Point Group Symmetry Applications

1. Introduction.- 1.1. A Guide to the Use of the Text.- 1.2. Notation and Phase Conventions.- 2. Basic Concepts.- 2.1. Irrep Spaces.- 2.2. Group-Subgroup Bases.- 2.3. Coupling Coefficients.- 2.4. Character Theory.- 2.5. Complex Conjugation.- 2.6. Spin Irreps and Labeling Irreps.- 3. The jm Factors and j Symbols.- 3.1. The jm Factors.- 3.2. The j Symbols.- 3.3. Properties of jmFactors and j Symbols.- 3.4. Computational Methods.- 3.5. Phase and Multiplicity Choices.- 4. The Wigner-Eckart Theorem.- 4. 1. Basis Operators.- 4.2. The Wigner-Eckart Theorem.- 4.3. Coupled Tensors.- 4.4. The Standard Racah Tensors s of SO3.- 5. O3 and Its Subgroups.- 5.1. Direct Product Groups.- 5.2. Isomorphic Subsgroups.- 5.3. Specification of x,y,z Axes and Bases.- 6. Properties of Dihedral Groups.- 6. 1. The Structure of the Dihedral Groups.- 62. The Chain SO3 ? D? ? SO2.- 6.3. Finite Subgroups of D?.- 7. Fractional Parentage Coefficients.- 7. 1. The Parentage Concept.- 7.2. Continuous Matrix Groups.- 7.3. Complete Parentage Schemes.- 7.4. Strong-Field Parentage Schemes.- 8. Time Reversal.- 8. 1. Time of States.- 8.2 Time Reversal and Selection Rules.- 9. Applications.- 9.1. The Free-Ion Hamiltonian.- 9.2. The Zeeman Interaction.- 9.3. Ligand Fields.- 10. Programming Notes.- 11. Group Information Tables.- 11.1. The Cyclic Groups.- 11.2.The Dihedral Groups.- 11.3. The Tetrahedral Groups.- 11.4. The Octahedral Groups.- 11.5. The Icosahedzal Groups.- 12. Branching Rule Tables.- Tables.- 13. jm Factor Tables.- Tables.- 14. 3j and 6j Symbol Tables.- Tables.- 15. 9j Symbols.- Tables.- 16. Bases in Terms of Spherical Harmonics.- 16.1. Rotation Matrices in the JM Basis.- 16.2. Spherical Harmonics in Rectangular Coordinates.- Tables.- References.- Table Index.