1
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Zhang Y, Ke D, Wu J, Zhang C, Hou L, Lin B, Chen Z, Perdew JP, Sun J. Challenges for density functional theory in simulating metal-metal singlet bonding: A case study of dimerized VO2. J Chem Phys 2024; 160:134101. [PMID: 38557836 DOI: 10.1063/5.0180315] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2023] [Accepted: 03/03/2024] [Indexed: 04/04/2024] Open
Abstract
VO2 is renowned for its electric transition from an insulating monoclinic (M1) phase, characterized by V-V dimerized structures, to a metallic rutile (R) phase above 340 K. This transition is accompanied by a magnetic change: the M1 phase exhibits a non-magnetic spin-singlet state, while the R phase exhibits a state with local magnetic moments. Simultaneous simulation of the structural, electric, and magnetic properties of this compound is of fundamental importance, but the M1 phase alone has posed a significant challenge to the density functional theory (DFT). In this study, we show none of the commonly used DFT functionals, including those combined with on-site Hubbard U to treat 3d electrons better, can accurately predict the V-V dimer length. The spin-restricted method tends to overestimate the strength of the V-V bonds, resulting in a small V-V bond length. Conversely, the spin-symmetry-breaking method exhibits the opposite trends. Each of these two bond-calculation methods underscores one of the two contentious mechanisms, i.e., Peierls lattice distortion or Mott localization due to electron-electron repulsion, involved in the metal-insulator transition in VO2. To elucidate the challenges encountered in DFT, we also employ an effective Hamiltonian that integrates one-dimensional magnetic sites, thereby revealing the inherent difficulties linked with the DFT computations.
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Affiliation(s)
- Yubo Zhang
- Minjiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou, China
| | - Da Ke
- Minjiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou, China
| | - Junxiong Wu
- Minjiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou, China
| | - Chutong Zhang
- Minjiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou, China
| | - Lin Hou
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
| | - Baichen Lin
- School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798, Republic of Singapore
- Institute of Materials Research and Engineering (IMRE), Agency for Science, Technology and Research (A*STAR), Singapore 138634, Republic of Singapore
| | - Zuhuang Chen
- School of Materials Science and Engineering, Harbin Institute of Technology, Shenzhen, Shenzhen 518055, China
- Flexible Printed Electronics Technology Center, Harbin Institute of Technology, Shenzhen, Shenzhen 518055, China
| | - John P Perdew
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
| | - Jianwei Sun
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
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2
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Xiao X, Zhao H, Ren J, Fang WH, Li Z. Physics-Constrained Hardware-Efficient Ansatz on Quantum Computers That Is Universal, Systematically Improvable, and Size-Consistent. J Chem Theory Comput 2024; 20:1912-1922. [PMID: 38354395 DOI: 10.1021/acs.jctc.3c00966] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/16/2024]
Abstract
Variational wave function ansätze are at the heart of solving quantum many-body problems in physics and chemistry. Previous designs of hardware-efficient ansatz (HEA) on quantum computers are largely based on heuristics and lack rigorous theoretical foundations. In this work, we introduce a physics-constrained approach for designing HEA with rigorous theoretical guarantees by imposing a few fundamental constraints. Specifically, we require that the target HEA to be universal, systematically improvable, and size-consistent, which is an important concept in quantum many-body theories for scalability but has been overlooked in previous designs of HEA. We extend the notion of size-consistency to HEA and present a concrete realization of HEA that satisfies all these fundamental constraints while only requiring linear qubit connectivity. The developed physics-constrained HEA is superior to other heuristically designed HEA in terms of both accuracy and scalability, as demonstrated numerically for the Heisenberg model and some typical molecules. In particular, we find that restoring size-consistency can significantly reduce the number of layers needed to reach a certain accuracy. In contrast, the failure of other HEA to satisfy these constraints severely limits their scalability to larger systems with more than 10 qubits. Our work highlights the importance of incorporating physical constraints into the design of HEA for efficiently solving many-body problems on quantum computers.
