1
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Zielinski P, Black JA, Köhn A. Performance Tests of the Second-Order Approximate Internally Contracted Multireference Coupled-Cluster Singles and Doubles Method icMRCC2. J Chem Theory Comput 2023; 19:8671-8688. [PMID: 37991987 PMCID: PMC10720349 DOI: 10.1021/acs.jctc.3c00969] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2023] [Revised: 11/03/2023] [Accepted: 11/06/2023] [Indexed: 11/24/2023]
Abstract
Benchmark results are presented for the second-order approximation of the internally contracted multireference coupled-cluster method with single and double excitations, icMRCC2 [Köhn, Bargholz, J. Chem. Phys. 2019, 151, 041106], which was designed as a multireference analogue of the single-reference second-order approximate coupled-cluster method CC2 [Christiansen, Koch, Jørgensen, Chem. Phys. Lett. 1995, 243, 409-418]. Vertical excitation energies of various small to medium-sized organic molecules are investigated based on established test sets from the literature. Additionally, the spectroscopic constants of ground and excited states of diatomics and the geometric parameters of excited triatomic molecules were determined and compared to the experimental data. The results show that the method clearly extends the applicability of single-reference CC2, including doubly excited states, and also artifacts of CC2 like too low Rydberg excitations and too weak multiple bonds are eliminated. The method is computationally more demanding than standard multireference second-order perturbation theories but improves significantly in accuracy, as shown by the benchmark results. In addition, it is demonstrated that small active spaces are often sufficient to obtain accurate energies with icMRCC2. Example applications like the automerization of cyclobutadiene, the deactivation pathway of ethylene, and the excited states of an iron complex with a noninnocent nitrosyl ligand demonstrate the potential of icMRCC2 in cases with strong multireference character.
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Affiliation(s)
- Patrik Zielinski
- Institute for Theoretical
Chemistry, University of Stuttgart, Paffenwaldring 55, Stuttgart D-70569, Germany
| | | | - Andreas Köhn
- Institute for Theoretical
Chemistry, University of Stuttgart, Paffenwaldring 55, Stuttgart D-70569, Germany
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2
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Huang M, Evangelista FA. A study of core-excited states of organic molecules computed with the generalized active space driven similarity renormalization group. J Chem Phys 2023; 158:124112. [PMID: 37003756 DOI: 10.1063/5.0137096] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023] Open
Abstract
This work examines the accuracy and precision of x-ray absorption spectra computed with a multireference approach that combines generalized active space (GAS) references with the driven similarity renormalization group (DSRG). We employ the x-ray absorption benchmark of organic molecule (XABOOM) set, consisting of 116 transitions from mostly organic molecules [Fransson et al., J. Chem. Theory Comput. 17, 1618 (2021)]. Several approximations to a full-valence active space are examined and benchmarked. Absolute excitation energies and intensities computed with the GAS-DSRG truncated to second-order in perturbation theory are found to systematically underestimate experimental and reference theoretical values. Third-order perturbative corrections significantly improve the accuracy of GAS-DSRG absolute excitation energies, bringing the mean absolute deviation from experimental values down to 0.32 eV. The ozone molecule and glyoxylic acid are particularly challenging for second-order perturbation theory and are examined in detail to assess the importance of active space truncation and intruder states.
