14: Appendix
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- 14.1: Advanced Group Theory
- The theory of symmetry groups is a powerful tool for the prediction of physical properties of molecules and crystals. It is, for example, possible to determine whether a molecule can have a dipole moment. Many important predictions of spectroscopic experiments (optical, IR or Raman) can be made purely by group theoretical considerations.
- 14.1.1: The Exploitation of Symmetry Can Help Simplify Numerical Calculations
- 14.1.2: Symmetry Elements and Operations Define the Point Groups
- 14.1.3: Symmetry Operations Define Groups
- 14.1.4: Symmetry Operations as Matrices
- 14.1.5: Molecules can be Represented by Reducible Representations
- 14.1.6: Character Tables Summarize the Properties of a Point Group
- 14.1.7: Characters of Irreducible Representations
- 14.1.8: Using Symmetry to Solve Secular Determinants
- 14.1.9: Generating Operators
- 14.1.10: Molecular Motions of a Molecule can be Represented by a Reducible Reperesentation
- 14.1.11: Reducible Representations are Comprised of Irreducible Representations
- 14.1.12: Normal Modes of Vibrations Describe how Molecules Vibrate
- 14.1.13: Symmetry of Vibrations Describes their Spectroscopic Behavior
- 14.1.14: Symmetry Adapted Linear Combinations are the Sum over all Basis functions
- 14.1.15: Molecular Orbitals can be Constructed on the Basis of Symmetry
- 14.1.E: Group Theory - The Exploitation of Symmetry (Exercises)
- 14.1.T: Character Tables
- 14.1.T: Correlation Tables
- 14.2: Derivation of Laporte Rule
- The Laporte Rule is a selection rule in electron absorption spectroscopy that applies to centrosymmetric molecules. It says that transitions between states of the same symmetry with respect to inversion are forbidden. Electronic transitions from waveunfunctions with g symmetry to wavefunctions with g symmetry are forbidden, as are transitions from wavefunctions with u symmetry to wavefunctions with u symmetry. Transitions from g to u and u to g, where the symmetry switches, may be allowed.