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Affiliation(s)
- Xiaoxiao Xiao
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Hewang Zhao
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Jiajun Ren
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Wei-Hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Zhendong Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
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3
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Goshen Y, Kraisler E. Ensemble Ground State of a Many-Electron System with Fractional Electron Number and Spin: Piecewise-Linearity and Flat-Plane Condition Generalized. J Phys Chem Lett 2024; 15:2337-2343. [PMID: 38386920 PMCID: PMC10926161 DOI: 10.1021/acs.jpclett.3c03509] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2023] [Revised: 02/05/2024] [Accepted: 02/09/2024] [Indexed: 02/24/2024]
Abstract
Description of many-electron systems with a fractional electron number (Ntot) and fractional spin (Mtot) is of great importance in physical chemistry, solid-state physics, and materials science. In this Letter, we provide an exact description of the zero-temperature ensemble ground state of a general, finite, many-electron system and characterize the dependence of the energy and the spin-densities on both Ntot and Mtot, when the total spin is at its equilibrium value. We generalize the piecewise-linearity principle and the flat-plane condition and determine which pure states contribute to the ground-state ensemble. We find a new derivative discontinuity, which manifests for spin variation at a constant Ntot, as a jump in the Kohn-Sham potential. We identify a previously unknown degeneracy of the ground state, such that the total energy and density are unique, but the spin-densities are not. Our findings serve as a basis for development of advanced approximations in density functional theory and other many-electron methods.
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Affiliation(s)
- Yuli Goshen
- Fritz Haber Research Center for Molecular
Dynamics and Institute of Chemistry, The
Hebrew University of Jerusalem, 9091401 Jerusalem, Israel
| | - Eli Kraisler
- Fritz Haber Research Center for Molecular
Dynamics and Institute of Chemistry, The
Hebrew University of Jerusalem, 9091401 Jerusalem, Israel
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4
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Laestadius A, Csirik MA, Penz M, Tancogne-Dejean N, Ruggenthaler M, Rubio A, Helgaker T. Exchange-only virial relation from the adiabatic connection. J Chem Phys 2024; 160:084115. [PMID: 38421067 DOI: 10.1063/5.0184934] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2023] [Accepted: 01/25/2024] [Indexed: 03/02/2024] Open
Abstract
The exchange-only virial relation due to Levy and Perdew is revisited. Invoking the adiabatic connection, we introduce the exchange energy in terms of the right-derivative of the universal density functional w.r.t. the coupling strength λ at λ = 0. This agrees with the Levy-Perdew definition of the exchange energy as a high-density limit of the full exchange-correlation energy. By relying on v-representability for a fixed density at varying coupling strength, we prove an exchange-only virial relation without an explicit local-exchange potential. Instead, the relation is in terms of a limit (λ ↘ 0) involving the exchange-correlation potential vxcλ, which exists by assumption of v-representability. On the other hand, a local-exchange potential vx is not warranted to exist as such a limit.
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Affiliation(s)
- 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
| | - Markus Penz
- Department of Computer Science, Oslo Metropolitan University, 0130 Oslo, Norway
- 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
| | - 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
| | - 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
| | - Trygve Helgaker
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, 0315 Oslo, Norway
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5
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Ning J, Lane C, Barbiellini B, Markiewicz RS, Bansil A, Ruzsinszky A, Perdew JP, Sun J. Comparing first-principles density functionals plus corrections for the lattice dynamics of YBa2Cu3O6. J Chem Phys 2024; 160:064106. [PMID: 38341785 DOI: 10.1063/5.0181349] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2023] [Accepted: 01/15/2024] [Indexed: 02/13/2024] Open
Abstract
The enigmatic mechanism underlying unconventional high-temperature superconductivity, especially the role of lattice dynamics, has remained a subject of debate. Theoretical insights have long been hindered due to the lack of an accurate first-principles description of the lattice dynamics of cuprates. Recently, using the r2SCAN meta-generalized gradient approximation (meta-GGA) functional, we have been able to achieve accurate phonon spectra of an insulating cuprate YBa2Cu3O6 and discover significant magnetoelastic coupling in experimentally interesting Cu-O bond stretching optical modes [Ning et al., Phys. Rev. B 107, 045126 (2023)]. We extend this work by comparing Perdew-Burke-Ernzerhof and r2SCAN performances with corrections from the on-site Hubbard U and the D4 van der Waals (vdW) methods, aiming at further understanding on both the materials science side and the density functional side. We demonstrate the importance of vdW and self-interaction corrections for accurate first-principles YBa2Cu3O6 lattice dynamics. Since r2SCAN by itself partially accounts for these effects, the good performance of r2SCAN is now more fully explained. In addition, the performances of the Tao-Mo series of meta-GGAs, which are constructed in a different way from the strongly constrained and appropriately normed (SCAN) meta-GGA and its revised version r2SCAN, are also compared and discussed.
