1
|
Ranka K, Isborn CM. Size-dependent errors in real-time electron density propagation. J Chem Phys 2023; 158:2887545. [PMID: 37125706 DOI: 10.1063/5.0142515] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2023] [Accepted: 04/14/2023] [Indexed: 05/02/2023] Open
Abstract
Real-time (RT) electron density propagation with time-dependent density functional theory (TDDFT) or Hartree-Fock (TDHF) is one of the most popular methods to model the charge transfer in molecules and materials. However, both RT-TDHF and RT-TDDFT within the adiabatic approximation are known to produce inaccurate evolution of the electron density away from the ground state in model systems, leading to large errors in charge transfer and erroneous shifting of peaks in absorption spectra. Given the poor performance of these methods with small model systems and the widespread use of the methods with larger molecular and material systems, here we bridge the gap in our understanding of these methods and examine the size-dependence of errors in RT density propagation. We analyze the performance of RT density propagation for systems of increasing size during the application of a continuous resonant field to induce Rabi-like oscillations, during charge-transfer dynamics, and for peak shifting in simulated absorption spectra. We find that the errors in the electron dynamics are indeed size dependent for these phenomena, with the largest system producing the results most aligned with those expected from linear response theory. The results suggest that although the RT-TDHF and RT-TDDFT methods may produce severe errors for model systems, the errors in charge transfer and resonantly driven electron dynamics may be much less significant for more realistic, large-scale molecules and materials.
Collapse
Affiliation(s)
- Karnamohit Ranka
- Chemistry and Biochemistry, University of California Merced, Merced, California 95343, USA
| | - Christine M Isborn
- Chemistry and Biochemistry, University of California Merced, Merced, California 95343, USA
| |
Collapse
|
2
|
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.
Collapse
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
| |
Collapse
|
3
|
Tarantino W, Ullrich CA. A reformulation of time-dependent Kohn-Sham theory in terms of the second time derivative of the density. J Chem Phys 2021; 154:204112. [PMID: 34241164 DOI: 10.1063/5.0039962] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The Kohn-Sham approach to time-dependent density-functional theory (TDDFT) can be formulated, in principle, exactly by invoking the force-balance equation for the density, which leads to an explicit expression for the exchange-correlation potential as an implicit density functional. It is shown that this suggests a reformulation of TDDFT in terms of the second time derivative of the density, rather than the density itself. The result is a time-local Kohn-Sham scheme of second-order in time whose causal structure is more transparent than that of the usual Kohn-Sham formalism. The scheme can be used to construct new approximations at the exchange-only level and beyond, and it offers a straightforward definition of the exact adiabatic approximation.
Collapse
Affiliation(s)
- Walter Tarantino
- Dipartimento di Fisica, Università degli Studi di Cagliari, Cittadella Universitaria, I-09042 Monserrato, Cagliari, Italy
| | - Carsten A Ullrich
- Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA
| |
Collapse
|
4
|
Gill NM, Fontes CJ, Starrett CE. Time-dependent density functional theory applied to average atom opacity. Phys Rev E 2021; 103:043206. [PMID: 34005858 DOI: 10.1103/physreve.103.043206] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2021] [Accepted: 03/24/2021] [Indexed: 11/07/2022]
Abstract
We focus on studying the opacity of iron, chromium, and nickel plasmas at conditions relevant to experiments carried out at Sandia National Laboratories [J. E. Bailey et al., Nature (London) 517, 56 (2015)NATUAS0028-083610.1038/nature14048]. We calculate the photoabsorption cross sections and subsequent opacity for plasmas using linear-response time-dependent density functional theory (TD-DFT). Our results indicate that the physics of channel mixing accounted for in linear-response TD-DFT leads to an increase in the opacity in the bound-free quasicontinuum, where the Sandia experiments indicate that models underpredict iron opacity. However, the increase seen in our calculations is only in the range of 5%-10%. Further, we do not see any change in this trend for chromium and nickel. This behavior indicates that channel mixing effects do not explain the trends in opacity observed in the Sandia experiments.
