How Does Group Theory Aid in Predicting Vibrational Modes in Spectroscopy?

[excalibur313]

Hi Everyone,
I am giving a talk on group theory as related to spectroscopy (IR & Raman) and I was curious about how to explain the jump from knowing which modes in the charcter table are Raman active to predicting what kind of vibration they will have. For example the Td point group has raman modes: A1, T3, E and then consequentially you know that the A1 is x^2+y^2+z^2, the T3 has xy,zy,zx, etc. How can I then take that information to infer what kind of vibrational mode it is? So I know the x^2+y^2+z^2 will be this breathing mode because it is simple to visualize and I know that A1 is totally symmetric, but the others are more difficult to see what kind of motion it is. I want to know this because I want to correlate it back to the raman spectrum I have and I have to know the types of modes so I can then figure out the energy shift they should have.

I was told there is a chart that will tell me what a xy vibration is, for example, but I haven't found one. Additionally, I'd also want to find a chart that could correlate a particular vibration to an energy shift, so the students can predict what each of the peaks are. Thanks a lot for your help!
Take care,
Stephen

PS- I basically want to do what they do on this website in general: http://fy.chalmers.se/~brodin/MolecularMotions/CCl4modes.html

 

[Dr Transport]

It is a tedious process to calculate how all of the atoms in a 3-d lattice move according to the different modes. The classic example is a triangle which takes about 5 pages and a square taking about 10-12 to do.

try here as a start...

http://symmetry.jacobs-university.de/cgi-bin/group.cgi?group=902&option=2&a1=12&a2=0&a3=0&a4=0&a5=2