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Basumallick S, Sajeev Y, Pal S, Vaval N. Negative Ion Resonance States: The Fock-Space Coupled-Cluster Way. J Phys Chem A 2020; 124:10407-10421. [PMID: 33327725 DOI: 10.1021/acs.jpca.0c09148] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
The negative ion resonance states, which are electron-molecule metastable compound states, play the most important role in free-electron controlled molecular reactions and low-energy free-electron-induced DNA damage. Their electronic structure is often only poorly described but crucial to an understanding of their reaction dynamics. One of the most important challenges to current electronic structure theory is the computation of negative ion resonance states. As a major step forward, coupled-cluster theories, which are well-known for their ability to produce the best approximate bound state electronic eigen solutions, are upgraded to offer the most accurate and effective approximations for negative ion resonance states. The existing Fock-space coupled-cluster (FSCC) and the equation-of-motion coupled-cluster (EOM-CC) approaches that compute bound states are redesigned for the direct and simultaneous determination of both the kinetic energy of the free electron at which the electron-molecule compound states are resonantly formed and the corresponding autodetachment decay rate of the electron from the metastable compound state. This Feature Article reviews the computation of negative ion resonances using the FSCC approach and, in passing, provides the highlights of the equivalent EOM-CC approach.
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Affiliation(s)
- Suhita Basumallick
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
| | - Y Sajeev
- Theoretical Chemistry Section, Bhabha Atomic Research Centre, Mumbai 400 094, India
| | - Sourav Pal
- Indian Institute of Science Education and Research Kolkata, Mohanpur, Nadia 741 246, West Bengal, India
| | - Nayana Vaval
- Physical and Materials Chemistry Division, CSIR-National Chemical Laboratory, Pune 411 008, India
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2
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Yi J, Chen F. Multireference Rayleigh–Schrödinger perturbation theory and its application. J Chem Phys 2019; 150:124108. [DOI: 10.1063/1.5081814] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jiang Yi
- Department of Chemistry and Chemical Engineering, School of Chemistry and Biological Engineering, University of Science and Technology Beijing, Beijing 100083, People’s Republic of China and Beijing Key Laboratory for Science and Application of Functional Molecular and Crystalline Materials, Beijing 100083, People’s Republic of China
| | - Feiwu Chen
- Department of Chemistry and Chemical Engineering, School of Chemistry and Biological Engineering, University of Science and Technology Beijing, Beijing 100083, People’s Republic of China and Beijing Key Laboratory for Science and Application of Functional Molecular and Crystalline Materials, Beijing 100083, People’s Republic of China
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Faulstich FM, Máté M, Laestadius A, Csirik MA, Veis L, Antalik A, Brabec J, Schneider R, Pittner J, Kvaal S, Legeza Ö. Numerical and Theoretical Aspects of the DMRG-TCC Method Exemplified by the Nitrogen Dimer. J Chem Theory Comput 2019; 15:2206-2220. [PMID: 30802406 PMCID: PMC7002028 DOI: 10.1021/acs.jctc.8b00960] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
![]()
In
this article, we investigate the numerical and theoretical aspects
of the coupled-cluster method tailored by matrix-product states. We
investigate formal properties of the used method, such as energy size
consistency and the equivalence of linked and unlinked formulation.
The existing mathematical analysis is here elaborated in a quantum
chemical framework. In particular, we highlight the use of what we
have defined as a complete active space-external space gap describing
the basis splitting between the complete active space and the external
part generalizing the concept of a HOMO–LUMO gap. Furthermore,
the behavior of the energy error for an optimal basis splitting, i.e.,
an active space choice minimizing the density matrix renormalization
group-tailored coupled-cluster singles doubles error, is discussed.
We show numerical investigations on the robustness with respect to
the bond dimensions of the single orbital entropy and the mutual information,
which are quantities that are used to choose a complete active space.
Moreover, the dependence of the ground-state energy error on the complete
active space has been analyzed numerically in order to find an optimal
split between the complete active space and external space by minimizing
the density matrix renormalization group-tailored coupled-cluster
error.