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Affiliation(s)
- Meng Huang
- 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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3
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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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4
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Khokhlov D, Belov A. Low-Lying Excited States of Natural Carotenoids Viewed by Ab Initio Methods. J Phys Chem A 2022; 126:4376-4391. [PMID: 35767689 DOI: 10.1021/acs.jpca.2c02485] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Low-lying excited states of carotenoids (the optically dark 2Ag- and bright 1Bu+) are deeply involved in energy transfer processes in photosynthetic antennas, such as light harvesting and non-photochemical quenching. Though any ab initio modeling of these phenomena has to rely on precise energies of the carotenoid electronic states, the accurate evaluation of these states remains a challenging problem due to their different natures. The paper aims to study the accuracy of the excitation energies of the low-lying excited states of certain open- and closed-chain carotenoids obtained by a state-of-the-art multireference approach for electronic structure calculation. Here, density matrix renormalization group SCF (DMRGSCF) and a perturbative approach based on driven similarity renormalization group second-order multireference perturbation theory (DSRG-MRPT2) were used to treat the static and dynamic correlation, respectively. Nuclear geometries of the electronic states were optimized with DFT-based approaches. It is demonstrated that spin-flip TD-DFT can replace multiconfigurational methods for the geometry optimization of the 2Ag- state but not for the calculation of the excitation energy. Adiabatic excitation energies to the 1Bu+ state were shown to be within a margin of 1000 cm-1 with an appropriate flow parameter value. Adiabatic excitation energies to the 2Ag- state for the open-chain carotenoids lie within a range of experimental values (taking into account the broad range of experimental estimates); for the closed-chain ones, the error does not exceed 2000 cm-1. Ab initio stationary (1Ag- → 1Bu+) and transient (2Ag- → 1Bu+) absorption spectra were modeled for violaxanthin and lycopene, and these spectra showed good agreement with the experimental ones both in terms of the vibronic structure and the transition energies.
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Affiliation(s)
- Daniil Khokhlov
- Department of Chemistry, Lomonosov Moscow State University, Moscow 119991, Russia
| | - Aleksandr Belov
- Department of Chemistry, Lomonosov Moscow State University, Moscow 119991, Russia
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5
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de Moura CEV, Sokolov AY. Simulating X-ray photoelectron spectra with strong electron correlation using multireference algebraic diagrammatic construction theory. Phys Chem Chem Phys 2022; 24:4769-4784. [DOI: 10.1039/d1cp05476g] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
A new theoretical approach for the simulations of X-ray photoelectron spectra of strongly correlated molecular systems that combines multireference algebraic diagrammatic construction theory (MR-ADC) with a core–valence separation (CVS) technique.
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Affiliation(s)
- Carlos E. V. de Moura
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio, 43210, USA
| | - Alexander Yu. Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio, 43210, USA
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6
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Mazin IM, Sokolov AY. Multireference Algebraic Diagrammatic Construction Theory for Excited States: Extended Second-Order Implementation and Benchmark. J Chem Theory Comput 2021; 17:6152-6165. [PMID: 34553937 DOI: 10.1021/acs.jctc.1c00684] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present an implementation and benchmark of new approximations in multireference algebraic diagrammatic construction theory for simulations of neutral electronic excitations and UV/vis spectra of strongly correlated molecular systems (MR-ADC). Following our work on the first-order MR-ADC approximation [J. Chem. Phys. 2018, 149, 204113], we report the strict and extended second-order MR-ADC methods (MR-ADC(2) and MR-ADC(2)-X) that combine the description of static and dynamic electron correlation in the ground and excited electronic states without relying on state-averaged reference wave functions. We present an extensive benchmark of the new MR-ADC methods for excited states in several small molecules, including the carbon dimer, ethylene, and butadiene. Our results demonstrate that, for weakly correlated electronic states, the MR-ADC(2) and MR-ADC(2)-X methods outperform the third-order single-reference ADC approximation and are competitive with the results from equation-of-motion coupled cluster theory. For states with multireference character, the performance of the MR-ADC methods is similar to that of an N-electron valence perturbation theory. In contrast to conventional multireference perturbation theories, the MR-ADC methods have many attractive features, such as a straightforward and efficient calculation of excited-state properties and a direct access to excitations outside of the frontier (active) orbitals.
