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Kanungo B, Hatch J, Zimmerman PM, Gavini V. Exact and Model Exchange-Correlation Potentials for Open-Shell Systems. J Phys Chem Lett 2023; 14:10039-10045. [PMID: 37910134 DOI: 10.1021/acs.jpclett.3c01713] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2023]
Abstract
The conventional approaches to the inverse density functional theory problem typically assume nondegeneracy of the Kohn-Sham (KS) eigenvalues, greatly hindering their use in open-shell systems. We present a generalization of the inverse density functional theory problem that can seamlessly admit degenerate KS eigenvalues. Additionally, we allow for fractional occupancy of the Kohn-Sham orbitals to also handle noninteracting ensemble-v-representable densities, as opposed to just noninteracting pure-v-representable densities. We present the exact exchange-correlation (XC) potentials for six open-shell systems─four atoms (Li, C, N, and O) and two molecules (CN and CH2)─using accurate ground-state densities from configuration interaction calculations. We compare these exact XC potentials with model XC potentials obtained using nonlocal (B3LYP, SCAN0) and local/semilocal (SCAN, PBE, PW92) XC functionals. Although the relative errors in the densities obtained from these DFT functionals are of O (10-3 to 10-2), the relative errors in the model XC potentials remain substantially large─O (10-1 to 100).
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Affiliation(s)
- Bikash Kanungo
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Jeffrey Hatch
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Paul M Zimmerman
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Vikram Gavini
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
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2
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Oueis Y, Sizov GN, Staroverov VN. Local Potentials Reconstructed within Linearly Independent Product Basis Sets of Increasing Size. J Phys Chem A 2023; 127:2664-2669. [PMID: 36898043 PMCID: PMC10042162 DOI: 10.1021/acs.jpca.3c00119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2023] [Revised: 02/24/2023] [Indexed: 03/12/2023]
Abstract
Given a matrix representation of a local potential v(r) within a one-electron basis set of functions that form linearly independent products (LIP), it is possible to construct a well-defined local potential v ~ ( r ) that is equivalent to v(r) within that basis set and has the form of an expansion in basis function products. Recently, we showed that for exchange-correlation potentials vXC(r) defined on the infinite-dimensional Hilbert space, the potentials v ~ XC ( r ) reconstructed from matrices of vXC(r) within minimal LIP basis sets of occupied Kohn-Sham orbitals bear only qualitative resemblance to the originals. Here, we show that if the LIP basis set is enlarged by including low-lying virtual Kohn-Sham orbitals, the agreement between v ~ XC ( r ) and vXC(r) improves to the extent that the basis function products are appropriate as a basis for vXC(r). These findings validate the LIP technology as a rigorous potential reconstruction method.
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Affiliation(s)
- Yan Oueis
- Department of Chemistry, The
University of Western Ontario, London, Ontario N6A 5B7, Canada
| | - Georgii N. Sizov
- Department of Chemistry, The
University of Western Ontario, London, Ontario N6A 5B7, Canada
| | - Viktor N. Staroverov
- Department of Chemistry, The
University of Western Ontario, London, Ontario N6A 5B7, 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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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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5
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Oueis Y, Staroverov VN. Reconstruction of Exchange-Correlation Potentials from Their Matrix Representations. J Chem Theory Comput 2022; 18:6092-6098. [PMID: 36094818 DOI: 10.1021/acs.jctc.2c00655] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Within a basis set of one-electron functions that form linearly independent products (LIPs), it is always possible to construct a unique local (multiplicative) real-space potential that is precisely equivalent to an arbitrary given operator. Although standard basis sets of quantum chemistry rarely form LIPs in a numerical sense, occupied and low-lying virtual canonical Kohn-Sham orbitals often do so, at least for small atoms and molecules. Using these principles, we construct atomic and molecular exchange-correlation potentials from their matrix representations in LIP basis sets of occupied canonical Kohn-Sham orbitals. The reconstructions are found to imitate the original potentials in a consistent but exaggerated way. Since the original and reconstructed potentials produce the same ground-state electron density and energy within the associated LIP basis set, the procedure may be regarded as a rigorous solution to the Kohn-Sham inversion problem within the subspace spanned by the occupied Kohn-Sham orbitals.
