1
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Žibert T, Likozar B, Huš M. Modelling Photocatalytic N 2 Reduction to Ammonia: Where We Stand and Where We Are Going. CHEMSUSCHEM 2024; 17:e202301730. [PMID: 38523408 DOI: 10.1002/cssc.202301730] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2023] [Revised: 03/18/2024] [Accepted: 03/19/2024] [Indexed: 03/26/2024]
Abstract
Artificial ammonia synthesis via the Haber-Bosch process is environmentally problematic due to the high energy consumption and corresponding CO2 ${_2 }$ emissions, produced during the reaction and before hand in hydrogen production upon methane steam reforming. Photocatalytic nitrogen fixation as a greener alternative to the conventional Haber-Bosch process enables us to perform nitrogen reduction reaction (NRR) under mild conditions, harnessing light as the energy source. Herein, we systematically review first-principles calculations used to determine the electronic/optical properties of photocatalysts, N2 adsorption and to expound possible NRR mechanisms. The most commonly studied photocatalysts for nitrogen fixation are usually modified with dopants, defects, co-catalysts and Z-scheme heterojunctions to prevent charge carrier recombination, improve charge separation efficiency and adjust a band gap to for utilizing a broader light spectrum. Most studies at the atomistic level of modeling are grounded upon density functional theory (DFT) calculations, wholly foregoing excitation effects paramount in photocatalysis. Hence, there is a dire need to consider methods beyond DFT to study the excited state properties more accurately. Furthermore, a few studies have been examined, which include higher level kinetics and macroscale simulations. Ultimately, we show there is still ample room for improvement with regard to first principles calculations and their integration in multiscale models.
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Affiliation(s)
- Taja Žibert
- National Institute of Chemistry, Department of Catalysis and Chemical Reaction Engineering, Hajdrihova 19, SI-1001, Ljubljana, Slovenia
- University of Nova Gorica, Vipavska 13, 5000, Nova Gorica, Slovenia
| | - Blaž Likozar
- National Institute of Chemistry, Department of Catalysis and Chemical Reaction Engineering, Hajdrihova 19, SI-1001, Ljubljana, Slovenia
| | - Matej Huš
- National Institute of Chemistry, Department of Catalysis and Chemical Reaction Engineering, Hajdrihova 19, SI-1001, Ljubljana, Slovenia
- University of Nova Gorica, Vipavska 13, 5000, Nova Gorica, Slovenia
- Institute for the Protection of Cultural Heritage, Poljanska 40, SI-1000, Ljubljana, Slovenia
- Association for Technical Culture (ZOTKS), Zaloška 65, SI, 1001, Ljubljana, Slovenia
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2
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Kaupp M, Wodyński A, Arbuznikov AV, Fürst S, Schattenberg CJ. Toward the Next Generation of Density Functionals: Escaping the Zero-Sum Game by Using the Exact-Exchange Energy Density. Acc Chem Res 2024; 57:1815-1826. [PMID: 38905497 PMCID: PMC11223257 DOI: 10.1021/acs.accounts.4c00209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2024] [Revised: 05/29/2024] [Accepted: 06/03/2024] [Indexed: 06/23/2024]
Abstract
ConspectusKohn-Sham density functional theory (KS DFT) is arguably the most widely applied electronic-structure method with tens of thousands of publications each year in a wide variety of fields. Its importance and usefulness can thus hardly be overstated. The central quantity that determines the accuracy of KS DFT calculations is the exchange-correlation functional. Its exact form is unknown, or better "unknowable", and therefore the derivation of ever more accurate yet efficiently applicable approximate functionals is the "holy grail" in the field. In this context, the simultaneous minimization of so-called delocalization errors and static correlation errors is the greatest challenge that needs to be overcome as we move toward more accurate yet computationally efficient methods. In many cases, an improvement on one of these two aspects (also often termed fractional-charge and fractional-spin errors, respectively) generates a deterioration in the other one. Here we report on recent notable progress in escaping this so-called "zero-sum-game" by constructing new functionals based on the exact-exchange energy density. In particular, local hybrid and range-separated local hybrid functionals are discussed that incorporate additional terms that deal with static correlation as well as with delocalization errors. Taking hints from other coordinate-space models of nondynamical and strong electron correlations (the B13 and KP16/B13 models), position-dependent functions that cover these aspects in real space have been devised and incorporated into the local-mixing functions determining the position-dependence of exact-exchange admixture of local hybrids as well as into the treatment of range separation in range-separated local hybrids. While initial functionals followed closely the B13 and KP16/B13 frameworks, meanwhile simpler real-space functions based on ratios of semilocal and exact-exchange energy densities have been found, providing a basis for relatively simple and numerically convenient functionals. Notably, the correction terms can either increase or decrease exact-exchange admixture locally in real space (and in interelectronic-distance space), leading even to regions with negative admixture in cases of particularly strong static correlations. Efficient implementations into a fast computer code (Turbomole) using seminumerical integration techniques make such local hybrid and range-separated local hybrid functionals promising new tools for complicated composite systems in many research areas, where simultaneously small delocalization errors and static correlation errors are crucial. First real-world application examples of the new functionals are provided, including stretched bonds, symmetry-breaking and hyperfine coupling in open-shell transition-metal complexes, as well as a reduction of static correlation errors in the computation of nuclear shieldings and magnetizabilities. The newest versions of range-separated local hybrids (e.g., ωLH23tdE) retain the excellent frontier-orbital energies and correct asymptotic exchange-correlation potential of the underlying ωLH22t functional while improving substantially on strong-correlation cases. The form of these functionals can be further linked to the performance of the recent impactful deep-neural-network "black-box" functional DM21, which itself may be viewed as a range-separated local hybrid.
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Affiliation(s)
- Martin Kaupp
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Artur Wodyński
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Alexei V. Arbuznikov
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Susanne Fürst
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Caspar J. Schattenberg
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
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3
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Schattenberg C, Kaupp M. Implementation and First Evaluation of Strong-Correlation-Corrected Local Hybrid Functionals for the Calculation of NMR Shieldings and Shifts. J Phys Chem A 2024; 128:2253-2271. [PMID: 38456430 PMCID: PMC10961831 DOI: 10.1021/acs.jpca.3c08507] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2023] [Revised: 02/01/2024] [Accepted: 02/09/2024] [Indexed: 03/09/2024]
Abstract
Local hybrid functionals containing strong-correlation factors (scLHs) and range-separated local hybrids (RSLHs) have been integrated into an efficient coupled-perturbed Kohn-Sham implementation for the calculation of nuclear shielding constants. Several scLHs and the ωLH22t RSLH have then been evaluated for the first time for the extended NS372 benchmark set of main-group shieldings and shifts and the TM70 benchmark of 3d transition-metal shifts. The effects of the strong-correlation corrections have been analyzed with respect to the spatial distribution of the sc-factors, which locally diminish exact-exchange admixture at certain regions in a molecule. The scLH22t, scLH23t-mBR, and scLH23t-mBR-P functionals, which contain a "damped" strong-correlation factor to retain the excellent performance of the underlying LH20t functional for weakly correlated situations, tend to make smaller corrections to shieldings and shifts than the "undamped" scLH22ta functional. While the latter functional can also deteriorate agreement with the reference data in certain weakly correlated cases, it provides overall better performance, in particular for systems where static correlation is appreciable. This pertains only to a minority of systems in the NS372 main-group test set but to many more systems in the TM70 transition-metal test set, in particular for high-oxidation-state complexes, e.g., Cr(+VI) complexes and other systems with stretched bonds. Another undamped scLH, the simpler LDA-based scLH21ct-SVWN-m, also tends to provide significant improvements in many cases. The differences between the functionals and species can be rationalized on the basis of one-dimensional plots of the strong-correlation factors, augmented by isosurface plots of the fractional orbital density (FOD). Position-dependent exact-exchange admixture is thus shown to provide substantial flexibility in treating response properties like NMR shifts for both weakly and strongly correlated systems.
