Time-Dependent Density Functional Theory beyond Linear Response: An Exchange-Correlation Potential with Memory

Dobson, John F.; Bünner, M. J.; Gross, E. K. U.

doi:10.1103/physrevlett.79.1905

Cited by 105 publications

(95 citation statements)

References 21 publications

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“…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%

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: (A4)mentioning

confidence: 99%

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

2002

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“…To date, such a prescription is only partially available [3,4]. A recently published method by Tokatly et al [11] also attempts to achieve this goal in a different way, based on the Landau Fermi-liquid theory where the local Lorentz force is a divergence of a stress tensor.…”

Section: Introductionmentioning

confidence: 99%

“…It is therefore robust and, one hopes, applicable beyond linear response. The present formulations of memory prescriptions [3,4,13] apply directly to potentials and usually cannot be derived from a 3-dimensional action principle.…”

Section: Introductionmentioning

confidence: 99%

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Time-dependent exchange-correlation current density functionals with memory

Kurzweil

Baer

2004

The Journal of Chemical Physics

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Most present applications of time-dependent density functional theory use adiabatic functionals, i.e. the effective potential at time t is determined solely by the density at the same time. This paper discusses a method that aims to go beyond this approximation, by incorporating "memory" effects: the potential will depend not only on present behavior but also on the past. In order to ensure the derived potentials are causal, we formulate the action on the Keldysh contour for electrons in electromagnetic fields, from which we derive suitable Kohn-Sham equations. The exchange correlation action is now a functional of the electron density and velocity field. A specific action functional is constructed which is Galilean invariant and yields a causal vector potential term to the Kohn-Sham equations that incorporates causal memory effects. We show explicitly that the exchange-correlation Lorentz force is zero. The potential is consistent with known dynamical properties of the homogeneous electron gas (in the linear response limit).

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“…Recently, the feasibility of excitation-energy computations relying on two other, widely applicable, DFT-based formalisms has been demonstrated for atoms and small molecules. The first [4][5][6][7][8][9] starts from the extension of DFT to time-dependent (TD) phenomena [12][13][14] (TDDFT). The second [10,11,15], due to Görling and Levy, builds a perturbation theory (GLPT) in the difference between the many-body and the second-quantized Kohn-Sham (KS) Hamiltonians, where the parameter of the perturbation is the coupling constant of the particle interaction, in such a way that, at each order, the exact density is recovered.…”

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Exchange and Correlation Kernels at the Resonance Frequency: Implications for Excitation Energies in Density-Functional Theory

Gonze

Scheffler

1999

Phys. Rev. Lett.

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Specific matrix elements of exchange and correlation kernels in time-dependent density-functional theory are computed. The knowledge of these matrix elements not only constrains approximate timedependent functionals. It also allows one to link different practical approaches to excited states, based either on density-functional theory or on many-body perturbation theory, despite the approximations that have been performed to derive them. [S0031-9007(99) [10,11,15], due to Görling and Levy, builds a perturbation theory (GLPT) in the difference between the many-body and the second-quantized Kohn-Sham (KS) Hamiltonians, where the parameter of the perturbation is the coupling constant of the particle interaction, in such a way that, at each order, the exact density is recovered.As an alternative to these DFT-based efforts, one may start from many-body perturbation theory and perform partial resummations of diagrams such as to build a screened interaction between dressed particles (quasiparticles) [16]. At the lowest order in the screened interaction, one obtains Hedin's GW approximation [17] to quasiparticle energies (one particle is added or subtracted to the system), while the energy of excited states for which the number of particles is conserved can be deduced, in a subsequent step, from a Bethe-Salpeter (BS) equation describing the interaction between quasiparticles (e.g., electron-hole pairs). The application of these techniques to real materials is very demanding [18].In the present Letter, we explore the relationships between excitation energies derived from time-dependent density-functional theory, the Görling-Levy perturbation theory, and the screened-interaction many-body perturbation theory. If excitation energies were derived without approximations, in the three formalisms, the results should be identical. Because of the specific theoretical developments, the most obvious simplifications are different, so that the practical schemes derived from these formalisms also differ. We find that some approximations used for practical calculations leave a connection between the approaches, at variance with the usual adiabatic local-density approximation (ALDA) in TDDFT [4][5][6], that leads to a different physical picture.The expressions from different approaches are linked thanks to a new technique for computing selected elements of TD functional kernels at resonance, that is, at the frequencies corresponding to differences in KS eigenvalues, for which the independent-particle susceptibility of the KS system is resonant. It is first applied to the exact exchange kernel, whose matrix elements appear in a simplified TDDFT treatment of excitation energies based on a Laurent expansion, and are found identical to the first-order corrections to KS eigenvalues differences, in the GLPT. The knowledge of these matrix elements imposes a new constraint on approximate functionals. The same technique is then applied to an explicit exchangecorrelation (XC) functional that includes an approximate correlation contribution. It i...

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Time-Dependent Density Functional Theory beyond Linear Response: An Exchange-Correlation Potential with Memory

Cited by 105 publications

References 21 publications

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

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

Time-dependent exchange-correlation current density functionals with memory

Exchange and Correlation Kernels at the Resonance Frequency: Implications for Excitation Energies in Density-Functional Theory

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