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Affiliation(s)
- Yan Oueis
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
| | - Viktor N Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
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6
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Erhard J, Trushin E, Görling A. Numerically stable inversion approach to construct Kohn-Sham potentials for given electron densities within a Gaussian basis set framework. J Chem Phys 2022; 156:204124. [PMID: 35649824 DOI: 10.1063/5.0087356] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a Kohn-Sham (KS) inversion approach to construct KS exchange-correlation potentials corresponding to given electron densities. This method is based on an iterative procedure using linear response to update potentials. All involved quantities, i.e., orbitals, potentials, and response functions, are represented by Gaussian basis functions. In contrast to previous KS inversion methods relying on Gaussian basis sets, the method presented here is numerically stable even for standard basis sets from basis set libraries due to a preprocessing of the auxiliary basis used to represent an exchange-correlation charge density that generates the exchange-correlation potential. The new KS inversion method is applied to reference densities of various atoms and molecules obtained by full configuration interaction or CCSD(T) (coupled cluster singles doubles perturbative triples). The considered examples encompass cases known to be difficult, such as stretched hydrogen or lithium hydride molecules or the beryllium isoelectronic series. For the stretched hydrogen molecule, potentials of benchmark quality are obtained by employing large basis sets. For the carbon monoxide molecule, we show that the correlation potential from the random phase approximation (RPA) is in excellent qualitative and quantitative agreement with the correlation potential from the KS inversion of a CCSD(T) reference density. This indicates that RPA correlation potentials, in contrast to those from semi-local density-functionals, resemble the exact correlation potential. Besides providing exchange-correlation potentials for benchmark purposes, the proposed KS inversion method may be used in density-partition-based quantum embedding and in subsystem density-functional methods because it combines numerical stability with computational efficiency.
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Affiliation(s)
- Jannis Erhard
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
| | - Egor Trushin
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
| | - Andreas Görling
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
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7
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Shi Y, Chávez VH, Wasserman A. n2v
: A density‐to‐potential inversion suite. A sandbox for creating, testing, and benchmarking density functional theory inversion methods. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1617] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Yuming Shi
- Department of Physics and Astronomy Purdue University West Lafayette Indiana USA
| | - Victor H. Chávez
- Department of Chemistry Purdue University West Lafayette Indiana USA
| | - Adam Wasserman
- Department of Physics and Astronomy Purdue University West Lafayette Indiana USA
- Department of Chemistry Purdue University West Lafayette Indiana USA
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8
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Bousiadi S, Gidopoulos N, Lathiotakis N. Density inversion method for local basis sets without potential auxiliary functions: inverting densities from RDMFT. Phys Chem Chem Phys 2022; 24:19279-19286. [DOI: 10.1039/d2cp01866g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A density inversion method is presented, to obtain the constrained, optimal, local potential that has a prescribed asymptotic behaviour and reproduces optimally any given ground-state electronic density. This work builds...
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9
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Kanungo B, Zimmerman PM, Gavini V. A Comparison of Exact and Model Exchange-Correlation Potentials for Molecules. J Phys Chem Lett 2021; 12:12012-12019. [PMID: 34898217 DOI: 10.1021/acs.jpclett.1c03670] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Accurate exchange-correlation (XC) potentials for three-dimensional systems─via solution of the inverse density functional theory (DFT) problem─are now available to test the quality of DFT approximations. Herein, the exact XC potential for seven molecules─dihydrogen at four different bond-lengths, lithium hydride, water, and ortho-benzyne─are computed from full configuration interaction reference densities. These are compared to model XC potentials from nonlocal (B3LYP, HSE06, SCAN0, and M08-HX) and semilocal/local (SCAN, PBE, and PW92) XC functionals. Whereas for most systems, relative errors in the ground-state densities are O(10-3-10-2), the model XC potentials have much higher errors of O(10-1-100). Among the model XC functionals, SCAN0 offers the best agreement with the exact XC potential, underlining the significance of satisfying exact conditions as well as including nonlocal effects in XC functionals. This work indicates that tests against the exact XC potential will provide a promising new direction for building more accurate XC functionals for DFT.
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Affiliation(s)
- Bikash Kanungo
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Paul M Zimmerman
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Vikram Gavini
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
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10
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Kumar A, Harbola MK. Using random numbers to obtain Kohn-Sham potential for a given density. Chem Phys Lett 2021. [DOI: 10.1016/j.cplett.2021.138851] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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11
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Diaz CM, Basurto L, Adhikari S, Yamamoto Y, Ruzsinszky A, Baruah T, Zope RR. Self-interaction-corrected Kohn-Sham effective potentials using the density-consistent effective potential method. J Chem Phys 2021; 155:064109. [PMID: 34391355 DOI: 10.1063/5.0056561] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Density functional theory (DFT) and beyond-DFT methods are often used in combination with photoelectron spectroscopy to obtain physical insights into the electronic structure of molecules and solids. The Kohn-Sham eigenvalues are not electron removal energies except for the highest occupied orbital. The eigenvalues of the highest occupied molecular orbitals often underestimate the electron removal or ionization energies due to the self-interaction (SI) errors in approximate density functionals. In this work, we adapt and implement the density-consistent effective potential method of Kohut, Ryabinkin, and Staroverov [J. Chem. Phys. 140, 18A535 (2014)] to obtain SI-corrected local effective potentials from the SI-corrected Fermi-Löwdin orbitals and density in the Fermi-Löwdin orbital self-interaction correction scheme. The implementation is used to obtain the density of states (photoelectron spectra) and HOMO-LUMO gaps for a set of molecules and polyacenes. Good agreement with experimental values is obtained compared to a range of SI uncorrected density functional approximations.
