1
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Vidal L, Nottoli T, Lipparini F, Cancès E. Geometric Optimization of Restricted-Open and Complete Active Space Self-Consistent Field Wave Functions. J Phys Chem A 2024. [PMID: 39073092 DOI: 10.1021/acs.jpca.4c03213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/30/2024]
Abstract
We explore Riemannian optimization methods for Restricted-Open-shell Hartree-Fock (ROHF) and Complete Active Space Self-Consistent Field (CASSCF) methods. After showing that ROHF and CASSCF can be reformulated as optimization problems on so-called "flag manifolds", we review Riemannian optimization basics and their application to these specific problems. We compare these methods to traditional ones and find robust convergence properties without fine-tuning of numerical parameters. Our study suggests that Riemannian optimization is a valuable addition to orbital optimization for ROHF and CASSCF, warranting further investigation.
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Affiliation(s)
- Laurent Vidal
- CERMICS, Ecole des Ponts and Inria Paris, 6 & 8 Avenue Blaise Pascal, 77455 Marne-la-Vallée, France
| | - Tommaso Nottoli
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, 56124 Pisa, Italy
| | - Filippo Lipparini
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, 56124 Pisa, Italy
| | - Eric Cancès
- CERMICS, Ecole des Ponts and Inria Paris, 6 & 8 Avenue Blaise Pascal, 77455 Marne-la-Vallée, France
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2
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Leyser da Costa Gouveia T, Maganas D, Neese F. Restricted Open-Shell Hartree-Fock Method for a General Configuration State Function Featuring Arbitrarily Complex Spin-Couplings. J Phys Chem A 2024; 128:5041-5053. [PMID: 38886177 PMCID: PMC11215774 DOI: 10.1021/acs.jpca.4c00688] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2024] [Revised: 05/30/2024] [Accepted: 05/30/2024] [Indexed: 06/20/2024]
Abstract
In this work, we present a general spin restricted open-shell Hartree-Fock (ROHF) implementation that is able to generate self-consistent field (SCF) wave functions for an arbitrary configuration state function (CSF). These CSFs can contain an arbitrary number of unpaired electrons in arbitrary spin-couplings. The resulting method is named CSF-ROHF. We demonstrate that starting from the ROHF energy expression, for example, the one given by Edwards and Zerner, it is possible to obtain the values of the ROHF vector-coupling coefficients by setting up an open-shell for each group of consecutive parallel-coupled spins dictated by the unique spin-coupling pattern of any given CSF. To achieve this important and nontrivial goal, we employ the machinery of the iterative configuration expansion configuration interaction (ICE-CI) method, which is able to tackle general CI problems on the basis of spin-adapted CSFs. This development allows for the efficient generation of SCF spin-eigenfunctions for systems with complex spin-coupling patterns, such as polymetallic chains and metal clusters, while maintaining SCF scaling with system size (quadratic or less, depending on the specific algorithm and approximations chosen).
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Affiliation(s)
| | - Dimitrios Maganas
- Max-Planck-Institut für
Kohlenforschung, Kaiser-Wilhelm-Platz 1, Mülheim an der Ruhr 45470, Germany
| | - Frank Neese
- Max-Planck-Institut für
Kohlenforschung, Kaiser-Wilhelm-Platz 1, Mülheim an der Ruhr 45470, Germany
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3
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Daas K, Klute E, Seidl M, Gori-Giorgi P. Møller-Plesset Adiabatic Connection at Large Coupling Strengths for Open-Shell Systems. J Phys Chem A 2024; 128:4138-4149. [PMID: 38717868 PMCID: PMC11129316 DOI: 10.1021/acs.jpca.4c00788] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2024] [Revised: 03/29/2024] [Accepted: 04/05/2024] [Indexed: 05/24/2024]
Abstract
We study the adiabatic connection that has as weak-coupling expansion the Møller-Plesset perturbation series, generalizing to the open-shell case previous closed-shell results for the large-coupling limit. We first focus on the hydrogen atom with fractional spins, providing results along the adiabatic connection from small to large coupling strengths. We reveal an intriguing phase diagram and an equation for the large-coupling leading order that has closed-form solutions for specific choices of its relevant quantum numbers. We then show that the hydrogen atom results provide variational estimates for the large-coupling leading terms for the general many-electron open-shell case in terms of functionals of the Hartree-Fock α-spin and β-spin densities.
