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Chakravarti D, Sen S, Mukherjee D. A systematic improvement to UGA-SSMRCCSD equations and its implication for potential energy curves. J Chem Phys 2023; 159:134102. [PMID: 37787129 DOI: 10.1063/5.0168941] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2023] [Accepted: 09/14/2023] [Indexed: 10/04/2023] Open
Abstract
The Unitary Group Adaptation (UGA) offers a very compact and efficient spin adaptation strategy for any spin-free Hamiltonian in a many body framework. Our use of UGA in the context of state-specific (SS) Jeziorski-Monkhorst Ansatz based multireference coupled cluster (MRCC) theory obviates the non-commutativity between the spin-free cluster operators via a normal ordered exponential parametrization in the wave operator. A previous formulation of UGA-SSMRCC by us [R. Maitra, D. Sinha, and D. Mukherjee, J. Chem. Phys. 137, 024105 (2012)], using the same ansatz, employed certain sufficiency conditions to reach the final working equations, which cannot be improved systematically. In this article, we will present a more rigorous formulation that follows from an exact factorization of the unlinked terms of the Bloch equation, resulting in equations on which a hierarchy of approximations can be systematically performed on the emergent additional terms. This derivation was shown in our recent article [D. Chakravarti, S. Sen, and D. Mukherjee, Mol. Phys. 119, e1979676 (2021)] in the context of a single open shell CC formalism and was applied to spectroscopic energy differences where the contribution of the new terms was found to be of the order of ∼0.001 eV for ionization potential, electron affinity, and excitation energy. In the current work, we will present a comparison between the earlier and current formulations via both a theoretical analysis and a numerical demonstration of the dramatic effect of the additional terms brought in by the factorization on potential energy curves. The contribution of such terms was found to gain importance with an increase in the number of singly occupied active orbitals in the model space functions.
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Affiliation(s)
- Dibyajyoti Chakravarti
- Centre for Quantum Engineering, Research, and Education (CQuERE), TCG CREST, Kolkata, India
| | - Sangita Sen
- Department of Chemical Sciences, Indian Institute of Science, Education and Research, Kolkata, India
| | - Debashis Mukherjee
- Centre for Quantum Engineering, Research, and Education (CQuERE), TCG CREST, Kolkata, India
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Tada K, Maruyama T, Koga H, Okumura M, Tanaka S. Extent of Spin Contamination Errors in DFT/Plane-wave Calculation of Surfaces: A Case of Au Atom Aggregation on a MgO Surface. Molecules 2019; 24:molecules24030505. [PMID: 30704148 PMCID: PMC6385026 DOI: 10.3390/molecules24030505] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2018] [Revised: 01/28/2019] [Accepted: 01/30/2019] [Indexed: 11/16/2022] Open
Abstract
The aggregation of Au atoms onto a Au dimer (Au₂) on a MgO (001) surface was calculated by restricted (spin-un-polarized) and unrestricted (spin-polarized) density functional theory calculations with a plane-wave basis and the approximate spin projection (AP) method. The unrestricted calculations included spin contamination errors of 0.0⁻0.1 eV, and the errors were removed using the AP method. The potential energy curves for the aggregation reaction estimated by the restricted and unrestricted calculations were different owing to the estimation of the open-shell structure by the unrestricted calculations. These results show the importance of the open-shell structure and correction of the spin contamination error for the calculation of small-cluster-aggregations and molecule dimerization on surfaces.
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Affiliation(s)
- Kohei Tada
- Research Institute of Electrochemical Energy, National Institute of Advanced Industrial Science and Technology (AIST), 1-8-31, Midorigaoka, Ikeda, Osaka 563-8577, Japan.
| | - Tomohiro Maruyama
- Department of Chemistry, Graduate School of Science, Osaka University, 1-1, Machikaneyama, Toyonaka, Osaka 560-0043, Japan.
| | - Hiroaki Koga
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, 1-30 Goryo Ohara, Nishikyo, Kyoto 615-8245, Japan.
| | - Mitsutaka Okumura
- Department of Chemistry, Graduate School of Science, Osaka University, 1-1, Machikaneyama, Toyonaka, Osaka 560-0043, Japan.