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Affiliation(s)
- Carlos M Diaz
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Luis Basurto
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Santosh Adhikari
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Yoh Yamamoto
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Adrienn Ruzsinszky
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Tunna Baruah
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Rajendra R Zope
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
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12
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Shi Y, Wasserman A. Inverse Kohn-Sham Density Functional Theory: Progress and Challenges. J Phys Chem Lett 2021; 12:5308-5318. [PMID: 34061541 DOI: 10.1021/acs.jpclett.1c00752] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Inverse Kohn-Sham (iKS) methods are needed to fully understand the one-to-one mapping between densities and potentials on which density functional theory is based. They can contribute to the construction of empirical exchange-correlation functionals and to the development of techniques for density-based embedding. Unlike the forward Kohn-Sham problems, numerical iKS problems are ill-posed and can be unstable. We discuss some of the fundamental and practical difficulties of iKS problems with constrained-optimization methods on finite basis sets. Various factors that affect the performance are systematically compared and discussed, both analytically and numerically, with a focus on two of the most practical methods: the Wu-Yang method (WY) and the partial differential equation constrained optimization (PDE-CO). Our analysis of the WY and PDE-CO highlights the limitation of finite basis sets. We introduce new ideas to make iKS problems more tractable, provide an overall strategy for performing numerical density-to-potential inversions, and discuss challenges and future directions.
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Affiliation(s)
- Yuming Shi
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, United States
| | - Adam Wasserman
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, United States
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, United States
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13
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Nam S, McCarty RJ, Park H, Sim E. KS-pies: Kohn–Sham inversion toolkit. J Chem Phys 2021; 154:124122. [DOI: 10.1063/5.0040941] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Seungsoo Nam
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, South Korea
| | - Ryan J. McCarty
- Department of Chemistry, University of California Irvine, Irvine, California 92697, USA
| | - Hansol Park
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, South Korea
| | - Eunji Sim
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, South Korea
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14
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Stückrath JB, Bischoff FA. Reduction of Hartree-Fock Wavefunctions to Kohn-Sham Effective Potentials Using Multiresolution Analysis. J Chem Theory Comput 2021; 17:1408-1420. [PMID: 33620202 DOI: 10.1021/acs.jctc.0c01103] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present a highly accurate numerical implementation for computing the Kohn-Sham effective potentials for molecules based on a Hartree-Fock wavefunction and density, following the RKS approach of Staroverov and co-workers [ J. Chem. Phys. 2014, 140, 18A535]. Potentials and orbitals are represented in a multiresolution wavelet basis, avoiding basis set incompleteness-related issues. Together with the RKS method, the often occurring problems of oscillating potentials are removed. The MRA implementation of the RKS method allows the generation of molecular Kohn-Sham potentials of benchmark quality. Numerical data for atoms up to Kr and a number of molecules are given, with a special emphasis on the role of nodal planes in the calculations, as showcased in HCN and benzene.
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Affiliation(s)
- Julius B Stückrath
- Institut für Chemie, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
| | - Florian A Bischoff
- Institut für Chemie, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
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15
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El-Samman AM, Staroverov VN. Asymptotic behavior of the average local ionization energy in finite basis sets. J Chem Phys 2020; 153:134109. [PMID: 33032433 DOI: 10.1063/5.0023459] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The average local ionization energy (ALIE) has important applications in several areas of electronic structure theory. Theoretically, the ALIE should asymptotically approach the first vertical ionization energy (IE) of the system, as implied by the rate of exponential decay of the electron density; for one-determinantal wavefunctions, this IE is the negative of the highest-occupied orbital energy. In practice, finite-basis-set representations of the ALIE exhibit seemingly irregular and sometimes dramatic deviations from the expected asymptotic behavior. We analyze the long-range behavior of the ALIE in finite basis sets and explain the puzzling observations. The findings have implications for practical calculations of the ALIE, the construction of Kohn-Sham potentials from wavefunctions and electron densities, and basis-set development.