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Affiliation(s)
- Kimberly
J. Daas
- Department
of Chemistry & Pharmaceutical Sciences and Amsterdam Institute
of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, Amsterdam 1081 HV, The Netherlands
| | - Eveline Klute
- Department
of Chemistry & Pharmaceutical Sciences and Amsterdam Institute
of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, Amsterdam 1081 HV, The Netherlands
| | - Michael Seidl
- Department
of Chemistry & Pharmaceutical Sciences and Amsterdam Institute
of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, Amsterdam 1081 HV, The Netherlands
| | - Paola Gori-Giorgi
- Department
of Chemistry & Pharmaceutical Sciences and Amsterdam Institute
of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, Amsterdam 1081 HV, The Netherlands
- Microsoft
Research AI for Science, Evert van de Beekstraat 354, Schiphol 1118 CZ, The Netherlands
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4
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Paul née Matveeva R, Folkestad SD, Sannes BS, Høyvik IM. Particle-Breaking Unrestricted Hartree-Fock Theory for Open Molecular Systems. J Phys Chem A 2024; 128:1533-1542. [PMID: 38351699 PMCID: PMC10910564 DOI: 10.1021/acs.jpca.3c07231] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Revised: 02/02/2024] [Accepted: 02/02/2024] [Indexed: 03/01/2024]
Abstract
We recently introduced the particle-breaking restricted Hartree-Fock (PBRHF) model, a mean-field approach to address the fractional charging of molecules when they interact with an electronic environment. In this paper, we present an extension of the model referred to as particle-breaking unrestricted Hartree-Fock (PBUHF). The unrestricted formulation contains odd-electron states necessary for a realistic description of fractional charging. Within the PBUHF parametrization, we use two-body operators as they yield convenient operator transformations. However, two-body operators can change only the particle number by two. Therefore, we include noninteracting zero-energy bath orbitals to generate a linear combination of even and odd electron states. Depending on whether the occupied or virtual orbitals of a molecule interact with the environment, the average number of electrons is either decreased or increased. Without interaction, PBUHF reduces to the unrestricted Hartree-Fock wave function.
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Affiliation(s)
- Regina Paul née Matveeva
- Department of Chemistry, The
Norwegian University of Science and Technology, Trondheim 7491, Norway
| | - Sarai Dery Folkestad
- Department of Chemistry, The
Norwegian University of Science and Technology, Trondheim 7491, Norway
| | - Bendik Støa Sannes
- Department of Chemistry, The
Norwegian University of Science and Technology, Trondheim 7491, Norway
| | - Ida-Marie Høyvik
- Department of Chemistry, The
Norwegian University of Science and Technology, Trondheim 7491, Norway
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5
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Irimia M, Wang J. Self-consistent field method for open-shell systems within the density-matrix functional theory. J Comput Chem 2024; 45:222-229. [PMID: 37702200 DOI: 10.1002/jcc.27232] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2023] [Revised: 08/22/2023] [Accepted: 09/05/2023] [Indexed: 09/14/2023]
Abstract
The unrestricted Hartree-Fock method is extended to correlation calculation within the density-matrix functional theory. The method is derived from an entropic cumulant functional for the correlation energy. The eigenvalue equations for the spin-orbitals are modified by the orbital occupation numbers. The Euler equation for the occupation numbers results in the Fermi-Dirac distribution, which is very efficient to update as soon as the orbital eigenvalue equations are solved. The method is demonstrated on the ground state of O2 .
