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Kety K, Joubert D. Can the Kohn-Sham gap be larger than the fundamental gap? Phys Chem Chem Phys 2024; 26:24624-24630. [PMID: 39279487 DOI: 10.1039/d4cp02688h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/18/2024]
Abstract
It is often stated that the exact Kohn-Sham HOMO-LUMO gap underestimates the fundamental gap. Here, using the Hubbard dimer as a model Hamiltonian, we show numerically that the exact Kohn-Sham gap can be larger than the fundamental gap.
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Affiliation(s)
- Kossi Kety
- African Institute for Mathematical Sciences (AIMS-Cameroon), P.O. Box 608 Limbe, Crystal Gardens, South West Region, Cameroon.
| | - Daniel Joubert
- School of Physics, University of the Witwatersrand, P.O. Wits, Johannesburg 2050, South Africa
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2
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Cernatic F, Fromager E. Extended N-centered ensemble density functional theory of double electronic excitations. J Comput Chem 2024; 45:1945-1962. [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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3
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Kaupp M, Wodyński A, Arbuznikov AV, Fürst S, Schattenberg CJ. Toward the Next Generation of Density Functionals: Escaping the Zero-Sum Game by Using the Exact-Exchange Energy Density. Acc Chem Res 2024; 57:1815-1826. [PMID: 38905497 PMCID: PMC11223257 DOI: 10.1021/acs.accounts.4c00209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2024] [Revised: 05/29/2024] [Accepted: 06/03/2024] [Indexed: 06/23/2024]
Abstract
ConspectusKohn-Sham density functional theory (KS DFT) is arguably the most widely applied electronic-structure method with tens of thousands of publications each year in a wide variety of fields. Its importance and usefulness can thus hardly be overstated. The central quantity that determines the accuracy of KS DFT calculations is the exchange-correlation functional. Its exact form is unknown, or better "unknowable", and therefore the derivation of ever more accurate yet efficiently applicable approximate functionals is the "holy grail" in the field. In this context, the simultaneous minimization of so-called delocalization errors and static correlation errors is the greatest challenge that needs to be overcome as we move toward more accurate yet computationally efficient methods. In many cases, an improvement on one of these two aspects (also often termed fractional-charge and fractional-spin errors, respectively) generates a deterioration in the other one. Here we report on recent notable progress in escaping this so-called "zero-sum-game" by constructing new functionals based on the exact-exchange energy density. In particular, local hybrid and range-separated local hybrid functionals are discussed that incorporate additional terms that deal with static correlation as well as with delocalization errors. Taking hints from other coordinate-space models of nondynamical and strong electron correlations (the B13 and KP16/B13 models), position-dependent functions that cover these aspects in real space have been devised and incorporated into the local-mixing functions determining the position-dependence of exact-exchange admixture of local hybrids as well as into the treatment of range separation in range-separated local hybrids. While initial functionals followed closely the B13 and KP16/B13 frameworks, meanwhile simpler real-space functions based on ratios of semilocal and exact-exchange energy densities have been found, providing a basis for relatively simple and numerically convenient functionals. Notably, the correction terms can either increase or decrease exact-exchange admixture locally in real space (and in interelectronic-distance space), leading even to regions with negative admixture in cases of particularly strong static correlations. Efficient implementations into a fast computer code (Turbomole) using seminumerical integration techniques make such local hybrid and range-separated local hybrid functionals promising new tools for complicated composite systems in many research areas, where simultaneously small delocalization errors and static correlation errors are crucial. First real-world application examples of the new functionals are provided, including stretched bonds, symmetry-breaking and hyperfine coupling in open-shell transition-metal complexes, as well as a reduction of static correlation errors in the computation of nuclear shieldings and magnetizabilities. The newest versions of range-separated local hybrids (e.g., ωLH23tdE) retain the excellent frontier-orbital energies and correct asymptotic exchange-correlation potential of the underlying ωLH22t functional while improving substantially on strong-correlation cases. The form of these functionals can be further linked to the performance of the recent impactful deep-neural-network "black-box" functional DM21, which itself may be viewed as a range-separated local hybrid.
