- Time-dependent density functional theory
**Time-dependent density functional theory (TDDFT)**is a quantum mechanical method used inphysics and chemistry to investigate the proprieties of many-body systems beyond the ground statestructure. It's an extension ofdensity functional theory (DFT) to the time-dependent domain asa method to describe such systems when a time dependent perturbation is applied and, asDFT, it's becoming one of the the most popular and versatilemethods available in condensed matter physics, computational physics, and computational chemistry.The main ideas of such approach are the same we can find in DFT being the density of the system,at least in the first formulation of the method, the key quantity. So, respect to the direct quantum mechanical approach, one has to play with a single variable quantity and not with themulti-variable wave-function. Still as for the ground state approach one can construct aKohn-Sham (KS) time dependent systems of non interacting particles which gives the same density of the physical interacting system and in which all the effects of the interaction are shiftedin a local effective potential. The main difference here with respect to DFT is that the exacteffective potential in a generic instant will depend on the density of the systems at all the previous instants.

The main success of TDDFT till now has been its application in the calculation of electron excitedstates, mainly for isolated systems, where the method is used in the linear regime domain.The excited states energies can be computed as the poles of the response function of the systemwhich can be computed using a Dyson equation. The key ingredients become the KS not interacting response function and the Hartree plus exchange-correlation kernel which is the

functional derivative of the effective potential with respect to the density.As for DFT one has to do approximations. The most popular is the adiabatic approximationwhich is the respective of the Local Density Approximation (LDA) in the time domain, so thatthe effective potential in a generic instantdepends only the density of the systems at that instant; the excitation's energies are usually computedwithin Adiabatic + Local Density approximation (ALDA). The results are quite good but still the approachsuffer of some problems, some of which are due to the errors in the DFT/LDA ground state calculation, as theunderestimation ionization energy, some others which are due to the adiabatic approximation, such as thelack of multi-electron excitations within this approximation.

The equations of TDDFT rely on the Runge-Gross theorem (1984) which is the time-dependent analogof the Hohenberg-Kohn theorem (1964) for DFT. The complete theorem is valid only for isolated systems, while for periodic infinite systems one as to use some more general approach asfor example Time Dependet Current Density Functional Theory (TDCDFT) developed by Vignale, in which thefundamental quantity is the current density.

**Formalism of TDDFT****Introduction**Consider a many body system described by the Hamiltonian::$H=T+V\text{'}^\{ext\}+W$where $T$ is the kinetic energy, $V^\{ext\}$ is an external potentialand $W$ is a two body operator which describes the interactions among the particlesof the system.The basic assumption of DFT uses Kohn-Sham orbitals in the following way. For a fixed nuclear framework, the KS-Hamiltonian contains three terms: $T$ is the kinetic energyof the electrons, $V^\{ext\}$ is the potential due to the nuclei and$W=sum\_\{i\; eq\; j\}frac\{e^2\}+f\_\{xc\}(mathbf\{r\}\_2\text{'}t\_2\text{'},mathbf\{r\}\_1\text{'}t\_1\text{'})\; ight)chi(mathbf\{r\}\_1\text{'}t\_1\text{'},mathbf\{r\}\_2t\_2)$

From this last equation it is possible to derive the excitations energies of the system, as these are simply the poles of the response function.

**Key papers*** [

*http://dx.doi.org/10.1103/PhysRev.136.B864 P. Hohenberg and W. Kohn, Phys. Rev. 136 (1964) B864*]

* [*http://dx.doi.org/10.1103/PhysRevLett.52.997 E. Runge and E.K.U. Gross, Phys. Rev. Lett. 52 (1984) 997*]**Books on TDDFT*** M.A. L.Marques, C.A. Ullrich, F. Nogueira, A. Rubio, K. Burke, and E.K.U. Gross, Time-Dependent Density Functional Theory. (Springer-Verlag, 2006). ISBN 978-3-540-35422-2

**External links*** [

*http://tddft.org tddft.org*]

* [*http://th.physik.uni-frankfurt.de/~engel/tddft.html Brief introduction of TD-DFT*]

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Density functional theory**— Electronic structure methods Tight binding Nearly free electron model Hartree–Fock method Modern valence bond Generalized valence bond Møller–Plesset perturbation theory … Wikipedia**Perturbation theory (quantum mechanics)**— In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a … Wikipedia**Dynamical mean field theory**— (DMFT) is a method to determine the electronic structure of strongly correlated materials. In such materials, the approximation of independent electrons, which is used in Density Functional Theory and usual band structure calculations, breaks… … Wikipedia**Optimal foraging theory**— Ants dismember a larger insect. Optimal foraging theory predicts these insects will forage in such a way as to maximize their colony s energy intake per unit time. Optimal foraging theory is an idea in ecology based on the study of foraging… … Wikipedia**Scalar-tensor theory**— Scalar tensor theories are theories that include a scalar field as well as a tensor field to represent an interaction, especially the gravitational one. Tensor fields and field theory Modern physics tries to derive all physical theories from as… … Wikipedia**Scalar field theory**— In theoretical physics, scalar field theory can refer to a classical or quantum theory of scalar fields. A field which is invariant under any Lorentz transformation is called a scalar , in contrast to a vector or tensor field. The quanta of the… … Wikipedia**Entropy (information theory)**— In information theory, entropy is a measure of the uncertainty associated with a random variable. The term by itself in this context usually refers to the Shannon entropy, which quantifies, in the sense of an expected value, the information… … Wikipedia**Theorie de la fonctionnelle de la densite**— Théorie de la fonctionnelle de la densité Méthodes numériques pour le calcul de la structure électronique Hartree Fock Théorie de la perturbation de Møller Plesset Interaction de configuration Méthode du cluster couplé Champ multi… … Wikipédia en Français**Théorie de la fonctionnelle de la densité**— Pour les articles homonymes, voir DFT. La théorie de la fonctionnelle de la densité (pour Density Functional Theory, sous entendu électronique : DFT) constitue au début du XXIe siècle l une des méthodes les plus utilisées dans les… … Wikipédia en Français**Théorie de la fonctionnelle densité**— Théorie de la fonctionnelle de la densité Méthodes numériques pour le calcul de la structure électronique Hartree Fock Théorie de la perturbation de Møller Plesset Interaction de configuration Méthode du cluster couplé Champ multi… … Wikipédia en Français