Computational Quantum Chemistry II - The Group Theory Calculator


  • Charles M. Quinn, National University of Ireland, Maynooth, Co. Kildare, Ireland
  • Patrick Fowler, Department of Chemistry, Sheffield University, UK
  • David Redmond, National University of Ireland, Maynooth, Co. Kildare, Ireland

Modern Computational Quantum Chemistry is indispensable for research in the chemical sciences. Computational Quantum Chemistry II - The Group Theory Calculator describes the group theory that the authors have developed in the past twenty-five years and illustrates how this approach, known as the 'Spherical Shell' method, can be applied to solve a variety of problems that benefit from a group theory analysis.
To complement the theory, the book is supplied with a CD-ROM (Windows ™ application), on which interactive files, based on EXCEL spreadsheet technology controlled by Visual Basic code, can be used to perform straightforwardly group-theory analyses for direct application to the simplification of physical problems in Chemistry, Physics and even Engineering Science.
The Group Theory Calculator Web page is located at The primary purpose of this Web page is to identify and resolve any problems encountered while using the MS EXCEL files on the CD-ROM (included with the book). The Web page is maintained by Charles M. Quinn and allows readers to gain updates and news relating to this publication.
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Undergraduate and graduate students, lecturers, and professionals in theoretical or physical chemistry, as well as those interested in computational chemistry and its applications with Excel.


Book information

  • Published: December 2005
  • ISBN: 978-0-12-370456-6

Table of Contents

1 Operating instructions for the Group Theory Calculator 1.1 Overview
1.2 Characters from orbits
1.3 Error traps
1.4 Reduce a character
1.5 Direct sums
1.6 Direct products
1.7 Spherical harmonics
1.8 Isomers
1.9 Symmetric and antisymmetric powers
1.10 Basis functions
1.11 Operation of the GT_Calculator for cases involving complex algebra
2 Geometry, orbits and decorations 2.1 Structure orbits
2.2 Orbits and geometry
2.3 The platonic solids, the Archimedean polyhedra and general orbits
2.4 Polyhedral orbits in Oh point symmetry
2.5 Polyhedral orbits of cubic symmetry lower than Oh
2.6 Orbits and polyhedra in Ih point symmetry
2.7 The orbits of structures exhibiting I symmetry
2.8 Orbits in space group theory
2.9 Crystals as 'point' structures
3 Decorations of orbits using local functions: reducible characters for s, p, d, ... local functions; central polynomial functions as basis sets for the irreducible representations of the point groups; the construction of group orbitals 3.1 &sgr; Characters: Local &sgr;, &pgr; and &dgr;, ... harmonic functions
3.2 The characters of the representations generated by local functions
3.3 The general, kubic and icosahedral harmonics
3.4 Examples
4 Symmetrized powers and their applications 4.1 Symmetrized squares, electronic states and the Jahn-Teller effect
4.2 Electric and magnetic properties of molecules
4.3 Counting molecular force constants
4.4 Symmetries of central functions with arbitrarily high angular momentum
4.5 Isomer counting using point group symmetry