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Affiliation(s)
- Jinliang Ning
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
| | - Christopher Lane
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Bernardo Barbiellini
- Department of Physics, School of Engineering Science, LUT University, FI-53851 Lappeenranta, Finland
- Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA
| | - Robert S Markiewicz
- Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA
| | - Arun Bansil
- Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA
| | - Adrienn Ruzsinszky
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
| | - John P Perdew
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
| | - Jianwei Sun
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
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6
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Yu JM, Tsai J, Rajabi A, Rappoport D, Furche F. Natural determinant reference functional theory. J Chem Phys 2024; 160:044102. [PMID: 38252940 DOI: 10.1063/5.0180319] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2023] [Accepted: 12/27/2023] [Indexed: 01/24/2024] Open
Abstract
The natural determinant reference (NDR) or principal natural determinant is the Slater determinant comprised of the N most strongly occupied natural orbitals of an N-electron state of interest. Unlike the Kohn-Sham (KS) determinant, which yields the exact ground-state density, the NDR only yields the best idempotent approximation to the interacting one-particle reduced density matrix, but it is well-defined in common atom-centered basis sets and is representation-invariant. We show that the under-determination problem of prior attempts to define a ground-state energy functional of the NDR is overcome in a grand-canonical ensemble framework at the zero-temperature limit. The resulting grand potential functional of the NDR ensemble affords the variational determination of the ground state energy, its NDR (ensemble), and select ionization potentials and electron affinities. The NDR functional theory can be viewed as an "exactification" of orbital optimization and empirical generalized KS methods. NDR functionals depending on the noninteracting Hamiltonian do not require troublesome KS-inversion or optimized effective potentials.
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Affiliation(s)
- Jason M Yu
- Department of Chemistry, University of California Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Jeffrey Tsai
- Department of Chemistry, University of California Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Ahmadreza Rajabi
- Department of Chemistry, University of California Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Dmitrij Rappoport
- Department of Chemistry, University of California Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Filipp Furche
- Department of Chemistry, University of California Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
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7
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Shi Y, Shi Y, Wasserman A. Stretching Bonds without Breaking Symmetries in Density Functional Theory. J Phys Chem Lett 2024; 15:826-833. [PMID: 38232318 DOI: 10.1021/acs.jpclett.3c03073] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2024]
Abstract
Kohn-Sham density functional theory (KS-DFT) stands out among electronic structure methods due to its balance of accuracy and computational efficiency. However, to achieve chemically accurate energies, standard density functional approximations in KS-DFT often need to break underlying symmetries, a long-standing "symmetry dilemma". By employing fragment spin densities as the main variables in calculations (rather than total molecular densities, as in KS-DFT), we present an embedding framework in which this symmetry dilemma is understood and partially resolved. The spatial overlap between fragment densities is used as the main ingredient to construct a simple, physically motivated approximation to a universal functional of the fragment densities. This "overlap approximation" is shown to significantly improve semilocal KS-DFT binding energies of molecules without artificially breaking either charge or spin symmetries. The approach is shown to be applicable to covalently bonded molecules and to systems of the "strongly correlated" type.