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Affiliation(s)
- Amer M El-Samman
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
| | - Viktor N Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
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16
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Nam S, Song S, Sim E, Burke K. Measuring Density-Driven Errors Using Kohn-Sham Inversion. J Chem Theory Comput 2020; 16:5014-5023. [PMID: 32667787 DOI: 10.1021/acs.jctc.0c00391] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Kohn-Sham (KS) inversion, that is, the finding of the exact KS potential for a given density, is difficult in localized basis sets. We study the precision and reliability of several inversion schemes, finding estimates of density-driven errors at a useful level of accuracy. In typical cases of substantial density-driven errors, Hartree-Fock density functional theory (HF-DFT) is almost as accurate as DFT evaluated on CCSD(T) densities. A simple approximation in practical HF-DFT also makes errors much smaller than the density-driven errors being calculated. Two paradigm examples, stretched NaCl and the HO·Cl- radical, illustrate just how accurate HF-DFT is.
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Affiliation(s)
- Seungsoo Nam
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - Suhwan Song
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - Eunji Sim
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - Kieron Burke
- Departments of Chemistry and of Physics, University of California, Irvine, California 92697, United States
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17
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Giarrusso S, Gori-Giorgi P. Exchange-Correlation Energy Densities and Response Potentials: Connection between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond. J Phys Chem A 2020; 124:2473-2482. [PMID: 32118422 PMCID: PMC7104238 DOI: 10.1021/acs.jpca.9b10538] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
![]()
We
analyze in depth two widely used definitions (from the theory
of conditional probability amplitudes and from the adiabatic connection
formalism) of the exchange-correlation energy density and of the response
potential of Kohn–Sham density functional theory. We introduce
a local form of the coupling-constant-dependent Hohenberg–Kohn functional, showing that
the difference between the two definitions is due to a corresponding
local first-order term in the coupling constant, which disappears
globally (when integrated over all space), but not locally. We also
design an analytic representation for the response potential in the
strong-coupling limit of density functional theory for a model single
stretched bond.
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Affiliation(s)
- Sara Giarrusso
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, Amsterdam, 1081HV, The Netherlands
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, Amsterdam, 1081HV, The Netherlands
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18
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Vuckovic S, Song S, Kozlowski J, Sim E, Burke K. Density Functional Analysis: The Theory of Density-Corrected DFT. J Chem Theory Comput 2019; 15:6636-6646. [DOI: 10.1021/acs.jctc.9b00826] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Stefan Vuckovic
- Departments of Chemistry and of Physics, University of California, Irvine, California 92697, United States
| | - Suhwan Song
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - John Kozlowski
- Departments of Chemistry and of Physics, University of California, Irvine, California 92697, United States
| | - Eunji Sim
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - Kieron Burke
- Departments of Chemistry and of Physics, University of California, Irvine, California 92697, United States
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19
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Kanungo B, Zimmerman PM, Gavini V. Exact exchange-correlation potentials from ground-state electron densities. Nat Commun 2019; 10:4497. [PMID: 31582755 PMCID: PMC6776552 DOI: 10.1038/s41467-019-12467-0] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2019] [Accepted: 09/05/2019] [Indexed: 11/09/2022] Open
Abstract
The quest for accurate exchange-correlation functionals has long remained a grand challenge in density functional theory (DFT), as it describes the many-electron quantum mechanical behavior through a computationally tractable quantity-the electron density-without resorting to multi-electron wave functions. The inverse DFT problem of mapping the ground-state density to its exchange-correlation potential is instrumental in aiding functional development in DFT. However, the lack of an accurate and systematically convergent approach has left the problem unresolved, heretofore. This work presents a numerically robust and accurate scheme to evaluate the exact exchange-correlation potentials from correlated ab-initio densities. We cast the inverse DFT problem as a constrained optimization problem and employ a finite-element basis-a systematically convergent and complete basis-to discretize the problem. We demonstrate the accuracy and efficacy of our approach for both weakly and strongly correlated molecular systems, including up to 58 electrons, showing relevance to realistic polyatomic molecules.
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Affiliation(s)
- Bikash Kanungo
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, 48109, USA
| | - Paul M Zimmerman
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan, 48109, USA
| | - Vikram Gavini
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, 48109, USA. .,Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan, 48109, USA.
