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Statistical mechanics can be a challenging subject to
introduce to a class of chemists who are not necessarily
theoretically oriented. While it constitutes one of the
foundations of physical chemistry, it requires a certain mathematical
rigor, which can sometimes seem overwhelming to the
beginning student. In the preface to Statistical Mechanics for
Chemists, author Jerry Goodisman addresses this issue and points
out some of the problems he sees with the many excellent
books that are available on the subject. Some are too
specialized, some are too fundamental, and some are simply too old
and don't reflect recent advances. What is missing is the book
that is "just right", one which includes step-by-step
derivations at a level accessible to most students and at the same
time covers some of the more difficult topics that are of
special interest to chemists, knowing that for most students a
more advanced course is unlikely to follow. On this point I
heartily agree, and I tip my hat to the author for having put
together the present book. I know of only one other book that
fits this description, and it is one that I rely on heavily.
Statistical Mechanics for
Chemists starts out with a cursory discussion of thermodynamics and ensembles in the
first two chapters. Some familiarity with the basic ideas is
assumed, and the intent is clearly to avoid getting bogged down in
the technical details. This may be problematic, however, both
for less advanced students who may need more emphasis on the
fundamentals and for more advanced students who
would miss the benefits of a more systematic treatment. The
next two chapters present the relatively standard topics of
non-interacting particles and molecular partition functions.
This section is considerably more thorough and contains an
impressive level of detail. This is the core material. However a
full two thirds of the text is reserved for the final four
chapters. Chapter 5 deals with quantum statistics and provides a
very thorough discussion of Fermi and Bose systems, including
a detailed section on semiconductors. Chapter 6 addresses
classical systems, beginning with Hamilton's equations,
continuing to a classical treatment of molecular collisions, and
wrapping up with a detailed derivation of dielectric response.
Chapter 7 concerns the structure of liquids and includes sections
on correlation functions and integral equations, highlighted
by an excellent derivation of the Debye-Hückel equation.
The final chapter discusses relaxation and includes sections
on time correlation functions, linear response theory, and
the Langevin equation.
While this is certainly an impressive list of subjects,
it represents a particular choice of emphasis; and it is also
important to point out some areas that are overlooked but
which might be expected in a book at this level. For example,
there is no mention at all of phase transitions or associated
topics such as mean-field theory or order parameters. While
some readers may consider that best left to physicists, others
will find it sorely missed. There is also virtually no discussion
of computer simulation, which is a rapidly expanding
application of classical statistical mechanics in chemistry.
Like the choice of material, the overall style of the
book is also to some extent a question of taste. The author
makes use of lengthy derivations, which has the pedagogical
advantage of leading the student along and introducing new
ideas in the context of a particular problem. On the other
hand, there are places where important subjects turn up in
unlikely places, such as the only mention of Monte Carlo
simulation in a section entitled "Properties of Correlation
Functions", and the concept of a potential of mean force which
appears only in the section on the Debye-Hückel equation. This
also sometimes leads to an uneven level of rigor, giving an
impression of trying to cheat a little in order to skip ahead to
the good stuff. This is a necessary compromise given the intent
of the book, which is clearly an extension of the author's
lecture notes and not intended to be an encyclopedic reference.
Overall, there is more material here than would be
needed for a single course, leaving ample room to pick and
choose among the later topics. A little patchiness towards the end
is amply made up for by a number of excellent sections
which guide the reader to some interesting and useful results at
a level appropriate for a graduate course. The large selection
of problems, including many numerical examples, is also
greatly appreciated. While not perfect, this book largely lives up
to its billing, and I consider it a welcome addition to my
collection. It will undoubtedly be getting a lot of mileage.
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