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Affiliation(s)
- Ilia M Mazin
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Alexander Yu Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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7
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Khokhlov D, Belov A. Toward an Accurate Ab Initio Description of Low-Lying Singlet Excited States of Polyenes. J Chem Theory Comput 2021; 17:4301-4315. [PMID: 34125516 DOI: 10.1021/acs.jctc.0c01293] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Abstract
The low-lying excited states of carotenoids play a crucial role in many important biophysical processes such as photosynthesis. Most of these excited states are strongly correlated, which makes them both challenging for a qualitative ab initio description and an engaging model system for trying out emerging multireference methods. Among these methods, driven similarity renormalization group (DSRG) and its perturbative version (DSRG-MRPT2) are especially attractive in terms of both accuracy and moderate numerical complexity. In this paper, we applied density matrix renormalization group (DMRG) followed by DSRG-MRPT2 for the calculation of vertical and adiabatic excitation energies into the 2Ag-, 1Bu-, and 1Bu+ electronic states of polyenes containing from 8 to 13 conjugating double bonds acting as a model for natural carotenoids. It was shown that the DSRG flow parameter should be adjusted to ensure both the energy convergence with respect to it and the agreement with the experimental data. With the increased flow parameter, the proposed combination of methods provides a reasonable agreement with the experiment. The deviations of the adiabatic excitation energies are less than 1000 cm-1 for the 2Ag- and less than 3000 cm-1 for the excited states of the Bu symmetry, which in terms of accuracy significantly outperforms the N-electron valence state perturbation theory. At the same time, DSRG-MRPT2 is shown to be robust with respect to variation of quality of the DMRG reference wave function such as the orbital optimization or the number of electronic states in the averaging.
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Affiliation(s)
- Daniil Khokhlov
- Department of Chemistry, Lomonosov Moscow State University, Moscow, 119991, Russia
| | - Aleksandr Belov
- Department of Chemistry, Lomonosov Moscow State University, Moscow, 119991, Russia
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8
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Lechner MH, Izsák R, Nooijen M, Neese F. A perturbative approach to multireference equation-of-motion coupled cluster. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1939185] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Affiliation(s)
- Marvin H. Lechner
- Max-Planck-Institut für Kohlenforschung, Mülheim an der Ruhr, Germany
| | - Róbert Izsák
- Max-Planck-Institut für Kohlenforschung, Mülheim an der Ruhr, Germany
- Department of Chemistry and Biochemistry, Middlebury College, Middlebury, USA
| | - Marcel Nooijen
- Department of Chemistry, University of Waterloo, Waterloo, Canada
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Mülheim an der Ruhr, Germany
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9
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Musiał M, Kucharski SA, Bewicz A, Skupin P, Tomanek M. Electronic states of NaLi molecule: Benchmark results with Fock space coupled cluster approach. J Chem Phys 2021; 154:054109. [PMID: 33557573 DOI: 10.1063/5.0037441] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Accurate potential energy curves (PECs) are obtained for 20 lowest lying electronic states of the NaLi molecule. The computational scheme used here is based on the multireference coupled cluster theory formulated in the (2,0) sector of the Fock space. The latter sector provides the description of states obtained by attachment of two electrons to the reference system. This makes it possible to adopt the doubly ionized NaLi+2 molecule as a Fermi vacuum. The latter has a very concrete advantage in calculations of the PECs since it dissociates into closed shell fragments (NaLi+2 → Na+ + Li+); hence, the restricted Hartree-Fock method can be used within the whole range of interatomic distances. Computed PECs and spectroscopic constants stay very close to the experimental values (if the latter are available) with the accuracy exceeding the other theoretical approaches including those based on the effective core polarization potentials. Relativistic corrections included at the infinite-order two-component level have a non-negligible effect on the accuracy of computed excitation and dissociation energies with contributions up to 50 cm-1.
