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Desmarais JK, Maul J, Civalleri B, Erba A, Vignale G, Pittalis S. Spin Currents via the Gauge Principle for Meta-Generalized Gradient Exchange-Correlation Functionals. PHYSICAL REVIEW LETTERS 2024; 132:256401. [PMID: 38996240 DOI: 10.1103/physrevlett.132.256401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Accepted: 05/15/2024] [Indexed: 07/14/2024]
Abstract
The prominence of density functional theory in the field of electronic structure computation stems from its ability to usefully balance accuracy and computational effort. At the base of this ability is a functional of the electron density: the exchange-correlation energy. This functional satisfies known exact conditions that guide the derivation of approximations. The strongly constrained and appropriately normed (SCAN) approximation stands out as a successful, modern, example. In this Letter, we demonstrate how the SU(2) gauge invariance of the exchange-correlation functional in spin current density functional theory allows us to add an explicit dependence on spin currents in the SCAN functional (here called JSCAN)-and similar meta-generalized-gradient functional approximations-solely invoking first principles. In passing, a spin-current dependent generalization of the electron localization function (here called JELF) is also derived. The extended forms are implemented in a developer's version of the crystal23 program. Applications on molecules and materials confirm the practical relevance of the extensions.
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Affiliation(s)
| | | | | | | | | | - Stefano Pittalis
- Istituto Nanoscienze, Consiglio Nazionale delle Ricerche, Via Campi 213A, I-41125 Modena, Italy
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2
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Grotjahn R, Furche F. Gauge-Invariant Excited-State Linear and Quadratic Response Properties within the Meta-Generalized Gradient Approximation. J Chem Theory Comput 2023. [PMID: 37399786 DOI: 10.1021/acs.jctc.3c00259] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/05/2023]
Abstract
Gauge invariance is a fundamental symmetry connected to charge conservation and is widely accepted as indispensable for any electronic structure method. Hence, the gauge variance of the time-dependent kinetic energy density τ used in many meta-generalized gradient approximations (MGGAs) to the exchange-correlation (XC) functional presents a major obstacle for applying MGGAs within time-dependent density functional theory (TDDFT). Replacing τ by the gauge-invariant generalized kinetic energy density τ̂ significantly improves the accuracy of various functionals for vertical excitation energies [R. Grotjahn, F. Furche, and M. Kaupp. J. Chem. Phys. 2022, 157, 111102]. However, the dependence of the resulting current-MGGAs (cMGGAs) on the paramagnetic current density gives rise to new exchange-correlation kernels and hyper-kernels ignored in previous implementations of quadratic and higher-order response properties. Here we report the first implementation of cMGGAs and hybrid cMGGAs for excited-state gradients and dipole moments, as well as an extension to quadratic response properties including dynamic hyperpolarizabilities and two-photon absorption cross sections. In the first comprehensive benchmark study of MGGAs and cMGGAs for two-photon absorption cross sections, the M06-2X functional is found to be superior to the GGA hybrid PBE0. Additionally, two case studies from the literature for the practical prediction of nonlinear optical properties are revisited and potential advantages of hybrid (c)MGGAs compared to hybrid GGAs are discussed. The effect of restoring gauge invariance varies depending on the employed MGGA functional, the type of excitation, and the property under investigation: While some individual excited-state equilibrium structures are significantly affected, on average, these changes result in marginal improvements when compared against high-level reference data. Although the gauge-variant MGGA quadratic response properties are generally close to their gauge-invariant counterparts, the resulting errors are not bounded and significantly exceed typical method errors in some of the cases studied. Despite the limited effects seen in benchmark studies, gauge-invariant implementations of cMGGAs for excited-state properties are desirable from a fundamental perspective, entail little additional computational cost, and are necessary for response properties consistent with cMGGA linear response calculations such as excitation energies.
