Symmetry Theory in Molecular Physics with Mathematica

A new kind of tutorial book

  • William McClain

Table of contents

  1. Front Matter
    Pages i-xiv
  2. William Martin McClain
    Pages 1-6
  3. William Martin McClain
    Pages 7-11
  4. William Martin McClain
    Pages 13-27
  5. William Martin McClain
    Pages 29-54
  6. William Martin McClain
    Pages 55-58
  7. William Martin McClain
    Pages 59-72
  8. William Martin McClain
    Pages 73-79
  9. William Martin McClain
    Pages 81-98
  10. William Martin McClain
    Pages 99-112
  11. William Martin McClain
    Pages 113-135
  12. William Martin McClain
    Pages 137-147
  13. William Martin McClain
    Pages 149-161
  14. William Martin McClain
    Pages 163-172
  15. William Martin McClain
    Pages 173-181
  16. William Martin McClain
    Pages 183-194
  17. William Martin McClain
    Pages 195-205
  18. William Martin McClain
    Pages 207-215
  19. William Martin McClain
    Pages 217-249
  20. William Martin McClain
    Pages 251-267

About this book

Introduction

Prof. McClain has indeed produced "a new kind of tutorial book."  It is written using the logic engine Mathematica, which permits concrete exploration and development of every concept involved in Symmetry Theory.  The book may be read in your hand, or on a computer screen with Mathematica running behind it.  It is intended for students of chemistry and molecular physics who need to know mathematical group theory and its applications, either for their own research or for understanding the language and concepts of their field.  The book has three major parts:

Part I begins with the most elementary symmetry concepts, showing how to express them in terms of matrices and permutations.  These are then combined into mathematical groups.  Many chemically important point groups are constructed and kept in a Mathematica package for easy reference.  No other book gives such easy access to the groups themselves.  The automated group construction machinery allows you to tabulate new groups that may be needed in research, such as permutation groups that describe flexible molecules.

In Part II, mathematical group theory is presented with motivating questions and experiments coming first, and theorems that answer those questions coming second.  You learn to make representations of groups based on any set of symmetric objects, and then to make Mathematica operators that carry out rep construction as a single call.  Automated construction of representations is offered by no other book.  Part II follows a reconstructed trail of questions, clues and solid results that led Issai Schur to a complete proof of the Great Orthogonality.

In Part III, the projection operators that flow from the Great Orthogonality are automated and applied to chemical and spectroscopic problems, which are now seen to fall within a unified intellectual framework.  The topics include chemical bonding in symmetric molecules, molecular vibrations and rigorous reasoning about quantum mechanical matrix elements.  As a concrete example of the enormous power of the automated projectors, the tensor operators for two- and three- photon processes are projected under all tabulated groups.  All the machinery presented is general, and will work with new groups that you may construct.  Finally, there is machinery that accepts as input the multiplication table of any group and returns as output its character table.  This will be of great use to spectroscopists who deal with flexible molecules belonging to permutation groups, which are too numerous even for a Mathematica package.

Keywords

Group theory Point group analysis of flexible molecules applied group theory character table group theory for molecules interactive examples using mathematica mathematical exercises in physics molecule permutation groups symmetry theory with mathematica

Authors and affiliations

  • William McClain
    • 1
  1. 1.Dept. ChemistryWayne State UniversityDetroitU.S.A.

Bibliographic information

  • DOI https://doi.org/10.1007/b13137
  • Copyright Information Springer Science+Business Media, LLC 2008
  • Publisher Name Springer, New York, NY
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-0-387-73469-9
  • Online ISBN 978-0-387-73470-5
  • About this book