Theoretical and Mathematical Physics

An Advanced Course

By: Eberhard Engel, Reiner M. Dreizler

Write A Review

Hardcover | 17 February 2011

At a Glance

Hardcover
552 Pages

Dimensions(cm)
23.5 x 15.88 x 3.18

Hardcover

$229.00

or 4 interest-free payments of $57.25 with

Ships in 5 to 7 business days

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.

Industry Reviews

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)

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $89.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Science Physics Materials & States of Matter Condensed Matter Physics including Liquid State & Solid State Physics Plasma Physics Engineering & Technology Mechanical Engineering & Materials Materials Science Chemistry Physical Chemistry Quantum & Theoretical Chemistry

Quantum Physics & Quantum Mechanics & Quantum Field Theory Atomic & Molecular Physics Mathematical Physics Nuclear Physics

Other Editions and Formats

Paperback

Published: 21st April 2013

View Product

Introduction	p. 1
Foundations of Density Functional Theory: Existence Theorems	p. 11
Hohenberg-Kohn Theorem	p. 11
Degenerate Ground States	p. 18
Variational Equation, Interacting v-Representability, Functional Differentiability	p. 21
Fractional Particle Numbers, Derivative Discontinuity	p. 37
Spin-Polarized Systems	p. 40
Current Density Functional Theory	p. 46
Excited States: Part 1	p. 55
Effective Single-Particle Equations	p. 57
Kohn-Sham Equations	p. 57
Noninteracting v-Representability	p. 70
Degenerate Kohn-Sham Ground States	p. 73
Janak's Theorem, Fractional Particle Numbers	p. 76
Kohn-Sham Equations for Spin-Polarized Systems	p. 80
Interpretation of Kohn-Sham Eigenvalues: Relation to Ionization Potential, Fermi Surface and Band Gap	p. 84
Ionization Potential	p. 84
Fermi Surface	p. 88
Band Gap	p. 99
Kohn-Sham Equations of Current Density Functional Theory	p. 101
Exchange-Correlation Energy Functional	p. 109
Definition of Exact Exchange within DFT	p. 109
Exact Representations of E_xc[n]	p. 115
Variant (a): Kohn-Sham Perturbation Theory	p. 115
Variant (b): Adiabatic Connection	p. 126
Local Density Approximation (LDA)	p. 129
Exchange	p. 131
Correlation: High-Density Limit	p. 132
Correlation: Low-Density Limit	p. 135
Correlation: Interpolation Between High- and Low-Density Regime	p. 135
Density Functional: Local Density Approximation (LDA)	p. 137
Spin-Polarized Electron Gas: Local Spin-Density Approximation (LSDA)	p. 142
Nonlocal Corrections to the LDA	p. 145
Weakly Inhomogeneous Electron Gas	p. 145
Complete Linear Response	p. 152
Gradient Expansion	p. 153
Generalized Gradient Approximation (GGA)	p. 169
Momentum Space Variant	p. 170
Real Space Variant	p. 175
Combination of Momentum and Real Space Variants	p. 179
Semi-Empirical Construction of GGAs	p. 182
Merits and Limitations of GGAs	p. 185
Weighted Density Approximation (WDA)	p. 201
Self-Interaction Corrections (SIC)	p. 202
Meta-GGA (MGGA)	p. 204
LDA+U	p. 211
Virial Theorems	p. 219
Scaling Behavior of Energy Contributions	p. 219
Conventional Virial Theorem	p. 221
DFT Virial Theorem	p. 222
Hellmann-Feynman Theorem	p. 224
Orbital Functionals: Optimized Potential Method	p. 227
Motivation	p. 227
Atomic Negative Ions	p. 227
Dispersion Forces	p. 228
Strongly Correlated Systems	p. 230
Third Generation of DFT	p. 232
Derivation of OPM Integral Equation	p. 233
Compact Notation	p. 233
Direct Functional Derivative	p. 234
Total Energy Minimization	p. 239
Invariance of Density	p. 241
Exact Relation's Based on OPM Integral Equation	p. 244
Krieger-Li-Iafrate Approximation (KLI)	p. 248
OPM in Case of Degeneracy	p. 250
Exchange-Only Results	p. 254
First-Principles Implicit Correlation Functionals	p. 271
Kohn-Sham Perturbation Theory	p. 272
Kohn-Sham-Based Random Phase Approximation	p. 276
Interaction Strength Interpolation (ISI)	p. 278
Model-Based Orbital-Dependent Exchange-Correlation Functionals	p. 279
Self-Interaction Corrected LDA	p. 280
Colle-Salvetti Functional	p. 280
Meta-GGA	p. 281
Global, Screened and Local Hybrid Functionals	p. 281
Analysis of Orbital-Dependent Correlation Functionals	p. 288
Dispersion Force	p. 288
Correlation Energy	p. 294
Correlation Potential	p. 298
Orbital-Dependent Representation of 2-Particle Density	p. 304
Time-Dependent Density Functional Theory	p. 307
Runge-Gross Theorem	p. 307
Time-Dependent Kohn-Sham Equations	p. 325
Exchange-Correlation Action: Adiabatic Local Density Approximation and Beyond	p. 329
Time-Dependent Linear Response	p. 331
Spin-Polarized Time-Dependent Density Functional Theory	p. 335
Excited States: Part II	p. 336
Relativistic Density Functional Theory	p. 351
Notation	p. 352
Field Theoretical Background	p. 353
Existence Theorem	p. 361
Relativistic Kohn-Sham Equations	p. 367
Towards a Workable RDFT Scheme: No-pair Approximation	p. 371
No-pair RDFT	p. 373
Variants of RDFT	p. 376
Relativistic Exchange-Correlation Functional: Concepts and Illustrative Results	p. 384
Relativistic Implicit Functionals: Optimized Potential Method	p. 384
Role of Relativistic Corrections in E_xc: I. Prototype Results for Atoms	p. 388
Relativistic Local Density Approximation	p. 393
Relativistic Generalized Gradient Approximation	p. 397
Role of Relativistic Corrections in E_xc: II. Prototype Results for Molecules and Solids	p. 398
Further Reading	p. 401
Functionals and the Functional Derivative	p. 403
Definition of the Functional	p. 403
Functional Derivative	p. 405
Calculational Rules	p. 409
Variational Principle	p. 411
Second Quantization in Many-Body Theory	p. 413
N-Particle Hilbert Space	p. 413
Realization in First Quantized Form	p. 413
Formal Representation	p. 417
Fock Space	p. 421
Creation and Annihilation Operators	p. 421
1-Particle Operators	p. 425
2-Particle Operators	p. 428
Scaling Behavior of Many-Body Methods	p. 433
Explicit Density Functionals for the Kinetic Energy: Thomas-Fermi Models and Beyond	p. 437
Asymptotic Behavior of Quasi-Particle Amplitudes	p. 445
Quantization of Noninteracting Fermions in Relativistic Quantum Field Theory	p. 449
Renormalization Scheme of Vacuum QED	p. 457
Relativistic Homogeneous Electron Gas	p. 467
Basic Propagators	p. 467
Response Functions	p. 468
Ground State Energy	p. 473
Ground State Four Current	p. 478
Renormalization of Inhomogeneous Electron Gas	p. 481
Gradient Corrections to the Relativistic LDA	p. 485
Gordon Decomposition	p. 489
Some Useful Formulae	p. 493
References	p. 499
Index	p. 517
Table of Contents provided by Ingram. All Rights Reserved.