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Affiliation(s)
- Martin Kaupp
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Artur Wodyński
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Alexei V. Arbuznikov
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Susanne Fürst
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Caspar J. Schattenberg
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
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4
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McPherson PAC, McKenna N, Johnston BM. Physicochemical Properties of 4-(4-Hydroxyphenyl)-butan-2-one ("Raspberry Ketone") Evaluated Using a Computational Chemistry Approach. ACS OMEGA 2024; 9:23963-23970. [PMID: 38854552 PMCID: PMC11154730 DOI: 10.1021/acsomega.4c02293] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/08/2024] [Revised: 04/02/2024] [Accepted: 05/10/2024] [Indexed: 06/11/2024]
Abstract
Raspberry ketone (RK) is a product of the phenylpropanoid pathway in a variety of plants and is the second most expensive natural flavouring in the world. It is also widely used as a nutritional supplement due to its reported ability to promote lipolysis and fat oxidation in vivo. We have evaluated the thermodynamics of RK using the correlation consistent ccCA-CBS-2 approach which afforded calculation of (inter alia) the enthalpy of formation. To obtain pK a, log D, electrode potential, solubility, and reactivity indices, we used TPSS/def2-TZVP geometries followed by single-point energies obtained at the M06-2X/def2-TZVPP level of theory. We obtained Δf H o = -299.4 ± 0.17 kJ·mol-1; the pK a and logD were found to be 9.95 and 1.84, respectively, consistent with chemometric predictions. Using the enthalpy of fusion obtained from theory, we evaluated the aqueous solubility of RK to be in the region of 2.5 mg·mL-1 which is in agreement with limited literature reports. In terms of reactivity, we obtained a formal electrode potential of 1.29 V (vs SHE) at pH 7.4 and 298.15 K. The HOMO-LUMO energy separation in an aqueous environment was found to be ca. 7.8 eV, suggesting moderate chemical reactivity. Analysis of the frontier molecular orbitals using conceptual density functional theory supported this and revealed a reactivity pattern consistent with the metabolite profile obtained in mammals, namely, a propensity for nucleophilic attack at the carbonyl carbon and electrophilic addition of the benzene ring.
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Affiliation(s)
- Peter A. C. McPherson
- School
of Pharmacy & Pharmaceutical Science, Ulster University, Coleraine BT52 1SA, U.K.
| | - Niamh McKenna
- School
of Pharmacy, University of North Carolina, Chapel Hill 27599, North Carolina, United
States
| | - Ben M. Johnston
- School
of Science, Engineering & Construction, Belfast Metropolitan College, Belfast BT3 9DT, U.K.
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5
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Benítez FJ, Gutiérrez-Oliva S, Herrera B, Toro-Labbé A. Basis Electronic Activity of Molecular Systems. A Theory of Bond Reactivity. J Phys Chem A 2024. [PMID: 38437616 DOI: 10.1021/acs.jpca.4c00359] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/06/2024]
Abstract
In this paper, we present a new finding, the basis electronic activity (BEA) of molecular systems; it corresponds to the significant, although nonreactive, vibrationally induced electronic activity that takes place in any molecular system. Although the molecule's BEA is composed of an equal number of local contributions as the vibrational degrees of freedom, our results indicate that only stretching modes contribute to it. To account for this electronic activity, a new descriptor, the bond electronic flux (BEF), is introduced. The BEF combined with the force constant of the potential well hosting the electronic activity gives rise to the effective bond reactivity index (EBR), which turns out to be the first density functional theory-based descriptor that simultaneously accounts for structural and electronic effects. Besides quantifying the bond reactivity, EBR provides a basis to compare the reactivities of bonds inserted in different chemical environments and paves the way for the exertion of selective control to enhance or inhibit their reactivities. The new concepts formulated in this paper and the associated computational tools are illustrated with characterization of the BEA of a set of representative molecules. In all cases, the BEFs follow the same linear pattern, whose slopes indicate the intensity of the electronic activity and quantify the reactivity of chemical bonds.
