1
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Constantin LA, Jana S, Śmiga S, Della Sala F. Adiabatic connection interaction strength interpolation method made accurate for the uniform electron gas. J Chem Phys 2023; 159:244111. [PMID: 38149733 DOI: 10.1063/5.0178800] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2023] [Accepted: 11/27/2023] [Indexed: 12/28/2023] Open
Abstract
The adiabatic connection interaction strength interpolation (ISI)-like method provides a high-level expression for the correlation energy, being, in principle, exact not only in the weak-interaction limit, where it recovers the second-order Görling-Levy perturbation term, but also in the strong-interaction limit that is described by the strictly correlated electron approach. In this work, we construct a genISI functional made accurate for the uniform electron gas, a solid-state physics paradigm that is a very difficult test for ISI-like correlation functionals. We assess the genISI functional for various jellium spheres with the number of electrons Z ≤ 912 and for the non-relativistic noble atoms with Z ≤ 290. For the jellium clusters, the genISI is remarkably accurate, while for the noble atoms, it shows a good performance, similar to other ISI-like methods. Then, the genISI functional can open the path using the ISI-like method in solid-state calculations.
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Affiliation(s)
- Lucian A Constantin
- Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
| | - Subrata Jana
- Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovoth 76100, Israel
| | - Szymon Śmiga
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, ul. Grudziądzka 5, 87-100 Toruń, Poland
| | - Fabio Della Sala
- Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center for Biomolecular Nanotechnologies, Istituto Italiano di Tecnologia, Via Barsanti 14, 73010 Arnesano (LE), Italy
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2
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Jana S, Śmiga S, Constantin LA, Samal P. Semilocal Meta-GGA Exchange-Correlation Approximation from Adiabatic Connection Formalism: Extent and Limitations. J Phys Chem A 2023; 127:8685-8697. [PMID: 37811903 PMCID: PMC10591512 DOI: 10.1021/acs.jpca.3c03976] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2023] [Revised: 08/24/2023] [Indexed: 10/10/2023]
Abstract
The incorporation of a strong-interaction regime within the approximate semilocal exchange-correlation functionals still remains a very challenging task for density functional theory. One of the promising attempts in this direction is the recently proposed adiabatic connection semilocal correlation (ACSC) approach [Constantin, L. A.; Phys. Rev. B 2019, 99, 085117] allowing one to construct the correlation energy functionals by interpolation of the high and low-density limits for the given semilocal approximation. The current study extends the ACSC method to the meta-generalized gradient approximations (meta-GGA) level of theory, providing some new insights in this context. As an example, we construct the correlation energy functional on the basis of the high- and low-density limits of the Tao-Perdew-Staroverov-Scuseria (TPSS) functional. Arose in this way, the TPSS-ACSC functional is one-electron self-interaction free and accurate for the strictly correlated and quasi-two-dimensional regimes. Based on simple examples, we show the advantages and disadvantages of ACSC semilocal functionals and provide some new guidelines for future developments in this context.
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Affiliation(s)
- Subrata Jana
- Department
of Chemistry & Biochemistry, The Ohio
State University, Columbus, Ohio 43210, United States
| | - Szymon Śmiga
- Institute
of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, ul. Grudzikadzka 5, 87-100 Toruń, Poland
| | - Lucian A. Constantin
- Istituto
di Nanoscienze, Consiglio Nazionale delle
Ricerche CNR-NANO, 41125 Modena, Italy
| | - Prasanjit Samal
- School
of Physical Sciences, National Institute of Science Education and
Research, HBNI, Bhubaneswar 752050, India
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3
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Vuckovic S, Bahmann H. Nonlocal Functionals Inspired by the Strongly Interacting Limit of DFT: Exact Constraints and Implementation. J Chem Theory Comput 2023; 19:6172-6184. [PMID: 37611177 DOI: 10.1021/acs.jctc.3c00437] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/25/2023]
Abstract
Capturing strong correlation effects remains a key challenge for the development of improved exchange-correlation (XC) functionals in density functional theory. The recently proposed multiple radii functional (MRF) [J. Phys. Chem. Lett. 2017, 8, 2799; J. Chem. Theory Comput. 2019, 15, 3580] was designed to capture strong correlation effects seamlessly, as its mathematical structure draws from that of the exact XC functional in the limit of infinite correlations. The MRF functional provides a framework for building approximations along the density-fixed adiabatic connection, delivers accurate XC energy densities in the standard DFT gauge (same as that of the exact exchange energy density), and is free of one-electron self-interaction errors. To facilitate the development of XC functionals based on the MRF, we examine the behavior of the MRF functional when applied to uniform and scaled densities and consider how it can be made exact for the uniform electron gas. These theoretical insights are then used to build improved forms for the fluctuation function, an object that defines XC energy densities within the MRF framework. We also show how the MRF fluctuation function for physical correlation can be easily readjusted to accurately capture the XC functional in the limit of infinite correlations, demonstrating the versatility of MRF for building approximations for different correlation regimes. We describe the implementation of MRF using densities expanded on Gaussian basis sets, which improves the efficiency of previous grid-based MRF implementations.
