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Trushin E, Görling A. Avoiding spin contamination and spatial symmetry breaking by exact-exchange-only optimized-effective-potential methods within the symmetrized Kohn-Sham framework. J Chem Phys 2023; 159:244109. [PMID: 38149736 DOI: 10.1063/5.0171546] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2023] [Accepted: 11/16/2023] [Indexed: 12/28/2023] Open
Abstract
For open-shell atoms and molecules, Kohn-Sham (KS) methods typically resort to spin-polarized approaches that exhibit spin-contamination and often break spatial symmetries. As a result, the KS Hamiltonian operator and the KS orbitals do not exhibit the space and spin symmetry of the physical electron system. The KS formalism can be symmetrized in a rigorous way only in real space, only in spin space, or both in real and spin space. Within such symmetrized KS frameworks, we present exact-exchange-only optimized-effective-potential (OEP) methods that are free of spin contamination and/or spatial symmetry breaking. The effect of symmetrizations on the total energy and its parts and on the exchange potential is analyzed. The presented exact-exchange-only OEP methods may serve as a starting point for high-level symmetrized KS methods based, e.g., on the adiabatic-connection fluctuation-dissipation theorem.
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Affiliation(s)
- Egor Trushin
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany and Erlangen National High Performance Computing Center (NHR@FAU), Martensstr. 1, D-91058 Erlangen, Germany
| | - Andreas Görling
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany and Erlangen National High Performance Computing Center (NHR@FAU), Martensstr. 1, D-91058 Erlangen, Germany
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2
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Haasler M, Maier TM, Kaupp M. Toward a correct treatment of core properties with local hybrid functionals. J Comput Chem 2023; 44:2461-2477. [PMID: 37635647 DOI: 10.1002/jcc.27211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2023] [Revised: 08/01/2023] [Accepted: 08/03/2023] [Indexed: 08/29/2023]
Abstract
In local hybrid functionals (LHs), a local mixing function (LMF) determines the position-dependent exact-exchange admixture. We report new LHs that focus on an improvement of the LMF in the core region while retaining or partly improving upon the high accuracy in the valence region exhibited by the LH20t functional. The suggested new pt-LMFs are based on a Padé form and modify the previously used ratio between von Weizsäcker and Kohn-Sham local kinetic energies by different powers of the density to enable flexibly improved approximations to the correct high-density and iso-orbital limits relevant for the innermost core region. Using TDDFT calculations for a set of K-shell core excitations of second- and third-period systems including accurate state-of-the-art relativistic orbital corrections, the core part of the LMF is optimized, while the valence part is optimized as previously reported for test sets of atomization energies and reaction barriers (Haasler et al., J Chem Theory Comput 2020, 16, 5645). The LHs are completed by a calibration function that minimizes spurious nondynamical correlation effects caused by the gauge ambiguities of exchange-energy densities, as well as by B95c meta-GGA correlation. The resulting LH23pt functional relates to the previous LH20t functional but specifically improves upon the core region.
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Affiliation(s)
- Matthias Haasler
- Technische Universität Berlin, Institute of Chemistry Theoretical Chemistry/Quantum Chemistry, Berlin, Germany
| | - Toni M Maier
- Technische Universität Braunschweig, Institute of Physical and Theoretical Chemistry, Braunschweig, Germany
| | - Martin Kaupp
- Technische Universität Berlin, Institute of Chemistry Theoretical Chemistry/Quantum Chemistry, Berlin, Germany
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3
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Teale AM, Helgaker T, Savin A, Adamo C, Aradi B, Arbuznikov AV, Ayers PW, Baerends EJ, Barone V, Calaminici P, Cancès E, Carter EA, Chattaraj PK, Chermette H, Ciofini I, Crawford TD, De Proft F, Dobson JF, Draxl C, Frauenheim T, Fromager E, Fuentealba P, Gagliardi L, Galli G, Gao J, Geerlings P, Gidopoulos N, Gill PMW, Gori-Giorgi P, Görling A, Gould T, Grimme S, Gritsenko O, Jensen HJA, Johnson ER, Jones RO, Kaupp M, Köster AM, Kronik L, Krylov AI, Kvaal S, Laestadius A, Levy M, Lewin M, Liu S, Loos PF, Maitra NT, Neese F, Perdew JP, Pernal K, Pernot P, Piecuch P, Rebolini E, Reining L, Romaniello P, Ruzsinszky A, Salahub DR, Scheffler M, Schwerdtfeger P, Staroverov VN, Sun J, Tellgren E, Tozer DJ, Trickey SB, Ullrich CA, Vela A, Vignale G, Wesolowski TA, Xu X, Yang W. DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science. Phys Chem Chem Phys 2022; 24:28700-28781. [PMID: 36269074 PMCID: PMC9728646 DOI: 10.1039/d2cp02827a] [Citation(s) in RCA: 54] [Impact Index Per Article: 27.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2022] [Accepted: 08/09/2022] [Indexed: 12/13/2022]
Abstract
In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.
