Understanding Properties of Atoms, Molecules and Materials

Cover Page
Half Title
Title Page
Contents
Preface
Authors
1 The Science of Materials
	1.1 Introduction: The Age of Materials
	1.2 Atoms, Molecules and Solids
	1.2.1 More on Unit Cells
	1.3 From Atoms and Molecules to Materials
	1.4 The Need for Theoretical Understanding
	1.5 Topics Covered
		1.5.1 The Mechanics of the Microworld
		1.5.2 Quantum Mechanics of Atoms
		1.5.3 Quantum Mechanics of Molecules
		1.5.4 Quantum States in Solids
		1.5.5 Classical Statistical Mechanics
		1.5.6 Quantum Statistical Mechanics
		1.5.7 Traditional Materials
		1.5.8 Smart Materials
		1.5.9 Magnetic Materials
		1.5.10 Low-Dimensional Materials
		1.5.11 NLO and Energy Materials
		1.5.12 Materials Design
	1.6 Classification of Materials
	1.7 Future Outlook
	References
2 Quantum Mechanics
	2.1 Introduction: Mechanics of the Microworld
	2.2 Law of Quantum Evolution: The Schrödinger Equation
		2.2.1 Axiomatic Foundation of Quantum Mechanics
		2.2.2 Postulates of Quantum Mechanics
	2.3 Observables, Operators and Their Eigenfunctions
		2.3.1 More About Hermiticity and Hermitian Conjugates
	2.4 Commuting and Non-Commuting Observables
	2.5 Stationary States of Quantum Systems
		2.5.1 The Free Particle
		2.5.2 Stationary States of a Simple Harmonic Oscillator
	2.6 The Tunnel Effect
		2.6.1 Tunneling Across a Rectangular Potential Barrier
	2.7 Heisenberg’s Formulation of Quantum Mechanics
		2.7.1 Matrix Representations for x and px
		2.7.2 Zero Point Oscillation
		2.7.3 Harmonic Oscillator in Three Dimensions
		2.7.4 Quantum States in Infinitely Deep Potential Wells
	2.8 Representations in Quantum Mechanics
		2.8.1 Coordinate Representation
		2.8.2 Momentum Representation
		2.8.3 Matrix Representation
		2.8.4 Vector Space Formulation
	References
3 Quantum Mechanics of Atoms
	3.1 Introduction
	3.2 The Periodic Table of Elements
	3.3 The Quantum States of the Hydrogenic Atoms: Symmetry
	3.4 Rotational Symmetry, Angular Momentum, Eigenstates and Parity
	3.5 Orbital Angular Momentum of Electron
		3.5.1 Spherical Harmonics and Eigenstates of Rigid Rotator
		3.5.2 Radial Motion of the Electron in H-Atom
		3.5.3 Asymptotic Forms of R(r) and Continuous Energy Spectrum
		3.5.4 Discrete Spectrum of Energy
		3.5.5 Energy Degeneracy: Discrete Spectrum
		3.5.6 Complete Wavefunction of a Hydrogen Atom
	3.6 Spin Angular Momentum
	3.7 Total Angular Momentum (J): General Addition of Angular Momentum
	3.8 Many Electron Atoms: Aufbau Principle
		3.8.1 Periods and Shells
		3.8.2 Groups and Outer Shells
		3.8.3 A Case Study of Two-Electrons Atoms: He
		3.8.4 Designating Electronic States of a He Atom
		3.8.5 Constructing Wavefunctions for the Two-Electron States of the He Atom
		3.8.6 Calculating Energy of He Atom in the Ground State: Variational Approximation
	3.9 More on Variational Methods
	References
4 Molecular Quantum Mechanics
	4.1 Introduction: Molecules as Building Blocks
	4.2 The Quantum States of Hydrogen Molecule Ion (H+2 )
	4.3 The Quantum States of Hydrogen Molecule
	4.4 Quantum Mechanics of Covalent Bond
