Physical chemistry ; Quantum Chemistry and Spectroscopy (What's New in Chemistry)

570 Pages·2018·69.314 MB·English

by  Thomas Engel, Philip Reid

Quantum Chemistry
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PHYSICAL CHEMISTRY
Quantum Chemistry
and Spectroscopy
FOURTH EDITION
Thomas Engel
University of Washington
Chapter 15, “Computational Chemistry,”
was contributed by
Warren Hehre
CEO, Wavefunction, Inc.
Chapter 17, “Nuclear Magnetic Resonance Spectroscopy,”
was coauthored by
Alex Angerhofer
University of Florida
A01_ENGE4590_04_SE_FM_i-xvi.indd 1 30/11/17 9:51 AM
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Library of Congress Cataloging-in-Publication Data
Names: Engel, Thomas, 1942- author. | Hehre, Warren, author. | Angerhofer,
Alex, 1957- author. | Engel, Thomas, 1942- Physical chemistry.
Title: Physical chemistry, quantum chemistry, and spectroscopy / Thomas Engel
(University of Washington), Warren Hehre (CEO, Wavefunction, Inc.), Alex
Angerhofer (University of Florida).
Description: Fourth edition. | New York : Pearson Education, Inc., [2019] |
Chapter 15, Computational chemistry, was contributed by Warren Hehre, CEO,
Wavefunction, Inc. Chapter 17, Nuclear magnetic resonance spectroscopy,
was contributed by Alex Angerhofer, University of Florida. | Previous
edition: Physical chemistry / Thomas Engel (Boston : Pearson, 2013). |
Includes index.
Identifiers: LCCN 2017046193 | ISBN 9780134804590
Subjects: LCSH: Chemistry, Physical and theoretical--Textbooks. | Quantum
chemistry--Textbooks. | Spectrum analysis--Textbooks.
Classification: LCC QD453.3 .E55 2019 | DDC 541/.28--dc23
LC record available at https://lccn.loc.gov/2017046193
1 17
ISBN 10: 0-13-480459-7; ISBN 13: 978-0-13-480459-0 (Student edition)
ISBN 10: 0-13-481394-4; ISBN 13: 978-0-13-481394-3 (Books A La Carte edition)
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To Walter and Juliane,
my first teachers,
and to Gloria,
Alex,
Gabrielle, and Amelie.
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Brief Contents
QUANTUM CHEMISTRY AND SPECTROSCOPY
1 From Classical to Quantum Mechanics 19 11 Quantum States for Many-Electron Atoms
and Atomic Spectroscopy 257
2 The Schrödinger Equation 45
12 The Chemical Bond in Diatomic
3 The Quantum-Mechanical Postulates 67
Molecules 285
4 Applying Quantum-Mechanical Principles
13 Molecular Structure and Energy Levels
to Simple Systems 77
for Polyatomic Molecules 315
5 Applying the Particle in the Box Model
14 Electronic Spectroscopy 349
to Real-World Topics 95
15 Computational Chemistry 377
6 Commuting and Noncommuting Operators
and the Surprising Consequences of 16 Molecular Symmetry and an Introduction
Entanglement 119 to Group Theory 439
7 A Quantum-Mechanical Model for the 17 Nuclear Magnetic Resonance
Vibration and Rotation of Molecules 143 Spectroscopy 467
8 Vibrational and Rotational Spectroscopy APPENDIX A Point Group Character Tables 513
of Diatomic Molecules 171
Credits 521
9 The Hydrogen Atom 209
Index 523
1 0 Many-Electron Atoms 233
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Detailed Contents
QUANTUM CHEMISTRY AND SPECTROSCOPY
Preface ix 3.2 Every Observable Has a Corresponding
Operator 69
Math Essential 1 Units, Significant Figures, and 3.3 The Result of an Individual Measurement 69
Solving End of Chapter Problems
3.4 The Expectation Value 70
Math Essential 2 Differentiation and Integration 3.5 The Evolution in Time of a Quantum-Mechanical
System 73
Math Essential 3 Partial Derivatives
4 Applying Quantum-Mechanical
Math Essential 4 Infinite Series
Principles to Simple Systems 77
1 From Classical to Quantum
4.1 The Free Particle 77
Mechanics 19
4.2 The Case of the Particle in a One-Dimensional
1.1 Why Study Quantum Mechanics? 19 Box 79
1.2 Quantum Mechanics Arose out of the Interplay 4.3 Two- and Three-Dimensional Boxes 83
of Experiments and Theory 20
4.4 Using the Postulates to Understand the Particle
1.3 Blackbody Radiation 21 in the Box and Vice Versa 84
1.4 The Photoelectric Effect 22
5 Applying the Particle in the Box
1.5 Particles Exhibit Wave-Like Behavior 24
1.6 Diffraction by a Double Slit 26 Model to Real-World Topics 95
1.7 Atomic Spectra and the Bohr Model of the 5.1 The Particle in the Finite Depth Box 95