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Affiliation(s)
- Andrew M. Teale
- School of Chemistry, University of Nottingham, University ParkNottinghamNG7 2RDUK
| | - Trygve Helgaker
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.
| | - Andreas Savin
- Laboratoire de Chimie Théorique, CNRS and Sorbonne University, 4 Place Jussieu, CEDEX 05, 75252 Paris, France.
| | - Carlo Adamo
- PSL University, CNRS, ChimieParisTech-PSL, Institute of Chemistry for Health and Life Sciences, i-CLeHS, 11 rue P. et M. Curie, 75005 Paris, France.
| | - Bálint Aradi
- Bremen Center for Computational Materials Science, University of Bremen, P.O. Box 330440, D-28334 Bremen, Germany.
| | - Alexei V. Arbuznikov
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7Straße des 17. Juni 13510623Berlin
| | | | - Evert Jan Baerends
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands.
| | - Vincenzo Barone
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56125 Pisa, Italy.
| | - Patrizia Calaminici
- Departamento de Química, Centro de Investigación y de Estudios Avanzados (Cinvestav), CDMX, 07360, Mexico.
| | - Eric Cancès
- CERMICS, Ecole des Ponts and Inria Paris, 6 Avenue Blaise Pascal, 77455 Marne-la-Vallée, France.
| | - Emily A. Carter
- Department of Mechanical and Aerospace Engineering and the Andlinger Center for Energy and the Environment, Princeton UniversityPrincetonNJ 08544-5263USA
| | | | - Henry Chermette
- Institut Sciences Analytiques, Université Claude Bernard Lyon1, CNRS UMR 5280, 69622 Villeurbanne, France.
| | - Ilaria Ciofini
- PSL University, CNRS, ChimieParisTech-PSL, Institute of Chemistry for Health and Life Sciences, i-CLeHS, 11 rue P. et M. Curie, 75005 Paris, France.
| | - T. Daniel Crawford
- Department of Chemistry, Virginia TechBlacksburgVA 24061USA,Molecular Sciences Software InstituteBlacksburgVA 24060USA
| | - Frank De Proft
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium.
| | | | - Claudia Draxl
- Institut für Physik and IRIS Adlershof, Humboldt-Universität zu Berlin, 12489 Berlin, Germany. .,Fritz-Haber-Institut der Max-Planck-Gesellschaft, 14195 Berlin, Germany
| | - Thomas Frauenheim
- Bremen Center for Computational Materials Science, University of Bremen, P.O. Box 330440, D-28334 Bremen, Germany. .,Beijing Computational Science Research Center (CSRC), 100193 Beijing, China.,Shenzhen JL Computational Science and Applied Research Institute, 518110 Shenzhen, China
| | - Emmanuel Fromager
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, 4 rue Blaise Pascal, 67000 Strasbourg, France.
| | - Patricio Fuentealba
- Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile.
| | - Laura Gagliardi
- Department of Chemistry, Pritzker School of Molecular Engineering, The James Franck Institute, and Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, USA.
| | - Giulia Galli
- Pritzker School of Molecular Engineering and Department of Chemistry, The University of Chicago, Chicago, IL, USA.
| | - Jiali Gao
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, China. .,Department of Chemistry, University of Minnesota, Minneapolis, MN 55455, USA
| | - Paul Geerlings
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium.
| | - Nikitas Gidopoulos
- Department of Physics, Durham University, South Road, Durham DH1 3LE, UK.
| | - Peter M. W. Gill
- School of Chemistry, University of SydneyCamperdown NSW 2006Australia
| | - Paola Gori-Giorgi
- Department of Chemistry and Pharmaceutical Sciences, Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands.
| | - Andreas Görling
- Chair of Theoretical Chemistry, University of Erlangen-Nuremberg, Egerlandstrasse 3, 91058 Erlangen, Germany.
| | - Tim Gould
- Qld Micro- and Nanotechnology Centre, Griffith University, Gold Coast, Qld 4222, Australia.
| | - Stefan Grimme
- Mulliken Center for Theoretical Chemistry, University of Bonn, Beringstrasse 4, 53115 Bonn, Germany.
| | - Oleg Gritsenko
- Department of Chemistry and Pharmaceutical Sciences, Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands.
| | - Hans Jørgen Aagaard Jensen
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark.
| | - Erin R. Johnson
- Department of Chemistry, Dalhousie UniversityHalifaxNova ScotiaB3H 4R2Canada
| | - Robert O. Jones
- Peter Grünberg Institut PGI-1, Forschungszentrum Jülich52425 JülichGermany
| | - Martin Kaupp
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, 10623, Berlin.
| | - Andreas M. Köster
- Departamento de Química, Centro de Investigación y de Estudios Avanzados (Cinvestav)CDMX07360Mexico
| | - Leeor Kronik
- Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovoth, 76100, Israel.
| | - Anna I. Krylov
- Department of Chemistry, University of Southern CaliforniaLos AngelesCalifornia 90089USA
| | - Simen Kvaal
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.
| | - Andre Laestadius
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.
| | - Mel Levy
- Department of Chemistry, Tulane University, New Orleans, Louisiana, 70118, USA.
| | - Mathieu Lewin
- CNRS & CEREMADE, Université Paris-Dauphine, PSL Research University, Place de Lattre de Tassigny, 75016 Paris, France.
| | - Shubin Liu
- Research Computing Center, University of North Carolina, Chapel Hill, NC 27599-3420, USA. .,Department of Chemistry, University of North Carolina, Chapel Hill, NC 27599-3290, USA
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, France.
| | - Neepa T. Maitra
- Department of Physics, Rutgers University at Newark101 Warren StreetNewarkNJ 07102USA
| | - Frank Neese
- Max Planck Institut für Kohlenforschung, Kaiser Wilhelm Platz 1, D-45470 Mülheim an der Ruhr, Germany.