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Affiliation(s)
- Caspar
Jonas Schattenberg
- Research
Unit of Structural Chemistry & Computational Biophysics, Leibniz-Forschungsinstitut für Molekulare Pharmakologie
(FMP), Robert-Roessle-Str.
10, 13125 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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4
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Wodyński A, Lauw B, Reimann M, Kaupp M. Spin-Symmetry Breaking and Hyperfine Couplings in Transition-Metal Complexes Revisited Using Density Functionals Based on the Exact-Exchange Energy Density. J Chem Theory Comput 2024; 20:2033-2048. [PMID: 38411554 PMCID: PMC10938646 DOI: 10.1021/acs.jctc.3c01422] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2023] [Revised: 02/02/2024] [Accepted: 02/07/2024] [Indexed: 02/28/2024]
Abstract
A small set of mononuclear manganese complexes evaluated previously for their Mn hyperfine couplings (HFCs) has been analyzed using density functionals based on the exact-exchange energy density─in particular, the spin symmetry breaking (SSB) found previously when using hybrid functionals. Employing various strong-correlation corrected local hybrids (scLHs) and strong-correlation corrected range-separated local hybrids (scRSLHs) with or without additional corrections to their local mixing functions (LMFs) to mitigate delocalization errors (DE), the SSB and the associated dipolar HFCs of [Mn(CN)4]2-, MnO3, [Mn(CN)4N]-, and [Mn(CN)5NO]2- (the latter with cluster embedding) have been examined. Both strong-correlation (sc)-correction and DE-correction terms help to diminish SSB and correct the dipolar HFCs. The DE corrections are more effective, and the effects of the sc corrections depend on their damping factors. Interestingly, the DE-corrections reduce valence-shell spin polarization (VSSP) and thus SSB by locally enhancing exact-exchange (EXX) admixture near the metal center and thereby diminishing spin-density delocalization onto the ligand atoms. In contrast, sc corrections diminish EXX admixture locally, mostly on specific ligand atoms. This then reduces VSSP and SSB as well. The performance of scLHs and scRSLHs for the isotropic Mn HFCs has also been analyzed, with particular attention to core-shell spin-polarization contributions. Further sc-corrected functionals, such as the KP16/B13 construction and the DM21 deep-neural-network functional, have been examined.
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Affiliation(s)
- Artur Wodyński
- Technische Universität
Berlin, Institut für Chemie, Theoretische
Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, Berlin, D-10623, Germany
| | - Bryan Lauw
- Technische Universität
Berlin, Institut für Chemie, Theoretische
Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, Berlin, D-10623, Germany
| | - Marc Reimann
- Technische Universität
Berlin, Institut für Chemie, Theoretische
Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, Berlin, D-10623, Germany
| | - Martin Kaupp
- Technische Universität
Berlin, Institut für Chemie, Theoretische
Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, Berlin, D-10623, Germany
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5
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Fürst S, Kaupp M, Wodyński A. Range-Separated Local Hybrid Functionals with Small Fractional-Charge and Fractional-Spin Errors: Escaping the Zero-Sum Game of DFT Functionals. J Chem Theory Comput 2023. [PMID: 37972297 DOI: 10.1021/acs.jctc.3c00877] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2023]
Abstract
Extending recent developments on strong-correlation (sc) corrections to local hybrid functionals to the recent accurate ωLH22t range-separated local hybrid, a series of highly flexible strong-correlation-corrected range-separated local hybrids (scRSLHs) has been constructed and evaluated. This has required the position-dependent reduction of both short- and long-range exact-exchange admixtures in regions of space characterized by strong static correlations. Using damping procedures provides scRSLHs that retain largely the excellent performance of ωLH22t for weakly correlated situations and, in particular, for accurate quasiparticle energies of a wide variety of systems while reducing dramatically static-correlation errors, e.g., in stretched-bond situations. An additional correction to the local mixing function to reduce delocalization errors in abnormal open-shell situations provides further improvements in thermochemical and kinetic parameters, making scRSLH functionals such as ωLH23tdE or ωLH23tdP promising tools for complex molecular or condensed-phase systems, where low fractional-charge and fractional-spin errors are simultaneously important. The proposed rung 4 functionals thereby largely escape the usual zero-sum game between these two quantities and are expected to open new areas of accurate computations by Kohn-Sham DFT. At the same time, they require essentially no extra computational effort over the underlying ωLH22t functional, which means that their use is only moderately more demanding than that of global, local, or range-separated hybrid functionals.
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Affiliation(s)
- Susanne Fürst
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Martin Kaupp
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Artur Wodyński
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 135, D-10623 Berlin, Germany
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6
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Franzke Y, Holzer C, Andersen JH, Begušić T, Bruder F, Coriani S, Della Sala F, Fabiano E, Fedotov DA, Fürst S, Gillhuber S, Grotjahn R, Kaupp M, Kehry M, Krstić M, Mack F, Majumdar S, Nguyen BD, Parker SM, Pauly F, Pausch A, Perlt E, Phun GS, Rajabi A, Rappoport D, Samal B, Schrader T, Sharma M, Tapavicza E, Treß RS, Voora V, Wodyński A, Yu JM, Zerulla B, Furche F, Hättig C, Sierka M, Tew DP, Weigend F. TURBOMOLE: Today and Tomorrow. J Chem Theory Comput 2023; 19:6859-6890. [PMID: 37382508 PMCID: PMC10601488 DOI: 10.1021/acs.jctc.3c00347] [Citation(s) in RCA: 37] [Impact Index Per Article: 37.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Indexed: 06/30/2023]
Abstract
TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.
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Affiliation(s)
- Yannick
J. Franzke
- Fachbereich
Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
| | - Christof Holzer
- Institute
of Theoretical Solid State Physics, Karlsruhe
Institute of Technology (KIT), Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany
| | - Josefine H. Andersen
- DTU
Chemistry, Department of Chemistry, Technical
University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
| | - Tomislav Begušić
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Florian Bruder
- Fachbereich
Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
| | - Sonia Coriani
- DTU
Chemistry, Department of Chemistry, Technical
University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
| | - 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, 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, 73010 Arnesano, Italy
| | - Daniil A. Fedotov
- DTU
Chemistry, Department of Chemistry, Technical
University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
- Institute
of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Susanne Fürst
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17 Juni 135, 10623, Berlin, Germany
| | - Sebastian Gillhuber
- Institute
of Inorganic Chemistry, Karlsruhe Institute
of Technology (KIT), Engesserstr. 15, 76131 Karlsruhe, Germany
| | - Robin Grotjahn
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Martin Kaupp
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17 Juni 135, 10623, Berlin, Germany
| | - Max Kehry
- Institute
of Physical Chemistry, Karlsruhe Institute
of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Marjan Krstić
- Institute
of Theoretical Solid State Physics, Karlsruhe
Institute of Technology (KIT), Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany
| | - Fabian Mack
- Institute
of Physical Chemistry, Karlsruhe Institute
of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Sourav Majumdar
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Brian D. Nguyen
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Shane M. Parker
- Department
of Chemistry, Case Western Reserve University, 10900 Euclid Ave, Cleveland, Ohio 44106 United States
| | - Fabian Pauly
- Institute
of Physics, University of Augsburg, Universitätsstr. 1, 86159 Augsburg, Germany
| | - Ansgar Pausch
- Institute
of Physical Chemistry, Karlsruhe Institute
of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Eva Perlt
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - Gabriel S. Phun
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Ahmadreza Rajabi
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Dmitrij Rappoport
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Bibek Samal
- Department
of Chemical Sciences, Tata Institute of
Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Tim Schrader
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - Manas Sharma
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - Enrico Tapavicza
- Department
of Chemistry and Biochemistry, California
State University, Long Beach, 1250 Bellflower Boulevard, Long
Beach, California 90840-9507, United States
| | - Robert S. Treß
- Lehrstuhl
für Theoretische Chemie, Ruhr-Universität
Bochum, 44801 Bochum, Germany
| | - Vamsee Voora
- Department
of Chemical Sciences, Tata Institute of
Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Artur Wodyński
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17 Juni 135, 10623, Berlin, Germany
| | - Jason M. Yu
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Benedikt Zerulla
- Institute
of Nanotechnology, Karlsruhe Institute of
Technology (KIT), Hermann-von-Helmholtz-Platz
1, 76344 Eggenstein-Leopoldshafen Germany
| | - Filipp Furche
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Christof Hättig
- Lehrstuhl
für Theoretische Chemie, Ruhr-Universität
Bochum, 44801 Bochum, Germany
| | - Marek Sierka
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - David P. Tew
- Physical
and Theoretical Chemistry Laboratory, University
of Oxford, South Parks
Road, Oxford OX1 3QZ, United Kingdom
| | - Florian Weigend
- Fachbereich
Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
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7
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Janesko BG. Projected Hybrid Density Functionals: Method and Application to Core Electron Ionization. J Chem Theory Comput 2023; 19:837-847. [PMID: 36656811 DOI: 10.1021/acs.jctc.2c01023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
This work introduces a new class of hybrid density functional theory (DFT) approximations, which incorporate different fractions of nonlocal exact exchange in predefined states such as core atomic orbitals (AOs). These projected hybrid density functionals are related to range-separated hybrid functionals, which incorporate different fractions of nonlocal exchange at different electron-electron separations. This work derives projected hybrids using the Adiabatic Projection formalism. One projects the electron-electron interaction operator onto the chosen predefined states, introduces the projected operator into the noninteracting Kohn-Sham reference system, and employs a formally exact density functional to model the remaining electron-electron interactions. Projected hybrids, like range-separated hybrids, approximate the partially interacting reference system's ground-state wave function as a single Slater determinant. Projected hybrids are readily implemented into existing density functional codes, requiring only a projection of the one-particle density matrices and exchange operators entering existing routines. This work also presents an application to core electron ionization. Projecting onto core atomic orbitals allows us to introduce additional nonlocal exchange into atomic core regions. This reduces the impact of self-interaction error on computed core electron properties. Benchmark studies are reported for PBE0c70, a core-projected variant of the Perdew-Burke-Ernzerhof global hybrid PBE0, in which the fraction of nonlocal exchange is increased from 25% to 70% in atomic core regions. PBE0c70-predicted core orbital energies accurately recover nonrelativistic core-electron binding energies of second-period elements Li-Ne and third-period elements Na-Ar, without degrading the good performance of PBE0 for atomization energies and valence ionization potentials.