Collapse
Affiliation(s)
- N M Gill
- Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545, USA
| | - C J Fontes
- Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545, USA
| | - C E Starrett
- Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
5
|
Tancogne-Dejean N, Oliveira MJT, Andrade X, Appel H, Borca CH, Le Breton G, Buchholz F, Castro A, Corni S, Correa AA, De Giovannini U, Delgado A, Eich FG, Flick J, Gil G, Gomez A, Helbig N, Hübener H, Jestädt R, Jornet-Somoza J, Larsen AH, Lebedeva IV, Lüders M, Marques MAL, Ohlmann ST, Pipolo S, Rampp M, Rozzi CA, Strubbe DA, Sato SA, Schäfer C, Theophilou I, Welden A, Rubio A. Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems. J Chem Phys 2020; 152:124119. [PMID: 32241132 DOI: 10.1063/1.5142502] [Citation(s) in RCA: 114] [Impact Index Per Article: 28.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Over the last few years, extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind, i.e., to provide a unique framework that allows us to describe non-equilibrium phenomena in molecular complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mechanical effects within a generalized time-dependent density functional theory. This article aims to present the new features that have been implemented over the last few years, including technical developments related to performance and massive parallelism. We also describe the major theoretical developments to address ultrafast light-driven processes, such as the new theoretical framework of quantum electrodynamics density-functional formalism for the description of novel light-matter hybrid states. Those advances, and others being released soon as part of the Octopus package, will allow the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in molecules and materials, and new emergent states of matter (quantum electrodynamical-materials).
Collapse
Affiliation(s)
- Nicolas Tancogne-Dejean
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, D-22761 Hamburg, Germany
| | - Micael J T Oliveira
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, D-22761 Hamburg, Germany
| | - Xavier Andrade
- Quantum Simulations Group, Lawrence Livermore National Laboratory, Livermore, California 94551, USA
| | - Heiko Appel
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, D-22761 Hamburg, Germany
| | - Carlos H Borca
- Quantum Simulations Group, Lawrence Livermore National Laboratory, Livermore, California 94551, USA
| | - Guillaume Le Breton
- Département de Physique, École Normale Supérieure de Lyon, 46 Allée d'Italie, Lyon Cedex 07, France
| | - Florian Buchholz
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, D-22761 Hamburg, Germany
| | - Alberto Castro
- Institute for Biocomputation and Physics of Complex Systems, University of Zaragoza, Calle Mariano Esquillor, 50018 Zaragoza, Spain
| | - Stefano Corni
- Dipartimento di Scienze Chimiche, Università degli studi di Padova, via F. Marzolo 1, 35131 Padova, Italy
| | - Alfredo A Correa
- Quantum Simulations Group, Lawrence Livermore National Laboratory, Livermore, California 94551, USA
| | - Umberto De Giovannini
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, D-22761 Hamburg, Germany
| | - Alain Delgado
- Xanadu, 777 Bay Street, Toronto, Ontario M5G 2C8, Canada
| | - Florian G Eich
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, D-22761 Hamburg, Germany
| | - Johannes Flick
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Gabriel Gil
- Dipartimento di Scienze Chimiche, Università degli studi di Padova, via F. Marzolo 1, 35131 Padova, Italy
| | - Adrián Gomez
- Institute for Biocomputation and Physics of Complex Systems, University of Zaragoza, Calle Mariano Esquillor, 50018 Zaragoza, Spain
| | - Nicole Helbig
- Nanomat/Qmat/CESAM and ETSF, Université de Liège, B-4000 Sart-Tilman, Belgium
| | - Hannes Hübener
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, D-22761 Hamburg, Germany
| | - René Jestädt
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, D-22761 Hamburg, Germany
| | - Joaquim Jornet-Somoza
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, D-22761 Hamburg, Germany
| | - Ask H Larsen
- Nano-Bio Spectroscopy Group and ETSF, Universidad del País Vasco, 20018 San Sebastián, Spain
| | - Irina V Lebedeva
- Nano-Bio Spectroscopy Group and ETSF, Universidad del País Vasco, 20018 San Sebastián, Spain
