Table Of ContentQuantum
Chemistry &
Spectroscopy
THIRD EDITION
Thomas Engel
University of Washington
Chapter 15, “Computational Chemistry,”
was contributed by
Warren Hehre
CEO, Wavefunction, Inc.
Editor in Chief: Adam Jaworski
Executive Editor: Jeanne Zalesky
Senior Marketing Manager: Jonathan Cottrell
Associate Editor: Jessica Neumann
VP/Executive Director, Development: Carol Trueheart
Development Editor: Michael Sypes
Editorial Assistant: Lisa Tarabokjia
Marketing Assistant: Nicola Houston
Managing Editor, Chemistry and Geosciences: Gina M. Cheselka
Senior Project Manager, Production: Beth Sweeten
Associate Media Producer: Ashley Eklund
Full Service/Compositor: GEX Publishing Services
Senior Technical Art Specialist: Connie Long
Illustrator: Imagineering Media Services, Inc.
Design Manager: Mark Ong
Interior Designer: Integra Software Services, Inc.
Cover Designer: BigWig Designs
Photo Manager and Researcher: Maya Melenchuk
Text Permissions Manager: Beth Wollar
Text Permissions Researcher: Beth Keister
Operations Specialist: Jeff Sargent
Cover Photo Credit: Artwork courtesy of Kim Kopp; photo credit: Frank Huster.
Credits and acknowledgments borrowed from other sources and reproduced, with permission, in this
textbook appear on the appropriate page within the text or on p. 489.
Copyright ©2013, 2010, 2006 Pearson Education, Inc. All rights reserved. Manufactured in the United
States of America. This publication is protected by Copyright, and permission should be obtained from the
publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or
by any means, electronic, mechanical, photocopying, recording, or likewise. To obtain permission(s) to use
material from this work, please submit a written request to Pearson Education, Inc., Permissions
Department, 1900 E. Lake Ave., Glenview, IL 60025. For information regarding permissions, call
(847) 486-2635.
Many of the designations used by manufacturers and sellers to distinguish their products are claimed as
trademarks. Where those designations appear in this book, and the publisher was aware of a trademark
claim, the designations have been printed in initial caps or all caps.
Library of Congress Cataloging-in-Publication Data
Engel, Thomas
Quantum chemistry and spectroscopy / Thomas Engel, Philip Reid. -- 3rd ed.
p. cm.
Includes index.
ISBN 978-0-321-76619-9 (casebound)
1. Quantum chemistry--Textbooks. 2. Spectrum analysis--Textbooks. I. Reid, Philip (Philip J.) II. Title.
QD462.E53 2012
541'.28--dc23
2011046906
1 2 3 4 5 6 7 8 9 10— CRK—15 14 13 12 11
ISBN-10:0-321-76619-9; ISBN-13:978-0-321-76619-9
www.pearsonhighered.com
To Walter and Juliane,
my first teachers,
and to Gloria,
Alex,
and Gabrielle.
