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Hodecker M, Dempwolff AL, Schirmer J, Dreuw A. Theoretical analysis and comparison of unitary coupled-cluster and algebraic-diagrammatic construction methods for ionization. J Chem Phys 2022; 156:074104. [DOI: 10.1063/5.0070967] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Affiliation(s)
- Manuel Hodecker
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Adrian L. Dempwolff
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Jochen Schirmer
- Theoretical Chemistry, Heidelberg University, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
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2
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Beizaei N, Sauer SPA. Benchmarking Correlated Methods for Static and Dynamic Polarizabilities: The T145 Data Set Evaluated with RPA, RPA(D), HRPA, HRPA(D), SOPPA, SOPPA(CC2), SOPPA(CCSD), CC2, and CCSD. J Phys Chem A 2021; 125:3785-3792. [PMID: 33899480 DOI: 10.1021/acs.jpca.1c01931] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Due to the importance of predicting static and dynamic polarizabilities, the performance of various correlated linear response methods including random phase approximation (RPA), RPA(D), higher-order random phase approximation (HRPA), HRPA(D), second-order polarization propagator approximation (SOPPA), SOPPA(CC2), SOPPA(CCSD), CC2, and CCSD has been evaluated against CCSD(T) (static case) and CCSD (dynamic cases) for the T145 set of 145 organic molecules. The benchmark reveals that the HRPA(D) method has the best performance for both static and dynamic polarizabilities apart from CCSD. RPA(D) ranks second for the dynamic cases and third for the static case. Using coupled-cluster amplitudes in SOPPA(CCSD) and SOPPA(CC2), the SOPPA results are significantly improved. The HRPA method has the largest deviations from the reference values for both cases. In general, according to the performance and computational cost of the methods, the HRPA(D) and RPA(D) methods are proposed for calculations of static and dynamic polarizabilities of this and similar sets of molecules.
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Affiliation(s)
- Nazanin Beizaei
- Department of Chemistry, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
| | - Stephan P A Sauer
- Department of Chemistry, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
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3
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Rishi V, Perera A, Bartlett RJ. A route to improving RPA excitation energies through its connection to equation-of-motion coupled cluster theory. J Chem Phys 2020; 153:234101. [DOI: 10.1063/5.0023862] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Affiliation(s)
- Varun Rishi
- Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Ajith Perera
- 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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4
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Jørgensen MW, Sauer SPA. Benchmarking doubles-corrected random-phase approximation methods for frequency dependent polarizabilities: Aromatic molecules calculated at the RPA, HRPA, RPA(D), HRPA(D), and SOPPA levels. J Chem Phys 2020; 152:234101. [DOI: 10.1063/5.0011195] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Maria W. Jørgensen
- Department of Chemistry, University of Copenhagen, Copenhagen Ø, Denmark
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5
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Hodecker M, Thielen SM, Liu J, Rehn DR, Dreuw A. Third-Order Unitary Coupled Cluster (UCC3) for Excited Electronic States: Efficient Implementation and Benchmarking. J Chem Theory Comput 2020; 16:3654-3663. [PMID: 32396348 DOI: 10.1021/acs.jctc.0c00335] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The efficient implementation of the third-order unitary coupled-cluster scheme (UCC3) for the calculation of excited electronic states is reported. The UCC3 scheme and its second-order UCC2 variant have been benchmarked and compared to Jacquemin's recently introduced, as well as Thiel's well-established, benchmark sets for excitation energies and oscillator strengths. For the latter, the calculation of 134 excited singlet and 71 excited triplet states of 28 small- to medium-sized organic molecules has revealed that UCC2 exhibits a mean error and standard deviation of 0.36 ± 0.41 eV for singlet states and 0.22 ± 0.21 eV for triplet states, whereas UCC3 revealed an accuracy of 0.06 ± 0.27 eV for singlet and -0.22 ± 0.15 eV for triplet states. In addition, the oscillator strengths obtained with effective transition moments correct through second order in perturbation theory are in very good agreement with literature data.
