1
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Cernatic F, Fromager E. Extended N-centered ensemble density functional theory of double electronic excitations. J Comput Chem 2024. [PMID: 38700389 DOI: 10.1002/jcc.27387] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2024] [Revised: 04/12/2024] [Accepted: 04/19/2024] [Indexed: 05/05/2024]
Abstract
A recent work (arXiv:2401.04685) has merged N-centered ensembles of neutral and charged electronic ground states with ensembles of neutral ground and excited states, thus providing a general and in-principle exact (so-called extended N-centered) ensemble density functional theory of neutral and charged electronic excitations. This formalism made it possible to revisit the concept of density-functional derivative discontinuity, in the particular case of single excitations from the highest occupied Kohn-Sham (KS) molecular orbital, without invoking the usual "asymptotic behavior of the density" argument. In this work, we address a broader class of excitations, with a particular focus on double excitations. An exact implementation of the theory is presented for the two-electron Hubbard dimer model. A thorough comparison of the true physical ground- and excited-state electronic structures with that of the fictitious ensemble density-functional KS system is also presented. Depending on the choice of the density-functional ensemble as well as the asymmetry of the dimer and the correlation strength, an inversion of states can be observed. In some other cases, the strong mixture of KS states within the true physical system makes the assignment "single excitation" or "double excitation" irrelevant.
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Affiliation(s)
- Filip Cernatic
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, Strasbourg, France
| | - Emmanuel Fromager
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, Strasbourg, France
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2
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Tozer DJ. Effective homogeneity of Fermi-Amaldi-containing exchange-correlation functionals. J Chem Phys 2023; 159:244102. [PMID: 38131479 DOI: 10.1063/5.0179111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2023] [Accepted: 11/30/2023] [Indexed: 12/23/2023] Open
Abstract
Parr and Ghosh [Phys. Rev. A. 51 3564 (1995)] demonstrated that when near-exact electron densities and potentials are used, the exchange-correlation energies of first- and second-row atoms are well-described by a combination of the Fermi-Amaldi functional with a functional that is homogeneous of degree one under density scaling. Insight into this observation is provided by considering their work from the perspective of the effective homogeneity of the overall exchange-correlation functional. By considering a general form that combines the Fermi-Amaldi functional with a functional that is homogeneous of degree k, it is shown that for these atoms, the functional of Parr and Ghosh (k = 1) exhibits essentially optimal effective homogeneities on the electron-deficient side of the integer. Percentage errors in effective homogeneities are close to percentage errors in exchange-correlation energies.
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Affiliation(s)
- David J Tozer
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
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3
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Racioppi S, Lolur P, Hyldgaard P, Rahm M. A Density Functional Theory for the Average Electron Energy. J Chem Theory Comput 2023; 19:799-807. [PMID: 36693279 PMCID: PMC9933435 DOI: 10.1021/acs.jctc.2c00899] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
A formally exact density functional theory (DFT) determination of the average electron energy is presented. Our theory, which is based on a different accounting of energy functional terms, partially solves one well-known downside of conventional Kohn-Sham (KS) DFT: that electronic energies have but tenuous connections to physical quantities. Calculated average electron energies are close to experimental ionization potentials (IPs) in one-electron systems, demonstrating a surprisingly small effect of self-interaction and other exchange-correlation errors in established DFT methods. Remarkable agreement with ab initio quantum mechanical calculations of multielectron systems is demonstrated using several flavors of DFT, and we argue for the use of the average electron energy as a design criterion for density functional approximations.
