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Overview
Intended for graduate and advanced undergraduate students, this text explores quantum mechanical techniques from the viewpoint of chemistry and materials science. Dynamics, symmetry, and formalism are emphasized. An initial review of basic concepts from introductory quantum mechanics is followed by chapters examining symmetry, rotations, and angular momentum addition. Chapter 4 introduces the basic formalism of time-dependent quantum mechanics, emphasizing time-dependent perturbation theory and Fermi's golden rule. Chapter 5 sees this formalism applied to the interaction of radiation and matter. In Chapter 6, the authors introduce occupation number representations, including applications to both quantized radiation fields and electronic structure; while chapters 7 and 8 focus on scattering theory and basic theories of chemical reaction rates. The remaining three chapters deal with the use of correlation functions and density matrices in quantum mechanics. Problems and a bibliography appear at the end of each chapter; and at the end of the book there is an Appendix C, "Solutions to Problems," new to this edition.
Product Details
| ISBN-13: | 9780486420035 |
|---|---|
| Publisher: | Dover Publications |
| Publication date: | 01/28/2002 |
| Series: | Dover Books on Chemistry |
| Edition description: | DOVER |
| Pages: | 384 |
| Product dimensions: | 6.14(w) x 9.21(h) x (d) |
Read an Excerpt
PREFACE
This book is intended as a follow-up to the many introductory quantum chemistry texts used in teaching graduate and advanced undergraduate students. It is the result of our many years of teaching at Northwestern University, in courses taken by hundreds of students. Like many universities, we have a one-term introductory quantum chemistry course taken by graduate and advanced undergraduate students, for which several excellent introductory texts exist. This is followed by an additional term (or sometimes two) in which more advanced topics are considered.
We have always been frustrated by the lack of texts that treat many of the advanced topics, so over the years we developed an extensive set of lecture notes to remedy the problem, and the present book evolved from those notes. There are a large number of physics-oriented texts that cover many of the topics we consider, but the absence of chemical, solid-state, and materials applications has always been a problem for our students. One advanced topic, advanced methods for describing the electronic structure of molecules (i.e., beyond Hartree–Fock), is covered in depth in a few textbooks, so this topic is not dealt with directly in this text. Instead, we emphasize areas of dynamics, of symmetry, and of formalism in quantum mechanics that contain essential tools for both experimental and theoretical students working in a wide variety of subdisciplines of chemistry and materials science. In addition, many of the topics in this book are relevant to the interests of students in certain areas of physics, biology, and engineering. One venerable but unfortunately outdated text that provided much inspiration for our text is Quantum Chemistry by Eyring, Walter, and Kimball (1944).
Our choice of topics has several themes, which can roughly be grouped as follows: symmetry and rotations in quantum mechanics, time-dependent quantum mechanics and its applications to spectroscopy, collisions and rate processes, occupation number representations of quantum mechanics, and the use of correlation functions and density matrices in quantum mechanics. After an introductory chapter that reviews basic concepts from introductory quantum mechanics, our second and third chapters focus on symmetry and rotations. Chapter 2 is partially a review of elementary concepts associated with point groups and is partially a consideration of the symmetry properties of many-electron wavefunctions. In Chapter 3 we consider the two- and three-dimensional rotation groups as they apply to electronic structure, and examine the related topic of angular momentum addition. In Chapter 4 we introduce the basic formalism of time-dependent quantum mechanics with an emphasis on time-dependent perturbation theory and Fermi's golden rule, and in Chapter 5 provide applications of this formalism to the interaction of radiation and matter (light absorption, emission, scattering). In Chapter 6 we introduce occupation number representations, including applications to both quantized radiation fields and electronic structure; it is lengthy and detailed, because the material is relatively new to most scientists. In Chapter 7 we present an introduction to scattering theory, especially as it applies to chemical problems. These concepts are then used in Chapter 8 to develop basic theories of chemical reaction rates. Along the way we discover that rates can be obtained from correlation functions, and in Chapters 9 and 10 the subject of correlation functions is extended in many other directions with an emphasis on spectroscopy and on theories of electron transfer. Finally, in Chapter 11 we combine many of topics of the previous chapters to describe electronic structure, optical and magnetic resonance spectroscopy, and condensed phase dynamics using density matrices.
