Overview
Culminates with chapters that use permutation groups to analyze flexible molecules, a topic which is on the frontier of current research and is not covered in any commonly adopted textbook
Makes use of modern methods of Mathematica to develop the subject of group theory as applied to molecular structure and to automate the complicated and tedious calculations involved
Begins with careful definitions of symmetry and group, and then proceeds to an explicit proof that symmetry transforms always come in groups - the basic explanation of why group theory helps with the study of symmetry
Includes supplementary material: sn.pub/extras
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Table of contents (48 chapters)
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Front Matter
Keywords
About this book
After a few initial chapters on the basics of Mathematica, the logic of the book is controlled by group theory. It continues to teach Mathematica by example as the need arises, so an important use is always at hand for any new operator that is taught. To many science students, this is a greatly preferred way of learning a new computer language.
The main part of the book follows a strictly logical development that should be acceptable to the most rigorous minded people, while maintaining an engaging style in the spirit of Numerical Recipes by Press, Flannery, Teukolsky, and Vetterling. The essence of this style is to be just a little opinionated about good and bad ways to calculate things, but to give such advice without provoking offense, and always on an objective basis.
After this comes the development of classes and irreducible representations, culminating in a complete proof that for every group the number of classes is equal to the number of representations, so that all character tables must be square. The proof is motivated throughout by numerical constructions that rouse curiosity, and draw the reader into a rediscovery of Schur’s Lemmas, which thereby become truly interesting results, rather than the mysterious, dry statements often presented. This section culminates in a method for calculating the entire character table of a group. This is especially important for permutation groups that describe flexible molecules, for which are there very few published character tables.
Once the character tables are established, the real meat of physical applications can begin. The author emphasizes that every application has the same structure: (1) The construction of a reducible representation on the basis of some physical property, (2) its separation into irreducible components, and (3) the interpretation in terms of the "symmetry species" so produced. Because Mathematica and the xyz representations are close at hand, the separation into irreducible components can be done quickly.
Reviews
From the reviews:
“The layout of McClain’s book definitely reflects the author’s idea of the book, together with multiple examples … . First of all it is partitioned into three Parts which are further spilt into 48 Chapters and three Appendices. … Summarizing, it is likely that tutorial book that many students and PhD students of chemistry, atomic and molecular physics are expected to percept the concept of molecular symmetry practically, interactively via Mathematica with molecules and thus to directly apply them in their own research.” (Eugene Kryachko, Zentralblatt MATH, Vol. 1187, 2010)Authors and Affiliations
About the author
Bibliographic Information
Book Title: Symmetry Theory in Molecular Physics with Mathematica
Book Subtitle: A new kind of tutorial book
Authors: William McClain
DOI: https://doi.org/10.1007/b13137
Publisher: Springer New York, NY
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer-Verlag New York 2008
Hardcover ISBN: 978-0-387-73469-9Published: 09 September 2009
Softcover ISBN: 978-1-4899-9518-6Published: 24 November 2014
eBook ISBN: 978-0-387-73470-5Published: 12 March 2010
Edition Number: 1
Number of Pages: XV, 689
Topics: Particle and Nuclear Physics, Theoretical and Computational Chemistry, Theoretical, Mathematical and Computational Physics, Group Theory and Generalizations, Physical Chemistry, Atomic/Molecular Structure and Spectra