ebook img

Quantum chemistry PDF

704 Pages·2008·80.08 MB·English
Save to my drive
Quick download
Download
Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

Preview Quantum chemistry

QUANTUM CHEMISTRY SECOND EDITION QUANTUM CHEMISTRY SECOND EDITION Donald A. McQuarrie DEPARTM ENT O F C HEMISTRY UNIVERSITY O F CALIFORN IA, DAVIS UN IVERSITY SCIENCE BOOKS Mill Va lley, California University Science Books www.uscibooks.com Production Manager: .Jennifer Uhlich at Wilsted and Taylor Manuscript Editor: .John Murdzek Proofreader: .Jennifer McClain Design: Yvonne Tsang at Wilsted and Taylor lllustrator: Mervin Hanson Compositor: Windfall Software, using Zz7j;;X Printer & Binder: Edwards Brothers Malloy This book is printed on acid-free paper. Copyright © 2008 by University Science Books Reproduction or translation of any part of this work beyond that pem1itted by Section 107 or 108 of the 1976 United States Copyright Act without the pem1ission of the copyright owner is tmlawful. Requests for permission or further information should be addressed to the Pen11issions Department, University Science Books. Library of Congress Cataloging-in-Publication Data McQua1Tie, Donald A. (Donald Allan) Quantum chemistry I Donald A. McQua1Tie.-2nd ed. p. cm. Includes index. ISBN 978-1-891389-50-4 (alk. paper) Quantum chemistry. I. Title. QD462.M4 2007 541'.28-dc22 2007023879 Printed in the United States of America 10 9 8 7 6 5 4 3 Contents Preface to the Second Edition xi CHAPTER 1 I The Dawn of the Quantum Theory 1.1 Blackbody Rad iation 2 1 .2 Planck's Quantum Hypothesis 4 1 .3 The Photoelectric Effect 8 1 .4 Vibrations of Atoms in Crystals 11 1 .5 The Hydrogen Atomic Spectrum 12 1 .6 The Rydberg Formula 15 1 .7 Angular Momentum 16 1 .8 Quantized Angular Momentum 1 8 1 .9 Reduced Mass 22 1.10 De Broglie Waves 26 1 .11 The Relation between de Broglie Waves and Quantized Angu lar Momentum 28 1.12 De Broglie Waves Observed 29 1 .13 Two-Sli t Experiments 30 1 .14 The Heisenberg Uncertainty Princip le 34 Problems 36 References 44 MATHCHAPTER A I Complex Numbers 45 Problems 49 CHAPTER 2 I The Classical Wave Equation 53 2.1 The One-Dimensiona l Classical Wave Equation 54 2 .2 Separation of Variables 54 2.3 Oscillatory Solutions to Differential Equat ions 58 2 .4 Superposition of Normal Modes 61 2.5 A Vibrating Membrane 64 2.6 Interference of Waves 68 Problems 72 References 84 v VI Contents M ATHCH APTER B I Probabi lity and Statistics 85 Problems 93 CHAPTER 3 I The Schrodinger Equation and a Particle in a Box 97 3.1 The Schrodinger Equation 97 3.2 Linear Operators in Quantum Mechanics 99 3.3 Eigenvalue Problems In Quantum Mechanics 101 3.4 Wave Functions and Their Probabilistic Interpretation 103 3.5 Quantized Energies 105 3.6 Normalized Wave Functions 107 3.7 Average Quantities in Quantum Mechan ics 110 3.8 The Uncertainty Principle and Operators 112 3.9 Particl e in a Three-D imensional Box 114 Problems 120 References 128 M ATHCH APTER C I Vectors 129 Problems 139 CHAPTER 4 I The Postu lates and General Principles of Quantum Mechanics 143 4.1 State Functions 143 4.2 Quantum-Mechanical Operators and Classical Variables 147 4.3 Observable Quantities and Eigenvalues 149 4.4 Commutators and the Uncerta inty Principle 153 4.5 Hermitian Operators 1 56 4.6 Hermitian Operators and Orthogona I ity 160 4.7 Commuting Operators and Mutua l Eigenfunctions 164 4.8 Probabil ty of a Measurement and Fourier Coefficients 165 4.9 The Time-Dependent Schrodinger Equation 1 70 4.1 0 Quantum Mechanics and the Two-SI it Experiment 175 Problems 179 References 196 MATHC HAPTER 0 I Ser ies and Limits 197 Problems 202 CH APTER 5 I The Harmonic Oscillator and Vibrational Spectroscopy 207 5.1 Classical Harmon ic Oscillator 207 5.2 Conservation of Energy of a Classical Harmonic Oscillator 210 5.3 Harmonic-Oscillator Model of a Diatom ic Molecu le 213 5.4 The Harmonic-Osci llator Approximation 215 5.5 The Energy Levels of a Quantum-Mechan ical Harmonic Oscillator 218 5.6 Infrared Spectra of D iatomic Molecu