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Wang M, Fang WH, Li C. Assessment of State-Averaged Driven Similarity Renormalization Group on Vertical Excitation Energies: Optimal Flow Parameters and Applications to Nucleobases. J Chem Theory Comput 2023; 19:122-136. [PMID: 36534617 DOI: 10.1021/acs.jctc.2c00966] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
We present a comprehensive excited-state benchmark for the state-averaged (SA) driven similarity renormalization group (DSRG) [Li, C.; Evangelista, F. A. J. Chem. Phys. 2018, 148, 124106]. Following the QUEST database [Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio-Pasqua, M.; Jacquemin, D.; Loos, P.-F. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2021, 11, e1517], 280 vertical transition energies of 35 medium-sized molecules are computed using the SA-DSRG derived second- and third-order perturbation theories (PT2/PT3) along with a nonperturbative approach [sq-LDSRG(2)]. Comparing to the theoretical best estimates, the optimal flow parameter is found to be 0.35 and 2.0 Eh-2 for SA-DSRG-PT2 and SA-DSRG-PT3, respectively. For SA-sq-LDSRG(2), a flow parameter of 1.5 Eh-2 provides converged equations without compromising the accuracy. We then assess the accuracy of the SA-DSRG hierarchy using these parameters. The SA-DSRG-PT2 scheme outperforms the level-shifted CASPT2 by 0.10 eV in mean absolute error (MAE), yet this accuracy is slightly inferior than that of CASPT2 with the ionization-potential-electron-affinity shift. Both SA-DSRG-PT3 and SA-sq-LDSRG(2) yield a MAE of 0.10 eV, which is comparable to that of CASPT3 (0.09 eV). Finally, we compute vertical excitation energies of several low-lying singlet states of nucleobases. The SA-sq-LDSRG(2) approach provides highly accurate results for π → π* excitations, while n → π* transitions are better described by SA-DSRG-PT3.
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Affiliation(s)
- Meng Wang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Wei-Hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Chenyang Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
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Papastathopoulos-Katsaros A, Jiménez-Hoyos CA, Henderson TM, Scuseria GE. Coupled Cluster and Perturbation Theories Based on a Cluster Mean-Field Reference Applied to Strongly Correlated Spin Systems. J Chem Theory Comput 2022; 18:4293-4303. [PMID: 35729717 DOI: 10.1021/acs.jctc.2c00338] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We introduce perturbation and coupled-cluster theories based on a cluster mean-field reference for describing the ground state of strongly correlated spin systems. In cluster mean-field, the ground state wave function is written as a simple tensor product of optimized cluster states. The cluster language and the mean-field nature of the ansatz allow for a straightforward improvement which uses perturbation theory and coupled-cluster to account for intercluster correlations. We present benchmark calculations on the 1D chain and 2D square J1-J2 Heisenberg model, using cluster mean-field, perturbation theory, and coupled-cluster. We also present an extrapolation scheme that allows us to compute thermodynamic limit energies accurately. Our results indicate that, with sufficiently large clusters, the correlated methods (cPT2, cPT4, and cCCSD) can provide a relatively accurate description of the Heisenberg model in the regimes considered, which suggests that the methods presented can be used for other strongly correlated systems. Some ways to improve upon the methods presented in this work are discussed.
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Affiliation(s)
| | - Carlos A Jiménez-Hoyos
- Department of Chemistry, Wesleyan University, Middletown, Connecticut 06459, United States
| | - Thomas M Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, United States.,Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Gustavo E Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, United States.,Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
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Abraham V, Mayhall NJ. Selected Configuration Interaction in a Basis of Cluster State Tensor Products. J Chem Theory Comput 2020; 16:6098-6113. [DOI: 10.1021/acs.jctc.0c00141] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Affiliation(s)
- Vibin Abraham
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, United States
| | - Nicholas J. Mayhall
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, United States
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Li C, Evangelista FA. Driven similarity renormalization group for excited states: A state-averaged perturbation theory. J Chem Phys 2018; 148:124106. [DOI: 10.1063/1.5019793] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Chenyang Li
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Francesco A. Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
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Mayhall NJ. Using Higher-Order Singular Value Decomposition To Define Weakly Coupled and Strongly Correlated Clusters: The n-Body Tucker Approximation. J Chem Theory Comput 2017; 13:4818-4828. [DOI: 10.1021/acs.jctc.7b00696] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Affiliation(s)
- Nicholas J. Mayhall
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, United States
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Li Z, Liu W. Critical Assessment of TD-DFT for Excited States of Open-Shell Systems: I. Doublet–Doublet Transitions. J Chem Theory Comput 2015; 12:238-60. [DOI: 10.1021/acs.jctc.5b01158] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Zhendong Li
- Beijing National Laboratory
for Molecular Sciences, Institute of Theoretical and Computational
Chemistry, State Key Laboratory of Rare Earth Materials Chemistry
and Applications, College of Chemistry and Molecular Engineering,