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Affiliation(s)
- Stefano Racioppi
- †Department
of Chemistry and Chemical Engineering, ‡Department of Microtechnology and
Nanoscience—MC2, Chalmers University
of Technology, Kemigården 4, Gothenburg, 41296, Sweden
| | - Phalgun Lolur
- †Department
of Chemistry and Chemical Engineering, ‡Department of Microtechnology and
Nanoscience—MC2, Chalmers University
of Technology, Kemigården 4, Gothenburg, 41296, Sweden
| | - Per Hyldgaard
- †Department
of Chemistry and Chemical Engineering, ‡Department of Microtechnology and
Nanoscience—MC2, Chalmers University
of Technology, Kemigården 4, Gothenburg, 41296, Sweden,
| | - Martin Rahm
- †Department
of Chemistry and Chemical Engineering, ‡Department of Microtechnology and
Nanoscience—MC2, Chalmers University
of Technology, Kemigården 4, Gothenburg, 41296, Sweden,
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4
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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: 59] [Impact Index Per Article: 29.5] [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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5
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Kato T, Saito S. Kohn–Sham
potentials by an inverse
Kohn–Sham
equation and accuracy assessment by virial theorem. J CHIN CHEM SOC-TAIP 2022. [DOI: 10.1002/jccs.202200355] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Tsuyoshi Kato
- Department of Chemistry School of Science, The University of Tokyo Tokyo Japan
| | - Shinji Saito
- Department of Theoretical and Computational Molecular Science Institute for Molecular Science Okazaki Japan
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6
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Dillon DJ, Tozer DJ. Incorporation of the Fermi-Amaldi Term into Direct Energy Kohn-Sham Calculations. J Chem Theory Comput 2022; 18:703-709. [PMID: 34978791 DOI: 10.1021/acs.jctc.1c00840] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In direct energy Kohn-Sham (DEKS) theory, the density functional theory electronic energy equals the sum of occupied orbital energies, obtained from Kohn-Sham-like orbital equations involving a shifted Hartree exchange-correlation potential, which must be approximated. In the present study, the Fermi-Amaldi term is incorporated into approximate DEKS calculations, introducing the required -1/r contribution to the exchange-correlation component of the shifted potential in asymptotic regions. It also provides a mechanism for eliminating one-electron self-interaction error, and it introduces a nonzero exchange-correlation component of the shift in the potential that is of appropriate magnitude. The resulting electronic energies are very sensitive to the methodologies considered, whereas the highest occupied molecular orbital energies and exchange-correlation potentials are much less sensitive and are similar to those obtained from DEKS calculations using a conventional exchange-correlation functional.
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Affiliation(s)
- Daisy J Dillon
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, U.K
| | - David J Tozer
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, U.K
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7
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Ensemble Density Functional Theory of Neutral and Charged Excitations : Exact Formulations, Standard Approximations, and Open Questions. Top Curr Chem (Cham) 2021; 380:4. [PMID: 34825294 DOI: 10.1007/s41061-021-00359-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2021] [Accepted: 11/02/2021] [Indexed: 10/19/2022]
Abstract
Recent progress in the field of (time-independent) ensemble density-functional theory (DFT) for excited states are reviewed. Both Gross-Oliveira-Kohn (GOK) and N-centered ensemble formalisms, which are mathematically very similar and allow for an in-principle-exact description of neutral and charged electronic excitations, respectively, are discussed. Key exact results, for example, the equivalence between the infamous derivative discontinuity problem and the description of weight dependencies in the ensemble exchange-correlation density functional, are highlighted. The variational evaluation of orbital-dependent ensemble Hartree-exchange (Hx) energies is discussed in detail. We show in passing that state-averaging individual exact Hx energies can lead to severe (although solvable) v-representability issues. Finally, we explore the possibility of using the concept of density-driven correlation, which has been introduced recently and does not exist in regular ground-state DFT, for improving state-of-the-art correlation density-functional approximations for ensembles. The present review reflects the efforts of a growing community to turn ensemble DFT into a rigorous and reliable low-cost computational method for excited states. We hope that, in the near future, this contribution will stimulate new formal and practical developments in the field.
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8
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Gu Y, Xu X. Extended Koopmans’ theorem in the adiabatic connection formalism: Applied to doubly hybrid density functionals. J Chem Phys 2020; 153:044109. [DOI: 10.1063/5.0010743] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yonghao Gu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, 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, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai 200433, China
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9
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Shu Y, Truhlar DG. Relationships between Orbital Energies, Optical and Fundamental Gaps, and Exciton Shifts in Approximate Density Functional Theory and Quasiparticle Theory. J Chem Theory Comput 2020; 16:4337-4350. [PMID: 32453951 DOI: 10.1021/acs.jctc.0c00320] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
The relationships between Kohn-Sham (KS) and generalized KS (GKS) density functional orbital energies and fundamental gaps or optical gaps raise many interesting questions including the physical meanings of KS and GKS orbital energies when computed with currently available approximate density functionals (ADFs). In this work, by examining three diverse databases with various ADFs, we examine such relations from the point of view of the exciton shift of quasiparticle theory. We start by calculating a large number of excitation energies by time-dependent density functional theory (TDDFT) with a large number of ADFs. To relate the exciton shift implicit in TDDFT to the exciton shift that is explicit in Green's function theory, we define the exciton shift in TDDFT as the difference of the response shift and the quasiparticle shift. We found a strong correlation between the response shift and the amount of Hartree-Fock exchange included in the density functional, with the response shift varying between -1 and 5 eV. This range is an order of magnitude larger than the mean errors of the TDDFT excitation energies. This result suggests that, with currently available functionals, the KS or GKS orbital energies should be treated as intermediate mathematical variables in the calculation of excitation energies rather than as the energies of independent-particle reference states for quasiparticle theory.
