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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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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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Brown J, Yang J, Whitfield JD. Solver for the Electronic V-Representation Problem of Time-Dependent Density Functional Theory. J Chem Theory Comput 2020; 16:6014-6026. [DOI: 10.1021/acs.jctc.9b00583] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- James Brown
- Dartmouth College, Hanover, New Hampshire 03755-3529, United States
| | - Jun Yang
- Dartmouth College, Hanover, New Hampshire 03755-3529, 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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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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Gould T, Pittalis S, Toulouse J, Kraisler E, Kronik L. Asymptotic behavior of the Hartree-exchange and correlation potentials in ensemble density functional theory. Phys Chem Chem Phys 2019; 21:19805-19815. [DOI: 10.1039/c9cp03633d] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We show that the Hartree-exchange and correlation potentials of ensemble systems can have unexpected features, including non-vanishing asymptotic constants and non-trivial screening of electrons. These features are demonstrated here on Li, C, and F.
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Affiliation(s)
- Tim Gould
- Qld Micro- and Nanotechnology Centre
- Griffith University
- Nathan
- Australia
| | | | - Julien Toulouse
- Laboratoire de Chimie Théorique
- Sorbonne Université and CNRS
- F-75005 Paris
- France
| | - Eli Kraisler
- Fritz Haber Center for Molecular Dynamics and Institute of Chemistry
- The Hebrew University of Jerusalem
- 9091401 Jerusalem
- Israel
| | - Leeor Kronik
- Department of Materials and Interfaces
- Weizmann Institute of Science
- Rehovoth 76100
- Israel
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Suzuki Y, Hagiwara S, Watanabe K. Time-Dependent Multicomponent Density Functional Theory for Coupled Electron-Positron Dynamics. PHYSICAL REVIEW LETTERS 2018; 121:133001. [PMID: 30312034 DOI: 10.1103/physrevlett.121.133001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2018] [Indexed: 06/08/2023]
Abstract
Electron-positron interactions have been utilized in various fields of science. Here we develop time-dependent multicomponent density functional theory to study the coupled electron-positron dynamics from first principles. We prove that there are coupled time-dependent single-particle equations that can provide the electron and positron density dynamics, and derive the formally exact expression for their effective potentials. Introducing the adiabatic local density approximation to time-dependent electron-positron correlation, we apply the theory to the dynamics of a positronic lithium hydride molecule under a laser field. We demonstrate the significance of the coupling between electronic and positronic motion by revealing the complex positron detachment mechanism and the suppression of electronic resonant excitation by the screening effect of the positron.
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Affiliation(s)
- Yasumitsu Suzuki
- Department of Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
| | - Satoshi Hagiwara
- Department of Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
| | - Kazuyuki Watanabe
- Department of Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
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Dittmann N, Splettstoesser J, Helbig N. Nonadiabatic Dynamics in Single-Electron Tunneling Devices with Time-Dependent Density-Functional Theory. PHYSICAL REVIEW LETTERS 2018; 120:157701. [PMID: 29756889 DOI: 10.1103/physrevlett.120.157701] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2017] [Revised: 11/28/2017] [Indexed: 06/08/2023]
Abstract
We simulate the dynamics of a single-electron source, modeled as a quantum dot with on-site Coulomb interaction and tunnel coupling to an adjacent lead in time-dependent density-functional theory. Based on this system, we develop a time-nonlocal exchange-correlation potential by exploiting analogies with quantum-transport theory. The time nonlocality manifests itself in a dynamical potential step. We explicitly link the time evolution of the dynamical step to physical relaxation timescales of the electron dynamics. Finally, we discuss prospects for simulations of larger mesoscopic systems.