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Affiliation(s)
- Monika Musiał
- Institute of Chemistry, University of Silesia in Katowice, Szkolna 9, 40-006 Katowice, Poland
| | - Stanisław A Kucharski
- Institute of Chemistry, University of Silesia in Katowice, Szkolna 9, 40-006 Katowice, Poland
| | - Anna Bewicz
- Institute of Chemistry, University of Silesia in Katowice, Szkolna 9, 40-006 Katowice, Poland
| | - Patrycja Skupin
- Institute of Chemistry, University of Silesia in Katowice, Szkolna 9, 40-006 Katowice, Poland
| | - Magdalena Tomanek
- Institute of Chemistry, University of Silesia in Katowice, Szkolna 9, 40-006 Katowice, Poland
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10
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Meissner L, Musiał M, Kucharski SA. Extension of the Fock-space coupled-cluster method with singles and doubles to the three-valence sector. J Chem Phys 2020; 153:114115. [PMID: 32962357 DOI: 10.1063/5.0014941] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The single-reference coupled-cluster method has proven very effective in the ab initio description of atomic and molecular systems, but its successful application is limited to states dominated by a single Slater determinant, which is used as the reference. In cases where several determinants are important in the wave function expansion, i.e., we have to deal with nondynamic correlation effects, a multi-reference version of the coupled-cluster method is required. The multi-reference coupled-cluster approaches are based on the effective Hamiltonian formulation providing a two-step procedure, in which dynamic correlation effects can be efficiently evaluated by the wave operator, while nondynamic correlation contributions are given by diagonalization of the effective Hamiltonian in the final step. There are two classical multi-reference coupled-cluster formulations. In this paper, the focus is on the so-called Fock-space coupled-cluster method in its basic version with one- and two-particle operators in the exponent. Computational schemes using this truncation of the cluster operator have been successfully applied in calculations in one- and two-valence sectors of the Fock space. In this paper, we show that the approach can be easily extended and effectively employed in the three-valence sector calculations.
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Affiliation(s)
- Leszek Meissner
- Institute of Physics, Nicholaus Copernicus University, Grudziadzka 5/7, 87-100 Toruń, Poland
| | - Monika Musiał
- Institute of Chemistry, University of Silesia in Katowice, Szkolna 9, 40-006 Katowice, Poland
| | - Stanisław A Kucharski
- Institute of Chemistry, University of Silesia in Katowice, Szkolna 9, 40-006 Katowice, Poland
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11
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Chatterjee K, Sokolov AY. Extended Second-Order Multireference Algebraic Diagrammatic Construction Theory for Charged Excitations. J Chem Theory Comput 2020; 16:6343-6357. [DOI: 10.1021/acs.jctc.0c00778] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Koushik Chatterjee
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Alexander Yu. Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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12
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Khokhlov D, Belov A. Ab Initio Study of Low-Lying Excited States of Carotenoid-Derived Polyenes. J Phys Chem A 2020; 124:5790-5803. [PMID: 32573233 DOI: 10.1021/acs.jpca.0c01678] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Knowledge about excited states of carotenoids is essential for understanding photophysical processes underlying photosynthesis. However, due to the presence of a large number of optically dark states, experimental study of the excited-state manifold is limited to a significant extent. In this paper, we apply high-level ab initio quantum chemical methods to study the low-lying excited states of polyenes containing from 8 to 13 conjugated double bonds, which serve as a model for natural carotenoids. Vertical and adiabatic excitation energies from the ground 1Ag- state to the excited 2Ag-, 1Bu+, and 1Bu- states were evaluated by means of density matrix renormalization group (DMRG) with NEVPT2 perturbative correction. The energies of all excited states are highly sensitive to nuclear geometry, especially the 2Ag- state. Thus, the 2Ag- and 1Bu+ states interchange their relative positions upon geometry relaxation, while the vertical excitation energy to the 2Ag- state is rather high. At the same time, the 1Bu- state energy is shown to be higher than other studied excited states at any geometry. With relaxed geometries of the excited states, absorption and transient absorption spectra were calculated within the Franck-Condon approximation bridging the gap between experimental spectroscopic data and computational results.
