Chapter 11: Chemical Bonding II: Valence Bond and Molecular Orbital Theories

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Welcome back to another Deep Dive.

Today, we're doing something a little different.

We're not just scratching the surface of a topic.

We are drilling all the way down to the bedrock of reality.

We're talking about the invisible glue that holds, well, the entire universe together.

It's really the fundamental question of chemistry, isn't it?

Why do atoms stick together?

Because if you don't understand that, you're just memorizing lists of chemicals without knowing how the machine actually works.

Exactly.

And I think for most of us, and I'm definitely including myself here, our understanding of this glue is based on cartoons.

You know what I mean?

You take a chemistry class in high school and you learn to draw stick figures.

You put a C for carbon and H for hydrogen, and you draw a little line connecting them.

And voila, that's a bond.

The Lewis structure.

It's an absolute icon.

It's comforting.

It's like connecting the dots.

It's clean.

It's binary.

There is a line or there isn't.

But today, based on chapter 11 of general chemistry, principles and modern applications, we are going to tear up those drawings.

We are going to completely ruin your childhood stick figures.

We kind of have to, because while Lewis structures are great for bookkeeping and counting electrons, making sure everything adds up, they are actually terrible at explaining reality.

Yeah.

They don't tell you why a bond forms.

They don't tell you why methane is shaped like a pyramid.

And they definitely don't explain why liquid oxygen sticks to a magnet.

Which, spoiler alert for everyone listening, liquid oxygen is magnetic, which just blew my mind when I read this chapter.

It's one of the coolest demonstrations in physics.

And the stick figure drawings say it shouldn't happen.

So to understand the real world, we have to move into the quantum world.

We have to talk about waves, energy wells, and probability maps.

So if you are listening to this, consider this your survival guide.

If you're a college student, say staring down a massive exam on valence bond theory and molecular orbital theory, this deep dive is for you.

Absolutely.

We're going to walk through this chapter linearly, translating the really dense academic text into human language.

My role today is to be the curious student who is frankly slightly overwhelmed by the math.

And your role is to talk me off the ledge.

I can definitely do that.

It's a steep climb, but the view from the top is totally worth it.

Awesome.

Let's start at the very beginning.

Section 11 to one.

The text calls this what a bonding theory should do.

It sets the scene with the thought experiment.

So imagine we have two hydrogen atoms floating in a void, right?

Just simple items, one proton, one electron each.

And we imagine them infinitely far apart.

Infinitely far sounds a bit dramatic.

I mean, it just means they're far enough away that they don't know the other one exists.

There's no interaction, no force.

So by convention, we say the energy of this system is zero.

Okay.

Zero energy, clean slate.

Now we play god, we grab these atoms with molecular tweezers and we start pushing them closer together.

What happens?

Well, immediately a drama starts to unfold.

It's a tug of war between three different forces.

The text breaks this down in figure 11 to one.

Let's visualize that for the listener.

Who are the players in this tug of war?

Player one is the attractive force.

This is the good force.

The electron on atom A looks across the gap and sees the nucleus of atom B.

It sees that positive charge and thinks, oh, hello there.

Because opposites attract.

The negative electron wants to be near the positive proton.

Exactly.

And the same thing happens in reverse.

The electron from atom B sees the nucleus of atom A.

This mutual attraction pulls the atoms together.

It lowers the energy of the system.

In thermodynamics,

nature loves lower energy.

That's relaxing.

So that's the force pulling them into a hug.

But if that were the only force, wouldn't they just crash into each other and implode?

They would.

And that's where the other players come in.

You have the repulsive force.

The bad forces.

Right.

You have the two electrons.

They're both negative.

They hate each other.

They want to push apart.

And deep in the center, you have the two nuclei.

They're both positive, so they repel each other too.

So as I'm pushing these atoms together, I have attraction trying to snap them together and repulsion trying to push them apart.

It's a fight.

It is.

And we can see who wins by looking at the energy graph.

This is figure 11 to two in the text.

It plots energy versus distance.

Okay.

Let's paint this picture.

Imagine a graph.

The x -axis is distance.

Far right is far apart.

Far left is smashed together.

The axis is energy.

Correct.

So start on the far right.

Zero energy.

As we move left, as the atoms get closer, the line creates a curve that slopes downward.

It goes down.

Yes.

Down means stability.

It means the attractive forces are winning.

The atoms want to be closer.

The energy is dropping.

Okay.

So it drops and drops.

It's like rolling a ball down a hill.

