Picking Up the Pieces

I think I failed my inorganic midterm.

Topics: Symmetry, representation theory, diatomic MOs. Not much, just the usual second-year first-term inorganic subjects.

As is the usual student gripe: "if I had more time..."

My mind blanked as soon as I had to assign point groups. Yes I remember the algorithm (one of many). Why is this molecule trigonal on top and square on the bottom? That rules out rotational axes, maybe? There's a mirror plane though. *Easily confused* (In retrospect: apparently, the molecule is hexagonal on the bottom, in which case it'll be C_3v. Darn it darn it darn it. I knew I was shortsighted; I didn't know I was blind.)

I was sad there wasn't more math. I *heart* the Great Orthogonality Theorem! We didn't prove it in class, but it shouldn't be hard to prove. It does require characterizing exactly what an irreducible representation *is* (using matrices? or vectors?), though, and then showing that they span the normed vector space (standard norm) of all representations of the point group with respect to some binary operation (addition) over some field (presumably the set of reals). The rest is just the formula of a projection, and using the fact that the norm of a irreducible representation is the number of classes in that group.

I was even sadder that I couldn't check my work, and changed one of my answers half-way, so that solution is now incoherent. (What happens when you want to flip the energies of an MO diagram, but didn't have time to erase...)

I hope I didn't write "staggered" instead of "eclipsed" ethane by accident as an example of a D_3h molecule. (Meep.)

Assuming that the markers are their usual marvelously efficient selves (judging from the first midterm and the assignments, they mark *very* fast, even granting that the class size is small), I should be able to get my midterm back on Monday, or Tuesday at the latest. Then I will use to that to make a decision. (That decision is not whether I'll drop the course or not...it involves an alcohol.)

Meanwhile, picking up the shards of my broken ego (whether it can be mended is debatable), I need to get back to work. More midterms and a final next week; no surprises there. Also need to work on my project; what I thought would have worked...didn't. I have come to hate Matlab (stupid but powerful CAS's with help files containing false claims...*mutters*).

Assuming that I make it to the end of next week, anyway.

[Edited]
Well. I got my midterm back, and I am still alive. That's always a good sign. Onwards...