1
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Tozer DJ. Effective homogeneity of Fermi-Amaldi-containing exchange-correlation functionals. J Chem Phys 2023; 159:244102. [PMID: 38131479 DOI: 10.1063/5.0179111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2023] [Accepted: 11/30/2023] [Indexed: 12/23/2023] Open
Abstract
Parr and Ghosh [Phys. Rev. A. 51 3564 (1995)] demonstrated that when near-exact electron densities and potentials are used, the exchange-correlation energies of first- and second-row atoms are well-described by a combination of the Fermi-Amaldi functional with a functional that is homogeneous of degree one under density scaling. Insight into this observation is provided by considering their work from the perspective of the effective homogeneity of the overall exchange-correlation functional. By considering a general form that combines the Fermi-Amaldi functional with a functional that is homogeneous of degree k, it is shown that for these atoms, the functional of Parr and Ghosh (k = 1) exhibits essentially optimal effective homogeneities on the electron-deficient side of the integer. Percentage errors in effective homogeneities are close to percentage errors in exchange-correlation energies.
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Affiliation(s)
- David J Tozer
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
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2
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Dillon DJ, Tozer DJ. Incorporation of the Fermi-Amaldi Term into Direct Energy Kohn-Sham Calculations. J Chem Theory Comput 2022; 18:703-709. [PMID: 34978791 DOI: 10.1021/acs.jctc.1c00840] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In direct energy Kohn-Sham (DEKS) theory, the density functional theory electronic energy equals the sum of occupied orbital energies, obtained from Kohn-Sham-like orbital equations involving a shifted Hartree exchange-correlation potential, which must be approximated. In the present study, the Fermi-Amaldi term is incorporated into approximate DEKS calculations, introducing the required -1/r contribution to the exchange-correlation component of the shifted potential in asymptotic regions. It also provides a mechanism for eliminating one-electron self-interaction error, and it introduces a nonzero exchange-correlation component of the shift in the potential that is of appropriate magnitude. The resulting electronic energies are very sensitive to the methodologies considered, whereas the highest occupied molecular orbital energies and exchange-correlation potentials are much less sensitive and are similar to those obtained from DEKS calculations using a conventional exchange-correlation functional.
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Affiliation(s)
- Daisy J Dillon
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, U.K
| | - David J Tozer
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, U.K
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3
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Ryley MS, Withnall M, Irons TJP, Helgaker T, Teale AM. Robust All-Electron Optimization in Orbital-Free Density-Functional Theory Using the Trust-Region Image Method. J Phys Chem A 2021; 125:459-475. [PMID: 33356245 DOI: 10.1021/acs.jpca.0c09502] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a Gaussian-basis implementation of orbital-free density-functional theory (OF-DFT) in which the trust-region image method (TRIM) is used for optimization. This second-order optimization scheme has been constructed to provide benchmark all-electron results with very tight convergence of the particle-number constraint, associated chemical potential, and electron density. It is demonstrated that, by preserving the saddle-point nature of the optimization and simultaneously optimizing the density and chemical potential, an order of magnitude reduction in the number of iterations required for convergence is obtained. The approach is compared and contrasted with a new implementation of the nested optimization scheme put forward by Chan, Cohen, and Handy. Our implementation allows for semilocal kinetic-energy (and exchange-correlation) functionals to be handled self-consistently in all-electron calculations. The all-electron Gaussian-basis setting for these calculations will enable direct comparison with a wide range of standard high-accuracy quantum-chemical methods as well as with Kohn-Sham density-functional theory. We expect that the present implementation will provide a useful tool for analyzing the performance of approximate kinetic-energy functionals in finite systems.
