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# Principles and Applications of Quantum Chemistry

- 1st Edition - October 15, 2015
- Author: V.P. Gupta
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 8 0 3 4 7 8 - 1
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 0 3 5 0 1 - 6

Principles and Applications of Quantum Chemistry offers clear and simple coverage based on the author’s extensive teaching at advanced universities around the globe. Where needed… Read more

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Request a sales quote*Principles and Applications of Quantum Chemistry*offers clear and simple coverage based on the author’s extensive teaching at advanced universities around the globe. Where needed, derivations are detailed in an easy-to-follow manner so that you will understand the physical and mathematical aspects of quantum chemistry and molecular electronic structure. Building on this foundation, this book then explores applications, using illustrative examples to demonstrate the use of quantum chemical tools in research problems. Each chapter also uses innovative problems and bibliographic references to guide you, and throughout the book chapters cover important advances in the field including: Density functional theory (DFT) and time-dependent DFT (TD-DFT), characterization of chemical reactions, prediction of molecular geometry, molecular electrostatic potential, and quantum theory of atoms in molecules.

- Simplified mathematical content and derivations for reader understanding
- Useful overview of advances in the field such as Density Functional Theory (DFT) and Time-Dependent DFT (TD-DFT)
- Accessible level for students and researchers interested in the use of quantum chemistry tools

High-level students and researchers in chemistry, material science, biochemistry, chemical engineering

Dedication

List of Figures

List of Tables

Biography

Preface

Acknowledgment

1. Basic Principles of Quantum Chemistry

- 1.1. Introduction
- 1.2. Particle–Wave Duality
- 1.3. Matrix Mechanics and Wave Mechanics
- 1.4. Relativistic Quantum Mechanics
- 1.5. Schrödinger Wave Equation
- 1.6. Operators—General Properties, Eigenvalues, and Expectation Values
- 1.7. Postulates of Quantum Mechanics
- 1.8. Hydrogen Atom
- 1.9. Atomic Orbitals
- 1.10. Electron Spin
- 1.11. Linear Vector Space and Matrix Representation
- 1.12. Atomic Units
- 1.13. Approximate Methods of Solution of Schrödinger Equation
- 1.14. Molecular Symmetry

2. Many-Electron Atoms and Self-consistent Fields

- 2.1. Wavefunction of Many-Electron Atoms
- 2.2. Slater Determinants for Wavefunctions
- 2.3. Central Field Approximation
- 2.4. Self-consistent Field (SCF) Approximation—Hartree Theory
- 2.5. Electronic Configuration and Electronic States
- 2.6. Restricted and Unrestricted Wavefunctions

3. Self-consistent Field Molecular Orbital Theory

- 3.1. Introduction
- 3.2. Born–Oppenheimer Approximation
- 3.3. Chemical Bonding and Structure of Molecules
- 3.4. Molecular Orbitals as Linear Contribution of Atomic Orbitals (LCAO)
- 3.5. VB Theory for Hydrogen Molecule—Heitler–London Model
- 3.6. One-Electron Density Function and Charge Distribution in Hydrogen Molecule
- 3.7. Formation of Molecular Quantum Numbers for Diatomic Molecules
- 3.8. HF Theory of Molecules
- 3.9. Closed-Shell and Open-Shell Molecules
- 3.10. Atomic Orbitals—Their Types and Properties
- 3.11. Classification of Basis Sets
- 3.12. Quality of HF Results
- 3.13. Beyond HF Theory

4. Approximate Molecular Orbital Theories

- 4.1. Introduction
- 4.2. Semiempirical Methods
- 4.3. Semiempirical Methods for Planar-Conjugated Systems
- 4.4. Comparative Study of the Performance of Semiempirical Methods

5. Density Functional Theory (DFT) and Time Dependent DFT (TDDFT)

- 5.1. Introduction
- 5.2. Theoretical Motivation—Thomas–Fermi Model
- 5.3. Formalism of the DFT
- 5.4. Kohn–Sham Equations
- 5.5. LCAO Ansatz in the KS Equations
- 5.6. Comparison between HF and DFT
- 5.7. Exchange–Correlation Functional
- 5.8. Applications and Performance of DFT
- 5.9. Challenges for DFT
- 5.10. Time-Dependent DFT
- 5.11. Approximate Exchange–Correlation Functionals for TDDFT
- 5.12. Advantages of TDDFT