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Affiliation(s)
- Daniil Khokhlov
- Department of Chemistry, Lomonosov Moscow State University, Moscow 119991, Russia
| | - Aleksandr Belov
- Department of Chemistry, Lomonosov Moscow State University, Moscow 119991, Russia
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13
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Musiał M, Meissner L, Cembrzynska J. The intermediate Hamiltonian Fock-space coupled-cluster method with approximate evaluation of the three-body effects. J Chem Phys 2019; 151:184102. [DOI: 10.1063/1.5124806] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Monika Musiał
- Institute of Chemistry, University of Silesia in Katowice, Szkolna 9, 40-006 Katowice, Poland
| | - Leszek Meissner
- Institute of Physics, Nicholaus Copernicus University, Grudziadzka 5/7, 87-100 Toruń, Poland
| | - Justyna Cembrzynska
- Institute of Physics, Nicholaus Copernicus University, Grudziadzka 5/7, 87-100 Toruń, Poland
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14
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Chatterjee K, Sokolov AY. Second-Order Multireference Algebraic Diagrammatic Construction Theory for Photoelectron Spectra of Strongly Correlated Systems. J Chem Theory Comput 2019; 15:5908-5924. [DOI: 10.1021/acs.jctc.9b00528] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Koushik Chatterjee
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Alexander Yu. Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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15
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Köhn A, Bargholz A. The second-order approximate internally contracted multireference coupled-cluster singles and doubles method icMRCC2. J Chem Phys 2019; 151:041106. [DOI: 10.1063/1.5115045] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
Affiliation(s)
- Andreas Köhn
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
| | - Arne Bargholz
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
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16
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Abstract
The accuracy of three different complete active space (CAS) self-consistent field (CASSCF) methods is investigated for the electronically excited-state benchmark set of Schreiber , M. ; et al. J. Chem. Phys. 2008 , 128 , 134110 . Comparison of the CASSCF linear response (LR) methods MC-RPA and MC-TDA and the state-averaged (SA) CASSCF method is made for 122 singlet excitation energies and 69 oscillator strengths. Of all CASSCF methods, when considering the complete test set, MC-RPA performs best for both excitation energies and oscillator strengths with a mean absolute error (MAE) of 0.74 eV and 51%, respectively. MC-TDA and SA-CASSCF show a similar accuracy for the excitation energies with a MAE of ∼1 eV with respect to more accurate coupled cluster (CC3) excitation energies. The opposite trend is observed for the subset of n → π* excitation energies for which SA-CASSCF exhibits the least deviations (MAE 0.65 eV). By looking at s-tetrazine in more detail, we conclude that better performance for the n → π* SA-CASSCF excitation energies can be attributed to a fortunate error compensation. For oscillator strengths, SA-CASSCF performs worst for the complete test set (MAE 100%) as well as for the subsets of n → π* (MAE 192%) and π → π* excitations (MAE 84.9%). In general, CASSCF gives the worst performance for excitation energies of all excited-state ab initio methods considered so far due to lacking the major part of dynamic electron correlation, though MC-RPA and TD-DFT (BP86) show similar performance. Among all LR-type methods, LR-CASSCF oscillator strengths are the ones with the least accuracy for the same reason. As state-specific orbital relaxation effects are accounted for in LR-CASSCF, oscillator strengths are significantly more accurate than those of MS-CASPT2. Our findings should encourage further developments of response theory-based multireference methods with higher accuracy and feasibility.
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Affiliation(s)
- Benjamin Helmich-Paris
- Max-Planck-Institut für Kohlenforschung , Kaiser-Wilhelm-Platz 1 , D-45470 Mülheim an der Ruhr , Germany
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17
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Helmich-Paris B. CASSCF linear response calculations for large open-shell molecules. J Chem Phys 2019; 150:174121. [PMID: 31067879 DOI: 10.1063/1.5092613] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The complete active space self-consistent-field (CASSCF) linear response method for the simulation of ultraviolet-visible (UV/Vis) absorption and electronic circular dichroism (ECD) spectra of large open-shell molecules is presented. By using a one-index transformed Hamiltonian, the computation of the most time-consuming intermediates can be pursued in an integral-direct fashion, which allows us to employ the efficient resolution-of-the-identity and overlap-fitted chain-of-spheres approximation. For the iterative diagonalization, pairs of Hermitian and anti-Hermitian trial vectors are used which facilitate, on the one hand, an efficient solution of the pair-structured generalized eigenvalue problem in the reduced space, and on the other hand, make the full multiconfigurational random phase approximation as efficient as the corresponding Tamm-Dancoff approximation. Electronic transitions are analyzed and characterized in the particle-hole picture by natural transition orbitals that are introduced for CASSCF linear response theory. For a small organic radical, we can show that the accuracy of simulated UV/Vis absorption spectra with the CASSCF linear response approach is significantly improved compared to the popular state-averaged CASSCF method. To demonstrate the efficiency of the implementation, the 50 lowest roots of a large Ni triazole complex with 231 atoms are computed for the simulated UV/Vis and ECD spectra.
