# Benasque 2010: Time-Dependent Density-Functional Theory: Prospects and Applications

## 4th International Workshop and School

### 2010, January 2 - 15

## History

The first three Schools and Workshops were hosted by the Centro de Ciencias de Benasque Pedro Pascual, Spain from August 28th to September 12th, 2004, from August 27th to September 11th, 2006, and from August 31st to September 15th, 2008. The aim of the school was to introduce theoretical, practical, and numerical aspects of time-dependent density-functional theory (TDDFT) to young graduate students, post-docs and even older scientists that are envisaging a project for which TDDFT would be the tool of choice.

Time-dependent density-functional theory (TDDFT) is an extension of density functional theory (DFT) to time-dependent problems, and can be viewed as an alternative formulation of time-dependent quantum mechanics. As in DFT, the wave-function no longer has the leading role: the basic variable of TDDFT is the one-body electron density, n(r,t). The advantages are clear: a complex function in 3N-dimensional space (where N is the number of electrons in the system) - the many-body wave-function - is replaced by a real function that depends solely on the 3-dimensional vector r - the density. Usually n(r,t) 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.

The use of TDDFT 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. 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...).

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