Now what I want to do is switch gears and talk about a type of notation that's very
common in organic chemistry and it's a model that we use to really predict what molecular
orbitals are going to look like.
And it's called the Linear Combination of Atomic Orbitals, so if you ever see LCAO,
that just means this little diagram that I have drawn right here.
So let's go ahead and just get right into it, figure out what's going on.
So the first thing you need to do is learn how to read this.
So there are two orbitals on the sides, here and here.
These are your atomic orbitals, so write in AO, AO.
Just so you know, these are the same types of orbitals that we were dealing with when
we talked about atomic orbitals, so basically just orbitals that have two electrons in them.
They don't interfere with each other.
Those are just the orbitals with the atoms by themselves.
Now these orbitals in the middle have to do with interference.
They have to do with how the atomic orbitals coming together.
These are called molecular orbitals.
So what molecular orbitals do is they predict where electrons are going to be in the entire
molecule, not just for the atom.
Does that make sense?
So basically they predict the way the bond is going to behave.
So let's look at these three different possibilities of the way that atoms can interfere with each
other, orbitals can interfere with each other.
Let's go ahead and start off with the simplest form of interference, which would be nonbonding.
Now, I did not talk about nonbonding in the previous topic, so I want to ask you guys,
what do you think nonbonding is?
Well, just like it sounds, it means that they're not bonding.
It means they're not interfering with each other.
So you could almost think of it as I'm holding one hydrogen in one hand and one orbital in
the other, one orbital in the other.
They're not interfering with each other.
Maybe they're too far apart or whatever, but they are just like freestanding.
So in that case, nonbonding, as you can see I just have like a comma here, that just means
I have two orbitals that are not interacting.
And the way that I would draw these is as atomic orbitals because they don't have any
bond at all.
So let's go ahead and try and figure out what the atomic orbitals would look like.
What I want you guys to do is just pretend that this is a hydrogen atom and what type
of orbital does a hydrogen atom have?
Do you guys remember?
Well, if you think about it, a hydrogen atom only has one electron, so that one electron
should be in the 1s orbital so that's why as you notice, I have 1sa and 1sb.
What that means is that this is the 1s orbital for the (a) hydrogen and this is the 1s orbital
for the (b) hydrogen.
Does that make sense?
I hope that's not too confusing.
Basically, what I'm doing is I'm just going to map out where the electron is going to
be for this atomic orbital and where the electron is going to be for this one.
Now that I know which orbitals correspond to which atoms, you guys have to tell me how
many electrons do I have in the nonbonding orbitals.
How many electrons do I have in 1sa and in 1sb?
Well, what's the atomic number of hydrogen?
One.
So how many electrons should I have?
One.
So what I'm going to do is I'm going to draw one electron here, one electron here.
I'm done.
That represents the one electron that's in this orbital here and the one electron that's
in that orbital there.
Does that make sense so far?
I hope so.
I know it's a little bit complicated.
I'm trying to make it as easy as possible.
So those are my atomic orbitals.
Now remember that I said, these orbitals in the middle, the molecular orbitals, have to
do with how they're interfering, so let's talk about the easiest form of interfering
first, which is bonding.
Remember that bonding would be a constructive interference.
The way that you can – let me just write constructive.
Go ahead and write down constructive.
The constructive interference can be represented by just like a positive, I mean not a positive,
a plus, meaning that one orbital is adding to another orbital and making the chances
of finding an electron there better.
The way that you would denote that on my model is that I would have this electron jump down
to this energy state and this electron just down to this energy state because they're
being shared between both atoms.
So what I'd have is that now one becomes an up spin and one becomes a down spin.
And the way that I've heard this as analogy before is that imagine that these are like
two people that are financially unstable and they like can't pay their bills and they decide
to move in together and like share costs.
Imagine you're not cutting it and you're like, “Hey, let's just go ahead and room for a
few months or whatever.”
What that's going to do is it's going to make both of them more energetically favorable
and I'm going to talk about that in a second.
When they constructively overlap like this, that's going to make what we call a sigma
bond.
Remember a sigma bond is a region of one overlap.
The reason it's called sigma 1s is because that's the sigma bond created by 1s orbitals,
two 1s orbitals.
Cool.
So hopefully that makes sense so far.
That when they constructively interfere, you're going to wind up filling what's called the
bonding orbital, which is this one right here.
Now let's see what happens when they destructively interfere.
Let's say that these two people try and move in together, but they just hate each other's
guts.
Well, that would be an antibonding association, where you use a minus charge to show that
they're actually going to form a node in the middle and there's going to be no overlap
at all.