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Affiliation(s)
- Benjamin Helmich-Paris
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
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18
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Sokolov AY. Multi-reference algebraic diagrammatic construction theory for excited states: General formulation and first-order implementation. J Chem Phys 2018; 149:204113. [DOI: 10.1063/1.5055380] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Alexander Yu. Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
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19
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Nanda KD, Krylov AI, Gauss J. Communication: The pole structure of the dynamical polarizability tensor in equation-of-motion coupled-cluster theory. J Chem Phys 2018; 149:141101. [DOI: 10.1063/1.5053727] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kaushik D. Nanda
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, USA
| | - Anna I. Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, USA
- Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Jürgen Gauss
- Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
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20
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Sen A, de Souza B, Huntington LMJ, Krupička M, Neese F, Izsák R. An efficient pair natural orbital based configuration interaction scheme for the calculation of open-shell ionization potentials. J Chem Phys 2018; 149:114108. [DOI: 10.1063/1.5048688] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Avijit Sen
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
| | - Bernardo de Souza
- Max-Planck-Institute for Chemical Energy Conversion, Mülheim an der Ruhr, Germany
- Universidade Federal de Santa Catarina, Florianópolis, Brazil
| | - Lee M. J. Huntington
- Max-Planck-Institute for Chemical Energy Conversion, Mülheim an der Ruhr, Germany
| | - Martin Krupička
- Max-Planck-Institute for Chemical Energy Conversion, Mülheim an der Ruhr, Germany
- University of Chemistry and Technology, Prague, Czech Republic
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
| | - Róbert Izsák
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
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21
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Pastorczak E, Pernal K. Electronic Excited States from the Adiabatic-Connection Formalism with Complete Active Space Wave Functions. J Phys Chem Lett 2018; 9:5534-5538. [PMID: 30192553 DOI: 10.1021/acs.jpclett.8b02391] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
It is demonstrated how the recently proposed multireference adiabatic-connection (AC) approximation for electron correlation energy ( Pernal , K. Electron Correlation from the Adiabatic Connection for Multireference Wave Functions . Phys. Rev. Lett. 2018 , 120 , 013001 ) can be extended to predicting correlation energy in excited states of molecules. It is the first successful application of the AC approach to computing excited-states energies of molecules using a complete active space (CAS) wave function as a reference. The unique feature of the AC-CAS approach with respect to popular methods such as CASPT2 and NEVPT2 is that it requires only one- and two-particle reduced density matrices, making it possible to efficiently treat large spaces of active electrons. Application of the simpler variant of AC, the AC0, which is based on the first-order expansion of the AC integrand at the uncorrelated system limit, to excited states yields excitation energies with accuracy rivaling that of the NEVPT2 method but at greatly reduced computational cost.