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Affiliation(s)
- Niklas Dittmann
- Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, SE-41298 Göteborg, Sweden
- Institute for Theory of Statistical Physics, RWTH Aachen, 52056 Aachen, Germany
- Peter-Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Janine Splettstoesser
- Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, SE-41298 Göteborg, Sweden
| | - Nicole Helbig
- Peter-Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
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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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Luo K, Fuks JI, Maitra NT. Studies of spuriously shifting resonances in time-dependent density functional theory. J Chem Phys 2016; 145:044101. [DOI: 10.1063/1.4955447] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kai Luo
- 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
- Department of Chemistry and Chemical Biology, Cornell University, 259 East Ave., Ithaca, New York 14850, USA
| | - Johanna I. Fuks
- 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
| | - 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. 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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Andrade X, Strubbe D, De Giovannini U, Larsen AH, Oliveira MJT, Alberdi-Rodriguez J, Varas A, Theophilou I, Helbig N, Verstraete MJ, Stella L, Nogueira F, Aspuru-Guzik A, Castro A, Marques MAL, Rubio A. Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems. Phys Chem Chem Phys 2016; 17:31371-96. [PMID: 25721500 DOI: 10.1039/c5cp00351b] [Citation(s) in RCA: 186] [Impact Index Per Article: 23.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Real-space grids are a powerful alternative for the simulation of electronic systems. One of the main advantages of the approach is the flexibility and simplicity of working directly in real space where the different fields are discretized on a grid, combined with competitive numerical performance and great potential for parallelization. These properties constitute a great advantage at the time of implementing and testing new physical models. Based on our experience with the Octopus code, in this article we discuss how the real-space approach has allowed for the recent development of new ideas for the simulation of electronic systems. Among these applications are approaches to calculate response properties, modeling of photoemission, optimal control of quantum systems, simulation of plasmonic systems, and the exact solution of the Schrödinger equation for low-dimensionality systems.
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Affiliation(s)
- Xavier Andrade
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA. and Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA
| | - David Strubbe
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Umberto De Giovannini
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Universidad del País Vasco CFM CSIC-UPV/EHU-MPC & DIPC, 20018 Donostia-San Sebastián, Spain
| | - Ask Hjorth Larsen
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Universidad del País Vasco CFM CSIC-UPV/EHU-MPC & DIPC, 20018 Donostia-San Sebastián, Spain
| | - Micael J T Oliveira
- Unité Nanomat, Département de Physique, Université de Liège, Allée du 6 Août 17, B-4000 Liège, Belgium
| | - Joseba Alberdi-Rodriguez
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Universidad del País Vasco CFM CSIC-UPV/EHU-MPC & DIPC, 20018 Donostia-San Sebastián, Spain and Dept. of Computer Architecture and Technology, University of the Basque Country UPV/EHU, M. Lardizabal, 1, 20018 Donostia-San Sebastian, Spain
| | - Alejandro Varas
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Universidad del País Vasco CFM CSIC-UPV/EHU-MPC & DIPC, 20018 Donostia-San Sebastián, Spain
| | - Iris Theophilou
- Peter-Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Nicole Helbig
- Peter-Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Matthieu J Verstraete
- Unité Nanomat, Département de Physique, Université de Liège, Allée du 6 Août 17, B-4000 Liège, Belgium
| | - Lorenzo Stella
- Atomistic Simulation Centre, School of Mathematics and Physics, Queen's University Belfast, University Road, Belfast BT7 1NN, Northern Ireland, UK
| | - Fernando Nogueira
- Center for Computational Physics, University of Coimbra, Rua Larga, 3004-516 Coimbra, Portugal
| | - Alán Aspuru-Guzik
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA
| | - Alberto Castro
- Institute for Biocomputation and Physics of Complex Systems (BIFI) and Zaragoza Center for Advanced Modeling (ZCAM), University of Zaragoza, E-50009 Zaragoza, Spain and ARAID Foundation, María de Luna 11, Edificio CEEI Aragón, Zaragoza E-50018, Spain
| | - Miguel A L Marques
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, Von-Seckendorff-Platz 1, 06120 Halle (Saale), Germany
| | - Angel Rubio
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Universidad del País Vasco CFM CSIC-UPV/EHU-MPC & DIPC, 20018 Donostia-San Sebastián, Spain and Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany
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Fuks JI, Nielsen SEB, Ruggenthaler M, Maitra NT. Time-dependent density functional theory beyond Kohn–Sham Slater determinants. Phys Chem Chem Phys 2016; 18:20976-85. [DOI: 10.1039/c6cp00722h] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
Different choices of initial Kohn Sham wavefunction shape the time-dependent exchange–correlation potential.
