1
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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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2
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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: 62] [Impact Index Per Article: 31.0] [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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3
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Sinha A, Banerjee S, Gangopadhyay J. An account of chronological computational investigations to ascertain the role of pπ-pπ bonding in influencing the Lewis acidity of BX3 (X = F, Cl, Br and I): Evolution of novel parameters and relegation of π-type back bonding concept. Coord Chem Rev 2022. [DOI: 10.1016/j.ccr.2022.214519] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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4
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Brütting M, Bahmann H, Kümmel S. Hybrid functionals with local range separation: Accurate atomization energies and reaction barrier heights. J Chem Phys 2022; 156:104109. [PMID: 35291795 DOI: 10.1063/5.0082957] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Range-separated hybrid approximations to the exchange-correlation density functional mix exact and semi-local exchange in a position-dependent manner. In their conventional form, the range separation is controlled by a constant parameter. Turning this constant into a density functional leads to a locally space-dependent range-separation function and thus a more powerful and flexible range-separation approach. In this work, we explore the self-consistent implementation of a local range-separated hybrid, taking into account a one-electron self-interaction correction and the behavior under uniform density scaling. We discuss different forms of the local range-separation function that depend on the electron density, its gradient, and the kinetic energy density. For test sets of atomization energies, reaction barrier heights, and total energies of atoms, we demonstrate that our best model is a clear improvement over common global range-separated hybrid functionals and can compete with density functionals that contain multiple empirical parameters. Promising results for equilibrium bond lengths, harmonic vibrational frequencies, and vertical ionization potentials further underline the potential and flexibility of our approach.
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Affiliation(s)
- Moritz Brütting
- Theoretical Physics IV, University of Bayreuth, 95440 Bayreuth, Germany
| | - Hilke Bahmann
- Physical and Theoretical Chemistry, Saarland University, 66123 Saarbrücken, Germany
| | - Stephan Kümmel
- Theoretical Physics IV, University of Bayreuth, 95440 Bayreuth, Germany
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5
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Daas TJ, Grossi J, Vuckovic S, Musslimani ZH, Kooi DP, Seidl M, Giesbertz KJH, Gori-Giorgi P. Large coupling-strength expansion of the Møller–Plesset adiabatic connection: From paradigmatic cases to variational expressions for the leading terms. J Chem Phys 2020; 153:214112. [DOI: 10.1063/5.0029084] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Timothy J. Daas
- 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
| | - Juri Grossi
- 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
| | - Stefan Vuckovic
- Department of Chemistry, University of California, Irvine, California 92697, USA
| | - Ziad H. Musslimani
- 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
| | - Derk P. Kooi
- 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
| | - Michael Seidl
- 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
| | - Klaas J. H. Giesbertz
- 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
| | - 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
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6
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Savin A. Models and corrections: Range separation for electronic interaction—Lessons from density functional theory. J Chem Phys 2020; 153:160901. [DOI: 10.1063/5.0028060] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Affiliation(s)
- Andreas Savin
- Laboratoire de Chimie Théorique, CNRS and Sorbonne University, 4 Place Jussieu, 75252 Paris Cedex 05, France
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7
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Giner E, Scemama A, Loos PF, Toulouse J. A basis-set error correction based on density-functional theory for strongly correlated molecular systems. J Chem Phys 2020; 152:174104. [DOI: 10.1063/5.0002892] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Emmanuel Giner
- Laboratoire de Chimie Théorique (UMR 7616), Sorbonne Université, CNRS, Paris, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique (UMR 7616), Sorbonne Université, CNRS, Paris, France
- Institut Universitaire de France, Paris, France
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8
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Aschebrock T, Kümmel S. Exploring local range separation: The role of spin scaling and one-electron self-interaction. J Chem Phys 2019; 151:154108. [DOI: 10.1063/1.5121731] [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)
- Thilo Aschebrock
- Theoretical Physics IV, University of Bayreuth, 95440 Bayreuth, Germany
| | - Stephan Kümmel
- Theoretical Physics IV, University of Bayreuth, 95440 Bayreuth, Germany
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9
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Baerends EJ. On derivatives of the energy with respect to total electron number and orbital occupation numbers. A critique of Janak's theorem. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1612955] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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10
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Kooi DP, Gori-Giorgi P. Local and global interpolations along the adiabatic connection of DFT: a study at different correlation regimes. Theor Chem Acc 2018; 137:166. [PMID: 30464722 PMCID: PMC6223841 DOI: 10.1007/s00214-018-2354-5] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2018] [Accepted: 09/21/2018] [Indexed: 11/16/2022]
Abstract
Interpolating the exchange-correlation energy along the density-fixed adiabatic connection of density functional theory is a promising way to build approximations that are not biased toward the weakly correlated regime. These interpolations can be performed at the global (integrated over all spaces) or at the local level, using energy densities. Many features of the relevant energy densities as well as several different ways to construct these interpolations, including comparisons between global and local variants, are investigated here for the analytically solvable Hooke's atom series, which allows for an exploration of different correlation regimes. We also analyze different ways to define the correlation kinetic energy density, focusing on the peak in the kinetic correlation potential.
