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Shi Y, Chávez VH, Wasserman A. n2v
: A density‐to‐potential inversion suite. A sandbox for creating, testing, and benchmarking density functional theory inversion methods. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1617] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Yuming Shi
- Department of Physics and Astronomy Purdue University West Lafayette Indiana USA
| | - Victor H. Chávez
- Department of Chemistry Purdue University West Lafayette Indiana USA
| | - Adam Wasserman
- Department of Physics and Astronomy Purdue University West Lafayette Indiana USA
- Department of Chemistry Purdue University West Lafayette Indiana USA
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Schäfer C, Buchholz F, Penz M, Ruggenthaler M, Rubio A. Making ab initio QED functional(s): Nonperturbative and photon-free effective frameworks for strong light-matter coupling. Proc Natl Acad Sci U S A 2021; 118:e2110464118. [PMID: 34625493 PMCID: PMC8521676 DOI: 10.1073/pnas.2110464118] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 08/18/2021] [Indexed: 11/30/2022] Open
Abstract
Strong light-matter coupling provides a promising path for the control of quantum matter where the latter is routinely described from first principles. However, combining the quantized nature of light with this ab initio tool set is challenging and merely developing as the coupled light-matter Hilbert space is conceptually different and computational cost quickly becomes overwhelming. In this work, we provide a nonperturbative photon-free formulation of quantum electrodynamics (QED) in the long-wavelength limit, which is formulated solely on the matter Hilbert space and can serve as an accurate starting point for such ab initio methods. The present formulation is an extension of quantum mechanics that recovers the exact results of QED for the zero- and infinite-coupling limit and the infinite-frequency as well as the homogeneous limit, and we can constructively increase its accuracy. We show how this formulation can be used to devise approximations for quantum-electrodynamical density-functional theory (QEDFT), which in turn also allows us to extend the ansatz to the full minimal-coupling problem and to nonadiabatic situations. Finally, we provide a simple local density-type functional that takes the strong coupling to the transverse photon degrees of freedom into account and includes the correct frequency and polarization dependence. This QEDFT functional accounts for the quantized nature of light while remaining computationally simple enough to allow its application to a large range of systems. All approximations allow the seamless application to periodic systems.
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Affiliation(s)
- Christian Schäfer
- Department of Physics, Max Planck Institute for the Structure and Dynamics of Matter, Center for Free-Electron Laser Science, 22 761 Hamburg, Germany;
- The Hamburg Center for Ultrafast Imaging, 22 761 Hamburg, Germany
- Department of Physics, Chalmers University of Technology, 412 96 Göteborg, Sweden
- Department of Microtechnology and Nanoscience - MC2, Chalmers University of Technology, 412 96 Göteborg, Sweden
| | - Florian Buchholz
- Department of Physics, Max Planck Institute for the Structure and Dynamics of Matter, Center for Free-Electron Laser Science, 22 761 Hamburg, Germany
| | - Markus Penz
- Department of Mathematics, University of Innsbruck, A-6020 Innsbruck, Austria
| | - Michael Ruggenthaler
- Department of Physics, Max Planck Institute for the Structure and Dynamics of Matter, Center for Free-Electron Laser Science, 22 761 Hamburg, Germany
- The Hamburg Center for Ultrafast Imaging, 22 761 Hamburg, Germany
| | - Angel Rubio
- Department of Physics, Max Planck Institute for the Structure and Dynamics of Matter, Center for Free-Electron Laser Science, 22 761 Hamburg, Germany;
- The Hamburg Center for Ultrafast Imaging, 22 761 Hamburg, Germany
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Shi Y, Wasserman A. Inverse Kohn-Sham Density Functional Theory: Progress and Challenges. J Phys Chem Lett 2021; 12:5308-5318. [PMID: 34061541 DOI: 10.1021/acs.jpclett.1c00752] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Inverse Kohn-Sham (iKS) methods are needed to fully understand the one-to-one mapping between densities and potentials on which density functional theory is based. They can contribute to the construction of empirical exchange-correlation functionals and to the development of techniques for density-based embedding. Unlike the forward Kohn-Sham problems, numerical iKS problems are ill-posed and can be unstable. We discuss some of the fundamental and practical difficulties of iKS problems with constrained-optimization methods on finite basis sets. Various factors that affect the performance are systematically compared and discussed, both analytically and numerically, with a focus on two of the most practical methods: the Wu-Yang method (WY) and the partial differential equation constrained optimization (PDE-CO). Our analysis of the WY and PDE-CO highlights the limitation of finite basis sets. We introduce new ideas to make iKS problems more tractable, provide an overall strategy for performing numerical density-to-potential inversions, and discuss challenges and future directions.