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Affiliation(s)
- Johanna I. Fuks
- 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 & Department of Physics
- 22761 Hamburg
- Germany
- Institut für Theoretische Physik
- Universität Innsbruck
| | - Michael Ruggenthaler
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science & Department of Physics
- 22761 Hamburg
- Germany
- Institut für Theoretische Physik
- Universität Innsbruck
| | - 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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Marian D, Colomés E, Oriols X. Time-dependent exchange and tunneling: detection at the same place of two electrons emitted simultaneously from different sources. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:245302. [PMID: 26030519 DOI: 10.1088/0953-8984/27/24/245302] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Two-particle scattering probabilities in tunneling scenarios with exchange interaction are analyzed with quasi-particle wave packets. Two initial one-particle wave packets (with opposite central momentums) are spatially localized at each side of a barrier. After impinging upon a tunneling barrier, each wave packet splits into transmitted and reflected components. When the initial two-particle anti-symmetrical state is defined as a Slater determinant of any type of (normalizable) one-particle wave packet, it is shown that the probability of detecting two (identically injected) electrons at the same side of the barrier is different from zero in very common (single or double barrier) scenarios. In some particular scenarios, the transmitted and reflected components become orthogonal and the mentioned probabilities reproduce those values associated to distinguishable particles. These unexpected non-zero probabilities are still present when non-separable Coulomb interaction or non-symmetrical potentials are considered. On the other hand, for initial wave packets close to Hamiltonian eigenstates, the usual zero two-particle probability for electrons at the same side of the barrier found in the literature is recovered. The generalization to many-particle scattering probabilities with quasi-particle wave packets for low and high phase-space density are also analyzed. The far-reaching consequences of these non-zero probabilities in the accurate evaluation of quantum noise in mesoscopic systems are briefly indicated.
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Affiliation(s)
- D Marian
- Dipartimento di Fisica dell'Università di Genova and INFN sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
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Ruggenthaler M, Penz M, van Leeuwen R. Existence, uniqueness, and construction of the density-potential mapping in time-dependent density-functional theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:203202. [PMID: 25921322 DOI: 10.1088/0953-8984/27/20/203202] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
In this work we review the mapping from densities to potentials in quantum mechanics, which is the basic building block of time-dependent density-functional theory and the Kohn-Sham construction. We first present detailed conditions such that a mapping from potentials to densities is defined by solving the time-dependent Schrödinger equation. We specifically discuss intricacies connected with the unboundedness of the Hamiltonian and derive the local-force equation. This equation is then used to set up an iterative sequence that determines a potential that generates a specified density via time propagation of an initial state. This fixed-point procedure needs the invertibility of a certain Sturm-Liouville problem, which we discuss for different situations. Based on these considerations we then present a discussion of the famous Runge-Gross theorem which provides a density-potential mapping for time-analytic potentials. Further we give conditions such that the general fixed-point approach is well-defined and converges under certain assumptions. Then the application of such a fixed-point procedure to lattice Hamiltonians is discussed and the numerical realization of the density-potential mapping is shown. We conclude by presenting an extension of the density-potential mapping to include vector-potentials and photons.
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Affiliation(s)
- Michael Ruggenthaler
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21a, A-6020 Innsbruck, Austria
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Fuks JI, Luo K, Sandoval ED, Maitra NT. Time-resolved spectroscopy in time-dependent density functional theory: an exact condition. PHYSICAL REVIEW LETTERS 2015; 114:183002. [PMID: 26000998 PMCID: PMC6135656 DOI: 10.1103/physrevlett.114.183002] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2014] [Indexed: 05/17/2023]
Abstract
A fundamental property of a quantum system driven by an external field is that when the field is turned off the positions of its response frequencies are independent of the time at which the field is turned off. We show that this leads to an exact condition for the exchange-correlation potential of time-dependent density functional theory. The Kohn-Sham potential typically continues to evolve after the field is turned off, which leads to time dependence in the response frequencies of the Kohn-Sham response function. The exchange-correlation kernel must cancel out this time dependence. The condition is typically violated by approximations currently in use, as we demonstrate by several examples, which has severe consequences for their predictions of time-resolved spectroscopy.
