1st Edition

Electronic Structure of Materials

By Rajendra Prasad Copyright 2013
    469 Pages 200 B/W Illustrations
    by CRC Press

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    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.


    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
    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

    Surfaces, Interfaces, and Superlattices
    Geometry of Surfaces
    Surface Electronic Structure
    Surface Relaxation and Reconstruction

    Graphene and Nanotubes
    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
    Born Effective Charge
    Ferroelectric Materials
    Multiferroic Materials

    High-Temperature Superconductors
    Iron-Based Superconductors

    Spintronic Materials
    Magnetic Multilayers
    Half-Metallic Ferromagnets (HMF)
    Dilute Magnetic Semiconductors (DMS)

    Battery Materials

    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



    Exercises and Further Reading appear at the end of each chapter.


    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