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Affiliation(s)
- Benjamin G Janesko
- Department of Chemistry & Biochemistry, Texas Christian University, Fort Worth, Texas76129, United States
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8
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Application of two-component neural network for exchange-correlation functional interpolation. Sci Rep 2022; 12:14133. [PMID: 35986067 PMCID: PMC9391383 DOI: 10.1038/s41598-022-18083-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2022] [Accepted: 08/04/2022] [Indexed: 11/09/2022] Open
Abstract
Density functional theory (DFT) is one of the primary approaches to solving the many-body Schrodinger equation. The essential part of the DFT theory is the exchange-correlation (XC) functional, which can not be obtained in analytical form. Accordingly, the accuracy improvement of the DFT is mainly based on the development of XC functional approximations. Commonly, they are built upon analytic solutions in low- and high-density limits and result from quantum Monte Carlo or post-Hartree-Fock numerical calculations. However, there is no universal functional form to incorporate these data into XC functional. Instead, various parameterizations use heuristic rules to build a specific XC functional. The neural network (NN) approach to interpolate the data from higher precision theories can give a unified path to parametrize an XC functional. Moreover, data from many existing quantum chemical databases could provide the XC functional with improved accuracy. We develop NN XC functional, which gives exchange potential and energy density without direct derivatives of exchange-correlation energy density. Proposed NN architecture consists of two parts NN-E and NN-V, which could be trained in separate ways, adding new flexibility to XC functional. We also show that the developed NN XC functional converges in the self-consistent cycle and gives reasonable energies when applied to atoms, molecules, and crystals.
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9
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Baerends EJ. Chemical potential, derivative discontinuity, fractional electrons, jump of the Kohn-Sham potential, atoms as thermodynamic open systems, and other (mis)conceptions of the density functional theory of electrons in molecules. Phys Chem Chem Phys 2022; 24:12745-12766. [PMID: 35593143 DOI: 10.1039/d2cp01585d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Many references exist in the density functional theory (DFT) literature to the chemical potential of the electrons in an atom or a molecule. The origin of this notion has been the identification of the Lagrange multiplier μ = ∂E/∂N in the Euler-Lagrange variational equation for the ground state density as the chemical potential of the electrons. We first discuss why the Lagrange multiplier in this case is an arbitrary constant and therefore cannot be a physical characteristic of an atom or molecule. The switching of the energy derivative ("chemical potential") from -I to -A when the electron number crosses the integer, called integer discontinuity or derivative discontinuity, is not physical but only occurs when the nonphysical noninteger electron systems and the corresponding energy and derivative ∂E/∂N are chosen in a specific discontinuous way. The question is discussed whether in fact the thermodynamical concept of a chemical potential can be defined for the electrons in such few-electron systems as atoms and molecules. The conclusion is that such systems lack important characteristics of thermodynamic systems and do not afford the definition of a chemical potential. They also cannot be considered as analogues of the open systems of thermodynamics that can exchange particles with an environment (a particle bath or other members of a Gibbsian ensemble). Thermodynamical (statistical mechanical) concepts like chemical potential, open systems, grand canonical ensemble etc. are not applicable to a few electron system like an atom or molecule. A number of topics in DFT are critically reviewed in light of these findings: jumps in the Kohn-Sham potential when crossing an integer number of electrons, the band gap problem, the deviation-from-straight-lines error, and the role of ensembles in DFT.
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10
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Bajaj A, Duan C, Nandy A, Taylor MG, Kulik HJ. Molecular orbital projectors in non-empirical jmDFT recover exact conditions in transition-metal chemistry. J Chem Phys 2022; 156:184112. [DOI: 10.1063/5.0089460] [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
Low-cost, non-empirical corrections to semi-local density functional theory are essential for accurately modeling transition-metal chemistry. Here, we demonstrate the judiciously modified density functional theory (jmDFT) approach with non-empirical U and J parameters obtained directly from frontier orbital energetics on a series of transition-metal complexes. We curate a set of nine representative Ti(III) and V(IV) d1 transition-metal complexes and evaluate their flat-plane errors along the fractional spin and charge lines. We demonstrate that while jmDFT improves upon both DFT+U and semi-local DFT with the standard atomic orbital projectors (AOPs), it does so inefficiently. We rationalize these inefficiencies by quantifying hybridization in the relevant frontier orbitals. To overcome these limitations, we introduce a procedure for computing a molecular orbital projector (MOP) basis for use with jmDFT. We demonstrate this single set of d1 MOPs to be suitable for nearly eliminating all energetic delocalization error and static correlation error. In all cases, MOP jmDFT outperforms AOP jmDFT, and it eliminates most flat-plane errors at non-empirical values. Unlike DFT+U or hybrid functionals, jmDFT nearly eliminates energetic delocalization error and static correlation error within a non-empirical framework.
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Affiliation(s)
- Akash Bajaj
- Massachusetts Institute of Technology, United States of America
| | - Chenru Duan
- Massachusetts Institute of Technology, United States of America
| | - Aditya Nandy
- Massachusetts Institute of Technology, United States of America
| | | | - Heather J. Kulik
- Dept of Chemical Engineering, Massachusetts Institute of Technology, United States of America
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11
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Gedeon J, Schmidt J, Hodgson MJP, Wetherell J, Benavides-Riveros CL, Marques MAL. Machine learning the derivative discontinuity of density-functional theory. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2022. [DOI: 10.1088/2632-2153/ac3149] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Abstract
Machine learning is a powerful tool to design accurate, highly non-local, exchange-correlation functionals for density functional theory. So far, most of those machine learned functionals are trained for systems with an integer number of particles. As such, they are unable to reproduce some crucial and fundamental aspects, such as the explicit dependency of the functionals on the particle number or the infamous derivative discontinuity at integer particle numbers. Here we propose a solution to these problems by training a neural network as the universal functional of density-functional theory that (a) depends explicitly on the number of particles with a piece-wise linearity between the integer numbers and (b) reproduces the derivative discontinuity of the exchange-correlation energy. This is achieved by using an ensemble formalism, a training set containing fractional densities, and an explicitly discontinuous formulation.