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, 1-30 Goryo Ohara, Nishikyo, Kyoto 615-8245, Japan.
| | - Shingo Tanaka
- Research Institute of Electrochemical Energy, National Institute of Advanced Industrial Science and Technology (AIST), 1-8-31, Midorigaoka, Ikeda, Osaka 563-8577, Japan.
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Estimation of spin contamination error in dissociative adsorption of Au2 onto MgO(0 0 1) surface: First application of approximate spin projection (AP) method to plane wave basis. Chem Phys Lett 2018. [DOI: 10.1016/j.cplett.2018.03.064] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Lang J, Švaňa M, Demel O, Brabec J, Kedžuch S, Noga J, Kowalski K, Pittner J. A MRCC study of the isomerisation of cyclopropane. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1317112] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Jakub Lang
- J. Heyrovsky Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Prague 8, Czech Republic
- Faculty of Science, Charles University in Prague, Prague 2, Czech Republic
| | - Matej Švaňa
- J. Heyrovsky Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Prague 8, Czech Republic
| | - Ondřej Demel
- J. Heyrovsky Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Prague 8, Czech Republic
| | - Jiri Brabec
- J. Heyrovsky Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Prague 8, Czech Republic
| | - Stanislav Kedžuch
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Bratislava, Slovakia
| | - Jozef Noga
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Bratislava, Slovakia
- Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University, Bratislava, Slovakia
| | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, Richland, WA 99352, USA
| | - Jiří Pittner
- J. Heyrovsky Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Prague 8, Czech Republic
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Brabec J, Banik S, Kowalski K, Pittner J. Perturbative universal state-selective correction for state-specific multi-reference coupled cluster methods. J Chem Phys 2016; 145:164106. [PMID: 27802607 DOI: 10.1063/1.4965826] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, we report an extension of our previous development of the universal state-selective (USS) multireference coupled-cluster (MRCC) formalism. It was shown [Brabec et al., J. Chem. Phys. 136, 124102 (2012)] and [Banik et al., J. Chem. Phys. 142, 114106 (2015)] that the USS(2) approach significantly improves the accuracy of Brillouin-Wigner and Mukherjee MRCC formulations, however, the numerical and storage costs associated with calculating highly excited intermediates pose a significant challenge, which can restrict the applicability of the USS(2) method. Therefore, we introduce a perturbative variant of the USS(2) approach (USS(pt)), which substantially reduces numerical overhead of the full USS(2) correction while preserving its accuracy. Since the new USS(pt) implementation calculates the triple and quadruple projections in on-the-fly manner, the memory bottleneck associated with the need of storing expensive recursive intermediates is entirely eliminated. On the example of several benchmark systems, we demonstrate accuracies of USS(pt) and USS(2) approaches and their efficiency in describing quasidegenerate electronic states. It is also shown that the USS(pt) method significantly alleviates problems associated with the lack of invariance of MRCC theories upon the rotation of active orbitals.