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Affiliation(s)
- Robin Grotjahn
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Filipp Furche
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
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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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Pausch A, Holzer C. Linear Response of Current-Dependent Density Functional Approximations in Magnetic Fields. J Phys Chem Lett 2022; 13:4335-4341. [PMID: 35536920 DOI: 10.1021/acs.jpclett.2c01082] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
This Letter outlines the steps and derivations that are necessary to apply density functional approximations that depend on the current and kinetic energy density rigorously within the framework of linear-response methods, including adiabatic time-dependent current density functional theory. This includes systems with a non-zero current density in the ground state. The necessary exchange-correlation kernel for these density functional approximations is derived, and the matrix elements are given explicitly. Due to the gauge variance of the kinetic energy density in an external magnetic field, having access to the proper current-dependent exchange-correlation kernel is necessary to recover gauge invariance for excited states. As a proof of principle application, the excited states of two small molecules in strong external magnetic fields are calculated using linear-response time-dependent current density functional theory. Finally, the implications of the derived current density-dependent exchange-correlation kernel for systems with strong spin-orbit coupling are discussed.
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Affiliation(s)
- Ansgar Pausch
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany
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Chowdhury STUR, Perdew JP. Spherical vs non-spherical and symmetry-preserving vs symmetry-breaking densities of open-shell atoms in density functional theory. J Chem Phys 2021; 155:234110. [PMID: 34937366 DOI: 10.1063/5.0072020] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The atomization energies of molecules from first-principles density functional approximations improve from the local spin-density approximation to the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) to the strongly constrained and appropriately normed (SCAN) meta-GGA, and their sensitivities to non-spherical components of the density increase in the same order. Thus, these functional advances increase density sensitivity and imitate the exact constrained search over correlated wavefunctions better than that over ensembles. The diatomic molecules studied here, singlet C2 and F2 plus triplet B2 and O2, have cylindrically symmetric densities. Because the densities of the corresponding atoms are non-spherical, the approximate Kohn-Sham potentials for the atoms have a lower symmetry than that of the external (nuclear) potential so that the non-interacting wavefunctions are not eigenstates of the square of total orbital angular momentum, breaking a symmetry that yields a feature of the exact ground-state density. That spatial symmetry can be preserved by a non-self-consistent approach in which a self-consistent equilibrium-ensemble calculation is followed by integer re-occupation of the Kohn-Sham orbitals as the first of several steps. The symmetry-preserving approach is different from symmetry restoration based on projection. First-step space- (and space-spin-) symmetry preservation in atoms is shown to have a small effect on the atomization energies of molecules, quantifying earlier observations by Fertig and Kohn. Thus, the standard Kohn-Sham way of calculating atomization energies, with self-consistent symmetry breaking to minimize the energy, is justified at least for the common cases where the molecules cannot break symmetry. Unless symmetry breaking is allowed in the molecule, SCAN strongly underestimates the atomization energy of strongly correlated singlet C2.
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Affiliation(s)
| | - John P Perdew
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
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6
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Schattenberg CJ, Kaupp M. Effect of the Current Dependence of Tau-Dependent Exchange-Correlation Functionals on Nuclear Shielding Calculations. J Chem Theory Comput 2021; 17:1469-1479. [DOI: 10.1021/acs.jctc.0c01223] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Caspar Jonas Schattenberg
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Martin Kaupp
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
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7
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Kvaal S, Laestadius A, Tellgren E, Helgaker T. Lower Semicontinuity of the Universal Functional in Paramagnetic Current-Density Functional Theory. J Phys Chem Lett 2021; 12:1421-1425. [PMID: 33522817 PMCID: PMC7883387 DOI: 10.1021/acs.jpclett.0c03422] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2020] [Accepted: 01/20/2021] [Indexed: 06/12/2023]
Abstract
A cornerstone of current-density functional theory (CDFT) in its paramagnetic formulation is proven. After a brief outline of the mathematical structure of CDFT, the lower semicontinuity and expectation-valuedness of the CDFT constrained-search functional is proven, meaning that there is always a minimizing density matrix in the CDFT constrained-search universal density functional. These results place the mathematical framework of CDFT on the same footing as that of standard DFT.
