Time-Dependent Density Functional Theory Beyond the Adiabatic Local Density Approximation

Vignale, Giovanni; Ullrich, Carsten A.; Conti, Sergio

doi:10.1103/physrevlett.79.4878

Cited by 249 publications

(317 citation statements)

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“…It turns out that this static long-range contribution to the kernel is sufficient to reproduce strong continuum excitonic effects in semiconductors. Promising results were also obtained for the optical spectrum of some simple semiconductors by Kim et al (2002) using the exact exchange Kohn-Sham formalism together with a TDLDA f xc , and by de Boeij et al (2001) using a polarizationdependent functional within the current-density functional proposed by Vignale and Kohn (1996). This procedure shows the influence of macroscopic electric fields in the response function.…”

Section: The Exchange-correlation Kernel F XCmentioning

confidence: 71%

“…This means that f xc is a strongly nonlocal functional of the density. This problem can be overcome if the current density is added as a basic variable in a generalized Kohn-Sham scheme (Vignale and Kohn, 1996). In this way one can derive a local current-density-functional theory of both current and density responses valid for slowly varying densities and potentials.…”

Section: (A4)mentioning

confidence: 99%

“…Note that the TDLDA approximation to TDDFT satisfies the harmonic-potential theorem because the exchangecorrelation potential follows the density when the latter is moved (that is, the exchange-correlation potential is local in both time and space; see below). The Gross and Kohn (1985) approximation violates the harmonicpotential theorem as shown by Dobson (1994), but it is possible to perform a simple modification for frequencydependent local theories to satisfy this theorem (Vignale and Kohn, 1996;Dobson, Bü nner, and Gross, 1997;Vignale et al, 1997). The essential idea is to make the action functional depend on the relative density rel (r,t)ϵ "r ϩR CM (t),t…, where R CM (t) is the time evolution of the center of mass of the system.…”

Section: (A4)mentioning

confidence: 99%

“…In this way one can derive a local current-density-functional theory of both current and density responses valid for slowly varying densities and potentials. This scheme was generalized by Vignale et al (1997) to include dynamical contributions beyond the linear response. In particular, exchange and correlation beyond the TDLDA lead to the appearance of complex and frequency-dependent viscoelasticity stresses that, in the homogeneous electron-gas case, provide an additional damping mechanism to the decay into electron-hole pairs.…”

Section: (A4)mentioning

confidence: 99%

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Electronic excitations: density-functional versus many-body Green’s-function approaches

2002

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Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green's-function equations, starting with a one-electron propagator and considering the electron-hole Green's function for the response. Key ingredients are the electron's self-energy ⌺ and the electron-hole interaction. A good approximation for ⌺ is obtained with Hedin's GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of ⌺. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green's functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green's functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress. CONTENTS

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Section: The Exchange-correlation Kernel F XCmentioning

confidence: 71%

Section: (A4)mentioning

confidence: 99%

Section: (A4)mentioning

confidence: 99%

Section: (A4)mentioning

confidence: 99%

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Electronic excitations: density-functional versus many-body Green’s-function approaches

2002

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“…11,12 By studying a weakly inhomogeneous electron gas, they found a dynamical exchange-correlation vector potential as a functional of the current density that is nonlocal in time but still local in space. It was later shown by Vignale et al 23 that the exchange-correlation vector potential obtained by Vignale and Kohn 11,12 could be recast in terms of a viscoelastic stress tensor, making the formalism physically more transparent. The Vignale-Kohn ͑VK͒ functional was derived under the constraints k , q Ӷ k F , / v F , where k is the length of the wave vector of the external perturbation, q is the length of the wave vector of the inhomogeneity of the ground-state density, and k F and v F are the local Fermi wave vector and velocity, respectively.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Vignale-Kohn current functional in the calculation of the optical spectra of semiconductors

2007

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Analysis of the Vignale-Kohn current functional in the calculation of the optical spectra of semiconductors Berger, J. A.; de Boeij, P. L.; van Leeuwen, R. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. In this work, we investigate the Vignale-Kohn current functional when applied to the calculation of optical spectra of semiconductors. We discuss our results for silicon. We found qualitatively similar results for other semiconductors. These results show that there are serious limitations to the general applicability of the VignaleKohn functional. We show that the constraints on the degree of nonuniformity of the ground-state density and on the degree of the spatial variation of the external potential under which the Vignale-Kohn functional was derived are almost all violated. We argue that the Vignale-Kohn functional is not suited to use in the calculation of optical spectra of semiconductors since the functional was derived for a weakly inhomogeneous electron gas in the region above the particle-hole continuum, whereas the systems we study are strongly inhomogeneous and the absorption spectrum is closely related to the particle-hole continuum. DOI: 10.1103/PhysRevB.75.035116 PACS number͑s͒: 71.45.Gm, 31.15.Ew, 78.20.Ϫe, 78.66.Db I. INTRODUCTIONTime-dependent density functional theory ͑TDDFT͒ developed by Runge and Gross 1 makes it possible to describe the dynamic properties of interacting many-particle systems in an exact manner. 1-4 Dhara and Ghosh 5 and Ghosh and Dhara 6 showed that the Runge-Gross theorem could be extended to systems that are subjected to general timedependent electromagnetic fields ͑see also Ref. 7͒. The method has proven to be an accurate tool in the study of electronic response properties. 3,8,9 In this paper, we study infinite systems for which we use time-dependent currentdensity-functional theory ͑TDCDFT͒. 7,[10][11][12] In this approach, the electron density of TDDFT is substituted by the electron current density as the fundamental quantity. There are mainly three reasons to use TDCDFT instead of ordinary TDDFT. The first reason is related to the use of periodic boundary conditions, which provide an efficient way to describe infinite systems but that artificially remove the effects of density changes at the surface. 13 For example, when a system is perturbed by an electric field there will be a macroscopic response of the system and a current will be flowing through the interior with a n...

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Excited States from Time‐Dependent Density Functional Theory

Elliott¹,

Furche²,

Burke³

2008

Reviews in Computational Chemistry

222

195

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Time-dependent density functional theory (TDDFT) is presently enjoying enormous popularity in quantum chemistry, as a useful tool for extracting electronic excited state energies. This article explains what TDDFT is, and how it differs from ground-state DFT. We show the basic formalism, and illustrate with simple examples. We discuss its implementation and possible sources of error. We discuss many of the major successes and challenges of the theory, including weak fields, strong fields, continuum states, double excitations, charge transfer, high harmonic generation, multiphoton ionization, electronic quantum control, van der Waals interactions, transport through single molecules, currents, quantum defects, and, elastic electron-atom scattering. ContentsVII. Beyond standard functionals 22 A. Double excitations 22 B. Polymers 23 C. Solids 23 D. Charge transfer 23 VIII. Other topics 23 A. Ground-state XC energy 23 B. Strong fields 24 C. Transport 25

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Time-Dependent Density Functional Theory Beyond the Adiabatic Local Density Approximation

Cited by 249 publications

References 18 publications

Electronic excitations: density-functional versus many-body Green’s-function approaches

Electronic excitations: density-functional versus many-body Green’s-function approaches

Analysis of the Vignale-Kohn current functional in the calculation of the optical spectra of semiconductors

Excited States from Time‐Dependent Density Functional Theory

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