H(2), BeH(2), CH(2), and SiH(2) systems. Comparisons with FCI and CC calculations show that in most cases the effective valence shell Hamiltonian (H(v)) method is more accurate than other low-order multireference perturbation theories, although none of the perturbative methods is as accurate as the CC approximations. We also briefly discuss some of the basic differences among the multireference perturbation theories considered in this work.
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Affiliation(s)
- Rajat K Chaudhuri
- Department of Chemistry, The James Franck Institute, University of Chicago, Chicago, IL 60637, USA
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Sherrill CD, Piecuch P. The XΣg+1, BΔg1, and B′Σg+1 states of C2: A comparison of renormalized coupled-cluster and multireference methods with full configuration interaction benchmarks. J Chem Phys 2005; 122:124104. [PMID: 15836366 DOI: 10.1063/1.1867379] [Citation(s) in RCA: 86] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Unusual bonding and electronic near degeneracies make the lowest-lying singlet states of the C2 molecule particularly challenging for electronic structure theory. Here we compare two alternative approaches to modeling bond-breaking reactions and excited states: sophisticated multireference configuration interaction and multireference perturbation theory methods, and a more "black box," single-reference approach, the completely renormalized coupled-cluster method. These approximate methods are assessed in light of their ability to reproduce the full configuration interaction potential energy curves for the X1Sigmag+, B1Deltag, and B' 1Sigmag+ states of C2, which are numerically exact solutions of the electronic Schrodinger equation within the space spanned by a 6-31G* basis set. Both the multireference methods and the completely renormalized coupled-cluster approach provide dramatic improvements over the standard single-reference methods. The multireference methods are nearly as reliable for this challenging test case as for simpler reactions which break only single bonds. The completely renormalized coupled-cluster approach has difficulty for large internuclear separations R in this case, but over the wide range of R=1.0-2.0 A, it compares favorably with the more complicated multireference methods.
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Affiliation(s)
- C David Sherrill
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA.
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Kowalski K, Piecuch P. Extensive generalization of renormalized coupled-cluster methods. J Chem Phys 2005; 122:074107. [PMID: 15743221 DOI: 10.1063/1.1848093] [Citation(s) in RCA: 82] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The recently developed completely renormalized (CR) coupled-cluster (CC) methods with singles, doubles, and noniterative triples or triples and quadruples [CR-CCSD(T) or CR-CCSD(TQ), respectively], which are based on the method of moments of CC equations (MMCC) [K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 18 (2000)], eliminate the failures of the standard CCSD(T) and CCSD(TQ) methods at larger internuclear separations, but they are not rigorously size extensive. Although the departure from strict size extensivity of the CR-CCSD(T) and CR-CCSD(TQ) methods is small, it is important to examine the possibility of formulating the improved CR-CC methods, which are as effective in breaking chemical bonds as the existing CR-CCSD(T) and CR-CCSD(TQ) approaches, which are as easy to use as the CR-CCSD(T) and CR-CCSD(TQ) methods, and which can be made rigorously size extensive. This may be particularly useful for the applications of CR-CC methods and other MMCC approaches in calculations of potential energy surfaces of large many-electron systems and van der Waals molecules, where the additive separability of energies in the noninteracting limit is very important. In this paper, we propose different types of CR-CC approximations, termed the locally renormalized (LR) CCSD(T) and CCSD(TQ) methods, which become rigorously size extensive if the orbitals are localized on nointeracting fragments. The LR-CCSD(T) and LR-CCSD(TQ) methods rely on the form of the energy expression in terms of the generalized moments of CC equations, derived in this work, termed the numerator-denominator-connected MMCC expansion. The size extensivity and excellent performance of the LR-CCSD(T) and LR-CCSD(TQ) methods are illustrated numerically by showing the results for the dimers of stretched HF and LiH molecules and bond breaking in HF and H2O.
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Affiliation(s)
- Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, Richland, Washington 99352, USA.
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