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20
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Kaur J, Ospadov E, Staroverov VN. What Is the Accuracy Limit of Adiabatic Linear-Response TDDFT Using Exact Exchange-Correlation Potentials and Approximate Kernels? J Chem Theory Comput 2019; 15:4956-4964. [PMID: 31386366 DOI: 10.1021/acs.jctc.9b00618] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Calculation of vertical excitation energies by the adiabatic linear-response time-dependent density-functional theory (TDDFT) requires static Kohn-Sham potentials and exchange-correlation kernels. When these quantities are derived from standard density-functional approximations (DFA), mean absolute errors (MAE) of the method are known to range from 0.2 eV to over 1 eV, depending on the functional and type of excitation. We investigate how the performance of TDDFT varies when increasingly accurate exchange-correlation potentials derived from Hartree-Fock (HF) and post-HF wavefunctions are combined with different approximate kernels. The lowest MAEs obtained in this manner for valence excitations are about 0.15-0.2 eV, which appears to be the practical limit of the accuracy of TDDFT that can be achieved by improving the Kohn-Sham potentials alone. These findings are consistent with previous reports on the benefits of accurate exchange-correlation potentials in TDDFT, but provide new insights and afford more definitive conclusions.
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Affiliation(s)
- Jaspreet Kaur
- Department of Chemistry , The University of Western Ontario , London , Ontario N6A 5B7 , Canada
| | - Egor Ospadov
- Department of Chemistry , The University of Western Ontario , London , Ontario N6A 5B7 , Canada
| | - Viktor N Staroverov
- Department of Chemistry , The University of Western Ontario , London , Ontario N6A 5B7 , Canada
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21
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Fabiano E, Śmiga S, Giarrusso S, Daas KJ, Della Sala F, Grabowski I, Gori-Giorgi P. Investigation of the Exchange-Correlation Potentials of Functionals Based on the Adiabatic Connection Interpolation. J Chem Theory Comput 2019; 15:1006-1015. [PMID: 30620596 DOI: 10.1021/acs.jctc.8b01037] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We have studied the correlation potentials produced by various adiabatic connection models (ACMs) for several atoms and molecules. The results have been compared to accurate reference potentials (coupled cluster and quantum Monte Carlo results) as well as to state-of-the-art ab initio DFT approaches. We have found that all the ACMs yield correlation potentials that exhibit a correct behavior, quite resembling scaled second-order Görling-Levy (GL2) potentials and including most of the physically meaningful features of the accurate reference data. The behavior and contribution of the strong-interaction limit potentials have also been investigated and discussed.
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Affiliation(s)
- Eduardo Fabiano
- Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni , Campus Unisalento, 73100 Lecce , Italy
- Center for Biomolecular Nanotechnologies @UNILE , Istituto Italiano di Tecnologia , Via Barsanti , I-73010 Arnesano , Italy
| | - Szymon Śmiga
- Institute of Physics, Faculty of Physics, Astronomy and Informatics , Nicolaus Copernicus University , Grudziadzka 5 , 87-100 Torun , Poland
| | - Sara Giarrusso
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, Faculty of Science , Vrije Universiteit , De Boelelaan 1083 , 1081HV Amsterdam , The Netherlands
| | - Kimberly J Daas
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, Faculty of Science , Vrije Universiteit , De Boelelaan 1083 , 1081HV Amsterdam , The Netherlands
| | - Fabio Della Sala
- Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni , Campus Unisalento, 73100 Lecce , Italy
- Center for Biomolecular Nanotechnologies @UNILE , Istituto Italiano di Tecnologia , Via Barsanti , I-73010 Arnesano , Italy
| | - Ireneusz Grabowski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics , Nicolaus Copernicus University , Grudziadzka 5 , 87-100 Torun , Poland
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, Faculty of Science , Vrije Universiteit , De Boelelaan 1083 , 1081HV Amsterdam , The Netherlands
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22
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Zhu T, de Silva P, Van Voorhis T. Implementation of the Many-Pair Expansion for Systematically Improving Density Functional Calculations of Molecules. J Chem Theory Comput 2019; 15:1089-1101. [DOI: 10.1021/acs.jctc.8b01127] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Tianyu Zhu
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Piotr de Silva
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
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23
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Gould T, Pittalis S, Toulouse J, Kraisler E, Kronik L. Asymptotic behavior of the Hartree-exchange and correlation potentials in ensemble density functional theory. Phys Chem Chem Phys 2019; 21:19805-19815. [DOI: 10.1039/c9cp03633d] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We show that the Hartree-exchange and correlation potentials of ensemble systems can have unexpected features, including non-vanishing asymptotic constants and non-trivial screening of electrons. These features are demonstrated here on Li, C, and F.