and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
| | - Wenjian Liu
- Beijing National Laboratory
for Molecular Sciences, Institute of Theoretical and Computational
Chemistry, State Key Laboratory of Rare Earth Materials Chemistry
and Applications, College of Chemistry and Molecular Engineering,
and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
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Zhang C, Yuan D, Guo Y, Li S. Efficient Implementation of Local Excitation Approximation for Treating Excited States of Molecules in Condensed Phase. J Chem Theory Comput 2014; 10:5308-17. [DOI: 10.1021/ct500551p] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Chenyang Zhang
- School of Chemistry and Chemical
Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of
Education, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210093, P. R. China
| | - Dandan Yuan
- School of Chemistry and Chemical
Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of
Education, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210093, P. R. China
| | - Yang Guo
- School of Chemistry and Chemical
Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of
Education, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210093, P. R. China
| | - Shuhua Li
- School of Chemistry and Chemical
Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of
Education, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210093, P. R. China
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Schmalz TG, Serrano-Andrés L, Sauri V, Merchán M, Oliva JM. A distance-dependent parameterization of the extended Hubbard model for conjugated and aromatic hydrocarbons derived from stretched ethene. J Chem Phys 2011; 135:194103. [DOI: 10.1063/1.3659294] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
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Datta D, Kong L, Nooijen M. A state-specific partially internally contracted multireference coupled cluster approach. J Chem Phys 2011; 134:214116. [DOI: 10.1063/1.3592494] [Citation(s) in RCA: 66] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Li Z, Liu W. Spin-adapted open-shell random phase approximation and time-dependent density functional theory. I. Theory. J Chem Phys 2010; 133:064106. [PMID: 20707560 DOI: 10.1063/1.3463799] [Citation(s) in RCA: 64] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The spin-adaptation of single-reference quantum chemical methods for excited states of open-shell systems has been nontrivial. The primary reason is that the configuration space, generated by a truncated rank of excitations from only one component of a reference multiplet, is spin-incomplete. Those "missing" configurations are of higher ranks and can, in principle, be recaptured by a particular class of excitation operators. However, the resulting formalisms are then quite involved and there are situations [e.g., time-dependent density functional theory (TD-DFT) under the adiabatic approximation] that prevent one from doing so. To solve this issue, we propose here a tensor-coupling scheme that invokes all the components of a reference multiplet (i.e., a tensor reference) rather than increases the excitation ranks. A minimal spin-adapted n-tuply excited configuration space can readily be constructed by tensor products between the n-tuple tensor excitation operators and the chosen tensor reference. Further combined with the tensor equation-of-motion formalism, very compact expressions for excitation energies can be obtained. As a first application of this general idea, a spin-adapted open-shell random phase approximation is first developed. The so-called "translation rule" is then adopted to formulate a spin-adapted, restricted open-shell Kohn-Sham (ROKS)-based TD-DFT (ROKS-TD-DFT). Here, a particular symmetry structure has to be imposed on the exchange-correlation kernel. While the standard ROKS-TD-DFT can access only excited states due to singlet-coupled single excitations, i.e., only some of the singly excited states of the same spin (S(i)) as the reference, the new scheme can capture all the excited states of spin S(i)-1, S(i), or S(i)+1 due to both singlet- and triplet-coupled single excitations. The actual implementation and computation are very much like the (spin-contaminated) unrestricted Kohn-Sham-based TD-DFT. It is also shown that spin-contaminated spin-flip configuration interaction approaches can easily be spin-adapted via the tensor-coupling scheme.
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Affiliation(s)
- Zhendong Li
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871, People's Republic of China
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Shen J, Li S. Comparison of some multireference electronic structure methods in illustrative applications. Sci China Chem 2010. [DOI: 10.1007/s11426-010-0034-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Chaudhuri RK, Chattopadhyay S, Mahapatra US, Freed KF. Molecular applications of analytical gradient approach for the improved virtual orbital-complete active space configuration interaction method. J Chem Phys 2010; 132:034105. [DOI: 10.1063/1.3290203] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
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Shen J, Li S. Block correlated coupled cluster method with the complete active-space self-consistent-field reference function: Applications for low-lying electronic excited states. J Chem Phys 2009; 131:174101. [DOI: 10.1063/1.3256297] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
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Multi-reference coupled-cluster study of the potential energy surface of the hydrogen fluoride dissociation including excited states. ACTA ACUST UNITED AC 2009. [DOI: 10.1016/j.theochem.2009.02.012] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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