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Density Functional Theory

An Advanced Course

Eberhard Engel, Reiner M. Dreizler (Autoren)

Buch | Hardcover

XV, 531 Seiten

2011 | 2011
Springer Berlin (Verlag)
978-3-642-14089-1 (ISBN)

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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.

Introduction.- Foundations of Density Functional Theory: Existence Theorems.- Effective Single-Particle Equations.- Exchange-Correlation Energy Functional.- Virial Theorems.- Orbital Functionals: Optimized Potential Method.- Time-Dependent Density Functional Theory.- Relativistic Density Functional Theory.- Further Reading.- Appendices: Functionals and the Functional Derivative.- Second Quantization in Many-Body Theory.- Scaling Behavior of Many-Body Methods.- Explicit Density Functionals for the Kinetic Energy: Thomas-Fermi Models and Beyond.- Asymptotic Behavior of Quasi-Particle Amplitudes.- Quantization of Noninteracting Fermions in Relativistic Quantum Field Theory.- Renormalization Scheme of Vacuum QED.- Relativistic Homogeneous Electron Gas.- Renormalization of Inhomogeneous Electron Gas.- Gradient Corrections to the Relativistic LDA.- Gordon Decomposition.- Some Useful Formulae.- Index.

From the reviews:

"This book is an introduction to density functional theory (DFT) ... . The presentation is ... aimed at a general scientific audience (physics, chemistry, etc.). ... There are ... many interesting choices in the covered topics. ... Several appendices help in making the book self-contained." (Gabriel Stoltz, Mathematical Reviews, Issue 2011 m)

"The book is remarkable for a down-to-earth exposition of DFT that makes it accessible for students specialized in different fields of theoretical physics. ... The book may be useful both for beginners as an introduction to DFT and for specialists who would like to expand their view on rigorous foundations of this theory and to keep an eye on the cutting edge of computational methods in condense matter physics." (Peter Kazinski, Zentralblatt MATH, Vol. 1216, 2011)

Erscheint lt. Verlag	17.2.2011
Reihe/Serie	Theoretical and Mathematical Physics
Zusatzinfo	XV, 531 p. 15 illus., 10 illus. in color.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	912 g
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
Schlagworte	density functional theory • Exchange-Correlation Energy • Kohn-Sham Equations
ISBN-10	3-642-14089-0 / 3642140890
ISBN-13	978-3-642-14089-1 / 9783642140891
Zustand	Neuware