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Affiliation(s)
- Yinan Shu
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431, United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431, United States
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10
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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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11
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Jana S, Patra A, Constantin LA, Samal P. Screened range-separated hybrid by balancing the compact and slowly varying density regimes: Satisfaction of local density linear response. J Chem Phys 2020; 152:044111. [PMID: 32007058 DOI: 10.1063/1.5131530] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
Due to their quantitative accuracy and ability to solve several difficulties, screened range-separated hybrid exchange-correlation functionals are now a standard approach for ab initio simulation of condensed matter systems. However, the screened range-separated hybrid functionals proposed so far are biased either toward compact or slowly varying densities. In this paper, we propose a screened range-separated hybrid functional, named HSEint, which can well describe these density regimes, achieving good accuracy for both molecular and solid-state systems. The semilocal part of the proposed functional is based on the PBEint generalized gradient approximation [E. Fabiano et al., Phys. Rev. B 82, 113104 (2010)], constructed for hybrid interfaces. To improve the functional performance, we employ exact or nearly exact constraints in the construction of range-separated hybrid functional, such as recovering of the local density linear response and semiclassical atom linear response.
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Affiliation(s)
- Subrata Jana
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Abhilash Patra
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Lucian A Constantin
- Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
| | - Prasanjit Samal
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
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12
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Gerolin A, Grossi J, Gori-Giorgi P. Kinetic Correlation Functionals from the Entropic Regularization of the Strictly Correlated Electrons Problem. J Chem Theory Comput 2020; 16:488-498. [PMID: 31855421 PMCID: PMC6964418 DOI: 10.1021/acs.jctc.9b01133] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2019] [Indexed: 11/29/2022]
Abstract
In this work, we study the entropic regularization of the strictly correlated electrons formalism, discussing the implications for density functional theory and establishing a link with earlier works on quantum kinetic energy and classical entropy. We carry out a very preliminary investigation (using simplified models) on the use of the solution of the entropic regularized problem to build approximations for the kinetic correlation functional at large coupling strengths. We also analyze lower and upper bounds to the Hohenberg-Kohn functional using the entropic regularized strictly correlated electrons problem.
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Affiliation(s)
- Augusto Gerolin
- Department of Theoretical
Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Juri Grossi
- 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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13
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Andrés J, Ayers PW, Boto RA, Carbó-Dorca R, Chermette H, Cioslowski J, Contreras-García J, Cooper DL, Frenking G, Gatti C, Heidar-Zadeh F, Joubert L, Martín Pendás Á, Matito E, Mayer I, Misquitta AJ, Mo Y, Pilmé J, Popelier PLA, Rahm M, Ramos-Cordoba E, Salvador P, Schwarz WHE, Shahbazian S, Silvi B, Solà M, Szalewicz K, Tognetti V, Weinhold F, Zins ÉL. Nine questions on energy decomposition analysis. J Comput Chem 2019; 40:2248-2283. [PMID: 31251411 DOI: 10.1002/jcc.26003] [Citation(s) in RCA: 88] [Impact Index Per Article: 17.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2019] [Accepted: 05/16/2019] [Indexed: 01/05/2023]
Abstract
The paper collects the answers of the authors to the following questions: Is the lack of precision in the definition of many chemical concepts one of the reasons for the coexistence of many partition schemes? Does the adoption of a given partition scheme imply a set of more precise definitions of the underlying chemical concepts? How can one use the results of a partition scheme to improve the clarity of definitions of concepts? Are partition schemes subject to scientific Darwinism? If so, what is the influence of a community's sociological pressure in the "natural selection" process? To what extent does/can/should investigated systems influence the choice of a particular partition scheme? Do we need more focused chemical validation of Energy Decomposition Analysis (EDA) methodology and descriptors/terms in general? Is there any interest in developing common benchmarks and test sets for cross-validation of methods? Is it possible to contemplate a unified partition scheme (let us call it the "standard model" of partitioning), that is proper for all applications in chemistry, in the foreseeable future or even in principle? In the end, science is about experiments and the real world. Can one, therefore, use any experiment or experimental data be used to favor one partition scheme over another? © 2019 Wiley Periodicals, Inc.
