1
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Li J, Yang W. Chemical Potentials and the One-Electron Hamiltonian of the Second-Order Perturbation Theory from the Functional Derivative Approach. J Phys Chem A 2024; 128:4876-4885. [PMID: 38842399 DOI: 10.1021/acs.jpca.4c01574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2024]
Abstract
We develop a functional derivative approach to calculate the chemical potentials of second-order perturbation theory (MP2). In the functional derivative approach, the correlation part of the MP2 chemical potential, which is the derivative of the MP2 correlation energy with respect to the occupation number of frontier orbitals, is obtained from the chain rule via the noninteracting Green's function. First, the MP2 correlation energy is expressed in terms of the noninteracting Green's function, and its functional derivative to the noninteracting Green's function is the second-order self-energy. Then, the derivative of the noninteracting Green's function to the occupation number is obtained by including the orbital relaxation effect. We show that the MP2 chemical potentials obtained from the functional derivative approach agree with that obtained from the finite difference approach. The one-electron Hamiltonian, defined as the derivative of the MP2 energy with respect to the one particle density matrix, is also derived using the functional derivative approach, which can be used in the self-consistent calculations of MP2 and double-hybrid density functionals. The developed functional derivative approach is promising for calculating the chemical potentials and the one-electron Hamiltonian of approximate functionals and many-body perturbation approaches dependent explicitly on the noninteracting Green's function.
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Affiliation(s)
- Jiachen Li
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
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2
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Richer M, Heidar-Zadeh F, Ríos-Gutiérrez M, Yang XD, Ayers PW. Spin-Polarized Conceptual Density Functional Theory from the Convex Hull. J Chem Theory Comput 2024; 20:4616-4628. [PMID: 38819213 DOI: 10.1021/acs.jctc.4c00213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/01/2024]
Abstract
We present a new, nonarbitrary, internally consistent, and unambiguous framework for spin-polarized conceptual density-functional theory (SP-DFT). We explicitly characterize the convex hull of energy, as a function of the number of electrons and their spin, as the only accessible ground states in spin-polarized density functional theory. Then, we construct continuous linear and quadratic models for the energy. The nondifferentiable linear model exactly captures the simplicial geometry of the complex hull about the point of interest and gives exact representations for the conceptual DFT reactivity indicators. The continuous quadratic energy model is the paraboloid of maximum curvature, which most tightly encloses the point of interest and neighboring vertices. The quadratic model is invariant to the choice of coordinate system (i.e., {N, S} vs {Nα, Nβ}) and reduces to a sensible formulation of spin-free conceptual DFT in the appropriate limit. Using the quadratic model, we generalize the Parr functions {P+(r), P-(r)} (and their derivatives with respect to number of electrons) to this new spin-polarized framework, integrating the Parr function concept into the context of (spin-polarized) conceptual DFT, and extending it to include higher-order effects.
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Affiliation(s)
- Michelle Richer
- Department of Chemistry, Queen's University, 90 Bader Lane, Kingston, Ontario K7L 3N6, Canada
- Department of Chemistry, McMaster University, 1280 Main St. West, Hamilton, Ontario L8S 4M1, Canada
| | - Farnaz Heidar-Zadeh
- Department of Chemistry, Queen's University, 90 Bader Lane, Kingston, Ontario K7L 3N6, Canada
| | - Mar Ríos-Gutiérrez
- Department of Organic Chemistry, University of Valencia, Dr. Moliner 50, 46100 Burjassot, Valencia, Spain
| | - Xiaotian Derrick Yang
- Department of Chemistry, McMaster University, 1280 Main St. West, Hamilton, Ontario L8S 4M1, Canada
| | - Paul W Ayers
- Department of Chemistry, McMaster University, 1280 Main St. West, Hamilton, Ontario L8S 4M1, Canada
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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: 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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4
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Wei Z, Göltl F, Steinmann SN, Sautet P. Modeling Electrochemical Processes with Grand Canonical Treatment of Many-Body Perturbation Theory. J Phys Chem Lett 2022; 13:6079-6084. [PMID: 35758931 DOI: 10.1021/acs.jpclett.2c01376] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Electrocatalysis plays a key role in sustainable energy conversion and storage. It is critical to model the grand canonical treatment of electrons, which accounts for the electrochemical potential explicitly, at the atomic scale and understand these reactions at electrified interfaces. However, such a grand canonical treatment for electrocatalytic modeling is in practice restricted to a treatment of electronic structure with density functional theory, and more accurate methods are in many cases desirable. Here, we develop an original workflow combining the grand canonical treatment of electrons with many-body perturbation theory in its random phase approximation (RPA). Using the potential dependent adsorption of carbon monoxide on the copper (100) facet, we show that the grand canonical RPA energetics provide the correct on-top Cu geometry for CO at reducing potential. The match with experimental results is significantly improved compared to the functionals at the generalized gradient approximation level, which is the most commonly used approximation for electrochemical applications. We expect this development to pave the way to further electrochemical applications using RPA.
