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This slender volume is evidence for the claim that some people really want
to do things in their own way. Michael Mueller has written a textbook that is
apparently unique in its approach and even in its sequence of topics. The author’s
institution, Rose-Hulman Institute of Technology in Terre Haute, Indiana, offers
a two-quarter physical chemistry course that does not include any quantum chemistry.
It is followed by a one-quarter course in quantum chemistry and molecular spectroscopy,
presumably taught by Mueller from this textbook. Most of the topics covered in
the quantum chemistry portion of a standard physical chemistry course are included
in a highly condensed form. Several topics are treated in more detail and at a
higher level than in a standard physical chemistry course and some topics, such
as molecular symmetry, are completely omitted. The author appears to have tried
to eliminate all possible details about some topics in order to dwell at greater
length on other topics.
There are nine chapters in the book. Chapter 1 treats classical mechanics,
based on Hamilton’s equations rather than directly on Newton’s Second
Law. Chapter 2 is entitled “Fundamentals of Quantum Mechanics,” and
it typifies the author’s omission of background information and detail.
In 22 small pages, it introduces the following topics: de Broglie waves, classical
waves, quantum mechanical postulates, the time-independent Schrödinger equation,
the Born interpretation of the wave function, the particle in a one-dimensional
box and in a three-dimensional box, Hermitian operators, expectation values, and
the Heisenberg uncertainty principle.
From this point, the author’s sequence of topics is unusual. The third
chapter presents rotational motion. Instead of treating a rigid rotor, the author
treats the particle on a ring and the particle on a sphere. The fourth chapter
discusses approximation techniques, including variation theory and perturbation
theory. In this chapter the author abandons his policy of omitting all of the
details and includes a relatively complete discussion of perturbation theory,
including second-order energy corrections and degenerate perturbation theory.
Much of the next chapter is also more complete than is customary in most physical
chemistry textbooks. It begins with a slightly condensed standard treatment of
the harmonic oscillator and ends with a rather detailed treatment of reflection,
transmission, and tunneling through a finite potential barrier.
The sixth chapter treats the vibrational and rotational spectroscopy of diatomic
molecules. In an in-depth manner, the corrections to the rigid-rotor-harmonic-oscillator
model are derived using perturbation theory. The time-dependent Schrödinger
equation is finally introduced in a rather idiosyncratic way. The author asserts
that the operator i(h/2π)∂/∂t corresponds to the
energy. He then replaces EΨ in the time-independent Schrödinger equation by i(h/2π)∂Ψ/∂t
to obtain the time-dependent equation. Time-dependent perturbation theory is presented
in some detail and is used to derive selection rules for diatomic molecules. The
seventh chapter treats the spectroscopy of polyatomic molecules. The treatment
includes explicit expression for the energy levels of oblate and prolate symmetric
tops and also includes a treatment of hindered internal rotations.
Chapter 8 treats the electronic structure of atoms. A nice treatment of the
hydrogen atom leads to a very sketchy discussion of orbitals and probability densities.
The helium atom is treated in a standard way using perturbation and variation
theory. Multi-electron atoms are discussed briefly and Slater-type orbitals are
introduced. Several pages are devoted to a detailed theoretical discussion of
spin–orbit interaction. The chapter closes with a section on selection rules
for atomic spectra.
The final chapter treats the electronic structure of molecules. The hydrogen
molecule ion H2+ is discussed only in the LCAOMO approximation.
Homonuclear diatomic molecules and the CO molecule are mentioned only briefly.
Most of the chapter is devoted to a survey of computational methods.
The book is clearly written and is mostly free from typographical and conceptual
errors. There are not many figures and only a few worked examples (from zero to
three per chapter). There are some exercises within the chapters, called “Points
of Further Understanding.” There are also a few items called “Chemical
Connections,” in which the student is introduced to a chemical application
of the topic at hand. The end-of-chapter problems seem to be well chosen, but
are few in number (only four to 14 problems per chapter).
The book could serve as the text for part of a two-semester physical chemistry
course if an instructor is willing to adopt Mueller’s approach. Because
of its brevity, it could also serve as a text for part of a one-semester physical
chemistry course. Additional sources would be required to fill in some of the
details and to cover some of the omitted topics. It could also serve as a text
for a refresher course in quantum chemistry for first-year graduate students in
areas other than physical chemistry. If so used, it would provide new insights
into the topics that Mueller discusses at length.
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