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Jana S, Constantin LA, Samal P. Density functional applications of jellium with a local gap model correlation energy functional. J Chem Phys 2023; 159:114109. [PMID: 37721324 DOI: 10.1063/5.0160961] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2023] [Accepted: 08/31/2023] [Indexed: 09/19/2023] Open
Abstract
We develop a realistic density functional approximation for the local gap, which is based on a semilocal indicator that shows good screening properties. The local band model has remarkable density scaling behaviors and works properly for the helium isoelectronic series for the atoms of the Periodic Table, as well as for the non-relativistic noble atom series (up to 2022 e-). Due to these desirable properties, we implement the local gap model in the jellium-with-gap correlation energy, developing the local-density-approximation-with-gap correlation functional (named LDAg) that correctly gives correlation energies of atoms comparable with the LDA ones but shows an improvement for ionization potential of atoms and molecules. Thus, LDAg seems to be an interesting and useful tool in density functional theory.
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Affiliation(s)
- Subrata Jana
- Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovoth 76100, Israel
| | - Lucian A Constantin
- Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
| | - Prasanjit Samal
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
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Kraisler E. Asymptotic Behavior of the Exchange‐Correlation Energy Density and the Kohn‐Sham Potential in Density Functional Theory: Exact Results and Strategy for Approximations. Isr J Chem 2020. [DOI: 10.1002/ijch.201900103] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Eli Kraisler
- Fritz Haber Center for Molecular Dynamics and Institute of Chemistry The Hebrew University of Jerusalem 9091401 Jerusalem Israel
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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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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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Chiodo L, Constantin LA, Fabiano E, Della Sala F. Nonuniform scaling applied to surface energies of transition metals. PHYSICAL REVIEW LETTERS 2012; 108:126402. [PMID: 22540602 DOI: 10.1103/physrevlett.108.126402] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2011] [Indexed: 05/31/2023]
Abstract
We construct a generalized gradient approximation of the exchange-correlation energy that satisfies the nonuniform scaling in one dimension and is accurate in the whole quasi-two-dimensional (Q2D) regime. Using spatial and energetic analyses of metal (111) surfaces, we show that the Q2D behavior is important at the surface of most transition metals, and that the here proposed Q2D-generalized gradient approximation functional predicts for these metals accurate surface energies as well as bulk properties.
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Affiliation(s)
- Letizia Chiodo
- Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, and European Theoretical Spectroscopy Facility (ETSF), Via Barsanti, I-73010 Arnesano, Italy
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Perdew JP, Tao J. When does static correlation scale to the high-density limit as exchange does? ACTA ACUST UNITED AC 2010. [DOI: 10.1016/j.theochem.2009.09.006] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Constantin LA, Perdew JP, Pitarke JM. Collapse of the electron gas to two dimensions in density functional theory. PHYSICAL REVIEW LETTERS 2008; 101:016406. [PMID: 18764133 DOI: 10.1103/physrevlett.101.016406] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2008] [Indexed: 05/26/2023]
Abstract
Local and semilocal density functional approximations for the exchange-correlation energy fail badly in the zero-thickness limit of a quasi-two-dimensional electron gas, where the density variation is rapid almost everywhere. Here we show that a fully nonlocal fifth-rung functional, the inhomogeneous Singwi-Tosi-Land-Sjölander (STLS) approach, which employs both occupied and unoccupied Kohn-Sham orbitals, recovers the true two-dimensional STLS limit and appears to be remarkably accurate for any thickness of the slab (and thus for the dimensional crossover). We also show that this good behavior is only partly due to the use of the full exact exchange energy.