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Affiliation(s)
- Matthew S Ryley
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, U.K
| | - Michael Withnall
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, U.K
| | - Tom J P Irons
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, U.K
| | - Trygve Helgaker
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Andrew M Teale
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, U.K.,Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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4
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Vibert CP, Tozer DJ. Simple DFT Scheme for Estimating Negative Electron Affinities. J Chem Theory Comput 2019; 15:241-248. [PMID: 30495952 DOI: 10.1021/acs.jctc.8b00938] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A simple density functional theory (DFT) scheme is proposed for estimating negative vertical electron affinities of neutral systems, based on a consideration of the integer discontinuity and density scaling homogeneity. The key feature is the derivation of two system-dependent exchange-correlation functionals, one appropriate for the electron deficient side of the integer and one appropriate for the electron abundant side. The electron affinity is evaluated as a linear combination of frontier orbital energies from self-consistent Kohn-Sham calculations on the neutral system using these functionals. For two assessments comprising a total of 43 molecules, the scheme provides electron affinities that are in good agreement with experimental values and which are an improvement over those from the DFT method of Tozer and De Proft [ J. Phys. Chem. A 2005 , 109 , 8923 ]. The scheme is trivial to implement in any Kohn-Sham program, and the computational cost is that of a series of generalized gradient approximation Kohn-Sham calculations. More generally, the study provides a prescription for performing low-cost, self-consistent Kohn-Sham calculations that yield frontier orbital energies that approximately satisfy the appropriate Koopmans conditions, without the need for exact exchange.
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Affiliation(s)
| | - David J Tozer
- Department of Chemistry , Durham University , South Road , Durham , DH1 3LE U.K
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5
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Bircher MP, Rothlisberger U. Exploiting Coordinate Scaling Relations To Accelerate Exact Exchange Calculations. J Phys Chem Lett 2018; 9:3886-3890. [PMID: 29940111 DOI: 10.1021/acs.jpclett.8b01620] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Exact exchange is an important constituent in many state-of-the-art approximations to the exchange-correlation (xc) functional of Kohn-Sham DFT. However, its evaluation can be computationally intensive, which can be particularly prohibitive in DFT-based molecular dynamics (MD) simulations, often restricted to semilocal functionals. We derive a scheme based on the formal coordinate scaling properties of the exact xc functional that allows for a substantial reduction of the cost of the evaluation of both the exact exchange energy and potential. We show that within a plane-wave/pseudopotential framework, excellent accuracy is retained, while speed ups from up to ∼6 can be reached. The coordinate scaling thus accelerates hybrid-functional-based first-principles MD simulations by nearly one order of magnitude.
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Affiliation(s)
- Martin P Bircher
- Laboratoire de Chimie et Biochimie Computationnelles , Ecole Polytechnique Fédérale de Lausanne , Lausanne 1015 , Switzerland
| | - Ursula Rothlisberger
- Laboratoire de Chimie et Biochimie Computationnelles , Ecole Polytechnique Fédérale de Lausanne , Lausanne 1015 , Switzerland
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6
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Sharpe DJ, Levy M, Tozer DJ. Approximating the Shifted Hartree-Exchange-Correlation Potential in Direct Energy Kohn-Sham Theory. J Chem Theory Comput 2018; 14:684-692. [PMID: 29298061 DOI: 10.1021/acs.jctc.7b01060] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Levy and Zahariev [Phys. Rev. Lett. 113 113002 (2014)] have proposed a new approach for performing density functional theory calculations, termed direct energy Kohn-Sham (DEKS) theory. In this approach, the electronic energy equals the sum of orbital energies, obtained from Kohn-Sham-like orbital equations involving a shifted Hartree-exchange-correlation potential, which must be approximated. In the present study, density scaling homogeneity considerations are used to facilitate DEKS calculations on a series of atoms and molecules, leading to three nonlocal approximations to the shifted potential. The first two rely on preliminary Kohn-Sham calculations using a standard generalized gradient approximation (GGA) exchange-correlation functional and the results illustrate the benefit of describing the dominant Hartree component of the shift exactly. A uniform electron gas analysis is used to eliminate the need for these preliminary Kohn-Sham calculations, leading to a potential with an unconventional form that yields encouraging results, providing strong motivation for further research in DEKS theory.
