Preview Physical chemistry Quantum Chemistry and Spectroscopy (Whats New in Chemistry), 4th Edition by Thomas Engel, Philip Reid (2018) Preview Physical chemistry Quantum Chemistry and Spectroscopy (Whats New in Chemistry), 4th Edition by Thomas Engel, Philip Reid (2018) Preview Physical chemistry Quantum Chemistry and Spectroscopy (Whats New in Chemistry), 4th Edition by Thomas Engel, Philip Reid (2018) Preview Physical chemistry Quantum Chemistry and Spectroscopy (Whats New in Chemistry), 4th Edition by Thomas Engel, Philip Reid (2018)
MasteringTM Chemistry, with a new enhanced Pearson eText, has been significantly expanded to include a wealth of new end-of-chapter problems from the 4th edition, new self-guided, adaptive Dynamic Study Modules with wrong answer feedback and remediation, and the new Pearson eText which is mobile friendly www.pearson.com Chemistry and Spectroscopy 4e Please visit us at www.pearson.com for more information To order any of our products, contact our customer service department at (800) 824-7799, or (201) 767-5021 outside of the U.S., or visit your campus bookstore PHYSICAL CHEMISTRY Quantum The fourth edition of Quantum Chemistry & 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 ENGEL A visual, conceptual and contemporary approach to the fascinating field of Physical Chemistry guides students through core concepts with visual narratives and connections to cutting-edge applications and research Quantum Chemistry and Spectroscopy 4e Thomas Engel 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 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 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 30/11/17 9:51 AM Brief Contents QUANTUM CHEMISTRY AND SPECTROSCOPY From Classical to Quantum Mechanics 19 The Schrödinger Equation 45 The Quantum-Mechanical Postulates 67 Applying Quantum-Mechanical Principles to Simple Systems 77 Applying the Particle in the Box Model to Real-World Topics 95 Commuting and Noncommuting Operators and the Surprising Consequences of Entanglement 119 A Quantum-Mechanical Model for the Vibration and Rotation of Molecules 143 Vibrational and Rotational Spectroscopy of Diatomic Molecules 171 The Hydrogen Atom 209 Many-Electron Atoms 233 11 Quantum States for Many-Electron Atoms and Atomic Spectroscopy 257 12 The Chemical Bond in Diatomic Molecules 285 13 Molecular Structure and Energy Levels for Polyatomic Molecules 315 14 Electronic Spectroscopy 349 15 Computational Chemistry 377 16 Molecular Symmetry and an Introduction to Group Theory 439 17 Nuclear Magnetic Resonance Spectroscopy 467 APPENDIX A Point Group Character Tables 513 Credits 521 Index 523 iv A01_ENGE4590_04_SE_FM_i-xvi.indd 30/11/17 9:51 AM Detailed Contents QUANTUM CHEMISTRY AND SPECTROSCOPY Preface ix Math Essential Units, Significant Figures, and Solving End of Chapter Problems Math Essential Differentiation and Integration Math Essential Partial Derivatives Math Essential Infinite Series From Classical to Quantum Mechanics 19 1.1 Why Study Quantum Mechanics? 19 1.2 Quantum Mechanics Arose out of the Interplay of Experiments and Theory 20 1.3 Blackbody Radiation 21 1.4 The Photoelectric Effect 22 1.5 Particles Exhibit Wave-Like Behavior 24 1.6 Diffraction by a Double Slit 26 1.7 Atomic Spectra and the Bohr Model of the Hydrogen Atom 29 Math Essential Differential Equations Math Essential Complex Numbers and Functions The Schrödinger Equation 45 2.1 What Determines If a System Needs to Be Described Using Quantum Mechanics? 45 2.2 Classical Waves and the Nondispersive Wave Equation 49 2.3 Quantum-Mechanical Waves and the Schrödinger Equation 54 2.4 Solving the Schrödinger Equation: Operators, Observables, Eigenfunctions, and Eigenvalues 55 2.5 The Eigenfunctions of a Quantum-Mechanical Operator Are Orthogonal 57 2.6 The Eigenfunctions of a Quantum-Mechanical Operator Form a Complete Set 59 2.7 Summarizing the New Concepts 61 The Quantum-Mechanical Postulates 67 3.1 The Physical Meaning Associated with the Wave Function is Probability 67 3.2 Every Observable Has a Corresponding Operator 69 3.3 The Result of an Individual Measurement 69 3.4 The Expectation Value 70 3.5 The Evolution in Time of a Quantum-Mechanical System 73 Applying Quantum-Mechanical Principles to Simple Systems 77 4.1 The Free Particle 77 4.2 The Case