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Affiliation(s)
| | - Jian Wang
- School of Science, Huzhou University, Zhejiang, China
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6
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King DS, Truhlar DG, Gagliardi L. Variational Active Space Selection with Multiconfiguration Pair-Density Functional Theory. J Chem Theory Comput 2023; 19:8118-8128. [PMID: 37905518 DOI: 10.1021/acs.jctc.3c00792] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2023]
Abstract
The selection of an adequate set of active orbitals for modeling strongly correlated electronic states is difficult to automate because it is highly dependent on the states and molecule of interest. Although many approaches have shown some success, no single approach has worked well in all cases. In light of this, we present the "discrete variational selection" (DVS) approach to active space selection, in which one generates multiple trial wave functions from a diverse set of systematically constructed active spaces and then selects between these wave functions variationally. We apply this DVS approach to 207 vertical excitations of small-to-medium-sized organic and inorganic molecules (with 3 to 18 atoms) in the QUESTDB database by (i) constructing various sets of active space orbitals through diagonalization of parametrized operators and (ii) choosing the result with the lowest average energy among the states of interest. This approach proves ineffective when variationally selecting between wave functions using the density matrix renormalization group (DMRG) or complete active space self-consistent field (CASSCF) energy but is able to provide good results when variationally selecting between wave functions using the energy of the translated PBE (tPBE) functional from multiconfiguration pair-density functional theory (MC-PDFT). Applying this DVS-tPBE approach to selection among state-averaged DMRG wave functions, we obtain a mean unsigned error of only 0.17 eV using hybrid MC-PDFT. This result matches that of our previous benchmark without the need to filter out poor active spaces and with no further orbital optimization following active space selection of the SA-DMRG wave functions. Furthermore, we find that DVS-tPBE is able to robustly and effectively select between the new SA-DMRG wave functions and our previous SA-CASSCF results.
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Affiliation(s)
- Daniel S King
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Group, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Laura Gagliardi
- Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois 60637, United States
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7
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Hostaš J, Pérez-Becerra KO, Calaminici P, Barrios-Herrera L, Lourenço MP, Tchagang A, Salahub DR, Köster AM. How important is the amount of exact exchange for spin-state energy ordering in DFT? Case study of molybdenum carbide cluster, Mo4C2. J Chem Phys 2023; 159:184301. [PMID: 37947508 DOI: 10.1063/5.0169409] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2023] [Accepted: 10/23/2023] [Indexed: 11/12/2023] Open
Abstract
Since the form of the exact functional in density functional theory is unknown, we must rely on density functional approximations (DFAs). In the past, very promising results have been reported by combining semi-local DFAs with exact, i.e. Hartree-Fock, exchange. However, the spin-state energy ordering and the predictions of global minima structures are particularly sensitive to the choice of the hybrid functional and to the amount of exact exchange. This has been already qualitatively described for single conformations, reactions, and a limited number of conformations. Here, we have analyzed the mixing of exact exchange in exchange functionals for a set of several hundred isomers of the transition metal carbide, Mo4C2. The analysis of the calculated energies and charges using PBE0-type functional with varying amounts of exact exchange yields the following insights: (1) The sensitivity of spin-energy splitting is strongly correlated with the amount of exact exchange mixing. (2) Spin contamination is exacerbated when correlation is omitted from the exchange-correlation functional. (3) There is not one ideal value for the exact exchange mixing which can be used to parametrize or choose among the functionals. Calculated energies and electronic structures are influenced by exact exchange at a different magnitude within a given distribution; therefore, to extend the application range of hybrid functionals to the full periodic table the spin-energy splitting energies should be investigated.
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Affiliation(s)
- Jiří Hostaš
- Department of Chemistry, CMS - Centre for Molecular Simulation, IQST - Institute for Quantum Science and Technology, Quantum Alberta, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
| | - Kevin O Pérez-Becerra
- Departamento de Química, Cinvestav, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740, CDMX C.P. 07360, Mexico
| | - Patrizia Calaminici
- Departamento de Química, Cinvestav, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740, CDMX C.P. 07360, Mexico
| | - Lizandra Barrios-Herrera
- Department of Chemistry, CMS - Centre for Molecular Simulation, IQST - Institute for Quantum Science and Technology, Quantum Alberta, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
| | - Maicon Pierre Lourenço
- Departamento de Química e Física - Centro de Ciências Exatas, Naturais e da Saúde - CCENS - Universidade Federal do Espírito Santo, 29500-000 Alegre, Espírito Santo, Brazil
| | - Alain Tchagang
- Digital Technologies Research Centre, National Research Council of Canada, 1200 Montréal Road, Ottawa, Ontario K1A 0R6, Canada
| | - Dennis R Salahub
- Department of Chemistry, CMS - Centre for Molecular Simulation, IQST - Institute for Quantum Science and Technology, Quantum Alberta, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
| | - Andreas M Köster
- Departamento de Química, Cinvestav, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740, CDMX C.P. 07360, Mexico
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8
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Yu H, Song S, Nam S, Burke K, Sim E. Density-Corrected Density Functional Theory for Open Shells: How to Deal with Spin Contamination. J Phys Chem Lett 2023; 14:9230-9237. [PMID: 37811877 DOI: 10.1021/acs.jpclett.3c02017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/10/2023]
Abstract
Density functional theory (DFT) is usually used self-consistently to predict chemical properties, but the use of the Hartree-Fock (HF) density improves energetics in certain, well-characterized cases. Density-corrected (DC) DFT provides the theory behind this, but unrestricted Hartree-Fock (UHF) densities yield poor energetics in cases of strong spin contamination. Here we compare with restricted open-shell HF (ROHF) across 13 different functionals and two DC-DFT methods. For significant spin contamination, ROHF densities outperform UHF densities by as much as a factor of 3, depending on the energy functional, and ROHF-DFT improves over self-consistent DFT for most of the tested functionals. We refine the DC(HF)-DFT algorithm to use ROHF densities in cases of severe spin contamination.