| | - John P. Perdew
- Departments of Physics and Chemistry, Temple UniversityPhiladelphiaPA 19122USA
| | - Katarzyna Pernal
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland.
| | - Pascal Pernot
- Institut de Chimie Physique, UMR8000, CNRS and Université Paris-Saclay, Bât. 349, Campus d'Orsay, 91405 Orsay, France.
| | - Piotr Piecuch
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA. .,Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
| | - Elisa Rebolini
- Institut Laue Langevin, 71 avenue des Martyrs, 38000 Grenoble, France.
| | - Lucia Reining
- Laboratoire des Solides Irradiés, CNRS, CEA/DRF/IRAMIS, École Polytechnique, Institut Polytechnique de Paris, F-91120 Palaiseau, France. .,European Theoretical Spectroscopy Facility
| | - Pina Romaniello
- Laboratoire de Physique Théorique (UMR 5152), Université de Toulouse, CNRS, UPS, France.
| | - Adrienn Ruzsinszky
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA.
| | - Dennis R. Salahub
- Department of Chemistry, Department of Physics and Astronomy, CMS – Centre for Molecular Simulation, IQST – Institute for Quantum Science and Technology, Quantum Alberta, University of Calgary2500 University Drive NWCalgaryAlbertaT2N 1N4Canada
| | - Matthias Scheffler
- The NOMAD Laboratory at the FHI of the Max-Planck-Gesellschaft and IRIS-Adlershof of the Humboldt-Universität zu Berlin, Faradayweg 4-6, D-14195, Germany.
| | - Peter Schwerdtfeger
- Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland, 0632 Auckland, New Zealand.
| | - Viktor N. Staroverov
- Department of Chemistry, The University of Western OntarioLondonOntario N6A 5B7Canada
| | - Jianwei Sun
- Department of Physics and Engineering Physics, Tulane University, New Orleans, LA 70118, USA.
| | - Erik Tellgren
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.
| | - David J. Tozer
- Department of Chemistry, Durham UniversitySouth RoadDurhamDH1 3LEUK
| | - Samuel B. Trickey
- Quantum Theory Project, Deptartment of Physics, University of FloridaGainesvilleFL 32611USA
| | - Carsten A. Ullrich
- Department of Physics and Astronomy, University of MissouriColumbiaMO 65211USA
| | - Alberto Vela
- Departamento de Química, Centro de Investigación y de Estudios Avanzados (Cinvestav), CDMX, 07360, Mexico.
| | - Giovanni Vignale
- Department of Physics, University of Missouri, Columbia, MO 65203, USA.
| | - Tomasz A. Wesolowski
- Department of Physical Chemistry, Université de Genève30 Quai Ernest-Ansermet1211 GenèveSwitzerland
| | - Xin Xu
- Shanghai Key Laboratory of Molecular Catalysis and Innovation Materials, Collaborative Innovation Centre of Chemistry for Energy Materials, MOE Laboratory for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200433, China.
| | - Weitao Yang
- Department of Chemistry and Physics, Duke University, Durham, NC 27516, USA.
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Trushin E, Görling A. Numerically stable optimized effective potential method with standard Gaussian basis sets. J Chem Phys 2021; 155:054109. [PMID: 34364359 DOI: 10.1063/5.0056431] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
We present a numerically stable optimized effective potential (OEP) method based on Gaussian basis sets. The key point of the approach is a sequence of preprocessing steps of the auxiliary basis set used to represent exchange or correlation potentials, the Kohn-Sham (KS) response function, and the right-hand side of the OEP equation in conjunction with a representation of exchange or correlation potentials via exchange or correlation charge densities whose electrostatic potentials generate the potentials. Due to the preprocessing, standard Gaussian basis sets from basis set libraries can be used in OEP calculations. As examples, we present numerical stable computational setups based on aux-cc-pwCVXZ basis sets with X = T, Q, 5 for the orbitals and aux-cc-pVDZ/mp2fit and aux-cc-pVTZ/mp2fit auxiliary basis sets and use them to calculate KS exchange potentials with the exact exchange-only KS method for various atoms and molecules. The resulting exchange potentials not only are numerically stable and physically reasonable but also show convergence with increasing quality of the orbital basis sets. The effect of incorporating exact conditions that the KS exchange potential has to obey is discussed. Moreover, it is briefly demonstrated that the presented approach not only works for KS exchange potentials but equally well for correlation potentials within the direct random phase approximation. Besides for OEP methods, the introduced preprocessing of auxiliary basis sets should also be beneficial in procedures to calculate back effective KS potentials from given electron densities.
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Affiliation(s)
- Egor Trushin
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany and Erlangen National High Performance Computing Center (NHR@FAU), Martensstr. 1, D-91058 Erlangen, Germany
| | - Andreas Görling
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany and Erlangen National High Performance Computing Center (NHR@FAU), Martensstr. 1, D-91058 Erlangen, Germany
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Ikabata Y, Nakai H. Picture-change correction in relativistic density functional theory. Phys Chem Chem Phys 2021; 23:15458-15474. [PMID: 34278401 DOI: 10.1039/d1cp01773j] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Relativistic quantum chemical calculations are performed based on one of two physical pictures, namely the Dirac picture and the Schrödinger picture. With regard to the latter, the so-called picture-change effect (PCE) and picture-change correction (PCC) have been studied. The PCE, which is the change in the expectation value associated with the transformation, is not commonly a minor effect. The electron density, which is given by the expectation value of the density operator, is a fundamental variable in relativistic density functional theory (RDFT). Thus, performing the PCC in RDFT calculations is essential not only in terms of numerical agreement with the Dirac picture, but also from the viewpoint of fundamental theory. This paper explains theories and numerical studies of PCE and PCC in RDFT after overviewing those in properties, which involves the authors' works on the development of RDFT in the Schrödinger picture and relativistic exchange-correlation functionals based on picture-change-corrected variables.