| | - Martin Lüders
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, D-22761 Hamburg, Germany
| | - Miguel A L Marques
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06120 Halle (Saale), Germany
| | - Sebastian T Ohlmann
- Max Planck Computing and Data Facility, Gießenbachstraße 2, 85741 Garching, Germany
| | - Silvio Pipolo
- Université de Lille, CNRS, Centrale Lille, ENSCL, Université d' Artois UMR 8181-UCCS Unité de Catalyse et Chimie du Solide, F-59000 Lille, France
| | - Markus Rampp
- Max Planck Computing and Data Facility, Gießenbachstraße 2, 85741 Garching, Germany
| | - Carlo A Rozzi
- CNR - Istituto Nanoscienze, via Campi 213a, 41125 Modena, Italy
| | - David A Strubbe
- Department of Physics, School of Natural Sciences, University of California, Merced, California 95343, USA
| | - Shunsuke A Sato
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, D-22761 Hamburg, Germany
| | - Christian Schäfer
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, D-22761 Hamburg, Germany
| | - Iris Theophilou
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, D-22761 Hamburg, Germany
| | - Alicia Welden
- Quantum Simulations Group, Lawrence Livermore National Laboratory, Livermore, California 94551, USA
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, D-22761 Hamburg, Germany
| |
Collapse
|
6
|
Yost DC, Yao Y, Kanai Y. First-Principles Modeling of Electronic Stopping in Complex Matter under Ion Irradiation. J Phys Chem Lett 2020; 11:229-237. [PMID: 31829604 DOI: 10.1021/acs.jpclett.9b02975] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Electronic stopping refers to the dynamical energy-transfer process to electrons in matter from highly energetic charged particles such as high-velocity protons. We discuss recent progress in theoretical studies of electronic stopping in condensed matter under ion irradiation, focusing on modern electronic structure theory's role in enabling the study of electronic excitation dynamics that result from the energy transfer. In the last few decades, first-principles simulation approaches based on real-time time-dependent density functional theory have greatly advanced the field. While linear response theory is widely used to study electronic stopping processes, especially for simple solids, novel first-principles dynamics approaches now allow us to study chemically complex systems and also yield detailed descriptions of electronic excitations at the molecular scale. Outstanding challenges for further advancement of electronic stopping modeling are also discussed from the viewpoint of electronic structure theory.
Collapse
Affiliation(s)
- Dillon C Yost
- Department of Chemistry , University of North Carolina at Chapel Hill , Chapel Hill , North Carolina 27514-3290 , United States
| | - Yi Yao
- Department of Chemistry , University of North Carolina at Chapel Hill , Chapel Hill , North Carolina 27514-3290 , United States
| | - Yosuke Kanai
- Department of Chemistry , University of North Carolina at Chapel Hill , Chapel Hill , North Carolina 27514-3290 , United States
| |
Collapse
|
7
|
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.
Collapse
Affiliation(s)
- Lionel Lacombe
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA.
| | | |
Collapse
|
8
|
Brütting M, Trepl T, de Las Heras D, Schmidt M. Superadiabatic Forces via the Acceleration Gradient in Quantum Many-Body Dynamics. Molecules 2019; 24:molecules24203660. [PMID: 31614514 PMCID: PMC6832129 DOI: 10.3390/molecules24203660] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2019] [Revised: 09/15/2019] [Accepted: 09/30/2019] [Indexed: 11/30/2022] Open
Abstract
We apply the formally exact quantum power functional framework (J. Chem. Phys.2015, 143, 174108) to a one-dimensional Hooke’s helium model atom. The physical dynamics are described on the one-body level beyond the density-based adiabatic approximation. We show that gradients of both the microscopic velocity and acceleration field are required to correctly describe the effects due to interparticle interactions. We validate the proposed analytical forms of the superadiabatic force and transport contributions by comparison to one-body data from exact numerical solution of the Schrödinger equation. Superadiabatic contributions beyond the adiabatic approximation are important in the dynamics and they include effective dissipation.