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Affiliation(s)
- Hayoung Yu
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - Suhwan Song
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - Seungsoo Nam
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - Kieron Burke
- Department of Chemistry, University of California, Irvine, California 92697, United States
| | - Eunji Sim
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
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9
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Izsák R, Ivanov AV, Blunt NS, Holzmann N, Neese F. Measuring Electron Correlation: The Impact of Symmetry and Orbital Transformations. J Chem Theory Comput 2023; 19:2703-2720. [PMID: 37022051 PMCID: PMC10210250 DOI: 10.1021/acs.jctc.3c00122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Indexed: 04/07/2023]
Abstract
In this perspective, the various measures of electron correlation used in wave function theory, density functional theory and quantum information theory are briefly reviewed. We then focus on a more traditional metric based on dominant weights in the full configuration solution and discuss its behavior with respect to the choice of the N-electron and the one-electron basis. The impact of symmetry is discussed, and we emphasize that the distinction among determinants, configuration state functions and configurations as reference functions is useful because the latter incorporate spin-coupling into the reference and should thus reduce the complexity of the wave function expansion. The corresponding notions of single determinant, single spin-coupling and single configuration wave functions are discussed and the effect of orbital rotations on the multireference character is reviewed by analyzing a simple model system. In molecular systems, the extent of correlation effects should be limited by finite system size and in most cases the appropriate choices of one-electron and N-electron bases should be able to incorporate these into a low-complexity reference function, often a single configurational one.
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Affiliation(s)
- Róbert Izsák
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Aleksei V. Ivanov
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Nick S. Blunt
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Nicole Holzmann
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Frank Neese
- Max-Planck
Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
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10
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Tian XY, Zheng YZ, Zhang YC. Molecular design of efficient SO3H-functionalized ionic liquid to catalyse chitin into levulinic acid: NMR and DFT study. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.120735] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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11
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Izsák R. Second quantisation for unrestricted references: formalism and quasi-spin-adaptation of excitation and spin-flip operators. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2126802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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12
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De Vriendt X, Lemmens L, De Baerdemacker S, Bultinck P, Acke G. Quantifying Delocalization and Static Correlation Errors by Imposing (Spin)Population Redistributions through Constraints on Atomic Domains. J Chem Theory Comput 2021; 17:6808-6818. [PMID: 34597030 DOI: 10.1021/acs.jctc.1c00326] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The failure of many density functional approximations can be traced to their behavior under fractional (spin)population redistributions in the asymptotic limit toward infinite bonding distances, which should obey the flat-plane conditions. However, such errors can only be characterized sufficiently in terms of those redistributions if exact energies are available for many possible (spin)population redistributions at different bonding distances. In this study, we propose to model such redistributions by imposing (spin)populations on atomic domains by constraining full configuration interaction wave functions. The resulting N-representable descriptions of small hydrogen chains at different bonding distances allow us to computationally illustrate the effects of the flat-plane conditions in the limit to infinite bond distances, leading to more chemical insight into those flat-plane conditions. As the proposed methodology is able to capture the effects of the flat plane conditions, it could be used to generate the reference data that is required to measure the extent to which approximate methods violate the requirements of the exact functional, leading to a quantification of the delocalization and static correlation error of such methods.
