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## 9th Workshop on Time-Dependent Density-Functional Theory: Prospects and Applications

#### Benasque Center for Science (Benasque, Spain)

#### Organisers

This will be the ninth edition of a combined event (School + Workshop) that regularly reviews the fundamentals, progress, and applications of time-dependent density-functional theory, and related electronic structure techniques. While this is an application for the Workshop, we will organize the full event, that includes a previous School, at which early stage researchers are exposed to the

fundamentals of the theory, and practice hand-on exercises.

Time-dependent density-functional theory (TDDFT) is one of the many methods that can be used to understand the excited electronic structure of atoms, molecules, or materials. It can be viewed as an extension of density functional theory (DFT) to time-dependent problems, and as an alternative formulation of time-dependent quantum mechanics. The basic rationale behind DFT is the reformulation of the many-electron problem (roughly speaking, an equation with 3N variables, where N is the number of electrons) as a problem whose basic variable is the one-particle density, an object depending on the three spatial variables. Alternatively, we can view DFT as a manner to tackle with the interacting many-electron problem by studying a much easier non-interacting one (since in almost all cases it is the Kohn-Sham formulation of DFT that is used). TDDFT is based on the same reduction of complexity. The advantages are clear: a complex function in 3N-dimensional space is replaced by a real function that depends solely on 3-dimensional vector - the density. Usually this is obtained using an auxiliary system of non-interacting electrons that feel an effective time dependent potential, the time-dependent Kohn-Sham potential. Its exact form is, however, unknown, and has to be approximated.

TDDFT is by no means the only approach to the excitations of many-electron systems. In fact, more accurate (yet more expensive) techniques (based on many-body perturbation theory, for example) exist, and therefore these alternatives will also be covered at the workshop, in particular their relation and comparison to TDDFT. However, TDDFT achieves a good balance between accuracy and

computational cost. In consequence, its use is increasing, and it is fast becoming one of the tools of choice to get accurate and reliable predictions for excited-state properties in solid state physics, chemistry and biophysics, both in the linear and non-linear regimes. Around 300 publications every year contain results computed with TDDFT, and this number is increasing. This interest has been motivated by the recent developments of TDDFT (and time-dependent current functional theory) and include the description of photo-absorption cross section of molecules and nanostructures, electron-ion dynamics in the excited state triggered by either a small or high intense laser fields, van der Waals interactions, development of new functionals coping with memory and non-locality

effects, applications to biological systems (chromophores), transport phenomena, optical spectra of solids and low- dimensional structures (as nanotubes, polymers, surfaces...). All these possibilities add up to the scientific success of TDDFT.

TDDFT is still a young discipline. For example, pretty much as it happened with ground state DFT, it has taken a few decades since the “official” birth of the theory until we are witnessing fully rigorous mathematical studies of its foundations. Likewise, the youth of the discipline is demonstrated by the fact that it is only recently that somehow “obvious” applications of it, such as real-time simulations of high intensity laser irradiation of solids, have appeared. Technical and theoretical difficulties slowed the progress of these studies for years.

## References

**Germany**

Miguel Marques (Martin-Luther University Halle Wittenberg) - Organiser

Angel Rubio (Max Planck Institute for the Structure and Dynamics of Matter) - Organiser

**Israel**

Hardy Gross (The Hebrew University of Jerusalem) - Organiser

**Portugal**

Fernando Nogueira (University of Coimbra) - Organiser

**Spain**

Alberto Castro (ARAID Foundation) - Organiser

**United States**

Neepa Maitra (Rutgers University at Newark) - Organiser