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Feldmann R, Mörchen M, Lang J, Lesiuk M, Reiher M. Complete Active Space Iterative Coupled Cluster Theory. J Phys Chem A 2024. [PMID: 39344976 DOI: 10.1021/acs.jpca.4c02316] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/01/2024]
Abstract
In this work, we investigate the possibility of improving multireference-driven coupled cluster (CC) approaches with an algorithm that iteratively combines complete active space (CAS) calculations with tailored CC and externally corrected CC. This is accomplished by establishing a feedback loop between the CC and CAS parts of a calculation through a similarity transformation of the Hamiltonian with those CC amplitudes that are not encompassed by the active space. We denote this approach as the complete active space iterative coupled cluster (CASiCC) ansatz. We investigate its efficiency and accuracy in the singles and doubles approximation by studying the prototypical molecules H4, H8, H2O, and N2. Our results demonstrate that CASiCC systematically improves on the single-reference CCSD and the externally corrected CCSD methods across entire potential energy curves while retaining modest computational costs. However, the tailored coupled cluster method shows superior performance in the strong correlation regime, suggesting that its accuracy is based on error compensation. We find that the iterative versions of externally corrected and tailored coupled cluster methods converge to the same results.
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Affiliation(s)
- Robin Feldmann
- Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Maximilian Mörchen
- Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Jakub Lang
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Michał Lesiuk
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Markus Reiher
- Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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Feldmann R, Reiher M. Renormalized Internally Contracted Multireference Coupled Cluster with Perturbative Triples. J Chem Theory Comput 2024; 20. [PMID: 39158160 PMCID: PMC11360144 DOI: 10.1021/acs.jctc.4c00679] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2024] [Revised: 07/17/2024] [Accepted: 07/22/2024] [Indexed: 08/20/2024]
Abstract
In this work, we combine the many-body formulation of the internally contracted multireference coupled cluster (ic-MRCC) method with Evangelista's multireference formulation of the driven similarity renormalization group (DSRG). The DSRG method can be viewed as a unitary multireference coupled cluster theory, which renormalizes the amplitudes based on a flow equation approach to eliminate numerical instabilities. We extend this approach by demonstrating that the unitary flow equation approach can be adapted for nonunitary transformations, rationalizing the renormalization of ic-MRCC amplitudes. We denote the new approach, the renormalized ic-MRCC (ric-MRCC) method. To achieve high accuracy with a reasonable computational cost, we introduce a new approximation to the Baker-Campbell-Hausdorff expansion. We fully consider the linear commutator while approximating the quadratic commutator, for which we neglect specific contractions involving amplitudes with active indices. Moreover, we introduce approximate perturbative triples to obtain the ric-MRCCSD[T] method. We demonstrate the accuracy of our approaches in comparison to advanced multireference methods for the potential energy curves of H8, F2, H2O, N2, and Cr2. Additionally, we show that ric-MRCCSD and ric-MRCSSD[T] match the accuracy of CCSD(T) for evaluating spectroscopic constants and of full configuration interaction energies for a set of small molecules.
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Affiliation(s)
- Robin Feldmann
- Department of Chemistry and
Applied Biosciences, ETH Zürich,, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Markus Reiher
- Department of Chemistry and
Applied Biosciences, ETH Zürich,, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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Szenes K, Mörchen M, Fischill P, Reiher M. Striking the right balance of encoding electron correlation in the Hamiltonian and the wavefunction ansatz. Faraday Discuss 2024. [PMID: 39092888 DOI: 10.1039/d4fd00060a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/04/2024]
Abstract
Multi-configurational electronic structure theory delivers the most versatile approximations to many-electron wavefunctions, flexible enough to deal with all sorts of transformations, ranging from electronic excitations, to open-shell molecules and chemical reactions. Multi-configurational models are therefore essential to establish universally applicable, predictive ab initio methods for chemistry. Here, we present a discussion of explicit correlation approaches which address the nagging problem of dealing with static and dynamic electron correlation in multi-configurational active-space approaches. We review the latest developments and then point to their key obstacles. Our discussion is supported by new data obtained with tensor network methods. We argue in favor of simple electron-only correlator expressions that may allow one to define transcorrelated models in which the correlator does not bear a dependence on molecular structure.