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Affiliation(s)
- Fabian M Faulstich
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Oslo , P.O. Box 1033 Blindern, N-0315 Oslo , Norway
| | - Mihály Máté
- Strongly Correlated Systems "Lendület" Research Group , Wigner Research Center for Physics , H-1525 , P.O. Box 49, Budapest , Hungary.,Department of Physics of Complex Systems , Eötvös Loránd University , Pf. 32 , H-1518 Budapest , Hungary
| | - Andre Laestadius
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Oslo , P.O. Box 1033 Blindern, N-0315 Oslo , Norway
| | - Mihály András Csirik
- Strongly Correlated Systems "Lendület" Research Group , Wigner Research Center for Physics , H-1525 , P.O. Box 49, Budapest , Hungary
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry , Academy of Sciences of the Czech Republic , v.v.i., Dolejškova 3 , 18223 Prague 8 , Czech Republic
| | - Andrej Antalik
- J. Heyrovský Institute of Physical Chemistry , Academy of Sciences of the Czech Republic , v.v.i., Dolejškova 3 , 18223 Prague 8 , Czech Republic.,Faculty of Mathematics and Physics , Charles University , 11636 Prague , Czech Republic
| | - Jiří Brabec
- J. Heyrovský Institute of Physical Chemistry , Academy of Sciences of the Czech Republic , v.v.i., Dolejškova 3 , 18223 Prague 8 , Czech Republic
| | - Reinhold Schneider
- Modeling, Simulation and Optimization in Science, Department of Mathematics , Technische Universität Berlin , Sekretariat MA 5-3, Straße des 17. Juni 136 , 10623 Berlin , Germany
| | - Jiří Pittner
- J. Heyrovský Institute of Physical Chemistry , Academy of Sciences of the Czech Republic , v.v.i., Dolejškova 3 , 18223 Prague 8 , Czech Republic
| | - Simen Kvaal
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Oslo , P.O. Box 1033 Blindern, N-0315 Oslo , Norway
| | - Örs Legeza
- Strongly Correlated Systems "Lendület" Research Group , Wigner Research Center for Physics , H-1525 , P.O. Box 49, Budapest , Hungary
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Tsuchimochi T, Ten-No SL. Extending spin-symmetry projected coupled-cluster to large model spaces using an iterative null-space projection technique. J Comput Chem 2018; 40:265-278. [PMID: 30520115 DOI: 10.1002/jcc.25587] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2018] [Revised: 07/31/2018] [Accepted: 08/01/2018] [Indexed: 11/06/2022]
Abstract
Recently, we introduced an orbital-invariant approximate coupled-cluster (CC) method in the spin-projection manifold. The multi-determinantal property of spin-projection means that the parametrization in the spin-extended CC (ECC) ansatz is nonorthogonal and overcomplete. Therefore, the linear dependencies must be removed by an orthogonalization procedure to obtain meaningful solutions. Multi-reference methods often achieve this by diagonalizing a metric of the equation system, but this is not feasible with ECC because of the enormous size of the metric, a consequence of the incomplete active space of the spin-projected Hartree-Fock reference. As a result, the applicability of ECC has been limited to small benchmark systems, for which the ansatz was shown to be superior to the configuration interaction and linearized approximations. In this article, we provide a solution to this problem that completely avoids the metric diagonalization by iteratively projecting out its null-space from the working equations. As the additional computational cost required for this iterative projection is only marginal, it greatly expands the application range of ECC. We demonstrate the potential of approximate ECC by studying the complete basis set limit of F2 and transition metal complexes such as NiO, Mn2 , and [Cu2 O2 ]2+ , which have all been hindered by the prohibitively large metric size. We also identify the potential inadequacy of the molecular orbitals given by spin-projected Hartree-Fock in some cases, and propose possible solutions. © 2018 Wiley Periodicals, Inc.