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Affiliation(s)
- Yasuhiro Ikabata
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan.
| | - Hiromi Nakai
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan. and Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan and Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520, Japan
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6
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Paquier J, Giner E, Toulouse J. Relativistic short-range exchange energy functionals beyond the local-density approximation. J Chem Phys 2020; 152:214106. [DOI: 10.1063/5.0004926] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Julien Paquier
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
| | - Emmanuel Giner
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
- Institut Universitaire de France, F-75005 Paris, France
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7
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Maier TM, Ikabata Y, Nakai H. Relativistic local hybrid functionals and their impact on 1s core orbital energies. J Chem Phys 2020; 152:214103. [DOI: 10.1063/5.0010400] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Toni M. Maier
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Yasuhiro Ikabata
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Hiromi Nakai
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520, Japan
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8
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Maier TM, Ikabata Y, Nakai H. Restoring the iso-orbital limit of the kinetic energy density in relativistic density functional theory. J Chem Phys 2019; 151:174114. [DOI: 10.1063/1.5125634] [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)
- Toni M. Maier
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Yasuhiro Ikabata
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Hiromi Nakai
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520, Japan
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9
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Paquier J, Toulouse J. Four-component relativistic range-separated density-functional theory: Short-range exchange local-density approximation. J Chem Phys 2018; 149:174110. [DOI: 10.1063/1.5049773] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Affiliation(s)
- Julien Paquier
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
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Abstract
The foundations, formalisms, technicalities, and practicalities of relativistic time-dependent density functional theories (R-TD-DFT) for spinor excited states of molecular systems containing heavy elements are critically reviewed.
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Affiliation(s)
- Wenjian Liu
- Beijing National Center for Molecular Sciences
- Institute of Theoretical and Computational Chemistry
- College of Chemistry and Molecular Engineering
- Peking University
- Beijing 100871
| | - Yunlong Xiao
- Beijing National Center for Molecular Sciences
- Institute of Theoretical and Computational Chemistry
- College of Chemistry and Molecular Engineering
- Peking University
- Beijing 100871
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11
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Aucar IA, Giménez CA, Aucar GA. Influence of the nuclear charge distribution and electron correlation effects on magnetic shieldings and spin-rotation tensors of linear molecules. RSC Adv 2018; 8:20234-20249. [PMID: 35541654 PMCID: PMC9080724 DOI: 10.1039/c8ra03948h] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2018] [Accepted: 05/13/2018] [Indexed: 12/02/2022] Open
Abstract
The nuclear charge distribution effects (NChDE) on two response properties, the NMR magnetic shielding (σ) and the nuclear spin-rotation (SR) constants (M), are analyzed. We do it employing point-like and Gaussian-like models for describing the nuclear charge density of three linear molecules: HBr, HI and HAt. According to our results, both properties are sensitive to the NChDE. We show that the NChDE are almost completely relativistic, i.e., they nearly vanish in the non-relativistic limit of both properties. We calculated the NChDE on σ and M, and analyzed the differences between them in terms of a relativistic relation between these two properties. Using that relation we found that the electronic core mechanisms are the main ones for the NChDE on the shielding of nuclei of both, molecules and free atoms. The NChDE are smaller on SR constants than on shieldings. Nevertheless, within the relativistic polarization propagator formalism at the RPA level of approach they are very important for SR constants of nuclei in heavy-atom-containing compounds. Astatine in HAt has the largest influence: MAt = −9.95 kHz for a point-like model and −50.10 kHz for a Gaussian-like model. Correlation effects must be included and we do it using different DFT schemes. The PBE0 functional gives results that are closest to experiments for Br and I, though the LDA gives the closest for hydrogen. The value of the SR constant of At is reduced among 350 kHz and 500 kHz from its RPA value, when different and usual functionals are applied. Given that the NChDE on M and σ are mostly relativistic in their origin, these effects are also dependent on electron correlation. They have also a nonvanishing dependence with the Gaunt electron–electron interactions. The origin and the size of both, electron correlation and nuclear charge distribution on shieldings and spin-rotations of heavy-atom containing linear molecules are shown. The analysis is performed on the relativistic and non relativistic regimes.![]()
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Affiliation(s)
- I. Agustín Aucar
- Instituto de Modelado e Innovación Tecnológica
- CONICET
- Departamento de Física – Facultad de Ciencias Exactas y Naturales
- UNNE
- Corrientes
| | - Carlos A. Giménez
- Instituto de Modelado e Innovación Tecnológica
- CONICET
- Departamento de Física – Facultad de Ciencias Exactas y Naturales
- UNNE
- Corrientes
| | - Gustavo A. Aucar
- Instituto de Modelado e Innovación Tecnológica
- CONICET
- Departamento de Física – Facultad de Ciencias Exactas y Naturales
- UNNE
- Corrientes
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12
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Wang F, Liu W. Comparison of Different Polarization Schemes in Open-shell Relativistic Density Functional Calculations. J CHIN CHEM SOC-TAIP 2013. [DOI: 10.1002/jccs.200300087] [Citation(s) in RCA: 66] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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13
