[minimal]

I'm pretty ignorant when it comes to the physics of chemistry, and I was going to ask this over in the organic chem section, but I figured it would do better here.
Since the 8 valence electron theory is actually incredibly weak (let's say we're talking about oxygen here), and oxygen can have any number of bonds practically, including a lot of ones that lie in between whole numbers, there has to be some sort of way to figure out what will happen.  For instance, oxygen usually accepts 1 or 2 bonds, but we know that's not all that it can do, but every time we look at a reaction, rarely do we consider all the other options unless they're already known to us. 
The whole point of this, is that there must be some sort of mathematical function (whether we know it or not) to help explain what the chances are of 'alternate' numbers of bonds appearing, I sincerely hope this is not all determined empirically after the fact.
Would the Klopman equation have anything to do with this?

[azmanam]

the term you're looking for is bond order.

http://en.wikipedia.org/wiki/Bond_order
http://en.wikipedia.org/wiki/Covalent_bond

There may be more complex equations than in the wikipedia page (and there probably are), but I don't know them off the top of my head.

[FeLiXe]

maybe you are talking about computational chemstry? if you want to know what's going on, you can solve the schroedinger equation for a molecule. if you take a high level ab initio method, then you can find all kinds of non-standard bonds

[minimal]

maybe you are talking about computational chemstry? if you want to know what's going on, you can solve the schroedinger equation for a molecule. if you take a high level ab initio method, then you can find all kinds of non-standard bonds

Where can I find out more about this? Any books or long online tutorials you know of?

[FeLiXe]

you can start out from wikipedia: http://en.wikipedia.org/wiki/Computational_chemistry
or any book about quantum chemsitry will do. I like Levine "Quantum Chemistry"

but I don't know if that's really what you are asking for. the problem is that you quickly move away from things that are easy to visualise and draw. basically it comes down to having a computer run for 10 hours and then you know something more about a specific molecule

[minimal]

the problem is that you quickly move away from things that are easy to visualise and draw.

I don't consider that a problem in the slightest.  As far as I'm concerned math represents the truer form anyways.  I think it will be more difficult in the sense it will be harder to work through, but once I've arrived at whatever answers, I'll feel a little more justified in them if that makes sense.

Thanks for the info.