u/phatcat9000

I’m in my 2nd year of my degree, and one of the things I struggle with is group theory. I’m managing to get to grips with it a bit more, and am trying to construct the methane MO diagram using group theory.

I’ve determined that the C 2S orbital is of course A1, and that the hydrogen orbitals are A1 + T2. The bit I’m stuck on is using the projection formula. There are 24 operations in total, and I’m taking one of the s orbitals and figuring out what each of the transformations would do to it. Fine. Thing is, there are 8 C3 transformations and each of them is going to have a different effect, and this seems like a really tedious way to do it, not to mention easy to mess up.

Is there a shortcut I’m missing when it comes to this sort of thing?