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Affiliation(s)
- Ziyang Wei
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States
| | - Florian Göltl
- Department of Biosystems Engineering, The University of Arizona, Tucson, Arizona 85721, United States
| | - Stephan N Steinmann
- ENS de Lyon, CNRS UMR 5182, Laboratoire de Chimie, 46 Allée d'Italie, 69342, Lyon, France
| | - Philippe Sautet
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States
- Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, California 90095, United States
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5
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Kraisler E, Hodgson MJP, Gross EKU. From Kohn-Sham to Many-Electron Energies via Step Structures in the Exchange-Correlation Potential. J Chem Theory Comput 2021; 17:1390-1407. [PMID: 33595312 PMCID: PMC8363072 DOI: 10.1021/acs.jctc.0c01093] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
Accurately
describing excited states within Kohn–Sham (KS)
density functional theory (DFT), particularly those which induce ionization
and charge transfer, remains a great challenge. Common exchange-correlation
(xc) approximations are unreliable for excited states owing, in part,
to the absence of a derivative discontinuity in the xc energy (Δ),
which relates a many-electron energy difference to the corresponding
KS energy difference. We demonstrate, analytically and numerically,
how the relationship between KS and many-electron energies leads to
the step structures observed in the exact xc potential in four scenarios:
electron addition, molecular dissociation, excitation of a finite
system, and charge transfer. We further show that steps in the potential
can be obtained also with common xc approximations, as simple as the
LDA, when addressed from the ensemble perspective. The article therefore
highlights how capturing the relationship between KS and many-electron
energies with advanced xc approximations is crucial for accurately
calculating excitations, as well as the ground-state density and energy
of systems which consist of distinct subsystems.
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Affiliation(s)
- Eli Kraisler
- Fritz Haber Center for Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, 9091401 Jerusalem, Israel
| | - M J P Hodgson
- Department of Physics, Durham University, South Road, Durham DH1 3LE, United Kingdom.,Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
| | - E K U Gross
- Fritz Haber Center for Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, 9091401 Jerusalem, Israel
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6
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Peters LDM, Kussmann J, Ochsenfeld C. A Fermi smearing variant of the Tamm–Dancoff approximation for nonadiabatic dynamics involving S 1–S 0 transitions: Validation and application to azobenzene. J Chem Phys 2020; 153:094104. [DOI: 10.1063/5.0016487] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Laurens D. M. Peters
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany
| | - Jörg Kussmann
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, D-70569 Stuttgart, Germany
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7
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Zhang IY, Xu X. On the top rung of Jacob's ladder of density functional theory: Toward resolving the dilemma of
SIE
and
NCE. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2020. [DOI: 10.1002/wcms.1490] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Igor Ying Zhang
- 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 China
| | - 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 China
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8
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Loos PF, Fromager E. A weight-dependent local correlation density-functional approximation for ensembles. J Chem Phys 2020; 152:214101. [DOI: 10.1063/5.0007388] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Emmanuel Fromager
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS, Université de Strasbourg, Strasbourg, France
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9
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Kraisler E. Asymptotic Behavior of the Exchange‐Correlation Energy Density and the Kohn‐Sham Potential in Density Functional Theory: Exact Results and Strategy for Approximations. Isr J Chem 2020. [DOI: 10.1002/ijch.201900103] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Eli Kraisler
- Fritz Haber Center for Molecular Dynamics and Institute of Chemistry The Hebrew University of Jerusalem 9091401 Jerusalem Israel
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10
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Marut C, Senjean B, Fromager E, Loos PF. Weight dependence of local exchange–correlation functionals in ensemble density-functional theory: double excitations in two-electron systems. Faraday Discuss 2020; 224:402-423. [DOI: 10.1039/d0fd00059k] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We discuss the construction of first-rung weight-dependent exchange–correlation density-functional approximations for He and H2 specifically designed for the computation of double excitations within Gross–Oliveira–Kohn-DFT.