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Affiliation(s)
- Tim Gould
- Qld Micro- and Nanotechnology Centre
- Griffith University
- Nathan
- Australia
| | | | - Julien Toulouse
- Laboratoire de Chimie Théorique
- Sorbonne Université and CNRS
- F-75005 Paris
- France
| | - Eli Kraisler
- Fritz Haber Center for Molecular Dynamics and Institute of Chemistry
- The Hebrew University of Jerusalem
- 9091401 Jerusalem
- Israel
| | - Leeor Kronik
- Department of Materials and Interfaces
- Weizmann Institute of Science
- Rehovoth 76100
- Israel
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24
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Mostafanejad M, Haney J, DePrince AE. Kinetic-energy-based error quantification in Kohn–Sham density functional theory. Phys Chem Chem Phys 2019; 21:26492-26501. [DOI: 10.1039/c9cp04595c] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present a basis-independent metric to assess the quality of the electron density obtained from Kohn–Sham (KS) density functional theory (DFT).
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Affiliation(s)
| | - Jessica Haney
- Department of Chemistry and Biochemistry
- Florida State University
- Tallahassee
- USA
| | - A. Eugene DePrince
- Department of Chemistry and Biochemistry
- Florida State University
- Tallahassee
- USA
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25
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Unified construction of Fermi, Pauli and exchange-correlation potentials. ADVANCES IN QUANTUM CHEMISTRY 2019. [DOI: 10.1016/bs.aiq.2019.04.002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/12/2023]
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26
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Visualizing atomic sizes and molecular shapes with the classical turning surface of the Kohn-Sham potential. Proc Natl Acad Sci U S A 2018; 115:E11578-E11585. [PMID: 30463943 DOI: 10.1073/pnas.1814300115] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The Kohn-Sham potential [Formula: see text] is the effective multiplicative operator in a noninteracting Schrödinger equation that reproduces the ground-state density of a real (interacting) system. The sizes and shapes of atoms, molecules, and solids can be defined in terms of Kohn-Sham potentials in a nonarbitrary way that accords with chemical intuition and can be implemented efficiently, permitting a natural pictorial representation for chemistry and condensed-matter physics. Let [Formula: see text] be the maximum occupied orbital energy of the noninteracting electrons. Then the equation [Formula: see text] defines the surface at which classical electrons with energy [Formula: see text] would be turned back and thus determines the surface of any electronic object. Atomic and ionic radii defined in this manner agree well with empirical estimates, show regular chemical trends, and allow one to identify the type of chemical bonding between two given atoms by comparing the actual internuclear distance to the sum of atomic radii. The molecular surfaces can be fused (for a covalent bond), seamed (ionic bond), necked (hydrogen bond), or divided (van der Waals bond). This contribution extends the pioneering work of Z.-Z. Yang et al. [Yang ZZ, Davidson ER (1997) Int J Quantum Chem 62:47-53; Zhao DX, et al. (2018) Mol Phys 116:969-977] by our consideration of the Kohn-Sham potential, protomolecules, doubly negative atomic ions, a bond-type parameter, seamed and necked molecular surfaces, and a more extensive table of atomic and ionic radii that are fully consistent with expected periodic trends.
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27
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Potential Functional Embedding Theory with an Improved Kohn–Sham Inversion Algorithm. J Chem Theory Comput 2018; 14:5680-5689. [DOI: 10.1021/acs.jctc.8b00717] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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28
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Uniform electron gas limit of an exact expression for the Kohn–Sham exchange-correlation potential. Theor Chem Acc 2018. [DOI: 10.1007/s00214-018-2303-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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29
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Giarrusso S, Vuckovic S, Gori-Giorgi P. Response Potential in the Strong-Interaction Limit of Density Functional Theory: Analysis and Comparison with the Coupling-Constant Average. J Chem Theory Comput 2018; 14:4151-4167. [PMID: 29906106 PMCID: PMC6096453 DOI: 10.1021/acs.jctc.8b00386] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Using the formalism of the conditional amplitude, we study the response part of the exchange-correlation potential in the strong-coupling limit of density functional theory, analyzing its peculiar features and comparing it with the response potential averaged over the coupling constant for small atoms and for the hydrogen molecule. We also use a simple one-dimensional model of a stretched heteronuclear molecule to derive exact properties of the response potential in the strong-coupling limit. The simplicity of the model allows us to unveil relevant features also of the exact Kohn-Sham potential and its different components, namely the appearance of a second peak in the correlation kinetic potential on the side of the most electronegative atom.
