Contents 

PREFACE  

1 THE SCHRDINGER EQUATION   

1.1 Quantum Chemistry  

1.2 Historical Background of Quantum Mechanics 

1.3 The Uncertainty Principle  

1.4 The Time-Dependent Schrdinger Equation  

1.5 The Time-Independent Schrdinger Equation  

1.6 Probability  

1.7 Complex Numbers  

1.8 Units 

1.9 Calculus  

1.10 Summary 

2 THE PARTICLE IN A BOX   

2.1 Differential Equations  

2.2 Particle in a One-Dimensional Box  

2.3 The Free Particle in One Dimension  

2.4 Particle in a Rectangular Well  

2.5 Tunneling  

2.6 Summary 

3 OPERATORS   

3.1 Operators  

3.2 Eigenfunctions and Eigenvalues  

3.3 Operators and Quantum Mechanics  

3.4 The Three-Dimensional Many-Particle Schrdinger Equation  

3.5 The Particle in a Three-Dimensional Box  

3.6 Degeneracy  

3.7 Average Values  

3.8 Requirements for an Acceptable Wave Function  

3.9 Summary 

4 THE HARMONIC OSCILLATOR   

4.1 Power-Series Solution of Differential Equations  

4.2 The One-Dimensional Harmonic Oscillator  

4.3 Vibration of Molecules  

4.4 Numerical Solution of the One-Dimensional Time-Independent Schrdinger Equation  

4.5 Summary 

5 ANGULAR MOMENTUM   

5.1 Simultaneous Specification of Several Properties  

5.2 Vectors  

5.3 Angular Momentum of a One-Particle System  

5.4 The Ladder-Operator Method for Angular Momentum  

5.5 Summary 

6 THE HYDROGEN ATOM   

6.1 The One-Particle Central-Force Problem  

6.2 Noninteracting Particles and Separation of Variables  

6.3 Reduction of the Two-Particle Problem to Two One-Particle Problems  

6.4 The Two-Particle Rigid Rotor  

6.5 The Hydrogen Atom  

6.6 The Bound-State Hydrogen-Atom Wave Functions  

6.7 Hydrogenlike Orbitals  

6.8 The Zeeman Effect  

6.9 Numerical Solution of the Radial Schrdinger Equation  

6.10 Summary 

7 THEOREMS OF QUANTUM MECHANICS  

7.1 Introduction  

7.2 Hermitian Operators  

7.3 Expansion in Terms of Eigenfunctions  

7.4 Eigenfunctions of Commuting Operators  

7.5 Parity  

7.6 Measurement and the Superposition of States  

7.7 Position Eigenfunctions  

7.8 The Postulates of Quantum Mechanics  

7.9 Measurement and the Interpretation of Quantum Mechanics  

7.10 Matrices  

7.11 Summary 8 THE VARIATION METHOD  

8.1 The Variation Theorem  8.2 Extension of the Variation Method  

8.3 Determinants  8.4 Simultaneous Linear Equations  

8.5 Linear Variation Functions  

8.6 Matrices, Eigenvalues, and Eigenvectors  

8.7 Summary 

9 PERTURBATION THEORY  9.1 Introduction  9.2 Nondegenerate Perturbation Theory  9.3 Perturbation Treatment of the Helium-Atom Ground State  9.4 Variation Treatments of the Ground State of Helium  9.5 Perturbation Theory for a Degenerate Energy Level  9.6 Simplification of the Secular Equation  9.7 Perturbation Treatment of the First Excited States of Helium  9.8 Comparison of the Variation and Perturbation Methods  9.9 Time-Dependent Perturbation Theory  9.10 Interaction of Radiation and Matter  9.11 Summary 10 ELECTRON SPIN AND THE SPINSTATISTICS THEOREM  10.1 Electron Spin  10.2 Spin and the Hydrogen Atom  10.3 The SpinStatistics Theorem  10.4 The Helium Atom  10.5 The Pauli Exclusion Principle  10.6 Slater Determinants  10.7 Perturbation Treatment of the Lithium Ground State  10.8 Variation Treatments of the Lithium Ground State  10.9 Spin Magnetic Moment  10.10 Ladder