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Affiliation(s)
- Yuming Shi
- Department of Physics and Astronomy, 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
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, United States
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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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Detailed investigation of N-(4-n-pentyl-oxybenzylidene)-4′-n-hexylaniline liquid crystal molecule. J Mol Struct 2019. [DOI: 10.1016/j.molstruc.2019.06.068] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
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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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Lacombe L, Maitra NT. Density-Matrix Coupled Time-Dependent Exchange-Correlation Functional Approximations. J Chem Theory Comput 2019; 15:1672-1678. [DOI: 10.1021/acs.jctc.8b01159] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Lionel Lacombe
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, United States
| | - Neepa T. Maitra
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, United States
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Theophilou I, Buchholz F, Eich FG, Ruggenthaler M, Rubio A. Kinetic-Energy Density-Functional Theory on a Lattice. J Chem Theory Comput 2018; 14:4072-4087. [PMID: 29969552 PMCID: PMC6096452 DOI: 10.1021/acs.jctc.8b00292] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
We
present a kinetic-energy density-functional theory and the corresponding
kinetic-energy Kohn–Sham (keKS) scheme on a lattice and show
that, by including more observables explicitly in a density-functional
approach, already simple approximation strategies lead to very accurate
results. Here, we promote the kinetic-energy density to a fundamental
variable alongside the density and show for specific cases (analytically
and numerically) that there is a one-to-one correspondence between
the external pair of on-site potential and site-dependent hopping
and the internal pair of density and kinetic-energy density. On the
basis of this mapping, we establish two unknown effective fields,
the mean-field exchange-correlation potential and the mean-field exchange-correlation
hopping, which force the keKS system to generate the same kinetic-energy
density and density as the fully interacting one. We show, by a decomposition
based on the equations of motions for the density and the kinetic-energy
density, that we can construct simple orbital-dependent functionals
that outperform the corresponding exact-exchange Kohn–Sham
(KS) approximation of standard density-functional theory. We do so
by considering the exact KS and keKS systems and comparing the unknown
correlation contributions as well as by comparing self-consistent
calculations based on the mean-field exchange (for the effective potential)
and a uniform (for the effective hopping) approximation for the keKS
and the exact-exchange approximation for the KS system, respectively.
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Affiliation(s)
- Iris Theophilou
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free Electron Laser Science , Hamburg 22761 , Germany
| | - Florian Buchholz
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free Electron Laser Science , Hamburg 22761 , Germany
| | - F G Eich
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free Electron Laser Science , Hamburg 22761 , Germany
| | - Michael Ruggenthaler
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free Electron Laser Science , Hamburg 22761 , Germany
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free Electron Laser Science , Hamburg 22761 , Germany.,Center for Computational Quantum Physics (CCQ) , Flatiron Institute , New York , New York 10010 , United States
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Fuks JI, Lacombe L, Nielsen SEB, Maitra NT. Exploring non-adiabatic approximations to the exchange–correlation functional of TDDFT. Phys Chem Chem Phys 2018; 20:26145-26160. [DOI: 10.1039/c8cp03957g] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Decomposition of the exact time-dependent exchange–correlation potential offers a new starting point to build approximations with memory.