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Maier TM, Ikabata Y, Nakai H. Relativistic local hybrid functionals and their impact on 1s core orbital energies. J Chem Phys 2020; 152:214103. [DOI: 10.1063/5.0010400] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Toni M. Maier
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Yasuhiro Ikabata
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Hiromi Nakai
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520, Japan
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9
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Maier TM, Ikabata Y, Nakai H. Restoring the iso-orbital limit of the kinetic energy density in relativistic density functional theory. J Chem Phys 2019; 151:174114. [DOI: 10.1063/1.5125634] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Toni M. Maier
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Yasuhiro Ikabata
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Hiromi Nakai
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520, Japan
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10
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Desmarais JK, Flament JP, Erba A. Fundamental Role of Fock Exchange in Relativistic Density Functional Theory. J Phys Chem Lett 2019; 10:3580-3585. [PMID: 31188603 DOI: 10.1021/acs.jpclett.9b01401] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
We perform a formal analysis of relativistic density functional theory for the treatment of spin-orbit coupling (SOC), noncollinear magnetization (NCM), and orbital current density (OCD). We identify specific components of the spinors (namely, those mapped onto imaginary diagonal spin-blocks of the density matrix) that arise from the SOC operator and define the OCD. We show that these pieces of the spinors only enter in the bielectronic part of the potential through the exact Fock exchange (FE) operator. The lack of FE therefore leads to a correspondingly incorrect physical description of SOC, NCM, and OCD. This analysis is complemented with an illustrative example, where we show that, while in the absence of FE, the theory fails even at reproducing the expected right-hand relationship between the NCM and OCD, its inclusion provides results that match those from a reference SOC configuration-interaction calculation.
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Affiliation(s)
- Jacques K Desmarais
- Dipartimento di Chimica , Università di Torino , via Giuria 5 , 10125 Torino , Italy
- Department of Geological Sciences , University of Saskatchewan , Saskatoon , SK S7N 5E2 , Canada
- Department of Physics and Engineering Physics , University of Saskatchewan , Saskatoon , SK S7N 5E2 , Canada
| | - Jean-Pierre Flament
- Laboratoire de Physique des Lasers et des Molecules , UFR de Physique, Batiment P5, Universite de Lille, 59655 Villeneuve D'Ascq Cedex, France
| | - Alessandro Erba
- Dipartimento di Chimica , Università di Torino , via Giuria 5 , 10125 Torino , Italy
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11
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Sen S, Tellgren EI. A local tensor that unifies kinetic energy density and vorticity in density functional theory. J Chem Phys 2018; 149:144109. [DOI: 10.1063/1.5041931] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Affiliation(s)
- Sangita Sen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Erik I. Tellgren
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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12
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Zhu W, Zhang L, Trickey SB. Random phase approximation with second-order screened exchange for current-carrying atomic states. J Chem Phys 2016; 145:224106. [DOI: 10.1063/1.4971377] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Affiliation(s)
- Wuming Zhu
- Department of Physics, Hangzhou Normal University, 16 Xuelin Street, Hangzhou, Zhejiang 310036, China
| | - Liang Zhang
- Institute of Service Engineering, Hangzhou Normal University, 2318 Yuhangtang Road, Cangqian, Hangzhou, Zhejiang 311121, China
| | - S. B. Trickey
- Quantum Theory Project, Department of Physics and Department of Chemistry, University of Florida, P.O. Box 118435, Gainesville, Florida 32611-8435, USA
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Sato SA, Taniguchi Y, Shinohara Y, Yabana K. Nonlinear electronic excitations in crystalline solids using meta-generalized gradient approximation and hybrid functional in time-dependent density functional theory. J Chem Phys 2015; 143:224116. [DOI: 10.1063/1.4937379] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Shunsuke A. Sato
- Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571, Japan
| | - Yasutaka Taniguchi
- Center for Computational Science, University of Tsukuba, Tsukuba 305-8571, Japan
- Department of Medical and General Sciences, Nihon Institute of Medical Science, 1276 Shimogawara, Moroyama-Machi, Iruma-Gun, Saitama 350-0435, Japan
| | - Yasushi Shinohara
- Max Planck Institute of Microstructure Physics, 06120 Halle, Germany
| | - Kazuhiro Yabana
- Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571, Japan
- Center for Computational Science, University of Tsukuba, Tsukuba 305-8571, Japan
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14
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Furness JW, Verbeke J, Tellgren EI, Stopkowicz S, Ekström U, Helgaker T, Teale AM. Current Density Functional Theory Using Meta-Generalized Gradient Exchange-Correlation Functionals. J Chem Theory Comput 2015; 11:4169-81. [DOI: 10.1021/acs.jctc.5b00535] [Citation(s) in RCA: 47] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- James W. Furness
- School
of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom
| | - Joachim Verbeke
- School
of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom
| | - Erik I. Tellgren
- Centre
for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O.