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Affiliation(s)
- Derk P. Kooi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
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11
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Vuckovic S, Gori-Giorgi P, Della Sala F, Fabiano E. Restoring Size Consistency of Approximate Functionals Constructed from the Adiabatic Connection. J Phys Chem Lett 2018; 9:3137-3142. [PMID: 29787273 PMCID: PMC5994725 DOI: 10.1021/acs.jpclett.8b01054] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2018] [Accepted: 05/22/2018] [Indexed: 05/24/2023]
Abstract
Approximate exchange-correlation functionals built by modeling in a nonlinear way the adiabatic connection (AC) integrand of density functional theory have many attractive features, being virtually parameter-free and satisfying different exact properties, but they also have a fundamental flaw: they violate the size-consistency condition, crucial to evaluate interaction energies of molecular systems. We show that size consistency in the AC-based functionals can be restored in a very simple way at no extra computational cost. Results on a large set of benchmark molecular interaction energies show that functionals based on the interaction strength interpolation approximations are significantly more accurate than second-order perturbation theory.
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Affiliation(s)
- Stefan Vuckovic
- Department
of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling,
FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Paola Gori-Giorgi
- Department
of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling,
FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Fabio Della Sala
- Institute
for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center
for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
| | - Eduardo Fabiano
- Institute
for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center
for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
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12
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Giarrusso S, Gori-Giorgi P, Della Sala F, Fabiano E. Assessment of interaction-strength interpolation formulas for gold and silver clusters. J Chem Phys 2018; 148:134106. [DOI: 10.1063/1.5022669] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Affiliation(s)
- Sara Giarrusso
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Fabio Della Sala
- Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
| | - Eduardo Fabiano
- Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
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13
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Gould T, Pittalis S. Hartree and Exchange in Ensemble Density Functional Theory: Avoiding the Nonuniqueness Disaster. PHYSICAL REVIEW LETTERS 2017; 119:243001. [PMID: 29286753 DOI: 10.1103/physrevlett.119.243001] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2017] [Indexed: 06/07/2023]
Abstract
Ensemble density functional theory is a promising method for the efficient and accurate calculation of excitations of quantum systems, at least if useful functionals can be developed to broaden its domain of practical applicability. Here, we introduce a guaranteed single-valued "Hartree-exchange" ensemble density functional, E_{Hx}[n], in terms of the right derivative of the universal ensemble density functional with respect to the coupling constant at vanishing interaction. We show that E_{Hx}[n] is straightforwardly expressible using block eigenvalues of a simple matrix [Eq. (14)]. Specialized expressions for E_{Hx}[n] from the literature, including those involving superpositions of Slater determinants, can now be regarded as originating from the unifying picture presented here. We thus establish a clear and practical description for Hartree and exchange in ensemble systems.