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12
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13
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Matusalem F, Bechstedt F, Guilhon I, Marques M, Teles LK. DFT-1/2 method applied to 2D topological insulators: fluorinated and hydrogenated group-IV honeycomb systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:435501. [PMID: 34315138 DOI: 10.1088/1361-648x/ac1820] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2021] [Accepted: 07/27/2021] [Indexed: 06/13/2023]
Abstract
We present a computationally efficient and accurate methodology to computeZ2topological invariants for systems without inversion symmetry including quasiparticle (QP) effects within the density functional theory (DFT)-1/2 method. The Wannier charge center evolution is applied to compute theZ2topological invariant and investigate the topological properties of group-IV graphene-like systems, graphene, silicene, germanene and stanene, whose inversion symmetry is broken by simultaneous functionalization with hydrogen and fluorine atoms. Different atomic arrangements are studied. The systems are stable with cohesive energy decreasing along the row from carbon to tin. A similar trend is observed for band gaps. The resulting topological invariants are compared with values obtained within conventional DFT and using a hybrid exchange-correlation functional. The variation of the results with the treatment of exchange and correlation demonstrates the importance of QP corrections for the prediction of the topological or trivial character.
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Affiliation(s)
- Filipe Matusalem
- Group of Semiconductor Materials and Nanotechnology (GMSN), Aeronautics Institute of Technology (ITA), 12228-900 São José dos Campos/SP, Brazil
| | - Friedhelm Bechstedt
- Institut für Festkörpertheorie und -optik, Friedrich-Schiller-Universität, Max-Wien-Platz 1, D-07743 Jena, Germany
| | - Ivan Guilhon
- Group of Semiconductor Materials and Nanotechnology (GMSN), Aeronautics Institute of Technology (ITA), 12228-900 São José dos Campos/SP, Brazil
| | - Marcelo Marques
- Group of Semiconductor Materials and Nanotechnology (GMSN), Aeronautics Institute of Technology (ITA), 12228-900 São José dos Campos/SP, Brazil
| | - Lara K Teles
- Group of Semiconductor Materials and Nanotechnology (GMSN), Aeronautics Institute of Technology (ITA), 12228-900 São José dos Campos/SP, Brazil
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14
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Assessment of DFT methods for the prediction of detachment energies and electronic structures of complex and multiply charged anions. COMPUT THEOR CHEM 2021. [DOI: 10.1016/j.comptc.2021.113295] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
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15
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Bajaj A, Kulik HJ. Molecular DFT+U: A Transferable, Low-Cost Approach to Eliminate Delocalization Error. J Phys Chem Lett 2021; 12:3633-3640. [PMID: 33826346 DOI: 10.1021/acs.jpclett.1c00796] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
While density functional theory (DFT) is widely applied for its combination of cost and accuracy, corrections (e.g., DFT+U) that improve it are often needed to tackle correlated transition-metal chemistry. In principle, the functional form of DFT+U, consisting of a set of localized atomic orbitals (AOs) and a quadratic energy penalty for deviation from integer occupations of those AOs, enables the recovery of the exact conditions of piecewise linearity and the derivative discontinuity. Nevertheless, for practical transition-metal complexes, where both atomic states and ligand orbitals participate in bonding, standard DFT+U can fail to eliminate delocalization error (DE). Here, we show that by introducing an alternative valence-state (i.e., molecular orbital or MO) basis to the DFT+U approach, we recover exact conditions in cases for which standard DFT+U corrections have no error-reducing effect. This MO-based DFT+U also eliminates DE where standard AO-based DFT+U is already successful. We demonstrate the transferability of our approach on representative transition-metal complexes with a range of ligand field strengths, electron configurations (i.e., from Sc to Zn), and spin states.
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Affiliation(s)
- Akash Bajaj
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Heather J Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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16
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Kraisler E, Hodgson MJP, Gross EKU. From Kohn-Sham to Many-Electron Energies via Step Structures in the Exchange-Correlation Potential. J Chem Theory Comput 2021; 17:1390-1407. [PMID: 33595312 PMCID: PMC8363072 DOI: 10.1021/acs.jctc.0c01093] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
Accurately
describing excited states within Kohn–Sham (KS)
density functional theory (DFT), particularly those which induce ionization
and charge transfer, remains a great challenge. Common exchange-correlation
(xc) approximations are unreliable for excited states owing, in part,
to the absence of a derivative discontinuity in the xc energy (Δ),
which relates a many-electron energy difference to the corresponding
KS energy difference. We demonstrate, analytically and numerically,
how the relationship between KS and many-electron energies leads to
the step structures observed in the exact xc potential in four scenarios:
electron addition, molecular dissociation, excitation of a finite
system, and charge transfer. We further show that steps in the potential
can be obtained also with common xc approximations, as simple as the
LDA, when addressed from the ensemble perspective. The article therefore
highlights how capturing the relationship between KS and many-electron
energies with advanced xc approximations is crucial for accurately
calculating excitations, as well as the ground-state density and energy
of systems which consist of distinct subsystems.
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Affiliation(s)
- Eli Kraisler
- Fritz Haber Center for Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, 9091401 Jerusalem, Israel
| | - M J P Hodgson
- Department of Physics, Durham University, South Road, Durham DH1 3LE, United Kingdom.,Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
| | - E K U Gross
- Fritz Haber Center for Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, 9091401 Jerusalem, Israel
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17
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Mariano LA, Vlaisavljevich B, Poloni R. Biased Spin-State Energetics of Fe(II) Molecular Complexes within Density-Functional Theory and the Linear-Response Hubbard U Correction. J Chem Theory Comput 2020; 16:6755-6762. [DOI: 10.1021/acs.jctc.0c00628] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Affiliation(s)
- Lorenzo A. Mariano
- Grenoble-INP, SIMaP, University of Grenoble-Alpes, CNRS, F-38042 Grenoble, France
| | - Bess Vlaisavljevich
- Department of Chemistry, University of South Dakota, Vermillion, South Dakota 57069, United States
| | - Roberta Poloni
- Grenoble-INP, SIMaP, University of Grenoble-Alpes, CNRS, F-38042 Grenoble, France
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18
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Mancuso JL, Mroz AM, Le KN, Hendon CH. Electronic Structure Modeling of Metal-Organic Frameworks. Chem Rev 2020; 120:8641-8715. [PMID: 32672939 DOI: 10.1021/acs.chemrev.0c00148] [Citation(s) in RCA: 96] [Impact Index Per Article: 24.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
Owing to their molecular building blocks, yet highly crystalline nature, metal-organic frameworks (MOFs) sit at the interface between molecule and material. Their diverse structures and compositions enable them to be useful materials as catalysts in heterogeneous reactions, electrical conductors in energy storage and transfer applications, chromophores in photoenabled chemical transformations, and beyond. In all cases, density functional theory (DFT) and higher-level methods for electronic structure determination provide valuable quantitative information about the electronic properties that underpin the functions of these frameworks. However, there are only two general modeling approaches in conventional electronic structure software packages: those that treat materials as extended, periodic solids, and those that treat materials as discrete molecules. Each approach has features and benefits; both have been widely employed to understand the emergent chemistry that arises from the formation of the metal-organic interface. This Review canvases these approaches to date, with emphasis placed on the application of electronic structure theory to explore reactivity and electron transfer using periodic, molecular, and embedded models. This includes (i) computational chemistry considerations such as how functional, k-grid, and other model variables are selected to enable insights into MOF properties, (ii) extended solid models that treat MOFs as materials rather than molecules, (iii) the mechanics of cluster extraction and subsequent chemistry enabled by these molecular models, (iv) catalytic studies using both solids and clusters thereof, and (v) embedded, mixed-method approaches, which simulate a fraction of the material using one level of theory and the remainder of the material using another dissimilar theoretical implementation.
