Principles and Applications of Quantum Chemistry

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