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Affiliation(s)
- Tim Gould
- Qld Micro- and Nanotechnology Centre, Griffith University, Nathan, QLD 4111, Australia
| | - Stefano Pittalis
- CNR-Istituto di Nanoscienze, Via Campi 213A, I-41125 Modena, Italy
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14
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A Diagonally Updated Limited-Memory Quasi-Newton Method for the Weighted Density Approximation. COMPUTATION 2017. [DOI: 10.3390/computation5040042] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
We propose a limited-memory quasi-Newton method using the bad Broyden update and apply it to the nonlinear equations that must be solved to determine the effective Fermi momentum in the weighted density approximation for the exchange energy density functional. This algorithm has advantages for nonlinear systems of equations with diagonally dominant Jacobians, because it is easy to generalize the method to allow for periodic updates of the diagonal of the Jacobian. Systematic tests of the method for atoms show that one can determine the effective Fermi momentum at thousands of points in less than fifteen iterations.
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15
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Fabiano E, Gori-Giorgi P, Seidl M, Della Sala F. Interaction-Strength Interpolation Method for Main-Group Chemistry: Benchmarking, Limitations, and Perspectives. J Chem Theory Comput 2016; 12:4885-4896. [DOI: 10.1021/acs.jctc.6b00713] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Eduardo Fabiano
- Euromediterranean
Center for Nanomaterial Modelling and Technology (ECMT), Istituto Nanoscienze-CNR, Via per Arnesano 16, 73100 Lecce, Italy
- Center
for Biomolecular Nanotechnologies@UNILE, Istituto Italiano di Tecnologia (IIT), Via Barsanti, 73010 Arnesano, Italy
| | - Paola Gori-Giorgi
- Department
of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling,
FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Michael Seidl
- Department
of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling,
FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Fabio Della Sala
- Euromediterranean
Center for Nanomaterial Modelling and Technology (ECMT), Istituto Nanoscienze-CNR, Via per Arnesano 16, 73100 Lecce, Italy
- Center
for Biomolecular Nanotechnologies@UNILE, Istituto Italiano di Tecnologia (IIT), Via Barsanti, 73010 Arnesano, Italy
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16
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Miranda-Quintana RA, Ayers PW. Systematic treatment of spin-reactivity indicators in conceptual density functional theory. Theor Chem Acc 2016. [DOI: 10.1007/s00214-016-1995-5] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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17
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Mussard B, Toulouse J. Fractional-charge and fractional-spin errors in range-separated density-functional theory. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1213910] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Bastien Mussard
- Institut des sciences du calcul et des données, Université Pierre et Marie Curie, Sorbonne Universités, Paris, France
- Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, Sorbonne Universités, CNRS, Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, Sorbonne Universités, CNRS, Paris, France
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18
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Yang XD, Patel AHG, Miranda-Quintana RA, Heidar-Zadeh F, González-Espinoza CE, Ayers PW. Communication: Two types of flat-planes conditions in density functional theory. J Chem Phys 2016; 145:031102. [DOI: 10.1063/1.4958636] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Xiaotian Derrick Yang
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario LBS 4M1, Canada
| | - Anand H. G. Patel
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario LBS 4M1, Canada
| | - Ramón Alain Miranda-Quintana
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario LBS 4M1, Canada
- Laboratory of Computational and Theoretical Chemistry, Faculty of Chemistry, University of Havana, Havana, Cuba
| | - Farnaz Heidar-Zadeh
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario LBS 4M1, Canada
- Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | | | - Paul W. Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario LBS 4M1, Canada
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19
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Vuckovic S, Irons TJP, Savin A, Teale AM, Gori-Giorgi P. Exchange-Correlation Functionals via Local Interpolation along the Adiabatic Connection. J Chem Theory Comput 2016; 12:2598-610. [PMID: 27116427 PMCID: PMC4910137 DOI: 10.1021/acs.jctc.6b00177] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
The construction
of density-functional approximations is explored
by modeling the adiabatic connection locally, using
energy densities defined in terms of the electrostatic potential of
the exchange–correlation hole. These local models are more
amenable to the construction of size-consistent approximations than
their global counterparts. In this work we use accurate input local
ingredients to assess the accuracy of a range of local interpolation
models against accurate exchange–correlation energy densities.