Until it hits the bottom of the valley.

The potential energy well.

For hydrogen, this happens at a very specific distance.

74 picometers.

74 picometers.

That's the bond length.

That is the bond length.

At exactly that distance, the attractive forces and repulsive forces are perfectly balanced.

The system is at its lowest possible energy.

Specifically, it's at negative 436 kilojoules per mole.

And that negative number means energy was released, right?

Like a big sigh of relief.

Exactly.

To pull them apart again, you'd have to pay that energy back.

You'd have to put in 436 kilojoules to break the bond.

That's why we call it the bond dissociation energy.

Okay.

So we're at the bottom of the well.

Cozy and stable.

What happens if I keep pushing?

What if I try to force them closer than 74 picometers?

Look at the graph.

To the left of that well, the line doesn't just go up.

It shoots up vertically.

It hits a wall.

The wall of repulsion.

Yes.

If you get too close, the nucleus repulsion takes over completely.

The energy costs skyrockets.

You're basically trying to fuse the atoms, which requires the heat of a star.

Wow.

So a chemical bond is basically just atoms finding the Goldilocks distance.

Not too far.

Not too close.

That is the simple electrostatic view.

It's intuitive.

It makes sense.

Oh no.

Here comes the butt.

The text includes a section called a quantum mechanical concept.

It throws a wrench in this simple magnets attracting idea.

Because if you actually run the numbers using quantum mechanics, something weird happens with the energy.

Weird how?

Well, we usually think bond forms, things slow down, everything gets calm.

But the text says that when a bond forms, the kinetic energy of the electrons actually increases.

Wait, hang on.

Kinetic energy is the energy of motion.

You're saying the electrons speed up and they get stuck in a bond.

That sounds backwards.

I mean, if I'm stuck in a room, I'm not running a marathon.

It does sound backwards.

But think about the Heisenberg uncertainty principle.

Or actually think about a guitar string.

Okay.

I'm picturing a guitar string.

If you have a long loose string, the wave is long and lazy, low energy.

But what happens if you pin that string down?

If you force it into a smaller space?

It vibrates faster, higher pitch.

Exactly.

Electrons behave like waves.

When you form a bond, you are confining that electron wave to the tiny space between the two nuclei.

You're shortening its box.

So the electron starts vibrating frantically.

Effectively, yes.

Its wavelength decreases, which means its momentum and kinetic energy shoot up.

The electron is screaming, I'm too cramped in here.

So the kinetic energy is actually fighting against the bond.

It wants to blow the whole thing apart.

Correct.

The rise in kinetic energy is a destabilizing force.

Then why does the bond form at all?

If the electrons are freaking out, why don't they just leave?

Because the potential energy drops even more.

This is the key insight of the chapter.

It's called contraction.

Contraction, like shrinking.

Yes.

Figure 11 -3 shows this beautifully.

As the atoms approach, the electron cloud doesn't just sit there, it shrinks.

It contracts tightly around the nuclei.

The electrons get much, much closer to the protons than they were before.

And being closer proton is the electron's happy place.

It is its blissful place.

That drop in potential energy is massive.

It is so huge that it pays the bill for the increased kinetic energy and still leaves a giant profit of stability.

So it's a trade -off.

The electrons have to run faster, which they hate, but they get to live in a much better neighborhood, which they love.

That is a brilliant analogy.

The better neighborhood of low potential energy drives the bond formation.

Okay, I feel like I get the why now.

Energy wins.

Now we need to talk about the how.

This brings us to the first big theory of the chapter, section 11 -2, introduction to the valence bond method.

This is the bridge between the quantum stuff we just talked about and the pictures we draw.

Valence bond theory, or VB, basically says a bond is what happens when atomic orbitals overlap.

Overlap, okay.

So I have hydrogen A with its little spherical ones orbital, and hydrogen B with its spherical ones orbital.

They smash together.

They merge.

The spheres overlap in space.

And that overlapping region is where the electrons hang out.

But there's a catch.

You can't just shove any electrons in there.

The bouncer at the club has rules.

The rule is spin pairing, the Pauli exclusion principle.

You can only put two electrons in that overlap zone if they have opposite spins.

One up, one down.

If they're both spin up.

They repel.

No bond.

Okay, simple enough for hydrogen spheres, but atoms aren't all spheres.

The text uses hydrogen sulfide H2S to show how this works with more complex shapes.

Right.

Let's look at sulfur.

Sulfur is in the third row of the periodic table.

Its valence electrons, the ones doing the bonding, are in the 3P orbitals.

