Submitted by Anthony L. Fernandez / Merrimack College on Wed, 09/26/2018 - 18:45

As I begin my 19th year of teaching I realize that I do not have a good grasp of group theory or how to formally use it to determine the number of IR active vibrations in a species. I am trying to come up with a good exercise for my students that could introduce them to point groups and character tables.

In one of their early lab experiments, my students synthesize cis-MoO2(acac)2 and characterize it using IR and NMR (1H and 13C) spectroscopy. I would love to do an analysis of the Mo-O vibrations that would demonstrate that the cis isomer (C2 symmetry) would have two IR active Mo-O stretching vibrations (sym and asym) while the trans isomer (D2h symmetry) would have only one IR active Mo-O stretching vibration (asym). The problem is that I have gotten myself a bit muddled in my thinking and I need some help finding my way out. (Or if someone would want to help me develop an LO on this I would jump at the chance...)

Any thoughts or suggestions or offer of help would be greatly appreciated.

Joseph Keane / Muhlenberg College


I have an activity that I think does a reasonable job of this.  However,

1) It is a POGIL-type activity, so if you are not comfortable with that approach, you would need to substantially rework it.

2) I am intending to publish my POGIL stuff at some point, so I would need you to agree to some specifics about distribution and sharing.

3) I can't post it on VIPEr for the same reason.

If you are interested despite all of that, please let me know.  I have a substantial collection of activities (enough to fill most of a one-semester workbook), and I welcome feedback on them.

Be well.

- Joe Keane

Wed, 09/26/2018 - 23:55 Permalink
Anthony L. Fernandez / Merrimack College

Hi Joe,

Thanks for the offer. I would love to even just look at your activity because it may help me work through my misunderstandings. I totally understand the issues around publishing and wanting to keep it "private." If you are comfortable with sharing this activity with me, I would love to see it.

Thanks, Anthony

Thu, 09/27/2018 - 09:34 Permalink
Kyle Grice / DePaul University

Hi Anthony,

I use MFT to teach my 10-week inorganic course and using group theory for IR analysis is one of the major things I want them to do is be able to (it's always on the exam).

I teach it in class and also have a pencast (or two) that I can send you. 

I've made an exercise for learning point groups  (using Otterbein) that I use, but I don't have any In-class exercises for learning to do the vibrational analyss. I'd be interested in developing one or giving feedback on anything you develop. 


Thu, 09/27/2018 - 10:05 Permalink
Chip Nataro / Lafayette College


Here you go.

Because you are only interested in the Mo-O vibrations you can use the simplified approach. That means you only have to ask the following question, does the bond move or doesn't it when I perform the given symmetry opperation? 

cis-form which is C2

For E: neither bond moves so it gets a character of 2 (2 bonds total, neither move)

For C2: both bonds move so it gets a character of 0

That gives you the reducible representation of 2 0

You then have to reduce it

A: 1/2 (2x1x1 + 0x1x1) = 1 A

B1: 1/2 (2x1x1 + 0x-1x1) = 1 B

Two IR active vibrations.


For the trans-form which is D2h

The reducible representation would be (assuming the Mo-O are along the Z axis)

2 2 0 0 0 0 2 2

For this one you only need to consider the B1u, B2u and B3u irreducible representations since they are the ones that contain x, y and/or z components and you were asking about IR active vibrations.

B1u: 1/8 (2x1x1 + 2x1x1 + 0x-1x1 + 0x-1x1 + 0x-1x1 + 0x-1x1 + 2x1x1 + 2x1x1) = 1 B1u

B2u: 1/8 (2x1x1 + 2x-1x1 + 0x1x1 + 0x-1x1 + 0x-1x1 + 0x1x1 + 2x-1x1 + 2x1x1) = 0 B2u

B3u: 1/8 (2x1x1 + 2x-1x1 + 0x-1x1 + 0x1x1 + 0x-1x1 + 0x1x1 + 2x1x1 + 2x-1x1) = 0 B3u

So that gets us the 1 IR active vibration


If you aren't sure about any of the steps just let me know. As an alternative option you could go to

Click on D2h for example

Scroll down a bit and it will reduce a reducible representation for you. Enter the one from above and be sure to click the radio button from its default general to the one for vib (vibrations). Hit submit and you will get a nice force field analysis  where it will list the IR (and Raman) allowed and forbidden vibrational transitions.


Thu, 09/27/2018 - 10:33 Permalink
Anthony L. Fernandez / Merrimack College


I just looked at your LO for use in conjunction with the Otterbein site. I did not use it this semester but will adapt it in the future for my course.

I would love to write up a vibrational analysis LO and I think that the comment by Chip may be a place to start for the MoO2(acac)2 lab. I am going to think a bit more deeply and get back to you on how we (and perhaps with Chip) to develop a LO about vibrational analysis.

Cheers, A.

Thu, 09/27/2018 - 14:09 Permalink
Anthony L. Fernandez / Merrimack College


That is awesome! I am going to now try to cram that into my brain and make it fit with the stuff that I think I know about the process.

I will most likely reach out to you separately as I try to work through this a bit more...

Cheers, A.

Thu, 09/27/2018 - 14:10 Permalink