Operators for Electron Spin  10.11 Summary 11 MANY-ELECTRON ATOMS  11.1 The HartreeFock Self-Consistent-Field Method  11.2 Orbitals and the Periodic Table  11.3 Electron Correlation  11.4 Addition of Angular Momenta  11.5 Angular Momentum in Many-Electron Atoms  11.6 SpinOrbit Interaction  11.7 The Atomic Hamiltonian  11.8 The CondonSlater Rules  11.9 Summary 12 MOLECULAR SYMMETRY  12.1 Symmetry Elements and Operations  12.2 Symmetry Point Groups  12.3 Summary 13 ELECTRONIC STRUCTURE OF DIATOMIC MOLECULES  13.1 The BornOppenheimer Approximation  13.2 Nuclear Motion in Diatomic Molecules  13.3 Atomic Units  13.4 The Hydrogen Molecule Ion  13.5 Approximate Treatments of the Ground Electronic State  13.6 Molecular Orbitals for Excited States  13.7 MO Configurations of Homonuclear Diatomic Molecules  13.8 Electronic Terms of Diatomic Molecules  13.9 The Hydrogen Molecule  13.10 The Valence-Bond Treatment of   13.11 Comparison of the MO and VB Theories  13.12 MO and VB Wave Functions for Homonuclear Diatomic Molecules  13.13 Excited States of   13.14 SCF Wave Functions for Diatomic Molecules  13.15 MO Treatment of Heteronuclear Diatomic Molecules  13.16 VB Treatment of Heteronuclear Diatomic Molecules  13.17 The Valence-Electron Approximation  13.18 Summary 14 THEOREMS OF MOLECULAR QUANTUM MECHANICS  14.1 Electron Probability Density  14.2 Dipole Moments  14.3 The HartreeFock Method for Molecules  14.4 The Virial Theorem  14.5 The Virial Theorem and Chemical Bonding  14.6 The HellmannFeynman Theorem  14.7 The Electrostatic Theorem  14.8 Summary 15 MOLECULAR ELECTRONIC STRUCTURE  15.1 Ab Initio, Density-Functional, Semiempirical, and Molecular-Mechanics Methods  15.2 Electronic Terms of Polyatomic Molecules  15.3 The SCF MO Treatment of Polyatomic Molecules  15.4 Basis Functions  15.5 The SCF MO Treatment of   15.6 Population Analysis and Bond Orders  15.7 The Molecular Electrostatic Potential, Molecular Surfaces, and Atomic Charges  15.8 Localized MOs  15.9 The SCF MO Treatment of Methane, Ethane, and Ethylene  15.10 Molecular Geometry  15.11 Conformational Searching  15.12 Molecular Vibrational Frequencies  15.13 Thermodynamic Properties  15.14 Ab Initio Quantum Chemistry Programs  15.15 Performing Ab Initio Calculations  15.16 Speeding Up HartreeFock Calculations  15.17 Solvent Effects   16 ELECTRON-CORRELATION METHODS  16.1 Configuration Interaction  16.2 MllerPlesset (MP) Perturbation Theory  16.3 The Coupled-Cluster Method  16.4 Density-Functional Theory  16.5 Composite Methods for Energy Calculations  16.6 The Diffusion Quantum Monte Carlo Method  16.7 Relativistic Effects  16.8 Valence-Bond Treatment of Polyatomic Molecules  16.9 The GVB, VBSCF, and BOVB Methods  16.10 Chemical Reactions 17 SEMIEMPIRICAL AND MOLECULAR-MECHANICS TREATMENTS OF  MOLECULES  17.1 Semiempirical MO Treatments of Planar Conjugated Molecules  17.2 The Hckel MO Method  17.3 The PariserParrPople Method  17.4 General Semiempirical MO and DFT Methods  17.5 The Molecular-Mechanics Method  17.6 Empirical and Semiempirical Treatments of Solvent Effects  17.7 Chemical Reactions 18 COMPARISONS OF METHODS  18.1 Molecular Geometry  18.2 Energy Changes  18.3 Other Properties  18.4 Hydrogen Bonding  18.5 Conclusion  18.6 The Future of Quantum Chemistry APPENDIX BIBLIOGRAPHY ANSWERS TO SELECTED PROBLEMS INDEX