And orbitals don't look like spheres.

They look like dumbbells or peanuts.

Peanuts works.

And remember, there are three of them.

3Px, 3P, and 3Pz.

They oriented along the axis.

Up, down, left, right, forward, back.

So they're 90 degrees apart, like the corner of a box.

Exactly.

So if sulfur uses two of these peanut -shaped orbitals to bond with two hydrogen atoms, what angle would you expect the molecule to have?

Well, if the orbitals are 90 degrees apart and the hydrogens just stick to the ends of them, the bond angle should be exactly 90 degrees.

That is the prediction.

Now, we go to the lab.

We measure the actual bond angle of H2S.

And the answer is?

The text says 92 degrees.

92 is extremely close to 90.

I'd call that a win.

It is a win.

It tells us that for simple molecules like H2S, this idea of localized overlap works.

The sulfur uses the orbitals it was born with.

The electrons stay between the atoms.

The geometry matches the atomic parts.

So Valent's bond theory is looking pretty good.

It explains the bond.

It explains the shape.

Why do we need the rest of the chapter?

Because while H2S behaves, carbon does not.

Carbon.

The element of life.

And the element of headaches for early chemists.

This brings us to section 11 -3, hybridization of atomic orbitals, or as I like to call it, the crisis of methane.

Let's unpack the crisis.

Methane is CH4.

One carbon, four hydrogens.

We know this molecule exists.

It's natural gas.

We burn it.

But if you look at carbon's electron configuration, it shouldn't exist.

Help me through that.

Carbon is 2S2 2P2.

The 2's orbital is full.

It has two electrons.

The orbitals have two electrons total.

Because of Hund's rule, those two electrons are in separate orbitals.

So carbon has two unpaired electrons.

And generally, the number of unpaired electrons equals the number of bonds you can form.

Correct.

So simple valence bond theory predicts that carbon should form CH2.

But methane is CH4.

So the theory predicts the wrong formula.

That's a big problem.

It gets worse.

Even if you could somehow excite an electron to make four bonds, you are still using p orbitals.

And p orbitals are 90 degrees apart.

So methane should be shaped like a cross.

90 degree angles.

But methane isn't a cross.

It's a tetrahedron.

It's a tripod shape.

The angle is 109 .5 degrees.

Exactly.

So the simple overlap model fails twice.

It gets the formula wrong and it gets the shape wrong.

So did chemists just throw the theory in the trash?

No.

They tweaked it.

They realized that atoms might not keep the orbitals they are born with.

They might modify them to fit the situation.

This is hybridization.

It sounds like genetic engineering for atoms.

It's mathematical mixing.

Think of it as a blender.

To fix the methane problem, we do two steps.

First, we promote an electron.

We take one of those paired 2s electrons and kick it upstairs to an empty 2p orbital.

So now we have one electron in the s and three electrons in the p's.

That's four unpaired electrons.

Right.

That solves the CH4 formula problem.

But we still have the shape problem.

An s orbital is a sphere.

P orbitals are dumbbells.

If you bonded with those, you'd have one weird bond and three normal ones at wrong angles.

So we put them in the blender.

We mix the 1s orbital and the 3p orbitals together.

Mathematically, we average them out.

The rule is conservation of orbitals.

If you put four orbitals into the blender, you have to get four orbitals out.

Precisely.

We get four new identical orbitals.

We call them sp3 hybrid orbitals.

Sp3.

Because they are made of one s and three p's.

Chemists are not creative with names.

But here is the magic.

If you have four identical balloons tied together at a center point, how do they arrange themselves?

They push apart as much as possible.

In 3D space, the farthest they can get from each other is to point to the corners of a tetrahedron.

The angle is exactly 109 .5 degrees.

Boom.

It matches methane perfectly.

It matches perfectly.

Hybridization is essentially reverse engineering the orbitals to explain the shapes we see in the lab.

It feels a little like cheating.

Oh, the shape is a tetrahedron.

Let's just mix the orbitals until they look like a tetrahedron.

It is a bit cynical, but it works.

We use VSEPR theory, the electron counting method, to predict the shape first.

Then we choose the hybridization scheme that explains that shape.

Let's quickly run through the other flavors, because students definitely need to know these for the exam.

Methane was sp3.

What if I have a flat triangle shape?

Like boron trifluoride, bf3, or ethylene.

That's trigonal planar.

120 degrees.

To get three corners of a triangle, you need three orbitals.

So you mix one s and two p orbitals.