The importance of the strictly correlated electrons (SCE) functional
describing the strong coupling limit is emphasized, enabling the corresponding
interpolated functionals to treat strong correlation effects. In addition
to exploring the performance of such models numerically for the helium
and beryllium isoelectronic series and the dissociation of the hydrogen
molecule, an approximate analytic model is presented for the initial
slope of the local adiabatic connection. Comparisons are made with
approaches based on global models, and prospects for future approximations
based on the local adiabatic connection are discussed.
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Affiliation(s)
- Stefan Vuckovic
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit , De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Tom J P Irons
- School of Chemistry, University of Nottingham , University Park, Nottingham NG7 2RD, United Kingdom
| | - Andreas Savin
- Laboratoire de Chimie Théorique, UPMC, Paris 06, UMR 7616, Sorbonne Universités , F-75005 Paris, France.,Laboratoire de Chimie Théorique, UMR 7616, CNRS F-75005, Paris, France
| | - Andrew M Teale
- School of Chemistry, University of Nottingham , University Park, Nottingham NG7 2RD, United Kingdom
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit , De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
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20
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21
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Teale AM, Helgaker T, Savin A. Alternative Representations of the Correlation Energy in Density-Functional Theory: A Kinetic-Energy Based Adiabatic Connection. J CHIN CHEM SOC-TAIP 2015. [DOI: 10.1002/jccs.201500132] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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22
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Vuckovic S, Wagner LO, Mirtschink A, Gori-Giorgi P. Hydrogen Molecule Dissociation Curve with Functionals Based on the Strictly Correlated Regime. J Chem Theory Comput 2015; 11:3153-62. [DOI: 10.1021/acs.jctc.5b00387] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Stefan Vuckovic
- Department of Theoretical
Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Lucas O. Wagner
- Department of Theoretical
Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - André Mirtschink
- Department of Theoretical
Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Paola Gori-Giorgi
- Department of Theoretical
Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
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23
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van Aggelen H, Yang Y, Yang W. Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random phase approximation. J Chem Phys 2015; 140:18A511. [PMID: 24832319 DOI: 10.1063/1.4865816] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Despite their unmatched success for many applications, commonly used local, semi-local, and hybrid density functionals still face challenges when it comes to describing long-range interactions, static correlation, and electron delocalization. Density functionals of both the occupied and virtual orbitals are able to address these problems. The particle-hole (ph-) Random Phase Approximation (RPA), a functional of occupied and virtual orbitals, has recently known a revival within the density functional theory community. Following up on an idea introduced in our recent communication [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013)], we formulate more general adiabatic connections for the correlation energy in terms of pairing matrix fluctuations described by the particle-particle (pp-) propagator. With numerical examples of the pp-RPA, the lowest-order approximation to the pp-propagator, we illustrate the potential of density functional approximations based on pairing matrix fluctuations. The pp-RPA is size-extensive, self-interaction free, fully anti-symmetric, describes the strong static correlation limit in H2, and eliminates delocalization errors in H2(+) and other single-bond systems. It gives surprisingly good non-bonded interaction energies--competitive with the ph-RPA--with the correct R(-6) asymptotic decay as a function of the separation R, which we argue is mainly attributable to its correct second-order energy term. While the pp-RPA tends to underestimate absolute correlation energies, it gives good relative energies: much better atomization energies than the ph-RPA, as it has no tendency to underbind, and reaction energies of similar quality. The adiabatic connection in terms of pairing matrix fluctuation paves the way for promising new density functional approximations.