Box 1033, Blindern, N-0315, Oslo, Norway
| | - Stella Stopkowicz
- Centre
for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O.
Box 1033, Blindern, N-0315, Oslo, Norway
| | - Ulf Ekström
- Centre
for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O.
Box 1033, Blindern, N-0315, Oslo, Norway
| | - Trygve Helgaker
- Centre
for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O.
Box 1033, Blindern, N-0315, Oslo, Norway
| | - Andrew M. Teale
- School
of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom
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15
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Sun J, Ruzsinszky A, Perdew JP. Strongly Constrained and Appropriately Normed Semilocal Density Functional. PHYSICAL REVIEW LETTERS 2015; 115:036402. [PMID: 26230809 DOI: 10.1103/physrevlett.115.036402] [Citation(s) in RCA: 1160] [Impact Index Per Article: 128.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2015] [Indexed: 05/08/2023]
Abstract
The ground-state energy, electron density, and related properties of ordinary matter can be computed efficiently when the exchange-correlation energy as a functional of the density is approximated semilocally. We propose the first meta-generalized-gradient approximation (meta-GGA) that is fully constrained, obeying all 17 known exact constraints that a meta-GGA can. It is also exact or nearly exact for a set of "appropriate norms," including rare-gas atoms and nonbonded interactions. This strongly constrained and appropriately normed meta-GGA achieves remarkable accuracy for systems where the exact exchange-correlation hole is localized near its electron, and especially for lattice constants and weak interactions.
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Affiliation(s)
- Jianwei Sun
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Adrienn Ruzsinszky
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - John P Perdew
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, USA
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16
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Johnson LE, Dalton LR, Robinson BH. Optimizing calculations of electronic excitations and relative hyperpolarizabilities of electrooptic chromophores. Acc Chem Res 2014; 47:3258-65. [PMID: 24967617 DOI: 10.1021/ar5000727] [Citation(s) in RCA: 105] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
CONSPECTUS: Organic glasses containing chromophores with large first hyperpolarizabilities (β) are promising for compact, high-bandwidth, and energy-efficient electro-optic devices. Systematic optimization of device performance requires development of materials with high acentric order and enhanced hyperpolarizability at operating wavelengths. One essential component of the design process is the accurate calculation of optical transition frequencies and hyperpolarizability. These properties can be computed with a wide range of electronic structure methods implemented within commercial and open-source software packages. A wide variety of methods, especially hybrid density-functional theory (DFT) variants have been used for this purpose. However, in order to provide predictions useful to chromophore designers, a method must be able to consistently predict the relative ordering of standard and novel materials. Moreover, it is important to distinguish between the resonant and nonresonant contribution to the hyperpolarizabiliy and be able to estimate the trade-off between improved β and unwanted absorbance (optical loss) at the target device's operating wavelength. Therefore, we have surveyed a large variety of common methods for computing the properties of modern high-performance chromophores and compared these results with prior experimental hyper-Rayleigh scattering (HRS) and absorbance data. We focused on hybrid DFT methods, supplemented by more computationally intensive Møller-Plesset (MP2) calculations, to determine the relative accuracy of these methods. Our work compares computed hyperpolarizabilities in chloroform relative to standard chromophore EZ-FTC against HRS data versus the same reference. We categorized DFT methods used by the amount of Hartree-Fock (HF) exchange energy incorporated into each functional. Our results suggest that the relationship between percentage of long-range HF exchange and both βHRS and λmax is nearly linear, decreasing as the fraction of long-range HF exchange increases. Mild hybrid DFT methods are satisfactory for prediction of λmax. However, mild hybrid methods provided qualitatively incorrect predictions of the relative hyperpolarizabilities of three high-performance chromophores. DFT methods with approximately 50% HF exchange, and especially the Truhlar M062X functional, provide superior predictions of relative βHRS values but poorer predictions of λmax. The observed trends for these functionals, as well as range-separated hybrids, are similar to MP2, though predicting smaller absolute magnitudes for βHRS. Frequency dependence for βHRS can be calculated using time-dependent DFT and HF methods. However, calculation quality is sensitive not only to a method's ability to predict static hyperpolarizability but also to its prediction of optical resonances. Due to the apparent trade-off in accuracy of prediction of these two properties and the need to use static finite-field methods for MP2 and higher-level hyperpolarizability calculations in most codes, we suggest that composite methods could greatly improve the accuracy of calculations of β and λmax.