Collapse
Affiliation(s)
- Moritz Brütting
- Theoretische Physik II, Physikalisches Institut, Universitat Bayreuth, D-95440 Bayreuth, Germany
| | - Thomas Trepl
- Theoretische Physik II, Physikalisches Institut, Universitat Bayreuth, D-95440 Bayreuth, Germany
| | - Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universitat Bayreuth, D-95440 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universitat Bayreuth, D-95440 Bayreuth, Germany.
| |
Collapse
|
9
|
Yost DC, Yao Y, Kanai Y. Propagation of maximally localized Wannier functions in real-time TDDFT. J Chem Phys 2019; 150:194113. [DOI: 10.1063/1.5095631] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
Affiliation(s)
- Dillon C. Yost
- Department of Chemistry, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
| | - Yi Yao
- Department of Chemistry, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
| | - Yosuke Kanai
- Department of Chemistry, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
| |
Collapse
|
10
|
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
| |
Collapse
|
11
|
Schelter I, Kümmel S. Accurate Evaluation of Real-Time Density Functional Theory Providing Access to Challenging Electron Dynamics. J Chem Theory Comput 2018; 14:1910-1927. [DOI: 10.1021/acs.jctc.7b01013] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ingo Schelter
- Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
| | - Stephan Kümmel
- Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
| |
Collapse
|
12
|
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.
Collapse
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
| |
Collapse
|
13
|
Liao SL, Ho TS, Rabitz H, Chu SI. Time-Local Equation for the Exact Optimized Effective Potential in Time-Dependent Density Functional Theory. PHYSICAL REVIEW LETTERS 2017; 118:243001. [PMID: 28665665 DOI: 10.1103/physrevlett.118.243001] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2015] [Indexed: 06/07/2023]
Abstract
A long-standing challenge in the time-dependent density functional theory is to efficiently solve the exact time-dependent optimized effective potential (TDOEP) integral equation derived from orbital-dependent functionals, especially for the study of nonadiabatic dynamics in time-dependent external fields. In this Letter, we formulate a completely equivalent time-local TDOEP equation that admits a unique real-time solution in terms of time-dependent Kohn-Sham and effective memory orbitals. The time-local formulation is numerically implemented, with the incorporation of exponential memory loss to address the unaccounted for correlation component in the exact-exchange-only functional, to enable the study of the many-electron dynamics of a one-dimensional hydrogen chain. It is shown that the long time behavior of the electric dipole converges correctly and the zero-force theorem is fulfilled in the current implementation.
Collapse
Affiliation(s)
- Sheng-Lun Liao
- Center for Quantum Science and Engineering and Department of Physics, National Taiwan University, Taipei 10617, Taiwan
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - Tak-San Ho
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - Herschel Rabitz
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - Shih-I Chu
- Center for Quantum Science and Engineering and Department of Physics, National Taiwan University, Taipei 10617, Taiwan
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, USA
| |
Collapse
|
14
|
Eich FG, Di Ventra M, Vignale G. Functional theories of thermoelectric phenomena. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:063001. [PMID: 27991434 DOI: 10.1088/1361-648x/29/6/063001] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We review the progress that has been recently made in the application of time-dependent density functional theory to thermoelectric phenomena. As the field is very young, we emphasize open problems and fundamental issues. We begin by introducing the formal structure of thermal density functional theory, a density functional theory with two basic variables-the density and the energy density-and two conjugate fields-the ordinary scalar potential and Luttinger's thermomechanical potential. The static version of this theory is contrasted with the familiar finite-temperature density functional theory, in which only the density is a variable. We then proceed to constructing the full time-dependent non equilibrium theory, including the practically important Kohn-Sham equations that go with it. The theory is shown to recover standard results of the Landauer theory for thermal transport in the steady state, while showing greater flexibility by allowing a description of fast thermal response, temperature oscillations and related phenomena. Several results are presented here for the first time, i.e. the proof of invertibility of the thermal response function in the linear regime, the full expression of the thermal currents in the presence of Luttinger's thermomechanical potential, an explicit prescription for the evaluation of the Kohn-Sham potentials in the adiabatic local density approximation, a detailed discussion of the leading dissipative corrections to the adiabatic local density approximation and the thermal corrections to the resistivity that follow from it.
