Quantum Chemistry Book

Preface to the Second Edition     xi
The Dawn of the Quantum Theory     1
Blackbody Radiation     2
Planck's Quantum Hypothesis     4
The Photoelectric Effect     8
Vibrations of Atoms in Crystals     11
The Hydrogen Atomic Spectrum     12
The Rydberg Formula     15
Angular Momentum     16
Quantized Angular Momentum     18
Reduced Mass     22
De Broglie Waves     26
The Relation between de Broglie Waves and Quantized Angular Momentum     28
De Broglie Waves Observed     29
Two-Slit Experiments     30
The Heisenberg Uncertainty Principle     34
Problems     36
References     44
Complex Numbers     45
Problems     49
The Classical Wave Equation     53
The One-Dimensional Classical Wave Equation     54
Separation of Variables     54
Oscillatory Solutions to Differential Equations     58
Superposition of Normal Modes     61
A Vibrating Membrane     64
Interference of Waves     68
Problems     72
References     84
Probability and Statistics     85
Problems     93
The Schrodinger Equation and a Particle in a Box     97
The Schrodinger Equation     97
Linear Operators in Quantum Mechanics     99
Eigenvalue Problems In Quantum Mechanics     101
Wave Functions and Their Probabilistic Interpretation     103
Quantized Energies     105
Normalized Wave Functions     107
Average Quantities in Quantum Mechanics     110
The Uncertainty Principle and Operators     112
Particle in a Three-Dimensional Box     114
Problems     120
References     128
Vectors     129
Problems     139
The Postulates and General Principles of Quantum Mechanics     143
State Functions     143
Quantum-Mechanical Operators and Classical Variables     147
Observable Quantities and Eigenvalues     149
Commutators and the Uncertainty Principle     153
Hermitian Operators     156
Hermitian Operators and Orthogonality     160
Commuting Operators and Mutual Eigenfunctions     164
Probabilty of a Measurement and Fourier Coefficients     165
The Time-Dependent Schrodinger Equation     170
Quantum Mechanics and the Two-Slit Experiment     175
Problems     179
References     196
Series and Limits     197
Problems     202
The Harmonic Oscillator and Vibrational Spectroscopy     207
Classical Harmonic Oscillator     207
Conservation of Energy of a Classical Harmonic Oscillator     210
Harmonic-Oscillator Model of a Diatomic Molecule     213
The Harmonic-Oscillator Approximation     215
The Energy Levels of a Quantum-Mechanical Harmonic Oscillator     218
Infrared Spectra of Diatomic Molecules     219
Overtones in Vibrational Spectra     222
Harmonic-Oscillator Wave Functions     225
Parity of Hermite Polynomials     228
Relations Among Hermite Polynomials     230
Normal Coordinates     233
Harmonic-Oscillator Selection Rule     237
Operator Method Solution to the Schrodinger Equation for a Harmonic Oscillator     239
Problems     243
References     254
Spherical Coordinates     255
Problems     263
The Rigid Rotator and Rotational Spectroscopy     267
The Energy Levels of a Rigid Rotator     267
The Rigid Rotator Model of a Diatomic Molecule     272
Rotation-Vibrational Spectra     275
Rotation-Vibration Interaction     278
A Nonrigid Rotator     281
Spherical Harmonics     282
Rigid-Rotator Selection Rule     288
Angular Momentum and Measurements     290
Determination of the Eigenvalues of L[superscript 2] and L[subscript z] by Operator Methods     296
Problems     300
References     308
Determinants     309
Problems     317
The Hydrogen Atom     321
The Schrodinger Equation for a Hydrogen Atom     321
s Orbitals     327
p Orbitals     334
The Zeeman Effect     339
Electron Spin     344
Spin-Orbit Interaction     349
Hydrogen Atomic Term Symbols     353
The Zeeman Effect Revisited     357
The Schrodinger Equation for a Helium Atom     359
Problems     360
References     366
Matrices     367
Problems     376
Approximation Methods     381
The Variational Method      381
Trial Functions That Depend Linearly on Variational Parameters     387
Trial Functions That Depend Nonlinearly on Variational Parameters     395
Introduction to Perturbation Theory     396
First-Order Pertubation Theory     399
Selection Rules and Time-Dependent Perturbation Theory     404
Problems     410
References     426
Matrix Eigenvalue Problems     427
Problems     432
Many-Electron Atoms     435
Atomic Units     435
Classic Calculations on a Helium Atom     439
Hartree-Fock Equations for a Helium Atom     444
Antisymmetry of Electronic Wave Functions     447
Slater Determinants     450
The Hartree-Fock-Roothaan Method     453
Hartree-Fock-Roothaan Results for Atoms     458
Correlation Energy     463
Atomic Term Symbols     466
Addition of Angular Momenta     470
Hund's Rules     474
Atomic Term Symbols and Atomic Spectra     475
Russell-Saunders Coupling     479
An SCF Calculation of a Helium Atom     482
Problems     489
References     497
The Chemical Bond: One- and Two-Electron Molecules     499
The Born-Oppenheimer Approximation     500
The Hydrogen Molecular Ion, [Characters not reproducible]     501
Molecular Orbitals Constructed from a Linear Combination of Atomic Orbitals     506
Bonding and Antibonding Orbitals     513
Molecular Orbital Theory and the Virial Theorem     515
Polarization Terms in Basis Sets     521
The Schrodinger Equation for H[subscript 2]     523
Molecular Orbital Theory Results for H[subscript 2]     526
Configuration Interaction     531
An SCF Calculation on H[subscript 2]     537
Molecular Orbital Theory of H[subscript 2]     543
Problems     547
References     557
Qualitative Theory of Chemical Bonding     559
Molecular Orbitals     560
Molecular Electron Configurations     564
Molecular Orbital Theory and Heteronuclear Diatomic Molcules     570
Molecular Term Symbols     573
Molecular Term Symbols and Symmetry Properties     577
The [pi]-Electron Approximation     581
Huckel Molecular Orbital Theory and Bond Orders     588
Huckel Molecular Orbital Theory in Matrix Notation      595
Problems     597
References     605
The Hartree-Fock-Roothaan Method     607
The Hartree-Fock-Roothaan Equations     608
Minimal Gaussian Basis Sets     614
Extended Gaussian Basis Sets     621
Basis Sets with Orbital Polarization Terms     626
Using Gaussian 03 and WebMO     631
Hartree-Fock-Roothaan Results     636
Post-Hartree-Fock Methods     643
Problems     653
References     660
References for Post-Hartree-Fock Methods     660
Answers to the Numerical Problems     663
Index     683
Illustration Credits     690