Thomas Engel
Brief Contents
1 12
From Classical to Quantum Mechanics 1 The Chemical Bond in Diatomic
2 Molecules 245
The Schrödinger Equation 17
13
3 Molecular Structure and Energy Levels for
The Quantum Mechanical Postulates 39
Polyatomic Molecules 275
4
Using Quantum Mechanics on Simple
14
Electronic Spectroscopy 309
Systems 51
15
5 Computational Chemistry 339
The Particle in the Box and the Real
16
World 69 Molecular Symmetry 395
6 17
Commuting and Noncommuting Operators Nuclear Magnetic Resonance
and the Surprising Consequences of Spectroscopy 423
Entanglement 91
A
APPENDIX Math Supplement 455
7
A Quantum Mechanical Model for the
B
Vibration and Rotation of Molecules 113 APPENDIX Point Group Character
Tables 477
8
The Vibrational and Rotational Spectroscopy
C
of Diatomic Molecules 139 APPENDIX Answers to Selected End-of-Chapter
9 Problems 485
The Hydrogen Atom 173
10 Many-Electron Atoms 191 CREDITS 489
11
Quantum States for Many-Electron Atoms and INDEX 491
Atomic Spectroscopy 215
iv
Contents
PREFACE x 4 Using Quantum Mechanics on
Simple Systems
51
1
From Classical to Quantum 4.1 The Free Particle 51
Mechanics 1 4.2 The Particle in a One-Dimensional Box 53
4.3 Two- and Three-Dimensional Boxes 57
1.1 Why Study Quantum Mechanics? 1
4.4 Using the Postulates to Understand the Particle in
1.2 Quantum Mechanics Arose out of the Interplay of
the Box and Vice Versa 58
Experiments and Theory 2
1.3 Blackbody Radiation 3
5
The Particle in the Box and the
1.4 The Photoelectric Effect 4
Real World
69
1.5 Particles Exhibit Wave-Like Behavior 6
1.6 Diffraction by a Double Slit 8 5.1 The Particle in the Finite Depth Box 69
1.7 Atomic Spectra and the Bohr Model of the 5.2 Differences in Overlap between Core and Valence
Hydrogen Atom 11 Electrons 70
5.3 Pi Electrons in Conjugated Molecules Can Be
2 Treated as Moving Freely in a Box 71
The Schrödinger Equation
17
5.4 Why Does Sodium Conduct Electricity and Why
2.1 What Determines If a System Needs to Be Is Diamond an Insulator? 72
Described Using Quantum Mechanics? 17
5.5 Traveling Waves and Potential Energy Barriers 73
2.2 Classical Waves and the Nondispersive Wave
5.6 Tunneling through a Barrier 75
Equation 21
5.7 The Scanning Tunneling Microscope and the
2.3 Waves Are Conveniently Represented as
Atomic Force Microscope 77
Complex Functions 25
5.8 Tunneling in Chemical Reactions 82
2.4 Quantum Mechanical Waves and the Schrödinger
5.9 (Supplemental) Quantum Wells and
Equation 26
Quantum Dots 83
2.5 Solving the Schrödinger Equation: Operators,
Observables, Eigenfunctions, and Eigenvalues 28
6
Commuting and Noncommuting
2.6 The Eigenfunctions of a Quantum Mechanical
Operator Are Orthogonal 30 Operators and the Surprising
2.7 The Eigenfunctions of a Quantum Mechanical Consequences of Entanglement
91
Operator Form a Complete Set 32
6.1 Commutation Relations 91
2.8 Summing Up the New Concepts 34
6.2 The Stern–Gerlach Experiment 93
6.3 The Heisenberg Uncertainty Principle 96
3
The Quantum Mechanical
6.4 (Supplemental) The Heisenberg Uncertainty
Postulates
39 Principle Expressed in Terms of Standard
Deviations 100
3.1 The Physical Meaning Associated with the Wave
Function Is Probability 40 6.5 (Supplemental) A Thought Experiment Using a
Particle in a Three-Dimensional Box 102
3.2 Every Observable Has a Corresponding
Operator 41 6.6 (Supplemental) Entangled States, Teleportation,
and Quantum Computers 104
3.3 The Result of an Individual Measurement 42
3.4 The Expectation Value 42
3.5 The Evolution in Time of a Quantum
Mechanical System 46
3.6 Do Superposition Wave Functions Really Exist? 46
v
vi
CONTENTS
7 10
A Quantum Mechanical Model for Many-Electron Atoms
191
the Vibration and Rotation of
10.1 Helium: The Smallest Many-Electron Atom 191
Molecules