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Affiliation(s)
- Jiri Brabec
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, CZ-18223 Prague 8, Czech Republic
| | - Subrata Banik
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, CZ-18223 Prague 8, Czech Republic
| | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
| | - Jiří Pittner
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, CZ-18223 Prague 8, Czech Republic
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Aprà E, Kowalski K. Implementation of High-Order Multireference Coupled-Cluster Methods on Intel Many Integrated Core Architecture. J Chem Theory Comput 2016; 12:1129-38. [DOI: 10.1021/acs.jctc.5b00957] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- E. Aprà
- William R. Wiley Environmental
Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, United States
| | - K. Kowalski
- William R. Wiley Environmental
Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, United States
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Banik S, Ravichandran L, Brabec J, Hubač I, Kowalski K, Pittner J. Iterative universal state selective correction for the Brillouin-Wigner multireference coupled-cluster theory. J Chem Phys 2015; 142:114106. [PMID: 25796230 DOI: 10.1063/1.4914311] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
As a further development of the previously introduced a posteriori Universal State-Selective (USS) corrections [K. Kowalski, J. Chem. Phys. 134, 194107 (2011); J. Brabec et al., ibid. 136, 124102 (2012)], we suggest an iterative form of the USS correction by means of correcting effective Hamiltonian matrix elements. We also formulate USS corrections via the left Bloch equations. The convergence of the USS corrections with excitation level towards the full configuration interaction (FCI) limit is also investigated. Various forms of the USS and simplified diagonal USS corrections at the singles and doubles and perturbative triple levels are numerically assessed on several model systems and on the ozone and tetramethyleneethane molecules. It is shown that the iterative USS correction can successfully replace the previously developed a posteriori Brillouin-Wigner coupled cluster size-extensivity correction, while it is not sensitive to intruder states and performs well also in other cases when the a posteriori one fails, like, e.g., for the asymmetric vibration mode of ozone.
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Affiliation(s)
- Subrata Banik
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, CZ-18223 Prague 8, Czech Republic
| | - Lalitha Ravichandran
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, CZ-18223 Prague 8, Czech Republic
| | - Jiří Brabec
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Ivan Hubač
- Department of Chemical Physics, Faculty of Mathematics and Physics, Comenius University, 84215 Bratislava, Slovakia
| | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
| | - Jiří Pittner
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, CZ-18223 Prague 8, Czech Republic
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Lutz JJ, Piecuch P. Performance of the completely renormalized equation-of-motion coupled-cluster method in calculations of excited-state potential cuts of water. COMPUT THEOR CHEM 2014. [DOI: 10.1016/j.comptc.2014.05.008] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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9
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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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10
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Demel O, Kedžuch S, Noga J, Pittner J. Perturbative triples correction for explicitly correlated Mukherjee’s state-specific coupled cluster method. Mol Phys 2013. [DOI: 10.1080/00268976.2013.809488] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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11
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Bhaskaran-Nair K, Kowalski K. Bridging single and multireference coupled cluster theories with universal state selective formalism. J Chem Phys 2013; 138:204114. [DOI: 10.1063/1.4806768] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [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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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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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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Bhaskaran-Nair K, Brabec J, Aprà E, van Dam HJJ, Pittner J, Kowalski K. Implementation of the multireference Brillouin-Wigner and Mukherjee's coupled cluster methods with non-iterative triple excitations utilizing reference-level parallelism. J Chem Phys 2012; 137:094112. [DOI: 10.1063/1.4747698] [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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16
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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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Mahapatra US, Chattopadhyay S. Diagnosis of the performance of the state-specific multireference coupled-cluster method with different truncation schemes. J Comput Chem 2012; 33:1285-303. [PMID: 22419455 DOI: 10.1002/jcc.22960] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2011] [Revised: 02/06/2012] [Accepted: 02/07/2012] [Indexed: 11/06/2022]
Abstract
We have tested the linked version of a iterative (partial) triples correction for the Jeziorski-Monkhorst ansatz based state-specific multireference coupled cluster (SS-MRCC) approach with singles and doubles (SD) excitations [abbreviated as SS-MRCCSDT-1a and SS-MRCCSDT-1a+d]. The assessments of SS-MRCCSDT-1a and SS-MRCCSDT-1a+d schemes have been performed on the ground potential energy surface (PES) of P4, Li(2),Be(2) systems which demand the MR description, and on study of the excitation energy between the ground and first excited state for P4 system. Illustrations in the isomerization of cyclobutadiene also show the power of the schemes. One of the designed features of the SS-MRCCSDT-n methods introduced here is that they do not require storage of the triples amplitudes. In the entire range of geometries, we found a definite improvement provided by SS-MRCC with SDT-1a and SDT-1a+d schemes over the standard SD one. In the nondegenerate regions of PES, the closeness of the performance of the single-reference CC to the SS-MRCC methods increases after inclusion of even partial triple excitations. Generally, the performance of the SS-MRCCSDT-1a+d approach is closer to the corresponding full configuration interaction (FCI) one than to the SS-MRCCSDT-1a specially in the degenerate geometries (as is evident from nonparallelism error). The deviation from FCI for the first excited state of the P4 model using various SS-MRCC theories with different truncation schemes obtained by converging on the second root of the effective Hamiltonian has also been reported. We also compare our results with the current generation state-of-the-art single and multireference CC calculations to envisage the usefulness of the present approach. Initial implementation indicates that the SS-MRCCSDT-n formalism can provide not only reliable excitation energies and barrier height even when used in a relatively small model space, but also offers a considerable promise in generating the entire energy surface with low nonparallelity error.