The ordering of these chapters follows largely from our own need to divide the material covered between two courses that are taken by students with different interests. Chapters 1 to 6 cover one course that is taken by a fairly broad spectrum of students from all areas of chemistry. These chapters emphasize topics in symmetry, spectroscopy, and electronic structure that find widespread application, and in addition introduce elements in the formalism of quantum mechanics that have become part of the "language" of chemistry. Chapters 7 to 11 cover topics that are of more specific interest to physical chemists and materials scientists, with an emphasis on dynamical processes. There are several subthemes that make the pairs of chapters 4 and 5, 7 and 8, 9 and 10, and 6 and 11 closely connected, so these four chapter pairs could easily be presented in any order, and one could also omit pairs according to the needs of the students taking the material. Chapters 8, 9, 10, and 11 go beyond a straightforward consideration of quantum-mechanical methods: Statistical considerations are important in all four, and all point strongly toward forefront areas of current research.
With each chapter we include problems that we have used in our courses, designed to illustrate further applications of the theory as it is developed. Many of these problems extend our development in directions that represent important areas of modern research, while others provide classic examples that illustrate important physical effects. Some of the problems are quite lengthy and challenging.
An attempt is made throughout the book to be concise and to make the formal development useful to chemists and materials scientists. The relatively informal wording in parts of the book reflects the pedagogic nature of much of the material. Extensive discussions of interpretation, as well as digressions to deal with special cases and pedagogic asides, have been held to a minimum in an attempt to produce a useful and rational guide to quantum mechanics for chemists and materials scientists.
The development of this book would have been very difficult without the assistance of an unusually talented typist, Jan Goranson. We are extremely indebted to her for the countless hours of careful, painstaking effort needed to get all the formulas right. A change in word-processing software halfway through development of the manuscript required that most equations be typed twice. Despite this, Jan persevered, and the result is a testimony to her efforts.
We should also acknowledge Dan Joraanstad, Diana Farrell, and Lynne Breitfeller of Prentice Hall for their encouragement during this long project. In addition, a large number of graduate students at Northwestern have used portions of this book in their courses, and they have made countless suggestions for the improvement of both text and problems. We have further benefitted from the suggestions of B. Whalley and N. Snider, both of whom carefully read the text, from Stacy Ratner's careful proofreading, and from Daniel Ratner's and Matt Todd's exemplary work with the figures. The presentation of the occupation number formalism for electrons is based on ideas presented by Jan Linderberg. Finally, the patience, inspiration, and encouragement of our wives, Margaret and Nancy, have been crucial to the book since its inception.
George Schatz / Mark Ratner
(Continues…)
Excerpted from "Quantum Mechanics in Chemistry"
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Copyright © 2002 George C. Schatz and Mark A. Ratner.
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Table of Contents
Preface,
1 Review of Basic Concepts in Quantum Mechanics,
2 Symmetry Considerations: Point Groups and Electronic Structure,
3 Symmetry Considerations: Continuous Groups and Rotations,
4 Time-Dependent Quantum Mechanics,
5 Interaction of Radiation with Matter,
6 Occupation Number Representations,
7 Quantum Scattering Theory,
8 Theories of Reaction Rates,
9 Time-Dependent Approach to Spectroscopy: Electronic, Vibrational, and Rotational Spectra,
10 Correlation Functions and Dynamical Processes: Nonadiabatic Intramolecular Electron Transfer,
11 Density Matrices,
Appendix A: Dirac Delta Function,
Appendix B: Laplace Tranforms,
Appendix C: Solutions to Problems,
Index,