of the Particle in a One-Dimensional Box 79 4.3 Two- and Three-Dimensional Boxes 83 4.4 Using the Postulates to Understand the Particle in the Box and Vice Versa 84 Applying the Particle in the Box Model to Real-World Topics 95 5.1 The Particle in the Finite Depth Box 95 5.2 Differences in Overlap between Core and Valence Electrons 96 5.3 Pi Electrons in Conjugated Molecules Can Be Treated as Moving Freely in a Box 97 5.4 Understanding Conductors, Insulators, and Semiconductors Using the Particle in a Box Model 98 5.5 Traveling Waves and Potential Energy Barriers 100 5.6 Tunneling through a Barrier 103 5.7 The Scanning Tunneling Microscope and the Atomic Force Microscope 104 5.8 Tunneling in Chemical Reactions 109 5.9 Quantum Wells and Quantum Dots 110 Commuting and Noncommuting Operators and the Surprising Consequences of Entanglement 119 6.1 Commutation Relations 119 6.2 The Stern–Gerlach Experiment 121 6.3 The Heisenberg Uncertainty Principle 124 v A01_ENGE4590_04_SE_FM_i-xvi.indd 30/11/17 9:51 AM vi CONTENTS 6.4 The Heisenberg Uncertainty Principle Expressed in Terms of Standard Deviations 128 6.5 A Thought Experiment Using a Particle in a Three-Dimensional Box 130 6.6 Entangled States, Teleportation, and Quantum Computers 132 Math Essential 7 Vectors Math Essential Polar and Spherical Coordinates A Quantum-Mechanical Model for the Vibration and Rotation of Molecules 143 7.1 The Classical Harmonic Oscillator 143 7.2 Angular Motion and the Classical Rigid Rotor 147 7.3 The Quantum-Mechanical Harmonic Oscillator 149 7.4 Quantum-Mechanical Rotation in Two Dimensions 154 7.5 Quantum-Mechanical Rotation in Three Dimensions 157 7.6 Quantization of Angular Momentum 159 7.7 Spherical Harmonic Functions 161 7.8 Spatial Quantization 164 Vibrational and Rotational Spectroscopy of Diatomic Molecules 171 8.1 An Introduction to Spectroscopy 171 8.2 Absorption, Spontaneous Emission, and Stimulated Emission 174 8.3 An Introduction to Vibrational Spectroscopy 175 8.4 The Origin of Selection Rules 178 8.5 Infrared Absorption Spectroscopy 180 8.6 Rotational Spectroscopy 184 8.7 Fourier Transform Infrared Spectroscopy 190 8.8 Raman Spectroscopy 194 8.9 How Does the Transition Rate between States Depend on Frequency? 196 The Hydrogen Atom 209 9.1 Formulating the Schrödinger Equation 209 9.2 Solving the Schrödinger Equation for the Hydrogen Atom 210 9.3 Eigenvalues and Eigenfunctions for the Total Energy 211 9.4 Hydrogen Atom Orbitals 217 A01_ENGE4590_04_SE_FM_i-xvi.indd 9.5 The Radial Probability Distribution Function 219 9.6 Validity of the Shell Model of an Atom 224 Math Essential Working with Determinants 10 Many-Electron Atoms 233 10.1 Helium: The Smallest Many-Electron Atom 233 10.2 Introducing Electron Spin 235 10.3 Wave Functions Must Reflect the Indistinguishability of Electrons 236 10.4 Using the Variational Method to Solve the Schrödinger Equation 239 10.5 The Hartree–Fock Self-Consistent Field Model 240 10.6 Understanding Trends in the Periodic Table from Hartree–Fock Calculations 247 11 Quantum States for ManyElectron Atoms and Atomic Spectroscopy 257 11.1 Good Quantum Numbers, Terms, Levels, and States 257 11.2 The Energy of a Configuration Depends on Both Orbital and Spin Angular Momentum 259 11.3 Spin–Orbit Coupling Splits a Term into Levels 266 11.4 The Essentials of Atomic Spectroscopy 267 11.5 Analytical Techniques Based on Atomic Spectroscopy 269 11.6 The Doppler Effect 272 11.7 The Helium–Neon Laser 273 11.8 Auger Electron Spectroscopy and X-Ray Photoelectron Spectroscopy 277 12 The Chemical Bond in Diatomic Molecules 285 12.1 Generating Molecular Orbitals from Atomic Orbitals 285 12.2 The Simplest One-Electron Molecule: H2+ 289 12.3 Energy Corresponding to the H2+ Molecular Wave Functions cg and cu 291 12.4 A Closer Look at the H2+ Molecular Wave Functions cg and cu 294 12.5 Homonuclear Diatomic Molecules 297 12.6 Electronic Structure of Many-Electron Molecules 299 12.7 Bond Order, Bond Energy, and Bond Length 302 12.8 Heteronuclear Diatomic Molecules 304 12.9 The Molecular Electrostatic Potential 307 30/11/17 9:51 AM vii CONTENTS 13 Molecular Structure and Energy Levels for Polyatomic Molecules 315 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 13.10 Lewis Structures and the VSEPR Model 315 Describing Localized Bonds Using Hybridization for Methane, Ethene, and Ethyne 318 Constructing Hybrid Orbitals for Nonequivalent Ligands 321 Using Hybridization to Describe Chemical Bonding 324 Predicting Molecular Structure Using Qualitative Molecular Orbital Theory 326 How Different Are Localized and Delocalized Bonding Models? 