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Affiliation(s)
- Francisca J Benítez
- Laboratorio de Química Teórica Computacional (QTC), Facultad de Química y de Farmacia, Pontificia Universidad Católica de Chile, Avda. Vicuña Mackenna 4860 Macul, Santiago 7820436, Chile
| | - Soledad Gutiérrez-Oliva
- Laboratorio de Química Teórica Computacional (QTC), Facultad de Química y de Farmacia, Pontificia Universidad Católica de Chile, Avda. Vicuña Mackenna 4860 Macul, Santiago 7820436, Chile
| | - Bárbara Herrera
- Laboratorio de Química Teórica Computacional (QTC), Facultad de Química y de Farmacia, Pontificia Universidad Católica de Chile, Avda. Vicuña Mackenna 4860 Macul, Santiago 7820436, Chile
| | - Alejandro Toro-Labbé
- Laboratorio de Química Teórica Computacional (QTC), Facultad de Química y de Farmacia, Pontificia Universidad Católica de Chile, Avda. Vicuña Mackenna 4860 Macul, Santiago 7820436, Chile
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6
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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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7
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Kasemthaveechok S, Abella L, Crassous J, Autschbach J, Favereau L. Organic radicals with inversion of SOMO and HOMO energies and potential applications in optoelectronics. Chem Sci 2022; 13:9833-9847. [PMID: 36128246 PMCID: PMC9430691 DOI: 10.1039/d2sc02480b] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Accepted: 07/06/2022] [Indexed: 11/21/2022] Open
Abstract
Organic radicals possessing an electronic configuration in which the energy of the singly occupied molecular orbital (SOMO) is below the highest doubly occupied molecular orbital (HOMO) level have recently attracted significant interest, both theoretically and experimentally. The peculiar orbital energetics of these SOMO-HOMO inversion (SHI) organic radicals set their electronic properties apart from the more common situation where the SOMO is the highest occupied orbital of the system. This review gives a general perspective on SHI, with key fundamental aspects regarding the electronic and structural factors that govern this particular electronic configuration in organic radicals. Selected examples of reported compounds with SHI are highlighted to establish molecular guidelines for designing this type of radical, and to showcase the potential of SHI radicals in organic spintronics as well as for the development of more stable luminescent radicals for OLED applications.
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Affiliation(s)
| | - Laura Abella
- Department of Chemistry, University at Buffalo, State University of New York Buffalo New York 14260 USA
| | | | - Jochen Autschbach
- Department of Chemistry, University at Buffalo, State University of New York Buffalo New York 14260 USA
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8
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Mao GQ, Yan ZY, Xue KH, Ai Z, Yang S, Cui H, Yuan JH, Ren TL, Miao X. DFT-1/2 and shell DFT-1/2 methods: electronic structure calculation for semiconductors at LDA complexity. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:403001. [PMID: 35856860 DOI: 10.1088/1361-648x/ac829d] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2022] [Accepted: 07/20/2022] [Indexed: 06/15/2023]
Abstract
It is known that the Kohn-Sham eigenvalues do not characterize experimental excitation energies directly, and the band gap of a semiconductor is typically underestimated by local density approximation (LDA) of density functional theory (DFT). An embarrassing situation is that one usually uses LDA+Ufor strongly correlated materials with rectified band gaps, but for non-strongly-correlated semiconductors one has to resort to expensive methods like hybrid functionals orGW. In spite of the state-of-the-art meta-generalized gradient approximation functionals like TB-mBJ and SCAN, methods with LDA-level complexity to rectify the semiconductor band gaps are in high demand. DFT-1/2 stands as a feasible approach and has been more widely used in recent years. In this work we give a detailed derivation of the Slater half occupation technique, and review the assumptions made by DFT-1/2 in semiconductor band structure calculations. In particular, the self-energy potential approach is verified through mathematical derivations. The aims, features and principles of shell DFT-1/2 for covalent semiconductors are also accounted for in great detail. Other developments of DFT-1/2 including conduction band correction, DFT+A-1/2, empirical formula for the self-energy potential cutoff radius, etc, are further reviewed. The relations of DFT-1/2 to hybrid functional, sX-LDA,GW, self-interaction correction, scissor's operator as well as DFT+Uare explained. Applications, issues and limitations of DFT-1/2 are comprehensively included in this review.