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Affiliation(s)
- Stefan Vuckovic
- Department of Chemistry, University of Fribourg, 1700 Fribourg, Switzerland
| | - Hilke Bahmann
- Physical and Theoretical Chemistry, University of Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany
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4
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Giarrusso S, Pribram-Jones A. Møller-Plesset and Density-Fixed Adiabatic Connections for a Model Diatomic System at Different Correlation Regimes. J Chem Theory Comput 2023; 19:5835-5850. [PMID: 37642270 DOI: 10.1021/acs.jctc.3c00529] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/31/2023]
Abstract
In recent years, adiabatic connection (AC) interpolations developed within density functional theory (DFT) have been found to provide good performances in the calculation of interaction energies when used with Hartree-Fock (HF) ingredients. The physical and mathematical reasons for such unanticipated performance have been clarified, to some extent, by studying the strong-interaction limit of the Møller-Plesset (MP) AC. In this work, we calculate both the MP and the DFT AC integrand for the asymmetric Hubbard dimer, which allows for a systematic investigation of different correlation regimes by varying two simple parameters in the Hamiltonian: the external potential, Δv, and the interaction strength, U. Notably, we find that, while the DFT AC integrand appears to be convex in the full parameter space, the MP integrand may change curvature twice. Furthermore, we discuss different aspects of the second-order expansion of the correlation energy in each AC, and we demonstrate why the derivative of the λ-dependent density in the MP AC at λ = 0 (i.e., at the HF density) is zero in the model. Concerning the strong-interaction limit of both ACs in the Hubbard dimer setting, we show that the asymptotic value of the MP AC, W∞HF, is lower than (or equal to) its DFT analogue, W∞KS, if the two are compared at a given density, just like in real space. However, we also show that this is not always the case if the two quantities are compared at a given external potential.
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Affiliation(s)
- Sara Giarrusso
- Department of Chemistry and Biochemistry, University of California Merced, 5200 North Lake Rd., Merced, California 95343, United States
| | - Aurora Pribram-Jones
- Department of Chemistry and Biochemistry, University of California Merced, 5200 North Lake Rd., Merced, California 95343, United States
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5
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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: 73] [Impact Index Per Article: 36.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2022] [Accepted: 08/09/2022] [Indexed: 12/13/2022]
Abstract
In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.
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Affiliation(s)
- Andrew M. Teale
- School of Chemistry, University of Nottingham, University ParkNottinghamNG7 2RDUK
| | - Trygve Helgaker
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.
| | - Andreas Savin
- Laboratoire de Chimie Théorique, CNRS and Sorbonne University, 4 Place Jussieu, CEDEX 05, 75252 Paris, France.
| | - Carlo Adamo
- PSL University, CNRS, ChimieParisTech-PSL, Institute of Chemistry for Health and Life Sciences, i-CLeHS, 11 rue P. et M. Curie, 75005 Paris, France.
| | - Bálint Aradi
- Bremen Center for Computational Materials Science, University of Bremen, P.O. Box 330440, D-28334 Bremen, Germany.
| | - Alexei V. Arbuznikov
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7Straße des 17. Juni 13510623Berlin
| | | | - Evert Jan Baerends
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands.
| | - Vincenzo Barone
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56125 Pisa, Italy.
| | - Patrizia Calaminici
- Departamento de Química, Centro de Investigación y de Estudios Avanzados (Cinvestav), CDMX, 07360, Mexico.
| | - Eric Cancès
- CERMICS, Ecole des Ponts and Inria Paris, 6 Avenue Blaise Pascal, 77455 Marne-la-Vallée, France.
| | - Emily A. Carter
- Department of Mechanical and Aerospace Engineering and the Andlinger Center for Energy and the Environment, Princeton UniversityPrincetonNJ 08544-5263USA
| | | | - Henry Chermette
- Institut Sciences Analytiques, Université Claude Bernard Lyon1, CNRS UMR 5280, 69622 Villeurbanne, France.
| | - Ilaria Ciofini
- PSL University, CNRS, ChimieParisTech-PSL, Institute of Chemistry for Health and Life Sciences, i-CLeHS, 11 rue P. et M. Curie, 75005 Paris, France.
| | - T. Daniel Crawford
- Department of Chemistry, Virginia TechBlacksburgVA 24061USA,Molecular Sciences Software InstituteBlacksburgVA 24060USA
| | - Frank De Proft
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium.
