Page 14 - Valence Bond Methods. Theory and Applications

Preface

One senses that it is out of style these days to write a book in the sciences all on
one’s own. Most works coming out today are edited compilations of others’ articles
collected into chapter-like organization. Perhaps one reason for this is the sheer size
of the scientific literature, and the resulting feelings of incompetence engendered,
although less honorable reasons are conceivable. Nevertheless, I have attempted
this task and submit this book on various aspects of what is called ab initio valence
bond theory. In it I hope to have made a presentation that is useful for bringing
the beginner along as well as presenting material of interest to one who is already
a specialist. I have taught quantum mechanics to many students in my career and
have come to the conclusion that the beginner frequently confuses the intricacies
of mathematical arguments with subtlety. In this book I have not attempted to shy
away from intricate presentations, but have worked at removing, insofar as possible,
the more subtle ones. One of the ways of doing this is to give good descriptions of
simple problems that can show the motivations we have for proceeding as we do
with more demanding problems.
This is a book on one sort of model or trial wave function that can be used for
molecular calculations of chemical or physical interest. It is in no way a book on the
foundations of quantum mechanics – there are many that can be recommended. For
the beginner one can still do little better than the books by Pauling and Wilson[1]
and Eyring, Walter, and Kimbal[2]. A more recent work is by Levine[3], and for
a more “physicsish” presentation the book by Messiah[4] is recommended. These
are a little weak on the practice of group theory for which Cotton[5] may serve. A
more fundamental work on group theory is by Hammermesh[6]. Some further group
theory developments, not to my knowledge in any other book, are in Chapter 5.
Some of what we do with the theory of symmetric groups is based fairly heavily
on a little book by Rutherford[7].
This is a book on ab initio valence bond (VB) theory. There is a vast literature
on “valence bond theory” – much of it devoted to semiempirical and qualitative

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