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Affiliation(s)
- Johanna I Fuks
- 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
| | - Kai Luo
- 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
| | - Ernesto D Sandoval
- 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
| | - 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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Luo K, Fuks JI, Sandoval ED, Elliott P, Maitra NT. Kinetic and interaction components of the exact time-dependent correlation potential. J Chem Phys 2015; 140:18A515. [PMID: 24832323 DOI: 10.1063/1.4867002] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
The exact exchange-correlation (xc) potential of time-dependent density functional theory has been shown to have striking features. For example, step and peak features are generically found when the system is far from its ground-state, and these depend nonlocally on the density in space and time. We analyze the xc potential by decomposing it into kinetic and interaction components and comparing each with their exact-adiabatic counterparts, for a range of dynamical situations in model one-dimensional two-electron systems. We find that often, but not always, the kinetic contribution is largely responsible for these features that are missed by the adiabatic approximation. The adiabatic approximation often makes a smaller error for the interaction component, which we write in two parts, one being the Coulomb potential due to the time-dependent xc hole. Non-adiabatic features of the kinetic component were also larger than those of the interaction component in cases that we studied when there is negligible step structure. In ground-state situations, step and peak structures arise in cases of static correlation, when more than one determinant is essential to describe the interacting state. We investigate the time-dependent natural orbital occupation numbers and find the corresponding relation between these and the dynamical step is more complex than for the ground-state case.
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Affiliation(s)
- Kai Luo
- 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
| | - Johanna I Fuks
- 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
| | - Ernesto D Sandoval
- 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
| | - Peter Elliott
- Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, 06120 Halle (Saale), Germany
| | - 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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Habenicht BF, Tani NP, Provorse MR, Isborn CM. Two-electron Rabi oscillations in real-time time-dependent density-functional theory. J Chem Phys 2014; 141:184112. [DOI: 10.1063/1.4900514] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Bradley F. Habenicht
- Chemistry and Chemical Biology, University of California Merced, Merced, California 95343, USA
| | - Noriyuki P. Tani
- Chemistry and Chemical Biology, University of California Merced, Merced, California 95343, USA
| | - Makenzie R. Provorse
- Chemistry and Chemical Biology, University of California Merced, Merced, California 95343, USA
| | - Christine M. Isborn
- Chemistry and Chemical Biology, University of California Merced, Merced, California 95343, USA
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Elliott P, Fuks JI, Rubio A, Maitra NT. Universal dynamical steps in the exact time-dependent exchange-correlation potential. PHYSICAL REVIEW LETTERS 2012; 109:266404. [PMID: 23368591 DOI: 10.1103/physrevlett.109.266404] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2012] [Indexed: 06/01/2023]
Abstract
We show that the exact exchange-correlation potential of time-dependent density-functional theory displays dynamical step structures that have a spatially nonlocal and time nonlocal dependence on the density. Using one-dimensional two-electron model systems, we illustrate these steps for a range of nonequilibrium dynamical situations relevant for modeling of photochemical or physical processes: field-free evolution of a nonstationary state, resonant local excitation, resonant complete charge transfer, and evolution under an arbitrary field. A lack of these steps in the usual approximations yields inaccurate dynamics, for example, predicting faster dynamics and incomplete charge transfer.
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Affiliation(s)
- P Elliott
- 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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Malet F, Gori-Giorgi P. Strong correlation in Kohn-Sham density functional theory. PHYSICAL REVIEW LETTERS 2012; 109:246402. [PMID: 23368350 DOI: 10.1103/physrevlett.109.246402] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2012] [Indexed: 06/01/2023]
Abstract
We use the exact strong-interaction limit of the Hohenberg-Kohn energy density functional to approximate the exchange-correlation energy of the restricted Kohn-Sham scheme. Our approximation corresponds to a highly nonlocal density functional whose functional derivative can be easily constructed, thus transforming exactly, in a physically transparent way, an important part of the electron-electron interaction into an effective local one-body potential. We test our approach on quasi-one-dimensional systems, showing that it captures essential features of strong correlation that restricted Kohn-Sham calculations using the currently available approximations cannot describe.
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Affiliation(s)
- Francesc Malet
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
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