Density Functional Theory: An Advanced Course

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Springer Science & Business Media, Feb 14, 2011 - Science - 531 pages
Density 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

Chapter 1 Introduction
1
Existence Theorems
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
Appendix K Gordon Decomposition
489
Appendix L Some Useful Formulae
492
References
499
Index
517
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