| | | | - Claudia Draxl
- Institut für Physik and IRIS Adlershof, Humboldt-Universität zu Berlin, 12489 Berlin, Germany. .,Fritz-Haber-Institut der Max-Planck-Gesellschaft, 14195 Berlin, Germany
| | - Thomas Frauenheim
- Bremen Center for Computational Materials Science, University of Bremen, P.O. Box 330440, D-28334 Bremen, Germany. .,Beijing Computational Science Research Center (CSRC), 100193 Beijing, China.,Shenzhen JL Computational Science and Applied Research Institute, 518110 Shenzhen, China
| | - Emmanuel Fromager
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, 4 rue Blaise Pascal, 67000 Strasbourg, France.
| | - Patricio Fuentealba
- Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile.
| | - Laura Gagliardi
- Department of Chemistry, Pritzker School of Molecular Engineering, The James Franck Institute, and Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, USA.
| | - Giulia Galli
- Pritzker School of Molecular Engineering and Department of Chemistry, The University of Chicago, Chicago, IL, USA.
| | - Jiali Gao
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, China. .,Department of Chemistry, University of Minnesota, Minneapolis, MN 55455, USA
| | - Paul Geerlings
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium.
| | - Nikitas Gidopoulos
- Department of Physics, Durham University, South Road, Durham DH1 3LE, UK.
| | - Peter M. W. Gill
- School of Chemistry, University of SydneyCamperdown NSW 2006Australia
| | - Paola Gori-Giorgi
- Department of Chemistry and Pharmaceutical Sciences, Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands.
| | - Andreas Görling
- Chair of Theoretical Chemistry, University of Erlangen-Nuremberg, Egerlandstrasse 3, 91058 Erlangen, Germany.
| | - Tim Gould
- Qld Micro- and Nanotechnology Centre, Griffith University, Gold Coast, Qld 4222, Australia.
| | - Stefan Grimme
- Mulliken Center for Theoretical Chemistry, University of Bonn, Beringstrasse 4, 53115 Bonn, Germany.
| | - Oleg Gritsenko
- Department of Chemistry and Pharmaceutical Sciences, Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands.
| | - Hans Jørgen Aagaard Jensen
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark.
| | - Erin R. Johnson
- Department of Chemistry, Dalhousie UniversityHalifaxNova ScotiaB3H 4R2Canada
| | - Robert O. Jones
- Peter Grünberg Institut PGI-1, Forschungszentrum Jülich52425 JülichGermany
| | - Martin Kaupp
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, 10623, Berlin.
| | - Andreas M. Köster
- Departamento de Química, Centro de Investigación y de Estudios Avanzados (Cinvestav)CDMX07360Mexico
| | - Leeor Kronik
- Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovoth, 76100, Israel.
| | - Anna I. Krylov
- Department of Chemistry, University of Southern CaliforniaLos AngelesCalifornia 90089USA
| | - Simen Kvaal
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.
| | - Andre Laestadius
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.
| | - Mel Levy
- Department of Chemistry, Tulane University, New Orleans, Louisiana, 70118, USA.
| | - Mathieu Lewin
- CNRS & CEREMADE, Université Paris-Dauphine, PSL Research University, Place de Lattre de Tassigny, 75016 Paris, France.
| | - Shubin Liu
- Research Computing Center, University of North Carolina, Chapel Hill, NC 27599-3420, USA. .,Department of Chemistry, University of North Carolina, Chapel Hill, NC 27599-3290, USA
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, France.
| | - Neepa T. Maitra
- Department of Physics, Rutgers University at Newark101 Warren StreetNewarkNJ 07102USA
| | - Frank Neese
- Max Planck Institut für Kohlenforschung, Kaiser Wilhelm Platz 1, D-45470 Mülheim an der Ruhr, Germany.
| | - John P. Perdew
- Departments of Physics and Chemistry, Temple UniversityPhiladelphiaPA 19122USA
| | - Katarzyna Pernal
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland.
| | - Pascal Pernot
- Institut de Chimie Physique, UMR8000, CNRS and Université Paris-Saclay, Bât. 349, Campus d'Orsay, 91405 Orsay, France.
| | - Piotr Piecuch
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA. .,Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
| | - Elisa Rebolini
- Institut Laue Langevin, 71 avenue des Martyrs, 38000 Grenoble, France.
| | - Lucia Reining
- Laboratoire des Solides Irradiés, CNRS, CEA/DRF/IRAMIS, École Polytechnique, Institut Polytechnique de Paris, F-91120 Palaiseau, France. .,European Theoretical Spectroscopy Facility
| | - Pina Romaniello
- Laboratoire de Physique Théorique (UMR 5152), Université de Toulouse, CNRS, UPS, France.
