## Density Functional Theory: An Advanced CourseDensity Functional Theory (DFT) has firmly established itself as the workhorse for atomic-level simulations of condensed phases, pure or composite materials and quantum chemical systems. This work offers a rigorous and detailed introduction to the foundations of this theory, up to and including such advanced topics as orbital-dependent functionals as well as both time-dependent and relativistic DFT. Given the many ramifications of contemporary DFT, the text concentrates on the self-contained presentation of the basics of the most widely used DFT variants: this implies a thorough discussion of the corresponding existence theorems and effective single particle equations, as well as of key approximations utilized in implementations. The formal results are complemented by selected quantitative results, which primarily aim at illustrating the strengths and weaknesses of particular approaches or functionals. The structure and content of this book allow a tutorial and modular self-study approach: the reader will find that all concepts of many-body theory which are indispensable for the discussion of DFT - such as the single-particle Green's function or response functions - are introduced step by step, along with the actual DFT material. The same applies to basic notions of solid state theory, such as the Fermi surface of inhomogeneous, interacting systems. In fact, even the language of second quantization is introduced systematically in an Appendix for readers without formal training in many-body theory. |

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### Contents

1 | |

10 | |

Chapter 3 Effective SingleParticle Equations | 57 |

Chapter 4 ExchangeCorrelation Energy Functional | 109 |

Chapter 5 Virial Theorems | 219 |

Optimized Potential Method | 227 |

Chapter 7 TimeDependent Density Functional Theory | 307 |

Chapter 8 Relativistic Density Functional Theory | 350 |

Appendix C Scaling Behavior of ManyBody Methods | 432 |

ThomasFermi Models and Beyond | 437 |

Appendix E Asymptotic Behavior of QuasiParticle Amplitudes | 445 |

Appendix F Quantization of Noninteracting Fermions in Relativistic Quantum Field Theory | 448 |

Appendix G Renormalization Scheme of Vacuum QED | 457 |

Appendix H Relativistic Homogeneous Electron Gas | 467 |

Appendix I Renormalization of Inhomogeneous Electron Gas | 481 |

Appendix J Gradient Corrections to the Relativistic LDA | 485 |

Chapter 9 Further Reading | 401 |

Introduction | 402 |

Density Functional Theory | 402 |

Density Functional Theory | 402 |

Appendix A Functionals and the Functional Derivative | 403 |

Appendix B Second Quantization in ManyBody Theory | 413 |

### Other editions - View all

Density Functional Theory: An Advanced Course Eberhard Engel,Reiner M. Dreizler No preview available - 2013 |

Density Functional Theory: An Advanced Course Eberhard Engel,Reiner M. Dreizler No preview available - 2011 |

Density Functional Theory: An Advanced Course Eberhard Engel,Reiner M. Dreizler No preview available - 2011 |

### Common terms and phrases

applied approximation atoms BLYP Bohr calculations Chem complete component contribution correlation energy corresponding Coulomb counterterms denotes Density Functional Theory discussion Dyson equation Eext eigenstates eigenvalues electron gas energy functional evaluation exact exchange exchange energy exchange potential expansion external potential Fermi fermion finite Fock space functional derivative gauge gauge transformation given gradient Green’s function ground state density ground state energy Hamiltonian inhomogeneous insertion integration interacting system kinetic energy KS equations KS orbitals leads limit linear magnetic many-body molecules N-particle noninteracting nonlocal nonrelativistic obtained operator orbital-dependent particle number perturbation Phys quantum RDFT relation relativistic renormalization representation response function REXX RHEG right-hand side second order Sect selfconsistent single-particle Slater determinant ſº space spin spin-density theorem tion total energy v-representable vacuum vanishes vext wavefunction x-only xc-energy xc-functional