Time-dependent density-functional theory for extended systems

S. Botti, A. Schindlmayr, R. Del Sole, L. Reining, Reports on Progress in Physics 70 (2007) 357–407.

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Abstract
For the calculation of neutral excitations, time-dependent density functional theory (TDDFT) is an exact reformulation of the many-body time-dependent Schrödinger 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 Schrödinger 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.
Publishing Year
Journal Title
Reports on Progress in Physics
Volume
70
Issue
3
Page
357-407
ISSN
eISSN
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Botti S, Schindlmayr A, Del Sole R, Reining L. Time-dependent density-functional theory for extended systems. Reports on Progress in Physics. 2007;70(3):357-407. doi:10.1088/0034-4885/70/3/r02
Botti, S., Schindlmayr, A., Del Sole, R., & Reining, L. (2007). Time-dependent density-functional theory for extended systems. Reports on Progress in Physics, 70(3), 357–407. https://doi.org/10.1088/0034-4885/70/3/r02
@article{Botti_Schindlmayr_Del Sole_Reining_2007, title={Time-dependent density-functional theory for extended systems}, volume={70}, DOI={10.1088/0034-4885/70/3/r02}, number={3}, journal={Reports on Progress in Physics}, publisher={IOP Publishing}, author={Botti, Silvana and Schindlmayr, Arno and Del Sole, Rodolfo and Reining, Lucia}, year={2007}, pages={357–407} }
Botti, Silvana, Arno Schindlmayr, Rodolfo Del Sole, and Lucia Reining. “Time-Dependent Density-Functional Theory for Extended Systems.” Reports on Progress in Physics 70, no. 3 (2007): 357–407. https://doi.org/10.1088/0034-4885/70/3/r02.
S. Botti, A. Schindlmayr, R. Del Sole, and L. Reining, “Time-dependent density-functional theory for extended systems,” Reports on Progress in Physics, vol. 70, no. 3, pp. 357–407, 2007.
Botti, Silvana, et al. “Time-Dependent Density-Functional Theory for Extended Systems.” Reports on Progress in Physics, vol. 70, no. 3, IOP Publishing, 2007, pp. 357–407, doi:10.1088/0034-4885/70/3/r02.
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