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Tancogne-Dejean N, Penz M, Laestadius A, Csirik MA, Ruggenthaler M, Rubio A. Exchange energies with forces in density-functional theory. J Chem Phys 2024; 160:024103. [PMID: 38189616 DOI: 10.1063/5.0177346] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2023] [Accepted: 12/12/2023] [Indexed: 01/09/2024] Open
Abstract
We propose exchanging the energy functionals in ground-state density-functional theory with physically equivalent exact force expressions as a new promising route toward approximations to the exchange-correlation potential and energy. In analogy to the usual energy-based procedure, we split the force difference between the interacting and auxiliary Kohn-Sham system into a Hartree, an exchange, and a correlation force. The corresponding scalar potential is obtained by solving a Poisson equation, while an additional transverse part of the force yields a vector potential. These vector potentials obey an exact constraint between the exchange and correlation contribution and can further be related to the atomic shell structure. Numerically, the force-based local-exchange potential and the corresponding exchange energy compare well with the numerically more involved optimized effective potential method. Overall, the force-based method has several benefits when compared to the usual energy-based approach and opens a route toward numerically inexpensive nonlocal and (in the time-dependent case) nonadiabatic approximations.
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Affiliation(s)
- Nicolas Tancogne-Dejean
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science and Department of Physics, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Markus Penz
- Department of Computer Science, Oslo Metropolitan University, 0130 Oslo, Norway
- Basic Research Community for Physics, Innsbruck, Austria
| | - Andre Laestadius
- Department of Computer Science, Oslo Metropolitan University, 0130 Oslo, Norway
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, 0315 Oslo, Norway
| | - Mihály A Csirik
- Department of Computer Science, Oslo Metropolitan University, 0130 Oslo, Norway
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, 0315 Oslo, Norway
| | - Michael Ruggenthaler
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science and Department of Physics, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science and Department of Physics, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
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Tarantino W, Ullrich CA. A reformulation of time-dependent Kohn-Sham theory in terms of the second time derivative of the density. J Chem Phys 2021; 154:204112. [PMID: 34241164 DOI: 10.1063/5.0039962] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The Kohn-Sham approach to time-dependent density-functional theory (TDDFT) can be formulated, in principle, exactly by invoking the force-balance equation for the density, which leads to an explicit expression for the exchange-correlation potential as an implicit density functional. It is shown that this suggests a reformulation of TDDFT in terms of the second time derivative of the density, rather than the density itself. The result is a time-local Kohn-Sham scheme of second-order in time whose causal structure is more transparent than that of the usual Kohn-Sham formalism. The scheme can be used to construct new approximations at the exchange-only level and beyond, and it offers a straightforward definition of the exact adiabatic approximation.
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Affiliation(s)
- Walter Tarantino
- Dipartimento di Fisica, Università degli Studi di Cagliari, Cittadella Universitaria, I-09042 Monserrato, Cagliari, Italy
| | - Carsten A Ullrich
- Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA
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Li X, Govind N, Isborn C, DePrince AE, Lopata K. Real-Time Time-Dependent Electronic Structure Theory. Chem Rev 2020; 120:9951-9993. [DOI: 10.1021/acs.chemrev.0c00223] [Citation(s) in RCA: 64] [Impact Index Per Article: 16.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195-1700, United States
| | - Niranjan Govind
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Christine Isborn
- Department of Chemistry and Chemical Biology, University of California, Merced, California 95343, United States
| | - A. Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - Kenneth Lopata
- Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, United States
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Lacombe L, Maitra NT. Developing new and understanding old approximations in TDDFT. Faraday Discuss 2020; 224:382-401. [PMID: 32926040 DOI: 10.1039/d0fd00049c] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
When a system has evolved far from a ground-state, the adiabatic approximations commonly used in time-dependent density functional theory calculations completely fail in some applications, while giving qualitatively good predictions in others, and sometimes even quantitative predictions. It is not clearly understood why this is so, and developing practical approximations going beyond the adiabatic approximation remains a challenge. This paper explores three different lines of investigation. First, an expression for the exact time-dependent exchange-correlation potential suggests that the accuracy of an adiabatic approximation is intimately related to the deviation between the natural orbital occupation numbers of the physical system and those of the Kohn-Sham system, and we explore this on some exactly-solvable model systems. The exact expression further suggests a path to go beyond the adiabatic approximations, and in the second part we discuss a newly proposed class of memory-dependent approximations developed in this way. Finally, we derive a new expression for the exact exchange-correlation potential from a coupling-constant path integration.
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Affiliation(s)
- Lionel Lacombe
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA.
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Tchenkoue MLM, Penz M, Theophilou I, Ruggenthaler M, Rubio A. Force balance approach for advanced approximations in density functional theories. J Chem Phys 2019; 151:154107. [DOI: 10.1063/1.5123608] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Affiliation(s)
- Mary-Leena M. Tchenkoue
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Markus Penz
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Iris Theophilou
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Michael Ruggenthaler
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
- Center for Computational Quantum Physics, The Flatiron Institute, New York, New York 10010, USA
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Nenov A, Segatta F, Bruner A, Mukamel S, Garavelli M. X-ray linear and non-linear spectroscopy of the ESCA molecule. J Chem Phys 2019; 151:114110. [DOI: 10.1063/1.5116699] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Affiliation(s)
- Artur Nenov
- Dipartimento di Chimica Industriale “Toso Montanari”, Università degli studi di Bologna, Viale del Risorgimento 4,
40136 Bologna, Italy
| | - Francesco Segatta
- Dipartimento di Chimica Industriale “Toso Montanari”, Università degli studi di Bologna, Viale del Risorgimento 4,
40136 Bologna, Italy
| | - Adam Bruner
- Department of Chemistry and Physics and Astronomy, University of California, Irvine, California 92697,
USA
| | - Shaul Mukamel
- Department of Chemistry and Physics and Astronomy, University of California, Irvine, California 92697,
USA
| | - Marco Garavelli
- Dipartimento di Chimica Industriale “Toso Montanari”, Università degli studi di Bologna, Viale del Risorgimento 4,
40136 Bologna, Italy
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