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Affiliation(s)
- Helen van Aggelen
- Department of Inorganic and Physical Chemistry, Ghent University, Ghent, Belgium
| | - Yang Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Weitao Yang
- Department of Chemistry and Department of Physics, Duke University, Durham, North Carolina 27708, USA
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24
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25
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Levy M, Anderson JSM, Zadeh FH, Ayers PW. Kinetic and electron-electron energies for convex sums of ground state densities with degeneracies and fractional electron number. J Chem Phys 2014; 140:18A538. [DOI: 10.1063/1.4871734] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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26
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Ayers PW, Levy M. Tight constraints on the exchange-correlation potentials of degenerate states. J Chem Phys 2014; 140:18A537. [DOI: 10.1063/1.4871732] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
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27
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Cuevas-Saavedra R, Chakraborty D, Rabi S, Cárdenas C, Ayers PW. Symmetric Nonlocal Weighted Density Approximations from the Exchange-Correlation Hole of the Uniform Electron Gas. J Chem Theory Comput 2012; 8:4081-93. [DOI: 10.1021/ct300325t] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Affiliation(s)
- Rogelio Cuevas-Saavedra
- Department
of Chemistry and
Chemical Biology, McMaster University,
Hamilton, Ontario, Canada
| | - Debajit Chakraborty
- Department
of Chemistry and
Chemical Biology, McMaster University,
Hamilton, Ontario, Canada
| | - Sandra Rabi
- Department
of Chemistry and
Chemical Biology, McMaster University,
Hamilton, Ontario, Canada
| | - Carlos Cárdenas
- Departamento de Física,
Facultad de Ciencias, Universidad de Chile, 653-Santiago, Chile
| | - Paul W. Ayers
- Department
of Chemistry and
Chemical Biology, McMaster University,
Hamilton, Ontario, Canada
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28
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Mirtschink A, Seidl M, Gori-Giorgi P. Energy Densities in the Strong-Interaction Limit of Density Functional Theory. J Chem Theory Comput 2012; 8:3097-107. [DOI: 10.1021/ct3003892] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- André Mirtschink
- Department of Theoretical Chemistry
and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit,
De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Michael Seidl
- Institute of Theoretical Physics,
University of Regensburg, D-93040 Regensburg, Germany
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry
and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit,
De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
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29
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Moussa JE, Schultz PA, Chelikowsky JR. Analysis of the Heyd-Scuseria-Ernzerhof density functional parameter space. J Chem Phys 2012; 136:204117. [DOI: 10.1063/1.4722993] [Citation(s) in RCA: 117] [Impact Index Per Article: 9.8] [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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van Aggelen H, Verstichel B, Bultinck P, Neck DV, Ayers PW, Cooper DL. Variational second order density matrix study of F3−: Importance of subspace constraints for size-consistency. J Chem Phys 2011; 134:054115. [DOI: 10.1063/1.3532409] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
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31
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Lathiotakis NN, Gidopoulos NI, Helbig N. Size consistency of explicit functionals of the natural orbitals in reduced density matrix functional theory. J Chem Phys 2010; 132:084105. [DOI: 10.1063/1.3324699] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.9] [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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Gori-Giorgi P, Seidl M. Density functional theory for strongly-interacting electrons: perspectives for physics and chemistry. Phys Chem Chem Phys 2010; 12:14405-19. [DOI: 10.1039/c0cp01061h] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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33
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Gori-Giorgi P, Ángyán JG, Savin A. Charge density reconstitution from approximate exchange-correlation holes. CAN J CHEM 2009. [DOI: 10.1139/v09-104] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
The electronic charge density and the expectation of any monoelectronic operator can be reconstructed by a density-weighted integral of the exchange-correlation hole. This property can be used to test and improve approximate holes that are not spherically averaged. As an example, we test the Becke–Roussel exhange-hole model in its nonspherical formulation on small atoms, finding that it accurately reproduces the density in the core region, while missing some of the features of the valence and core-valence regions. The same test on the local-density approximation shows poor results, as expected.
