I haven't posted to the main wall of this blog in soo long, omg. I've been shirking my responsibilities as a fetch loyalist, and for that I sincerely apologize.
I also apologize for the fact that this is the second post in a row that's going to be about urinals. Yeah, so apparently they're what I think about in my spare time?
No, not really. Anyway, in chemistry class we had this super awesome TA... let's call him Joey (since that's his name). He was kind of the coolest TA ever, and one day he was trying to figure out a good way to explain crystal field theory (CFT). You know, standard gen chem.
Well, somebody in our class came up with an amazing analogy to explain CFT, later referred to as Urinal Theory. It's actually a great explanation, and it kind of covers orbital filling as well. Christine and I argued about who came up with it (I feel like I pitched the original idea, but Christine insists she had some part in its generation), but it doesn't really matter, since it's really a brain child of the entire class.
Also, it's pretty easy to understand (even for women... I'm sure you can figure it out, even though it doesn't directly apply to you).
Okay, so let's get into it!
Imagine, you are in a class at college and you have an overwhelming desire to urinate (stay with me, please). You bolt out of the lecture hall, and find the nearest bathroom, which has ten urinals. Look below for a really bad diagram. Oh, and if the images look low-res, that's because they're really high-res. Click on them to make them look prettier!
Beautiful, right? Now, the reason there are ten urinals is that each urinal represents a slot for an electron. In this analogy, you are the electron. Cool, right? And in this example, we're only talking about CFT in terms of d-orbitals (hence the ten urinals/electron slots). For more information,
here's an image showing the s-, p-, and d-orbitals (in order from top to bottom).
So yes, here's an updated diagram with the energy axis as increasing to the right:
As you can see, all the urinals are roughly equal in effort from the electron, as they are at the same energy level. Oh, I forgot to add this: energy is distance in this analogy.
Now let's consider the possibility of another electron/person occupying one of the slots. According to the unspoken rules of urinal etiquette, you must leave one urinal in between you and the other person (let's assume for simplicity that the first five people to use urinals stay either on the even or odd urinals, so that the urinal gap between them is always an odd number). If this situation were to occur, these would be your possibilities:

So yes, as long as there is one urinal between the two people, each person is relatively happy. This is considered a stable state in terms of energy. Also, this would be considered high spin, since all the electrons are on either odd or even urinals (if I wanted to continue the analogy, I'd say that each even urinal has positive-spinning water when you flush or something like that, but that's stupid, so you're going to have to take my word for it). And when the alternating five urinals are filled, the sixth person has no choice other than to take one of the spots between two people (which sucks). So the order of filling would be 1, 3, 5, 7, 9, 2, 4, 6, 8, 10, or something similar. The evens and odds can be switched around among themselves, but not with each other (segregation!).
Now, if for example there were six ligands coordinated to the atom represented by this situation, two along each axis (called octahedral coordination), some orbitals would be more affected by the repulsion of the ligands than the others. Specifically, the dx2-y2 and the dz2 orbitals are of a higher energy since they are the only ones whose lobes reside directly on the axes (on which the ligands are coordinated). So these orbitals are then at a higher energy than the other orbitals. One can think about this by splitting the bathroom into two smaller bathrooms, one farther away and one closer.
And that energy gap in between the bathrooms is determined by the amount of repulsion from the ligand. But it makes sense, right? When you walk into the bathroom and see other people occupying every other urinal already, you have to decide whether it's worth walking to the next bathroom down the hall, or if you'd rather just use one in the current bathroom.
Most likely, if the energy gap
(ΔE) is larger, you'd decide that it's not worth going the extra distance to the second bathroom, unless you're like me and hate bathroom encounters with a hot and fiery (there's an STI joke there somewhere...) passion. This is similar to an electron's behavior when the energy gap is larger (often caused by more orbital overlap with the ligands): the new electron would rather share an orbital with another electron than expend the energy to get to the next empty orbital. This usually results in a low-spin situation, since each orbital holds two electrons of opposite spins (which cancel).
However, if the bathroom is just a couple feet away, you're more likely to just put in the extra energy to go to the wonderfully unoccupied bathroom down the hall! This ends in what is called a high-spin case in electron terms, because one atom could have five electrons with the same spin in five different d-orbitals, none of which cancel each other out. For more information on electron spin and spin states, go here.
Well, that concludes today's potty mouth description of chemical phenomena! I hope this made sense... it's hard since you can only take an analogy so far, and I always want my analogies to be perfect (but they never can be unless I just say, "an electron is like an electron").
So, until the next time I stop watching
Supernatural and decide to make a post!
Jacob