Collapse
Affiliation(s)
- F G Eich
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, D-22761 Hamburg, Germany. Department of Physics, University of Missouri-Columbia, Columbia, MO 65211, USA
| | | | | |
Collapse
|
15
|
Bruner A, LaMaster D, Lopata K. Accelerated Broadband Spectra Using Transition Dipole Decomposition and Padé Approximants. J Chem Theory Comput 2016; 12:3741-50. [DOI: 10.1021/acs.jctc.6b00511] [Citation(s) in RCA: 68] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Adam Bruner
- Department
of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, United States
| | - Daniel LaMaster
- Department
of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, United States
| | - Kenneth Lopata
- Department
of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, United States
- Center for Computation & Technology, Louisiana State University, Baton Rouge, Louisiana 70803, United States
| |
Collapse
|
16
|
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
| |
Collapse
|
17
|
Pellegrini C, Flick J, Tokatly IV, Appel H, Rubio A. Optimized Effective Potential for Quantum Electrodynamical Time-Dependent Density Functional Theory. PHYSICAL REVIEW LETTERS 2015; 115:093001. [PMID: 26371646 DOI: 10.1103/physrevlett.115.093001] [Citation(s) in RCA: 52] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2014] [Indexed: 05/20/2023]
Abstract
We propose an orbital exchange-correlation functional for applying time-dependent density functional theory to many-electron systems coupled to cavity photons. The time nonlocal equation for the electron-photon optimized effective potential (OEP) is derived. In the static limit our OEP energy functional reduces to the Lamb shift of the ground state energy. We test the new approximation in the Rabi model. It is shown that the OEP (i) reproduces quantitatively the exact ground-state energy from the weak to the deep strong coupling regime and (ii) accurately captures the dynamics entering the ultrastrong coupling regime. The present formalism opens the path to a first-principles description of correlated electron-photon systems, bridging the gap between electronic structure methods and quantum optics for real material applications.
Collapse
Affiliation(s)
- Camilla Pellegrini
- Departamento de Fisica de Materiales, Nano-bio Spectroscopy Group and ETSF Scientific Development Centre, Universidad del Pais Vasco UPV/EHU, E-20018 San Sebastian, Spain
| | - Johannes Flick
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
| | - Ilya V Tokatly
- Departamento de Fisica de Materiales, Nano-bio Spectroscopy Group and ETSF Scientific Development Centre, Universidad del Pais Vasco UPV/EHU, E-20018 San Sebastian, Spain
- IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain
| | - Heiko Appel
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Angel Rubio
- Departamento de Fisica de Materiales, Nano-bio Spectroscopy Group and ETSF Scientific Development Centre, Universidad del Pais Vasco UPV/EHU, E-20018 San Sebastian, Spain
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| |
Collapse
|
18
|
Curchod BFE, Rothlisberger U, Tavernelli I. Trajectory-Based Nonadiabatic Dynamics with Time-Dependent Density Functional Theory. Chemphyschem 2013; 14:1314-40. [DOI: 10.1002/cphc.201200941] [Citation(s) in RCA: 153] [Impact Index Per Article: 13.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2012] [Indexed: 11/11/2022]
|
19
|
Hofmann D, Kümmel S. Self-interaction correction in a real-time Kohn-Sham scheme: Access to difficult excitations in time-dependent density functional theory. J Chem Phys 2012; 137:064117. [DOI: 10.1063/1.4742763] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
20
|
Penka EF, Bandrauk AD. Nonperturbative time-dependent density functional theory (TDDFT) and time-dependent electron localization function (TDELF) study of the ionization of OCS and CS2 with ultrashort intense laser pulses — Orientational effects. CAN J CHEM 2012. [DOI: 10.1139/v2012-039] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
The nonlinear nonperturbative response of OCS and CS2 to ultrashort (few cycles) intense laser pulses was studied numerically by time-dependent density functional theory (TDDFT) methods to understand molecular ionization as a function of laser–molecule orientation. A time-dependent electron localization function(TDELF) was used to visualize the nonlinear nonperturbative electron transfer occurring during the laser pulse. It was found that, for intensities I > 3.5 × 1014 W/cm2, the inner shell Kohn–Sham (KS) molecular orbitals contribute significantly to the ionization, whereas for the intensity I < 3.5 × 1014 W/cm2, the highest occupied molecular orbital (HOMO) shows the dominant response to the field. In general, the ionization rate maxima correspond to the alignment of maximum KS orbital densities with the laser pulse polarization instead of orbital ionization potentials (IP). These findings are corroborated through analysis of the TDELF images, where the ionization occurs from the lone pair or bond regions of the corresponding molecules.