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Affiliation(s)
- Lewis E. Johnson
- Department of Chemistry, University of Washington, Seattle, Washington 98195-1700, United States
| | - Larry R. Dalton
- Department of Chemistry, University of Washington, Seattle, Washington 98195-1700, United States
| | - Bruce H. Robinson
- Department of Chemistry, University of Washington, Seattle, Washington 98195-1700, United States
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17
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Tellgren EI, Teale AM, Furness JW, Lange KK, Ekström U, Helgaker T. Non-perturbative calculation of molecular magnetic properties within current-density functional theory. J Chem Phys 2014; 140:034101. [DOI: 10.1063/1.4861427] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
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18
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Teale AM, Lutnæs OB, Helgaker T, Tozer DJ, Gauss J. Benchmarking density-functional theory calculations of NMR shielding constants and spin-rotation constants using accurate coupled-cluster calculations. J Chem Phys 2013; 138:024111. [PMID: 23320672 DOI: 10.1063/1.4773016] [Citation(s) in RCA: 131] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Accurate sets of benchmark nuclear-magnetic-resonance shielding constants and spin-rotation constants are calculated using coupled-cluster singles-doubles (CCSD) theory and coupled-cluster singles-doubles-perturbative-triples [CCSD(T)] theory, in a variety of basis sets consisting of (rotational) London atomic orbitals. The accuracy of the calculated coupled-cluster constants is established by a careful comparison with experimental data, taking into account zero-point vibrational corrections. Coupled-cluster basis-set convergence is analyzed and extrapolation techniques are employed to estimate basis-set-limit quantities, thereby establishing an accurate benchmark data set. Together with the set provided for rotational g-tensors and magnetizabilities in our previous work [O. B. Lutnæs, A. M. Teale, T. Helgaker, D. J. Tozer, K. Ruud, and J. Gauss, J. Chem. Phys. 131, 144104 (2009)], it provides a substantial source of consistently calculated high-accuracy data on second-order magnetic response properties. The utility of this benchmark data set is demonstrated by examining a wide variety of Kohn-Sham exchange-correlation functionals for the calculation of these properties. None of the existing approximate functionals provide an accuracy competitive with that provided by CCSD or CCSD(T) theory. The need for a careful consideration of vibrational effects is clearly illustrated. Finally, the pure coupled-cluster results are compared with the results of Kohn-Sham calculations constrained to give the same electronic density. Routes to future improvements are discussed in light of this comparison.