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Affiliation(s)
- Lucian A Constantin
- Department of Physics and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118, USA
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Perdew JP, Ruzsinszky A, Tao J, Staroverov VN, Scuseria GE, Csonka GI. Prescription for the design and selection of density functional approximations: more constraint satisfaction with fewer fits. J Chem Phys 2007; 123:62201. [PMID: 16122287 DOI: 10.1063/1.1904565] [Citation(s) in RCA: 464] [Impact Index Per Article: 27.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present the case for the nonempirical construction of density functional approximations for the exchange-correlation energy by the traditional method of "constraint satisfaction" without fitting to data sets, and present evidence that this approach has been successful on the first three rungs of "Jacob's ladder" of density functional approximations [local spin-density approximation (LSD), generalized gradient approximation (GGA), and meta-GGA]. We expect that this approach will also prove successful on the fourth and fifth rungs (hyper-GGA or hybrid and generalized random-phase approximation). In particular, we argue for the theoretical and practical importance of recovering the correct uniform density limit, which many semiempirical functionals fail to do. Among the beyond-LSD functionals now available to users, we recommend the nonempirical Perdew-Burke-Ernzerhof (PBE) GGA and the nonempirical Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA, and their one-parameter hybrids with exact exchange. TPSS improvement over PBE is dramatic for atomization energies of molecules and surface energies of solids, and small or moderate for other properties. TPSS is now or soon will be available in standard codes such as GAUSSIAN, TURBOMOLE, NWCHEM, ADF, WIEN, VASP, etc. We also discuss old and new ideas to eliminate the self-interaction error that plagues the functionals on the first three rungs of the ladder, bring up other related issues, and close with a list of "do's and don't's" for software developers and users.
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Affiliation(s)
- John P Perdew
- Department of Physics and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118, USA
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Perdew JP, Tao J, Staroverov VN, Scuseria GE. Meta-generalized gradient approximation: Explanation of a realistic nonempirical density functional. J Chem Phys 2004; 120:6898-911. [PMID: 15267588 DOI: 10.1063/1.1665298] [Citation(s) in RCA: 318] [Impact Index Per Article: 15.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Tao, Perdew, Staroverov, and Scuseria (TPSS) have constructed a nonempirical meta-generalized gradient approximation (meta-GGA) [Phys. Rev. Lett. 91, 146401 (2003)] for the exchange-correlation energy, imposing exact constraints relevant to the paradigm densities of condensed matter physics and quantum chemistry. Results of their extensive tests on molecules, solids, and solid surfaces are encouraging, suggesting that this density functional achieves uniform accuracy for diverse properties and systems. In the present work, this functional is explained and details of its construction are presented. In particular, the functional is constructed to yield accurate energies under uniform coordinate scaling to the low-density or strong-interaction limit. Its nonlocality is displayed by plotting the factor F(xc) that gives the enhancement relative to the local density approximation for exchange. We also discuss an apparently harmless order-of-limits problem in the meta-GGA. The performance of this functional is investigated for exchange and correlation energies and shell-removal energies of atoms and ions. Non-self-consistent molecular atomization energies and bond lengths of the TPSS meta-GGA, calculated with GGA orbitals and densities, agree well with those calculated self-consistently. We suggest that satisfaction of additional exact constraints on higher rungs of a ladder of density functional approximations can lead to further progress.
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Affiliation(s)
- John P Perdew
- Department of Physics and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118, USA
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Pino R. Application of the scaling properties of the correlation energy functional to local and gradient-dependent forms. Chem Phys Lett 2000. [DOI: 10.1016/s0009-2614(00)00476-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Erhard S, Gross EK. Scaling and virial theorems in current-density-functional theory. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1996; 53:R5-R8. [PMID: 9912928 DOI: 10.1103/physreva.53.r5] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Wilson LC. Development of non-local Wigner-like correlation-energy density functionals through coordinate scaling requirements and evaluation of contraint obedience in the construction of density functionals. Chem Phys 1994. [DOI: 10.1016/0301-0104(93)e0444-z] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Levy M, Perdew JP. Tight bound and convexity constraint on the exchange-correlation-energy functional in the low-density limit, and other formal tests of generalized-gradient approximations. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:11638-11645. [PMID: 10007499 DOI: 10.1103/physrevb.48.11638] [Citation(s) in RCA: 90] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Görling A, Levy M. Correlation-energy functional and its high-density limit obtained from a coupling-constant perturbation expansion. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:13105-13113. [PMID: 10005612 DOI: 10.1103/physrevb.47.13105] [Citation(s) in RCA: 232] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Görling A, Levy M. Requirements for correlation energy density functionals from coordinate transformations. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:1509-1517. [PMID: 9907133 DOI: 10.1103/physreva.45.1509] [Citation(s) in RCA: 40] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Levy M. Density-functional exchange correlation through coordinate scaling in adiabatic connection and correlation hole. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 43:4637-4646. [PMID: 9905580 DOI: 10.1103/physreva.43.4637] [Citation(s) in RCA: 147] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Levy M, Ou-Yang H. Nonuniform coordinate scaling requirements for exchange-correlation energy. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 42:651-652. [PMID: 9903847 DOI: 10.1103/physreva.42.651] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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