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Affiliation(s)
- Daniel J Sharpe
- Department of Chemistry, Durham University , South Road, Durham, DH1 3LE U.K
| | - Mel Levy
- Department of Chemistry, Duke University , Durham, North Carolina 27708 United States.,Department of Physics, North Carolina A&T State University , Greensboro, North Carolina 27411 United States.,Department of Chemistry and Quantum Theory Group, Tulane University , New Orleans, Louisiana 70118 United States
| | - David J Tozer
- Department of Chemistry, Durham University , South Road, Durham, DH1 3LE U.K
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7
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Constantin LA, Fabiano E, Della Sala F. Hartree potential dependent exchange functional. J Chem Phys 2016; 145:084110. [DOI: 10.1063/1.4961300] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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8
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Zech A, Aquilante F, Wesolowski TA. Homogeneity properties of the embedding potential in frozen-density embedding theory. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1125027] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Alexander Zech
- Département de Chimie Physique, Université de Genève, Genève, Switzerland
| | - Francesco Aquilante
- Dipartimento di Chimica “G. Ciamician”, Università di Bologna, Bologna, Italy
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9
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10
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Gledhill JD, Tozer DJ. System-dependent exchange–correlation functional with exact asymptotic potential and εHOMO ≈ − I. J Chem Phys 2015; 143:024104. [DOI: 10.1063/1.4926397] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jonathan D. Gledhill
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
| | - David J. Tozer
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
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11
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Merlot P, Izsák R, Borgoo A, Kjærgaard T, Helgaker T, Reine S. Charge-constrained auxiliary-density-matrix methods for the Hartree-Fock exchange contribution. J Chem Phys 2015; 141:094104. [PMID: 25194361 DOI: 10.1063/1.4894267] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Three new variants of the auxiliary-density-matrix method (ADMM) of Guidon, Hutter, and VandeVondele [J. Chem. Theory Comput. 6, 2348 (2010)] are presented with the common feature that they have a simplified constraint compared with the full orthonormality requirement of the earlier ADMM1 method. All ADMM variants are tested for accuracy and performance in all-electron B3LYP calculations with several commonly used basis sets. The effect of the choice of the exchange functional for the ADMM exchange-correction term is also investigated.
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Affiliation(s)
- Patrick Merlot
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Róbert Izsák
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Alex Borgoo
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Thomas Kjærgaard
- The qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
| | - Trygve Helgaker
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Simen Reine
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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12
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Morrison RC. Discontinuity of the exchange-correlation potential and the functional derivative of the noninteracting kinetic energy as the number of electrons crosses integer boundaries in Li, Be, and B. J Chem Phys 2015; 142:014101. [DOI: 10.1063/1.4905235] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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13
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Bohórquez HJ. Comment on “Scaling properties of information-theoretic quantities in density functional reactivity theory” by C. Rong, T. Lu, P. W. Ayers, P. K. Chattaraj and S. Liu, Phys. Chem. Chem. Phys., 2015, 17, 4977–4988. Phys Chem Chem Phys 2015; 17:32053-6. [DOI: 10.1039/c5cp05140a] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The linear dependence between the density per particle σ and the electron density ρ facilitates the theoretical study of the N-scaling rules for quantum information functionals and their atomic partitions.
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Affiliation(s)
- Hugo J. Bohórquez
- Quantum Biochemistry & Biomathematics
- Fundación Instituto de Inmunología de Colombia – FIDIC
- Bogotá D. C
- Colombia
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14
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Borgoo A, Green JA, Tozer DJ. Molecular Binding in Post-Kohn–Sham Orbital-Free DFT. J Chem Theory Comput 2014; 10:5338-45. [DOI: 10.1021/ct500670h] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Affiliation(s)
- Alex Borgoo
- Department
of Chemistry, Centre for Theoretical and Computational Chemistry, University of Oslo, P.O.
Box 1033, Blindern, Oslo N-0315, Norway
| | - James A. Green
- Department
of Chemistry, Durham University, South Road, Durham DH1 3LE, U.K
| | - David J. Tozer
- Department
of Chemistry, Durham University, South Road, Durham DH1 3LE, U.K
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15
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Tamblyn I, Refaely-Abramson S, Neaton JB, Kronik L. Simultaneous Determination of Structures, Vibrations, and Frontier Orbital Energies from a Self-Consistent Range-Separated Hybrid Functional. J Phys Chem Lett 2014; 5:2734-2741. [PMID: 26277972 DOI: 10.1021/jz5010939] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
A self-consistent optimally tuned range-separated hybrid density functional (scOT-RSH) approach is developed. It can simultaneously predict accurate geometries, vibrational modes, and frontier orbital energies. This is achieved by optimizing the range-separation parameter, γ, to both satisfy the ionization energy theorem and minimize interatomic forces. We benchmark our approach against an established hybrid functional, B3LYP, using the G2 test set. scOT-RSH greatly improves the accuracy of occupied frontier orbital energies, with a mean absolute error (MAE) of only 0.2 eV relative to experimental ionization energies compared to 2.96 eV with B3LYP. Geometries do not change significantly compared to those obtained from B3LYP, with a bond length MAE of 0.012 Å compared to 0.008 Å for B3LYP, and a 6.5% MAE for zero-point energies, slightly larger than that of B3LYP (3.1%). scOT-RSH represents a new paradigm in which accurate geometries and ionization energies can be predicted simultaneously from a single functional approach.
