Drawing Molecular Orbitals - Online Tutor, Practice Problems & Exam Prep

Molecular orbitals are derived from atomic orbitals, following specific rules. The total number of molecular orbitals equals the number of atomic orbitals. One molecular orbital remains unchanged in phase, while the last one alternates with energy increases. Nodes start at zero and increase with energy levels, maintaining symmetry. If a node intersects an orbital, that orbital is eliminated. Finally, fill molecular orbitals according to electron configuration rules: Aufbau principle, Pauli exclusion, and Hund's rule. Understanding these principles is crucial for grasping molecular structure and behavior in chemical reactions.

The 7 Rules of Drawing Molecular Orbitals

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.

MO of 1,3-butadiene

Provide the molecular orbitals of 1,3-butadiene. Cool guys. So the first part should be really easy. All we have to do is fill in the atomic orbitals. So let's go ahead and do that now. How many electrons should be in the atomic orbitals? It should be 4. So it should be 1, 2, 3, 4. Is everyone cool with that? Because we have 2 from each π bond. Perfect. So remember that the number of basically this one's already filled out for you mostly. All you have to do is fill in the phases and that's because we're starting off slow. Typically, you would have to actually draw all these molecular orbitals from scratch, but I'm handing to you half the problem already so that we can practice part of it. Okay?

So what we know by definition is that 4 atomic orbitals should turn into 4 molecular orbitals of increasing energy, right? Cool. We also know that your first atomic, your first molecular orbital should have 0 nodes, meaning there are no places that one that a phase changes. Okay, there are no phase changes happening in my first molecular orbital. That's good. Also guys, I want to just talk a little bit about the nomenclature here. It is common that when we're talking about molecular orbitals of 3 or more that we use the psi symbol to represent each increasing energy state. So the first one would be ψ₁, then ψ₂, all the way up to ψ₄, and it should be up to whatever number of conjugated atoms you have. Now when you're only dealing with 2 conjugated atoms, a lot of times you'll the letter π will be used because π would just be for a pibond, which is 2. So you may see π₁, π₂ for a double bond, but for anything bigger than a double bond, we use the psi symbol. Cool?

So guys, we know that we have 4 electrons and we need to use the molecular orbital rules to fill in what the other phases should look like. Cool? So right now, how would we know what the phases should look like here? What are the rules that we want to follow? Well, the first rule, well, I mean the first rule was that we have 4 orbitals. Let's go to the next one, which is that your first atomic orbital should not change phases. So that means that, and I keep saying atomic orbital, but I mean the first orbital of your molecular orbital. So that means that I'm going to shade in this one here just like it's shaded down here. Makes sense? And what I'm going to do is I'm also going to shade it in ψ₃ and ψ₄ because remember that the first rule is that, or remember that the rule for the first orbital is that it doesn't change. Cool? Now what's the rule for the last orbital? The last orbital must always be changing. So let's go ahead and start flipping this one. So that means that over here, it's going to look like this. And then it's going to flip again here. And then it's gonna flip again here. Cool? So everyone's got that? So my first orbital is staying the same, my last orbital keeps flipping. Awesome.

Now we look at nodes and what we say is that your nodes must increase 1 at a time. Right now, I have my nodes is equal to 0 for the first one right. I have 0 nodes, so that means that for ψ₂, I should have 1 node. For ψ₃, I should have 2 nodes. And for ψ₄, I should have 3 nodes. Cool? What I'm going to try to do is figure out symmetrical ways that I can keep these phases the way they are and have one place or or not have one place, but have have these phase changes happening in a symmetrical way. If ψ₂ needs to have one node that's symmetrical, where do you think is the best place to put it? Well guys, hopefully what you're saying is that it should be right down the middle because putting it right down the middle would make it symmetrical on both sides. And what that tells us is that if there's only one face change here, that means that this must be flipped up and this one must have stayed down.