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Affiliation(s)
- Sara Giarrusso
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW , Vrije Universiteit , De Boelelaan 1083 , 1081HV Amsterdam , The Netherlands
| | - Stefan Vuckovic
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW , Vrije Universiteit , De Boelelaan 1083 , 1081HV Amsterdam , The Netherlands
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW , Vrije Universiteit , De Boelelaan 1083 , 1081HV Amsterdam , The Netherlands
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30
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Theophilou I, Buchholz F, Eich FG, Ruggenthaler M, Rubio A. Kinetic-Energy Density-Functional Theory on a Lattice. J Chem Theory Comput 2018; 14:4072-4087. [PMID: 29969552 PMCID: PMC6096452 DOI: 10.1021/acs.jctc.8b00292] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
We
present a kinetic-energy density-functional theory and the corresponding
kinetic-energy Kohn–Sham (keKS) scheme on a lattice and show
that, by including more observables explicitly in a density-functional
approach, already simple approximation strategies lead to very accurate
results. Here, we promote the kinetic-energy density to a fundamental
variable alongside the density and show for specific cases (analytically
and numerically) that there is a one-to-one correspondence between
the external pair of on-site potential and site-dependent hopping
and the internal pair of density and kinetic-energy density. On the
basis of this mapping, we establish two unknown effective fields,
the mean-field exchange-correlation potential and the mean-field exchange-correlation
hopping, which force the keKS system to generate the same kinetic-energy
density and density as the fully interacting one. We show, by a decomposition
based on the equations of motions for the density and the kinetic-energy
density, that we can construct simple orbital-dependent functionals
that outperform the corresponding exact-exchange Kohn–Sham
(KS) approximation of standard density-functional theory. We do so
by considering the exact KS and keKS systems and comparing the unknown
correlation contributions as well as by comparing self-consistent
calculations based on the mean-field exchange (for the effective potential)
and a uniform (for the effective hopping) approximation for the keKS
and the exact-exchange approximation for the KS system, respectively.
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Affiliation(s)
- Iris Theophilou
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free Electron Laser Science , Hamburg 22761 , Germany
| | - Florian Buchholz
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free Electron Laser Science , Hamburg 22761 , Germany
| | - F G Eich
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free Electron Laser Science , Hamburg 22761 , Germany
| | - Michael Ruggenthaler
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free Electron Laser Science , Hamburg 22761 , Germany
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free Electron Laser Science , Hamburg 22761 , Germany.,Center for Computational Quantum Physics (CCQ) , Flatiron Institute , New York , New York 10010 , United States
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31
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Ospadov E, Staroverov VN. Construction of Fermi Potentials from Electronic Wave Functions. J Chem Theory Comput 2018; 14:4246-4253. [DOI: 10.1021/acs.jctc.8b00490] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Egor Ospadov
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
| | - Viktor N. Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
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32
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Affiliation(s)
- Viktor N. Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario, Canada
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33
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Local Effective Hartree–Fock Potentials Obtained by the Depurated Inversion Method. ADVANCES IN QUANTUM CHEMISTRY 2018. [DOI: 10.1016/bs.aiq.2017.07.004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register]
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34
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Kaplan IG. Symmetry properties of the electron density and following from it limits on the KS-DFT applications. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1393573] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Ilya G. Kaplan
- Instituto De Investigaciones en Materiales, Universidad Nacional Autónomo de México, Ciudad de México, México
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35
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Ryabinkin IG, Ospadov E, Staroverov VN. Exact exchange-correlation potentials of singlet two-electron systems. J Chem Phys 2017; 147:164117. [DOI: 10.1063/1.5003825] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ilya G. Ryabinkin
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4,
Canada
| | - Egor Ospadov
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
| | - Viktor N. Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
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36
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Chen GP, Voora VK, Agee MM, Balasubramani SG, Furche F. Random-Phase Approximation Methods. Annu Rev Phys Chem 2017; 68:421-445. [DOI: 10.1146/annurev-physchem-040215-112308] [Citation(s) in RCA: 88] [Impact Index Per Article: 12.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Guo P. Chen
- Department of Chemistry, University of California, Irvine, California 92697-2025;,
| | - Vamsee K. Voora
- Department of Chemistry, University of California, Irvine, California 92697-2025;,
| | - Matthew M. Agee
- Department of Chemistry, University of California, Irvine, California 92697-2025;,
| | | | - Filipp Furche
- Department of Chemistry, University of California, Irvine, California 92697-2025;,
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37
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Ospadov E, Ryabinkin IG, Staroverov VN. Improved method for generating exchange-correlation potentials from electronic wave functions. J Chem Phys 2017; 146:084103. [DOI: 10.1063/1.4975990] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Egor Ospadov