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Affiliation(s)
- Juan Andrés
- Departament de Ciències Experimentals Universitat Jaume I, 12080, Castelló, Spain
| | - Paul W Ayers
- Department of Chemistry and Chemical Biology, McMaster University, 1280 Main Street West, L8S 4M1, Hamilton, Ontario, Canada
| | | | - Ramon Carbó-Dorca
- Institut de Química Computational i Catàlisi, Universitat de Girona, C/M Aurelia Capmany 69, 17003, Girona, Spain
| | - Henry Chermette
- Université Lyon 1 et UMR CNRS 5280 Institut Sciences Analytiques, Université de Lyon, 69622, Paris, France
| | - Jerzy Cioslowski
- Institute of Physics, University of Szczecin, Wielkopolska, 15, 70-451, Szczecin, Poland
| | | | - David L Cooper
- Department of Chemistry, University of Liverpool, Liverpool, L69 7ZD, United Kingdom
| | - Gernot Frenking
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerweinstr. 4, 35032, Marburg, Germany
| | - Carlo Gatti
- CNR-ISTM Istituto di Scienze e Tecnologie Molecolari, via Golgi 19, 20133, Milan, Italy and Istituto Lombardo Accademia di Scienze e Lettere, via Brera 28, 20121, Milan, Italy
| | - Farnaz Heidar-Zadeh
- Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg and Department of Chemistry, Queen's University, Kingston, Ontario K7L 3N6, Canada
| | - Laurent Joubert
- COBRA UMR 6014 & FR 3038, INSA Rouen, CNRS, Université de Rouen Normandie, Mont-St-Aignan, France
| | - Ángel Martín Pendás
- Departamento de Química Física y Analítica, Universidad de Oviedo, 33006, Oviedo, Spain
| | - Eduard Matito
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), and Donostia International Physics Center (DIPC), P.K. 1072, 20080, Donostia, Euskadi, Spain.,IKERBASQUE, Basque Foundation for Science, 48011, Bilbao, Euskadi, Spain
| | - István Mayer
- Institute of Organic Chemistry, Research Centre for Natural Sciences, Hungarian Academy of Sciences, Budapest, 1117, Hungary
| | - Alston J Misquitta
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London, E1 4NS, United Kingdom
| | - Yirong Mo
- Chemistry Department, Western Michigan University, Kalamazoo, Michigan, 49008
| | - Julien Pilmé
- Sorbonne Université, CNRS, LCT, UMR 7616, 4 place Jussieu, 75005, Paris, France
| | - Paul L A Popelier
- Manchester Institute of Biotechnology (MIB), 131 Princess Street, Manchester, M1 7DN, United Kingdom.,School of Chemistry, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
| | - Martin Rahm
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology, 412 96, Gothenburg, Sweden
| | - Eloy Ramos-Cordoba
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), and Donostia International Physics Center (DIPC), P.K. 1072, 20080, Donostia, Euskadi, Spain
| | - Pedro Salvador
- Institut de Química Computacional i Catàlisi, Universitat de Girona, C/M Aurelia Capmany 69, 17003, Girona, Spain
| | - W H Eugen Schwarz
- Theoretical Chemistry Center at Tsinghua University, Beijing, 100084, China.,Physical and Theoretical Chemistry Laboratory, Faculty of Science and Engineering, University of Siegen, Siegen, 57068, Germany
| | - Shant Shahbazian
- Department of Physics, Shahid Beheshti University, P.O. Box 19395-4716, G. C., Evin, 19839, Tehran, Iran
| | - Bernard Silvi
- Sorbonne Université, CNRS, LCT, UMR 7616, 4 place Jussieu, 75005, Paris, France
| | - Miquel Solà
- Institut de Química Computacional i Catàlisi, Universitat de Girona, C/M Aurelia Capmany 69, 17003, Girona, Spain
| | - Krzysztof Szalewicz
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware
| | - Vincent Tognetti
- COBRA UMR 6014 & FR 3038, INSA Rouen, CNRS, Université de Rouen Normandie, Mont-St-Aignan, France
| | - Frank Weinhold
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin, 53706
| | - Émilie-Laure Zins
- Sorbonne Université, UPMC Univ. Paris 06, MONARIS, UMR 8233, Université Pierre et Marie Curie, 4 Place Jussieu, Case Courrier 49, 75252, Paris, France
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14
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Deur K, Fromager E. Ground and excited energy levels can be extracted exactly from a single ensemble density-functional theory calculation. J Chem Phys 2019; 150:094106. [DOI: 10.1063/1.5084312] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Killian Deur
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, 4 Rue Blaise Pascal, 67000 Strasbourg, France
| | - Emmanuel Fromager
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, 4 Rue Blaise Pascal, 67000 Strasbourg, France