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Pershina V, Anton J. Theoretical predictions of properties and gas-phase chromatography behaviour of carbonyl complexes of group-6 elements Cr, Mo, W, and element 106, Sg. J Chem Phys 2013; 138:174301. [DOI: 10.1063/1.4802765] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
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14
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Verma P, Autschbach J. Relativistic Density Functional Calculations of Hyperfine Coupling with Variational versus Perturbational Treatment of Spin–Orbit Coupling. J Chem Theory Comput 2013; 9:1932-48. [DOI: 10.1021/ct301114z] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Prakash Verma
- Department
of Chemistry, University at Buffalo, State University of New York, Buffalo, New York 14260-3000
| | - Jochen Autschbach
- Department
of Chemistry, University at Buffalo, State University of New York, Buffalo, New York 14260-3000
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15
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Pershina V, Borschevsky A, Anton J. Theoretical predictions of properties of group-2 elements including element 120 and their adsorption on noble metal surfaces. J Chem Phys 2012; 136:134317. [DOI: 10.1063/1.3699232] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
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16
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Pershina V, Borschevsky A, Anton J. Fully relativistic study of intermetallic dimers of group-1 elements K through element 119 and prediction of their adsorption on noble metal surfaces. Chem Phys 2012. [DOI: 10.1016/j.chemphys.2011.04.017] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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17
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Pershina V, Anton J. Theoretical predictions of properties and gas-phase chromatography behaviour of bromides of group-5 elements Nb, Ta, and element 105, Db. J Chem Phys 2012; 136:034308. [PMID: 22280761 DOI: 10.1063/1.3676176] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Affiliation(s)
- V Pershina
- GSI Helmholtzzentrum für Schwerionenforschung, Planckstr. 1, D-64291 Darmstadt, Germany.
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18
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Liu W, Wang F, Li L. The Beijing Density Functional (BDF) Program Package: Methodologies and Applications. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2011. [DOI: 10.1142/s0219633603000471] [Citation(s) in RCA: 115] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The Beijing Density Functional (BDF) program package is such a code that can perform nonrelativistic, one-, two-, and four-component relativistic density functional calculations on medium-sized molecular systems with various functionals in most compact and yet sufficient basis set expansions. The mergence of different approaches in a single code facilitates direct and systematic comparisons between different Hamiltonians, since they share all the same numerical and technical issues. In this account, the methodologies adopted in the code will be discussed in great detail and some applications of the code will be briefly presented.
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Affiliation(s)
- Wenjian Liu
- Institute of Theoretical and Computational Chemistry and State Key, Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, P. R. China
| | - Fan Wang
- Institute of Theoretical and Computational Chemistry and State Key, Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, P. R. China
| | - Lemin Li
- Institute of Theoretical and Computational Chemistry and State Key, Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, P. R. China
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19
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20
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Belpassi L, Storchi L, Quiney HM, Tarantelli F. Recent advances and perspectives in four-component Dirac–Kohn–Sham calculations. Phys Chem Chem Phys 2011; 13:12368-94. [DOI: 10.1039/c1cp20569b] [Citation(s) in RCA: 55] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
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21
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Pershina V, Borschevsky A, Anton J, Jacob T. Theoretical predictions of trends in spectroscopic properties of gold containing dimers of the 6p and 7p elements and their adsorption on gold. J Chem Phys 2010; 133:104304. [DOI: 10.1063/1.3476470] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
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22
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Pershina V, Borschevsky A, Anton J, Jacob T. Theoretical predictions of trends in spectroscopic properties of homonuclear dimers and volatility of the 7p elements. J Chem Phys 2010; 132:194314. [DOI: 10.1063/1.3425996] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
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23
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24
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van Wüllen C. Relativistic Density Functional Theory. CHALLENGES AND ADVANCES IN COMPUTATIONAL CHEMISTRY AND PHYSICS 2010. [DOI: 10.1007/978-1-4020-9975-5_5] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
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25
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Pershina V, Anton J, Jacob T. Electronic structures and properties of MAu and MOH, where M = Tl and element 113. Chem Phys Lett 2009. [DOI: 10.1016/j.cplett.2009.08.069] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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26
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Pershina V, Bastug T, Kratz JV. Quantum chemical predictions of properties and experimental behaviour of elements 106, 107, and 108. RADIOCHIM ACTA 2009. [DOI: 10.1524/ract.2001.89.11-12.729] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
Fully relativistic Density-Functional calculations have been performed for group 7 MO3Cl (M=Tc, Re, and element 107, Bh), for group 8 tetroxides MO4(M=Ru, Os, and element 108, Hs), and for various aqueous complexes of group 6 elements Mo, W, and element 106, Sg. The electronic structure analysis has shown the transactinide compounds to be very similar to those of the lighter homologs in the respective chemical groups with the covalence increasing with increasing atomic number. Results have shown BhO3Cl to have a trend in volatility in line with that of the lighter homologs in the group. Hydrolysis of element 106 with the formation of anionic oxo-complexes has, however, a reversed trend, so that hydrolysis decreases in the order Mo>Sg>W.