One s plus two p's equals sp2.

Correct.

You get three sp2 hybrids pointing in a flat triangle.

But here is the crucial detail that students often miss.

We started with three p orbitals in the atom.

We only put two in the blender.

So there is one left over.

Yes.

One unhybridized p orbital remains.

It sits there, untouched, sticking straight up and down, perpendicular to the flat triangle.

Okay.

I'm putting a pin in that.

The leftover p orbital.

That sounds important.

It is vital, but let's do the last of them.

Linear shapes.

Like beryllium chloride,

bcl2.

Straight line.

180 degrees.

To point in two opposite directions, I need two hybrids.

So I mix one s and one p.

One s plus one p equals sp.

You get two sp hybrids.

And since we only use one p orbital.

There are two p orbitals left over.

Exactly.

Sticking out sideways.

So the cheat code for students is just counting the electron groups or directions around the atom.

If it's four directions, sp3.

If it's three directions, sp2.

If it's two directions, .sp.

That is the cheat code.

It works practically every time in general chemistry.

Okay.

Let's go back to those left over.

The unhybridized p orbitals.

Section 11 to four says these are the secret to multiple covalent bonds.

Double and triple bonds.

They are.

This is where we distinguish between the two types of connections.

Sigma bonds and pi bonds.

The outline we have uses a great analogy here.

The handshake and the high five.

It works perfectly.

Let's talk about the sigma bond first.

It's what we've been describing so far.

It's end to end overlap.

So imagine two people walking up to each other and shaking hands.

The connection is directly between them.

Right.

The electron density is concentrated right on the line connecting the two nuclei.

All single bonds are single bonds.

They are strong, direct connections.

And like a handshake, you can rotate, right?

I'm shaking your hand.

I can walk around you, pivot, do a pirouette, my arm twists, but the connection holds.

Exactly.

Single bonds allow for free rotation.

This is huge for how molecules move in space.

Now the pi bond, this is the double bond.

To form a double bond, you need that leftover orbital we talked about in Zip -D2 hybridization.

Imagine two carbon atoms shaking hands.

That's the sigma bond.

But they each also have a orbital sticking straight up and down.

Standing parallel to each other.

Since they are standing side by side, they can lean in and overlap.

They touch above and below the handshake.

So it's a high five.

It's a high five and a low five at the same time.

The electron density is in two lobes.

One arching over the top, one scooping under the bottom.

That sounds encompassing.

It is.

This side to side overlap is the pi bond.

So a double bond, like an ethylene C2H4, is one handshake, the sigma plus one, high five the pi.

Now think about the rotation.

If I'm shaking your hand and high fiving you at the same time.

You are locked.

I can't spin.

If I try to spin away, I break the high five.

Exactly.

Pi bonds create rigidity.

Double bonds make molecules flat and stiff.

You cannot rotate around a double bond without breaking the interaction, which costs a lot of energy.

This is actually why our eye's work retinal sensing light relies on a double bond breaking and twisting.

That is so cool.

So logic follows.

A triple bind, like acetylene C2H2, is one handshake and...

One handshake sigma and two pi bonds.

Remember the hybrid has two leftover orbitals.

One is up down, one is in out.

So you have a high five, a low five, and a side five.

Essentially, you have overlap above and below and front and back.

It creates a cylinder of electron density wrapping around the middle.

It's incredibly strong and rigid.

Man, valence bond theory is killing it.

We have shapes, we have single double and triple bonds, we have restricted rotation.

It feels like a complete theory.

Why isn't the chapter over?

Why is there a section 11 to 5?

Because of the blue liquid.

Right.

The oxygen thing.

Here is the problem.

If you draw the Lewis structure for oxygen O2, or use valence bond theory, you draw a double bond, O equals O.

Everyone has an octet.

Every electron is paired up.

It looks perfect on paper.

In chemistry, as all your electrons are paired, you are diamagnetic.

That means you should be weakly repelled by a magnet.

If you poured liquid oxygen past a magnet, it should just flow right by.

But the experiment shows that it doesn't.

It sticks.

It is paramagnetic.

That means it is attracted to the magnet.

And the only way, the absolute only way something can be paramagnetic is if it has unpaired electrons.

But valence bond theory says they're all paired.

I can literally see them paired up on the drawing.

And that is why valence bond theory fails.

It gives the wrong answer for one of the most common elements in the universe.

We need a better map.

We need molecular orbital theory, or MO theory.

This is the part of the chapter that scares students.

It looks like calculus.