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Affiliation(s)
- Isaac Tamblyn
- †Department of Physics, University of Ontario Institute of Technology, Oshawa, Ontario L1H 7K4, Canada
| | - Sivan Refaely-Abramson
- ‡Department of Materials and Interfaces, Weizmann Institute of Science, Rehovoth 76100, Israel
| | - Jeffrey B Neaton
- ¶Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- §Department of Physics, University of California, Berkeley, California 94720, United States
- ∥Kavli Energy Nanosciences Institute at Berkeley, Berkeley, California 94720, United States
| | - Leeor Kronik
- ‡Department of Materials and Interfaces, Weizmann Institute of Science, Rehovoth 76100, Israel
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16
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Gas-Phase Valence-Electron Photoemission Spectroscopy Using Density Functional Theory. Top Curr Chem (Cham) 2014; 347:137-91. [DOI: 10.1007/128_2013_522] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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17
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Egger DA, Weissman S, Refaely-Abramson S, Sharifzadeh S, Dauth M, Baer R, Kümmel S, Neaton JB, Zojer E, Kronik L. Outer-valence Electron Spectra of Prototypical Aromatic Heterocycles from an Optimally Tuned Range-Separated Hybrid Functional. J Chem Theory Comput 2014; 10:1934-1952. [PMID: 24839410 PMCID: PMC4020925 DOI: 10.1021/ct400956h] [Citation(s) in RCA: 105] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2013] [Indexed: 11/29/2022]
Abstract
![]()
Density functional theory with optimally
tuned range-separated
hybrid (OT-RSH) functionals has been recently suggested [Refaely-Abramson
et al. Phys. Rev. Lett.2012, 109, 226405] as a nonempirical approach to predict the outer-valence
electronic structure of molecules with the same accuracy as many-body
perturbation theory. Here, we provide a quantitative evaluation of
the OT-RSH approach by examining its performance in predicting the
outer-valence electron spectra of several prototypical gas-phase molecules,
from aromatic rings (benzene, pyridine, and pyrimidine) to more complex
organic systems (terpyrimidinethiol and copper phthalocyanine). For
a range up to several electronvolts away from the frontier orbital
energies, we find that the outer-valence electronic structure obtained
from the OT-RSH method agrees very well (typically within ∼0.1–0.2
eV) with both experimental photoemission and theoretical many-body
perturbation theory data in the GW approximation. In particular, we
find that with new strategies for an optimal choice of the short-range
fraction of Fock exchange, the OT-RSH approach offers a balanced description
of localized and delocalized states. We discuss in detail the sole
exception found—a high-symmetry orbital, particular to small
aromatic rings, which is relatively deep inside the valence state
manifold. Overall, the OT-RSH method is an accurate DFT-based method
for outer-valence electronic structure prediction for such systems
and is of essentially the same level of accuracy as contemporary GW
approaches, at a reduced computational cost.
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Affiliation(s)
- David A Egger
- Institute of Solid State Physics, Graz University of Technology , 8010 Graz, Austria ; Department of Materials and Interfaces, Weizmann Institute of Science , Rehovoth 76100, Israel
| | - Shira Weissman
- Department of Materials and Interfaces, Weizmann Institute of Science , Rehovoth 76100, Israel
| | - Sivan Refaely-Abramson
- Department of Materials and Interfaces, Weizmann Institute of Science , Rehovoth 76100, Israel
| | - Sahar Sharifzadeh
- Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Matthias Dauth
- Theoretical Physics IV, University of Bayreuth , 95440 Bayreuth, Germany
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, Hebrew University , 91904 Jerusalem, Israel
| | - Stephan Kümmel
- Theoretical Physics IV, University of Bayreuth , 95440 Bayreuth, Germany
| | - Jeffrey B Neaton
- Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States ; Department of Physics and Kavli Energy Nanosciences Institute, University of California , Berkeley, California 94720, United States
| | - Egbert Zojer
- Institute of Solid State Physics, Graz University of Technology , 8010 Graz, Austria
| | - Leeor Kronik
- Department of Materials and Interfaces, Weizmann Institute of Science , Rehovoth 76100, Israel
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18
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Borgoo A, Teale AM, Tozer DJ. Revisiting the density scaling of the non-interacting kinetic energy. Phys Chem Chem Phys 2014; 16:14578-83. [DOI: 10.1039/c4cp00170b] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
Two different density scaling approaches are compared and their prospects for use in functional development are reviewed.