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15
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Nagai R, Akashi R, Sasaki S, Tsuneyuki S. Neural-network Kohn-Sham exchange-correlation potential and its out-of-training transferability. J Chem Phys 2018; 148:241737. [DOI: 10.1063/1.5029279] [Citation(s) in RCA: 41] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Ryo Nagai
- Department of Physics, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- Institute of Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan
| | - Ryosuke Akashi
- Department of Physics, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Shu Sasaki
- Department of Physics, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Shinji Tsuneyuki
- Department of Physics, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- Institute of Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan
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16
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Rupp M, von Lilienfeld OA, Burke K. Guest Editorial: Special Topic on Data-Enabled Theoretical Chemistry. J Chem Phys 2018; 148:241401. [DOI: 10.1063/1.5043213] [Citation(s) in RCA: 62] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Affiliation(s)
- Matthias Rupp
- Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany
| | - O. Anatole von Lilienfeld
- Department of Chemistry, Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, University of Basel, 4056 Basel, Switzerland
| | - Kieron Burke
- Departments of Chemistry and Physics, University of California, Irvine, California 92697, USA
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17
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Dumett Torres D, Jain PK. Strain Stabilization of Superionicity in Copper and Lithium Selenides. J Phys Chem Lett 2018; 9:1200-1205. [PMID: 29461839 DOI: 10.1021/acs.jpclett.8b00236] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Superionic (SI) phases have utility as solid electrolytes for next generation battery technology, but these phases are typically not stable at room temperature. Our density functional theory calculations demonstrate that compressive lattice strain can stabilize SI phases of Cu2Se and Li2Se, two potential solid electrolytes. Electronic and bonding insights into this effect are obtained. In the ordered, non-SI phase, cations are localized primarily in tetrahedral (T) interstices with little access to the higher-energy octahedral (O) sites, but 1-2% compressive strain promotes attractive stabilization of the O cations with 6-fold coordination to Se anions, at the expense of the stability of 4-fold-coordinated T cations. In such compressed lattices, cations can access both T and O sites, resulting in a cation-disordered, SI phase. Thus, lattice strain is demonstrated as a handle for controlling ionic structure and transport and accomplishing ambient temperature superionicity.
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18
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Sharpe DJ, Levy M, Tozer DJ. Approximating the Shifted Hartree-Exchange-Correlation Potential in Direct Energy Kohn-Sham Theory. J Chem Theory Comput 2018; 14:684-692. [PMID: 29298061 DOI: 10.1021/acs.jctc.7b01060] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Levy and Zahariev [Phys. Rev. Lett. 113 113002 (2014)] have proposed a new approach for performing density functional theory calculations, termed direct energy Kohn-Sham (DEKS) theory. In this approach, the electronic energy equals the sum of orbital energies, obtained from Kohn-Sham-like orbital equations involving a shifted Hartree-exchange-correlation potential, which must be approximated. In the present study, density scaling homogeneity considerations are used to facilitate DEKS calculations on a series of atoms and molecules, leading to three nonlocal approximations to the shifted potential. The first two rely on preliminary Kohn-Sham calculations using a standard generalized gradient approximation (GGA) exchange-correlation functional and the results illustrate the benefit of describing the dominant Hartree component of the shift exactly. A uniform electron gas analysis is used to eliminate the need for these preliminary Kohn-Sham calculations, leading to a potential with an unconventional form that yields encouraging results, providing strong motivation for further research in DEKS theory.
