Quantum Chemistry

by McQuarrie, Donald A.

• ISBN13: 9781891389504
• ISBN10: 1891389505
• Edition: 2nd
• Format: Hardcover
• Copyright: 2007-08-15
• Publisher: UNIVERSITY SCIENCE BOOKS

Summary

This is a thorough update of the classic text of the same title by Donald McQuarrie.

Author Biography

Arthur Kornberg shared (with Severo Ochoa) the Nobel Prize in Medicine in 1959 for his laboratory synthesis of DNA. He is the author of several major books, including DNA Replication, second edition (W.H. Freeman and Company, 1991) and a scientific autobiography, For the Love of Enzymes: the Odyssey of a Biochemist (Harvard University Press, 1989). He is Professor Emeritus of Biochemistry at the Stanford University School of Medicine.

Table of Contents

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