113 10.2 Introducing Electron Spin 193
7.1 The Classical Harmonic Oscillator 113 10.3 Wave Functions Must Reflect the
Indistinguishability of Electrons 194
7.2 Angular Motion and the Classical Rigid Rotor 117
10.4 Using the Variational Method to Solve the
7.3 The Quantum Mechanical Harmonic
Schrödinger Equation 198
Oscillator 119
10.5 The Hartree–Fock Self-Consistent Field
7.4 Quantum Mechanical Rotation in Two
Method 199
Dimensions 124
10.6 Understanding Trends in the Periodic Table
7.5 Quantum Mechanical Rotation in Three
from Hartree–Fock Calculations 207
Dimensions 127
7.6 The Quantization of Angular Momentum 129
7.7 The Spherical Harmonic Functions 131 11 Quantum States for
7.8 Spatial Quantization 133 Many-Electron Atoms and
Atomic Spectroscopy
215
8
The Vibrational and Rotational
11.1 Good Quantum Numbers, Terms, Levels, and
Spectroscopy of Diatomic States 215
Molecules 139 11.2 The Energy of a Configuration Depends on Both
Orbital and Spin Angular Momentum 217
8.1 An Introduction to Spectroscopy 139
11.3 Spin-Orbit Coupling Breaks Up a Term into
8.2 Absorption, Spontaneous Emission, and
Levels 224
Stimulated Emission 141
11.4 The Essentials of Atomic Spectroscopy 225
8.3 An Introduction to Vibrational Spectroscopy 143
11.5 Analytical Techniques Based on Atomic
8.4 The Origin of Selection Rules 146
Spectroscopy 227
8.5 Infrared Absorption Spectroscopy 148
11.6 The Doppler Effect 230
8.6 Rotational Spectroscopy 151
11.7 The Helium-Neon Laser 231
8.7 (Supplemental) Fourier Transform Infrared
11.8 Laser Isotope Separation 234
Spectroscopy 157
11.9 Auger Electron and X-Ray Photoelectron
8.8 (Supplemental) Raman Spectroscopy 159
Spectroscopies 235
8.9 (Supplemental) How Does the Transition Rate
11.10 Selective Chemistry of Excited States:
between States Depend on Frequency? 161
O(3P) and O(1D) 238
11.11 (Supplemental) Configurations with Paired and
9
The Hydrogen Atom 173 Unpaired Electron Spins Differ in Energy 239
9.1 Formulating the Schrödinger Equation 173
12
9.2 Solving the Schrödinger Equation for the The Chemical Bond in Diatomic
Hydrogen Atom 174 Molecules
245
9.3 Eigenvalues and Eigenfunctions for the
12.1 Generating Molecular Orbitals from Atomic
Total Energy 175
Orbitals 245
9.4 The Hydrogen Atom Orbitals 181
12.2 The Simplest One-Electron Molecule:
9.5 The Radial Probability Distribution +
H 249
2
Function 183 +
12.3 The Energy Corresponding to the H
2
9.6 The Validity of the Shell Model of Molecular Wave Functions c and c 251
g u
an Atom 187 +
12.4 A Closer Look at the H Molecular Wave
2
Functions c and c 254
g u
vii
CONTENTS
12.5 Homonuclear Diatomic Molecules 256 14.8 Intersystem Crossing and Phosphorescence 321
12.6 The Electronic Structure of Many-Electron 14.9 Fluorescence Spectroscopy and Analytical
Molecules 260 Chemistry 322
12.7 Bond Order, Bond Energy, and Bond 14.10 Ultraviolet Photoelectron Spectroscopy 323
Length 263
14.11 Single Molecule Spectroscopy 325
12.8 Heteronuclear Diatomic Molecules 265
14.12 Fluorescent Resonance Energy
12.9 The Molecular Electrostatic Potential 268 Transfer (FRET) 327
14.13 Linear and Circular Dichroism 331
13 Molecular Structure and Energy 14.14 Assigning + and - to © Terms of Diatomic
Molecules 333
Levels for Polyatomic Molecules
275
13.1 Lewis Structures and the VSEPR Model 275
15
Computational Chemistry
339
13.2 Describing Localized Bonds Using Hybridization
for Methane, Ethene, and Ethyne 278 15.1 The Promise of Computational Chemistry 339
13.3 Constructing Hybrid Orbitals for Nonequivalent 15.2 Potential Energy Surfaces 340
Ligands 281
15.3 Hartree–Fock Molecular Orbital Theory: A Direct
13.4 Using Hybridization to Describe Chemical Descendant of the Schrödinger Equation 344
Bonding 284
15.4 Properties of Limiting Hartree–Fock Models 346
