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Physical Chemistry: A Molecular Approach

Donald A. McQuarrie University of California, Davis
John D. Simon Duke University

To the Student

You are about to begin your study of physical chemistry. You may have been told that physical chemistry is the most difficult chemistry course that you will take, or you may have even seen the bumper stickers that says “Honk if you passed P Chem”. The anxiety that some students bring to their physical chemistry course has been eloquently adressed by the British professor, E. Brian Smith, in the preface of his introductory text, Basic Chemical Thermodynamics, by the Oxford University Press :

The first time I heard about Chemical Thermodynamics was when a second-year undergraduate brought me the news in my freshman year. He told a spine-chilling story of endless lecture with almost three hundred numbered equations, all of which, it appeared, had to be committed to memory and reproduced in exactly the same form in subsequent examinations. Not only did these equations contain all the normal algebraic symbols but in addition they were liberally sprinkled with stars, daggers, and circles so as to stretch even the most powerful of minds. Few would wish to deny the mind-improving and indeed character-building qualities of such a subject! However, many young chemists have more urgent pressures on their time.”

We certainly agree with this last sentence of Professor Smith. The fact is, however, that every year thousands upon thousands of students take and pass physical chemistry, and many of them really enjoy it. You may be taking it only because it is required by your major, but you should be aware that many recent developments in physical chemistry are having a major impact in all the areas of science that are concerned with the behavior of molecules. For example, in biophysical chemistry, the application of both experimental and theoretical aspects of physical chemistry to biological problems has greatly advanced our understanding of the structure and reactivity of proteins and nucleic acids. The design of pharmaceutical drugs, which has seen great advances in recent years, is a direct product of physical chemical research.

Traditionally, there are three principal areas of physical chemistry: thermodynamics (which concerns the energetics of chemical reactions), quantum chemistry (which concerns the structures of molecules), and chemical kinetics (which concerns the rates of chemical reactions). Many physical chemistry courses begin with a study of thermodynamics, then discuss quantum chemistry, and treat chemical kinetics last. This order is a reflection of the historic development of the field, and both of us learned physical chemistry in this order. Today, however, physical chemistry is based on quantum mechanics, and so we begin our studies with this topic. We first discuss the underlying principles of quantum mechanics and then show how they can be applied to a number of model systems. Many of the rules you have learned in general chemistry and organic chemistry are a natural result of the quantum theory. In organic chemistry, for example, you learned to assign molecular structures using infrared spectra and nuclear magnetic resonance spectra, and in Chapters 13 and 14 we explain how these spectra are governed by the quantum-mechanical properties of molecules.

Your education in chemistry has trained you to think in terms of molecules and their interactions, and we believe that a course in physical chemistry should reflect this viewpoint. The focus of modern physical chemistry is on the molecule. Current experimental research in physical chemistry uses equipment such as molecular beam machines to study the molecular details of gas-phase chemical reactions, high vacuum machines to study the structure and reactivity of molecules on solid interfaces, lasers to determine the structures of individual molecules and the dynamics of chemical reactions, and nuclear magnetic resonance spectrometers to learn about the structure and dynamics of molecules. Modern theoretical research in physical chemistry uses the tools of classical mechanics, quantum mechanics, and statistical mechanics along with computers to develop a detailed understanding of chemical phenomena in terms of the structure and dynamics of the molecules involved. For example, computer calculations of the electronic structure of molecules are providing fundamental insights into chemical bonding and computer simulations of the dynamical interaction between molecules and proteins are being used to understand how proteins function.

In general chemistry you learned about the three laws of thermodynamics and were introduced to the quantities, enthalpy, entropy, and the Gibbs energy (formerly called the free energy). Thermodynamics is used to describe macroscopic chemical systems. Armed with the tools of quantum mechanics, you shall learn that thermodynamics can be formulated in terms of the properties of the atoms and molecules that make up macroscopic chemical systems. Statistical thermodynamics provides a way to describe thermodynamics at a molecular level. You shall see that the three laws of thermodynamics can be explained simply and beautifully in molecular terms. We believe that a modern introduction to physical chemistry should, from the outset, develop the field of thermodynamics from a molecular viewpoint from the outset.

Our treatment of chemical kinetics, which constitutes the last five chapters, develops an understanding of chemical reactions from a molecular viewpoint. For example, we have devoted more than half of the chapter of gas-phase reactions (Chapter 28) to the reaction between a flourine atom and a hydrogen molecule to form a hydrogen flouride molecule and a hydrogen atom. Through our study of this seemingly simple reaction, many of the general molecular concepts of chemical reactivity are revealed. Again, quantum chemistry provides the necessary tools to develop a molecular understanding of the rates and the dynamics of chemical reactions.

Perhaps the most intimidating aspect of physical chemistry is the liberal use of mathematical topics you may have forgotten or never learned. As physicists say about physics, physical chemistry is difficult with mathematics; impossible without it. You may not have taken a math course recently, and your understanding of topics such as determinants, vectors, series expansions and probability may seem a bit fuzzy at this time. In our years of teaching physical chemistry, we have often found it helpful to review mathematical topics before using them to develop the physical chemical topics. Consequently, we have included a series of ten concise reviews of mathematical topics. We realize that not every one of these so-called reviews may actually be a review for you. Even if some of the topics are new to you (or seem that way), we discuss only the minimum amount that you need to know to understand the subsequent physical chemistry. We have positioned these reviews so that they immediately precede the chapter that uses them. By reading these review first (and doing the problems!), you will be able to spends less time worrying about the math, and more time learning the physical chemistry, which is, after all, your goal.