Collapse
Affiliation(s)
- Emmanuel Fowe Penka
- Laboratoire de Chimie Théorique, Faculté des Sciences, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
| | - André Dieter Bandrauk
- Laboratoire de Chimie Théorique, Faculté des Sciences, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
| |
Collapse
|
21
|
Hofmann D, Körzdörfer T, Kümmel S. Kohn-Sham self-interaction correction in real time. PHYSICAL REVIEW LETTERS 2012; 108:146401. [PMID: 22540810 DOI: 10.1103/physrevlett.108.146401] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2011] [Indexed: 05/31/2023]
Abstract
We present a solution scheme for the time-dependent Kohn-Sham self-interaction correction. Based on the generalized optimized effective potential approach, the multiplicative Kohn-Sham potential is constructed in real time and real space for the self-interaction corrected local density approximation. Excitations of different character, including charge-transfer excitations that had been regarded as prime examples for the failure of standard time-dependent density functionals, are described correctly by this approach. We analyze the time-dependent exchange-correlation potential and density, revealing features that are decisive for the correct description of the response.
Collapse
Affiliation(s)
- D Hofmann
- Theoretical Physics IV, University of Bayreuth, D-95440 Bayreuth, Germany
| | | | | |
Collapse
|
22
|
Abstract
The classic density-functional theory (DFT) formalism introduced by Hohenberg, Kohn, and Sham in the mid-1960s is based on the idea that the complicated N-electron wave function can be replaced with the mathematically simpler 1-electron charge density in electronic structure calculations of the ground stationary state. As such, ordinary DFT cannot treat time-dependent (TD) problems nor describe excited electronic states. In 1984, Runge and Gross proved a theorem making TD-DFT formally exact. Information about electronic excited states may be obtained from this theory through the linear response (LR) theory formalism. Beginning in the mid-1990s, LR-TD-DFT became increasingly popular for calculating absorption and other spectra of medium- and large-sized molecules. Its ease of use and relatively good accuracy has now brought LR-TD-DFT to the forefront for this type of application. As the number and the diversity of applications of TD-DFT have grown, so too has our understanding of the strengths and weaknesses of the approximate functionals commonly used for TD-DFT. The objective of this article is to continue where a previous review of TD-DFT in Volume 55 of the Annual Review of Physical Chemistry left off and highlight some of the problems and solutions from the point of view of applied physical chemistry. Because doubly-excited states have a particularly important role to play in bond dissociation and formation in both thermal and photochemistry, particular emphasis is placed on the problem of going beyond or around the TD-DFT adiabatic approximation, which limits TD-DFT calculations to nominally singly-excited states.
Collapse
Affiliation(s)
- M E Casida
- Laboratoire de Chimie Théorique, Département de Chimie Moléculaire, Institut de Chimie Moléculaire de Grenoble, Université Joseph Fourier, France.
| | | |
Collapse
|
23
|
MUNDT MICHAEL. REAL-TIME APPROACH TO TIME-DEPENDENT DENSITY-FUNCTIONAL THEORY IN THE LINEAR AND NONLINEAR REGIME. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2011. [DOI: 10.1142/s0219633609004915] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The linear and nonlinear response of Si 4 and Na 4 to an external perturbation is investigated in the framework of time-dependent density-functional theory. The time-dependent Kohn–Sham equations, which are the central equations in this approach, are solved in real space and real time. A parallelized implementation to solve these nonlinear, one-particle Schrödinger equations is presented. In contrast to Na 4, Si 4 shows high-harmonic generation far beyond the cut-off predicted by the quasiclassical model and predictions for extended systems.
