Many-body Diagrammatic Expansion for the Exchange-Correlation Kernel in Time Dependent Density Functional Theory

@article{Tokatly2002ManybodyDE,
  title={Many-body Diagrammatic Expansion for the Exchange-Correlation Kernel in Time Dependent Density Functional Theory},
  author={Ilya V. Tokatly and R. Stubner and O. A. Pankratov},
  journal={Physical Review B},
  year={2002},
  volume={65},
  pages={113107}
}
The central problem of time dependent density functional theory (TDDFT) 1 is to find an adequate approximation for the dynamic exchange-correlation (xc) potential vxc. In contrast to static DFT, where the local density approximation (LDA) has been extremely successful, no universal recipe for a dynamic vxc has been found, and it remains unclear if such a recipe exists. The adiabatic LDA (ALDA), which is most popular in practical TDDFT calculations, is valid, by its nature, only in a quasistatic… 
Time-dependent density-functional theory for extended systems
For the calculation of neutral excitations, time-dependent density functional theory (TDDFT) is an exact reformulation of the many-body time-dependent Schrodinger equation, based on knowledge of the
Time-dependent density-functional theory for periodic solids: assessment of excitonic exchange–correlation kernels
We review recent theoretical and computational developments in time-dependent density-functional theory (TDDFT) for periodic insulators and semiconductors. To capture excitonic effects within a
Double excitations in finite systems.
TLDR
A frequency-dependent xc kernel is introduced, which can reproduce, within TDDFT, double excitations in finite systems, and is used in the Bethe-Salpeter equation with a dynamically screened Coulomb interaction W(omega), which can describe these excitations.
Long-range contribution to the exchange-correlation kernel of time-dependent density functional theory
of time-dependent density functional theory. We show that the optical absorption spectrum of solids exhibiting a strong continuum excitonic effect is considerably improved with respect to
Many-Body Perturbation Theory (MBPT) and Time-Dependent Density-Functional Theory (TD-DFT): MBPT Insights About What Is Missing In, and Corrections To, the TD-DFT Adiabatic Approximation.
TLDR
This chapter focuses on many-body corrections to LR-TD-DFT as one way to build hybrid density-functional/wavefunction methodology for incorporating aspects of nonlocality in time not present in the AA.
Many-Body Perturbation Theory (MBPT) and Time-Dependent Density-Functional Theory (TD-DFT): MBPT Insights About What is Missing in, and Corrections to, the TD-DFT Adiabatic Approximation
In their famous paper Kohn and Sham formulated a formally exact density-functional theory (DFT) for the ground-state energy and density of a system of $N$ interacting electrons, albeit limited at the
Ab initiocalculation of the exchange-correlation kernel in extended systems
We develop a method to calculate the polarizability of a many-electron system within Green's function theory in a similar way as within time-dependent density functional theory and apply it to Si and
Time-dependent current-density-functional theory for the metallic response of solids
We extend the formulation of time-dependent current-density-functional theory for the linear response properties of dielectric and semi-metallic solids [Kootstra , J. Chem. Phys. 112, 6517 (2000)] to
Excitonic effects in time-dependent density-functional theory: An analytically solvable model
Calculation of electronic excitation spectra remains one of the central problems of the quantum theory of solids. Of special interest are two-particle electron-hole excitations, which determine the
Ultra-nonlocality in density functional theory for photo-emission spectroscopy.
TLDR
It is demonstrated that the density functional expression does not provide us with information on the kinetic energy distribution of the photo-electrons and can be obtained from TDCDFT by exactly modeling the experiment in which the photocurrent is split into energy contributions by means of an external electromagnetic field outside the sample, as is done in standard detectors.
...
...