Time-dependent Density-functional Theory

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. This is a very pedagogical introduction to the central ideas of time-dependent density-functional theory. The theory is described in depth and illustrated with many insightful examples and applications in atomic, molecular and condensed matter physics. This is a valuable book for both students and researchers. Robert van Leeuwen, University of Jyvaskyla1. Introduction ; 2. Review of ground-state density-functional theory ; 3. Fundamental existence theorems ; 4. Time-dependent Kohn-Sham scheme ; 5. Time-dependent observables ; 6. Properties of the time-dependent xc potential ; 7. The formal framework of linear-response TDDFT ; 8. The frequency-dependent xc kernel ; 9. Applications in atomic and molecular systems ; 10. Time-dependent current-DFT ; 11. Time-dependent optimized effective potential ; 12. Extended systems ; 13. TDDFT and many-body theory ; 14. Long-range correlations and dispersion interactions ; 15. Nanoscale transport and molecular junctions ; 16. Strong-field phenomena and optimal control ; 17. Nuclear motion ; A. Atomic units ; B. Functionals and functional derivatives ; C. Densities and density matrices ; D. Hartree-Fock and other wave-function approaches ; E. Constructing the xc potential from a given density ; F. DFT for excited states ; G. Systems with noncollinear spin ; H. The dipole approximation ; I. A brief review of classical fluid dynamics ; J. Constructing the scalar from the tensor xc kernel ; K. Semiconductor quantum wells ; L. TDDFT in a Lagrangian frame ; M. Inversion of the dielectric matrix ; N. Review literature in DFT and many-body theory ; O. TDDFT computer codes