| | - Adrienn Ruzsinszky
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA.
| | - Dennis R. Salahub
- Department of Chemistry, Department of Physics and Astronomy, CMS – Centre for Molecular Simulation, IQST – Institute for Quantum Science and Technology, Quantum Alberta, University of Calgary2500 University Drive NWCalgaryAlbertaT2N 1N4Canada
| | - Matthias Scheffler
- The NOMAD Laboratory at the FHI of the Max-Planck-Gesellschaft and IRIS-Adlershof of the Humboldt-Universität zu Berlin, Faradayweg 4-6, D-14195, Germany.
| | - Peter Schwerdtfeger
- Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland, 0632 Auckland, New Zealand.
| | - Viktor N. Staroverov
- Department of Chemistry, The University of Western OntarioLondonOntario N6A 5B7Canada
| | - Jianwei Sun
- Department of Physics and Engineering Physics, Tulane University, New Orleans, LA 70118, USA.
| | - Erik Tellgren
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.
| | - David J. Tozer
- Department of Chemistry, Durham UniversitySouth RoadDurhamDH1 3LEUK
| | - Samuel B. Trickey
- Quantum Theory Project, Deptartment of Physics, University of FloridaGainesvilleFL 32611USA
| | - Carsten A. Ullrich
- Department of Physics and Astronomy, University of MissouriColumbiaMO 65211USA
| | - Alberto Vela
- Departamento de Química, Centro de Investigación y de Estudios Avanzados (Cinvestav), CDMX, 07360, Mexico.
| | - Giovanni Vignale
- Department of Physics, University of Missouri, Columbia, MO 65203, USA.
| | - Tomasz A. Wesolowski
- Department of Physical Chemistry, Université de Genève30 Quai Ernest-Ansermet1211 GenèveSwitzerland
| | - Xin Xu
- Shanghai Key Laboratory of Molecular Catalysis and Innovation Materials, Collaborative Innovation Centre of Chemistry for Energy Materials, MOE Laboratory for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200433, China.
| | - Weitao Yang
- Department of Chemistry and Physics, Duke University, Durham, NC 27516, USA.
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6
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Daas T, Fabiano E, Della Sala F, Gori-Giorgi P, Vuckovic S. Noncovalent Interactions from Models for the Møller-Plesset Adiabatic Connection. J Phys Chem Lett 2021; 12:4867-4875. [PMID: 34003655 PMCID: PMC8280728 DOI: 10.1021/acs.jpclett.1c01157] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2021] [Accepted: 05/13/2021] [Indexed: 05/08/2023]
Abstract
Given the omnipresence of noncovalent interactions (NCIs), their accurate simulations are of crucial importance across various scientific disciplines. Here we construct accurate models for the description of NCIs by an interpolation along the Møller-Plesset adiabatic connection (MP AC). Our interpolation approximates the correlation energy, by recovering MP2 at small coupling strengths and the correct large-coupling strength expansion of the MP AC, recently shown to be a functional of the Hartree-Fock density. Our models are size consistent for fragments with nondegenerate ground states, have the same cost as double hybrids, and require no dispersion corrections to capture NCIs accurately. These interpolations greatly reduce large MP2 errors for typical π-stacking complexes (e.g., benzene-pyridine dimers) and for the L7 data set. They are also competitive with state-of-the-art dispersion enhanced functionals and can even significantly outperform them for a variety of data sets, such as CT7 and L7.
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Affiliation(s)
- Timothy
J. Daas
- Department
of Chemistry & Pharmaceutical Sciences and Amsterdam Institute
of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Eduardo Fabiano
- Institute
for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center
for Biomolecular Nanotechnologies, Istituto
Italiano di Tecnologia, Via Barsanti 14, 73010 Arnesano (LE), Italy
| | - Fabio Della Sala
- Institute
for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center
for Biomolecular Nanotechnologies, Istituto
Italiano di Tecnologia, Via Barsanti 14, 73010 Arnesano (LE), Italy
| | - Paola Gori-Giorgi
- Department
of Chemistry & Pharmaceutical Sciences and Amsterdam Institute
of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Stefan Vuckovic
- Department
of Chemistry & Pharmaceutical Sciences and Amsterdam Institute
of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
- Physical
and Theoretical Chemistry, University of
Saarland, 66123 Saarbrücken, Germany
- Department
of Chemistry, University of California, Irvine, California 92697, United States
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7
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Daas TJ, Grossi J, Vuckovic S, Musslimani ZH, Kooi DP, Seidl M, Giesbertz KJH, Gori-Giorgi P. Large coupling-strength expansion of the Møller–Plesset adiabatic connection: From paradigmatic cases to variational expressions for the leading terms. J Chem Phys 2020; 153:214112. [DOI: 10.1063/5.0029084] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- 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
| | - Juri Grossi
- 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
| | - Stefan Vuckovic
- Department of Chemistry, University of California, Irvine, California 92697, USA
| | - Ziad H. Musslimani
- 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
| | - Derk P. Kooi
- 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
| | - Michael Seidl
- 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
| | - Klaas J. H. Giesbertz
- 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
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8
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Kooi DP, Gori-Giorgi P. London dispersion forces without density distortion: a path to first principles inclusion in density functional theory. Faraday Discuss 2020; 224:145-165. [PMID: 32969448 DOI: 10.1039/d0fd00056f] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We analyse a path to construct density functionals for the dispersion interaction energy from an expression in terms of the ground state densities and exchange-correlation holes of the isolated fragments. The expression is based on a constrained search formalism for a supramolecular wavefunction that is forced to leave the diagonal of the many-body density matrix of each fragment unchanged, and is exact for the interaction between one-electron densities. We discuss several aspects: the necessary features of a density functional approximation for the exchange-correlation holes of the monomers, the optimal choice of the one-electron basis (named "dispersals"), and the functional derivative with respect to monomer density variations.
