Quantum chemistry

Preface to the Second Edition

Chapter 1. The Dawn of the Quantum Theory

1.1. Blackbody Radiation

1.2. Planck's Quantum Hypothesis

1.3. The Photoelectric Effect

1.4. Vibrations of Atoms in Crystals

1.5. The Hydrogen Atomic Spectrum

1.6. The Rydberg Formula

1.7. Angular Momentum

1.8. Quantized Angular Momentum

1.9. Reduced Mass

1.10. De Broglie Waves

1.11. The Relation between de Broglie Waves and Quantized Angular Momentum

1.12. De Broglie Waves Observed

1.13. Two-Slit Experiments

1.14. The Heisenberg Uncertainty Principle

Problems

References

MathChapter A. Complex Numbers

Problems

Chapter 2. The Classical Wave Equation

2.1. The One-Dimensional Classical Wave Equation

2.2. Separation of Variables

2.3. Oscillatory Solutions to Differential Equations

2.4. Superposition of Normal Modes

2.5. A Vibrating Membrane

2.6. Interference of Waves

Problems

References

MathChapter B. Probability and Statistics

Problems

Chapter 3. The Schrodinger Equation and a Particle in a Box

3.1. The Schrodinger Equation

3.2. Linear Operators in Quantum Mechanics

3.3. Eigenvalue Problems In Quantum Mechanics

3.4. Wave Functions and Their Probabilistic Interpretation

3.5. Quantized Energies

3.6. Normalized Wave Functions

3.7. Average Quantities in Quantum Mechanics

3.8. The Uncertainty Principle and Operators

3.9. Particle in a Three-Dimensional Box

Problems

References

MathChapter C. Vectors

Problems

Chapter 4. The Postulates and General Principles of Quantum Mechanics

4.1. State Functions

4.2. Quantum-Mechanical Operators and Classical Variables

4.3. Observable Quantities and Eigenvalues

4.4. Commutators and the Uncertainty Principle

4.5. Hermitian Operators

4.6. Hermitian Operators and Orthogonality

4.7. Commuting Operators and Mutual Eigenfunctions

4.8. Probabilty of a Measurement and Fourier Coefficients

4.9. The Time-Dependent Schrodinger Equation

4.10. Quantum Mechanics and the Two-Slit Experiment

Problems

References

MathChapter D. Series and Limits

Problems

Chapter 5. The Harmonic Oscillator and Vibrational Spectroscopy

5.1. Classical Harmonic Oscillator

5.2. Conservation of Energy of a Classical Harmonic Oscillator

5.3. Harmonic-Oscillator Model of a Diatomic Molecule

5.4. The Harmonic-Oscillator Approximation

5.5. The Energy Levels of a Quantum-Mechanical Harmonic Oscillator

5.6. Infrared Spectra of Diatomic Molecules

5.7. Overtones in Vibrational Spectra

5.8. Harmonic-Oscillator Wave Functions

5.9. Parity of Hermite Polynomials

5.10. Relations Among Hermite Polynomials

5.11. Normal Coordinates

5.12. Harmonic-Oscillator Selection Rule

Appendix. Operator Method Solution to the Schrodinger Equation for a Harmonic Oscillator

Problems

References

MathChapter E. Spherical Coordinates

Problems

Chapter 6. The Rigid Rotator and Rotational Spectroscopy

6.1. The Energy Levels of a Rigid Rotator

6.2. The Rigid Rotator Model of a Diatomic Molecule

6.3. Rotation-Vibrational Spectra

6.4. Rotation-Vibration Interaction

6.5. A Nonrigid Rotator

6.6. Spherical Harmonics

6.7. Rigid-Rotator Selection Rule

6.8. Angular Momentum and Measurements

Appendix. Determination of the Eigenvalues of L[superscript 2] and L[subscript z] by Operator Methods

Problems

References

MathChapter F. Determinants

Problems

Chapter 7. The Hydrogen Atom

7.1. The Schrodinger Equation for a Hydrogen Atom

7.2. s Orbitals

7.3. p Orbitals

7.4. The Zeeman Effect

7.5. Electron Spin

7.6. Spin-Orbit Interaction

7.7. Hydrogen Atomic Term Symbols

7.8. The Zeeman Effect Revisited

7.9. The Schrodinger Equation for a Helium Atom

Problems

References

MathChapter G. Matrices

Problems

Chapter 8. Approximation Methods

8.1. The Variational Method

8.2. Trial Functions That Depend Linearly on Variational Parameters

8.3. Trial Functions That Depend Nonlinearly on Variational Parameters

8.4. Introduction to Perturbation Theory

8.5. First-Order Pertubation Theory

8.6. Selection Rules and Time-Dependent Perturbation Theory

Problems

References

MathChapter H. Matrix Eigenvalue Problems

Problems

Chapter 9. Many-Electron Atoms

9.1. Atomic Units

9.2. Classic Calculations on a Helium Atom

9.3. Hartree-Fock Equations for a Helium Atom

9.4. Antisymmetry of Electronic Wave Functions

9.5. Slater Determinants

9.6. The Hartree-Fock-Roothaan Method

9.7. Hartree-Fock-Roothaan Results for Atoms

9.8. Correlation Energy

9.9. Atomic Term Symbols

9.10. Addition of Angular Momenta

9.11. Hund's Rules

9.12. Atomic Term Symbols and Atomic Spectra

9.13. Russell-Saunders Coupling

Appendix. An SCF Calculation of a Helium Atom

Problems

References

Chapter 10. The Chemical Bond: One- and Two-Electron Molecules

10.1. The Born-Oppenheimer Approximation

10.2. The Hydrogen Molecular Ion, [Characters not reproducible]

10.3. Molecular Orbitals Constructed from a Linear Combination of Atomic Orbitals

10.4. Bonding and Antibonding Orbitals

10.5. Molecular Orbital Theory and the Virial Theorem

10.6. Polarization Terms in Basis Sets

10.7. The Schrodinger Equation for H[subscript 2]

10.8. Molecular Orbital Theory Results for H[subscript 2]

10.9. Configuration Interaction

10.10. An SCF Calculation on H[subscript 2]

Appendix. Molecular Orbital Theory of H[subscript 2]

Problems

References

Chapter 11. Qualitative Theory of Chemical Bonding

11.1. Molecular Orbitals

11.2. Molecular Electron Configurations

11.3. Molecular Orbital Theory and Heteronuclear Diatomic Molcules

11.4. Molecular Term Symbols

11.5. Molecular Term Symbols and Symmetry Properties

11.6. The [pi]-Electron Approximation

11.7. Huckel Molecular Orbital Theory and Bond Orders

11.8. Huckel Molecular Orbital Theory in Matrix Notation

Problems

References

Chapter 12. The Hartree-Fock-Roothaan Method

12.1. The Hartree-Fock-Roothaan Equations

12.2. Minimal Gaussian Basis Sets

12.3. Extended Gaussian Basis Sets

12.4. Basis Sets with Orbital Polarization Terms

12.5. Using Gaussian 03 and WebMO

12.6. Hartree-Fock-Roothaan Results

12.7. Post-Hartree-Fock Methods

Problems

References

References for Post-Hartree-Fock Methods

Answers to the Numerical Problems

Index

Illustration Credits