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Affiliation(s)
- Yuming Shi
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, United States
| | - Yi Shi
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Adam Wasserman
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, United States
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
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8
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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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9
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Kanungo B, Kaplan AD, Shahi C, Gavini V, Perdew JP. Unconventional Error Cancellation Explains the Success of Hartree-Fock Density Functional Theory for Barrier Heights. J Phys Chem Lett 2024; 15:323-328. [PMID: 38170179 DOI: 10.1021/acs.jpclett.3c03088] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2024]
Abstract
Energy barriers, which control the rates of chemical reactions, are seriously underestimated by computationally efficient semilocal approximations for the exchange-correlation energy. The accuracy of a semilocal density functional approximation is strongly boosted for reaction barrier heights by evaluating that approximation non-self-consistently on Hartree-Fock electron densities, which has been known for ∼30 years. The conventional explanation is that the Hartree-Fock theory yields the more accurate density. This work presents a benchmark Kohn-Sham inversion of accurate coupled-cluster densities for the reaction H2 + F → HHF → H + HF and finds a strong, understandable cancellation between positive (excessively overcorrected) density-driven and large negative functional-driven errors (expected from stretched radical bonds in the transition state) within this Hartree-Fock density functional theory. This confirms earlier conclusions (Kaplan, A. D., et al. J. Chem. Theory Comput. 2023, 19, 532-543) based on 76 barrier heights and three less reliable, but less expensive, fully nonlocal density functional proxies for the exact density.
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Affiliation(s)
- Bikash Kanungo
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Aaron D Kaplan
- Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Chandra Shahi
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, United States
| | - Vikram Gavini
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - John P Perdew
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, United States
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10
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Perdew JP. My life in science: Lessons for yours? J Chem Phys 2024; 160:010402. [PMID: 38180261 DOI: 10.1063/5.0179606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2023] [Accepted: 10/26/2023] [Indexed: 01/06/2024] Open
Abstract
Because of an acquired obsession to understand as much as possible in a limited but important area of science and because of optimism, luck, and help from others, my life in science turned out to be much better than I or others could have expected or planned. This is the story of how that happened, and also the story of the groundstate density functional theory of electronic structure, told from a personal perspective.
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Affiliation(s)
- John P Perdew
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
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11
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Daas KJ, Kooi DP, Benyahia T, Seidl M, Gori-Giorgi P. Large-Z atoms in the strong-interaction limit of DFT: Implications for gradient expansions and for the Lieb-Oxford bound. J Chem Phys 2023; 159:234114. [PMID: 38112505 DOI: 10.1063/5.0174592] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2023] [Accepted: 11/26/2023] [Indexed: 12/21/2023] Open
Abstract
We numerically study the strong-interaction limit of the exchange-correlation functional for neutral atoms and Bohr atoms as the number of electrons increases. Using a compact representation, we analyze the second-order gradient expansion, comparing it with the one for exchange (weak interaction limit). The two gradient expansions, at strong and weak interaction, turn out to be very similar in magnitude but with opposite signs. We find that the point-charge plus continuum model is surprisingly accurate for the gradient expansion coefficient at strong coupling, while generalized gradient approximations, such as Perdew-Burke-Ernzerhof (PBE) and PBEsol, severely underestimate it. We then use our results to analyze the Lieb-Oxford bound from the point of view of slowly varying densities, clarifying some aspects on the bound at a fixed number of electrons.
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Affiliation(s)
- Kimberly J Daas
- Department of Chemistry and Pharmaceutical Sciences, Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Derk P Kooi
- Department of Chemistry and Pharmaceutical Sciences, Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
- Microsoft Research AI4Science, Amsterdam, The Netherlands
| | - Tarik Benyahia
- Department of Chemistry and Pharmaceutical Sciences, Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Michael Seidl
- Department of Chemistry and Pharmaceutical Sciences, Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Paola Gori-Giorgi
- Department of Chemistry and Pharmaceutical Sciences, Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
- Microsoft Research AI4Science, Amsterdam, The Netherlands
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12
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Burgess AC, Linscott E, O'Regan DD. The convexity condition of density-functional theory. J Chem Phys 2023; 159:211102. [PMID: 38038199 DOI: 10.1063/5.0174159] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2023] [Accepted: 11/08/2023] [Indexed: 12/02/2023] Open
Abstract
It has long been postulated that within density-functional theory (DFT), the total energy of a finite electronic system is convex with respect to electron count so that 2Ev[N0] ≤ Ev[N0 - 1] + Ev[N0 + 1]. Using the infinite-separation-limit technique, this Communication proves the convexity condition for any formulation of DFT that is (1) exact for all v-representable densities, (2) size-consistent, and (3) translationally invariant. An analogous result is also proven for one-body reduced density matrix functional theory. While there are known DFT formulations in which the ground state is not always accessible, indicating that convexity does not hold in such cases, this proof, nonetheless, confirms a stringent constraint on the exact exchange-correlation functional. We also provide sufficient conditions for convexity in approximate DFT, which could aid in the development of density-functional approximations. This result lifts a standing assumption in the proof of the piecewise linearity condition with respect to electron count, which has proven central to understanding the Kohn-Sham bandgap and the exchange-correlation derivative discontinuity of DFT.