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Affiliation(s)
- Manuel Hodecker
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Sebastian M Thielen
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Dirk R Rehn
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
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6
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Jørgensen MW, Faber R, Ligabue A, Sauer SPA. Benchmarking Correlated Methods for Frequency-Dependent Polarizabilities: Aromatic Molecules with the CC3, CCSD, CC2, SOPPA, SOPPA(CC2), and SOPPA(CCSD) Methods. J Chem Theory Comput 2020; 16:3006-3018. [DOI: 10.1021/acs.jctc.9b01300] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Maria W. Jørgensen
- Department of Chemistry, University of Copenhagen, Copenhagen 2100, Denmark
| | - Rasmus Faber
- Department of Chemistry, Technical University of Denmark, Kongens Lyngby 2800, Denmark
| | - Andrea Ligabue
- Game Science Research Center, University of Modena and Reggio Emilia, Modena 41121, Italy
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7
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Schnack-Petersen AK, Simmermacher M, Fasshauer E, Jensen HJA, Sauer SPA. The Second-Order-Polarization-Propagator-Approximation (SOPPA) in a four-component spinor basis. J Chem Phys 2020; 152:134113. [DOI: 10.1063/5.0002389] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Mats Simmermacher
- School of Chemistry, University of Edinburgh, Edinburgh, United Kingdom
| | - Elke Fasshauer
- Department of Physics and Astronomy, Aarhus University, Aarhus, Denmark
| | - Hans Jørgen Aa. Jensen
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Odense, Denmark
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8
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Loos PF, Scemama A, Jacquemin D. The Quest for Highly Accurate Excitation Energies: A Computational Perspective. J Phys Chem Lett 2020; 11:2374-2383. [PMID: 32125872 DOI: 10.1021/acs.jpclett.0c00014] [Citation(s) in RCA: 87] [Impact Index Per Article: 21.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
We provide an overview of the successive steps that made it possible to obtain increasingly accurate excitation energies with computational chemistry tools, eventually leading to chemically accurate vertical transition energies for small- and medium-size molecules. First, we describe the evolution of ab initio methods employed to define benchmark values, with the original Roos CASPT2 method, then the CC3 method as in the renowned Thiel set, and more recently the resurgence of selected configuration interaction methods. The latter method has been able to deliver consistently, for both single and double excitations, highly accurate excitation energies for small molecules, as well as medium-size molecules with compact basis sets. Second, we describe how these high-level methods and the creation of representative benchmark sets of excitation energies have allowed the fair and accurate assessment of the performance of computationally lighter methods. We conclude by discussing possible future theoretical and technological developments in the field.
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Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Denis Jacquemin
- Université de Nantes, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
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Hodecker M, Rehn DR, Dreuw A. Hermitian second-order methods for excited electronic states: Unitary coupled cluster in comparison with algebraic-diagrammatic construction schemes. J Chem Phys 2020; 152:094106. [PMID: 33480727 DOI: 10.1063/1.5142354] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Employing an intermediate state representation (ISR) approach, Hermitian second-order methods for the calculation of electronic excitation energies are presented and compared in detail. These comprise the algebraic-diagrammatic construction scheme for the polarization propagator, a hybrid second-order ISR scheme based on traditional coupled-cluster theory as well as two similar approaches based on a unitary coupled-cluster (UCC) ansatz. Although in a strict perturbation-theoretical framework all prove to be identical, differences emerge when the corresponding converged cluster amplitudes are used and depending on how the similarity-transformed UCC Hamiltonian is evaluated. The resulting excitation energies, however, do not significantly differ for systems well described by means of perturbation theory.
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Affiliation(s)
- Manuel Hodecker
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Dirk R Rehn
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
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Loos PF, Jacquemin D. Is ADC(3) as Accurate as CC3 for Valence and Rydberg Transition Energies? J Phys Chem Lett 2020; 11:974-980. [PMID: 31913639 DOI: 10.1021/acs.jpclett.9b03652] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The search for new models rapidly delivering accurate excited-state energies and properties is one of the most active research lines of theoretical chemistry. Along with these developments, the performance of known methods is constantly reassessed on the basis of new benchmark values. In this Letter, we show that the third-order algebraic diagrammatic construction, ADC(3), does not yield transition energies of the same quality as the third-order coupled cluster method, CC3. This is demonstrated by extensive comparisons with several hundred high-quality vertical transition energies obtained with FCI, CCSDTQ, and CCSDT. Direct comparisons with experimental 0-0 energies of small- and medium-size molecules support the same conclusion, which holds for both valence and Rydberg transitions. Considering these results, we introduce a composite approach, ADC(2.5), which consists of averaging the ADC(2) and ADC(3) excitation energies. Although ADC(2.5) does not match the CC3 accuracy, it significantly improves the ADC(3) results, especially for vertical energies.
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Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), CNRS , Université de Toulouse , 31077 Toulouse , France
| | - Denis Jacquemin
- Laboratoire CEISAM UMR UN-CNRS 6230 , Université de Nantes , F-44000 Nantes , France
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11
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Hodecker M, Rehn DR, Norman P, Dreuw A. Algebraic-diagrammatic construction scheme for the polarization propagator including ground-state coupled-cluster amplitudes. II. Static polarizabilities. J Chem Phys 2019; 150:174105. [DOI: 10.1063/1.5081665] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Manuel Hodecker
- Interdisciplinary Center for Scientific Computing (IWR), Ruprecht–Karls University Heidelberg, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Dirk R. Rehn
- Interdisciplinary Center for Scientific Computing (IWR), Ruprecht–Karls University Heidelberg, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
- Department of Theoretical Chemistry and Biology, KTH Royal Institute of Technology, Roslagstullsbacken 15, S-10691 Stockholm, Sweden
| | - Patrick Norman
- Department of Theoretical Chemistry and Biology, KTH Royal Institute of Technology, Roslagstullsbacken 15, S-10691 Stockholm, Sweden
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing (IWR), Ruprecht–Karls University Heidelberg, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
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