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Affiliation(s)
- Jenna L Mancuso
- Department of Chemistry and Biochemistry, University of Oregon, Eugene, Oregon 97405, United States
| | - Austin M Mroz
- Department of Chemistry and Biochemistry, University of Oregon, Eugene, Oregon 97405, United States
| | - Khoa N Le
- Department of Chemistry and Biochemistry, University of Oregon, Eugene, Oregon 97405, United States
| | - Christopher H Hendon
- Department of Chemistry and Biochemistry, University of Oregon, Eugene, Oregon 97405, United States
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19
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Morales-García Á, Rhatigan S, Nolan M, Illas F. On the use of DFT+U to describe the electronic structure of TiO 2 nanoparticles: (TiO 2) 35 as a case study. J Chem Phys 2020; 152:244107. [PMID: 32610938 DOI: 10.1063/5.0012271] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
One of the main drawbacks in the density functional theory (DFT) formalism is the underestimation of the energy gaps in semiconducting materials. The combination of DFT with an explicit treatment of the electronic correlation with a Hubbard-like model, known as the DFT+U method, has been extensively applied to open up the energy gap in materials. Here, we introduce a systematic study where the selection of the U parameter is analyzed considering two different basis sets: plane-waves and numerical atomic orbitals (NAOs), together with different implementations for including U, to investigate the structural and electronic properties of a well-defined bipyramidal (TiO2)35 nanoparticle. This study reveals, as expected, that a certain U value can reproduce the experimental value for the energy gap. However, there is a high dependence on the choice of basis set and on the U parameter employed. The present study shows that the linear combination of the NAO basis functions, as implemented in Fritz Haber Institute ab initio molecular simulation (FHI-aims), requires, requires a lower U value than the simplified rotationally invariant approach, as implemented in the Vienna ab initio simulation package (VASP). Therefore, the transfer of U values between codes is unfeasible and not recommended, demanding initial benchmark studies for the property of interest as a reference to determine the appropriate value of U.
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Affiliation(s)
- Ángel Morales-García
- Departament de Ciència de Materials i Química Física & Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona, c/Martí i Franquès 1-11, 08028 Barcelona, Spain
| | - Stephen Rhatigan
- Tyndall National Institute, University College Cork, Lee Maltings, Cork T12 R5CP, Ireland
| | - Michael Nolan
- Tyndall National Institute, University College Cork, Lee Maltings, Cork T12 R5CP, Ireland
| | - Francesc Illas
- Departament de Ciència de Materials i Química Física & Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona, c/Martí i Franquès 1-11, 08028 Barcelona, Spain
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20
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Skelton JM, Gunn DSD, Metz S, Parker SC. Accuracy of Hybrid Functionals with Non-Self-Consistent Kohn-Sham Orbitals for Predicting the Properties of Semiconductors. J Chem Theory Comput 2020; 16:3543-3557. [PMID: 32369352 DOI: 10.1021/acs.jctc.9b01218] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Accurately modeling the electronic structure of materials is a persistent challenge to high-throughput screening. A promising means of balancing accuracy against computational cost is non-self-consistent calculations with hybrid density-functional theory, where the electronic band energies are evaluated using a hybrid functional from orbitals obtained with a less demanding (semi)local functional. We have quantified the performance of this technique for predicting the physical properties of 16 tetrahedral semiconductors with bandgaps from 0.2 to 5.5 eV. Provided the base functional predicts a nonmetallic electronic structure, bandgaps within 5% of the PBE0 and HSE06 gaps can be obtained with an order of magnitude reduction in computing time. The positions of the valence and conduction band extrema and the Fermi level are well reproduced, enabling calculation of the band dispersion, density of states, and dielectric properties using Fermi's Golden Rule. While the error in the non-self-consistent total energies is ∼50 meV atom-1, the energy-volume curves are reproduced accurately enough to obtain the equilibrium volume and bulk modulus with minimal error. We also test the dielectric-dependent scPBE0 functional and obtain bandgaps and dielectric constants to within 2.5% of the self-consistent results, which amounts to a significant improvement over self-consistent PBE0 for a similar computational cost. We identify cases where the non-self-consistent approach is expected to perform poorly and demonstrate that partial self-consistency provides a practical and efficient workaround. Finally, we perform proof-of-concept calculations on CoO and NiO to demonstrate the applicability of the technique to strongly correlated open-shell transition-metal oxides.
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Affiliation(s)
- Jonathan M Skelton
- Department of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom.,Department of Chemistry, University of Bath, Bath BA2 7AY, United Kingdom
| | - David S D Gunn
- STFC Daresbury Laboratory, Keckwick Ln., Daresbury, Warrington WA4 4AD, United Kingdom
| | - Sebastian Metz
- STFC Daresbury Laboratory, Keckwick Ln., Daresbury, Warrington WA4 4AD, United Kingdom.,Fraunhofer Institute for Solar Energy Systems ISE, Heidenhofstraße 2, 79110 Freiburg, Germany
| | - Stephen C Parker
- Department of Chemistry, University of Bath, Bath BA2 7AY, United Kingdom
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21
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Neural network interpolation of exchange-correlation functional. Sci Rep 2020; 10:8000. [PMID: 32409657 PMCID: PMC7224278 DOI: 10.1038/s41598-020-64619-8] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2019] [Accepted: 04/17/2020] [Indexed: 11/24/2022] Open
Abstract
Density functional theory (DFT) is one of the most widely used tools to solve the many-body Schrodinger equation. The core uncertainty inside DFT theory is the exchange-correlation (XC) functional, the exact form of which is still unknown. Therefore, the essential part of DFT success is based on the progress in the development of XC approximations. Traditionally, they are built upon analytic solutions in low- and high-density limits and result from quantum Monte Carlo numerical calculations. However, there is no consistent and general scheme of XC interpolation and functional representation. Many different developed parametrizations mainly utilize a number of phenomenological rules to construct a specific XC functional. In contrast, the neural network (NN) approach can provide a general way to parametrize an XC functional without any a priori knowledge of its functional form. In this work, we develop NN XC functionals and prove their applicability to 3-dimensional physical systems. We show that both the local density approximation (LDA) and generalized gradient approximation (GGA) are well reproduced by the NN approach. It is demonstrated that the local environment can be easily considered by changing only the number of neurons in the first layer of the NN. The developed NN XC functionals show good results when applied to systems that are not presented in the training/test data. The generalizability of the formulated NN XC framework leads us to believe that it could give superior results in comparison with traditional XC schemes provided training data from high-level theories such as the quantum Monte Carlo and post-Hartree-Fock methods.
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22
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Nandy A, Chu DBK, Harper DR, Duan C, Arunachalam N, Cytter Y, Kulik HJ. Large-scale comparison of 3d and 4d transition metal complexes illuminates the reduced effect of exchange on second-row spin-state energetics. Phys Chem Chem Phys 2020; 22:19326-19341. [DOI: 10.1039/d0cp02977g] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
The origin of distinct 3d vs. 4d transition metal complex sensitivity to exchange is explored over a large data set.
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Affiliation(s)
- Aditya Nandy
- Department of Chemical Engineering
- Massachusetts Institute of Technology
- Cambridge
- USA
- Department of Chemistry
| | - Daniel B. K. Chu
- Department of Chemical Engineering
- Massachusetts Institute of Technology
- Cambridge
- USA
| | - Daniel R. Harper
- Department of Chemical Engineering
- Massachusetts Institute of Technology
- Cambridge
- USA
- Department of Chemistry
| | - Chenru Duan
- Department of Chemical Engineering
- Massachusetts Institute of Technology
- Cambridge
- USA
- Department of Chemistry
| | - Naveen Arunachalam
- Department of Chemical Engineering
- Massachusetts Institute of Technology
- Cambridge
- USA
| | - Yael Cytter
- Department of Chemical Engineering
- Massachusetts Institute of Technology
- Cambridge
- USA
| | - Heather J. Kulik
- Department of Chemical Engineering
- Massachusetts Institute of Technology
- Cambridge
- USA
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23
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Zhang Y, Zhang W, Singh DJ. Localization in the SCAN meta-generalized gradient approximation functional leading to broken symmetry ground states for graphene and benzene. Phys Chem Chem Phys 2020; 22:19585-19591. [DOI: 10.1039/d0cp03567j] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
SCAN over localizes orbitals leading to spin symmetry broken ground states in graphene and benzene.