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Affiliation(s)
- Xeno De Vriendt
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 S3, B-9000 Ghent, Belgium
| | - Laurent Lemmens
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 S3, B-9000 Ghent, Belgium
| | - Stijn De Baerdemacker
- Department of Chemistry, University of New Brunswick, 30 Dineen Drive, Fredericton, New Brunswick E3B 5A3, Canada
| | - Patrick Bultinck
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 S3, B-9000 Ghent, Belgium
| | - Guillaume Acke
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 S3, B-9000 Ghent, Belgium
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13
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Nottoli T, Gauss J, Lipparini F. A black-box, general purpose quadratic self-consistent field code with and without Cholesky decomposition of the two-electron integrals. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1974590] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Tommaso Nottoli
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Pisa, Italy
| | - Jürgen Gauss
- Department Chemie, Johannes Gutenberg-Universität Mainz, Mainz, Germany
| | - Filippo Lipparini
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Pisa, Italy
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14
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Lemmens L, De Vriendt X, Tolstykh D, Huysentruyt T, Bultinck P, Acke G. GQCP: The Ghent Quantum Chemistry Package. J Chem Phys 2021; 155:084802. [PMID: 34470369 DOI: 10.1063/5.0057515] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
The Ghent Quantum Chemistry Package (GQCP) is an open-source electronic structure software package that aims to provide an intuitive and expressive software framework for electronic structure software development. Its high-level interfaces (accessible through C++ and Python) have been specifically designed to correspond to theoretical concepts, while retaining access to lower-level intermediates and allowing structural run-time modifications of quantum chemical solvers. GQCP focuses on providing quantum chemical method developers with the computational "building blocks" that allow them to flexibly develop proof of principle implementations for new methods and applications up to the level of two-component spinor bases.
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Affiliation(s)
- Laurent Lemmens
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
| | - Xeno De Vriendt
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
| | - Daria Tolstykh
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
| | - Tobias Huysentruyt
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
| | - Patrick Bultinck
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
| | - Guillaume Acke
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
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15
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Tsuchimochi T, Yoshimura K, Shimomoto Y, Ten-No SL. Improved Description and Efficient Implementation of Spin-Projected Perturbation Theory for Practical Applications. J Chem Theory Comput 2021; 17:3471-3482. [PMID: 33971717 DOI: 10.1021/acs.jctc.1c00324] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
In this study, we continue to develop the recently proposed second-order perturbation theory for the spin-projected Hartree-Fock method [Tsuchimochi, T.; Ten-no, S. L. J. Chem. Theory Comput. 2019, 15, 6688] in various aspects. A new, stable imaginary level-shift scheme is derived to obtain a well-conditioned equation, enabling a significantly faster convergence. To achieve a further speed-up, we propose a preconditioning scheme considering the pair character on a spin-projected basis. We also eliminate the computational memory bottleneck in solving the linear equation for large systems using a distributed memory parallel implementation. Finally, for the description of open-shell molecules, several modified zeroth-order Hamiltonians are introduced and tested using the Mn2O2(NHCHCO2)4 complex. These developments enable practical calculations of a second-order perturbation theory with improved accuracy at a reduced computational cost.
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Affiliation(s)
- Takashi Tsuchimochi
- Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan
| | - Kosuke Yoshimura
- Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan
| | - Yuma Shimomoto
- Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan
| | - Seiichiro L Ten-No
- Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan.,Graduate School of Science, Technology, and Innovation, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan
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16
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Tao Y, Pei Z, Bellonzi N, Mao Y, Zou Z, Liang W, Yang Z, Shao Y. Constructing Spin-Adiabatic States for the Modeling of Spin-Crossing Reactions. I. A Shared-Orbital Implementation. INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 2020; 120:e26123. [PMID: 32773885 PMCID: PMC7409987 DOI: 10.1002/qua.26123] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2019] [Accepted: 11/19/2019] [Indexed: 06/11/2023]
Abstract
In the modeling of spin-crossing reactions, it has become popular to directly explore the spin-adiabatic surfaces. Specifically, through constructing spin-adiabatic states from a two-state Hamiltonian (with spin-orbit coupling matrix elements) at each geometry, one can readily employ advanced geometry optimization algorithms to acquire a "transition state" structure, where the spin crossing occurs. In this work, we report the implementation of a fully-variational spin-adiabatic approach based on Kohn-Sham density functional theory spin states (sharing the same set of molecular orbitals) and the Breit-Pauli one-electron spin-orbit operator. For three model spin-crossing reactions [predissociation of N2O, singlet-triplet conversion in CH2, and CO addition to Fe(CO)4], the spin-crossing points were obtained. Our results also indicated the Breit-Pauli one-electron spin-orbit coupling can vary significantly along the reaction pathway on the spin-adiabatic energy surface. On the other hand, due to the restriction that low-spin and high-spin states share the same set of molecular orbitals, the acquired spin-adiabatic energy surface shows a cusp (i.e. a first-order discontinuity) at the crossing point, which prevents the use of standard geometry optimization algorithms to pinpoint the crossing point. An extension with this restriction removed is being developed to achieve the smoothness of spin-adiabatic surfaces.