Hydrogen Atom 29
5.2 Differences in Overlap between Core and Valence
Electrons 96
Math Essential 5 Differential Equations
5.3 Pi Electrons in Conjugated Molecules Can Be
Math Essential 6 Complex Numbers and Functions Treated as Moving Freely in a Box 97
2 The Schrödinger Equation 45 5.4 Understanding Conductors, Insulators,
and Semiconductors Using the Particle in a
2.1 What Determines If a System Needs to Be Box Model 98
Described Using Quantum Mechanics? 45
5.5 Traveling Waves and Potential Energy
2.2 Classical Waves and the Nondispersive Wave Barriers 100
Equation 49
5.6 Tunneling through a Barrier 103
2.3 Quantum-Mechanical Waves and the Schrödinger
5.7 The Scanning Tunneling Microscope
Equation 54
and the Atomic Force Microscope 104
2.4 Solving the Schrödinger Equation: Operators,
5.8 Tunneling in Chemical Reactions 109
Observables, Eigenfunctions, and Eigenvalues 55
5.9 Quantum Wells and Quantum Dots 110
2.5 The Eigenfunctions of a Quantum-Mechanical
Operator Are Orthogonal 57
6 Commuting and Noncommuting
2.6 The Eigenfunctions of a Quantum-Mechanical
Operators and the Surprising
Operator Form a Complete Set 59
Consequences of
2.7 Summarizing the New Concepts 61
Entanglement 119
3 The Quantum-Mechanical
6.1 Commutation Relations 119
Postulates 67 6.2 The Stern–Gerlach Experiment 121
3.1 The Physical Meaning Associated with the Wave 6.3 The Heisenberg Uncertainty Principle 124
Function is Probability 67
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vi CONTENTS
6.4 The Heisenberg Uncertainty Principle Expressed 9.5 The Radial Probability Distribution Function 219
in Terms of Standard Deviations 128 9.6 Validity of the Shell Model of an Atom 224
6.5 A Thought Experiment Using a Particle
in a Three-Dimensional Box 130 Math Essential 9 Working with Determinants
6.6 Entangled States, Teleportation, and Quantum
Computers 132 10 Many-Electron Atoms 233
10.1 Helium: The Smallest Many-Electron Atom 233
Math Essential 7 Vectors 10.2 Introducing Electron Spin 235
10.3 Wave Functions Must Reflect the
Math Essential 8 Polar and Spherical Coordinates
Indistinguishability of Electrons 236
7 A Quantum-Mechanical Model 10.4 Using the Variational Method to Solve the
Schrödinger Equation 239
for the Vibration and Rotation
10.5 The Hartree–Fock Self-Consistent Field
of Molecules 143
Model 240
7.1 The Classical Harmonic Oscillator 143 10.6 Understanding Trends in the Periodic Table
7.2 Angular Motion and the Classical Rigid Rotor 147 from Hartree–Fock Calculations 247
7.3 The Quantum-Mechanical Harmonic
Oscillator 149 11 Quantum States for Many-
7.4 Quantum-Mechanical Rotation in Two Electron Atoms and Atomic
Dimensions 154
Spectroscopy 257
7.5 Quantum-Mechanical Rotation in Three
Dimensions 157 11.1 Good Quantum Numbers, Terms, Levels,
and States 257
7.6 Quantization of Angular Momentum 159
11.2 The Energy of a Configuration Depends on Both
7.7 Spherical Harmonic Functions 161
Orbital and Spin Angular Momentum 259
7.8 Spatial Quantization 164
11.3 Spin–Orbit Coupling Splits a Term into
Levels 266
8 Vibrational and Rotational
11.4 The Essentials of Atomic Spectroscopy 267
Spectroscopy of Diatomic
11.5 Analytical Techniques Based on Atomic
Molecules 171 Spectroscopy 269
11.6 The Doppler Effect 272
8.1 An Introduction to Spectroscopy 171
11.7 The Helium–Neon Laser 273
8.2 Absorption, Spontaneous Emission,
and Stimulated Emission 174 11.8 Auger Electron Spectroscopy and X-Ray
Photoelectron Spectroscopy 277
8.3 An Introduction to Vibrational
Spectroscopy 175
12 The Chemical Bond in Diatomic
8.4 The Origin of Selection Rules 178
8.5 Infrared Absorption Spectroscopy 180 Molecules 285
8.6 Rotational Spectroscopy 184 12.1 Generating Molecular Orbitals from Atomic
8.7 Fourier Transform Infrared Spectroscopy 190 Orbitals 285
8.8 Raman Spectroscopy 194 12.2 The Simplest One-Electron Molecule: H2+ 289
8.9 How Does the Transition Rate between States 12.3 Energy Corresponding to the H2+ Molecular Wave
Depend on Frequency? 196 Functions cg and cu 291
12.4 A Closer Look at the H+ Molecular Wave
2
9 The Hydrogen Atom 209 Functions cg and cu 294
12.5 Homonuclear Diatomic Molecules 297
9.1 Formulating the Schrödinger Equation 209
