Density Functional Theory

1. Front Matter

   Pages i-xv

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2. Introduction

   • Eberhard Engel, Reiner M. Dreizler

   Pages 1-9

3. Foundations of Density Functional Theory: Existence Theorems

   • Eberhard Engel, Reiner M. Dreizler

   Pages 11-56

4. Effective Single-Particle Equations

   • Eberhard Engel, Reiner M. Dreizler

   Pages 57-108

5. Exchange-Correlation Energy Functional

   • Eberhard Engel, Reiner M. Dreizler

   Pages 109-217

6. Virial Theorems

   • Eberhard Engel, Reiner M. Dreizler

   Pages 219-226

7. Orbital Functionals: Optimized Potential Method

   • Eberhard Engel, Reiner M. Dreizler

   Pages 227-306

8. Time-Dependent Density Functional Theory

   • Eberhard Engel, Reiner M. Dreizler

   Pages 307-349

9. Relativistic Density Functional Theory

   • Eberhard Engel, Reiner M. Dreizler

   Pages 351-399

10. Further Reading

    • Eberhard Engel, Reiner M. Dreizler

    Pages 401-402

11. Erratum to: Introduction

    • Eberhard Engel, Reiner M. Dreizler

    Pages E1-E1

12. Erratum to: Density Functional Theory

    • Eberhard Engel, Reiner M. Dreizler

    Pages E3-E4

13. Erratum to: Density Functional Theory

    • Eberhard Engel, Reiner M. Dreizler

    Pages E5-E7

14. Back Matter

    Pages 403-531

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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.

• Density Functional Theory
• Exchange-Correlation Energy
• Kohn-Sham Equations

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)

• Center for Scientific Computing and Institute of Theoretical Physics, Johann Wolfgang Goethe-Universität Frankfurt/Main, Frankfurt am Main, Germany

  Eberhard Engel

• Institute of Theoretical Physics Dept. of Physics, Johann Wolfgang Goethe-Universität Frankfurt/Main, Frankfurt am Main, Germany

  Reiner M. Dreizler

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