- Explains the quantum description of matter in terms of electrons and nuclei
- Discusses first-principles methods, including pseudopotential, KKR, and APW
- Describes many applications of electronic structure, including low-dimensional systems and nanomaterials
- Requires only basic knowledge of quantum mechanics, statistical mechanics, and condensed matter physics
- Includes exercises and further reading in each chapter and extensive references at the back of the book

*Solutions manual and figure slides available upon qualifying course adoption*

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**LiMnO

LiMn

**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, sp _{2}, and sp_{3} Hybrids**

References

Index

*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.