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Affiliation(s)
- Derk Pieter Kooi
- Department of Chemistry & Pharmaceutical Sciences, Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands.
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9
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Patra A, Jana S, Constantin LA, Samal P. Efficient yet accurate dispersion-corrected semilocal exchange–correlation functionals for non-covalent interactions. J Chem Phys 2020; 153:084117. [DOI: 10.1063/5.0011849] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
- Abhilash Patra
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Subrata Jana
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Lucian A. Constantin
- Istituto di Nanoscienze, Consiglio Nazionale delle Ricerche CNR-NANO, 41125 Modena, Italy
| | - Prasanjit Samal
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
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10
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Śmiga S, Constantin LA. Modified Interaction-Strength Interpolation Method as an Important Step toward Self-Consistent Calculations. J Chem Theory Comput 2020; 16:4983-4992. [PMID: 32559078 PMCID: PMC7588043 DOI: 10.1021/acs.jctc.0c00328] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
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The modified point charge plus continuum (mPC) model [ConstantinL. A.; 2019, 99, 085117] solves
the important failures of the original counterpart, namely, the divergences
when the reduced gradient of the density is large, such as in the
tail of the density and in quasi-dimensional density regimes. The
mPC allows us to define a modified interaction-strength interpolation
(mISI) method inheriting these good features, which are important
steps toward the full self-consistent treatment. Here, we provide
an assessment of mISI for molecular systems (i.e.,
considering thermochemistry properties, correlation energies, vertical
ionization potentials, and several noncovalent interactions), harmonium
atoms, and functional derivatives in the strong-interaction limit.
For all our tests, mISI provides a systematic improvement over the
original ISI method. Semilocal approximations of the second-order
Görling–Levy (GL2) perturbation theory are also considered
in the mISI method, showing considerable worsening of the results.
Possible further development of mISI is briefly discussed.
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Affiliation(s)
- Szymon Śmiga
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, 87-100 Toruń, Poland
| | - Lucian A Constantin
- Consiglio Nazionale delle Ricerche CNR-NANO, Istituto di Nanoscienze, 41125 Modena, Italy
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11
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Vuckovic S, Fabiano E, Gori-Giorgi P, Burke K. MAP: An MP2 Accuracy Predictor for Weak Interactions from Adiabatic Connection Theory. J Chem Theory Comput 2020; 16:4141-4149. [PMID: 32379454 DOI: 10.1021/acs.jctc.0c00049] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Second-order Møller-Plesset perturbation theory (MP2) approximates the exact Hartree-Fock (HF) adiabatic connection (AC) curve by a straight line. Thus, by using the deviation of the exact curve from the linear behavior, we construct an indicator for the accuracy of MP2. We then use an interpolation along the HF AC to transform the exact form of our indicator into a highly practical MP2 accuracy predictor (MAP) that comes at a negligible additional computational cost. We show that this indicator is already applicable to systems that dissociate into fragments with a nondegenerate ground state, and we illustrate its usefulness by applying it to the S22 and S66 datasets.