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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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Samanta PK, Köhn A. First-order properties from internally contracted multireference coupled-cluster theory with particular focus on hyperfine coupling tensors. J Chem Phys 2018; 149:064101. [DOI: 10.1063/1.5040587] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
| | - Andreas Köhn
- Institut für Theoretische Chemie, Universität Stuttgart, D-70569 Stuttgart, Germany
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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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7
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Lee J, Small DW, Epifanovsky E, Head-Gordon M. Coupled-Cluster Valence-Bond Singles and Doubles for Strongly Correlated Systems: Block-Tensor Based Implementation and Application to Oligoacenes. J Chem Theory Comput 2017; 13:602-615. [DOI: 10.1021/acs.jctc.6b01092] [Citation(s) in RCA: 50] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Joonho Lee
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - David W. Small
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Evgeny Epifanovsky
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Martin Head-Gordon
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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Dutta AK, Dar M, Vaval N, Pal S. Structure, stability, and properties of the trans peroxo nitrate radical: the importance of nondynamic correlation. J Phys Chem A 2014; 118:1350-62. [PMID: 24502288 DOI: 10.1021/jp409218c] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We report a comparative single-reference and multireference coupled-cluster investigation on the structure, potential energy surface, and IR spectroscopic properties of the trans peroxo nitrate radical, one of the key intermediates in stratospheric NOX chemistry. The previous single-reference ab initio studies predicted an unbound structure for the trans peroxo nitrate radical. However, our Fock space multireference coupled-cluster calculation confirms a bound structure for the trans peroxo nitrate radical, in accordance with the experimental results reported earlier. Further, the analysis of the potential energy surface in FSMRCC method indicates a well-behaved minima, contrary to the shallow minima predicted by the single-reference coupled-cluster method. The harmonic force field analysis, of various possible isomers of peroxo nitrate also reveals that only the trans structure leads to the experimentally observed IR peak at 1840 cm(-1). The present study highlights the critical importance of nondynamic correlation in predicting the structure and properties of high-energy stratospheric NOx radicals.
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Affiliation(s)
- Achintya Kumar Dutta
- Physical Chemistry Division, CSIR-National Chemical Laboratory , Pune 411008, India
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Zhang D, Steinmann SN, Yang W. Dynamical second-order Bethe-Salpeter equation kernel: A method for electronic excitation beyond the adiabatic approximation. J Chem Phys 2013; 139:154109. [DOI: 10.1063/1.4824907] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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10
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Zoboki T, Szabados Á, Surján PR. Linearized Coupled Cluster Corrections to Antisymmetrized Product of Strongly Orthogonal Geminals: Role of Dispersive Interactions. J Chem Theory Comput 2013; 9:2602-8. [DOI: 10.1021/ct400138m] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Tamás Zoboki
- Institute of Chemistry,
Laboratory of Theoretical Chemistry,
P.O.B. 32, H-1518 Budapest 112, Hungary
| | - Ágnes Szabados
- Institute of Chemistry,
Laboratory of Theoretical Chemistry,
P.O.B. 32, H-1518 Budapest 112, Hungary
| | - Péter R. Surján
- Institute of Chemistry,
Laboratory of Theoretical Chemistry,
P.O.B. 32, H-1518 Budapest 112, Hungary
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11
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Jeszenszki P, Surján PR, Szabados Á. Spin-adaptation and redundancy in state-specific multireference perturbation theory. J Chem Phys 2013; 138:124110. [DOI: 10.1063/1.4795436] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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12
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An alternative approximation to state-specific multireference second-order Brillouin-Wigner perturbation theory: size-extensivity correction. Theor Chem Acc 2013. [DOI: 10.1007/s00214-012-1325-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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13
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Jagau TC, Gauss J. Linear-response theory for Mukherjee's multireference coupled-cluster method: Static and dynamic polarizabilities. J Chem Phys 2012; 137:044115. [DOI: 10.1063/1.4734308] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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14
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Constrained variational approach for energy derivatives in Intermediate Hamiltonian Fock-space coupled-cluster theory. Chem Phys 2012. [DOI: 10.1016/j.chemphys.2011.10.018] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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15
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Das S, Pathak S, Datta D, Mukherjee D. Inactive excitations in Mukherjee's state-specific multireference coupled cluster theory treated with internal contraction: Development and applications. J Chem Phys 2012; 136:164104. [DOI: 10.1063/1.3703312] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [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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RAVICHANDRAN LALITHA, BHATTACHARYA DEBARATI, VAVAL NAYANA, PAL SOURAV. Fock-space multi-reference coupled-cluster response with the effect of triples on dipole moment of ClO and SF radicals#. J CHEM SCI 2012. [DOI: 10.1007/s12039-012-0220-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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17
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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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18
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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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Szabados A. Sensitivity analysis of state-specific multireference perturbation theory. J Chem Phys 2011; 134:174113. [DOI: 10.1063/1.3585604] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Affiliation(s)
- Agnes Szabados
- Laboratory of Theoretical Chemistry, Loránd Eötvös University, Budapest, Hungary.
