Computational Quantum Chemistry II - The Group Theory Calculator

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