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27
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Pershina V, Anton J, Jacob T. Theoretical predictions of adsorption behavior of elements 112 and 114 and their homologs Hg and Pb. J Chem Phys 2009; 131:084713. [DOI: 10.1063/1.3212449] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
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28
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Heßelmann A, Görling A. Comparison between optimized effective potential and Kohn–Sham methods. Chem Phys Lett 2008. [DOI: 10.1016/j.cplett.2008.02.042] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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29
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Pershina V, Anton J, Fricke B. Intermetallic compounds of the heaviest elements and their homologs: The electronic structure and bonding of MM′, where M=Ge, Sn, Pb, and element 114, and M′=Ni, Pd, Pt, Cu, Ag, Au, Sn, Pb, and element 114. J Chem Phys 2007; 127:134310. [DOI: 10.1063/1.2770712] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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30
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Hesselmann A, Götz AW, Della Sala F, Görling A. Numerically stable optimized effective potential method with balanced Gaussian basis sets. J Chem Phys 2007; 127:054102. [PMID: 17688329 DOI: 10.1063/1.2751159] [Citation(s) in RCA: 95] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A solution to the long-standing problem of developing numerically stable optimized effective potential (OEP) methods based on Gaussian basis sets is presented by introducing an approach consisting of an exact exchange OEP method with an accompanying construction and balancing scheme for the involved auxiliary and orbital Gaussian basis sets that is numerically stable and that properly represents an exact exchange Kohn-Sham method. The method is a purely analytical method that does not require any numerical grid, scales like Hartree-Fock or B3LYP procedures, is straightforward to implement, and is easily generalized to take into account orbital-dependent density functionals other than the exact exchange considered in this work. Thus, the presented OEP approach opens the way to the development and application of novel orbital-dependent exchange-correlation functionals. It is shown that adequately taking into account the continuum part of the Kohn-Sham orbital spectrum is crucial for numerically stable Gaussian basis set OEP methods. Moreover, it is mandatory to employ orbital basis sets that are converged with respect to the used auxiliary basis representing the exchange potential. OEP calculations in the past often did not meet the latter requirement and therefore may have led to erroneously low total energies.
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Affiliation(s)
- Andreas Hesselmann
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstrasse 3, D-91058 Erlangen, Germany
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31
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Witek HA, Köhler C, Frauenheim T, Morokuma K, Elstner M. Relativistic parametrization of the self-consistent-charge density-functional tight-binding method. 1. Atomic wave functions and energies. J Phys Chem A 2007; 111:5712-9. [PMID: 17567112 DOI: 10.1021/jp070786o] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A detailed treatment of a confined relativistic atom, needed as an initial step for the parametrization of the self-consistent-charge density-functional tight-binding method, is presented and discussed. The required one-component quantities, i.e., orbital energies, orbital wave functions, and Hubbard parameters, are obtained by weighted averaging of the corresponding numbers determined for the atomic spinors. The wave function and density confinement is achieved by introducing the Woods-Saxon potential in the atomic four-component Dirac-Kohn-Sham problem. The effect of the additional confining potential on energy eigenvalues and the shape of atomic wave functions and densities is discussed and numerical examples are presented for the valence spinors of carbon, germanium, and lead.
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Affiliation(s)
- Henryk A Witek
- Department of Applied Chemistry and Institute of Molecular Science, National Chiao Tung University, Hsinchu 30010, Taiwan.
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32
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Komorovský S, Repiský M, Malkina OL, Malkin VG, Malkin I, Kaupp M. Resolution of identity Dirac-Kohn-Sham method using the large component only: Calculations of g-tensor and hyperfine tensor. J Chem Phys 2006; 124:084108. [PMID: 16512709 DOI: 10.1063/1.2173995] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new relativistic two-component density functional approach, based on the Dirac-Kohn-Sham method and an extensive use of the technique of resolution of identity (RI), has been developed and is termed the DKS2-RI method. It has been applied to relativistic calculations of g and hyperfine tensors of coinage-metal atoms and some mercury complexes. The DKS2-RI method solves the Dirac-Kohn-Sham equations in a two-component framework using explicitly a basis for the large component only, but it retains all contributions coming from the small component. The DKS2-RI results converge to those of the four-component Dirac-Kohn-Sham with an increasing basis set since the error associated with the use of RI will approach zero. The RI approximation provides a basis for a very efficient implementation by avoiding problems associated with complicated integrals otherwise arising from the elimination of the small component. The approach has been implemented in an unrestricted noncollinear two-component density functional framework. DKS2-RI is related to Dyall's [J. Chem. Phys. 106, 9618 (1997)] unnormalized elimination of the small component method (which was formulated at the Hartree-Fock level and applied to one-electron systems only), but it takes advantage of the local Kohn-Sham exchange-correlation operators (as, e.g., arising from local or gradient-corrected functionals). The DKS2-RI method provides an attractive alternative to existing approximate two-component methods with transformed Hamiltonians (such as Douglas-Kroll-Hess [Ann. Phys. 82, 89 (1974); Phys. Rev. A 33, 3742 (1986)] method, zero-order regular approximation, or related approaches) for relativistic calculations of the structure and properties of heavy-atom systems. In particular, no picture-change effects arise in the property calculations.
