Symmetry Selection Rules

Predicting IR and Raman Activity via Group Theory

Unit 1: Vibrational Spectroscopy

The Isomer Challenge

Consider two vials of \( \text{PtCl}_2(\text{NH}_3)_2 \).

One is the cis-isomer (C\(_{2v}\))
One is the trans-isomer (D\(_{2h}\))

Question: How can we distinguish them using only IR and Raman spectroscopy?

Pt

cis

Pt

trans

Structural symmetry dictates the number of observable peaks.

Step 1: The Reducible Representation (\(\Gamma_{3N}\))

Methodology:

Identify the Point Group of the molecule.
Determine the characters for the total representation (\(\Gamma_{3N}\)) by observing unshifted atoms.
Apply the formula: \(\chi_{3N}(g) = (\text{atoms unshifted by } g) \times \chi_{\text{vector}}(g)\).

Key Concept

A vibration is IR active if its irreducible representation transforms as \(x, y, z\).

Key Concept

A vibration is Raman active if its irreducible representation transforms as quadratic functions (\(x^2, xy\), etc.).

The Rule of Mutual Exclusion

"For a molecule with a center of inversion (i), no normal mode can be both IR and Raman active."

Centrosymmetric

No overlap in bands.

Non-Centrosymmetric

Bands can be active in both.

Isomer Comparison: \( \text{ML}_4\text{X}_2 \)

cis-isomer (\(C_{2v}\))

Vibrational modes: \(4A_1 + A_2 + 2B_1 + 2B_2\)

IR Active: \(A_1, B_1, B_2\) (8 bands)
Raman Active: \(A_1, A_2, B_1, B_2\) (9 bands)

trans-isomer (\(D_{4h}\))

Vibrational modes: \(A_{1g} + A_{2u} + B_{1g} + B_{2g} + B_{2u} + 2E_u + E_g\)

IR Active: \(A_{2u}, E_u\) (3 bands)
Raman Active: \(A_{1g}, B_{1g}, B_{2g}, E_g\) (4 bands)

The significantly lower number of observed bands in the IR/Raman spectrum identifies the trans isomer due to its higher symmetry.

Workshop Summary

Symmetry selection rules provide a direct bridge between molecular geometry and experimental spectra.

Coming Up Next

Case Study: Predicting the Vibrational Landscape of Octahedral Carbonyls

Structural Elucidation Spectroscopy

Symmetry Selection Rules

NOE and Stereochemistry

Fragmentation Geometry

Anisotropic Effects

Structural Capstone

Vibrational Symmetry Slides

Vibrational Mode Workshop Handout

Vibrational Symmetry Facilitation Guide Teacher Guide

NOE Effect Slides Stereochemistry

Bicyclic Stereochemistry Challenge Worksheet

Fragmentation Geometry Slides Mass Spec

Fragmentation Pathways Discussion Guide Teacher Guide

Anisotropic Effects Ring Currents Slides

Anisotropy Shift Tables Reference Sheet

Cold Case Structural Project Brief

Structural Mastery Rubric Assessment Guide

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