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Affiliation(s)
- Kalman Szenes
- Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland.
| | - Maximilian Mörchen
- Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland.
| | - Paul Fischill
- Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland.
| | - Markus Reiher
- Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland.
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Filip MA, Thom AJW. A hybrid stochastic configuration interaction-coupled cluster approach for multireference systems. J Chem Phys 2023; 158:2889005. [PMID: 37154279 DOI: 10.1063/5.0145767] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2023] [Accepted: 04/19/2023] [Indexed: 05/10/2023] Open
Abstract
The development of multireference coupled cluster (MRCC) techniques has remained an open area of study in electronic structure theory for decades due to the inherent complexity of expressing a multiconfigurational wavefunction in the fundamentally single-reference coupled cluster framework. The recently developed multireference-coupled cluster Monte Carlo (mrCCMC) technique uses the formal simplicity of the Monte Carlo approach to Hilbert space quantum chemistry to avoid some of the complexities of conventional MRCC, but there is room for improvement in terms of accuracy and, particularly, computational cost. In this paper, we explore the potential of incorporating ideas from conventional MRCC-namely, the treatment of the strongly correlated space in a configuration interaction formalism-to the mrCCMC framework, leading to a series of methods with increasing relaxation of the reference space in the presence of external amplitudes. These techniques offer new balances of stability and cost against accuracy, as well as a means to better explore and better understand the structure of solutions to the mrCCMC equations.
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Affiliation(s)
- Maria-Andreea Filip
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
- Peterhouse, University of Cambridge, Cambridge, United Kingdom
| | - Alex J W Thom
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
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Margócsy Á, Szabados Á. Ring coupled cluster doubles at the multireference level. J Chem Phys 2020; 152:204114. [PMID: 32486660 DOI: 10.1063/5.0005075] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A ring approximation within an internally contracted multireference (MR) Coupled Cluster (CC) framework is worked out and tested. Derivation of equations utilizes MR based, generalized normal ordering and the corresponding generalized Wick-theorem (MR-GWT). Contractions among cluster operators are avoided by adopting a normal ordered exponential ansatz. The original version of the MR ring CC doubles (MR-rCCD) equations [Á. Szabados and Á. Margócsy, Mol. Phys. 115, 2731 (2017)] is rectified in two aspects. On the one hand, over-completeness of double excitations is treated by relying on the concept of frames. On the other hand, restriction on the maximal cumulant rank is lifted from two to four. This is found essential for obtaining reliable correlation corrections to the energy. The MR function underlying the approach is provided by the Generalized Valence Bond (GVB) model. The pair structure of the reference ensures a fragment structure of GVB cumulants. This represents a benefit when evaluating cumulant contractions appearing as a consequence of MR-GWT. In particular, cumulant involving terms remain less expensive than their traditional, pair-contracted counterpart, facilitating an O(N6) eventual scaling of the proposed MR-rCCD method. Pilot applications are presented for covalent bond breaking, deprotonation energies, and torsional potentials.
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Affiliation(s)
- Á Margócsy
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Faculty of Science, ELTE Eötvös Loránd University, Budapest, Hungary
| | - Á Szabados
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Faculty of Science, ELTE Eötvös Loránd University, Budapest, Hungary
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Tsuchimochi T, Ten-No SL. Orbital-invariant spin-extended approximate coupled-cluster for multi-reference systems. J Chem Phys 2018; 149:044109. [PMID: 30068163 DOI: 10.1063/1.5036542] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present an approximate treatment of spin-extended coupled-cluster (ECC) based on the spin-projection of the broken-symmetry coupled-cluster (CC) ansatz. ECC completely eliminates the spin-contamination of unrestricted CC and is therefore expected to provide better descriptions of dynamical and static correlation effects, but introduces two distinct problems. The first issue is the emergence of non-terminating amplitude equations, which are caused by the de-excitation effects inherent in symmetry projection operators. In this study, we take a minimalist approach and truncate the Taylor series of the exponential ansatz at a certain order such that the approximation safely recovers the traditional CC without spin-projection. The second issue is that the nonlinear equations of ECC become underdetermined, although consistent, yielding an infinitude of solutions. This problem arises because of the redundancies in the excitation manifold, as is common in other multi-reference approaches. We remove the linear dependencies in ECC by employing an orthogonal projection manifold. We also propose an efficient solver for our method, in which the components are usually sparse but not diagonal-dominant. It is shown that our approach is rigorously orbital-invariant and provides more accurate results than its configuration interaction and linearized CC analogues for chemical systems.