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Affiliation(s)
- Yunwen Tao
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, OK 73019
| | - Zheng Pei
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P. R. China
| | - Nicole Bellonzi
- Department of Chemistry, University of Pennsylvania, Philadelpha, PA 19104
| | - Yuezhi Mao
- Department of Chemistry, Stanford University, Stanford, CA 94305
| | - Zhu Zou
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, OK 73019
| | - Wanzhen Liang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P. R. China
| | - Zhibo Yang
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, OK 73019
| | - Yihan Shao
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, OK 73019
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17
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Tsuchimochi T, Ten-no SL. Second-Order Perturbation Theory with Spin-Symmetry-Projected Hartree–Fock. J Chem Theory Comput 2019; 15:6688-6702. [DOI: 10.1021/acs.jctc.9b00897] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
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18
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Gomez JA, Molla M, Garza AJ, Henderson TM, Scuseria GE. Assessing combinations of singlet-paired coupled cluster and density functional theory for treating electron correlation in closed and open shells. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1615144] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- John A. Gomez
- Department of Chemistry, Rice University, Houston, TX, USA
- Applied Physics Graduate Program, Rice University, Houston, TX, USA
| | - Mahlet Molla
- Department of Chemistry, Rice University, Houston, TX, USA
| | | | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, TX, USA
- Department of Physics and Astronomy, Rice University, Houston, TX, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, TX, USA
- Department of Physics and Astronomy, Rice University, Houston, TX, USA
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19
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Plakhutin BN. Koopmans’ theorem in the Hartree-Fock method. General formulation. J Chem Phys 2018. [DOI: 10.1063/1.5019330] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Boris N. Plakhutin
- Laboratory of Quantum Chemistry, Boreskov Institute of Catalysis, Russian Academy of Sciences, Novosibirsk 630090, Russian Federation
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20
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Tsuchimochi T, Ten-no S. Bridging Single- and Multireference Domains for Electron Correlation: Spin-Extended Coupled Electron Pair Approximation. J Chem Theory Comput 2017; 13:1667-1681. [DOI: 10.1021/acs.jctc.7b00073] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Takashi Tsuchimochi
- Graduate
School of Science, Technology, and Innovation, and ‡Graduate School
of System Informatics, Kobe University, Kobe, Hyogo 657-0025, Japan
| | - Seiichiro Ten-no
- Graduate
School of Science, Technology, and Innovation, and ‡Graduate School
of System Informatics, Kobe University, Kobe, Hyogo 657-0025, Japan
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21
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Tsuchimochi T, Ten-no S. General technique for analytical derivatives of post-projected Hartree-Fock. J Chem Phys 2017; 146:074104. [DOI: 10.1063/1.4976145] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Affiliation(s)
- Takashi Tsuchimochi
- Graduate School of Science, Technology, and Innovation, Kobe University, Kobe, Hyogo 657-0025, Japan
| | - Seiichiro Ten-no
- Graduate School of Science, Technology, and Innovation, Kobe University, Kobe, Hyogo 657-0025, Japan
- Graduate School of System Informatics, Kobe University, Kobe, Hyogo 657-0025, Japan
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22
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Tsuchimochi T, Ten-no S. Black-Box Description of Electron Correlation with the Spin-Extended Configuration Interaction Model: Implementation and Assessment. J Chem Theory Comput 2016; 12:1741-59. [DOI: 10.1021/acs.jctc.6b00137] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Takashi Tsuchimochi
- Graduate School of System
Informatics, Kobe University, Kobe 657-8501, Japan
| | - Seiichiro Ten-no
- Graduate School of System
Informatics, Kobe University, Kobe 657-8501, Japan
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23
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Tsuchimochi T. Spin-flip configuration interaction singles with exact spin-projection: Theory and applications to strongly correlated systems. J Chem Phys 2015; 143:144114. [DOI: 10.1063/1.4933113] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Takashi Tsuchimochi
- Department of Computational Science, Graduate School of System Informatics, Kobe University, Kobe 657-8501, Japan
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24
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Affiliation(s)
- Takashi Tsuchimochi
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA
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25