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Affiliation(s)
- Yubo Zhang
- Department of Physics and Shenzhen Institute for Quantum Science & Engineering
- Southern University of Science and Technology
- Shenzhen
- China
- Guangdong Provincial Key Lab for Computational Science and Materials Design, and Shenzhen Municipal Key Lab for Advanced Quantum Materials and Devices
| | - Wenqing Zhang
- Department of Physics and Shenzhen Institute for Quantum Science & Engineering
- Southern University of Science and Technology
- Shenzhen
- China
- Guangdong Provincial Key Lab for Computational Science and Materials Design, and Shenzhen Municipal Key Lab for Advanced Quantum Materials and Devices
| | - David J. Singh
- Department of Physics and Astronomy
- University of Missouri
- Columbia
- USA
- Department of Chemistry
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24
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Ditte M, Dubecký M. Fractional Charge by Fixed-Node Diffusion Monte Carlo Method. PHYSICAL REVIEW LETTERS 2019; 123:156402. [PMID: 31702309 DOI: 10.1103/physrevlett.123.156402] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2019] [Indexed: 06/10/2023]
Abstract
Fixed-node diffusion Monte Carlo (FNDMC) method is a stochastic quantum many-body approach that has a great potential in electronic structure theory. We examine how FNDMC total energy E(N) satisfies exact constraints, linearity and derivative discontinuity, versus fractional electron number N, if combined with mean-field trial wave functions that miss such features. H and Cl atoms with fractional charge reveal that FNDMC method is well able to restore the piecewise linearity of E(N). The method uses ensemble and projector ingredients to achieve the correct charge localization. A water-solvated Cl^{-} complex illustrates superior performance of FNDMC method for charged noncovalent systems.
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Affiliation(s)
- Matej Ditte
- Department of Physics, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic
| | - Matúš Dubecký
- Department of Physics, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic
- ATRI, Slovak University of Technology, J. Bottu 25, 917 24 Trnava, Slovakia
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25
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Mesta M, Chang JH, Shil S, Thygesen KS, Lastra JMG. A Protocol for Fast Prediction of Electronic and Optical Properties of Donor-Acceptor Polymers Using Density Functional Theory and the Tight-Binding Method. J Phys Chem A 2019; 123:4980-4989. [PMID: 31117588 DOI: 10.1021/acs.jpca.9b02391] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The ability of donor-acceptor (D-A) type polymers to control the positions of the highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbitals makes them a popular choice for organic solar cell applications. The alternating D-A pattern in a monomer leads to a weak electronic coupling between the constituent monomers within the polymer chain. Exploiting the weak electronic coupling characteristics, we developed a method to efficiently calculate (1) the electronic properties and (2) the optical gap of such polymer chains. The electronic properties (HOMO and LUMO energies, ionization potential, electron affinity, and quasiparticle gap of an oligomer of any length up to an infinitely long polymer) of the D-A polymers are predicted by combining density functional theory calculation results and a tight-binding model. The weak electronic coupling implies that the optical gap of the polymer is size-independent, and thus, it can be calculated using a monomer. We validated the methods using a set of 104 polymers by checking the consistency where the electronic gap of a polymer is larger than the optical gap. Furthermore, we establish relationships between the results obtained from more accurate, yet slower methods (i.e., B3LYP functional, singlet-ΔSCF) with those obtained from the faster counterparts (i.e., BLYP functional, triplet-ΔSCF). Leveraging the found relationships, we propose a way in which the electronic and optical properties of the polymers can be calculated efficiently while retaining high accuracy. The use of the tight-binding model combined with the approach to estimate more accurate results based on less expensive simulations is crucial in the applications where a large volume of computations needs to be carried out efficiently with sufficiently high accuracy, such as high-throughput computational screening or training a machine-learning model.
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Affiliation(s)
- Murat Mesta
- Department of Energy Conversion and Storage , Technical University of Denmark , 2800 Kgs. Lyngby , Denmark
| | - Jin Hyun Chang
- Department of Energy Conversion and Storage , Technical University of Denmark , 2800 Kgs. Lyngby , Denmark
| | - Suranjan Shil
- CAMD, Department of Physics , Technical University of Denmark , 2800 Kgs. Lyngby , Denmark
| | - Kristian S Thygesen
- CAMD, Department of Physics , Technical University of Denmark , 2800 Kgs. Lyngby , Denmark
| | - Juan Maria Garcia Lastra
- Department of Energy Conversion and Storage , Technical University of Denmark , 2800 Kgs. Lyngby , Denmark
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26
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Bajaj A, Liu F, Kulik HJ. Non-empirical, low-cost recovery of exact conditions with model-Hamiltonian inspired expressions in jmDFT. J Chem Phys 2019; 150:154115. [PMID: 31005112 DOI: 10.1063/1.5091563] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Abstract
Density functional theory (DFT) is widely applied to both molecules and materials, but well known energetic delocalization and static correlation errors in practical exchange-correlation approximations limit quantitative accuracy. Common methods that correct energetic delocalization errors, such as the Hubbard U correction in DFT+U or Hartree-Fock exchange in global hybrids, do so at the cost of worsening static correlation errors. We recently introduced an alternate approach [Bajaj et al., J. Chem. Phys. 147, 191101 (2017)] known as judiciously modified DFT (jmDFT), wherein the deviation from exact behavior of semilocal functionals over both fractional spin and charge, i.e., the so-called flat plane, was used to motivate functional forms of second order analytic corrections. In this work, we introduce fully nonempirical expressions for all four coefficients in a DFT+U+J-inspired form of jmDFT, where all coefficients are obtained only from energies and eigenvalues of the integer-electron systems. We show good agreement for U and J coefficients obtained nonempirically as compared with the results of numerical fitting in a jmDFT U+J/J' correction. Incorporating the fully nonempirical jmDFT correction reduces and even eliminates the fractional spin error at the same time as eliminating the energetic delocalization error. We show that this approach extends beyond s-electron systems to higher angular momentum cases including p- and d-electrons. Finally, we diagnose some shortcomings of the current jmDFT approach that limit its ability to improve upon DFT results for cases such as weakly bound anions due to poor underlying semilocal functional behavior.
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Affiliation(s)
- Akash Bajaj
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Fang Liu
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Heather J Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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27
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Artificial neural networks for density-functional optimizations in fermionic systems. Sci Rep 2019; 9:1886. [PMID: 30760812 PMCID: PMC6374439 DOI: 10.1038/s41598-018-37999-1] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2018] [Accepted: 12/17/2018] [Indexed: 11/08/2022] Open
Abstract
In this work we propose an artificial neural network functional to the ground-state energy of fermionic interacting particles in homogeneous chains described by the Hubbard model. Our neural network functional was proven to have an excellent performance: it deviates from numerically exact calculations by less than 0.15% for a vast regime of interactions and for all the regimes of filling factors and magnetizations. When compared to analytical functionals, the neural functional was found to be more precise for all the regimes of parameters, being particularly superior at the weakly interacting regime: where the analytical parametrization fails the most, ~7%, against only ~0.1% for the neural network. We have also applied our homogeneous functional to finite, localized impurities and harmonically confined systems within density-functional theory (DFT) methods. The results show that while our artificial neural network approach is substantially more accurate than other equivalently simple and fast DFT treatments, it has similar performance than more costly DFT calculations and other independent many-body calculations, at a fraction of the computational cost.