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Ravichandran L, Vaval N, Pal S. Effect of Triples to Dipole Moments in Fock-Space Multireference Coupled Cluster Method. J Chem Theory Comput 2011; 7:876-83. [PMID: 26606338 DOI: 10.1021/ct1007263] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
In this paper, we present the new implementation of partial triples for the dipole moment of doublet radicals in Lagrangian formulation of Fock-space multireference coupled cluster (Λ-FSMRCC) response method. We have implemented a specific scheme of noniterative triples, in addition to singles and doubles schemes, which accounts for the effects appearing at least at the third order in dipole moments. The method is applied to the ground states of OH, OOH, HCOO, CN, CH, and PO radicals.
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Affiliation(s)
| | - Nayana Vaval
- Physical Chemistry Division, National Chemical Laboratory , Pune-411008, India
| | - Sourav Pal
- Physical Chemistry Division, National Chemical Laboratory , Pune-411008, India
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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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Kobayashi M, Szabados Á, Nakai H, Surján PR. Generalized Møller−Plesset Partitioning in Multiconfiguration Perturbation Theory. J Chem Theory Comput 2010; 6:2024-33. [DOI: 10.1021/ct1001939] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Masato Kobayashi
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Eötvös University, H1518 Budapest POB 32, Hungary, Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo 169-8555, Japan, Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki 444-8585, Japan, and Research Institute for Science and Engineering (RISE), Waseda University, Tokyo 169-8555, Japan
| | - Ágnes Szabados
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Eötvös University, H1518 Budapest POB 32, Hungary, Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo 169-8555, Japan, Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki 444-8585, Japan, and Research Institute for Science and Engineering (RISE), Waseda University, Tokyo 169-8555, Japan
| | - Hiromi Nakai
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Eötvös University, H1518 Budapest POB 32, Hungary, Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo 169-8555, Japan, Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki 444-8585, Japan, and Research Institute for Science and Engineering (RISE), Waseda University, Tokyo 169-8555, Japan
| | - Péter R. Surján
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Eötvös University, H1518 Budapest POB 32, Hungary, Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo 169-8555, Japan, Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki 444-8585, Japan, and Research Institute for Science and Engineering (RISE), Waseda University, Tokyo 169-8555, Japan
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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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24
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Evangelista FA, Allen WD, Schaefer HF. Coupling term derivation and general implementation of state-specific multireference coupled cluster theories. J Chem Phys 2007; 127:024102. [PMID: 17640114 DOI: 10.1063/1.2743014] [Citation(s) in RCA: 242] [Impact Index Per Article: 14.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Simple closed-form expressions are derived for the "same vacuum" renormalization terms that arise in state-specific multireference coupled cluster (MRCC) theories. Explicit equations are provided for these coupling terms through the triple excitation level of MRCC theory, and a general expression is included for arbitrary-order excitations. The first production-level code (PSIMRCC) for state-specific and rigorously size-extensive Mukherjee multireference coupled cluster singles and doubles (MkCCSD) computations has been written. This code is also capable of evaluating analogous Brillouin-Wigner multireference energies (BWCCSD), including a posteriori size-extensivity corrections. Using correlation-consistent basis sets (cc-pVXZ, X=D,T,Q), MkCCSD and BWCCSD were tested and compared on two classic multireference problems: (1) the dissociation potential curve of molecular fluorine (F(2)) and (2) the structure and vibrational frequencies of ozone. Comparison with experimental data shows that the Mukherjee method is generally superior to the Brillouin-Wigner theory in predicting energies, structures, and vibrational frequencies. Particularly accurate results for F(2) are obtained by applying the MkCCSD method with localized molecular orbitals. Although the MkCCSD theory greatly improves upon single-reference CCSD for the geometric parameters and a(1) vibrational frequencies of ozone, the antisymmetric stretching frequency omega(3)(b(2)) remains pathological and cannot be properly treated without the inclusion of connected triple excitations. Finally, preliminary multireference MkCCSD results are reported for the singlet-triplet splittings in ortho-, meta-, and para-benzyne, coming within 1.5 kcal mol(-1) of experiment in all cases.
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25
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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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26
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Towards the Development and Applications of Manifestly Spin-free Multi-reference Coupled Electron-pair Approximation-like Methods: A State Specific Approach. Theor Chem Acc 2006. [DOI: 10.1007/s00214-006-0108-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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27
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Szabados A, Rolik Z, Tóth G, Surján PR. Multiconfiguration perturbation theory: Size consistency at second order. J Chem Phys 2005; 122:114104. [PMID: 15836198 DOI: 10.1063/1.1862235] [Citation(s) in RCA: 51] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A modified version of a previously elaborated multiconfiguration perturbation theory (MCPT) [Rolik et al. J. Chem. Phys. 119, 1922 (2003)] is presented. In the modified formulation size consistency is ensured at second order in energy, by omitting projectors from the zero order Hamiltonian operator. This MCPT formulation is abbreviated as SC2-MCPT (size consistent at second order). To ensure proper separability, we also require that energy denominators are constructed as differences of some one-particle energies. A similar choice for energy denominators also renders the well-known multireference Moller-Plesset (MRMP) energy size consistent at second order. The same thing applies to the related multireference perturbation theory by Witek, Nakano, and Hirao.
