[remeday86]

Main question: How do you determine the number of IR and Raman bands using the character tables of a molecule?

I know how to determine the point group symmetry. But after that, I am not sure what to do.
This is what I THINK I know so far: For methane, CH4



1)Determine point group:

T_d (tetrahedral)

2)Determine the Irreducible representation

_| E |8C3| 3C2| 6S4| 6d|

| 4|   1|   0  |   0 |    2|

I determined this by identifying the number of unchanged bonds after each operation.

4) Look at the character table of the point group



5) Determine the symmetry species in the character table that adds up to the irreducible representation

A₁ + T₂

6) 


Not sure what to do after that. All I know is that there are 2 IR bands but how was that determined?


My prof was drawing vectors of a symmetric stretch, asymmetric stretch and bending stretches of a molecule but I was confused because it was hard for me to determine where the arrows would go and determine if they were double degenerate or triple degenerate especially if the degrees of vibrational freedom was more than 4
Is there a tip of drawing vectors to determine which are degenerate?

What is the relationship between the number of degeneracies and the number of IR active bands?

I know that species A_i's, B_i's and are nondenegerate and that E and are double degenerate and T is triple dengenerate.


Sorry I asked a lot of questions and I hope it's understandable 
Any help would be greatly appreciated and I thank you for your time!

[Dan]

It's been a very long time since I've done this, so I can't help you much, but for 6 take a look at this link:

http://faculty.uscupstate.edu/llever/Chem%20542/ShortCl2O4/GroupTheor.htm

I think you'll have 1 band in IR, 2 bands in Raman.

[remeday86]

Thanks.

I have a question.
If you draw the number of degrees of vibrationals freedoms and you determined one of them is double degenerate (or triple degenerate), does that count as ONE IR active band?