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Affiliation(s)
- Andrew M Teale
- Department of Chemistry, Centre for Theoretical and Computational Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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19
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Affiliation(s)
- Espen Sagvolden
- a Centre for Theoretical and Computational Chemistry, Department of Chemistry , University of Oslo , P.O. Box 1033, Blindern, N-0315, Oslo , Norway
| | - Ulf Ekström
- a Centre for Theoretical and Computational Chemistry, Department of Chemistry , University of Oslo , P.O. Box 1033, Blindern, N-0315, Oslo , Norway
| | - Erik I. Tellgren
- a Centre for Theoretical and Computational Chemistry, Department of Chemistry , University of Oslo , P.O. Box 1033, Blindern, N-0315, Oslo , Norway
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20
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Bates JE, Furche F. Harnessing the meta-generalized gradient approximation for time-dependent density functional theory. J Chem Phys 2012; 137:164105. [DOI: 10.1063/1.4759080] [Citation(s) in RCA: 83] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
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21
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Baldo M, Burgio GF. Properties of the nuclear medium. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2012; 75:026301. [PMID: 22790345 DOI: 10.1088/0034-4885/75/2/026301] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We review our knowledge on the properties of the nuclear medium that have been studied, over many years, on the basis of many-body theory, laboratory experiments and astrophysical observations. Throughout the presentation particular emphasis is placed on the possible relationship and links between the nuclear medium and the structure of nuclei, including the limitations of such an approach. First we consider the realm of phenomenological laboratory data and astrophysical observations and the hints they can give on the characteristics that the nuclear medium should possess. The analysis is based on phenomenological models, that however have a strong basis on physical intuition and an impressive success. More microscopic models are also considered, and it is shown that they are able to give invaluable information on the nuclear medium, in particular on its equation of state. The interplay between laboratory experiments and astrophysical observations is particularly stressed, and it is shown how their complementarity enormously enriches our insights into the structure of the nuclear medium. We then introduce the nucleon-nucleon interaction and the microscopic many-body theory of nuclear matter, with a critical discussion about the different approaches and their results. The Landau-Fermi liquid theory is introduced and briefly discussed, and it is shown how fruitful it can be in discussing the macroscopic and low-energy properties of the nuclear medium. As an illustrative example, we discuss neutron matter at very low density, and it is shown how it can be treated within the many-body theory. The general bulk properties of the nuclear medium are reviewed to indicate at which stage of our knowledge we stand, taking into account the most recent developments both in theory and experiments. A section is dedicated to the pairing problem. The connection with nuclear structure is then discussed, on the basis of the energy density functional method. The possibility of linking the physics of exotic nuclei and the astrophysics of neutron stars is particularly stressed. Finally, we discuss the thermal properties of the nuclear medium, in particular the liquid-gas phase transition and its connection with the phenomenology on heavy ion reactions and the cooling evolution of neutron stars. The presentation has been taken for non-specialists and possibly for non-nuclear physicists.
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Affiliation(s)
- M Baldo
- Instituto Nazionale di Fisica Nucleare, Sez. di Catania, Via S Sofia 64 95123 Catania, Italy.
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22
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He 2++ molecular ion in a strong time-dependent magnetic field: a current-density functional study. J Comput Chem 2011; 32:2404-13. [PMID: 21598275 DOI: 10.1002/jcc.21822] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2010] [Revised: 02/10/2011] [Accepted: 03/22/2011] [Indexed: 11/07/2022]
Abstract
The He 2++ molecular ion exposed to a strong ultrashort time-dependent (TD) magnetic field of the order of 10(9) G is investigated through a quantum fluid dynamics (QFD) and current-density functional theory (CDFT) based approach using vector exchange-correlation (XC) potential and energy density functional that depend not only on the electronic charge-density but also on the current density. The TD-QFD-CDFT computations are performed in a parallel internuclear-axis and magnetic field-axis configuration at the field-free equilibrium internuclear separation R = 1.3 au with the field-strength varying between 0 and 10(11) G. The TD behavior of the exchange- and correlation energy of the He 2++ is analyzed and compared with that obtained using a [B-TD-QFD-density functional theory (DFT)] approach based on the conventional TD-DFT under similar computational constraints but using only scalar XC potential and energy density functional dependent on the electronic charge-density alone. The CDFT based approach yields TD exchange- and correlation energy and TD electronic charge-density significantly different from that obtained using the conventional TD-DFT based approach, particularly, at typical magnetic field strengths and during a typical time period of the TD field. This peculiar behavior of the CDFT-based approach is traced to the TD current-density dependent vector XC potential, which can induce nonadiabatic effects causing retardation of the oscillating electronic charge density. Such dissipative electron dynamics of the He 2++ molecular ion is elucidated by treating electronic charge density as an electron-"fluid" in the terminology of QFD.