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Affiliation(s)
- Ewa Pastorczak
- Institute of Physics , Lodz University of Technology , ul. Wolczanska 219 , 90-924 Lodz , Poland
| | - Katarzyna Pernal
- Institute of Physics , Lodz University of Technology , ul. Wolczanska 219 , 90-924 Lodz , Poland
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22
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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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23
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Lischka H, Nachtigallová D, Aquino AJA, Szalay PG, Plasser F, Machado FBC, Barbatti M. Multireference Approaches for Excited States of Molecules. Chem Rev 2018; 118:7293-7361. [DOI: 10.1021/acs.chemrev.8b00244] [Citation(s) in RCA: 197] [Impact Index Per Article: 32.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Hans Lischka
- School of Pharmaceutical Sciences and Technology, Tianjin University, Tianjin 300072, P.R. China
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, United States
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria
| | - Dana Nachtigallová
- Institute of Organic Chemistry and Biochemistry v.v.i., The Czech Academy of Sciences, Flemingovo nám. 2, 16610 Prague 6, Czech Republic
- Regional Centre of Advanced Technologies and Materials, Palacký University, 78371 Olomouc, Czech Republic
| | - Adélia J. A. Aquino
- School of Pharmaceutical Sciences and Technology, Tianjin University, Tianjin 300072, P.R. China
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, United States
- Institute for Soil Research, University of Natural Resources and Life Sciences Vienna, Peter-Jordan-Strasse 82, A-1190 Vienna, Austria
| | - Péter G. Szalay
- ELTE Eötvös Loránd University, Laboratory of Theoretical Chemistry, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
| | - Felix Plasser
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria
- Department of Chemistry, Loughborough University, Leicestershire LE11 3TU, United Kingdom
| | - Francisco B. C. Machado
- Departamento de Química, Instituto Tecnológico de Aeronáutica, São José dos Campos 12228-900, São Paulo, Brazil
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24
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Evangelista FA. Perspective: Multireference coupled cluster theories of dynamical electron correlation. J Chem Phys 2018; 149:030901. [DOI: 10.1063/1.5039496] [Citation(s) in RCA: 69] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Affiliation(s)
- Francesco A. Evangelista
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
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25
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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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26
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Rolik Z, Kállay M. Novel strategy to implement active-space coupled-cluster methods. J Chem Phys 2018; 148:124108. [PMID: 29604813 DOI: 10.1063/1.5004971] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new approach is presented for the efficient implementation of coupled-cluster (CC) methods including higher excitations based on a molecular orbital space partitioned into active and inactive orbitals. In the new framework, the string representation of amplitudes and intermediates is used as long as it is beneficial, but the contractions are evaluated as matrix products. Using a new diagrammatic technique, the CC equations are represented in a compact form due to the string notations we introduced. As an application of these ideas, a new automated implementation of the single-reference-based multi-reference CC equations is presented for arbitrary excitation levels. The new program can be considered as an improvement over the previous implementations in many respects; e.g., diagram contributions are evaluated by efficient vectorized subroutines. Timings for test calculations for various complete active-space problems are presented. As an application of the new code, the weak interactions in the Be dimer were studied.
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Affiliation(s)
- Zoltán Rolik
- MTA-BME "Lendület" Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, H-1521 Budapest, Hungary
| | - Mihály Kállay
- MTA-BME "Lendület" Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, H-1521 Budapest, Hungary
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27
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Coughtrie DJ, Giereth R, Kats D, Werner HJ, Köhn A. Embedded Multireference Coupled Cluster Theory. J Chem Theory Comput 2018; 14:693-709. [DOI: 10.1021/acs.jctc.7b01144] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- David J. Coughtrie
- Institute for Theoretical
Chemistry, University of Stuttgart, 70569 Stuttgart, Germany
| | - Robin Giereth
- Institute for Theoretical
Chemistry, University of Stuttgart, 70569 Stuttgart, Germany
| | - Daniel Kats
- Institute for Theoretical
Chemistry, University of Stuttgart, 70569 Stuttgart, Germany
| | - Hans-Joachim Werner
- Institute for Theoretical
Chemistry, University of Stuttgart, 70569 Stuttgart, Germany
| | - Andreas Köhn
- Institute for Theoretical
Chemistry, University of Stuttgart, 70569 Stuttgart, Germany
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28
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Chowdhury UD, Bag A. Excited state hyperpolarizability of LiAlH4 computed at the FSMRCCSD level and its use for mixed-frequency laser. Theor Chem Acc 2018. [DOI: 10.1007/s00214-018-2203-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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29