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Affiliation(s)
- Uttam Sinha Mahapatra
- Department of Physics, Maulana Azad College, 8 Rafi Ahmed KidwaiRoad, Kolkata 700013, India.
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Brabec J, van Dam HJJ, Pittner J, Kowalski K. Universal state-selective corrections to multi-reference coupled-cluster theories with single and double excitations. J Chem Phys 2012; 136:124102. [DOI: 10.1063/1.3692969] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Brabec J, Pittner J, van Dam HJJ, Aprà E, Kowalski K. Parallel Implementation of Multireference Coupled-Cluster Theories Based on the Reference-Level Parallelism. J Chem Theory Comput 2012; 8:487-97. [DOI: 10.1021/ct200809m] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jiří Brabec
- J. Heyrovský Institute
of Physical Chemistry, Academy of Sciences of the Czech Republic,
CZ-18223 Prague 8, Czech Republic
| | - Jiří Pittner
- J. Heyrovský Institute
of Physical Chemistry, Academy of Sciences of the Czech Republic,
CZ-18223 Prague 8, Czech Republic
| | - Hubertus J. J. van Dam
- William R. Wiley Environmental
Molecular Science Laboratory, Battelle, Pacific Northwest National
Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, United
States
| | - Edoardo Aprà
- William R. Wiley Environmental
Molecular Science Laboratory, Battelle, Pacific Northwest National
Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, United
States
| | - Karol Kowalski
- William R. Wiley Environmental
Molecular Science Laboratory, Battelle, Pacific Northwest National
Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, United
States
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Brabec J, Krishnamoorthy S, van Dam HJ, Kowalski K, Pittner J. Massively parallel implementation of the multireference Brillouin–Wigner CCSD method. Chem Phys Lett 2011. [DOI: 10.1016/j.cplett.2011.08.016] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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22
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Sørensen LK, Olsen J, Fleig T. Two- and four-component relativistic generalized-active-space coupled cluster method: Implementation and application to BiH. J Chem Phys 2011; 134:214102. [DOI: 10.1063/1.3592148] [Citation(s) in RCA: 24] [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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Kowalski K. A universal state-selective approach to multireference coupled-cluster non-iterative corrections. J Chem Phys 2011; 134:194107. [DOI: 10.1063/1.3589896] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
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Bhaskaran-Nair K, Demel O, Šmydke J, Pittner J. Multireference state-specific Mukherjee's coupled cluster method with noniterative triexcitations using uncoupled approximation. J Chem Phys 2011; 134:154106. [DOI: 10.1063/1.3573373] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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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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Gour JR, Piecuch P, Włoch M. Comparison of the completely renormalized equation-of-motion coupled-cluster and Quantum Monte Carlo results for the low-lying electronic states of methylene. Mol Phys 2010. [DOI: 10.1080/00268976.2010.518573] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Jeffrey R. Gour
- a Department of Chemistry , Michigan State University , East Lansing , Michigan 48824 , USA
| | - Piotr Piecuch
- a Department of Chemistry , Michigan State University , East Lansing , Michigan 48824 , USA
| | - Marta Włoch
- b Department of Chemistry , Michigan Technological University , Houghton , Michigan 49931 , USA
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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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30
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Demel O, Bhaskaran-Nair K, Pittner J. Uncoupled multireference state-specific Mukherjee’s coupled cluster method with triexcitations. J Chem Phys 2010; 133:134106. [DOI: 10.1063/1.3495679] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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31
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Bhaskaran-Nair K, Demel O, Pittner J. Multireference Mukherjee’s coupled cluster method with triexcitations in the linked formulation: Efficient implementation and applications. J Chem Phys 2010; 132:154105. [DOI: 10.1063/1.3376053] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
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32
