Electronic Structure of Materials

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 MaterialsBorn–Oppenheimer ApproximationHartree MethodHartree–Fock (H–F) MethodConfiguration Interaction (CI) MethodApplication of Hartree Method to Homogeneous Electron Gas (HEG)Application of H–F Method to HEGBeyond the H–F Theory for HEG Density Functional TheoryThomas–Fermi TheoryScreening: An Application of Thomas–Fermi TheoryHohenberg–Kohn TheoremsDerivation of Kohn–Sham (KS) EquationsLocal Density Approximation (LDA) Comparison of the DFT with the Hartree and H–F TheoriesComments on the KS Eigenvalues and KS OrbitalsExtensions to Magnetic SystemsPerformance of the LDA/LSDABeyond LDATime-Dependent Density Functional Theory (TDDFT) Energy Band TheoryCrystal PotentialBloch’s TheoremBrillouin Zone (BZ)Spin–Orbit InteractionSymmetryInversion Symmetry, Time Reversal, and Kramers’ TheoremBand Structure and Fermi SurfaceDensity of States, Local Density of States, and Projected Density of StatesCharge DensityBrillouin Zone Integration Methods of Electronic Structure Calculations IEmpty Lattice ApproximationNearly Free Electron (NFE) ModelPlane Wave Expansion MethodTight-Binding MethodHubbard ModelWannier FunctionsOrthogonalized Plane Wave (OPW) MethodPseudopotential Method Methods of Electronic Structure Calculations IIScattering Approach to PseudopotentialConstruction of First-Principles Atomic PseudopotentialsSecular EquationCalculation of the Total EnergyUltrasoft Pseudopotential and Projector-Augmented Wave MethodEnergy Cutoff and k-Point ConvergenceNonperiodic Systems and Supercells Methods of Electronic Structure Calculations IIIGreen’s FunctionPerturbation Theory Using Green’s FunctionFree Electron Green’s Function in Three DimensionsKorringa-Kohn-Rostoker (KKR) MethodLinear Muffin-Tin Orbital (LMTO) MethodAugmented Plane Wave (APW) MethodLinear Augmented Plane Wave (LAPW) MethodLinear Scaling Methods Disordered AlloysShort- and Long-Range OrderAn Impurity in an Ordered SolidDisordered Alloy: General TheoryApplication to the Single Band Tight-Binding Model of Disordered AlloyMuffin-Tin Model: KKR-CPAApplication of the KKR-CPA: Some ExamplesBeyond CPA First-Principles Molecular DynamicsClassical MDCalculation of Physical PropertiesFirst-Principles MD: Born–Oppenheimer Molecular Dynamics (BOMD) First-Principles MD: Car–Parrinello Molecular Dynamics (CPMD) Comparison of the BOMD and CPMDMethod of Steepest Descent (SD) Simulated AnnealingHellmann–Feynman TheoremCalculation of ForcesApplications of the First-Principles MD Materials Design Using Electronic Structure ToolsStructure–Property RelationshipFirst-Principles Approaches and Their LimitationsProblem of Length and Time Scales: Multi-Scale ApproachApplications of the First-Principles Methods to Materials Design Amorphous MaterialsPair Correlation and Radial Distribution FunctionsStructural ModelingAnderson LocalizationStructural Modeling of Amorphous Silicon and Hydrogenated Amorphous Silicon Atomic Clusters and NanowiresJellium Model of Atomic ClustersFirst-Principles Calculations of Atomic ClustersNanowires Surfaces, Interfaces, and SuperlatticesGeometry of SurfacesSurface Electronic StructureSurface Relaxation and ReconstructionInterfacesSuperlattices Graphene and NanotubesGrapheneCarbon Nanotubes Quantum Hall Effects and Topological InsulatorsClassical Hall EffectLandau LevelsInteger and Fractional Quantum Hall Effects (IQHE and FQHE) Quantum Spin Hall Effect (QSHE) Topological Insulators Ferroelectric and Multiferroic MaterialsPolarizationBorn Effective ChargeFerroelectric MaterialsMultiferroic Materials High-Temperature SuperconductorsCupratesIron-Based Superconductors Spintronic MaterialsMagnetic MultilayersHalf-Metallic Ferromagnets (HMF)Dilute Magnetic Semiconductors (DMS) Battery MaterialsLiMnO2LiMn2O4 Materials in Extreme EnvironmentsMaterials at High PressuresMaterials at High Temperatures Appendix A: Electronic Structure CodesAppendix B: List of ProjectsAppendix C: Atomic UnitsAppendix D: Functional, Functional Derivative, and Functional MinimizationAppendix E: Orthonormalization of Orbitals in the Car–Parrinello MethodAppendix F: Sigma (s) and Pi (p) BondsAppendix G: sp, sp2, and sp3 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.