I am not really a chemoinformatician though. So let's go back to chemistry. Today's molecule is methane. I optimised its geometry and calculated the vibrations in GAMESS. Since the best is just good enough I used a triple zeta basis with a bunch of polarisation and diffuse functions. For methane it is no problem because of the high symmetry. And for the geometry optimisation there is only one variable parameter.
Methane's 9 modes are grouped into 4 different symmetry races (and frequencies). They are Ti (3240/cm), A1 (3140/cm), E (1670/cm), Tj (1460/cm). I am afraid I don't know if the 3-dimensional races are T1 or T2. Again the frequencies are too high, mostly because anharmonicities are neglected. Before you read on you can ask yourself which ones are IR active.
Only the two T races are IR-active. You can tell from looking at them. I guess you could tell from the character table, too. Again I don't know how to. Maybe in a year I so I will know some more. For now it's all about the funny moving molecules.
Another thing to consider: there are 6 IR-active modes in methane (since the two T races are 3 times degenerate). That's why it's such a strong greenhouse gas.
The IR-active races are apparently T2 as mevans told me. The idea is that the (x, y, z) functions, which describe light, are of that race. In this case (xy, yz, zx) is also T2. Therefore Raman spectroscopy would give the same frequencies as IR-spectroscopy.
On the absurdity of classified information - The problem with keeping information secret is not that secrecy is never warranted, it's that it is always easier to classify something as secret than not...
3 days ago