Okay. Now notice I'm using the colors blue and black for different reasons. Black means that I already knew that by definition of my rules. Blue means I figured it out based on where the nodes were. Cool? So now I have one node and this is what my ψ₂ molecular orbital looks like. So now we know what ψ₁ looks like and what ψ₂ looks like. Let's see if we can figure out ψ₃. So ψ₃ needs to have 2 nodes. Where do you think is the best place to put those 2 nodes that it's symmetrical? So I'm hoping that you guys are gonna pick this and this. Okay? Because what that does is it gives me symmetrical nodes that are they're not lopsided make the thing make the thing look symmetrical, okay? So what that means is that my 2 nodes, my 2 orbitals in the middle should look like this, okay? And what this would do is it would allow my phases, my first one and my last one, to follow the rule while also having 2 nodes. Cool.

And lastly guys, what do you think for 3 nodes? How do we do 3 nodes? There's only one way, which is just in between each one. And that means that it's going to be flipping back and forth. So that means that this one is going this way and this one's going this way. Cool? And now we have 3 phase changes and still overall there's symmetry here. Cool? Awesome, guys. So now we have our molecular orbitals filled in and these are the rules we're going to be using throughout any type of of conjugated system. We're going to be using these rules to figure out what our molecular orbitals look like. Okay?

So now all we have to do is we have to use the principles of electron configuration to figure out in which ψ molecular orbitals are those 4 electrons going to reside in. So, for example, I'm going to draw something, please don't draw this, but I'm just going to give you an example. Should I do something like this? Does that make sense where I distribute them evenly throughout all of my ψ orbitals? Please don't do that because what we learned is that the principles of electron configuration applied in molecular orbitals as well. So that means Aufbau principle, build up, always fill your lowest ones first. Pauli Exclusion, you can only have 2 electrons at a time in an orbital. Hund's rule, if you have 2 equal energy level orbitals, fill them symmetrically. What that means is that I should put 2 electrons in ψ₁ because that is the lowest energy and I can only fit 2, and then 2 electrons in ψ₂ and I'm done. That's it. This is what the linear combination of atomic orbitals diagram or M.O. theory should look like. You should have your molecular orbitals filled in like this and then you should fill in your ψ₁ and your ψ₂.

I just want to bring up one last thing, which is that I actually have failed to mention what the stars mean. Remember that star is just another description for anti-bonding. So would you assume that this conjugated diene, is it going to be stable or unstable based on how these molecular orbitals are filled? Stable, because right now all I have is bonding orbitals that are filled. Anything basically below the halfway point is bonding. So right now what I have is 2 bonding orbitals that are totally filled. These are going to encourage the atoms to be bonded together. And then I have the anti-bonding orbitals that have no electrons, which is good because you don't want to have electrons in the anti-bonding orbitals. That makes the molecule more unstable, it increases the energy. Cool? Awesome, guys.

So that was that exercise. Let's move on to the next video.

Propose reasonable molecular orbitals for the following conjugated atomic orbitals.