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Affiliation(s)
- Takashi Tsuchimochi
- Graduate School of Science, Technology, and Innovation, Kobe University, Kobe, Hyogo 657-0025, Japan
| | - Seiichiro L Ten-No
- Graduate School of Science, Technology, and Innovation, Kobe University, Kobe, Hyogo 657-0025, Japan
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Xu E, Ten-No SL. Partially linearized external models to active-space coupled-cluster through connected hextuple excitations. J Comput Chem 2018; 39:875-880. [PMID: 29356050 DOI: 10.1002/jcc.25163] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2017] [Revised: 12/13/2017] [Accepted: 12/18/2017] [Indexed: 11/07/2022]
Abstract
Partially linearized external models to active-space coupled-cluster through hextuple excitations, for example, CC{SDtqph}L , CCSD{tqph}L , and CCSD{tqph}hyb, are implemented and compared with the full active-space CCSDtqph. The computational scaling of CCSDtqph coincides with that for the standard coupled-cluster singles and doubles (CCSD), yet with a much large prefactor. The approximate schemes to linearize the external excitations higher than doubles are significantly cheaper than the full CCSDtqph model. These models are applied to investigate the bond dissociation energies of diatomic molecules (HF, F2 , CuH, and CuF), and the potential energy surfaces of the bond dissociation processes of HF, CuH, H2 O, and C2 H4 . Among the approximate models, CCSD{tqph}hyb provides very accurate descriptions compared with CCSDtqph for all of the tested systems. © 2018 Wiley Periodicals, Inc.
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Affiliation(s)
- Enhua Xu
- Graduate School of System Informatics, Kobe University, Kobe, 657-8501, Japan
| | - Seiichiro L Ten-No
- Graduate School of System Informatics, Kobe University, Kobe, 657-8501, Japan
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Margraf JT, Perera A, Lutz JJ, Bartlett RJ. Single-reference coupled cluster theory for multi-reference problems. J Chem Phys 2017; 147:184101. [DOI: 10.1063/1.5003128] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Affiliation(s)
- Johannes T. Margraf
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Ajith Perera
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Jesse J. Lutz
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Rodney J. Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
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Saitow M, Kurashige Y, Yanai T. Fully Internally Contracted Multireference Configuration Interaction Theory Using Density Matrix Renormalization Group: A Reduced-Scaling Implementation Derived by Computer-Aided Tensor Factorization. J Chem Theory Comput 2015; 11:5120-31. [DOI: 10.1021/acs.jctc.5b00270] [Citation(s) in RCA: 59] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Masaaki Saitow
- The Graduate University for Advanced Studies, Myodaiji, Okazaki, Aichi 444-8585, Japan
| | - Yuki Kurashige
- The Graduate University for Advanced Studies, Myodaiji, Okazaki, Aichi 444-8585, Japan
- Department
of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan
- Japan Science and Technology Agency, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
| | - Takeshi Yanai
- The Graduate University for Advanced Studies, Myodaiji, Okazaki, Aichi 444-8585, Japan
- Department
of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan
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Zaporozhets IA, Ivanov VV, Lyakh DI, Adamowicz L. Discontinuities-free complete-active-space state–specific multi–reference coupled cluster theory for describing bond stretching and dissociation. J Chem Phys 2015; 143:024109. [DOI: 10.1063/1.4926392] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
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11
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Rolik Z, Kállay M. A quasiparticle-based multi-reference coupled-cluster method. J Chem Phys 2014; 141:134112. [DOI: 10.1063/1.4896703] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Zoltán Rolik
- MTA-BME “Lendület” Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, H-1521 Budapest, Hungary
| | - Mihály Kállay
- MTA-BME “Lendület” Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, H-1521 Budapest, Hungary
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Hu HS, Kowalski K. Excitation Energies with Cost-Reduced Variant of the Active-Space EOMCCSDT Method: The EOMCCSDt-3̅ Approach. J Chem Theory Comput 2013; 9:4761-8. [DOI: 10.1021/ct400501z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Han-Shi Hu
- William R. Wiley Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory , K8-91, P.O.Box 999, Richland, Washington 99352, United States
| | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory , K8-91, P.O.Box 999, Richland, Washington 99352, United States