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Affiliation(s)
- Clotilde Marut
- Laboratoire de Chimie et Physique Quantiques
- Université de Toulouse
- CNRS
- UPS
- France
| | - Bruno Senjean
- Instituut-Lorentz
- Universiteit Leiden
- 2300 RA Leiden
- The Netherlands
- Division of Theoretical Chemistry
| | - Emmanuel Fromager
- Laboratoire de Chimie Quantique
- Institut de Chimie
- CNRS
- Université de Strasbourg
- Strasbourg
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11
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Abstract
At zero temperature, coupled cluster theories are widely used to predict total energies, ground state expectation values, and even excited states for molecules and extended systems. However, for systems with a small band gap, such as metals, the zero-temperature approximation does not necessarily hold. Thermal effects may even give rise to interesting chemistry on metal surfaces. Most approaches to temperature dependent electronic properties employ finite temperature perturbation theory in the Matsubara frequency formulation. Computations require a large number of Matsubara frequencies to yield sufficiently accurate results, especially at low temperatures. This work, and independently the work of White and Chan J. Chem. Theory Comput. 2018 , DOI: 10.1021/acs.jctc.8b00773 , proposes a coupled cluster implementation directly in the imaginary time domain on the compact interval [0, β], closely related to the thermal cluster cumulant approach of Sanyal et al. [ Chem. Phys. Lett. 1992 , 192 , 55 - 61 ] , Sanyal et al. [ Phys. Rev. E 1993 , 48 , 3373 - 3389 ], and Mandal et al. [ Int. J. Mod. Phys. B 2003 , 17 , 5367 - 5377 ]. Here, the arising imaginary time dependent coupled cluster amplitude integral equations are solved in the linearized direct ring doubles approximation, also referred to as Tamm-Dancoff approximation with second order (linearized) screened exchange. In this framework, the transition from finite to zero temperature is uniform and comes at no extra costs, allowing to go to temperatures as low as room temperature. In this approximation, correlation grand potentials are calculated over a wide range of temperatures for solid lithium, a metallic system, and for solid silicon, a semiconductor.
