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The study of electronic structure of materials is at a momentous stage, with new computational methods and advances in basic theory. Many properties of materials can be determined from the fundamental equations, and electronic structure theory is now an integral part of research in physics, chemistry, materials science and other fields. This book provides a unified exposition of the theory and methods, with emphasis on understanding each essential component. New in the second edition are recent advances in density functional theory, an introduction to Berry phases and topological insulators explained in terms of elementary band theory, and many new examples of applications. Graduate students and research scientists will find careful explanations with references to original papers, pertinent reviews, and accessible books. Each chapter includes a short list of the most relevant works and exercises that reveal salient points and challenge the reader.
Overview and Background Topics
Introduction 
Overview 
Theoretical Background 
Periodic Solids and Electron Bands
Uniform Electron Gas and sp-Bonded Metals 
Density Functional Theory
Density Functional Theory: Foundations
The Kohn–Sham Auxiliary System 
Functionals for Exchange and Correlation I 
Functionals for Exchange and Correlation II 
Important Preliminaries on Atoms
Electronic Structure of Atoms 
Pseudopotentials 
Determination of Electronic Structure: The Basic Methods
Plane Waves and Grids: Basics 
Plane Waves and Real-Space Methods: Full Calculations
Localized Orbitals: Tight-Binding 
Localized Orbitals: Full Calculations 
Augmented Functions: APW, KKR, MTO 
Augmented Functions: Linear Methods
Locality and Linear-Scaling O(N) Methods 
From Electronic Structure to Properties of Matter
Quantum Molecular Dynamics (QMD) 
Response Functions: Phonons and Magnons 
Excitation Spectra and Optical Properties 
Surfaces, Interfaces, and Lower-Dimensional Systems
Wannier Functions 
Polarization, Localization, and Berry Phases 
Electronic Structure and Topology
Topology of the Electronic Structure of a Crystal: Introduction 
Two-Band Models: Berry Phase, Winding, and Topology 
Topological Insulators I: Two Dimensions 
Topological Insulators II: Three Dimensions 
Appendices
Appe Functional Equations 
LSDA and GGA Functionals 
Adiabatic Approximation 
Perturbation Theory, Response Functions, and Green’s Functions 
Dielectric Functions and Optical Properties 
Coulomb Interactions in Extended Systems 
Stress from Electronic Structure 
Energy and Stress Densities 
Alternative Force Expressions 
Scattering and Phase Shifts 
Useful Relations and Formulas 
Numerical Methods