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Kronik L, Kümmel S. Dielectric Screening Meets Optimally Tuned Density Functionals. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2018; 30:e1706560. [PMID: 29665112 DOI: 10.1002/adma.201706560] [Citation(s) in RCA: 64] [Impact Index Per Article: 10.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2017] [Revised: 12/19/2017] [Indexed: 06/08/2023]
Abstract
A short overview of recent attempts at merging two independently developed methods is presented. These are the optimal tuning of a range-separated hybrid (OT-RSH) functional, developed to provide an accurate first-principles description of the electronic structure and optical properties of gas-phase molecules, and the polarizable continuum model (PCM), developed to provide an approximate but computationally tractable description of a solvent in terms of an effective dielectric medium. After a brief overview of the OT-RSH approach, its combination with the PCM as a potentially accurate yet low-cost approach to the study of molecular assemblies and solids, particularly in the context of photocatalysis and photovoltaics, is discussed. First, solvated molecules are considered, with an emphasis on the challenge of balancing eigenvalue and total energy trends. Then, it is shown that the same merging of methods can also be used to study the electronic and optical properties of molecular solids, with a similar discussion of the pros and cons. Tuning of the effective scalar dielectric constant as one recent approach that mitigates some of the difficulties in merging the two approaches is considered.
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Affiliation(s)
- Leeor Kronik
- Department of Materials and Interfaces, Weizmann Institute of Science, Rehovoth, 76100, Israel
| | - Stephan Kümmel
- Theoretical Physics IV, Universität Bayreuth, 95440, Bayreuth, Germany
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29
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Mori-Sánchez P, Cohen AJ. Exact Density Functional Obtained via the Levy Constrained Search. J Phys Chem Lett 2018; 9:4910-4914. [PMID: 30096231 DOI: 10.1021/acs.jpclett.8b02332] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
A stochastic minimization method for a real-space wave function, Ψ(r1, r2...r n), constrained to a chosen density, ρ(r), is developed. It enables the explicit calculation of the Levy constrained search, F[ρ] = minΨ→ρ⟨Ψ| T̂ + V̂ ee|Ψ⟩, which gives the exact functional of density functional theory. This general method is illustrated in the evaluation of F[ρ] for densities in one dimension with a soft-Coulomb interaction. Additionally, procedures are given to determine the first and second functional derivatives, δ F/δρ(r) and δ2 F/[δρ(r)δρ(r')]. For a chosen external potential, v(r), the functional and its derivatives are used in minimizations over densities to give the exact energy, E v, without needing to solve the Schrödinger equation.
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Affiliation(s)
- Paula Mori-Sánchez
- Departamento de Química and Instituto de Física de la Materia Condensada (IFIMAC) , Universidad Autónoma de Madrid , 28049 , Madrid , Spain
| | - Aron J Cohen
- Max Planck Institute for Solid State Research , Heisenbergstrasse 1 , 70569 Stuttgart , Germany
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30
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Baerends EJ. Density functional approximations for orbital energies and total energies of molecules and solids. J Chem Phys 2018; 149:054105. [PMID: 30089375 DOI: 10.1063/1.5026951] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The relation of Kohn-Sham (KS) orbital energies to ionization energies and electron affinities is different in molecules and solids. In molecules, the local density approximation (LDA) and generalized gradient approximations (GGA) approximate the exact ionization energy (I) and affinity (A) rather well with self-consistently calculated (total energy based) ILDFA and ALDFA, respectively. The highest occupied molecular orbital (HOMO) energy and lowest unoccupied molecular orbital (LUMO) energy, however, differ significantly (by typically 4-6 eV) from these quantities, ϵHLDFA(mol)>-I(mol)≈-ILDFA(mol), ϵLLDFA(mol)<-A(mol)≈-ALDFA(mol). In solids, these relations are very different, due to two effects. The (almost) infinite extent of a solid makes the difference of orbital energies and (L)DFA calculated ionization energy and affinity disappear: in the solid state limit, ϵH(L)DFA(solid)=-I(L)DFA(solid) and ϵL(L)DFA(solid)=-A(L)DFA(solid). Slater's relation ∂E/∂ni = ϵi for local density functional approximations (LDFAs) [and Hartree-Fock (HF) and hybrids] is useful to prove these relations. The equality of LDFA orbital energies and LDFA calculated -ILDFA and -ALDFA in solids does not mean that they are good approximations to the exact quantities. The LDFA total energies of the ions with a delocalized charge are too low, hence ILDFA(solid) < I and ALDFA(solid) > A, due to the local-approximation error, also denoted delocalization error, of LDFAs in extended systems. These errors combine to make the LDFA orbital energy band gap considerably smaller than the exact fundamental gap, ϵLLDFA(solid)-ϵHLDFA(solid)=ILDFA(solid)-ALDFA(solid)<I-A (the LDFA band gap problem). These results for density functional approximations are compared to exact KS and to HF and hybrids. For the exact KS HOMO energy, one has ϵHKS=-I. The exact KS LUMO energy does not approximate the experimental -A (neither in molecules nor in solids), but is considerably below, which is the main reason for the exact KS HOMO-LUMO energy gap being considerably below the fundamental gap I - A (the exact KS band gap problem).
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Affiliation(s)
- Evert Jan Baerends
- Section Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands
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31
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Maier TM, Arbuznikov AV, Kaupp M. Local hybrid functionals: Theory, implementation, and performance of an emerging new tool in quantum chemistry and beyond. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2018. [DOI: 10.1002/wcms.1378] [Citation(s) in RCA: 65] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Toni M. Maier
- Institut für Chemie Theoretische Chemie/Quantenchemie Technische Universität Berlin Berlin Germany
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering Waseda University Tokyo Japan
| | - Alexei V. Arbuznikov
- Institut für Chemie Theoretische Chemie/Quantenchemie Technische Universität Berlin Berlin Germany
| | - Martin Kaupp
- Institut für Chemie Theoretische Chemie/Quantenchemie Technische Universität Berlin Berlin Germany
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32
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Zhao Q, Kulik HJ. Where Does the Density Localize in the Solid State? Divergent Behavior for Hybrids and DFT+U. J Chem Theory Comput 2018; 14:670-683. [PMID: 29298057 DOI: 10.1021/acs.jctc.7b01061] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Approximate density functional theory (DFT) is widely used in chemistry and physics, despite delocalization errors that affect energetic and density properties. DFT+U (i.e., semilocal DFT augmented with a Hubbard U correction) and global hybrid functionals are two commonly employed practical methods to address delocalization error. Recent work demonstrated that in transition-metal complexes both methods localize density away from the metal and onto surrounding ligands, regardless of metal or ligand identity. In this work, we compare density localization trends with DFT+U and global hybrids on a diverse set of 34 transition-metal-containing solids with varying magnetic state, electron configuration and valence shell, and coordinating-atom orbital diffuseness (i.e., O, S, Se). We also study open-framework solids in which the metal is coordinated by molecular ligands, i.e., MCO3, M(OH)2, M(NCNH)2, K3M(CN)6 (M = V-Ni). As in transition-metal complexes, incorporation of Hartree-Fock exchange consistently localizes density away from the metal, but DFT+U exhibits diverging behavior, localizing density (i) onto the metal in low-spin and late transition metals and (ii) away from the metal in other cases in agreement with hybrids. To isolate the effect of the crystal environment, we extract molecular analogues from open-framework transition-metal solids and observe consistent localization of the density away from the metal in all cases with both DFT+U and hybrid exchange. These observations highlight the limited applicability of trends established for functional tuning on transition-metal complexes even to equivalent coordination environments in the solid state.
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Affiliation(s)
- Qing Zhao
- Department of Chemical Engineering and ‡Department of Mechanical Engineering, Massachusetts Institute of Technology , Cambridge, Massachusetts 02139, United States
| | - Heather J Kulik
- Department of Chemical Engineering and ‡Department of Mechanical Engineering, Massachusetts Institute of Technology , Cambridge, Massachusetts 02139, United States
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33
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Hodgson MJP, Kraisler E, Schild A, Gross EKU. How Interatomic Steps in the Exact Kohn-Sham Potential Relate to Derivative Discontinuities of the Energy. J Phys Chem Lett 2017; 8:5974-5980. [PMID: 29179553 DOI: 10.1021/acs.jpclett.7b02615] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Accurate density functional calculations hinge on reliable approximations to the unknown exchange-correlation (xc) potential. The most popular approximations usually lack features of the exact xc potential that are important for an accurate prediction of the fundamental gap and the distribution of charge in complex systems. Two principal features in this regard are the spatially uniform shift in the potential, as the number of electrons infinitesimally surpasses an integer, and the spatial steps that form, for example, between the atoms of stretched molecules. Although both aforementioned concepts are well known, the exact relationship between them remained unclear. Here we establish this relationship via an analytical derivation. We support our result by numerically solving the many-electron Schrödinger equation to extract the exact Kohn-Sham potential and directly observe its features. Spatial steps in the exact xc potential of a full configuration-interaction (FCI) calculation of a molecule are presented in three dimensions.