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Plakhutin BN. General form of the total one-electron Hamiltonian in the restricted open shell Hartree-Fock method. J STRUCT CHEM+ 2015. [DOI: 10.1134/s0022476614060018] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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26
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27
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Plakhutin BN, Davidson ER. Canonical form of the Hartree-Fock orbitals in open-shell systems. J Chem Phys 2014; 140:014102. [PMID: 24410216 DOI: 10.1063/1.4849615] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Boris N Plakhutin
- Laboratory of Quantum Chemistry, Boreskov Institute of Catalysis, Russian Academy of Sciences, prospekt Lavrentieva 5, Novosibirsk 630090, Russian Federation
| | - Ernest R Davidson
- Department of Chemistry, University of Washington, Seattle, Washington 98195-1700, USA
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28
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Yamamoto JI, Mochizuki Y. Optimal damping algorithm for unrestricted Hartree-Fock calculations. CHEM-BIO INFORMATICS JOURNAL 2014. [DOI: 10.1273/cbij.14.14] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Affiliation(s)
| | - Yuji Mochizuki
- Department of Chemistry and Research Center for Smart Molecules, Faculty of Science, Rikkyo University
- Institute of Industrial Science, The University of Tokyo
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29
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Coulaud E, Guihéry N, Malrieu JP, Hagebaum-Reignier D, Siri D, Ferré N. Analysis of the physical contributions to magnetic couplings in broken symmetry density functional theory approach. J Chem Phys 2012; 137:114106. [DOI: 10.1063/1.4752412] [Citation(s) in RCA: 22] [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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30
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Lehtola J, Manninen P, Hakala M, Hämäläinen K. Completeness-optimized basis sets: Application to ground-state electron momentum densities. J Chem Phys 2012; 137:104105. [DOI: 10.1063/1.4749272] [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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31
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Jiménez-Hoyos CA, Henderson TM, Tsuchimochi T, Scuseria GE. Projected Hartree–Fock theory. J Chem Phys 2012; 136:164109. [DOI: 10.1063/1.4705280] [Citation(s) in RCA: 177] [Impact Index Per Article: 14.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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32
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Lehtola J, Hakala M, Sakko A, Hämäläinen K. ERKALE-A flexible program package for X-ray properties of atoms and molecules. J Comput Chem 2012; 33:1572-85. [DOI: 10.1002/jcc.22987] [Citation(s) in RCA: 59] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2011] [Revised: 02/02/2012] [Accepted: 03/16/2012] [Indexed: 02/04/2023]
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33
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Domin D, Benoit DM. Assessing Spin-Component-Scaled Second-Order Møller-Plesset Theory Using Anharmonic Frequencies. Chemphyschem 2011; 12:3383-91. [DOI: 10.1002/cphc.201100499] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2011] [Indexed: 11/08/2022]
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34
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Scuseria GE, Jiménez-Hoyos CA, Henderson TM, Samanta K, Ellis JK. Projected quasiparticle theory for molecular electronic structure. J Chem Phys 2011; 135:124108. [DOI: 10.1063/1.3643338] [Citation(s) in RCA: 133] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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35
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Ellis JK, Jiménez-Hoyos CA, Henderson TM, Tsuchimochi T, Scuseria GE. Constrained-pairing mean-field theory. V. Triplet pairing formalism. J Chem Phys 2011; 135:034112. [DOI: 10.1063/1.3610650] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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36
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Wilke JJ, Schaefer HF. Spin-Restriction in Explicitly Correlated Coupled Cluster Theory: The Z-Averaged CCSD(2)R12 Approach. J Chem Theory Comput 2011; 7:2416-26. [DOI: 10.1021/ct200292z] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Affiliation(s)
- Jeremiah J. Wilke
- Center for Computational Chemistry, University of Georgia, Athens, Georgia, United States
| | - Henry F. Schaefer
- Center for Computational Chemistry, University of Georgia, Athens, Georgia, United States
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37
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Tsuchimochi T, Scuseria GE. Constrained active space unrestricted mean-field methods for controlling spin-contamination. J Chem Phys 2011; 134:064101. [DOI: 10.1063/1.3549134] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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