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23
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Räsänen E, Pittalis S, Proetto CR. Universal correction for the Becke–Johnson exchange potential. J Chem Phys 2010; 132:044112. [DOI: 10.1063/1.3300063] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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24
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Tao J, Tretiak S, Zhu JX. Absorption Spectra of Blue-Light-Emitting Oligoquinolines from Time-Dependent Density Functional Theory. J Phys Chem B 2008; 112:13701-10. [DOI: 10.1021/jp804687j] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jianmin Tao
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, and Center for Integrated Nanotechnology, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
| | - Sergei Tretiak
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, and Center for Integrated Nanotechnology, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
| | - Jian-Xin Zhu
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, and Center for Integrated Nanotechnology, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
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25
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Vortex dynamics in the current–density of helium atom evolving in a time-dependent magnetic field: Exchange–correlation functionals of time-dependent current–density functional theory. Chem Phys Lett 2008. [DOI: 10.1016/j.cplett.2008.04.055] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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26
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Neese F, Schwabe T, Grimme S. Analytic derivatives for perturbatively corrected "double hybrid" density functionals: theory, implementation, and applications. J Chem Phys 2007; 126:124115. [PMID: 17411116 DOI: 10.1063/1.2712433] [Citation(s) in RCA: 163] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A recently proposed new family of density functionals [S. Grimme, J. Chem. Phys. 124, 34108 (2006)] adds a fraction of nonlocal correlation as a new ingredient to density functional theory (DFT). This fractional correlation energy is calculated at the level of second-order many-body perturbation theory (PT2) and replaces some of the semilocal DFT correlation of standard hybrid DFT methods. The new "double hybrid" functionals (termed, e.g., B2-PLYP) contain only two empirical parameters that have been adjusted in thermochemical calculations on parts of the G2/3 benchmark set. The methods have provided the lowest errors ever obtained by any DFT method for the full G3 set of molecules. In this work, the applicability of the new functionals is extended to the exploration of potential energy surfaces with analytic gradients. The theory of the analytic gradient largely follows the standard theory of PT2 gradients with some additional subtleties due to the presence of the exchange-correlation terms in the self-consistent field operator. An implementation is reported for closed-shell as well as spin-unrestricted reference determinants. Furthermore, the implementation includes external point charge fields and also accommodates continuum solvation models at the level of the conductor like screening model. The density fitting resolution of the identity (RI) approximation can be applied to the evaluation of the PT2 part with large gains in computational efficiency. For systems with approximately 500-600 basis functions the evaluation of the double hybrid gradient is approximately four times more expensive than the calculation of the standard hybrid DFT gradient. Extensive test calculations are provided for main group elements and transition metal containing species. The results reveal that the B2-PLYP functional provides excellent molecular geometries that are superior compared to those from standard DFT and MP2.
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Affiliation(s)
- Frank Neese
- Lehrstuhl für Theoretische Chemie, Institut für Physikalische und Theoretische Chemie, Universität Bonn, Wegelerstr. 12, D-53115 Bonn, Germany.
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27
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Pittalis S, Kurth S, Sharma S, Gross EKU. Orbital currents in the Colle-Salvetti correlation energy functional and the degeneracy problem. J Chem Phys 2007; 127:124103. [PMID: 17902889 DOI: 10.1063/1.2777140] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Popular density functionals for the exchange-correlation energy typically fail to reproduce the degeneracy of different ground states of open-shell atoms. As a remedy, functionals which explicitly depend on the current density have been suggested. We present an analysis of this problem by investigating functionals that explicitly depend on the Kohn-Sham orbitals. Going beyond the exact-exchange approximation by adding correlation in the form of the Colle-Salvetti functional, we show how current-dependent terms enter the Colle-Salvetti expression and their relevance is evaluated. A very good description of the degeneracy of ground states for atoms of the first and second rows of the Periodic Table is obtained.
