Most textbooks in the field are either too advanced for students or don’t adequately cover current research topics. Bridging this gap, Electronic Structure of Materials helps advanced undergraduate and graduate students understand electronic structure methods and enables them to use these techniques in their work.
Developed from the author’s lecture notes, this classroom-tested book takes a microscopic view of materials as composed of interacting electrons and nuclei. It explains all the properties of materials in terms of basic quantities of electrons and nuclei, such as electronic charge, mass, and atomic number. Based on quantum mechanics, this first-principles approach does not have any adjustable parameters.
The first half of the text presents the fundamentals and methods of electronic structure. Using numerous examples, the second half illustrates applications of the methods to various materials, including crystalline solids, disordered substitutional alloys, amorphous solids, nanoclusters, nanowires, graphene, topological insulators, battery materials, spintronic materials, and materials under extreme conditions.
Every chapter starts at a basic level and gradually moves to more complex topics, preparing students for more advanced work in the field. End-of-chapter exercises also help students get a sense of numbers and visualize the physical picture associated with the problem. Students are encouraged to practice with the electronic structure calculations via user-friendly software packages.
Introduction
Quantum Description of Materials
Born–Oppenheimer Approximation
Hartree Method
Hartree–Fock (H–F) Method
Configuration Interaction (CI) Method
Application of Hartree Method to Homogeneous Electron Gas (HEG)
Application of H–F Method to HEG
Beyond the H–F Theory for HEG
Density Functional Theory
Thomas–Fermi Theory
Screening: An Application of Thomas–Fermi Theory
Hohenberg–Kohn Theorems
Derivation of Kohn–Sham (KS) Equations
Local Density Approximation (LDA)
Comparison of the DFT with the Hartree and H–F Theories
Comments on the KS Eigenvalues and KS Orbitals
Extensions to Magnetic Systems
Performance of the LDA/LSDA
Beyond LDA
Time-Dependent Density Functional Theory (TDDFT)
Energy Band Theory
Crystal Potential
Bloch’s Theorem
Brillouin Zone (BZ)
Spin–Orbit Interaction
Symmetry
Inversion Symmetry, Time Reversal, and Kramers’ Theorem
Band Structure and Fermi Surface
Density of States, Local Density of States, and Projected Density of States
Charge Density
Brillouin Zone Integration
Methods of Electronic Structure Calculations I
Empty Lattice Approximation
Nearly Free Electron (NFE) Model
Plane Wave Expansion Method
Tight-Binding Method
Hubbard Model
Wannier Functions
Orthogonalized Plane Wave (OPW) Method
Pseudopotential Method
Methods of Electronic Structure Calculations II
Scattering Approach to Pseudopotential
Construction of First-Principles Atomic Pseudopotentials
Secular Equation
Calculation of the Total Energy
Ultrasoft Pseudopotential and Projector-Augmented Wave Method
Energy Cutoff and k-Point Convergence
Nonperiodic Systems and Supercells
Methods of Electronic Structure Calculations III
Green’s Function
Perturbation Theory Using Green’s Function
Free Electron Green’s Function in Three Dimensions
Korringa−Kohn−Rostoker (KKR) Method
Linear Muffin-Tin Orbital (LMTO) Method
Augmented Plane Wave (APW) Method
Linear Augmented Plane Wave (LAPW) Method
Linear Scaling Methods
Disordered Alloys
Short- and Long-Range Order
An Impurity in an Ordered Solid
Disordered Alloy: General Theory
Application to the Single Band Tight-Binding Model of Disordered Alloy
Muffin-Tin Model: KKR-CPA
Application of the KKR-CPA: Some Examples
Beyond CPA
First-Principles Molecular Dynamics
Classical MD
Calculation of Physical Properties
First-Principles MD: Born–Oppenheimer Molecular Dynamics (BOMD)
First-Principles MD: Car–Parrinello Molecular Dynamics (CPMD)
Comparison of the BOMD and CPMD
Method of Steepest Descent (SD)
Simulated Annealing
Hellmann–Feynman Theorem
Calculation of Forces
Applications of the First-Principles MD
Materials Design Using Electronic Structure Tools
Structure–Property Relationship
First-Principles Approaches and Their Limitations
Problem of Length and Time Scales: Multi-Scale Approach
Applications of the First-Principles Methods to Materials Design
Amorphous Materials
Pair Correlation and Radial Distribution Functions
Structural Modeling
Anderson Localization
Structural Modeling of Amorphous Silicon and Hydrogenated Amorphous Silicon
Atomic Clusters and Nanowires
Jellium Model of Atomic Clusters
First-Principles Calculations of Atomic Clusters
Nanowires
Surfaces, Interfaces, and Superlattices
Geometry of Surfaces
Surface Electronic Structure
Surface Relaxation and Reconstruction
Interfaces
Superlattices
Graphene and Nanotubes
Graphene
Carbon Nanotubes
Quantum Hall Effects and Topological Insulators
Classical Hall Effect
Landau Levels
Integer and Fractional Quantum Hall Effects (IQHE and FQHE)
Quantum Spin Hall Effect (QSHE)
Topological Insulators
Ferroelectric and Multiferroic Materials
Polarization
Born Effective Charge
Ferroelectric Materials
Multiferroic Materials
High-Temperature Superconductors
Cuprates
Iron-Based Superconductors
Spintronic Materials
Magnetic Multilayers
Half-Metallic Ferromagnets (HMF)
Dilute Magnetic Semiconductors (DMS)
Battery Materials
LiMnO2
LiMn2O4
Materials in Extreme Environments
Materials at High Pressures
Materials at High Temperatures
Appendix A: Electronic Structure Codes
Appendix B: List of Projects
Appendix C: Atomic Units
Appendix D: Functional, Functional Derivative, and Functional Minimization
Appendix E: Orthonormalization of Orbitals in the Car–Parrinello Method
Appendix F: Sigma (σ) and Pi (π) Bonds
Appendix G: sp, sp2, and sp3 Hybrids
References
Index
Exercises and Further Reading appear at the end of each chapter.
Biography
Rajendra Prasad is a professor of physics at the Indian Institute of Technology (IIT) Kanpur. He received a PhD in physics from the University of Roorkee (now renamed as IIT Roorkee) and completed postdoctoral work at Northeastern University. Dr. Prasad is a fellow of the National Academy of Sciences, India. Spanning over four decades, his research work focuses on the electronic structure of metals, disordered alloys, atomic clusters, transition metal oxides, ferroelectrics, multiferroics, and topological insulators.
"This book gives an excellent introduction to the electronic structure of materials for newcomers to the field. … very useful as a source of fundamental knowledge for theoretical calculations. … I can recommend this book without hesitation to all interested in electronic structure of materials, particularly to those entering the field. It is written at a level appropriate to advanced undergraduate and graduate students. Also, it is a good book for researchers with a chemistry, physics, or materials background."
—MRS Bulletin, Volume 39, August 2014