		4.4.1 Energetics of Covalent Bond in H2
		4.4.2 Electron Probability Density Distribution in Heitler-London States
		4.4.3 Valency and Quantum Mechanics
	4.5 Dynamics of Electron Exchange in Covalent Bond Formation
	4.6 Forces in Molecules, Bonding and Equilibrium Structures
	4.7 Bonding and Anti-bonding Region in a Molecule, Berlin Diagrams
	4.8 Ionic Bonds and Ionic Solids
		4.8.1 Cohesive Energy of Ionic Solids
	4.9 Weak-Binding
	4.10 Weak-Binding: Hydrogen Bonds
	4.11 Directed Valence and Chemical Binding
	4.12 Many Electron Systems
	4.13 Hartree Method
		4.13.1 Slater Condon Rules
	4.14 Hartree-Fock Method
	4.15 LCAO-MO-SCF-CI Calculations
	4.16 Perturbative Correction to HF Wavefunction and Energy
	4.17 The Rise of Density Functional Theory
		4.17.1 The Kohn-Sham Method
	4.18 The Basis Sets for Molecular Calculation
	References
5 Quantum States of Solids
	5.1 Introduction
	5.2 One-Electron Approximation, Translational Symmetry, Bloch States and Brillouin Zone
	5.3 Formation of Energy Bands
		5.3.1 Nearly Free Electron Model of Band Structure
		5.3.2 Kronig-Penny Problem and Structure of Energy Bands
		5.3.3 The Tight Binding Model of Periodic Solids
	5.4 The Idea of Band Gap and Electrical Transport in Solids
		5.4.1 Electrical Conductors: Partially Filled Valence Band
		5.4.2 Insulators: Completely Filled Valence Band
		5.4.3 Semiconductors
		5.4.4 Effective Mass (m*)
		5.4.5 Lattice Vibrations, Phonons and Electrical Conductivity
	5.5 Symmetry and Splitting of Bands
	5.6 Amorphous Solids and Localized Electronic States
		5.6.1 Localization in Disordered Solids
	References
6 Classical Statistical Mechanics
	6.1 Introduction
	6.2 Types of Probability Distributions
		6.2.1 Probability and Unexpectedness: The Entropy
	6.3 The Equilibrium State and Distribution Functions
		6.3.1 Maxwell’s Distribution
		6.3.2 The Equilibrium State and Boltzmann Distribution
		6.3.3 Maxwell-Boltzmann Distribution
	6.4 Gibbs Distribution
		6.4.1 Maxwell-Boltzmann Probability Density
		6.4.2 The Gibbs Distribution: Probability of an Equilibrium State
	6.5 Classical Statistical Mechanics
	6.6 Classical Statistical Mechanics and Macroscopic Properties
		6.6.1 Gibbs-Helmholtz Equation from Classical Statistical Mechanics: Internal Energy (U)
		6.6.2 Entropy: Statistical Mechanical and Thermodynamic Interpretation
	6.7 Statistical Mechanics and Numerical Simulation
		6.7.1 MD Simulations (Basic Idea)
		6.7.2 Calculation of Thermodynamic Properties
		6.7.3 Microcanonical Ensemble Molecular Dynamics
		6.7.4 Monte-Carlo Simulations
		6.7.5 Transition Probabilities and Metropolis Method
	References
7 Quantum Statistical Mechanics
	7.1 Introduction
	7.2 The Canonical Gibbs Distribution in Quantum Statistics
		7.2.1 Canonical Gibbs’ Distribution For Discrete States
		7.2.2 Quantum Gibbs’ Distribution and Entropy
	7.3 Entropy and the Entropy Maximal State
	7.4 The Grand Canonical Potential
		7.4.1 Thermodynamic Meaning of *, µ and T
	7.5 Quantum Statistics of Bosons and Fermions
		7.5.1 Bose-Einstein Distribution
		7.5.2 Fermi-Dirac Distribution
		7.5.3 Boson Statistics and Indistinguishability Principle