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Affiliation(s)
- Agnes Szabados
- Department of Theoretical Chemistry, Loránd Eötvös University, Budapest, Hungary
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28
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Ivanov VV, Adamowicz L, Lyakh DI. Multireference State-Specific Coupled-Cluster Theory and Multiconfigurationality Index. BH Dissociation. ACTA ACUST UNITED AC 2005. [DOI: 10.1135/cccc20051017] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
Multiconfigurationality index calculated for the coupled-cluster wave function based on an algorithm developed using a computer-aided generation approach is applied to analyze the multireference state-specific coupled-cluster method with the CAS reference (i.e. the so called the CAS(n,m)CCSD approach). The numerical results concern dissociation of the BH molecule where at larger displacement from the equilibrium significant quasi-degeneracy arises. The analysis shows that the CAS(n,m)CCSD approach performs very well in such a situation.
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Chattopadhyay S, Pahari D, Mukherjee D, Mahapatra US. A state-specific approach to multireference coupled electron-pair approximation like methods: Development and applications. J Chem Phys 2004; 120:5968-86. [PMID: 15267478 DOI: 10.1063/1.1650328] [Citation(s) in RCA: 96] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The traditional multireference (MR) coupled-cluster (CC) methods based on the effective Hamiltonian are often beset by the problem of intruder states, and are not suitable for studying potential energy surface (PES) involving real or avoided curve crossing. State-specific MR-based approaches obviate this limitation. The state-specific MRCC (SS-MRCC) method developed some years ago can handle quasidegeneracy of varying degrees over a wide range of PES, including regions of real or avoided curve-crossing. Motivated by its success, we have suggested and explored in this paper a suite of physically motivated coupled electron-pair approximations (SS-MRCEPA) like methods, which are designed to capture the essential strength of the parent SS-MRCC method without significant sacrificing its accuracy. These SS-MRCEPA theories, like their CC counterparts, are based on complete active space, treat all the reference functions on the same footing and provide a description of potentially uniform precision of PES of states with varying MR character. The combining coefficients of the reference functions are self-consistently determined along with the cluster amplitudes themselves. The newly developed SS-MRCEPA methods are size-extensive, and are also size-consistent with localized orbitals. Among the various versions, there are two which are invariant with respect to the restricted rotations among doubly occupied and active orbitals separately. Similarity of performance of this latter and the noninvariant versions at the crossing points of the degenerate orbitals imply that the all the methods presented are rather robust with respect to the rotations among degenerate orbitals. Illustrative numerical applications are presented for PES of the ground state of a number of difficult test cases such as the model H4, H(8) problems, the insertion of Be into H(2), and Li(2), where intruders exist and for a state of a molecule such as CH(2), with pronounced MR character. Results obtained with SS-MRCEPA methods are found to be comparable in accuracy to the parent SS-MRCC and FCI/large scale CI results throughout the PES, which indicates the efficacy of our SS-MRCEPA methods over a wide range of geometries, despite their neglect of a host of complicated nonlinear terms, even when the traditional MR-based methods based on effective Hamiltonians fail due to intruders.
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Affiliation(s)
- Sudip Chattopadhyay
- Department of Physical Chemistry, Indian Association for the Cultivation of Science, Calcutta 700 032, India
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State-specific Multi-reference Perturbation Theories with Relaxed Coefficients: Molecular Applications. Int J Mol Sci 2002. [DOI: 10.3390/i3060733] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
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State-specific multi-reference coupled electron-pair approximation like methods: formulation and molecular applications. Chem Phys Lett 2002. [DOI: 10.1016/s0009-2614(02)00534-1] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Chattopadhyay S, Mahapatra US, Mukherjee D. Development of a linear response theory based on a state-specific multireference coupled cluster formalism. J Chem Phys 2000. [DOI: 10.1063/1.481395] [Citation(s) in RCA: 54] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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