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 T

_{i}(3240/cm), A

_{1}(3140/cm), E (1670/cm), T

_{j}(1460/cm). I am afraid I don't know if the 3-dimensional races are T

_{1}or T

_{2}. 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 T

_{2}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 T

_{2}. Therefore Raman spectroscopy would give the same frequencies as IR-spectroscopy.

## 5 comments:

The T vibrations must be T2, my good man. Do you see in the character table where it says (x,y,z) on the T2 row? This means that x-, y-, and z-polarized light have the symmetry species of T2 for the Td point group. Light can only excite vibrations with its same symmetry species, so for tetrahedral molecules like methane, only T2 vibrations can be excited by IR light (read: are IR-active).

Figuring out the symmetry of the vibrations is the hard part (at least for me); once you know that, just find x, y, and z on the character table and you'll know right away the symmetry required for IR-active vibrations.

How can you tell just by looking?

Hah, forgot about just checking for dipole variation. Anyway...a little aside, the above applies to Raman-active vibrations too, but look for the products xy, yz, and xz on the character table instead of x, y, and z. The vibrations with those symmetries are Raman-active.

that makes sense, I have to remember that.

I got the symmetry group from the degeneracy in the original GAMESS output file. there is only one 2-dimensional race. and the 1-dimensional one is obviously A1 because everything is symmetrical

"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"

I've sat down and thought this out, but it totally makes sense now. I always wondered why methane was considered a greenhouse gas (or why it IS a greenhouse gas) but thinking about it in terms of IR/Raman opens everything up. Brilliant. Thanks.

I really liked that thought when I first heard it in a lecture. good thing our athmosphere is made up of IR inactive gases

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