To the Instructor

This text emphasizes a molecular approach to physical chemistry. Consequently, unlike most other physical chemistry books, we discuss the principles of quantum mechanics first and then use these ideas extensively in our subsequent development of thermodynamics and kinetics. For example, from the Contents you will see that chapters titled The Boltzmann Factor and Partition Functions (Chapter 17) and Partition Functions and Ideal Gases (Chapter 18) come before The First Law of Thermodynamics (Chapter 19). This approach is pedagogically sound because we treat only energy, pressure, and heat capacity (all mechanical properties that the students have dealt with in their general chemistry and physics courses) in Chapter 17 and 18. This approach allows us to immediately give a molecular interpretation to the three laws of thermodynamics and to many thermodynamic relations. The molecular interpretation of entropy is an obvious example (an introduction to entropy without a molecular interpretation is strictly for purists and not for the faint of heart), but even the concepts of work and heat in the First Law of Thermodynamics have a nice, physical, molecular interpretation in terms of energy levels and their populations.

Research advances during the last few decades have chanced the focus of physical chemical research and therefore should affect the topics covered in a modern physical chemistry course. To introduce the type of physical chemical research that is currently being done, we have included chapters such as Computational Quantum Chemistry (Chapter 11), Group Theory (Chapter 12), Nuclear Magnetic Resonance Spectroscopy (Chapter 14), Lasers , Laser Spectroscopy , and Photochemistry (Chapter 15), and Gas-Phase Reaction Dynamics (Chapter 30). The inclusion of new topics necessitated a rather large book, but one of the standard physical chemistry texts fifty years ago was Glasstone’s Textbook of Physical Chemistry, which was considerably larger.

Keeping in mind that our purpose is to teach the next generation of chemists, the quantities, units, and symbols used in this text are those presented in the 1993 International Union of Pure and Applied Chemistry (IUPAC) publication Quantities, Units, and Symbols in Physical Chemistry by Ian Mills et al. (Blackwell Scientific Publications, Oxford). Our decision to follow the IUPAC recommendations means that some of the symbols, units, and standard states presented in this book may differ from those used in the literature and older textbooks and may be unfamiliar to some instructors. In some instances, we took a while to come to grips with the new notation and units, but it turned out that indeed there was an underlying logic to their use, and we found that it was actually worth the effort to become facile with them.

A unique feature of this text is the introduction of ten so-called MathChapters, which are short reviews of the mathematical topics that are used in subsequent chapters. Some of the topics covered that should be familiar to most students are complex numbers, vectors, spherical coordinates, determinants, partial derivatives, and Taylor and Maclaurin series. Some topics that may be new are probability, matrices (used only in the chapter on group theory), numerical methods, and binomial coefficients. In each case, however, the discussions are brief, elementary, and self-contained. After reading each MathChapter and doing the problems, a student should be able to focus on the following physical chemical material rather than having to cope with the physical chemistry and the mathematics simultaneously. We believe that this feature greatly enhances the pedagogy of our text.

Today’s students are comfortable with computers. In the past few years we have seen homework assignments turned in for which students used programs such as MathCad and Mathematica to solve problems, rather than pencil and paper. Data obtained in laboratory courses are now graphed and fit to functions using programs such as Excel, Lotus123, and Kaliedagraph. Almost all students have access to personal computers, and a modern course in the physical sciences should encourage students to take advantage of these tremendous resources. As a result, we have written a number of our problems with the use of computers in mind. For example, MathChapter G introduces the Newton-Raphson method for solving higher-order algebraic equations and transcedental equations numerically. There is no reason nowadays that calculations in a physical chemistry course should be limited to solving quadratic equations and other artificial examples. Students should graph data, explore expressions that fit experimental data, and plot functions that describe physical behavior. The understanding of physical concepts is greatly enhanced by exploring the properties of real data. Such exercises remove the abstractness of many theories and enable students to appreciate the mathematics of physical chemistry so that they can describe and predict the physical behavior of chemical systems.

Our Web Site

You can visit the Web site for our book by clicking on its listing at We have posted various types of supplementary material on this site. For example, all the figures (in .EPS or GIF format) can be downloaded from the site. 


Many people have contributed to the writing of this book. We thank our colleagues, Paul Barbara, James T. Hynes, Veronica Vaida, John Crowell, Andy Kummel, Robert Continetti, Amit Sinha, John Weare, Kim Baldridge, Jack Kyte, and Bill Trogler for stimulating discussions on the topics that should be included in a modern physical chemistry course, and our students, Bary Bolding, Peijun Cong, Robert Dunn, Scott Feller, Susan Forest, Jeff Greathouse, Kerry Hanson, Bulang Li, and Sunney Xie for reading portions of the manuscript and making many helpful suggestions. We are especially indebted to our superb reviewers, Merv Hanson, John Frederick, Anne Meyers, George Shields, and Peter Rock, who read and commented on the entire manuscript; to Heather Cox, who also read the entire manuscript, made numerous insightful suggestions, and did every problem in the course of preparing the accompanying Solution Manual; to Carole McQuarrie, who spent many hours in the library and on the internet looking up experimental data and biographical data in order to write all the biographical sketches; and to Kenneth Pitzer and Karma Beal for supplying us with some critical biographical data. We also thank Susanna Tadlock for coordinating the entire project, Bob Ishi for designing what we think is a beautiful looking book, Jane Ellis for competently dealing with many of the production details, John Choi for creatively handling all the artwork, Ann McGuire for a very helpful copyediting of the manuscript, and our publisher, Bruce Armbruster, for encouraging us to write our own book and for being an exemplary publisher and a good friend. Last, we thank our wives, Carole and Diane, both of whom are chemists, for being great colleagues as well as great wives.