When that happens these two electrons are actually going to jump up to a higher energy
state and fill the antibonding orbital.
The antibonding orbital, just so you know, is denoted by this star.
If you ever see that star, that means this is antibonding.
As you can see, these electrons are actually having to become – see the energy is going
up.
They're actually having to become more energetic to do that and that's bad.
Remember that basically in all chemistry if you get more energetic, that's a bad thing
because you have to work for it and molecules are lazy.
They don't like to work.
Basically, that's the way we use this diagram.
You could show that you could either do antibonding or it could do bonding, but in this case,
we're just going to use the bonding orbital.
Now a question that you guys might have is, “Okay, Johnny, I understand what you're
saying, but why would atoms ever do the antibonding if it's so energetically bad, why would they
do it?”
The answer is they don't want to.
Antibonding orbitals are not favored.
What would happen is that these two hydrogen atoms would come together and then they would
realize that they're antibonding and then they would immediately split apart.
Why?
Because they're not energetically favorable.
Maybe, later on, they'll meet their match and find someone else to bond with, but those
two hydrogen atoms would not bond with each other.
That's an antibonding interaction.
Now, what I want to do is connect this to another really important diagram that's found
in your book.
What it shows is that there's a relationship between how stable atoms are and how close
they are together.
So basically when two atoms are nonbonding, remember that that's the picture that I have
here where they're nonbonding.
This is the nonbonding line.
When two atoms are nonbonding, they're kind of stable, but they're kind of not stable,
especially when they're hydrogen atoms.
Do you guys know why?
The reason why is because remember that each orbital can hold two electrons, but how many
electrons does each orbital have right now?
Only one.
The 1sa has only one electron.
The 1sb has only one electron, so those orbitals aren't completely filled, so they're not going
to be very stable.
Does that make sense so far?
If they can jump together and share electrons between each other, then what's going to happen
is that they're going to form a bond.
Remember that's the bonding diagram, where there's higher chances of finding electrons
right there.
That means that now they're going to have one molecular orbital that is completely filled.
That's actually a really, really good thing because now it's completely filled, it's more
stable.
One thing to keep in mind is look at the energy difference here.
Now, I do not need you to memorize this, but just so you know, when we talk about energy
and thermal dynamics in organic chemistry, we're going to talk in terms of kilojoules
per mole. 436 kJ per mole is the energy that is saved by coming together.
That's a huge amount of energy.
So what that means is this is going to be very, very favorable interaction.
Actually, if you think of hydrogen in real life, it actually does this.
When you breathe in hydrogen – there's lots of hydrogen in the air – you're not breathing
in just regular hydrogen, you're breathing in H2.Why?
Because the hydrogen saves a ton of energy by bonding together and filling its molecular
orbital.
Does that make more sense now?
It's like a real-world application.
This is very favorable reaction.
One more thing I want to point out is that I have this number 1.33Å, what is that?
A with a little dot over it.
It actually looks like this in case you can't see it.
Oops.
It looks like this.
Is an angstrom.
Do you guys remember what an angstrom is?
It's a tiny, tiny unit of measurement that we use to measure atomic-scale things.
For example, you would not want to measure your room in angstroms.
It would be a very, very big number.
What an angstrom is it's 1 x 10-10 meters.
So basically it's a very, very tiny amount.
The distance between these nuclei is 1.33 angstroms in this specific single bond.
So just keep that in mind that a sigma bond is about 1.33.
That changes a little bit, but in this case, that's what it is.
Now, what I want to do is I want to move on to talking about pi bonds and how they can
do the same thing, or p orbitals.
So p orbitals can also from nonbonding, antibonding, bonding.
Now I don't want to go through this as much in depth because we already did it and because
this one's more complicated.
There's some sigma bonds that I kind of ignored.
But what I do want to show is that once again, I would have one electron from my 2px, I could
have one electron from my other 2px over here.
Let's just say this is one and two, so this is one and two.
And what I would get is these atomic orbitals that aren't very stable just by themselves.
What they want to do is they want to combine constructively.
So if they combine constructively, which is like this, shown by the colors being the same
on both sides, then what's going to happen is that these electrons will jump down to
a lower energy state and they'll form a molecular orbital that is more stable.
Now notice that the name of this molecular orbital is different.
The name is called a pi bond because of the fact that the pi bond has to do with two regions
of overlap that are constructive, not just one.
In the same way, antibonding orbitals could form and that would be star pi.
That would not be as stable, so it would not form.
It would split apart and then it would form a bonding orbital later.
Cool.