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Affiliation(s)
- Andrew C Burgess
- School of Physics, Trinity College Dublin, The University of Dublin, Dublin, Ireland
| | - Edward Linscott
- Theory and Simulation of Materials (THEOS), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - David D O'Regan
- School of Physics, Trinity College Dublin, The University of Dublin, Dublin, Ireland
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13
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Pederson R, Burke K. The difference between molecules and materials: Reassessing the role of exact conditions in density functional theory. J Chem Phys 2023; 159:214113. [PMID: 38054515 DOI: 10.1063/5.0172058] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2023] [Accepted: 11/12/2023] [Indexed: 12/07/2023] Open
Abstract
Exact conditions have long been used to guide the construction of density functional approximations. However, hundreds of empirical-based approximations tailored for chemistry are in use, of which many neglect these conditions in their design. We analyze well-known conditions and revive several obscure ones. Two crucial distinctions are drawn: that between necessary and sufficient conditions and that between all electronic densities and the subset of realistic Coulombic ground states. Simple search algorithms find that many empirical approximations satisfy many exact conditions for realistic densities and non-empirical approximations satisfy even more conditions than those enforced in their construction. The role of exact conditions in developing approximations is revisited.
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Affiliation(s)
- Ryan Pederson
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
| | - Kieron Burke
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
- Department of Chemistry, University of California, Irvine, California 92697, USA
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14
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Dar DB, Maitra NT. Oscillator strengths and excited-state couplings for double excitations in time-dependent density functional theory. J Chem Phys 2023; 159:211104. [PMID: 38038212 DOI: 10.1063/5.0176705] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Accepted: 11/08/2023] [Indexed: 12/02/2023] Open
Abstract
Although useful to extract excitation energies of states of double-excitation character in time-dependent density functional theory that are missing in the adiabatic approximation, the frequency-dependent kernel derived earlier [Maitra et al., J. Chem. Phys. 120, 5932 (2004)] was not designed to yield oscillator strengths. These are required to fully determine linear absorption spectra, and they also impact excited-to-excited-state couplings that appear in dynamics simulations and other quadratic response properties. Here, we derive a modified non-adiabatic kernel that yields both accurate excitation energies and oscillator strengths for these states. We demonstrate its performance on a model two-electron system, the Be atom, and on excited-state transition dipoles in the LiH molecule at stretched bond-lengths, in all cases producing significant improvements over the traditional approximations.
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Affiliation(s)
- Davood B Dar
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
| | - Neepa T Maitra
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
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15
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Palos E, Caruso A, Paesani F. Consistent density functional theory-based description of ion hydration through density-corrected many-body representations. J Chem Phys 2023; 159:181101. [PMID: 37947509 DOI: 10.1063/5.0174577] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2023] [Accepted: 10/23/2023] [Indexed: 11/12/2023] Open
Abstract
Delocalization error constrains the accuracy of density functional theory in describing molecular interactions in ion-water systems. Using Na+ and Cl- in water as model systems, we calculate the effects of delocalization error in the SCAN functional for describing ion-water and water-water interactions in hydrated ions, and demonstrate that density-corrected SCAN (DC-SCAN) predicts n-body and interaction energies with an accuracy approaching coupled cluster theory. The performance of DC-SCAN is size-consistent, maintaining an accurate description of molecular interactions well beyond the first solvation shell. Molecular dynamics simulations at ambient conditions with many-body MB-SCAN(DC) potentials, derived from the many-body expansion, predict the solvation structure of Na+ and Cl- in quantitative agreement with reference data, while simultaneously reproducing the structure of liquid water. Beyond rationalizing the accuracy of density-corrected models of ion hydration, our findings suggest that our unified density-corrected MB formalism holds great promise for efficient DFT-based simulations of condensed-phase systems with chemical accuracy.