Collapse
Affiliation(s)
- MICHAEL MUNDT
- Institut für Theoretische Physik, Universität Bayreuth, D-95440 Bayreuth, Germany
| |
Collapse
|
24
|
Abstract
We investigate the accuracy and efficiency of the semiclassical frozen Gaussian method in describing electron dynamics in real time. Model systems of two soft-Coulomb-interacting electrons are used to study correlated dynamics under non-perturbative electric fields, as well as the excitation spectrum. The results show that a recently proposed method that combines exact-exchange with semiclassical correlation to propagate the one-body density-matrix holds promise for electron dynamics in many situations that either wavefunction or density-functional methods have difficulty describing. The results also however point out challenges in such a method that need to be addressed before it can become widely applicable.
Collapse
Affiliation(s)
- Peter Elliott
- Department of Physics and Astronomy, Hunter College and the City University of New York, 695 Park Avenue, New York, New York 10065, USA.
| | | |
Collapse
|
25
|
Rajam AK, Raczkowska I, Maitra NT. Semiclassical electron correlation in density-matrix time propagation. PHYSICAL REVIEW LETTERS 2010; 105:113002. [PMID: 20867568 DOI: 10.1103/physrevlett.105.113002] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2010] [Indexed: 05/29/2023]
Abstract
Lack of memory (locality in time) is a major limitation of almost all present time-dependent density-functional approximations. By using semiclassical dynamics to compute correlation effects in the time propagation of the density matrix, we incorporate memory, including initial-state dependence, as well as changing occupation numbers, and predict more observables in strong-field applications.
Collapse
Affiliation(s)
- A K Rajam
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Ave, New York, New York 10065, USA
| | | | | |
Collapse
|
26
|
Hellgren M, von Barth U. Exact-exchange kernel of time-dependent density functional theory: Frequency dependence and photoabsorption spectra of atoms. J Chem Phys 2009; 131:044110. [DOI: 10.1063/1.3179756] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
27
|
Vieira D, Capelle K, Ullrich CA. Physical signatures of discontinuities of the time-dependent exchange–correlation potential. Phys Chem Chem Phys 2009; 11:4647-54. [DOI: 10.1039/b902613d] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
|
28
|
Messud J, Dinh PM, Reinhard PG, Suraud E. Time-dependent density-functional theory with a self-interaction correction. PHYSICAL REVIEW LETTERS 2008; 101:096404. [PMID: 18851631 DOI: 10.1103/physrevlett.101.096404] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2007] [Indexed: 05/26/2023]
Abstract
We discuss an implementation of the self-interaction correction for the local-density approximation to time-dependent density-functional theory. A variational formulation is given, taking care of the necessary constraints. A manageable and transparent propagation scheme using two sets of wave functions is proposed and applied to laser excitation with subsequent ionization of a dimer molecule.
Collapse
Affiliation(s)
- J Messud
- Laboratoire de Physique Théorique, IRSAMC, CNRS, Université de Toulouse, F-31062 Toulouse, France
| | | | | | | |
Collapse
|
29
|
Li Y, Ullrich CA. Time-dependent V-representability on lattice systems. J Chem Phys 2008; 129:044105. [DOI: 10.1063/1.2955733] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
30
|
Thiele M, Gross EKU, Kümmel S. Adiabatic approximation in nonperturbative time-dependent density-functional theory. PHYSICAL REVIEW LETTERS 2008; 100:153004. [PMID: 18518104 DOI: 10.1103/physrevlett.100.153004] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2007] [Indexed: 05/26/2023]
Abstract
We construct the exact exchange-correlation potential of time-dependent density-functional theory and the approximation to it that is adiabatic but exact otherwise. For the strong-field double ionization of the Helium atom these two potentials are virtually identical. Thus, memory effects play a negligible role in this paradigm process of nonlinear, nonperturbative electron dynamics. We identify the regime of high-frequency excitations where the adiabatic approximation breaks down and explicitly calculate the nonadiabatic contribution to the exchange-correlation potential.
Collapse
Affiliation(s)
- M Thiele
- Physikalisches Institut, Universität Bayreuth, Bayreuth, Germany
| | | | | |
Collapse
|