Time-Dependent Density-Functional Theory Concepts and Applications Oxford Graduate Texts Series

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.

1. 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.

Carsten A. Ullrich, Department of Physics and Astronomy, University of Missouri - Columbia.

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.