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Affiliation(s)
- S Pittalis
- Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany
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28
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Pittalis S, Kurth S, Gross EKU. On the degeneracy of atomic states within exact-exchange (spin-) density functional theory. J Chem Phys 2006; 125:084105. [PMID: 16964999 DOI: 10.1063/1.2338038] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The problem of degenerate ground states of open-shell atoms is investigated in spin-restricted and spin-unrestricted density functional theories using the exact-exchange energy functional. For the spin-unrestricted case, spurious energy splittings of the order of 2-3 kcal/mol are found for atoms of the second and third periods which are larger than the splittings obtained from recently proposed approximate exchange functionals depending explicitly on the current density. In remarkable contrast, for spin-restricted calculations the degeneracy of different atomic ground states is recovered to within less than 0.6 kcal/mol.
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Affiliation(s)
- S Pittalis
- Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany
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29
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Tao J, Vignale G. Time-dependent density-functional theory beyond the local-density approximation. PHYSICAL REVIEW LETTERS 2006; 97:036403. [PMID: 16907522 DOI: 10.1103/physrevlett.97.036403] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2006] [Indexed: 05/11/2023]
Abstract
Approximations for the ground-state exchange-correlation potential of density-functional theory have reached a high level of sophistication. By contrast, time- or frequency-dependent exchange-correlation potentials are still being treated in a local approximation. Here we propose a novel approximation scheme, which effectively brings the power of the generalized gradient approximation (GGA) and meta-GGA to time-dependent density-functional theory. The theory should allow a more accurate treatment of strongly inhomogeneous electronic systems (e.g. molecular junctions) while remaining essentially exact for slowly varying densities and slowly varying external potentials.
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Affiliation(s)
- Jianmin Tao
- Department of Physics, University of Missouri-Columbia, Columbia, Missouri 65211, USA
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30
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Furche F, Perdew JP. The performance of semilocal and hybrid density functionals in 3d transition-metal chemistry. J Chem Phys 2006; 124:044103. [PMID: 16460145 DOI: 10.1063/1.2162161] [Citation(s) in RCA: 425] [Impact Index Per Article: 23.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the performance of contemporary semilocal and hybrid density functionals for bond energetics, structures, dipole moments, and harmonic frequencies of 3d transition-metal (TM) compounds by comparison with gas-phase experiments. Special attention is given to the nonempirical metageneralized gradient approximation (meta-GGA) of Tao, Perdew, Staroverov, and Scuseria (TPSS) [Phys. Rev. Lett. 91, 146401 (2003)], which has been implemented in TURBOMOLE for the present work. Trends and error patterns for classes of homologous compounds are analyzed, including dimers, monohydrides, mononitrides, monoxides, monofluorides, polyatomic oxides and halogenides, carbonyls, and complexes with organic pi ligands such as benzene and cyclopentadienyl. Weakly bound systems such as Ca(2), Mn(2), and Zn(2) are discussed. We propose a reference set of reaction energies for benchmark purposes. Our all-electron results with quadruple zeta valence basis sets validate semilocal density-functional theory as the workhorse of computational TM chemistry. Typical errors in bond energies are substantially larger than in (organic) main group chemistry, however. The Becke-Perdew'86 [Phys. Rev. A 38, 3098 (1988); Phys. Rev. B 33, 8822 (1986)] GGA and the TPSS meta-GGA have the best price/performance ratio, while the TPSS hybrid functional achieves a slightly lower mean absolute error in bond energies. The popular Becke three-parameter hybrid B3LYP underbinds significantly and tends to overestimate bond distances; we give a possible explanation for this. We further show that hybrid mixing does not reduce the width of the error distribution on our reference set. The error of a functional for the s-d transfer energy of a TM atom does not predict its error for TM bond energies and bond lengths. For semilocal functionals, self-interaction error in one- and three-electron bonds appears to be a major source of error in TM reaction energies. Nevertheless, TPSS predicts the correct ground-state symmetry in the vast majority of cases and rarely fails qualitatively. This further confirms TPSS as a general purpose functional that works throughout the periodic table. We also give workstation timing comparisons for the 645-atom protein crambin.
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Affiliation(s)
- Filipp Furche
- Institut für Physikalische Chemie, Universität Karlsruhe, Kaiserstrasse 12, 76128 Karlsruhe, Germany.
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