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Affiliation(s)
- Alex Borgoo
- Department of Chemistry
- Centre for Theoretical and Computational Chemistry
- University of Oslo
- Oslo N-0315, Norway
| | - Andrew M. Teale
- Department of Chemistry
- Centre for Theoretical and Computational Chemistry
- University of Oslo
- Oslo N-0315, Norway
- School of Chemistry
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19
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Borgoo A, Tozer DJ. Density Scaling of Noninteracting Kinetic Energy Functionals. J Chem Theory Comput 2013; 9:2250-5. [DOI: 10.1021/ct400129d] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Alex Borgoo
- Department of Chemistry, Durham University, South Road,
Durham DH1 3LE, United Kingdom
| | - David J. Tozer
- Department of Chemistry, Durham University, South Road,
Durham DH1 3LE, United Kingdom
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20
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Borgoo A, Tozer DJ. Negative Electron Affinities from DFT: Influence of Asymptotic Exchange-Correlation Potential and Effective Homogeneity under Density Scaling. J Phys Chem A 2012; 116:5497-500. [DOI: 10.1021/jp302801q] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Affiliation(s)
- Alex Borgoo
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, U.K
| | - David J. Tozer
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, U.K
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21
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Kronik L, Stein T, Refaely-Abramson S, Baer R. Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals. J Chem Theory Comput 2012; 8:1515-31. [PMID: 26593646 DOI: 10.1021/ct2009363] [Citation(s) in RCA: 477] [Impact Index Per Article: 39.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
Excitation gaps are of considerable significance in electronic structure theory. Two different gaps are of particular interest. The fundamental gap is defined by charged excitations, as the difference between the first ionization potential and the first electron affinity. The optical gap is defined by a neutral excitation, as the difference between the energies of the lowest dipole-allowed excited state and the ground state. Within many-body perturbation theory, the fundamental gap is the difference between the corresponding lowest quasi-hole and quasi-electron excitation energies, and the optical gap is addressed by including the interaction between a quasi-electron and a quasi-hole. A long-standing challenge has been the attainment of a similar description within density functional theory (DFT), with much debate on whether this is an achievable goal even in principle. Recently, we have constructed and applied a new approach to this problem. Anchored in the rigorous theoretical framework of the generalized Kohn-Sham equation, our method is based on a range-split hybrid functional that uses exact long-range exchange. Its main novel feature is that the range-splitting parameter is not a universal constant but rather is determined from first principles, per system, based on satisfaction of the ionization potential theorem. For finite-sized objects, this DFT approach mimics successfully, to the best of our knowledge for the first time, the quasi-particle picture of many-body theory. Specifically, it allows for the extraction of both the fundamental and the optical gap from one underlying functional, based on the HOMO-LUMO gap of a ground-state DFT calculation and the lowest excitation energy of a linear-response time-dependent DFT calculation, respectively. In particular, it produces the correct optical gap for the difficult case of charge-transfer and charge-transfer-like scenarios, where conventional functionals are known to fail. In this perspective, we overview the formal and practical challenges associated with gap calculations, explain our new approach and how it overcomes previous difficulties, and survey its application to a variety of systems.
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Affiliation(s)
- Leeor Kronik
- Department of Materials and Interfaces, Weizmann Institute of Science , Rehovoth 76100, Israel
| | - Tamar Stein
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, Hebrew University , Jerusalem 91904 Israel
| | - Sivan Refaely-Abramson
- Department of Materials and Interfaces, Weizmann Institute of Science , Rehovoth 76100, Israel
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, Hebrew University , Jerusalem 91904 Israel
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