Now that we know how to draw atomic orbitals, I want to take things one step further and show you guys how atomic orbitals can be turned into molecular orbitals. So guys, here are 7 rules for drawing molecular orbitals and just a heads up, you're not going to find these rules anywhere because I made most of them up, trying to look at all the different types of molecular orbitals you might have to arrange, and figuring out rules that would work for all of them. Now some of them are going to be so straightforward you know that you're not going to need to look at all 7 rules, but I just put the 7 rules there just in case you get to a really complicated one, you don't know where to start, you could follow these rules and always know what to do.
So let's go ahead and start with rule number 1, the simplest rule which says that the number of total molecular orbital energy states should be equal to the total number of atomic orbitals. So if you have 3 atomic orbitals, you should have 3 molecular orbitals of different energy. Pretty straightforward.
Next, one orbital of your molecular orbitals should never change phases. So what that means is that we're going to see that as these molecular orbitals increase in energy, some of the orbitals will start to flip, but one orbital should always stay the same. So that could be any orbital you want but I prefer that to be the first one because it just makes an easy reference to always see, look at the first one say that one is not going to change phases as energy increases.
The last orbital, however, must do the opposite. It must always be changing phases with each increasing energy level, so you must always be flipping it back and forth. 4, the number of nodes in your molecular orbitals must always begin at 0, so your first molecular orbital should have 0 nodes, and then increase by 1 with each increasing energy level. So the more energy levels you have, you would just increase the number of nodes by 1 each time until you get to the very last energy state.
5, your nodes should be as symmetrical as possible. Sometimes you're trying to like fit 3 nodes into a molecular orbital and you say why can't I just put the 3 nodes on this side and then 0 nodes on the other side. That's not the way it works. What you want to do is you want to space out your nodes as much as possible. When in doubt, sometimes when a molecular orbital gets complicated, like for example, if you're doing 8 atomic orbitals and you're trying to turn them into molecular orbitals, you're going to get a lot of orbitals there. And when in doubt, you could actually draw a sine wave, from a fake atom 0 to a fake atom n plus 1. I'll show you how to do this, and this helps you to balance out your nodes evenly because you're using a sine wave system to balance out your nodes. But we'll do that, we'll probably do that for a more complicated example. 6, if a node passes through an orbital, so let's say that a node of your sine wave passes directly through an orbital, you must delete that orbital. Okay? So that orbital should not exist because by definition if it's a node, electrons cannot exist there, so no electrons should be in that orbital.
And then finally, once you have everything drawn, fill the molecular orbitals according to the rules of electron configuration, which would be Aufbau principle, you have to build up; Pauli Exclusion Principle, you can only put 2 electrons in each orbital; and Hund's Rule, you have to fill degenerate or equal energy orbitals one at a time symmetrically. Cool. So let's go ahead and try to do the next following example.