6. Electron Density Analysis and Electrostatic Potential

- 6.1. Electron Density Distribution
- 6.2. Population Analysis
- 6.3. Electrostatic Potential
- 6.4. Analysis of Bonding and Interactions in Molecules
- 6.5. Electrostatic Potential-Derived Charges

7. Molecular Geometry Predictions

- 7.1. Introduction
- 7.2. Potential Energy Surface
- 7.3. Conical Intersections and Avoided Crossings
- 7.4. Evaluation of Energy Gradients
- 7.5. Optimization Methods and Algorithms
- 7.6. Practical Aspects of Optimization
- 7.7. Illustrative Examples

8. Vibrational Frequencies and Intensities

- 8.1. Introduction
- 8.2. Quantum Mechanical Model for Diatomic Vibrator–Rotator
- 8.3. Vibrations of Polyatomic Molecules
- 8.4. Quantum Chemical Determination of Force Field
- 8.5. Scaling Procedures
- 8.6. Vibrational Analysis and Thermodynamic Parameters
- 8.7. Anharmonic Polyatomic Oscillator—Anharmonicity and Vibrational Parameter
- 8.8. Illustration—Anharmonic Vibrational Analysis of Ketene

9. Interaction of Radiation and Matter and Electronic Spectra

- 9.1. Introduction
- 9.2. Time-Dependent Perturbation Theory
- 9.3. Interaction of Radiation with Matter—Semiclassical Theory
- 9.4. Lasers
- 9.5. Magnetic Dipole and Electrical Quadrupole Transitions
- 9.6. Selection Rules
- 9.7. Electronic Spectra and Vibronic Transitions in Molecules
- 9.8. Franck–Condon Principle and Intensity Distribution in Electronic Bands
- 9.9. Oscillator Strength and Intensity of Absorption Bands
- 9.10. Electronic Spectra of Polyatomic Molecules
- 9.11. Electronic Transitions and Absorption Bands
- 9.12. Theoretical Studies on Valence States
- 9.13. Rydberg States
- 9.14. Studies of Core Electrons

10. Energy and Force Concepts in Chemical Bonding

- 10.1. Introduction
- 10.2. Virial Theorem
- 10.3. Hellmann–Feynman Theorem
- 10.4. Hellmann-Feynman Electrostatic Theorem
- 10.5. Forces in a Diatomic Molecule and Physical Picture of Chemical Bond
- 10.6. Charge Density Maps

11. Topological Analysis of Electron Density—Quantum Theory of Atoms in Molecules

- 11.1. Introduction
- 11.2. Topological Analysis of Electron Density
- 11.3. Hessian Matrix and Laplacian of Density
- 11.4. Critical Points
- 11.5. Molecular Structure and Chemical Bond
- 11.6. Energy of Atom in Molecule
- 11.7. Applications

12. Characterization of Chemical Reactions

- 12.1. Introduction
- 12.2. Types of Chemical Reaction Mechanisms
- 12.3. Thermodynamic Requirements for Reactions
- 12.4. Kinetic Requirements for Reaction
- 12.5. Potential Energy Surfaces and Related Concept
- 12.6. Stationary Points and Their Characteristics
- 12.7. Determination of Potential Energy Surfaces
- 12.8. Potential Energy Surfaces in Molecular Mechanics
- 12.9. Prediction of Activation Barrier
- 12.10. Heats and Free Energies of Formation and Reaction
- 12.11. Reaction Pathways and Intrinsic Reaction Coordinates
- 12.12. Photodissociation of Molecules and Bond Dissociation Energies
- 12.13. Chemical Reactivity and Its Indicators
- 12.14. Electronegativity and Group Electronegativity
- 12.15. Chemical Reactivity Indices and Their Mathematical Formulation

Index

- No. of pages: 478
- Language: English
- Edition: 1
- Published: October 15, 2015
- Imprint: Academic Press
- Paperback ISBN: 9780128034781
- eBook ISBN: 9780128035016

VG

### V.P. Gupta

*Principles and Applications of Quantum Chemistry*on ScienceDirect