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Affiliation(s)
- Johanna I. Fuks
- Departamento de Física and IFIBA
- FCEN
- Universidad de Buenos Aires
- Ciudad Universitaria
- C1428EHA Ciudad de Buenos Aires
| | - Lionel Lacombe
- Department of Physics and Astronomy
- Hunter College and the Graduate Center of the City University of New York
- New York
- USA
| | - Søren E. B. Nielsen
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science
- 22761 Hamburg
- Germany
| | - Neepa T. Maitra
- Department of Physics and Astronomy
- Hunter College and the Graduate Center of the City University of New York
- New York
- USA
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Suzuki Y, Lacombe L, Watanabe K, Maitra NT. Exact Time-Dependent Exchange-Correlation Potential in Electron Scattering Processes. PHYSICAL REVIEW LETTERS 2017; 119:263401. [PMID: 29328727 DOI: 10.1103/physrevlett.119.263401] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2017] [Indexed: 06/07/2023]
Abstract
We identify peak and valley structures in the exact exchange-correlation potential of time-dependent density functional theory that are crucial for time-resolved electron scattering in a model one-dimensional system. These structures are completely missed by adiabatic approximations that, consequently, significantly underestimate the scattering probability. A recently proposed nonadiabatic approximation is shown to correctly capture the approach of the electron to the target when the initial Kohn-Sham state is chosen judiciously, and it is more accurate than standard adiabatic functionals but ultimately fails to accurately capture reflection. These results may explain the underestimation of scattering probabilities in some recent studies on molecules and surfaces.
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Affiliation(s)
- Yasumitsu Suzuki
- Department of Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
| | - Lionel Lacombe
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Kazuyuki Watanabe
- Department of Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
| | - Neepa T Maitra
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
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Maitra NT. Charge transfer in time-dependent density functional theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:423001. [PMID: 28766507 DOI: 10.1088/1361-648x/aa836e] [Citation(s) in RCA: 58] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Charge transfer plays a crucial role in many processes of interest in physics, chemistry, and bio-chemistry. In many applications the size of the systems involved calls for time-dependent density functional theory (TDDFT) to be used in their computational modeling, due to its unprecedented balance between accuracy and efficiency. However, although exact in principle, in practise approximations must be made for the exchange-correlation functional in this theory, and the standard functional approximations perform poorly for excitations which have a long-range charge-transfer component. Intense progress has been made in developing more sophisticated functionals for this problem, which we review. We point out an essential difference between the properties of the exchange-correlation kernel needed for an accurate description of charge-transfer between open-shell fragments and between closed-shell fragments. We then turn to charge-transfer dynamics, which, in contrast to the excitation problem, is a highly non-equilibrium, non-perturbative, process involving a transfer of one full electron in space. This turns out to be a much more challenging problem for TDDFT functionals. We describe dynamical step and peak features in the exact functional evolving over time, that are missing in the functionals currently used. The latter underestimate the amount of charge transferred and manifest a spurious shift in the charge transfer resonance position. We discuss some explicit examples.
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Affiliation(s)
- Neepa T Maitra
- Department of Physics and Astronomy, Hunter College and the Physics Program at the Graduate Center of the City University of New York, 695 Park Avenue, NY 10065, United States of America
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Shu Y, Parker KA, Truhlar DG. Dual-Functional Tamm-Dancoff Approximation: A Convenient Density Functional Method that Correctly Describes S 1/S 0 Conical Intersections. J Phys Chem Lett 2017; 8:2107-2112. [PMID: 28418680 DOI: 10.1021/acs.jpclett.7b00594] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Time-dependent Kohn-Sham density functional theory has been used successfully to compute vertical excitation energies, especially for large molecular systems. However, the lack of double excitation character in the excited amplitudes produced by linear response in the adiabatic approximation holds it back from broader applications in photochemistry; for example, it shows (3N - 7)-dimensional conical intersection seams (where N is the number of atoms) between ground and excited states, although the correct dimensionality is 3N - 8. In this letter, we present a new, conceptually simple, easy-to-implement, and easy-to-use way to employ time-dependent Kohn-Sham density functional theory that has global accuracy comparable with the conventional single-functional version and that recovers the double cone topology of the potential energy surfaces at S1/S0 conical intersection seams. The new method is called the dual-functional Tamm-Dancoff approximation (DF-TDA).
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Affiliation(s)
- Yinan Shu
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota , Minneapolis, Minnesota 55455-0431, United States
| | - Kelsey A Parker
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota , Minneapolis, Minnesota 55455-0431, United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota , Minneapolis, Minnesota 55455-0431, United States
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Maitra NT. Perspective: Fundamental aspects of time-dependent density functional theory. J Chem Phys 2016; 144:220901. [DOI: 10.1063/1.4953039] [Citation(s) in RCA: 228] [Impact Index Per Article: 28.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Neepa T. Maitra
- Department of Physics and Astronomy, Hunter College and the Physics Program at the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
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