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Affiliation(s)
- Stanislav Komorovský
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dúbravská cesta 9, SK-84536 Bratislava, Slovak Republic
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33
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van Wüllen C, Michauk C. Accurate and efficient treatment of two-electron contributions in quasirelativistic high-order Douglas-Kroll density-functional calculations. J Chem Phys 2005; 123:204113. [PMID: 16351246 DOI: 10.1063/1.2133731] [Citation(s) in RCA: 84] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Two-component quasirelativistic approaches are in principle capable of reproducing results from fully relativistic calculations based on the four-component Dirac equation (with fixed particle number). For one-electron systems, this also holds in practice, but in many-electron systems one has to transform the two-electron interaction, which is necessary because a picture change occurs when going from the Dirac equation to a two-component method. For one-electron properties, one can take full account of picture change in a manageable way, but for the electron interaction, this would spoil the computational advantages which are the main reason to perform quasirelativistic calculations. Exploiting those picture change effects are largest in the atomic cores, which in molecular applications do not differ too much from the cores of isolated neutral atoms, we propose an elegant, efficient, and accurate approximation to the two-electron picture change problem. The new approach, called the "model potential" approach because it makes use of atomic (four- and two-component) data to estimate picture change effects in molecules, shares with the nuclear-only approach that the Douglas-Kroll operator needs to be constructed only once (not in each self-consistent-field iteration) and that no time-consuming multicenter relativistic two-electron integrals need to be calculated. The new approach correctly describes the screening of both the nearest nucleus and distant nuclei, for the scalar-relativistic as well as the spin-orbit parts of the Hamiltonian. The approach is tested on atomic and molecular-orbital energies as well as spectroscopic constants of the lead dimer.
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Affiliation(s)
- Christoph van Wüllen
- Institute of Chemistry, Technical University Berlin, Strasse des 17. Juni 135, D-10623 Berlin, Germany.
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34
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Ren CY. Gradient-corrected density-functional potential with correct asymptotic behavior: Application to interconfigurational energies in transition-metal atoms. J Chem Phys 2005; 122:244109. [PMID: 16035748 DOI: 10.1063/1.1938188] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Based upon the optimized effective potential with the self-interaction correction, we present in this paper an alternative gradient-corrected density-functional approximation with the proper long-range behavior of the effective potential. As applied to the study of the interconfigurational energies of the whole transition-metal atoms, the present combination of the gradient-corrected contribution and the modified optimized effective potential lead the s ionization to the excellent agreement with the experiment. The calculated d ionizations and s-d transition energies are also discussed.
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Affiliation(s)
- Chung-Yuan Ren
- Department of Science Education, Taipei Municipal Teachers College, Taiwan, Republic of China.
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35
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Pershina V, Bastug T. Relativistic effects on experimentally studied gas-phase properties of the heaviest elements. Chem Phys 2005. [DOI: 10.1016/j.chemphys.2004.09.030] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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36
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37
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Pershina V, Bastug T, Fricke B. Relativistic effects on the electronic structure and volatility of group-8 tetroxides MO4, where M=Ru, Os, and element 108, Hs. J Chem Phys 2005; 122:124301. [PMID: 15836372 DOI: 10.1063/1.1862241] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The influence of relativistic effects on properties and volatility of the group-8 tetroxides MO4, where M=Ru, Os, and element 108, Hs, was studied on the basis of results of the fully relativistic (four component) and nonrelativistic density functional theory calculations. Relativistic effects were shown to increase bond strengths and decrease bond lengths in these molecules. They are responsible for a decrease in molecular polarizabilities and an increase in ionization potentials. The effects are much stronger in HsO4 than in the lighter congeners. Relativistic effects were also shown to slightly decrease dispersion interaction energies of RuO4, OsO4, and HsO4 with an inert (quartz or silicon nitride) surface, i.e., they increase volatility of these compounds as studied in the "one-atom-at-a-time" gas-phase chromatography experiments. They do, however, not influence the trend in group 8: both relativistically and nonrelativistically, volatility should change as RuO4<OsO4<HsO4. The reason for that is identical trends in the relativistic and nonrelativistic space distributions of the valence d electrons.
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Affiliation(s)
- V Pershina
- Gesellschaft für Schwerionenforschung, D-64291 Darmstadt, Germany
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38
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Gao J, Liu W, Song B, Liu C. Time-dependent four-component relativistic density functional theory for excitation energies. J Chem Phys 2004; 121:6658-66. [PMID: 15473721 DOI: 10.1063/1.1788655] [Citation(s) in RCA: 72] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Time-dependent four-component relativistic density functional theory within the linear response regime is developed for calculating excitation energies of heavy element containing systems. Since spin is no longer a good quantum number in this context, we resort to time-reversal adapted Kramers basis when deriving the coupled Dirac-Kohn-Sham equation. The particular implementation of the formalism into the Beijing density functional program package utilizes the multipolar expansion of the induced density to facilitate the construction of the induced Coulomb potential. As the first application, pilot calculations on the valence excitation energies and fine structures of the rare gas (Ne to Rn) and Group 12 (Zn to Hg) atoms are reported. To the best of our knowledge, it is the first time to be able to account for spin-orbit coupling within time-dependent density functional theory for excitation energies.
