27 Jun 2016

Uses for Character Tables: IR and Raman Spectroscopy

In-Class Activity

Submitted by Kristy L. Mardis, Chicago State University

A guided inquiry activity where students use group theory and character tables to practice determining reducible representations for all atoms and the individual bonds (like CO stretches).  The students then reduce the representation, determine which are vibrational modes, and then determine which are IR active using the character table.  For the second portion, they practice using this approach to differentiate between two metal isomers.

Learning Goals: 
  • Identify reduced representations as translations, rotations, and vibrations
  • Write reducible representations for both all-atom and particular vibrational motions
  • Identify reduced representations as IR-active or inactive
  • Use reduced representations and their IR activity to differentiate between molecular isomers
Equipment needs: 

A character table.  We have been using the online version at http://symmetry.jacobs-university.de/ if students forget their book.  It displays nicely on their phones.

Implementation Notes: 

This is used in the senior-level advanced inorganic class.  Students have practiced reducing representations in prior classes and should be comfortable with this step.  I also assume that students have read the text section (we use Miessler and Tarr) on this topic.  They have had a mini lecture on constructing gamma’s for molecular motions.  Students work in small groups of 3-4 while I circulate among the groups.  Generally, they check their work with another group at a nearby table.  If time is an issue, you can formally assign individuals in a group to determine if the representation contains the A1/A2/B1T/etc representation.  It is best to have the stronger students double check the weakest ones. 

Time Required: 
2 class periods (I stop between pages 5 and 6)
Evaluation Methods: 

The activity itself was not graded.  However, the summary sheets (there are two; one in the middle; one one the last page) are turned in and graded as homework.

The exam questions are very similar to those of summary sheet 2. Last semester, 5 out of my 6 students successfully answered the similar final exam question. One still used the all-atom approach and didn't successfully determine the representation.

Evaluation Results: 

The SF6 summary sheet question is too hard for my C-level students.  They tend to just give up before getting the representation correct.  I will swap this for a smaller/less symmetric molecule in the next iteration.  About 25% have trouble differentiating between the all atom gamma of the first summary sheet and the bond-only approach of the second and do the all-atom approach for the second summary sheet.

Creative Commons License: 
Creative Commons Licence


Thanks for sharing - this is a really nice problem set. I think I may have found an error in the answer key however, the point group for the trans-ML2(CO)2 is D2h not C2h. Thus the two irreducible reps for D2h are Ag and B1u, not Bu.

I've adopted this as an inclass activity for my graduate level advanced inorganic class to get them practicing group theory.



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