12.6 Electronic Structure of Many-Electron
9.2 Solving the Schrödinger Equation for the
Molecules 299
Hydrogen Atom 210
12.7 Bond Order, Bond Energy, and Bond Length 302
9.3 Eigenvalues and Eigenfunctions for the Total
Energy 211 12.8 Heteronuclear Diatomic Molecules 304
9.4 Hydrogen Atom Orbitals 217 12.9 The Molecular Electrostatic Potential 307
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CONTENTS vii
13 Molecular Structure and 15.3 Hartree–Fock Molecular Orbital Theory: A Direct
Descendant of the Schrödinger Equation 382
Energy Levels for Polyatomic
15.4 Properties of Limiting Hartree–Fock Models 384
Molecules 315
15.5 Theoretical Models and Theoretical Model
13.1 Lewis Structures and the VSEPR Model 315 Chemistry 389
13.2 Describing Localized Bonds Using Hybridization 15.6 Moving Beyond Hartree–Fock Theory 390
for Methane, Ethene, and Ethyne 318
15.7 Gaussian Basis Sets 395
13.3 Constructing Hybrid Orbitals for Nonequivalent
15.8 Selection of a Theoretical Model 398
Ligands 321
15.9 Graphical Models 412
13.4 Using Hybridization to Describe Chemical
15.10 Conclusion 420
Bonding 324
13.5 Predicting Molecular Structure Using
Math Essential 10 Working with Matrices
Qualitative Molecular Orbital Theory 326
13.6 How Different Are Localized and Delocalized 16 Molecular Symmetry and an
Bonding Models? 329 Introduction to Group Theory 439
13.7 Molecular Structure and Energy Levels from
16.1 Symmetry Elements, Symmetry Operations,
Computational Chemistry 332
and Point Groups 439
13.8 Qualitative Molecular Orbital Theory for
16.2 Assigning Molecules to Point Groups 441
Conjugated and Aromatic Molecules:
The Hückel Model 334 16.3 The H2O Molecule and the C2v Point Group 443
13.9 From Molecules to Solids 340 16.4 Representations of Symmetry Operators, Bases
for Representations, and the Character Table 448
13.10 Making Semiconductors Conductive at Room
Temperature 342 16.5 The Dimension of a Representation 450
16.6 Using the C Representations to Construct
2v
14 Electronic Spectroscopy 349 Molecular Orbitals for H2O 454
16.7 Symmetries of the Normal Modes of Vibration
14.1 The Energy of Electronic Transitions 349
of Molecules 456
14.2 Molecular Term Symbols 350
16.8 Selection Rules and Infrared versus Raman
14.3 Transitions between Electronic States
Activity 460
of Diatomic Molecules 353
16.9 Using the Projection Operator Method to
14.4 The Vibrational Fine Structure of Electronic
Generate MO That Are Bases for Irreducible
s
Transitions in Diatomic Molecules 354
Representations 461
14.5 UV-Visible Light Absorption in Polyatomic
Molecules 356
17 Nuclear Magnetic Resonance
14.6 Transitions among the Ground and Excited
Spectroscopy 467
States 359
14.7 Singlet–Singlet Transitions: Absorption 17.1 Intrinsic Nuclear Angular Momentum
and Fluorescence 360 and Magnetic Moment 467
14.8 Intersystem Crossing and Phosphorescence 361 17.2 The Nuclear Zeeman Effect 470
14.9 Fluorescence Spectroscopy and Analytical 17.3 The Chemical Shift 473
Chemistry 362 17.4 Spin–Spin Coupling and Multiplet Splittings 476
14.10 Ultraviolet Photoelectron Spectroscopy 363 17.5 Spin Dynamics 484
14.11 Single-Molecule Spectroscopy 365 17.6 Pulsed NMR Spectroscopy 491
14.12 Fluorescent Resonance Energy Transfer 366 17.7 Two-Dimensional NMR 498
14.13 Linear and Circular Dichroism 368 17.8 Solid-State NMR 503
14.14 Assigning + and - to g Terms of Diatomic 17.9 Dynamic Nuclear Polarization 505
Molecules 371
17.10 Magnetic Resonance Imaging 507
15 Computational Chemistry 377 APPENDIX A Point Group Character Tables 513
15.1 The Promise of Computational Chemistry 377 Credits 521
15.2 Potential Energy Surfaces 378
Index 523
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About the Author
THOMAS ENGEL 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, during 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 has published more than 80 articles and book chapters in the area
of surface chemistry. 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. Other than this textbook, his current primary sci-
ence interests are in energy policy and energy conservation. He serves on the citizen’s
advisory board of his local electrical utility, and his energy-efficient house could be