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Affiliation(s)
- Felix Hummel
- Institute for Theoretical Physics , TU Wien , Wiedner Hauptstraße 8-10/136 , 1040 Vienna , Austria
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12
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Staub R, Iannuzzi M, Khaliullin RZ, Steinmann SN. Energy Decomposition Analysis for Metal Surface-Adsorbate Interactions by Block Localized Wave Functions. J Chem Theory Comput 2018; 15:265-275. [PMID: 30462497 DOI: 10.1021/acs.jctc.8b00957] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The energy decomposition analysis based on block localized wave functions (BLW-EDA) allows one to gain physical insight into the nature of chemical bonding, decomposing the interaction energy in (1) a "frozen" term, accounting for the attraction due to electrostatic and dispersion interactions, modulated by Pauli repulsion, (2) the variationally assessed polarization energy, and (3) the charge transfer. This method has so far been applied to gas- and condensed-phase molecular systems. However, its standard version is not compatible with fractionally occupied orbitals (i.e., electronic smearing) and, as a consequence, cannot be applied to metallic surfaces. In this work, we propose a simple and practical extension of BLW-EDA to fractionally occupied orbitals, termed Ensemble BLW-EDA. As illustrative examples, we have applied the developed method to analyze the nature of the interaction of various adsorbates on Pt(111), ranging from physisorbed water to strongly chemisorbed ethylene. Our results show that polarization and charge transfer both contribute significantly at the adsorption minimum for all studied systems. The energy decomposition analysis provides details with respect to competing adsorption sites (e.g., CO on atop vs hollow sites) and elucidates the respective importance of polarization and charge transfer for the increased adsorption energy of H2S compared to H2O. Our development will enable a deeper understanding of the impact of charge transfer on catalytic processes in general.
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Affiliation(s)
- Ruben Staub
- Univ Lyon, Ecole Normale Supérieure de Lyon, CNRS Université Lyon 1 , Laboratoire de Chimie UMR 5182 , 46 allée d'Italie , Lyon , F-69364 , France
| | - Marcella Iannuzzi
- Institut für Chemie , University of Zurich , Winterthurerstrasse 190 , Zurich , CH-8057 , Switzerland
| | - Rustam Z Khaliullin
- Department of Chemistry , McGill University , 801 Sherbrooke Street West , Montreal , Québec H3A 0B8 , Canada
| | - Stephan N Steinmann
- Univ Lyon, Ecole Normale Supérieure de Lyon, CNRS Université Lyon 1 , Laboratoire de Chimie UMR 5182 , 46 allée d'Italie , Lyon , F-69364 , France
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13
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Jupp AR, Johnstone TC, Stephan DW. Improving the Global Electrophilicity Index (GEI) as a Measure of Lewis Acidity. Inorg Chem 2018; 57:14764-14771. [PMID: 30422644 DOI: 10.1021/acs.inorgchem.8b02517] [Citation(s) in RCA: 44] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The global electrophilicity index (GEI) has been further explored as a general and base-free metric for Lewis acidity. A number of computational methods, including post-Hartree-Fock, density functional theory, and time-dependent density functional theory, have been explored. In this fashion, we sought the method most applicable to a range of different Lewis acids with differing structural and electronic features, including boron trihalides, silicon tetrahalides, fluoroaryl boranes, and group 15 pentahalides. The most accurate and computationally efficient approach was found to use the energies of the orbitals from a geometry optimization at the B3LYP/def2-TZVP level of theory. In addition, the GEI is shown to act as an effective acidity metric that is complementary to the fluoride ion affinity. The GEI also proved to be a better gauge of Lewis acidity for softer bases, as confirmed by comparison to the iodide ion affinity of the group 15 pentahalides.