Propose reasonable molecular orbitals for the following conjugated atomic orbitals. So guys, this one is harder because notice that I'm not giving you a molecule, I'm just giving you the atomic orbitals and you have to draw the rest. I'm not even giving you what the first one looks like, what the other, however many other molecular orbitals are, we have to draw it all from scratch. The good part is that if you were given something like this, you can figure this out using my 7 rules. So let's go through them. First of all, how many atomic orbitals do we have that are conjugated? 3. Okay. You might say, but Johnny, what about this, it doesn't have an electron. That's fine. As long as it's an atomic orbital that's drawn there, that means it's conjugated. That means that there's probably a plus charge here, so there's no electron, but it's still conjugated. Okay? So there are 3 and what that means is that I should have 3 energy states of molecular orbitals. That means that I should have a ψ2 and I should have a ψ3. Cool? So I know for sure there should be 3 molecular orbitals. Now these 3 molecular orbitals must also contain 3 orbitals each. So let's draw those in. It should look like this, like this, like this and put a line and let's do the same thing here. So ugly but you get the point. Cool. Okay. So we're on our way. Now we need to shade it. Cool? So how are we going to shade this? Let's just always start by putting the dark phase of the orbitals at the bottom, just because that's the way I like to do it, but if you start at the top that would be completely fine as well. But let's just go ahead and move this more up so we have a little bit more space and shade the bottom. Cool. Awesome. So now based on the next rules, what should we do? What should I do with the first orbital? Let's keep it the same for each. So I keep it the same here and I keep it the same here. What should I do for the last orbital? I need to flip it every time. So let's flip it here and let's flip it again here. Cool. And now what do I do with the nodes? I have to increase them 1 at a time so this should be 0, this should be 1 node, and this should be 2 nodes. Cool, right? Now, all we need to do is decide where those nodes are and deciding where the nodes are is the hardest part. Okay? It is the hardest part of drawing like little orbitals, but I think we're going to get this. So one's already done for us. Let's go to side 2. Where could we put just one node and have it be symmetrical? So, for example, would this be a good spot for my node? What do you guys think? That's not symmetrical. What that's gonna do is it's gonna give me 2 on one side, 1 on the other. It's not symmetrical, it's not good. So what could we do? Well, guys, many times when you have odd-numbered conjugated systems, you're going to have to draw a node through an orbital. So the only way to keep one symmetrical is to actually draw the node straight through that orbital. Crazy, now what happens, what's a rule that says what happens when you draw a node through an orbital? You delete the orbital completely. So what we're going to Guys, by Guys, by definition, a node is a place where electrons cannot exist mathematically. So that orbital, for all purposes, doesn't exist to us because there's no way to put electrons in it in this arrangement. Cool? So there we go. That orbital is deleted. We're done with that one. Now what about 2? 2, I see a way to put 2 nodes, which would just be this. Cool. So that means that this one must go up to be another phase change. Cool. So guys, now we've drawn our molecular orbitals and now all we have to do is fill them with our pi electrons. Where should I put the two pi electrons that we have? Just in Psi 1. Cool? So that's it. We would just put them in side 1 and this is the full molecular orbital diagram for this molecule. Great job guys. You guys are on the right track. Let's move on to the next video.

Here’s what students ask on this topic:

What are the rules for drawing molecular orbitals?

To draw molecular orbitals, follow these rules: 1) The total number of molecular orbitals equals the number of atomic orbitals. 2) One molecular orbital should remain unchanged in phase, preferably the first one. 3) The last orbital must always change phases with each increasing energy level. 4) The number of nodes starts at zero and increases by one with each energy level. 5) Nodes should be as symmetrical as possible. 6) If a node passes through an orbital, that orbital is deleted. 7) Fill the molecular orbitals according to the Aufbau principle, Pauli exclusion principle, and Hund's rule.

How do you determine the number of nodes in molecular orbitals?

The number of nodes in molecular orbitals starts at zero for the lowest energy orbital and increases by one with each subsequent energy level. For example, the first molecular orbital has zero nodes, the second has one node, the third has two nodes, and so on. Nodes should be distributed symmetrically within the molecular orbital. This systematic increase helps in understanding the energy and phase changes in molecular orbitals.

What is the significance of the Aufbau principle in filling molecular orbitals?

The Aufbau principle states that electrons fill molecular orbitals starting from the lowest energy level to the highest. This principle is crucial for determining the electron configuration of molecules. By following the Aufbau principle, along with the Pauli exclusion principle and Hund's rule, you can accurately predict the distribution of electrons in molecular orbitals, which in turn helps in understanding the chemical properties and reactivity of the molecule.

Why must one molecular orbital remain unchanged in phase?

One molecular orbital must remain unchanged in phase to provide a reference point for the other orbitals. This consistency helps in tracking the phase changes as energy levels increase. Typically, the first molecular orbital is chosen to remain unchanged because it simplifies the process of identifying and comparing phase changes in higher energy orbitals. This rule ensures a systematic approach to drawing and understanding molecular orbitals.

How do you handle nodes that pass through an orbital?

If a node passes through an orbital, that orbital must be deleted. This is because a node represents a region where the probability of finding an electron is zero. Therefore, if a node intersects an orbital, it means that no electrons can exist in that orbital, and it should be removed from the molecular orbital diagram. This rule helps in accurately representing the electron distribution in molecular orbitals.