heated in winter using only a hand-held hair dryer. He currently drives a hybrid vehicle
and plans to transition to an electric vehicle soon to further reduce his carbon footprint.
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Preface
The fourth edition of Quantum Chemistry and Spectroscopy includes many changes to
the presentation and content at both a global and chapter level. These updates have been
made to enhance the student learning experience and update the discussion of research
areas. At the global level, changes that readers will see throughout the textbook include:
• Review of relevant mathematics skills. One of the primary reasons that students
experience physical chemistry as a challenging course is that they find it difficult to
transfer skills previously acquired in a mathematics course to their physical chemis-
try course. To address this issue, contents of the third edition Math Supplement have
been expanded and split into 11 two- to five-page Math Essentials, which are insert-
ed at appropriate places throughout this book, as well as in the companion volume
Thermodynamics, Statistical Thermodynamics, and Kinetics, just before the math
skills are required. Our intent in doing so is to provide “just-in-time” math help and
to enable students to refresh math skills specifically needed in the following chapter.
• Concept and Connection. A new Concept and Connection feature has been
added to each chapter to present students with a quick visual summary of the most
important ideas within the chapter. In each chapter, approximately 10–15 of the
most important concepts and/or connections are highlighted in the margins.
• End-of-Chapter Problems. Numerical Problems are now organized by section
number within chapters to make it easier for instructors to create assignments for
specific parts of each chapter. Furthermore, a number of new Conceptual Questions
and Numerical Problems have been added to the book. Numerical Problems from
the previous edition have been revised.
• Introductory chapter materials. Introductory paragraphs of all chapters have
been replaced by a set of three questions plus responses to those questions. This new
feature makes the importance of the chapter clear to students at the outset.
• Figures. All figures have been revised to improve clarity. Also, for many figures
additional annotation has been included to help tie concepts to the visual program.
• Key Equations. An end-of-chapter table that summarizes Key Equations has been
added to allow students to focus on the most important of the many equations in
each chapter. Equations in this table are set in red type where they appear in the
body of the chapter.
• Further Reading. A section on Further Reading has been added to each chapter
to provide references for students and instructors who would like a deeper under-
standing of various aspects of the chapter material.
• Guided Practice and Interactivity
° MasteringTM Chemistry, with a new enhanced eBook, has been significantly
expanded to include a wealth of new end-of-chapter problems from the fourth
edition, new self-guided, adaptive Dynamic Study Modules with wrong answer
feedback and remediation, and the new Pearson eBook, which is mobile friendly.
Students who solve homework problems using MasteringTM Chemistry obtain
immediate feedback, which greatly enhances learning associated with solving
homework problems. This platform can also be used for pre-class reading quiz-
zes linked directly to the eText that are useful in ensuring students remain cur-
rent in their studies and in flipping the classroom.
° NEW! Pearson eText, optimized for mobile gives students access to their
textbook anytime, anywhere.
Pearson eText mobile app offers offline access and can be downloaded for
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most iOS and Android phones/tablets from the Apple App Store or Google Play
Configurable reading settings, including resizable type and night-reading mode
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Instructor and student note-taking, highlighting, bookmarking, and search
■
functionalities
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