les 219 Contents vi i 5 .7 Overtones in Vibrational Spectra 222 5.8 Harmon ic-Oscillator Wave Functions 225 5.9 Parity of Hermite Polynomials 228 5.10 Relations Among Hermite Polynomials 230 5.11 Normal Coord inates 233 5.12 Harmon ic-Oscillator Selection Rule 237 Appendix: Operator Method Solution to the Schrodinger Equation for a Harmon ic Oscillator 239 Problems 243 References 254 MATHCHAPTER E I Spherical Coordinates 255 Problems 263 CHAPTER 6 I The Rigid Rotator and Rotational Spectroscopy 267 6.1 The Energy Levels of a Rigid Rotator 267 6.2 The Rigid Rotator Model of a D iatomic Molecule 272 6 .3 Rotation-Vibrational Spectra 2 75 6.4 Rotation- Vibration Interaction 278 6.5 A Nonrigid Rotator 281 6.6 Spherical Harmon ics 282 6.7 Rigid-Rotator Selection Rule 288 6 .8 Angular Momentum and Measurements 290 Append ix: Determ ination of the Eigenvalues of L2 and i., by Operator Methods 296 Problems 300 References 308 MATHCHAPTER F I Determ inants 309 Problems 317 CHAPTER 7 I The Hydrogen Atom 321 7.1 The Schrod inger Equation for a Hydrogen Atom 321 7 .2 s Orbitals 32 7 7.3 pOrbita ls 334 7.4 The Zeeman Effect 339 7.5 ElectronSpin 344 7 .6 Spin-Orbit Interaction 349 7.7 Hydrogen Atomic Term Symbols 353 7 .8 The Zeeman Effect Revisited 357 7 .9 The Schrod inger Equation for a Helium Atom 359 Problems 360 References 366 MATHCHAPTER G I Matrices 367 Problems 376 viii Contents CHAPTER 8 I Approx imation Methods 381 8.1 The Variationa l Method 381 8.2 Trial Functions That Depend Linearly on Variational Parameters 387 8.3 Trial Functions That Depend Non linearly on Variational Parameters 395 8.4 Introduction to Perturbation Theory 396 8.5 First-Order Pertubation Theory 399 8.6 Selection Rules and Time-Dependent Perturbation Theory 404 Problems 410 References 426 MATHCHAPTER H I Matrix Eigenvalue Problems 427 Problems 432 CHAPTER 9 I Many-Electron Atoms 435 9.1 Atomic U nits 435 9.2 Classic Ca lcu lations on a Helium Atom 439 9.3 Hartree-Fock Equations for a Helium Atom 444 9.4 Antisymmetry of Electronic Wave Functions 447 9.5 Slater Determ inants 450 9.6 The Hartree-Fock- Roothaan Method 453 9.7 Hartree-Fock- Roothaan Results for A toms 458 9.8 Correlation Energy 463 9.9 Atomic Term Symbols 466 9.10 Addition of Angu lar Momenta 470 9.11 Hund's Rules 474 9.12 Atomic Term Symbols and Atomic Spectra 475 9.13 Russell- Saunders Coupling 479 Appendix: An SCF Calculation of a Helium Atom 482 Problems 489 References 497 CHAPTER 10 I The Chemical Bond : One- and Two-Electron Molecu les 499 10.1 The Born- Oppenheimer Approximation 500 10.2 The Hydrogen Molecular Ion, Hi 501 10.3 Molecular Orbita ls Constructed from a Linear Combination of Atom ic Orbitals 506 10.4 Bonding and Antibonding Orbitals 513 10.5 Molecular Orbital Theory and the Vir ial Theorem 515 10.6 Polarization Terms in Basis Sets 521 10.7 The Sc hrodinger Equation for H2 523 10.8 Molecular Orbita l Theory Resu lts for H2 526 10.9 Configuration Interaction 531 10.10 An SCF Calcu lation on H2 537 Appendix: Molecular Orbital Theory of H2 543 Problems 547 References 557 Contents ix CH APTER 11 I Qual itative Theory of Chemical Bonding 559 11.1 Molecu lar Orbitals 560 11 .2 Molecu lar Electron Configurations 564 11.3 Molecu lar Orbital Theory and Heteronuclear Diatom ic Molcu les 570 11 .4 Molecu lar Term Symbols 573 11 .5 Molecu lar Term Symbols and Symmetry Properties 577 11 .6 The rr -Electron Approximation 581 11 .7 HOckel Molecular Orbital Theory and Bond Orders 588 11.8 HOckel Molecular Orbita l Theory in Matr ix Notation 595 Problems 597 References 605 CHAPTER 12 I The Hartree-Fock-Roothaan Method 607 12.1 The Hartree-Fock- Roothaan Equations 608 12.2 M inimal Gaussian Basis Sets 614 12.3 Extended Gaussian Basis Sets 621 12.4 Basis Sets w ith Orbita l Polarization Terms 626 12.5 Using Gaussian 03 and WebMO 631 12.6 Hartree- Fock- Roothaan Results 636 12.7 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

See more

The list of books you might like

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.