Time-dependent Density-functional Theory: Concepts and Applications

ISBN : 9780199563029

Carsten A. Ullrich
544 ページ
178 x 254 mm
Oxford Graduate Texts

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 Ullrich is Associate Professor of Physics at the University of Missouri-Columbia.