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Affiliation(s)
- Ge-Qi Mao
- School of Integrated Circuits, School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, 430074, People's Republic of China
- Hubei Yangtze Memory Laboratories, Wuhan 430205, People's Republic of China
| | - Zhao-Yi Yan
- School of Integrated Circuits, Tsinghua University, Beijing 100084, People's Republic of China
| | - Kan-Hao Xue
- School of Integrated Circuits, School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, 430074, People's Republic of China
- Hubei Yangtze Memory Laboratories, Wuhan 430205, People's Republic of China
| | - Zhengwei Ai
- School of Integrated Circuits, School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, 430074, People's Republic of China
- Hubei Yangtze Memory Laboratories, Wuhan 430205, People's Republic of China
| | - Shengxin Yang
- School of Integrated Circuits, School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, 430074, People's Republic of China
- Hubei Yangtze Memory Laboratories, Wuhan 430205, People's Republic of China
| | - Hanli Cui
- School of Integrated Circuits, School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, 430074, People's Republic of China
| | - Jun-Hui Yuan
- School of Integrated Circuits, School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, 430074, People's Republic of China
- Hubei Yangtze Memory Laboratories, Wuhan 430205, People's Republic of China
| | - Tian-Ling Ren
- School of Integrated Circuits, Tsinghua University, Beijing 100084, People's Republic of China
| | - Xiangshui Miao
- School of Integrated Circuits, School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, 430074, People's Republic of China
- Hubei Yangtze Memory Laboratories, Wuhan 430205, People's Republic of China
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9
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Baerends EJ. Chemical potential, derivative discontinuity, fractional electrons, jump of the Kohn-Sham potential, atoms as thermodynamic open systems, and other (mis)conceptions of the density functional theory of electrons in molecules. Phys Chem Chem Phys 2022; 24:12745-12766. [PMID: 35593143 DOI: 10.1039/d2cp01585d] [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
Many references exist in the density functional theory (DFT) literature to the chemical potential of the electrons in an atom or a molecule. The origin of this notion has been the identification of the Lagrange multiplier μ = ∂E/∂N in the Euler-Lagrange variational equation for the ground state density as the chemical potential of the electrons. We first discuss why the Lagrange multiplier in this case is an arbitrary constant and therefore cannot be a physical characteristic of an atom or molecule. The switching of the energy derivative ("chemical potential") from -I to -A when the electron number crosses the integer, called integer discontinuity or derivative discontinuity, is not physical but only occurs when the nonphysical noninteger electron systems and the corresponding energy and derivative ∂E/∂N are chosen in a specific discontinuous way. The question is discussed whether in fact the thermodynamical concept of a chemical potential can be defined for the electrons in such few-electron systems as atoms and molecules. The conclusion is that such systems lack important characteristics of thermodynamic systems and do not afford the definition of a chemical potential. They also cannot be considered as analogues of the open systems of thermodynamics that can exchange particles with an environment (a particle bath or other members of a Gibbsian ensemble). Thermodynamical (statistical mechanical) concepts like chemical potential, open systems, grand canonical ensemble etc. are not applicable to a few electron system like an atom or molecule. A number of topics in DFT are critically reviewed in light of these findings: jumps in the Kohn-Sham potential when crossing an integer number of electrons, the band gap problem, the deviation-from-straight-lines error, and the role of ensembles in DFT.
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10
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Gedeon J, Schmidt J, Hodgson MJP, Wetherell J, Benavides-Riveros CL, Marques MAL. Machine learning the derivative discontinuity of density-functional theory. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2022. [DOI: 10.1088/2632-2153/ac3149] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Abstract
Machine learning is a powerful tool to design accurate, highly non-local, exchange-correlation functionals for density functional theory. So far, most of those machine learned functionals are trained for systems with an integer number of particles. As such, they are unable to reproduce some crucial and fundamental aspects, such as the explicit dependency of the functionals on the particle number or the infamous derivative discontinuity at integer particle numbers. Here we propose a solution to these problems by training a neural network as the universal functional of density-functional theory that (a) depends explicitly on the number of particles with a piece-wise linearity between the integer numbers and (b) reproduces the derivative discontinuity of the exchange-correlation energy. This is achieved by using an ensemble formalism, a training set containing fractional densities, and an explicitly discontinuous formulation.
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11
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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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12
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Burton HGA, Marut C, Daas TJ, Gori-Giorgi P, Loos PF. Variations of the Hartree-Fock fractional-spin error for one electron. J Chem Phys 2021; 155:054107. [PMID: 34364354 DOI: 10.1063/5.0056968] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Fractional-spin errors are inherent in all current approximate density functionals, including Hartree-Fock theory, and their origin has been related to strong static correlation effects. The conventional way to encode fractional-spin calculations is to construct an ensemble density that scales between the high-spin and low-spin densities. In this article, we explore the variation of the Hartree-Fock fractional-spin (or ghost-interaction) error in one-electron systems using restricted and unrestricted ensemble densities and the exact generalized Hartree-Fock representation. By considering the hydrogen atom and H+ 2 cation, we analyze how the unrestricted and generalized Hartree-Fock schemes minimize this error by localizing the electrons or rotating the spin coordinates. We also reveal a clear similarity between the Coulomb hole of He-like ions and the density depletion near the nucleus induced by the fractional-spin error in the unpolarized hydrogen atom. Finally, we analyze the effect of the fractional-spin error on the Møller-Plesset adiabatic connection, excited states, and functional- and density-driven errors.