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Affiliation(s)
- Paola Gori-Giorgi
- Laboratoire de Chimie Théorique, CNRS UMR 7616, Université Pierre et Marie Curie, 4 Place Jussieu, F-75252 Paris, France
- Équipe Modélisation Quantique et Cristallographique, CRM2, UMR 7036, Institut Jean Barriol, Nancy-University - CNRS, B.P. 239, F-54506 Vandœuvre-lès-Nancy, France
| | - János G. Ángyán
- Laboratoire de Chimie Théorique, CNRS UMR 7616, Université Pierre et Marie Curie, 4 Place Jussieu, F-75252 Paris, France
- Équipe Modélisation Quantique et Cristallographique, CRM2, UMR 7036, Institut Jean Barriol, Nancy-University - CNRS, B.P. 239, F-54506 Vandœuvre-lès-Nancy, France
| | - Andreas Savin
- Laboratoire de Chimie Théorique, CNRS UMR 7616, Université Pierre et Marie Curie, 4 Place Jussieu, F-75252 Paris, France
- Équipe Modélisation Quantique et Cristallographique, CRM2, UMR 7036, Institut Jean Barriol, Nancy-University - CNRS, B.P. 239, F-54506 Vandœuvre-lès-Nancy, France
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34
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Sancho-García JC, Pérez-Jiménez AJ. Assessment of double-hybrid energy functionals for π-conjugated systems. J Chem Phys 2009; 131:084108. [DOI: 10.1063/1.3212881] [Citation(s) in RCA: 71] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
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35
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Savin A. Potential-Driven Adiabatic Connection in Density Functional Theory. J Chem Theory Comput 2009; 5:822-6. [PMID: 26609588 DOI: 10.1021/ct8005776] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
As density functional theory conventionally assumes that the density of a chosen model system (e.g., the Kohn-Sham system) is the same as the exact one, one might expect that approximations to the exact density introduce supplementary errors by falsifying the density. In fact, this is not true: by modeling the exchange-correlation holes for all densities, density functional approximations avoid this problem. The technique used to show it is a potential-driven adiabatic connection which hopefully will also permit constructing new approximations in the spirit of DFT.
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Affiliation(s)
- Andreas Savin
- Laboratoire de Chimie Théorique, UMR 7616, CNRS and Université Pierre et Marie, Curie-Paris VI, 4, place Jussieu, F-75252 Paris Cedex 5, France
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36
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Gori-Giorgi P, Vignale G, Seidl M. Electronic Zero-Point Oscillations in the Strong-Interaction Limit of Density Functional Theory. J Chem Theory Comput 2009; 5:743-53. [PMID: 26609579 DOI: 10.1021/ct8005248] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The exchange-correlation energy in Kohn-Sham density functional theory can be expressed exactly in terms of the change in the expectation of the electron-electron repulsion operator when, in the many-electron Hamiltonian, this same operator is multiplied by a real parameter λ varying between 0 (Kohn-Sham system) and 1 (physical system). In this process, usually called adiabatic connection, the one-electron density is kept fixed by a suitable local one-body potential. The strong-interaction limit of density functional theory, defined as the limit λ→∞, turns out to be like the opposite noninteracting Kohn-Sham limit (λ→0) mathematically simpler than the physical (λ = 1) case and can be used to build an approximate interpolation formula between λ→0 and λ→∞ for the exchange-correlation energy. Here we extend the systematic treatment of the λ→∞ limit [Phys. Rev. A 2007, 75, 042511] to the next leading term, describing zero-point oscillations of strictly correlated electrons, with numerical examples for small spherical atoms. We also propose an improved approximate functional for the zero-point term and a revised interpolation formula for the exchange-correlation energy satisfying more exact constraints.
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Affiliation(s)
- Paola Gori-Giorgi
- Laboratoire de Chimie Théorique, CNRS, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris, France, Afdeling Theoretische Chemie, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands, Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, and Institute of Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany
| | - Giovanni Vignale
- Laboratoire de Chimie Théorique, CNRS, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris, France, Afdeling Theoretische Chemie, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands, Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, and Institute of Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany
| | - Michael Seidl
- Laboratoire de Chimie Théorique, CNRS, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris, France, Afdeling Theoretische Chemie, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands, Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, and Institute of Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany
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