Principles of Quantum Chemistry

Principles of Quantum Chemistry focuses on the application of quantum mechanics in physical models and experiments of chemical systems.

This book describes chemical bonding and its two specific problems - bonding in complexes and in conjugated organic molecules. The very basic theory of spectroscopy is also considered. Other topics include the early development of quantum theory; particle-in-a-box; general formulation of the theory of quantum mechanics; and treatment of angular momentum in quantum mechanics. The examples of solutions of Schroedinger equations; approximation methods in quantum chemistry; symmetry in chemistry; and molecular-orbital theory are also covered.

This publication is recommended for students taking undergraduate and graduate courses in quantum chemistry.

Contenu

Preface

Chapter 1 Introduction

1-1 The Use of Models in the Sciences

1-2 Mathematics in the Sciences

1-3 Summary of the Book and how to Study it

Chapter 2 The Early Development of Quantum Theory

2-1 Review of the Earliest Work in Quantum Theory

2-2 Quantum Theory

2-3 The Schroedinger Equation

2-4 Interpretation of

2-5 Restrictions on the Wavefunction

Summary

Chapter 3 The Particle-in-a-Box

3-1 Introduction

3-2 The Particle-in-a-Box

3-3 Examination of the Solution of the Particle-in-a-Box Problem

Summary

Exercises

Chapter 4 General Formulation of the Theory of Quantum Mechanics

4-1 Introduction

4-2 Postulates of Quantum Mechanics

4-3 Normalization of the Wavefunction

4-4 Hermiticity of Operators

4-5 Orthogonality of Wavefunctions

4-6 Dirac Notation

4-7 Orthonormality and Completeness of Wavefunctions

4-8 Expansion of Wavefunctions

4-9 Average Values of Observables

4-10 Commutation of Operators

4-11 Quantum Mechanical Meaning of Commutation of Operators

4-12 Heisenberg Uncertainty Principle

4-13 The Hamiltonian Operator

4-14 Schroedinger's Equation for a Stationary State

Summary

Exercises

Chapter 5 The Treatment of Angular Momentum in Quantum Mechanics

5-1 Introduction

5-2 Operators for Angular Momentum

5-3 Eigenvalues of the Angular Momentum Operators

5-4 Treatment of Spin

Summary

Exercises

Chapter 6 Examples of Solutions of Schroedinger Equations

6-1 Introduction

6-2 The Rigid Rotator

6-3 Orthogonality and Normalization of the Solutions of the Rigid Rotator Problem

6-4 The Harmonic Oscillator

6-5 The Hydrogen Atom

Summary

Exercises

Chapter 7 Approximation Methods in Quantum Chemistry

7-1 Introduction

7-2 Variation Method

7-3 Perturbation Theory

Summary

Exercises

Chapter 8 Symmetry in Chemistry

8-1 Introduction

8-2 The Elements of Group Theory

8-3 Molecular Symmetry Operations

8-4 Representation of Groups

8-5 Characters of Representations and Character Tables

8-6 Properties of Irreducible Representations and their Characters

8-7 Relationship of Group Theory to Quantum Chemistry

8-8 The Direct Product

Summary

Exercises

Chapter 9 Many-Electron Atoms

9-1 Introduction

9-2 The Schroedinger Equation for Many-Electron Atoms

9-3 The Independent-Particle Model

9-4 The Helium Atom

9-5 Spin-Orbitals

9-6 Indistinguishable Particles: The Pauli Exclusion Principle

9-7 Wavefunctions for Many-Electron Systems: Slater Determinants

9-8 Periodic System of the Elements

9-9 Angular Momentum of Many-Electron Atoms

9-10 Relative Energies of Atomic States

9-11 Hartree-Fock Self-Consistent Field Method

9-12 Correlation Energy

9-13 Slater-Type Orbitals

Summary

Exercises

Chapter 10 Molecular-Orbital Theory

10-1 Introduction

10-2 The Born-Oppenheimer Approximation

10-3 The Molecular Orbital

10-4 Linear Combination of Atomic Orbitals

10-5 The Hydrogen Molecule Ion

10-6 The Hydrogen Molecule

10-7 MO Theory for more Complex Diatomic Molecules

10-8 Improvements on the Simple MO Method

Summary

Exercises

Chapter 11 Valence-Bond Theory

11-1 Introduction

11-2 The Hydrogen Molecule

11-3 Extension of the Heitler-London Treatment

11-4 Comparison of VB and MO Theory for Hydrogen

11-5 Hybridization of Orbitals and Resonance

Summary

Exercises

Chapter 12 Hückel Molecular-Orbital Theory

12-1 Introduction

12-2 Hückel MO theory

12-3 Ethylene

12-4 Butadiene

12-5 Benzene

12-6 HMO Coefficients and p-Electron Distribution

12-7 Alternant Hydrocarbons

12-8 Use of Molecular Symmetry Properties in HMO Theory

Summary

Exercises

Chapter 13 Bonding in Complexes

13-1 Introduction

13-2 Effect of an Octahedral Ligand Field

13-3 Use of Group Theory

13-4 Correlation Diagrams

13-5 Concluding Remarks

Summary

Exercises

Chapter 14 Spectroscopy

14-1 Introduction

14-2 Time-Dependent Perturbations

14-3 Radiation Theory

14-4 Experimental Spectroscopy

14-5 Pure Rotational Spectra

14-6 Vibration-Rotation Spectra

14-7 Electronic Spectra

Summary

Exercises

References

Bibliography

Index