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Dutta AK, Pal S, Ghosh D. Perturbative approximations to single and double spin flip equation of motion coupled cluster singles doubles methods. J Chem Phys 2013; 139:124116. [DOI: 10.1063/1.4821936] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [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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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. Combining active-space coupled-cluster methods with moment energy corrections via the CC(P;Q) methodology, with benchmark calculations for biradical transition states. J Chem Phys 2012; 136:144104. [PMID: 22502498 DOI: 10.1063/1.3700802] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We have recently suggested the CC(P;Q) methodology that can correct energies obtained in the active-space coupled-cluster (CC) or equation-of-motion (EOM) CC calculations, which recover much of the nondynamical and some dynamical electron correlation effects, for the higher-order, mostly dynamical, correlations missing in the active-space CC/EOMCC considerations. It is shown that one can greatly improve the description of biradical transition states, both in terms of the resulting energy barriers and total energies, by combining the CC approach with singles, doubles, and active-space triples, termed CCSDt, with the CC(P;Q)-style correction due to missing triple excitations defining the CC(t;3) approximation.
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Affiliation(s)
- Jun Shen
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
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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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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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Mao S, Cheng L, Liu W, Mukherjee D. A spin-adapted size-extensive state-specific multi-reference perturbation theory. I. Formal developments. J Chem Phys 2012; 136:024105. [DOI: 10.1063/1.3672083] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Lyakh DI, Musiał M, Lotrich VF, Bartlett RJ. Multireference Nature of Chemistry: The Coupled-Cluster View. Chem Rev 2011; 112:182-243. [DOI: 10.1021/cr2001417] [Citation(s) in RCA: 363] [Impact Index Per Article: 27.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Dmitry I. Lyakh
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, United States
| | - Monika Musiał
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, United States
| | - Victor F. Lotrich
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, United States
| | - Rodney J. Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, United States
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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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Ivanov VV, Lyakh DI, Adamowicz L. State-specific multireference coupled-cluster theory of molecular electronic excited states. ACTA ACUST UNITED AC 2011. [DOI: 10.1039/c1pc90007b] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
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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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Pittner J, Piecuch† P. Method of moments for the continuous transition between the Brillouin–Wigner-type and Rayleigh–Schrödinger-type multireference coupled cluster theories. Mol Phys 2010. [DOI: 10.1080/00268970902824235] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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28
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Xu E, Shen J, Kou Z, Li S. Coupled cluster with singles, doubles, and partial higher-order excitations based on the corresponding orbitals: The formulation and test applications for bond breaking processes. J Chem Phys 2010; 132:134110. [DOI: 10.1063/1.3381891] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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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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Shen J, Li S. Block correlated coupled cluster method with the complete active-space self-consistent-field reference function: Applications for low-lying electronic excited states. J Chem Phys 2009; 131:174101. [DOI: 10.1063/1.3256297] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
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Evangelista FA, Simmonett AC, Schaefer HF, Mukherjee D, Allen WD. A companion perturbation theory for state-specific multireference coupled cluster methods. Phys Chem Chem Phys 2009; 11:4728-41. [PMID: 19492126 DOI: 10.1039/b822910d] [Citation(s) in RCA: 62] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
A partitioning scheme is applied to the state-specific Mukherjee multireference coupled cluster method to derive a companion perturbation theory (Mk-MRPT2). A production-level implementation of Mk-MRPT2 is reported. The effectiveness of the Mk-MRPT2 method is demonstrated by application to the classic F(2) dissociation problem and the lowest-lying electronic states of meta-benzyne, including computations with up to 766 atomic orbitals. We show that Mk-MRPT2 theory is particularly useful in multireference focal point extrapolations to determine ab initio limits.