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Affiliation(s)
- Andrew R Jupp
- Department of Chemistry , University of Toronto , 80 St. George Street , Toronto , Ontario M5S 3H6 , Canada
| | - Timothy C Johnstone
- Department of Chemistry , University of Toronto , 80 St. George Street , Toronto , Ontario M5S 3H6 , Canada
| | - Douglas W Stephan
- Department of Chemistry , University of Toronto , 80 St. George Street , Toronto , Ontario M5S 3H6 , Canada
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14
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Heidar-Zadeh F, Ayers PW, Verstraelen T, Vinogradov I, Vöhringer-Martinez E, Bultinck P. Information-Theoretic Approaches to Atoms-in-Molecules: Hirshfeld Family of Partitioning Schemes. J Phys Chem A 2017; 122:4219-4245. [DOI: 10.1021/acs.jpca.7b08966] [Citation(s) in RCA: 68] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Farnaz Heidar-Zadeh
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
- Department of Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium
| | - Paul W. Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Toon Verstraelen
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | - Ivan Vinogradov
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Esteban Vöhringer-Martinez
- Departamento de Físico-Química, Facultad de Ciencias Químicas, Universidad de Concepción, Concepción, Chile
| | - Patrick Bultinck
- Department of Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium
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15
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Hirata S, Doran AE, Knowles PJ, Ortiz JV. One-particle many-body Green’s function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms. J Chem Phys 2017; 147:044108. [DOI: 10.1063/1.4994837] [Citation(s) in RCA: 44] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Alexander E. Doran
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Peter J. Knowles
- School of Chemistry, Cardiff University, Park Place, Cardiff CF10 3AT, United Kingdom
| | - J. V. Ortiz
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, USA
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16
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Affiliation(s)
- Bo Peng
- William R. Wiley Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, WA, USA
| | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, WA, USA
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17
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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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18
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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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19
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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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20
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Su NQ, Xu X. Second-Order Perturbation Theory for Fractional Occupation Systems: Applications to Ionization Potential and Electron Affinity Calculations. J Chem Theory Comput 2016; 12:2285-97. [DOI: 10.1021/acs.jctc.6b00197] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Neil Qiang Su
- Collaborative Innovation
Center of Chemistry for Energy Materials, Shanghai Key Laboratory
of Molecular Catalysis and Innovative Materials, MOE Laboratory for
Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200433, China
| | - Xin Xu
- Collaborative Innovation
Center of Chemistry for Energy Materials, Shanghai Key Laboratory
of Molecular Catalysis and Innovative Materials, MOE Laboratory for
Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200433, China
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21
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McKechnie S, Booth GH, Cohen AJ, Cole JM. On the accuracy of density functional theory and wave function methods for calculating vertical ionization energies. J Chem Phys 2015; 142:194114. [DOI: 10.1063/1.4921037] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Scott McKechnie
- Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - George H. Booth
- Theory and Simulation of Condensed Matter, King’s College London, The Strand, London WC2R 2LS, United Kingdom
| | - Aron J. Cohen
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Jacqueline M. Cole
- Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom
- Argonne National Laboratory, 9700 S Cass Avenue, Argonne, Illinois 60439, USA
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22
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Phillips JJ, Kananenka AA, Zgid D. Fractional charge and spin errors in self-consistent Green’s function theory. J Chem Phys 2015; 142:194108. [DOI: 10.1063/1.4921259] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jordan J. Phillips
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Alexei A. Kananenka
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
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23
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Su NQ, Yang W, Mori-Sánchez P, Xu X. Fractional Charge Behavior and Band Gap Predictions with the XYG3 Type of Doubly Hybrid Density Functionals. J Phys Chem A 2014; 118:9201-11. [DOI: 10.1021/jp5029992] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Neil Qiang Su
- Collaborative Innovation Center
of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular
Catalysis and Innovative Materials, MOE Laboratory for Computational
Physical Science, Department of Chemistry, Fudan University, Shanghai 200433, China
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Paula Mori-Sánchez
- Departamento de Quı́mica, Universidad Autónoma de Madrid, Madrid 28049, Spain
| | - Xin Xu
- Collaborative Innovation Center
of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular
Catalysis and Innovative Materials, MOE Laboratory for Computational
Physical Science, Department of Chemistry, Fudan University, Shanghai 200433, China
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24
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Mori-Sánchez P, Cohen AJ. The derivative discontinuity of the exchange–correlation functional. Phys Chem Chem Phys 2014; 16:14378-87. [DOI: 10.1039/c4cp01170h] [Citation(s) in RCA: 57] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Abstract
Manifestations of the derivative discontinuity of the energy in density functional theory are demonstrated in simple systems in chemistry and physics.
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Affiliation(s)
- Paula Mori-Sánchez
- Departamento de Química and Instituto de Física de la Materia Condensada (IFIMAC)
- Universidad Autónoma de Madrid
- Madrid, Spain
| | - Aron J. Cohen
- Department of Chemistry
- University of Cambridge
- Cambridge, UK
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