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 http://www.ucsibooks.com. 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.

**Acknowledgments**

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.