Molecular Symmetry, Group Theory, and Selection Rules
Symmetry as a Predictive Tool
Point Groups and Representations
Molecular symmetry is encoded in point groups, which organize vibrational, electronic, and rotational states into irreducible representations. This classification streamlines orbital construction, degeneracy analysis, and transition selection rules.
Important Symmetry Terms
Symmetry and Spectroscopy
Infrared transitions require a change in dipole moment, while Raman transitions require a change in polarizability. Group theory predicts which vibrational modes are active by examining the symmetry of the corresponding operators.
A vibration is infrared active if it is associated with a change in which quantity?
IR activity requires a transition to involve a change in dipole moment.
Correct answer: Dipole moment
What is the main use of character tables in molecular science?
Character tables help decompose representations and infer selection rules.
Correct answer: to classify symmetry and determine allowed transitions
IR vs Raman Activity
Infrared
- Depends on dipole-moment change
- Strongly tied to polar modes
Raman
- Depends on polarizability change
- Sensitive to symmetric vibrations
Practical Symmetry Workflow
In practice, symmetry analysis begins with identifying the molecular geometry and point group, assigning basis functions to irreducible representations, and then using the results to constrain electronic structure, vibrational analysis, and spectroscopy.
Symmetry Analysis in Five Steps
-
1
Identify the molecular point group.
-
2
Build or consult the character table.
-
3
Assign orbitals or vibrations to irreducible representations.
-
4
Apply selection rules for the relevant observable.
-
5
Use symmetry to reduce computational and interpretive complexity.