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Affiliation(s)
- Stefan Vuckovic
- Department of Chemistry, University of California, Irvine, California 92697, United States
| | - Eduardo Fabiano
- Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, Lecce 73100, Italy
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, Amsterdam 1081HV, The Netherlands
| | - Kieron Burke
- Department of Chemistry, University of California, Irvine, California 92697, United States
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12
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Giarrusso S, Gori-Giorgi P. Exchange-Correlation Energy Densities and Response Potentials: Connection between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond. J Phys Chem A 2020; 124:2473-2482. [PMID: 32118422 PMCID: PMC7104238 DOI: 10.1021/acs.jpca.9b10538] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
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We
analyze in depth two widely used definitions (from the theory
of conditional probability amplitudes and from the adiabatic connection
formalism) of the exchange-correlation energy density and of the response
potential of Kohn–Sham density functional theory. We introduce
a local form of the coupling-constant-dependent Hohenberg–Kohn functional, showing that
the difference between the two definitions is due to a corresponding
local first-order term in the coupling constant, which disappears
globally (when integrated over all space), but not locally. We also
design an analytic representation for the response potential in the
strong-coupling limit of density functional theory for a model single
stretched bond.
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Affiliation(s)
- Sara Giarrusso
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, Amsterdam, 1081HV, The Netherlands
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, Amsterdam, 1081HV, The Netherlands
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13
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Gerolin A, Grossi J, Gori-Giorgi P. Kinetic Correlation Functionals from the Entropic Regularization of the Strictly Correlated Electrons Problem. J Chem Theory Comput 2020; 16:488-498. [PMID: 31855421 PMCID: PMC6964418 DOI: 10.1021/acs.jctc.9b01133] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2019] [Indexed: 11/29/2022]
Abstract
In this work, we study the entropic regularization of the strictly correlated electrons formalism, discussing the implications for density functional theory and establishing a link with earlier works on quantum kinetic energy and classical entropy. We carry out a very preliminary investigation (using simplified models) on the use of the solution of the entropic regularized problem to build approximations for the kinetic correlation functional at large coupling strengths. We also analyze lower and upper bounds to the Hohenberg-Kohn functional using the entropic regularized strictly correlated electrons problem.
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Affiliation(s)
- Augusto Gerolin
- Department of Theoretical
Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Juri Grossi
- Department of Theoretical
Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Paola Gori-Giorgi
- Department of Theoretical
Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
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14
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Singh R, Patra B, Patra A, Harbola MK, Samal P. Adiabatic connection in density functional theory in two-dimensions: A semi-analytic wavefunction based study for two-electron atomic systems. J Chem Phys 2019; 151:204104. [PMID: 31779332 DOI: 10.1063/1.5120853] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This work focuses on studying the adiabatic-connection in density functional theory in two dimensions. It employs a recently developed accurate form of wavefunction for two-electron systems. The explicit semianalytic form of the wavefunction makes it possible to calculate ground state wavefunctions, energies, densities, and the resulting properties for the scaled Coulomb interaction between the electrons at fixed density accurately. The results so obtained for the correlation energies are then used as the reference values for studying the performance of two-dimensional correlation energy functionals.
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Affiliation(s)
- Rabeet Singh
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Bikash Patra
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Abhilash Patra
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Manoj K Harbola
- Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016, India
| | - Prasanjit Samal
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
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15
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Gould T, Vuckovic S. Range-separation and the multiple radii functional approximation inspired by the strongly interacting limit of density functional theory. J Chem Phys 2019; 151:184101. [DOI: 10.1063/1.5125692] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Tim Gould
- Qld Micro- and Nanotechnology Centre, Griffith University, Nathan, Qld 4111, Australia
| | - Stefan Vuckovic
- Department of Chemistry, University of California, Irvine, California 92697, USA
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16
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Vuckovic S, Song S, Kozlowski J, Sim E, Burke K. Density Functional Analysis: The Theory of Density-Corrected DFT. J Chem Theory Comput 2019; 15:6636-6646. [DOI: 10.1021/acs.jctc.9b00826] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Stefan Vuckovic
- Departments of Chemistry and of Physics, University of California, Irvine, California 92697, United States
| | - Suhwan Song
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - John Kozlowski
- Departments of Chemistry and of Physics, University of California, Irvine, California 92697, United States
| | - Eunji Sim
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - Kieron Burke
- Departments of Chemistry and of Physics, University of California, Irvine, California 92697, United States
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17
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Baerends EJ. On derivatives of the energy with respect to total electron number and orbital occupation numbers. A critique of Janak's theorem. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1612955] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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18
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Vuckovic S. Density Functionals from the Multiple-Radii Approach: Analysis and Recovery of the Kinetic Correlation Energy. J Chem Theory Comput 2019; 15:3580-3590. [DOI: 10.1021/acs.jctc.9b00129] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Stefan Vuckovic
- Department of Chemistry, University of California, Irvine, California 92697, United States
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19
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Seidl M, Giarrusso S, Vuckovic S, Fabiano E, Gori-Giorgi P. Communication: Strong-interaction limit of an adiabatic connection in Hartree-Fock theory. J Chem Phys 2018; 149:241101. [DOI: 10.1063/1.5078565] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Michael Seidl
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Sara Giarrusso
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Stefan Vuckovic
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
- Department of Chemistry, University of California, Irvine, California 92697, USA
| | - Eduardo Fabiano
- Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
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20
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Kooi DP, Gori-Giorgi P. Local and global interpolations along the adiabatic connection of DFT: a study at different correlation regimes. Theor Chem Acc 2018; 137:166. [PMID: 30464722 PMCID: PMC6223841 DOI: 10.1007/s00214-018-2354-5] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2018] [Accepted: 09/21/2018] [Indexed: 11/16/2022]
Abstract
Interpolating the exchange-correlation energy along the density-fixed adiabatic connection of density functional theory is a promising way to build approximations that are not biased toward the weakly correlated regime. These interpolations can be performed at the global (integrated over all spaces) or at the local level, using energy densities. Many features of the relevant energy densities as well as several different ways to construct these interpolations, including comparisons between global and local variants, are investigated here for the analytically solvable Hooke's atom series, which allows for an exploration of different correlation regimes. We also analyze different ways to define the correlation kinetic energy density, focusing on the peak in the kinetic correlation potential.