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Affiliation(s)
- Etienne Palos
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | - Alessandro Caruso
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
- Materials Science and Engineering, University of California San Diego, La Jolla, California 92093, USA
- San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093, USA
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16
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Bosko IP, Staroverov VN. Derivation and reinterpretation of the Fermi-Amaldi functional. J Chem Phys 2023; 159:131101. [PMID: 37800642 DOI: 10.1063/5.0166358] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2023] [Accepted: 09/13/2023] [Indexed: 10/07/2023] Open
Abstract
The Fermi-Amaldi correction to the electrostatic self-repulsion of the particle density is usually regarded as a semi-classical exchange functional that happens to be exact only for one- and closed-shell two-electron systems. We show that this functional can be derived quantum-mechanically and is exact for any number of fermions or bosons of arbitrary spin as long as the particles occupy the same spatial orbital. The Fermi-Amaldi functional is also size-consistent for such systems, provided that the factor N in its expression is understood as an orbital occupation number rather than the total number of particles. These properties of the Fermi-Amaldi functional are ultimately related to the fact that it is a special case of the self-exchange energy formula. Implications of our findings are discussed.
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Affiliation(s)
- Ivan P Bosko
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
| | - Viktor N Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
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17
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Kothakonda M, Kaplan AD, Isaacs EB, Bartel CJ, Furness JW, Ning J, Wolverton C, Perdew JP, Sun J. Testing the r 2SCAN Density Functional for the Thermodynamic Stability of Solids with and without a van der Waals Correction. ACS MATERIALS AU 2023; 3:102-111. [PMID: 38089726 PMCID: PMC9999476 DOI: 10.1021/acsmaterialsau.2c00059] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2022] [Revised: 10/27/2022] [Accepted: 10/28/2022] [Indexed: 01/23/2024]
Abstract
A central aim of materials discovery is an accurate and numerically reliable description of thermodynamic properties, such as the enthalpies of formation and decomposition. The r2SCAN revision of the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA) balances numerical stability with high general accuracy. To assess the r2SCAN description of solid-state thermodynamics, we evaluate the formation and decomposition enthalpies, equilibrium volumes, and fundamental band gaps of more than 1000 solids using r2SCAN, SCAN, and PBE, as well as two dispersion-corrected variants, SCAN+rVV10 and r2SCAN+rVV10. We show that r2SCAN achieves accuracy comparable to SCAN and often improves upon SCAN's already excellent accuracy. Although SCAN+rVV10 is often observed to worsen the formation enthalpies of SCAN and makes no substantial correction to SCAN's cell volume predictions, r2SCAN+rVV10 predicts marginally less accurate formation enthalpies than r2SCAN, and slightly more accurate cell volumes than r2SCAN. The average absolute errors in predicted formation enthalpies are found to decrease by a factor of 1.5 to 2.5 from the GGA level to the meta-GGA level. Smaller decreases in error are observed for decomposition enthalpies. For formation enthalpies r2SCAN improves over SCAN for intermetallic systems. For a few classes of systems-transition metals, intermetallics, weakly bound solids, and enthalpies of decomposition into compounds-GGAs are comparable to meta-GGAs. In total, r2SCAN and r2SCAN+rVV10 can be recommended as stable, general-purpose meta-GGAs for materials discovery.
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Affiliation(s)
- Manish Kothakonda
- Department
of Physics and Engineering Physics, Tulane
University, New Orleans, Louisiana70118, United States
| | - Aaron D. Kaplan
- Department
of Physics, Temple University, Philadelphia, Pennsylvania19122, United States
| | - Eric B. Isaacs
- HRL
Laboratories, LLC, Malibu, California90265, United States
| | - Christopher J. Bartel
- Department
of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota55455, United States
| | - James W. Furness
- Department
of Physics and Engineering Physics, Tulane
University, New Orleans, Louisiana70118, United States
| | - Jinliang Ning
- Department
of Physics and Engineering Physics, Tulane
University, New Orleans, Louisiana70118, United States
| | - Chris Wolverton
- Department
of Materials Science and Engineering, Northwestern
University, Evanston, Illinois60208, United States
| | - John P. Perdew
- Department
of Physics, Temple University, Philadelphia, Pennsylvania19122, United States
| | - Jianwei Sun
- Department
of Physics and Engineering Physics, Tulane
University, New Orleans, Louisiana70118, United States
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