329 Molecular Structure and Energy Levels from Computational Chemistry 332 Qualitative Molecular Orbital Theory for Conjugated and Aromatic Molecules: The Hückel Model 334 From Molecules to Solids 340 Making Semiconductors Conductive at Room Temperature 342 14 Electronic Spectroscopy 349 14.1 14.2 14.3 The Energy of Electronic Transitions 349 Molecular Term Symbols 350 Transitions between Electronic States of Diatomic Molecules 353 14.4 The Vibrational Fine Structure of Electronic Transitions in Diatomic Molecules 354 14.5 UV-Visible Light Absorption in Polyatomic Molecules 356 14.6 Transitions among the Ground and Excited States 359 14.7 Singlet–Singlet Transitions: Absorption and Fluorescence 360 14.8 Intersystem Crossing and Phosphorescence 361 14.9 Fluorescence Spectroscopy and Analytical Chemistry 362 14.10 Ultraviolet Photoelectron Spectroscopy 363 14.11 Single-Molecule Spectroscopy 365 14.12 Fluorescent Resonance Energy Transfer 366 14.13 Linear and Circular Dichroism 368 14.14 Assigning + and - to g Terms of Diatomic Molecules 371 15 Computational Chemistry 377 15.1 15.2 The Promise of Computational Chemistry 377 Potential Energy Surfaces 378 A01_ENGE4590_04_SE_FM_i-xvi.indd 15.3 Hartree–Fock Molecular Orbital Theory: A Direct Descendant of the Schrödinger Equation 382 15.4 Properties of Limiting Hartree–Fock Models 384 15.5 Theoretical Models and Theoretical Model Chemistry 389 15.6 Moving Beyond Hartree–Fock Theory 390 15.7 Gaussian Basis Sets 395 15.8 Selection of a Theoretical Model 398 15.9 Graphical Models 412 15.10 Conclusion 420 Math Essential 10 Working with Matrices 16 Molecular Symmetry and an Introduction to Group Theory 439 16.1 Symmetry Elements, Symmetry Operations, and Point Groups 439 16.2 Assigning Molecules to Point Groups 441 16.3 The H2O Molecule and the C2v Point Group 443 16.4 Representations of Symmetry Operators, Bases for Representations, and the Character Table 448 16.5 The Dimension of a Representation 450 16.6 Using the C2v Representations to Construct Molecular Orbitals for H2O 454 16.7 Symmetries of the Normal Modes of Vibration of Molecules 456 16.8 Selection Rules and Infrared versus Raman Activity 460 16.9 Using the Projection Operator Method to Generate MOs That Are Bases for Irreducible Representations 461 17 Nuclear Magnetic Resonance Spectroscopy 467 17.1 Intrinsic Nuclear Angular Momentum and Magnetic Moment 467 17.2 The Nuclear Zeeman Effect 470 17.3 The Chemical Shift 473 17.4 Spin–Spin Coupling and Multiplet Splittings 476 17.5 Spin Dynamics 484 17.6 Pulsed NMR Spectroscopy 491 17.7 Two-Dimensional NMR 498 17.8 Solid-State NMR 503 17.9 Dynamic Nuclear Polarization 505 17.10 Magnetic Resonance Imaging 507 APPENDIX A Point Group Character Tables 513 Credits 521 Index 523 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 science 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 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 chemistry 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 inserted 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 understanding of various aspects of the chapter material Guided Practice and Interactivity TM ° Mastering 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 quizzes linked directly to the eText that are useful in ensuring students remain current 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 ■ ■ ■ A01_ENGE4590_04_SE_FM_i-xvi.indd ix 30/11/17 9:51 AM ... Quantum Chemistry and Spectroscopy, our approach to teaching physical chemistry begins with our target audience, undergraduate students majoring in chemistry, biochemistry, and chemical engineering,... Tunneling Microscope and the Atomic Force Microscope 104 5.8 Tunneling in Chemical Reactions 109 5.9 Quantum Wells and Quantum Dots 110 Commuting and Noncommuting Operators and the Surprising... Names: Engel, Thomas, 1942- author | Hehre, Warren, author | Angerhofer, Alex, 1957- author | Engel, Thomas, 1942- Physical chemistry Title: Physical chemistry, quantum chemistry, and spectroscopy