1st Edition

# Understanding Properties of Atoms, Molecules and Materials

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In a technology driven civilization the quest for new and smarter materials is everlasting. They are required as platforms for developing new technologies or for improving an already existing technology. The discovery of a new material is no longer chance driven or accidental, but is based on careful reasoning structured by deep understanding of the microconstituents of materials - the atoms and molecules in isolation or in an assembly. That requires fair amount of exposure to quantum and statistical mechanics. `Understanding Properties of Atoms, Molecules and Materials' is an effort (perhaps the first ever) to bring all the necessary theoretical ingredients and relevant physical information in a single volume. The book introduces the readers (first year graduates) or researchers in material chemistry/engineering to elementary quantum mechanics of atoms, molecules and solids and then goes on to make them acquainted with methods of statistical mechanics (classical as well as quantum) along with elementary principles of classical MD simulation. The basic concepts are introduced with clarity and illustrated with easy to grasp examples, thus preparing the readers for an exploration through the world of materials - the exotic and the mundane. The emphasis has been on the phenomena and what shapes them at the fundamental level. A comprehensive description of modern designing principles for materials with examples is a unique feature of the book.

The highlights of the book are comprehensive introduction and analysis of

- Quantum states of atoms and molecules
- The translational symmetry and quantum states in periodic and amorphous solids
- Band structure and tuning
- Classical and quantum statistics with applications to ideal gases (photons, phonons and electrons, molecules)
- Quantum states in type-I and type-II superconductors (elementary theory included)
- Magnetic materials, materials with GMR and CMR
- Shape memory effects in alloys and materials
- 2D materials (graphene and graphene analogus)
- NLO and photovoltaic materials
- Hydrogen storage material for mitigating the looming energy crisis
- Quantum states in low and high band gap semiconductors
- Semimetals
- Designer materials, etc.

The volume is designed and organized to create interest in the science of materials and the silent revolution that is redefining the goals and boundaries of materials science continuously.