13.5 Predicting Molecular Structure Using
15.5 Theoretical Models and Theoretical Model
Qualitative Molecular Orbital Theory 286
Chemistry 351
13.6 How Different Are Localized and Delocalized
15.6 Moving Beyond Hartree–Fock Theory 352
Bonding Models? 289
15.7 Gaussian Basis Sets 357
13.7 Molecular Structure and Energy Levels from
15.8 Selection of a Theoretical Model 360
Computational Chemistry 292
15.9 Graphical Models 374
13.8 Qualitative Molecular Orbital Theory for
Conjugated and Aromatic Molecules: The 15.10 Conclusion 382
Hückel Mode 294
13.9 From Molecules to Solids 300
16
Molecular Symmetry
395
13.10 Making Semiconductors Conductive at Room
Temperature 301 16.1 Symmetry Elements, Symmetry Operations, and
Point Groups 395
16.2 Assigning Molecules to Point Groups 397
14
Electronic Spectroscopy
309 16.3 The H O Molecule and the C Point Group 399
2 2v
14.1 The Energy of Electronic Transitions 309 16.4 Representations of Symmetry Operators, Bases
14.2 Molecular Term Symbols 310 for Representations, and the Character Table 404
14.3 Transitions between Electronic States of 16.5 The Dimension of a Representation 406
Diatomic Molecules 313 16.6 Using the C Representations to Construct
2v
Molecular Orbitals for H O 410
14.4 The Vibrational Fine Structure of Electronic 2
Transitions in Diatomic Molecules 314 16.7 The Symmetries of the Normal Modes of
Vibration of Molecules 412
14.5 UV-Visible Light Absorption in Polyatomic
Molecules 316 16.8 Selection Rules and Infrared versus Raman
Activity 416
14.6 Transitions among the Ground and Excited
States 318 16.9 (Supplemental) Using the Projection Operator
Method to Generate MOs That Are Bases for
14.7 Singlet–Singlet Transitions: Absorption and
Irreducible Representations 417
Fluorescence 319
viii
CONTENTS
17 17.9 Peak Widths in NMR Spectroscopy 438
Nuclear Magnetic Resonance
17.10 Solid-State NMR 440
Spectroscopy
423
17.11 NMR Imaging 440
17.1 Intrinsic Nuclear Angular Momentum and
17.12 (Supplemental)The NMR Experiment in the
Magnetic Moment 423
Laboratory and Rotating Frames 442
17.2 The Energy of Nuclei of Nonzero Nuclear Spin
17.13 (Supplemental) Fourier Transform NMR
in a Magnetic Field 425
Spectroscopy 444
17.3 The Chemical Shift for an Isolated Atom 427
17.14 (Supplemental) Two-Dimensional NMR 448
17.4 The Chemical Shift for an Atom Embedded in a
Molecule 428 A
APPENDIX Math Supplement 455
17.5 Electronegativity of Neighboring Groups and
B
Chemical Shifts 429 APPENDIX Point Group Character Tables 477
17.6 Magnetic Fields of Neighboring Groups and
C
APPENDIX Answers to Selected End-of-Chapter
Chemical Shifts 430
17.7 Multiplet Splitting of NMR Peaks Arises Problems 485
through Spin–Spin Coupling 431
CREDITS489
17.8 Multiplet Splitting When More Than Two Spins
Interact 436 INDEX491
About the Author
Thomas Engel has taught chemistry at the University of Washington for more than
20 years, where he is currently professor emeritus of chemistry. Professor Engel
received his bachelor’s and master’s degrees in chemistry from the Johns Hopkins
University, and his Ph.D. in chemistry from the University of Chicago. He then spent
11 years as a researcher in Germany and Switzerland, in which time he received the
Dr. rer. nat. habil. degree from the Ludwig Maximilians University in Munich. In
1980, he left the IBM research laboratory in Zurich to become a faculty member at the
University of Washington.
Professor Engel’s research interests are in the area of surface chemistry, and he has
published more than 80 articles and book chapters in this field. He has received the
Surface Chemistry or Colloids Award from the American Chemical Society and a
Senior Humboldt Research Award from the Alexander von Humboldt Foundation.
ix