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Affiliation(s)
- Francesco A Evangelista
- Center for Computational Chemistry and Department of Chemistry, University of Georgia, Athens, GA 30602, USA
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Mahapatra US, Chattopadhyay S, Chaudhuri RK. Application of state-specific multireference Møller–Plesset perturbation theory to nonsinglet states. J Chem Phys 2009; 130:014101. [DOI: 10.1063/1.3043364] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
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Prochnow E, Evangelista FA, Schaefer HF, Allen WD, Gauss J. Analytic gradients for the state-specific multireference coupled cluster singles and doubles model. J Chem Phys 2009; 131:064109. [DOI: 10.1063/1.3204017] [Citation(s) in RCA: 68] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
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Ivanov VV, Lyakh DI, Adamowicz L. Multireference state-specific coupled-cluster methods. State-of-the-art and perspectives. Phys Chem Chem Phys 2009; 11:2355-70. [DOI: 10.1039/b818590p] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
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35
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Chattopadhyay S, Chaudhuri RK, Mahapatra US. Application of improved virtual orbital based multireference methods to N2, LiF, and C4H6 systems. J Chem Phys 2008; 129:244108. [DOI: 10.1063/1.3046454] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
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36
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Fang T, Shen J, Li S. Block correlated coupled cluster method with a complete-active-space self-consistent-field reference function: The implementation for low-lying excited states. J Chem Phys 2008; 129:234106. [DOI: 10.1063/1.3043728] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
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37
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Shen J, Fang T, Li S, Jiang Y. Performance of Block Correlated Coupled Cluster Method with the CASSCF Reference Function for the Prediction of Activation Barriers, Spectroscopic Constants in Diatomic Molecules, and Singlet−Triplet Gaps in Diradicals. J Phys Chem A 2008; 112:12518-25. [DOI: 10.1021/jp807183m] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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, P. R. 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, P. R. 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, P. R. China
| | - Yuansheng Jiang
- 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, P. R. China
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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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39
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Fang T, Shen J, Li S. Block correlated coupled cluster method with a complete-active-space self-consistent-field reference function: The formula for general active spaces and its applications for multibond breaking systems. J Chem Phys 2008; 128:224107. [DOI: 10.1063/1.2939014] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
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40
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Development and pilot molecular applications of the uncoupled state-specific MRCC (UC-SS-MRCC) theory. Chem Phys 2008. [DOI: 10.1016/j.chemphys.2008.03.012] [Citation(s) in RCA: 20] [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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41
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Evangelista FA, Simmonett AC, Allen WD, Schaefer HF, Gauss J. Triple excitations in state-specific multireference coupled cluster theory: Application of Mk-MRCCSDT and Mk-MRCCSDT-n methods to model systems. J Chem Phys 2008; 128:124104. [DOI: 10.1063/1.2834927] [Citation(s) in RCA: 120] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
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42
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Lyakh DI, Ivanov VV, Adamowicz L. A generalization of the state-specific complete-active-space coupled-cluster method for calculating electronic excited states. J Chem Phys 2008; 128:074101. [DOI: 10.1063/1.2828548] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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43
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Fang T, Li S. Block correlated coupled cluster theory with a complete active-space self-consistent-field reference function: The formulation and test applications for single bond breaking. J Chem Phys 2007; 127:204108. [DOI: 10.1063/1.2800027] [Citation(s) in RCA: 53] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
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44
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Lyakh DI, Ivanov VV, Adamowicz L. State-specific multireference complete-active-space coupled-cluster approach versus other quantum chemical methods: dissociation of the N2molecule. Mol Phys 2007. [DOI: 10.1080/00268970701332539] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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45
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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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46
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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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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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48
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An externally-corrected size-extensive single-root MRCC formalism: Its kinship with the rigorously size-extensive state-specific MRCC theory. ACTA ACUST UNITED AC 2006. [DOI: 10.1016/j.theochem.2006.03.017] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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49
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Ivanov VV, Adamowicz L, Lyakh DI. Potential energy surface of the electron excited states in the state-specific multi-reference coupled cluster theory. Hydrogen fluoride dissociation. ACTA ACUST UNITED AC 2006. [DOI: 10.1016/j.theochem.2006.04.043] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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50
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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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