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Affiliation(s)
- Jun Gao
- Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, People's Republic of China
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39
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The Chemistry of the Superheavy Elements and Relativistic Effects. ACTA ACUST UNITED AC 2004. [DOI: 10.1016/s1380-7323(04)80028-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023]
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40
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Wang F, Li L. Numerical examination of performance of some exchange-correlation functionals for molecules containing heavy elements. J Comput Chem 2004; 25:669-77. [PMID: 14978710 DOI: 10.1002/jcc.10421] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
The performance of 17 exchange-correlation functionals for molecules containing heavy elements are numerically examined through four-component relativistic density DFT calculations. The examined functionals show the similar accuracy as they do for the molecules containing light elements only except for bond lengths. LDA and OP86 produce good results for bond lengths and frequencies but bad bond energies. Different functionals do not show much different performance for bond energies except LDA. BP86 and GP86 produce results with average accuracy while LYP does not perform well. Although encouraging results are obtained with functional B97GGA-1, other heavily parameterized and meta-GGA functionals do not produce impressive results.
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Affiliation(s)
- Fan Wang
- State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry, and Molecular Engineering, Peking University, Beijing 100871, People's Republic of China
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41
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van Wüllen C. Relativistic Density Functional Calculations on Small Molecules. THEORETICAL AND COMPUTATIONAL CHEMISTRY 2004. [DOI: 10.1016/s1380-7323(04)80037-2] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
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42
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Filatov M, Cremer D. Calculation of electric properties using regular approximations to relativistic effects: The polarizabilities of RuO4, OsO4, and HsO4 (Z=108). J Chem Phys 2003. [DOI: 10.1063/1.1580473] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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43
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Orbital-Dependent Functionals for the Exchange-Correlation Energy: A Third Generation of Density Functionals. ACTA ACUST UNITED AC 2003. [DOI: 10.1007/3-540-37072-2_2] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/04/2023]
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44
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Matveev A, Rösch N. The electron–electron interaction in the Douglas–Kroll–Hess approach to the Dirac–Kohn–Sham problem. J Chem Phys 2003. [DOI: 10.1063/1.1540615] [Citation(s) in RCA: 38] [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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45
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Relativistic Density Functional Theory. ACTA ACUST UNITED AC 2003. [DOI: 10.1007/978-94-017-0105-1_11] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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46
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47
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Pershina V, Bastug T, Jacob T, Fricke B, Varga S. Intermetallic compounds of the heaviest elements: the electronic structure and bonding of dimers of element 112 and its homolog Hg. Chem Phys Lett 2002. [DOI: 10.1016/s0009-2614(02)01428-8] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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48
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Quiney HM, Belanzoni P. Relativistic density functional theory using Gaussian basis sets. J Chem Phys 2002. [DOI: 10.1063/1.1502245] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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49
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Abstract
The theoretical and technical foundations are presented for the efficient relativistic electronic structure theories to treat heavy-atomic molecular systems. This review contains two surveys of four-component and two-component quasi-relativistic approaches. First, we review our highly efficient computational scheme for four-component relativistic ab initio molecular orbital (MO) methods over generally contracted spherical harmonic Gaussian-type spinors (GTSs). Illustrative calculations, which are performed with a new four-component relativistic ab initio molecular orbital program package REL4D, clearly show the efficiency of our computational scheme by the Dirac-Hartree-Fock (DHF) and Dirac-Hartree-Fock (DKS) methods. Next, in the two-component quasi-relativistic framework, two relativistic Hamiltonians, RESC and higher order Douglas-Kroll (DK) Hamiltonians, are introduced, and several illustrative calculations are shown. Numerical results for several systems show that good accuracy can be obtained with our third-order DK (DK3) Hamiltonian.
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Affiliation(s)
- Takahito Nakajima
- Department of Applied Chemistry, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
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50
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Kaupp M, Reviakine R, Malkina OL, Arbuznikov A, Schimmelpfennig B, Malkin VG. Calculation of electronic g-tensors for transition metal complexes using hybrid density functionals and atomic meanfield spin-orbit operators. J Comput Chem 2002; 23:794-803. [PMID: 12012356 DOI: 10.1002/jcc.10049] [Citation(s) in RCA: 168] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
We report the first implementation of the calculation of electronic g-tensors by density functional methods with hybrid functionals. Spin-orbit coupling is treated by the atomic meanfield approximation. g-Tensors for a set of small main group radicals and for a series of ten 3d and two 4d transition metal complexes have been compared using the local density approximation (VWN functional), the generalized gradient approximation (BP86 functional), as well as B3-type (B3PW91) and BH-type (BHPW91) hybrid functionals. For main group radicals, the effect of exact-exchange mixing is small. In contrast, significant differences between the various functionals arise for transition metal complexes. As has been shown previously, local and in particular gradient-corrected functionals tend to underestimate the "paramagnetic" contributions to the g-tensors in these cases and thereby recover only about 40-50% of the range of experimental g-tensor components. This is improved to ca. 60% by the B3PW91 functional, which also gives slightly reduced standard deviations. The range increases to almost 100% using the half-and-half functional BHPW91. However, the quality of the correlation with experimental data worsens due to a significant overestimate of some intermediate g-tensor values. The worse performance of the BHPW91 functional in these cases is accompanied by spin contamination. Although none of the functionals tested thus appears to be ideal for the treatment of electronic g-tensors in transition metal complexes, the B3PW91 hybrid functional exhibited the overall most satisfactory performance. Apart from the validation of hybrid functionals, some aspects in the treatment of spin-orbit contributions to the g-tensor are discussed.
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Affiliation(s)
- Martin Kaupp
- Institut für Anorganische Chemie, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany.
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