## Time-Dependent Density-Functional Theory: Concepts and ApplicationsTime-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. |

### Contents

Introduction | 1 |

Review of groundstate densityfunctional theory | 10 |

The basic formalism of TDDFT | 43 |

Linear response and excitation energies | 121 |

Further developments | 211 |

Special topics | 331 |

Atomic units | 416 |

Functionals and functional derivatives | 419 |

Systems with noncollinear spins | 439 |

The dipole approximation | 445 |

A brief review of classical fluid dynamics | 450 |

Constructing the scalar xc kernel from the tensor xc kernel | 455 |

Semiconductor quantum wells | 458 |

TDDFT in a Lagrangian frame | 465 |

Inversion of the dielectric matrix | 477 |

Review literature on DFT and manybody theory | 479 |

### Other editions - View all

Time-dependent Density-functional Theory: Concepts and Applications Carsten A. Ullrich No preview available - 2019 |

Time-Dependent Density-Functional Theory: Concepts and Applications Carsten Ullrich No preview available - 2012 |

### Common terms and phrases

adiabatic adiabatic approximation ALDA atoms calculated Casida Chapter Chem correlation energy Coulomb current density d³r defined Density Functional Theory density functionals density matrix dependence derivative dipole discuss dynamics eigenvalues electric field exact excitation energies excitonic Exercise external potential finite formalism frequency frequency-dependent given Green's functions ground-state density Hamiltonian Hartree homogeneous electron liquid initial integral interaction ionization Kohn Kohn-Sham equation laser pulse Leeuwen linear linear-response many-body system matrix molecular molecules no(r nonadiabatic obtained oscillations parameter particle number permission from APS perturbation Phys plasmon propagation quantum response function Runge-Gross Schrödinger equation Section single-particle Slater determinant spatial spectra spectrum spin stress tensor t₁ TDDFT TDKS TDKS equation TDOEP theorem theory time-dependent density time-dependent Schrödinger equation Ullrich vector potential velocity Vignale wave function x-only xc energy xc functionals xc kernel xc potential хс