Sunday, April 12, 2009

Electron spin existential crisis

Last night while studying for an inorganic chemistry exam I have tomorrow, I suddenly had a huge existential crisis about not understanding magnetism.

It went something like this: how does MO theory tell us that oxygen should be paramagnetic and carbon should be diamagnetc?

Well, oxygen has unpaired electrons in its HOMO. Carbon has paired electrons in its HOMO. One or more unpaired electron leads to paramagnetism.

Okay, hold up. So why does oxygen want to have its electrons have the same spin when one goes into each degenerate orbital? Why, well, electrons repulse each other since they are negatively charged, thus if they can, they will go into separate degenerate orbitals (following Hund's rule). Due to the Pauli exclusion principle that means that electrons cannot have the same spin and position. If they have the same spin, they necessarily have different positions, which leads to less electrostatic repulsion. This is my qualitative understanding of the issue, and it is also--to my understanding--responsible for the phenomenon of exchange energy in half filled shells.

(Filling out orbital diagrams in this order has become intuitive to me after three years of undergraduate chemistry, but I guess I rarely step back and re-rationalize why it's the case).

So coming back to paramagnetism. This means that if those two electrons have the same spin, there is a permanent magnetic moment in the molecule (right? but what what is a magnetic moment anyway?!?! crap.) which means that it creates its own magnetic field. I recall the Lorentz Force law from physics (is this even exactly related?) although much of what I remember from electricity and magnetism involves a lot of fussing around with the right hand rule and being confused by which direction my thumb went. Anyway, if there is a permanent magnetic moment when put in an external magnetic field, the magnetic field can be parallel and thus be attracted. Whereas when a diamagnetic species is put in a magnetic field, since there are two electrons going in opposite directions, one of the vectors must necessarily oppose the magnetic field.

Okay, this makes sense, although I'm sure I butchered a few of the details. Then there's something something angular momentum vector something something spin momentum vector something something more quantum mechanics something something. But then I ask myself what is spin really? Why does it run parallel to the magnetic field. Why are parallel magnetic fields attracted to one another? Does it just have to do with the orientation of the electrons compared to the nucleus? WTF? Wait, wait, this was all beginning to make sense, and now it's all falling apart again.

So I waste hours of time on Wikipedia physics pages being confused.

It's funny that we use the same language as people who actually have a deeper level of understanding of these phenomena, but don't actually understand it at a deep level at all. It's all about shorthands to understand the parts we need to understand--in this case--for chemical reactivity and understanding MO theory.

The more chemistry I learn, the more of a head-case I become.

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