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Li C, Verma P, Hannon KP, Evangelista FA. A low-cost approach to electronic excitation energies based on the driven similarity renormalization group. J Chem Phys 2017; 147:074107. [DOI: 10.1063/1.4997480] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Affiliation(s)
- Chenyang Li
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Prakash Verma
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Kevin P. Hannon
- 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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30
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Saito T, Kitagawa Y, Takano Y. Reparameterization of PM6 Applied to Organic Diradical Molecules. J Phys Chem A 2016; 120:8750-8760. [DOI: 10.1021/acs.jpca.6b08530] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Toru Saito
- Department
of Biomedical Information Sciences, Graduate School of
Information Sciences, Hiroshima City University, 3-4-1 Ozuka-Higashi, Asa-Minami-Ku, Hiroshima 731-3194, Japan
| | - Yasutaka Kitagawa
- Division of Chemical
Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
- Center
for Spintronics Research Network (CSRN), Graduate School
of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Yu Takano
- Department
of Biomedical Information Sciences, Graduate School of
Information Sciences, Hiroshima City University, 3-4-1 Ozuka-Higashi, Asa-Minami-Ku, Hiroshima 731-3194, Japan
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31
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Segarra-Martí J, Garavelli M, Aquilante F. Multiconfigurational Second-Order Perturbation Theory with Frozen Natural Orbitals Extended to the Treatment of Photochemical Problems. J Chem Theory Comput 2016; 11:3772-84. [PMID: 26574459 DOI: 10.1021/acs.jctc.5b00479] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A new flavor of the frozen natural orbital complete active space second-order perturbation theory method (FNO-CASPT2, Aquilante et al., J. Chem. Phys. 131, 034113) is proposed herein. In this new implementation, the virtual space in Cholesky decomposition-based CASPT2 computations (CD-CASPT2) is truncated by excluding those orbitals that contribute the least toward preserving a predefined value of the trace of an approximate density matrix, as that represents a measure of the amount of dynamic correlation retained in the model. In this way, the amount of correlation included is practically constant at all nuclear arrangements, thus allowing for the computation of smooth electronic states surfaces and energy gradients-essential requirements for theoretical studies in photochemistry. The method has been benchmarked for a series of relevant biochromophores for which large speed-ups have been recorded while retaining the accuracy achieved in the corresponding CD-CASPT2 calculations. Both vertical excitation energies and gradient calculations have been carried out to establish general guidelines as to how much correlation needs to be retained in the calculation for the results to be consistent with the CD-CASPT2 findings. Our results feature errors within a tenth of an eV for the most difficult cases and have been validated to be used for gradient computations where an up to 3-fold speed-up is observed depending on the size of the system and the basis set employed.
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Affiliation(s)
- Javier Segarra-Martí
- Dipartimento di Chimica "G. Ciamician", Università di Bologna , Via Selmi 2, IT-40126 Bologna, Italy
| | - Marco Garavelli
- Dipartimento di Chimica "G. Ciamician", Università di Bologna , Via Selmi 2, IT-40126 Bologna, Italy.,Université de Lyon, CNRS , Institut de Chimie de Lyon, École Normale Supérieure de Lyon, 46 Allée d'Italie, F-69364 Lyon Cedex 07, France
| | - Francesco Aquilante
- Dipartimento di Chimica "G. Ciamician", Università di Bologna , Via Selmi 2, IT-40126 Bologna, Italy
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32
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Aoto YA, Köhn A. Internally contracted multireference coupled-cluster theory in a multistate framework. J Chem Phys 2016; 144:074103. [DOI: 10.1063/1.4941604] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Yuri Alexandre Aoto
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
| | - Andreas Köhn
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
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33
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Huntington LMJ, Demel O, Nooijen M. Benchmark Applications of Variations of Multireference Equation of Motion Coupled-Cluster Theory. J Chem Theory Comput 2015; 12:114-32. [DOI: 10.1021/acs.jctc.5b00799] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Lee M. J. Huntington
- Department
of Chemistry, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
| | - Ondřej Demel
- J.
Heyrovský Institute of Physical Chemistry, v. v. i., Academy of Sciences of the Czech Republic, Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Marcel Nooijen
- Department
of Chemistry, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
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34
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Rolik Z, Kállay M. A quasiparticle-based multi-reference coupled-cluster method. J Chem Phys 2014; 141:134112. [DOI: 10.1063/1.4896703] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Zoltán Rolik
- MTA-BME “Lendület” Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, H-1521 Budapest, Hungary
| | - Mihály Kállay
- MTA-BME “Lendület” Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, H-1521 Budapest, Hungary
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