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Affiliation(s)
- Derk P. Kooi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
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21
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Giarrusso S, Vuckovic S, Gori-Giorgi P. Response Potential in the Strong-Interaction Limit of Density Functional Theory: Analysis and Comparison with the Coupling-Constant Average. J Chem Theory Comput 2018; 14:4151-4167. [PMID: 29906106 PMCID: PMC6096453 DOI: 10.1021/acs.jctc.8b00386] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Using the formalism of the conditional amplitude, we study the response part of the exchange-correlation potential in the strong-coupling limit of density functional theory, analyzing its peculiar features and comparing it with the response potential averaged over the coupling constant for small atoms and for the hydrogen molecule. We also use a simple one-dimensional model of a stretched heteronuclear molecule to derive exact properties of the response potential in the strong-coupling limit. The simplicity of the model allows us to unveil relevant features also of the exact Kohn-Sham potential and its different components, namely the appearance of a second peak in the correlation kinetic potential on the side of the most electronegative atom.
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Affiliation(s)
- Sara Giarrusso
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW , Vrije Universiteit , De Boelelaan 1083 , 1081HV Amsterdam , The Netherlands
| | - Stefan Vuckovic
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW , Vrije Universiteit , De Boelelaan 1083 , 1081HV Amsterdam , The Netherlands
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW , Vrije Universiteit , De Boelelaan 1083 , 1081HV Amsterdam , The Netherlands
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22
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Vuckovic S, Gori-Giorgi P, Della Sala F, Fabiano E. Restoring Size Consistency of Approximate Functionals Constructed from the Adiabatic Connection. J Phys Chem Lett 2018; 9:3137-3142. [PMID: 29787273 PMCID: PMC5994725 DOI: 10.1021/acs.jpclett.8b01054] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2018] [Accepted: 05/22/2018] [Indexed: 05/24/2023]
Abstract
Approximate exchange-correlation functionals built by modeling in a nonlinear way the adiabatic connection (AC) integrand of density functional theory have many attractive features, being virtually parameter-free and satisfying different exact properties, but they also have a fundamental flaw: they violate the size-consistency condition, crucial to evaluate interaction energies of molecular systems. We show that size consistency in the AC-based functionals can be restored in a very simple way at no extra computational cost. Results on a large set of benchmark molecular interaction energies show that functionals based on the interaction strength interpolation approximations are significantly more accurate than second-order perturbation theory.
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Affiliation(s)
- Stefan Vuckovic
- Department
of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling,
FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Paola Gori-Giorgi
- Department
of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling,
FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Fabio Della Sala
- Institute
for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center
for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
| | - Eduardo Fabiano
- Institute
for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center
for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
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23
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Giarrusso S, Gori-Giorgi P, Della Sala F, Fabiano E. Assessment of interaction-strength interpolation formulas for gold and silver clusters. J Chem Phys 2018; 148:134106. [DOI: 10.1063/1.5022669] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Affiliation(s)
- Sara Giarrusso
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Fabio Della Sala
- Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
| | - Eduardo Fabiano
- Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
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24
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Vuckovic S, Levy M, Gori-Giorgi P. Augmented potential, energy densities, and virial relations in the weak- and strong-interaction limits of DFT. J Chem Phys 2017; 147:214107. [DOI: 10.1063/1.4997311] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Affiliation(s)
- Stefan Vuckovic
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Mel Levy
- Department of Chemistry and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118, USA
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
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25
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Grossi J, Kooi DP, Giesbertz KJH, Seidl M, Cohen AJ, Mori-Sánchez P, Gori-Giorgi P. Fermionic Statistics in the Strongly Correlated Limit of Density Functional Theory. J Chem Theory Comput 2017; 13:6089-6100. [PMID: 29111724 PMCID: PMC5729548 DOI: 10.1021/acs.jctc.7b00998] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Exact pieces of information on the adiabatic connection integrand, Wλ[ρ], which allows evaluation of the exchange-correlation energy of Kohn-Sham density functional theory, can be extracted from the leading terms in the strong coupling limit (λ → ∞, where λ is the strength of the electron-electron interaction). In this work, we first compare the theoretical prediction for the two leading terms in the strong coupling limit with data obtained via numerical implementation of the exact Levy functional in the simple case of two electrons confined in one dimension, confirming the asymptotic exactness of these two terms. We then carry out a first study on the incorporation of the Fermionic statistics at large coupling λ, both numerical and theoretical, confirming that spin effects enter at orders ∼e-√λ.