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Affiliation(s)
- M J P Hodgson
- Max-Planck-Institut für Mikrostrukturphysik , Weinberg 2, D-06120 Halle, Germany
| | - Eli Kraisler
- Max-Planck-Institut für Mikrostrukturphysik , Weinberg 2, D-06120 Halle, Germany
| | - Axel Schild
- Laboratorium für Physikalische Chemie, ETH Zürich , 8093 Zürich, Switzerland
| | - E K U Gross
- Max-Planck-Institut für Mikrostrukturphysik , Weinberg 2, D-06120 Halle, Germany
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem , Jerusalem 91904, Israel
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34
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Gani TZH, Kulik HJ. Unifying Exchange Sensitivity in Transition-Metal Spin-State Ordering and Catalysis through Bond Valence Metrics. J Chem Theory Comput 2017; 13:5443-5457. [DOI: 10.1021/acs.jctc.7b00848] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Terry Z. H. Gani
- Department
of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Heather J. Kulik
- Department
of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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35
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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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36
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Mahler A, Janesko BG, Moncho S, Brothers EN. Why are GGAs so accurate for reaction kinetics on surfaces? Systematic comparison of hybrid vs. nonhybrid DFT for representative reactions. J Chem Phys 2017. [DOI: 10.1063/1.4986404] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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37
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Abstract
The exact exchange energy and its energy density are useful but computationally expensive ingredients in density functional approximations for Kohn-Sham density functional theory. We present detailed tests of some exact nonempirical upper bounds to exact exchange. These "Rung 3.5" upper bounds contract the Kohn-Sham one-particle density matrix with model density matrices used to construct semilocal model exchange holes and invoke the Cauchy-Schwarz inequality. The contraction automatically eliminates the computationally expensive long-range component of the exact exchange hole. Numerical tests show that the exchange upper bounds underestimate total exchange energies while predicting other properties with accuracy approaching standard hybrid approximations.
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Affiliation(s)
- Emil Proynov
- Department of Chemistry and Biochemistry, Texas Christian University , Fort Worth, Texas 76110, United States
| | - Benjamin G Janesko
- Department of Chemistry and Biochemistry, Texas Christian University , Fort Worth, Texas 76110, United States
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38
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39
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Janet JP, Zhao Q, Ioannidis EI, Kulik HJ. Density functional theory for modelling large molecular adsorbate–surface interactions: a mini-review and worked example. MOLECULAR SIMULATION 2016. [DOI: 10.1080/08927022.2016.1258465] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Affiliation(s)
- Jon Paul Janet
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Qing Zhao
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Efthymios I. Ioannidis
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Heather J. Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
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40
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Gani TZH, Kulik HJ. Where Does the Density Localize? Convergent Behavior for Global Hybrids, Range Separation, and DFT+U. J Chem Theory Comput 2016; 12:5931-5945. [DOI: 10.1021/acs.jctc.6b00937] [Citation(s) in RCA: 53] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Terry Z. H. Gani
- Department
of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Heather J. Kulik
- Department
of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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41
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Miranda-Quintana RA, Ayers PW. Systematic treatment of spin-reactivity indicators in conceptual density functional theory. Theor Chem Acc 2016. [DOI: 10.1007/s00214-016-1995-5] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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42
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Zhao Q, Ioannidis EI, Kulik HJ. Global and local curvature in density functional theory. J Chem Phys 2016; 145:054109. [DOI: 10.1063/1.4959882] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Qing Zhao
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139,
USA
- Department of Mechanical Engineering,
Massachusetts Institute of Technology, Cambridge,
Massachusetts 02139, USA
| | - Efthymios I. Ioannidis
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139,
USA
| | - Heather J. Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139,
USA
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43
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Verma P, Bartlett RJ. Increasing the applicability of density functional theory. V. X-ray absorption spectra with ionization potential corrected exchange and correlation potentials. J Chem Phys 2016; 145:034108. [DOI: 10.1063/1.4955194] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Prakash Verma
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Rodney J. Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
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44
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Yang XD, Patel AHG, Miranda-Quintana RA, Heidar-Zadeh F, González-Espinoza CE, Ayers PW. Communication: Two types of flat-planes conditions in density functional theory. J Chem Phys 2016; 145:031102. [DOI: 10.1063/1.4958636] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Xiaotian Derrick Yang
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario LBS 4M1, Canada
| | - Anand H. G. Patel
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario LBS 4M1, Canada
| | - Ramón Alain Miranda-Quintana
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario LBS 4M1, Canada
- Laboratory of Computational and Theoretical Chemistry, Faculty of Chemistry, University of Havana, Havana, Cuba
| | - Farnaz Heidar-Zadeh
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario LBS 4M1, Canada
- Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | | | - Paul W. Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario LBS 4M1, Canada
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45
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Peach MJG, Teale AM, Helgaker T, Tozer DJ. Fractional Electron Loss in Approximate DFT and Hartree–Fock Theory. J Chem Theory Comput 2015; 11:5262-8. [DOI: 10.1021/acs.jctc.5b00804] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Michael J. G. Peach
- Department
of Chemistry, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - Andrew M. Teale
- School
of Chemistry, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Department
of Chemistry, Centre for Theoretical and Computational Chemistry, University of Oslo, P.O.
Box 1033, Blindern, Oslo N-0315, Norway
| | - Trygve Helgaker
- Department
of Chemistry, Centre for Theoretical and Computational Chemistry, University of Oslo, P.O.
Box 1033, Blindern, Oslo N-0315, Norway
| | - David J. Tozer
- Department
of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
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46
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Carrascal DJ, Ferrer J, Smith JC, Burke K. The Hubbard dimer: a density functional case study of a many-body problem. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:393001. [PMID: 26380948 DOI: 10.1088/0953-8984/27/39/393001] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of density functional theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy-Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green's function, demonstrating the 'failure' of the Kohn-Sham (KS) method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree-Fock and Bethe ansatz local density approximation) to show their successes and limitations. We also discuss and illustrate the concept of the derivative discontinuity. Useful appendices include analytic expressions for density functional energy components, several limits of the exact functional (weak- and strong-coupling, symmetric and asymmetric), various adiabatic connection results, proofs of exact conditions for this model, and the origin of the Hubbard model from a minimal basis model for stretched H2.
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Affiliation(s)
- D J Carrascal
- Department of Physics, Universidad de Oviedo, 33007 Oviedo, Spain. Nanomaterials and Nanotechnology Research Center, Oviedo, Spain
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47
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Vlček V, Eisenberg HR, Steinle-Neumann G, Kronik L, Baer R. Deviations from piecewise linearity in the solid-state limit with approximate density functionals. J Chem Phys 2015; 142:034107. [DOI: 10.1063/1.4905236] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Vojtěch Vlček
- Bayerisches Geoinstitut, Universität Bayreuth, D-95440 Bayreuth, Germany
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Helen R. Eisenberg
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | | | - Leeor Kronik
- Department of Materials and Interfaces, Weizmann Institute of Science, Rehovoth 76100, Israel
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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48
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49
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Mori-Sánchez P, Cohen AJ. Qualitative breakdown of the unrestricted Hartree-Fock energy. J Chem Phys 2014; 141:164124. [DOI: 10.1063/1.4898860] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Affiliation(s)
- Paula Mori-Sánchez
- Departamento de Química and Instituto de Física de la Materia Condensada (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid, Spain
| | - Aron J. Cohen
- Department of Chemistry, Lensfield Road, University of Cambridge, Cambridge CB2 1EW, United Kingdom
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50
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