Theoretical and Mathematical Physics

An Advanced Course

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

More in Materials Science

Mechanics of Materials, SI Edition

11th Edition

Microbiologically Influenced Corrosion

A Comprehensive Guide to Principles, Assessment and Mitigation

Sustainable Utilization of Industrial Wastes as Reinforcement in Composite Materials

Origin, Symmetry and Elastic Tuneability of Charge Density Waves in the Superconductor BaNi2(As1??P?)2

Springer Theses

Transition Metal-Based Layered Double Hydroxides

Chemistry and Applications

Advances in Mechanical and Power Engineering III

Selected Papers from The International Conference on Advanced Mechanical and Power Engineering (CAMPE 2025), October 20-21, 2025, Kharkiv, Ukraine

Biomimicry - A Functional Approach

Biologically-Inspired Systems

Proceedings of the 7th International Conference on Innovative and Smart Materials

ICISM 2025, May 16â"18, Cape Town, South Africa

Proceedings of the Global Conference on Green Construction Materials and Practices 2025

GCGC 2025, February 5-6, Karachi, Pakistan

Fluid Flow and Phase Change of a Solid

CISM International Centre for Mechanical Sciences

Agro-Textiles

Environmental and Ecological Perspectives

Supercapacitors

Current Trends and Future Perspectives

Materials

Corrosion and Protection

Austenitic Stainless Steels

Structure and Properties (Volume 4)

Austenitic Stainless Steels

Structure and Properties (Volume 3)

Austenitic Stainless Steels

Structure and Properties (Volume 2)

Austenitic Stainless Steels

Structure and Properties (Volume 1)

Advanced Materials for Energy Storage and Conversion

Structure and Properties of Alloys

Energy Storage and Conversion

Applications of Nanostructured Materials

Textile Science and Clothing Technology

Material World

A Substantial Story of Our Past and Future

Engineering Mechanics: Dynamics, SI Units

Global Edition

Adventures in Fermentation

From Ancient Origins to Culinary Frontiers, an Exploration of the Microbes That Shape the World We Live In

This product is categorised by