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Affiliation(s)
- Juri Grossi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit , De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Derk P Kooi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit , De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Klaas J H Giesbertz
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit , De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Michael Seidl
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit , De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Aron J Cohen
- Max-Planck Institute for Solid State Research , Heisenbergstrasse 1, 70569 Stuttgart, Germany
| | - Paula Mori-Sánchez
- Departamento de Quimíca and Instituto de Física de la Materia Condensada (IFIMAC), Universidad Autónoma de Madrid , 28049 Madrid, Spain
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit , De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
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26
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Vuckovic S, Gori-Giorgi P. Simple Fully Nonlocal Density Functionals for Electronic Repulsion Energy. J Phys Chem Lett 2017; 8:2799-2805. [PMID: 28581751 PMCID: PMC5502414 DOI: 10.1021/acs.jpclett.7b01113] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2017] [Accepted: 06/05/2017] [Indexed: 05/24/2023]
Abstract
From a simplified version of the mathematical structure of the strong coupling limit of the exact exchange-correlation functional, we construct an approximation for the electronic repulsion energy at physical coupling strength, which is fully nonlocal. This functional is self-interaction free and yields energy densities within the definition of the electrostatic potential of the exchange-correlation hole that are locally accurate and have the correct asymptotic behavior. The model is able to capture strong correlation effects that arise from chemical bond dissociation, without relying on error cancellation. These features, which are usually missed by standard density functional theory (DFT) functionals, are captured by the highly nonlocal structure, which goes beyond the "Jacob's ladder" framework for functional construction, by using integrals of the density as the key ingredient. Possible routes for obtaining the full exchange-correlation functional by recovering the missing kinetic component of the correlation energy are also implemented and discussed.
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27
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Vuckovic S, Irons TJP, Wagner LO, Teale AM, Gori-Giorgi P. Interpolated energy densities, correlation indicators and lower bounds from approximations to the strong coupling limit of DFT. Phys Chem Chem Phys 2017; 19:6169-6183. [DOI: 10.1039/c6cp08704c] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
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28
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Bahmann H, Zhou Y, Ernzerhof M. The shell model for the exchange-correlation hole in the strong-correlation limit. J Chem Phys 2016; 145:124104. [DOI: 10.1063/1.4962738] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Affiliation(s)
- Hilke Bahmann
- Department of Chemistry, Technische Universität Berlin, Strasse des 17 Juni 135, 10623 Berlin, Germany
| | - Yongxi Zhou
- Département de Chimie, Université de Montréal, C.P. 6128 Succursale A, Montréal, Québec H3C 3J7, Canada
| | - Matthias Ernzerhof
- Département de Chimie, Université de Montréal, C.P. 6128 Succursale A, Montréal, Québec H3C 3J7, Canada
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29
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Fabiano E, Gori-Giorgi P, Seidl M, Della Sala F. Interaction-Strength Interpolation Method for Main-Group Chemistry: Benchmarking, Limitations, and Perspectives. J Chem Theory Comput 2016; 12:4885-4896. [DOI: 10.1021/acs.jctc.6b00713] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Eduardo Fabiano
- Euromediterranean
Center for Nanomaterial Modelling and Technology (ECMT), Istituto Nanoscienze-CNR, Via per Arnesano 16, 73100 Lecce, Italy
- Center
for Biomolecular Nanotechnologies@UNILE, Istituto Italiano di Tecnologia (IIT), Via Barsanti, 73010 Arnesano, Italy
| | - Paola Gori-Giorgi
- Department
of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling,
FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Michael Seidl
- Department
of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling,
FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Fabio Della Sala
- Euromediterranean
Center for Nanomaterial Modelling and Technology (ECMT), Istituto Nanoscienze-CNR, Via per Arnesano 16, 73100 Lecce, Italy
- Center
for Biomolecular Nanotechnologies@UNILE, Istituto Italiano di Tecnologia (IIT), Via Barsanti, 73010 Arnesano, Italy
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