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
| | - Ilya G. Ryabinkin
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
| | - Viktor N. Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
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38
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Kohut SV, Cuevas-Saavedra R, Staroverov VN. Generalized average local ionization energy and its representations in terms of Dyson and energy orbitals. J Chem Phys 2016; 145:074113. [DOI: 10.1063/1.4961071] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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39
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Ryabinkin IG, Kohut SV, Cuevas-Saavedra R, Ayers PW, Staroverov VN. Response to "Comment on 'Kohn-Sham exchange-correlation potentials from second-order reduced density matrices'" [J. Chem. Phys. 145, 037101 (2016)]. J Chem Phys 2016; 145:037102. [PMID: 27448911 DOI: 10.1063/1.4958623] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ilya G Ryabinkin
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
| | - Sviataslau V Kohut
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
| | | | - Paul W Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Viktor N Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
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40
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Baerends EJ, Gritsenko O. Comment on “Kohn-Sham exchange-correlation potentials from second-order reduced density matrices” [J. Chem. Phys. 143, 244116 (2015)]. J Chem Phys 2016; 145:037101. [DOI: 10.1063/1.4958622] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
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41
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Huang C. Patching the Exchange-Correlation Potential in Density Functional Theory. J Chem Theory Comput 2016; 12:2224-33. [DOI: 10.1021/acs.jctc.6b00051] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Chen Huang
- Department
of Scientific
Computing, Florida State University, Tallahassee, Florida 32306-4120, United States
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42
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Abstract
The energy change per electron in a chemical or physical transformation, ΔE/n, may be expressed as Δχ̅ + Δ(VNN + ω)/n, where Δχ̅ is the average electron binding energy, a generalized electronegativity, ΔVNN is the change in nuclear repulsions, and Δω is the change in multielectron interactions in the process considered. The last term can be obtained by the difference from experimental or theoretical estimates of the first terms. Previously obtained consequences of this energy partitioning are extended here to a different analysis of bonding in a great variety of diatomics, including more or less polar ones. Arguments are presented for associating the average change in electron binding energy with covalence, and the change in multielectron interactions with electron transfer, either to, out, or within a molecule. A new descriptor Q, essentially the scaled difference between the Δχ̅ and Δ(VNN + ω)/n terms, when plotted versus the bond energy, separates nicely a wide variety of bonding types, covalent, covalent but more correlated, polar and increasingly ionic, metallogenic, electrostatic, charge-shift bonds, and dispersion interactions. Also, Q itself shows a set of interesting relations with the correlation energy of a bond.
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Affiliation(s)
- Martin Rahm
- Chemistry and Chemical Biology, Baker Laboratory, Cornell University , Ithaca, New York 14853, United States
| | - Roald Hoffmann
- Chemistry and Chemical Biology, Baker Laboratory, Cornell University , Ithaca, New York 14853, United States
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43
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Cuevas-Saavedra R, Staroverov VN. Exact expressions for the Kohn–Sham exchange-correlation potential in terms of wave-function-based quantities. Mol Phys 2016. [DOI: 10.1080/00268976.2015.1131861] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
| | - Viktor N. Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario, Canada
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44
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Kohut SV, Polgar AM, Staroverov VN. Origin of the step structure of molecular exchange–correlation potentials. Phys Chem Chem Phys 2016; 18:20938-44. [DOI: 10.1039/c6cp00878j] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The step structure of exact exchange–correlation potentials is linked to the properties of the average local electron energy (ALEE).
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45
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Cuevas-Saavedra R, Ayers PW, Staroverov VN. Kohn–Sham exchange-correlation potentials from second-order reduced density matrices. J Chem Phys 2015; 143:244116. [DOI: 10.1063/1.4937943] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
| | - Paul W. Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Viktor N. Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
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46
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Stuart D, Tecmer P, Ayers PW, Boguslawski K. The effect of nitrido, azide, and nitrosyl ligands on magnetization densities and magnetic properties of iridium PNP pincer-type complexes. RSC Adv 2015. [DOI: 10.1039/c5ra17507k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
The magnetisation density of different iridium PNP pincer-type complexes depends on the chosen quantum chemistry method.
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Affiliation(s)
- Daniel Stuart
- Department of Chemistry and Chemical Biology
- McMaster University
- Hamilton
- Canada
- Department of Chemistry and Biochemistry
| | - Paweł Tecmer
- Department of Chemistry and Chemical Biology
- McMaster University
- Hamilton
- Canada
- Institute of Physics, Faculty of Physics, Astronomy and Informatics
| | - Paul W. Ayers
- Department of Chemistry and Chemical Biology
- McMaster University
- Hamilton
- Canada
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics
- Nicolaus Copernicus University
- 87-100 Toruń
- Poland
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