The Science of Materials. Introduction: The Age of Materials. Atoms, Molecules and Solids. From Atoms and Molecules to Materials. The Need for Theoretical Understanding. Topics Covered. Classification of Materials. Future Outlook. **Quantum Mechanics**. Introduction: Mechanics of the Microworld. Law of Quantum Evolution: The Schrodinger Equation. Observables, Operators and Their Eigenfunctions. Commuting and Non-Commuting Observables. Stationary States of Quantum Systems. The Tunnel Effect. Heisenbergâ€™s Formulation of Quantum Mechanics. Representations in Quantum Mechanics. **Quantum Mechanics of Atoms**. Introduction. The Periodic Table of Elements. The Quantum States of the Hydrogenic Atoms : Symmetry. Rotational Symmetry, Angular Momentum, Eigenstates and Parity. Orbital Angular Momentum of Electron. Spin Angular Momentum. Total Angular Momentum (J): General Addition of Angular Momentum. Many Electron Atoms: Aufbau Principle. More on Variational Methods. **Molecular Quantum Mechanics**. Introduction: Molecules as Building Blocks. The Quantum States of Hydrogen Molecule Ion (H+). The Quantum States of Hydrogen Molecule. Quantum Mechanics of Covalent Bond. Dynamics of Electron Exchange in Covalent Bond Formation. Forces in Molecules, Bonding and Equilibrium Structures. Bonding and Anti-bonding Region in a Molecule, Berlin Diagrams. Ionic Bonds and Ionic Solids. Weak Binding. Weak-Binding : Hydrogen Bonds. Directed Valence and Chemical Binding. Many Electron Systems. Hartree Method. Hartree-Fock Method. LCAO-MO-SCF-CI Calculations. Perturbative Correction to HF Wavefunction and Energy. The Rise of Density Functional Theory. The Basis Sets for Molecular Calculation. **Quantum States of Solids**. Introduction. One Electron Approximation, Translational Symmetry, Bloch States and Bril-louin Zone. Formation of Energy Bands. The Idea of Band Gap and Electrical Transport in Solids. Symmetry and Splitting of Bands. Amorphous Solids and Localized Electronic States. . Localization in Disordered Solids. **Classical Statistical Mechanics**. Introduction. Types of Probability Distributions. The Equilibrium State and Distribution Functions. Gibbs Distribution. Classical Statistical Mechanics. Classical Statistical Mechanics and Microscopic Properties. Statistical Mechanics and Numerical Simulation. **Quantum Statistical Mechanics**. Introduction. The Canonical Gibbs Distribution in Quantum Statistics. Entropy and the Entropy Maximal State. The Grand Canonical Potential. Quantum Statistics of Bosons and Fermions. Applications of Bose Statistics to Ideal Photon and Phonon Gas. Quantum Statistics for Electron Gas in a Potential Well. Quantum Effects in Heat Capacity of Gases. Bose-Einstein Condensation. **Traditional Materials**. Introduction : Atom Based Materials. Conducting, Superconducting and Insulating Materials. Metallic Conductivity : A Rudimentary Theory. Quantum Theory of Metallic Conductivity, Electron Phonon Interactions. Superconductivity and Superconducting State. Semiconducting Materials and Insulators. Insulators. High Temperature or Type II Superconductors. Metal Alloys. **The Advent of Smart Materials**. Introduction. Electrochromic (EC) Materials. Piezoelectric Materials. Shape Memory Materials (SMM). Photochromic Materials (PM). Quantum Tunneling Composites (QTC). Quantum Materials (QMs). Organic Superconductors. **Magnetic Materials**. Introduction: Magnetic Materials. Important Magnetic Vectors. Types of Magnetism and Magnetic Materials. Types of Magnetism: Theoretical. Exchange Interaction, Heisenbergâ€™s Exchange Hamiltonian and Magnetic Hamiltonian. Paramagnetic Susceptibility of Gases and Conduction Electrons of Metals. Diamagnetism of Atoms and Conduction Electrons. Ferromagnetic Susceptibility. Giant Magneto Resistance (GMR). Materials with Ferromagnetic plus Ferroelectric Order. Molecular Magnets. Soft Magnetic Materials. **Low Dimensional Materials**. Introduction: The New Age Materials. Graphene. Graphene Nanoribbons. Carbon Nanotubes (CNTs). Graphene Quantum Dots (GQDs). New -D Carbon Allotropes: Defected Graphenes and Pentagraphene. White Graphene. Boron Nitride Nanoribbons (BNNRs). Boron Nitride Nanotubes (BNNTs). Phosphorene. Transition Metal Dichalcogenides (TMDs). Pristine and TM-doped PtSe Monolayers. Other Nanomaterials: Special Emphasis on Nanoclusters or Quantum Dots (QDs). Nanocomposites or Nanohybrid Materials. Nanomaterials for Energy Conversion Processes**Energy Materials**. Introduction. The Looming Energy Crisis. Materials for Hydrogen Storage. Optical Properties of Materials and LASERs. Photonic Materials. Photovoltaic Materials. Materials that Change Light. Non-Linear Optical Response of Materials. Thermoelectric Materials**Designer Materials**. Introduction: Design by Thumb Rules. Materials by Design: Beyond Thumb Rules. Designing Materials: Beyond Thumb Rules. The Advent Computational Material Science. **Current Status and Outlook for Future**. Introduction. Where Do We Stand. Future Outlook

### Biography

**Prof. Pranab Sarkar **received his PhD from Indian Association for the Cultivation of Science, Kolkata, India in 1997. After pursuing his postdoc- toral research in the University of Montreal, Canada, Dr. Sarkar started his professional career in the Dept. of Chemistry, Visva-Bharati, Santiniketan, India in the year 1999. He also served as a visiting Scientist at the University of Saarland, Germany during the period of 2001-2003. Presently, he is a Professor in the Dept. of Chemistry, Visva-Bharati, Santiniketan. Professor Sarkar is an expert in the field of Computational Materials Science and his primary research interest is to employ state of the art theoretical methods to understand and predict material properties at nanoscale. He has made significant contributions to the identification of suitable materials for green sustainable energy and also for spintronic applications. He has published more than 165 papers in internationally reputed journals and a number of book chapters and reviews.

**Prof. Sankar Prasad Bhattacharyya **is fellow of the Indian Academy of Sciences and spent three years (2012-2015) in the Dept. of Chemistry, IIT Bombay as Raja Ramanna Fellow, Department of Atomic Energy, GOI. He retired as Senior Professor of Physical Chemistry, Indian Association for the Cultivation of Science (IACS), Kolkata. Presently he is a visiting Professor at the School of Chemical Sciences, IACS Uni- versity, Kolkata, India. His main research interest is in the area of quantum chemistry and his distinguished career in the theoretical chemistry spans a period of over 35 years. His work on the development of new computational techniques, with particlular focus on global opti- mizations, for the treatment of complex problems in molecular chemistry and physics is well documented by an impressive list of highly influential publications in the field, devoted both to traditional mathematical techniques and more recently, to soft computing-oriented approaches. He has supervised more than 20 PhD and 30 undergraduate project students. His publications included more than 200 papers in peer-reviewed journals and a number of book chapters.