	7.6 Applications of Bose Statistics to Ideal Photon and Phonon Gas
		7.6.1 Photon Gas (Ideal)
		7.6.2 Phonon Gas (Ideal)
	7.7 Quantum Statistics for Electron Gas in a Potential Well
		7.7.1 Non-Degenerate Electron Gas
		7.7.2 Degenerate Electron Gas
	7.8 Quantum Effects in Heat Capacity of Gases
		7.8.1 AModel Application of Quantum Statistics
	7.9 Bose-Einstein Condensation
	References
8 Traditional Materials
	8.1 Introduction: Atom-Based Materials
	8.2 Conducting, Superconducting and Insulating Materials
	8.3 Metallic Conductivity: A Rudimentary Theory
	8.4 Quantum Theory of Metallic Conductivity, Electron Phonon Interactions
	8.5 Superconductivity and Superconducting State
		8.5.1 The Nature of the Superconducting State
		8.5.2 Binding Energy of a Cooper-Pair
		8.5.3 Superconducting State Function
		8.5.4 Special Features of the Superconducting State
	8.6 Semiconducting Materials and Insulators
		8.6.1 Equilibrium Statistics of Electrons in Semiconductors and Metal
		8.6.2 Equilibrium Statistics of Electron Gas in Semiconductors
		8.6.3 Semimetals
		8.6.4 Compound Semiconductors
	8.7 Insulators
		8.7.1 Ferroelectric Materials
	8.8 High Temperature or Type II Superconductors
		8.8.1 Ceramics and Their Structures
		8.8.2 High Tc Superconducting Materials
		8.8.3 Understanding High Tc Superconductivity
	8.9 Metal Alloys
		8.9.1 Ferrous Alloys
		8.9.2 Steels
		8.9.3 Non-Ferrous Alloys
		8.9.4 Special Materials
	References
9 The Advent of Smart Materials
	9.1 Introduction
	9.2 Electrochromic (EC) Materials
	9.3 Piezoelectric Materials
	9.4 Shape Memory Materials (SMM)
	9.5 Photochromic Materials (PM)
	9.6 Quantum Tunneling Composites (QTC)
	9.7 Quantum Materials (QMs)
	9.8 Organic Superconductors
	References
10 Magnetic Materials
	10.1 Introduction: Magnetic Materials
	10.2 Important Magnetic Vectors
	10.3 Types of Magnetism and Magnetic Materials
	10.4 Types of Magnetism: Theoretical
	10.5 Exchange Interaction, Heisenberg’s Exchange Hamiltonian and Magnetic Hamiltonian
		10.5.1 Diamagnetic Materials
		10.5.2 Paramagnetic Material
		10.5.3 Ferromagnetic, Antiferromagnetic and Ferrimagnetic Materials
			10.5.3.1 Ferromagnetic Ordering
			10.5.3.2 Antiferromagnetic Ordering
			10.5.3.3 Ferrimagnetic Ordering
		10.5.4 Superparamagnetism
	10.6 Paramagnetic Susceptibility of Gases and Conduction Electrons of Metals
		10.6.1 Quantum Model for Paramagnetic Susceptibility
		10.6.2 Paramagnetism of a Free-Electron Gas
		10.6.3 Paramagnetism of Conduction Electrons
		10.6.4 Paramagnetic Resonance
	10.7 Diamagnetism of Atoms and Conduction Electrons
	10.8 Ferromagnetic Susceptibility
	10.9 Giant Magneto Resistance (GMR)
	10.10 Materials with Ferromagnetic plus Ferroelectric Order
	10.11 Molecular Magnets
	10.12 Soft Magnetic Materials
	References
11 Low-Dimensional Materials
	11.1 Introduction: The New Age Materials
	11.2 Graphene
		11.2.1 Geometry and Crystal Structure
		11.2.2 Electronic Structure of Graphene
	11.3 Graphene Nanoribbons
		11.3.1 Electronic Structure of aGNRs
		11.3.2 Electronic Structure of zGNRs
		11.3.3 Transport Properties of GNRs
