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

570 Pages·2018·69.314 MB·English
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Quantum Chemistry E N G E A visual, conceptual and contemporary approach to the fascinating L field of Physical Chemistry guides students through core concepts and Spectroscopy 4e with visual narratives and connections to cutting-edge applications P H and research. Y S I C A The fourth edition of Quantum Chemistry & Spectroscopy includes L many changes to the presentation and content at both a global and C H chapter level. These updates have been made to enhance the student E M learning experience and update the discussion of research areas. I S T R Thomas Engel Y MasteringTM Chemistry, with a new enhanced Pearson eText, has Q been significantly expanded to include a wealth of new end-of-chapter u a problems from the 4th edition, new self-guided, adaptive Dynamic n Study Modules with wrong answer feedback and remediation, and t u the new Pearson eText which is mobile friendly. m C h e m i s t r y a n d S p Please visit us at www.pearson.com for more information. e To order any of our products, contact our customer service c department at (800) 824-7799, or (201) 767-5021 outside of t r the U.S., or visit your campus bookstore. o s c o www.pearson.com p y 4 e 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 Director, Courseware Portfolio Management: Jeanne Zalesky Product Manager: Elizabeth Bell Courseware Director, Content Development: Jennifer Hart Courseware Analyst: Spencer Cotkin Managing Producer, Science: Kristen Flathman Content Producer, Science: Beth Sweeten Rich Media Content Producer: Nicole Constantino Production Management and Composition: Cenveo Publishing Services Design Manager: Mark Ong Interior/Cover Designer: Preston Thomas Illustrators: Imagineering, Inc. Manager, Rights & Permissions: Ben Ferrini Photo Research Project Manager: Cenveo Publishing Services Senior Procurement Specialist: Stacey Weinberger Credits and acknowledgments borrowed from other sources and reproduced, with permission, in this textbook appear on the appropriate page within the text or on pages 521–522. Copyright © 2019, 2013, 2010 Pearson Education, Inc. All Rights Reserved. Printed 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 otherwise. For information regarding permissions, request forms and the appropriate contacts within the Pearson Education Global Rights & Permissions department, please visit www.pearsoned.com/permissions/. Unless otherwise indicated herein, any third-party trademarks that may appear in this work are the property of their respective owners and any references to third-party trademarks, logos or other trade dress are for demonstrative or descriptive purposes only. Such references are not intended to imply any sponsorship, endorsement, authorization, or promotion of Pearson’s products by the owners of such marks, or any relationship between the owner and Pearson Education, Inc. or its affiliates, authors, licensees or distributors. 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) A01_ENGE4590_04_SE_FM_i-xvi.indd 2 30/11/17 9:51 AM To Walter and Juliane, my first teachers, and to Gloria, Alex, Gabrielle, and Amelie. A01_ENGE4590_04_SE_FM_i-xvi.indd 3 30/11/17 9:51 AM 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 iv A01_ENGE4590_04_SE_FM_i-xvi.indd 4 30/11/17 9:51 AM 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 v A01_ENGE4590_04_SE_FM_i-xvi.indd 5 30/11/17 9:51 AM 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 A01_ENGE4590_04_SE_FM_i-xvi.indd 6 30/11/17 9:51 AM 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 A01_ENGE4590_04_SE_FM_i-xvi.indd 7 30/11/17 9:51 AM 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. viii A01_ENGE4590_04_SE_FM_i-xvi.indd 8 30/11/17 9:51 AM 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 ■ most iOS and Android phones/tablets from the Apple App Store or Google Play Configurable reading settings, including resizable type and night-reading mode ■ Instructor and student note-taking, highlighting, bookmarking, and search ■ functionalities ix A01_ENGE4590_04_SE_FM_i-xvi.indd 9 30/11/17 9:51 AM

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