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Affiliation(s)
- Hugh G A Burton
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, Oxford OX1 3QZ, United Kingdom
| | - Clotilde Marut
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Timothy J Daas
- Department of Chemistry and Pharmaceutical Sciences, Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - 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
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
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13
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Laplaza R, Cárdenas C, Chaquin P, Contreras-García J, Ayers PW. Orbital energies and nuclear forces in DFT: Interpretation and validation. J Comput Chem 2021; 42:334-343. [PMID: 33301201 DOI: 10.1002/jcc.26459] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2020] [Revised: 11/12/2020] [Accepted: 11/13/2020] [Indexed: 11/08/2022]
Abstract
The bonding and antibonding character of individual molecular orbitals has been previously shown to be related to their orbital energy derivatives with respect to nuclear coordinates, known as dynamical orbital forces. Albeit usually derived from Koopmans' theorem, in this work we show a more general derivation from conceptual DFT, which justifies application in a broader context. The consistency of the approach is validated numerically for valence orbitals in Kohn-Sham DFT. Then, we illustrate its usefulness by showcasing applications in aromatic and antiaromatic systems and in excited state chemistry. Overall, dynamical orbital forces can be used to interpret the results of routine ab initio calculations, be it wavefunction or density based, in terms of forces and occupations.
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Affiliation(s)
- Rubén Laplaza
- Laboratoire de Chimie Théorique, LCT, Sorbonne Université, CNRS, Paris, France.,Departamento de Química Física, Universidad de Zaragoza, Zaragoza, Spain
| | - Carlos Cárdenas
- Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile.,Centro para el desarrollo de la Nanociencias y Nanotecnologia, CEDENNA, Santiago, Chile
| | - Patrick Chaquin
- Laboratoire de Chimie Théorique, LCT, Sorbonne Université, CNRS, Paris, France
| | | | - Paul W Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario, Canada
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14
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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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15
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Amati M, Stoia S, Baerends EJ. The Electron Affinity as the Highest Occupied Anion Orbital Energy with a Sufficiently Accurate Approximation of the Exact Kohn-Sham Potential. J Chem Theory Comput 2020; 16:443-452. [PMID: 31794657 PMCID: PMC6964414 DOI: 10.1021/acs.jctc.9b00981] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
![]()
Negative ions are not accurately represented in density
functional
approximations (DFAs) such as (semi)local density functionals (LDA
or GGA or meta-GGA). This is caused by the much too high orbital energies
(not negative enough) with these DFAs compared to the exact Kohn–Sham
values. Negative ions very often have positive DFA HOMO energies,
hence they are unstable. These problems do not occur with the exact
Kohn–Sham potential, the anion HOMO energy then being equal
to minus the electron affinity. It is therefore desirable to develop
sufficiently accurate approximations to the exact Kohn–Sham
potential. There are further beneficial effects on the orbital shapes
and the density of using a good approximation to the exact KS potential.
Notably the unoccupied orbitals are not unduly diffuse, as they are
in the Hartree–Fock model, with hybrid functionals, and even
with (semi)local density functional approximations (LDFAs). We show
that the recently developed B-GLLB-VWN approximation [Gritsenko et
al. J. Chem. Phys.2016, 144, 204114] to the exact KS potential affords stable negative ions
with HOMO orbital energy close to minus the electron affinity.
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Affiliation(s)
- M Amati
- Università degli Studi della Basilicata , Viale dell'Ateneo Lucano 10 , 85100 Potenza , Italy
| | - S Stoia
- Università degli Studi della Basilicata , Viale dell'Ateneo Lucano 10 , 85100 Potenza , Italy
| | - E J Baerends
- Sectie Theoretische Chemie, FEW , Vrije Universiteit , De Boelelaan 1083 , 1081 HV Amsterdam , The Netherlands
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