1 Jul 2015

How to Determine the Irreducible Representation of a MO

Five Slides About

Submitted by Richard Lord, Grand Valley State University

Five slides about how to systematically determine the irreducible representation if provided an unlabeled SALC. These slides focus on molecular orbitals, but this tool can be extended to any kind of SALC.

File 5SlidesAbout_DetermineIrredRepMO.pptx270.7 KB
Learning Goals: 

Students should be able to:

- determine the dot product between two atomic orbitals (AOs) or molecular orbitals (MOs)

- calculate a character for a MO under each symmetry operation based on dot products

- assign the irreducible representation for a MO based on the calculated characters

Related activities: 
Implementation Notes: 

Students need to be familiar with symmetry operations, point groups, and the concept of molecular orbitals being expressed as a linear combination of atomic orbitals. It is helpful to use a literature example or computed MOs as motivation for an example where symmetry labels may not exist, as up to this point they have probably only seen SALCs after generating them with projection operators. A literature example that you can implement in a homework set, or on an exam, is linked to this LO (placeholder for when my other LO is approved).

Time Required: 
The slides can be covered in ~20 minutes but makes a nice lecture (~50 minutes) with student-worked examples after each new mechanic is introduced.
Evaluation Methods: 

Students were asked to predict the frontier pi orbitals of benzene based on "Frost's Magic Circle" and then to apply symmetry labels to those orbitals on a homework set. Students checked their sketches with me during office hours before attempting to assign labels, and I helped them with the 2:1 ratio since the method only provides relative phases and not sizes.

Evaluation Results: 

Most students earned full points on the homework (9/11). One student did not attempt the problem and another got confused and used the projection operator method to obtain the SALCs instead.

Creative Commons License: 
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