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Kowalski K, Valiev M. Extensive regularization of the coupled cluster methods based on the generating functional formalism: application to gas-phase benchmarks and to the SN2 reaction of CHCl3 and OH- in water. J Chem Phys 2010; 131:234107. [PMID: 20025314 DOI: 10.1063/1.3270957] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
Abstract
The recently introduced energy expansion based on the use of generating functional (GF) [K. Kowalski and P. D. Fan, J. Chem. Phys. 130, 084112 (2009)] provides a way of constructing size-consistent noniterative coupled cluster (CC) corrections in terms of moments of the CC equations. To take advantage of this expansion in a strongly interacting regime, the regularization of the cluster amplitudes is required in order to counteract the effect of excessive growth of the norm of the CC wave function. Although proven to be efficient, the previously discussed form of the regularization does not lead to rigorously size-consistent corrections. In this paper we address the issue of size-consistent regularization of the GF expansion by redefining the equations for the cluster amplitudes. The performance and basic features of proposed methodology are illustrated on several gas-phase benchmark systems. Moreover, the regularized GF approaches are combined with quantum mechanical molecular mechanics module and applied to describe the S(N)2 reaction of CHCl(3) and OH(-) in aqueous solution.
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Affiliation(s)
- Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, K8-91 Battelle, P.O. Box 999, Richland, Washington 99352, USA.
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Evangelista FA, Prochnow E, Gauss J, Schaefer HF. Perturbative triples corrections in state-specific multireference coupled cluster theory. J Chem Phys 2010; 132:074107. [DOI: 10.1063/1.3305335] [Citation(s) in RCA: 94] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kowalski K, Fan PD. Generating functionals based formulation of the method of moments of coupled cluster equations. J Chem Phys 2009; 130:084112. [DOI: 10.1063/1.3076138] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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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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Fleig T, Sørensen LK, Olsen J. A relativistic 4-component general-order multi-reference coupled cluster method: initial implementation and application to HBr. Theor Chem Acc 2007. [DOI: 10.1007/s00214-007-0265-y] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Li X, Paldus J. General-model-space state-universal coupled-cluster method: excitation energies of water. Mol Phys 2007. [DOI: 10.1080/00268970500416145] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Xiangzhu Li
- a Department of Applied Mathematics , University of Waterloo , Waterloo, Ontario, Canada N2L 3G1
| | - Josef Paldus
- a Department of Applied Mathematics , University of Waterloo , Waterloo, Ontario, Canada N2L 3G1
- b Department of Chemistry, and Guelph-Waterloo Center for Graduate Work in Chemistry , Waterloo Campus, University of Waterloo , Waterloo, Ontario, Canada N2L 3G1
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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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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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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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Rolik Z, Szabados Á, Kőhalmi D, Surján P. Coupled-cluster theory and the method of moments. ACTA ACUST UNITED AC 2006. [DOI: 10.1016/j.theochem.2006.05.014] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Li X, Paldus J. Diagonal perturbative triple corrections to the general‐model‐space state‐universal coupled‐cluster method: Are they warranted and useful? Mol Phys 2006. [DOI: 10.1080/00268976.2006.10384474] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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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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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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Webb SP. Ab initio electronic structure theory as an aid to understanding excited state hydrogen transfer in moderate to large systems. Theor Chem Acc 2005. [DOI: 10.1007/s00214-005-0011-2] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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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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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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