	11.4 Carbon Nanotubes (CNTs)
		11.4.1 Geometric Features of CNTs
		11.4.2 Electronic Structure of CNTs
		11.4.3 Effect of Curvature on Electronic Structure of CNTs
	11.5 Graphene Quantum Dots (GQDs)
		11.5.1 Electronic Structure of GQDs
	11.6 New 2D Carbon Allotropes: Defected Graphenes and Pentagraphene
	11.7 White Graphene
		11.7.1 Geometry and Crystal Structure
		11.7.2 Electronic Structure of h-BN
		11.7.3 General Properties and Applications of h-BN
	11.8 Boron Nitride Nanoribbons (BNNRs)
	11.9 Boron Nitride Nanotubes (BNNTs)
		11.9.1 Morphology and Crystal Structure of BNNTs
		11.9.2 Electronic Structure of BNNTs
		11.9.3 General Properties and Applications of BNNTs
	11.10 Phosphorene
		11.10.1 Geometry and Crystal Structure
		11.10.2 Mechanical Properties
		11.10.3 Electronic Structure and General Properties of Phosphorene
	11.11 Transition Metal Dichalcogenides (TMDs)
		11.11.1 Geometry and Crystal Structure of TMDs
		11.11.2 Mechanical Properties
		11.11.3 Electronic Structure of TMDs
		11.11.4 Optical Properties of TMDs
	11.12 Pristine and TM-doped PtSe2 Monolayers
	11.13 Other Nanomaterials: Special Emphasis on Nanoclusters or Quantum Dots (QDs)
		11.13.1 Classification of Nanoclusters
		11.13.2 Reactivity of Nanoclusters
	11.14 Nanocomposites or Nanohybrid Materials
	11.15 Nanomaterials for Energy Conversion Processes
	References
12 Energy Materials
	12.1 Introduction
	12.2 The Looming Energy Crisis
	12.3 Materials for Hydrogen Storage
		12.3.1 Microporous Materials for H2-Storage
		12.3.2 Carbon-Based Solid State Materials for Hydrogen Storage
		12.3.3 Zeolites
		12.3.4 Metal Organic Frameworks (MOFs)
		12.3.5 Organic Polymers for Hydrogen Storage
		12.3.6 Interstitial Hydrides
		12.3.7 Intermetallic Compounds
			12.3.7.1 AB5 Intermetallics
			12.3.7.2 AB2 Intermetallics
			12.3.7.3 AB – Intermetallics
		12.3.8 Modified Binary Hydrides
		12.3.9 Quasi-crystalline Materials
		12.3.10 Complex Hydrides
	12.4 Optical Properties of Materials and Lasers
		12.4.1 Optical Properties ofMetals and Nonmetals
			12.4.1.1 Metals
			12.4.1.2 Non-metals
	12.5 Photonic Materials
	12.6 Photovoltaic Materials
		12.6.1 Generation I Materials
		12.6.2 Generation II Materials
		12.6.3 Generation III Materials
	12.7 Materials that Change Light
	12.8 Non-Linear Optical Response of Materials
	12.9 Thermoelectric Materials
	References
13 Designer Materials
	13.1 Introduction: Design by Thumb Rules
	13.2 Materials by Design: Beyond Thumb Rules
	13.3 Designing Materials: Beyond Thumb Rules
	13.4 The Advent Computational Material Science
		13.4.1 Designing Hard and Superhard Materials
		13.4.2 Adaptive Design in Materials Discovery
		13.4.3 Accelerated Discovery of New Magnetic Materials
		13.4.4 Materials Informatics in the Search for Novel Materials
			13.4.4.1 Stannates
			13.4.4.2 Ruthenates
		13.4.5 Computational Design of New MOF-Based Material for Hydrogen Storage
		13.4.6 Miscellaneous Materials Designing Approach
	References
14 Current Status and Outlook for Future
	14.1 Introduction
	14.2 Where Do We Stand?
	14.3 Future Outlook
	References
Index