Principles of Quantum Chemistry

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 ψ


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 π-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