Time-dependent density-functional theory for extended systems

TitleTime-dependent density-functional theory for extended systems
Publication TypePalaiseau Article

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Author Address

Botti, S (Reprint Author), Ecole Polytech, ETSF, F-91128 Palaiseau, France. Ecole Polytech, ETSF, F-91128 Palaiseau, France. Ecole Polytech, CNRS, CEA, Solides Irradies Lab, F-91128 Palaiseau, France. Forschungszentrum Julich, Inst Festkorperforsch, D-52425 Julich, Germany. Max Planck Gesell, Fritz Haber Inst, D-14195 Berlin, Germany. Univ Roma Tor Vergata, CNR, INFM, Inst Stat Mech & Complex, I-00133 Rome, Italy. Univ Roma Tor Vergata, Dipartimento Fis, I-00133 Rome, Italy.

Botti, S, Schindlmayr, A, Del Sole, R, Reining, L
Year of Publication2007
JournalRep. Prog. Phys.
Type of WorkReview

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 density instead of the many-body wavefunction. The density can be determined in an efficient scheme by solving one-particle non-interacting Schrodinger equations -the Kohn-Sham equations. The complication of the problem is hidden in the unknown -time-dependent exchange and correlation potential that appears in the Kohn-Sham equations and for which it is essential to find good approximations. Many approximations have been suggested and tested for finite systems, where even the very simple adiabatic local-density approximation (ALDA) has often proved to be successful. In the case of solids, ALDA fails to reproduce optical absorption spectra, which are instead well described by solving the Bethe Salpeter equation of many-body perturbation theory (MBPT). On the other hand, ALDA can lead to excellent results for loss functions (at vanishing and finite momentum transfer). In view of this and thanks to recent successful developments of improved linear-response kernels derived from MBPT, TDDFT is today considered a promising alternative to MBPT for the calculation of electronic spectra, even for solids. After reviewing the fundamentals of TDDFT within linear response, we discuss different approaches and a variety of applications to extended systems.

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