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Affiliation(s)
- Daniel J Sharpe
- Department of Chemistry, Durham University , South Road, Durham, DH1 3LE U.K
| | - Mel Levy
- Department of Chemistry, Duke University , Durham, North Carolina 27708 United States.,Department of Physics, North Carolina A&T State University , Greensboro, North Carolina 27411 United States.,Department of Chemistry and Quantum Theory Group, Tulane University , New Orleans, Louisiana 70118 United States
| | - David J Tozer
- Department of Chemistry, Durham University , South Road, Durham, DH1 3LE U.K
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19
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Vuckovic S, Levy M, Gori-Giorgi P. Augmented potential, energy densities, and virial relations in the weak- and strong-interaction limits of DFT. J Chem Phys 2017; 147:214107. [DOI: 10.1063/1.4997311] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Affiliation(s)
- Stefan Vuckovic
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Mel Levy
- Department of Chemistry and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118, USA
| | - 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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Alam MM, Deur K, Knecht S, Fromager E. Combining extrapolation with ghost interaction correction in range-separated ensemble density functional theory for excited states. J Chem Phys 2017; 147:204105. [DOI: 10.1063/1.4999825] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Md. Mehboob Alam
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, 4 Rue Blaise Pascal, 67000 Strasbourg, France
| | - Killian Deur
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, 4 Rue Blaise Pascal, 67000 Strasbourg, France
| | - Stefan Knecht
- Laboratory of Physical Chemistry, ETH, Zürich, Vladimir-Prelog Weg 2, CH-8093 Zürich, Switzerland
| | - Emmanuel Fromager
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, 4 Rue Blaise Pascal, 67000 Strasbourg, France
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21
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Zahariev F, Levy M. Properties of Augmented Kohn–Sham Potential for Energy as Simple Sum of Orbital Energies. J Phys Chem A 2016; 121:342-347. [DOI: 10.1021/acs.jpca.6b10952] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Federico Zahariev
- Department of Chemistry and Ames Laboratory, Iowa State University, Ames, Iowa 50011, United States
| | - Mel Levy
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Department of Physics, North Carolina A&T State University, Greensboro, North Carolina 27411, United States
- Department
of Chemistry and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118, United States
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22
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Levy M, Zahariev F. On augmented Kohn–Sham potential for energy as a simple sum of orbital energies. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1153743] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Mel Levy
- Department of Chemistry, Duke University, Durham, NC, USA
- Department of Physics, North Carolina A&T State University, Greensboro, NC, USA
- Department of Chemistry and Quantum Theory Group, Tulane University, New Orleans, LA, USA
| | - Federico Zahariev
- Department of Chemistry and Ames Laboratory, Iowa State University, Ames, IA, USA
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23
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Nazarov VU, Vignale G. Derivative discontinuity with localized Hartree-Fock potential. J Chem Phys 2015; 143:064111. [PMID: 26277131 DOI: 10.1063/1.4928514] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The localized Hartree-Fock potential has proven to be a computationally efficient alternative to the optimized effective potential, preserving the numerical accuracy of the latter and respecting the exact properties of being self-interaction free and having the correct -1/r asymptotics. In this paper we extend the localized Hartree-Fock potential to fractional particle numbers and observe that it yields derivative discontinuities in the energy as required by the exact theory. The discontinuities are numerically close to those of the computationally more demanding Hartree-Fock method. Our potential enjoys a "direct-energy" property, whereby the energy of the system is given by the sum of the single-particle eigenvalues multiplied by the corresponding occupation numbers. The discontinuities c↑ and c↓ of the spin-components of the potential at integer particle numbers N↑ and N↓ satisfy the condition c↑N↑ + c↓N↓ = 0. Thus, joining the family of effective potentials which support a derivative discontinuity, but being considerably easier to implement, the localized Hartree-Fock potential becomes a powerful tool in the broad area of applications in which the fundamental gap is an issue.
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Affiliation(s)
- V U Nazarov
- Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan
| | - G Vignale
- Department of Physics, University of Missouri-Columbia, Columbia, Missouri 65211, USA
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24
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Kraisler E, Schmidt T, Kümmel S, Kronik L. Effect of ensemble generalization on the highest-occupied Kohn-Sham eigenvalue. J Chem Phys 2015; 143:104105. [DOI: 10.1063/1.4930119] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Eli Kraisler
- Department of Materials and Interfaces, Weizmann Institute of Science, Rehovoth 76100, Israel
| | - Tobias Schmidt
- Theoretical Physics IV, University of Bayreuth, 95440 Bayreuth, Germany
| | - Stephan Kümmel
- Theoretical Physics IV, University of Bayreuth, 95440 Bayreuth, Germany
| | - Leeor Kronik
- Department of Materials and Interfaces, Weizmann Institute of Science, Rehovoth 76100, Israel
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25
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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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26
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Morrison RC. Discontinuity of the exchange-correlation potential and the functional derivative of the noninteracting kinetic energy as the number of electrons crosses integer boundaries in Li, Be, and B. J Chem Phys 2015; 142:014101. [DOI: 10.1063/1.4905235] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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