The year 2004 was a remarkable one for the growing ?eld of time-dependent density functional theory (TDDFT). Not only did we celebrate the 40th - niversary of the Hohenberg-Kohn paper, which had laid the foundation for ground-state density functional theory (DFT), but it was also the 20th - niversary of the work by Runge and Gross, establishing a ?rm footing for the time-dependent theory. Because the ?eld has grown to such prominence, and has spread to so many areas of science (from materials to biochemistry), we feel that a volume dedicated to TDDFT is most timely. TDDFT is based on a set of ideas and theorems quite distinct from those governingground-stateDFT, butemployingsimilar techniques.Itisfarmore than just applying ground-state DFT to time-dependent problems, as it - volves its own exact theorems and new and di?erent density functionals. Presently, themostpopularapplicationistheextractionofelectronicexcit- state properties, especially transition frequencies. By applying TDDFT after thegroundstateofamoleculehasbeenfound, wecanexploreandunderstand the complexity of its spectrum, thus providing much more information about the species. TDDFT has a especially strong impact in the photochemistry of biological molecules, where the molecules are too large to be handled by t- ditional quantum chemical methods, and are too complex to be understood with simple empirical frontier orbital theo

Time-dependent density-functional theory (TDDFT) describes the quantum dynamics of interacting electronic many-body systems formally exactly and in a practical and efficient manner. TDDFT has become the leading method for calculating excitation energies and optical properties of large molecules, with accuracies that rival traditional wave-function based methods, but at a fraction of the computational cost. This book is the first graduate-level text on the concepts and applications of TDDFT, including many examples and exercises, and extensive coverage of the literature. The book begins with a self-contained review of ground-state DFT, followed by a detailed and pedagogical treatment of the formal framework of TDDFT. It is explained how excitation energies can be calculated from linear-response TDDFT. Among the more advanced topics are time-dependent current-density-functional theory, orbital functionals, and many-body theory. Many applications are discussed, including molecular excitations, ultrafast and strong-field phenomena, excitons in solids, van der Waals interactions, nanoscale transport, and molecular dynamics.