Colloquium on June 13th, 2005Eberhard K. U. Gross Freie Universität Berlin Timedependent density functional theory: Basic concepts and new developments For large manyparticle systems, the wave function is an illegitimate scientific concept [Walter Kohn, Nobel Lecture], illegitimate in the sense that it can neither be calculated nor stored. Modern density functional theory is based on the suprising fact that knowledge of the groundstate density alone is sufficient to calculate all physical observables of a stationary quantum system. In this lecture, a timedependent generalization of density functional theory (TDDFT) will be presented. After an overview of the basic concepts, several new developments will be described. Those include: (i) A generalizaion of TDDFT which treats both electrons and nuclei quantum mechanically. (ii) A timedependent generalization of the socalled electron localization function which allows the timeresolved visualization of the formation, the modulation, and the breaking of chemical bonds. Movies of a laserinduced pipi* transition and of a protonmolecule scattering process will be presented. (iii) Optimalcontrol theory will be generalized to treat timedependent targets. In this way, the timedependent density may be controlled directly. (iv) Finally, a novel approach treating molecular electronics with TDDFT will be shown.  