It looks scary, but the core concept is actually philosophical.

Valence bond theory is possessive.

It says this is my orbital, that is yours, and we touch.

Mine and yours.

MO theory says no.

The moment two atoms bond, they lose their individual identity.

Their atomic orbitals, the S, the P, dissolve.

They dissolve.

They merge to form new molecular orbitals that belong to the entire molecule.

The electrons don't belong to Oxygen A or Oxygen B anymore.

They belong to the molecule O2.

They roam the whole apartment complex.

Okay, so how do we build these new orbitals?

We use a method called LCAO, linear combination of atomic orbitals.

It's based on waves.

Constructive and destructive interference.

Yes.

Think of the atomic orbitals as waves.

If you bring two waves together and the peaks line up.

They amplify.

You get a bigger wave.

That is a bonding molecular orbital.

It creates a buildup of electron glue between the nuclei.

It is stable.

It has lower energy than the separated atoms.

We denote it with a sigma or a pi, depending on the overlap.

Okay, but waves can also cancel out.

If a peak meets a trough, they destroy each other.

You get zero amplitude.

A dead spot.

A node.

Yeah.

A region with zero electron density.

If this happens between the nuclei, the positive protons are just staring at each other with nothing in between to buffer them.

They repel violently.

That sounds really bad.

It is high energy.

Unstable.

We call this an anti -bonding molecular orbital.

We mark it with a little star or asterisk.

So every time atoms come together, they create both.

A let's stay together orbital and a let's break up orbital.

Yes.

Conservation of orbitals again.

If you mix two atomic orbitals, you must get two molecular orbitals.

One bonding lower energy and one anti -bonding higher energy.

So why do bonds form at all if we're creating breakup orbitals every time?

Because electrons are lazy.

They fill the lowest energy buckets first.

Take hydrogen, H2.

Two electrons total.

They both hop into the bonding orbital.

The anti -bonding orbital stays empty.

So you have two stabilizers and zero destabilizers.

The bond holds.

Exactly.

We calculate the bond order.

The formula is simple.

Number of bonding electrons minus number of anti -bonding electrons all divided by two.

For each two, that's two minus zero divided by two equals one.

Single bond.

What about helium?

H2.

Why doesn't helium gas form molecules?

Helium has two electrons each.

Four total.

The first two go into the bonding orbital.

Great.

But the next two, there's no room.

They have to go into the anti -bonding orbital.

Oh.

So you have two distinct glues and two distinct anti -glues.

Two minus two is zero.

Divided by two is zero.

Bond order zero.

The stabilizing force is perfectly canceled by the destabilizing force.

The molecule falls apart before it can even form.

That is why heat, too, does not exist.

That is surprisingly elegant.

The math just says, nope.

It is beautiful.

But the real triumph is oxygen.

This is the climax of the chapter.

Figures 1121 and 1126.

OK.

I'm looking at the diagram for O2.

We are mixing the orbitals of oxygen.

We have 12 valence electrons to place in this new apartment complex.

Right.

We fill the bottom floors first.

The bonding sigma is full.

The bonding pi orbitals are full.

We work our way up the energy ladder.

When we get to the top, we have two electrons left to place.

And the next available orbitals are the anti -bonding pi orbitals, the ones with the star.

Correct.

And here's the key.

There are two of these anti -bonding pi orbitals, and they are at the exact same energy level.

Like bunk beds.

Like two empty seats on a bus.

Yeah.

Hun's rule applies.

If you are getting on a bus and there are two empty rows, do you sit right next to a stranger?

No.

I take my own row.

Exactly.

Electrons do the same thing.

One electron goes into the first anti -bonding orbital.

The other electron goes into the second anti -bonding orbital.

They remain separate.

So they are unpaired.

They are unpaired.

The math demands it.

Valence bond theory tried to force them to hold hands.

MO theory shows that energetically, they prefer to sit in separate chairs.

And unpaired electrons means?

Paramagnetism.

MO theory correctly predicts that liquid oxygen is magnetic.

It explains what valence bond theory simply could not.

That is a mic drop moment for molecular orbital theory.

It really is.

It shows that while sticks and lines are useful, they aren't the whole truth.

So does MO theory explain anything else?

Section 11 -6 talks about delocalized electrons.

This is a huge concept for organic chemistry.

Remember benzene?

C6H6.

It's a ring of six carbons.

The classic hexagon.

Usually drawn with alternating double and single bonds.

Right.

The Kekuli structure.

Yeah.

But there's a problem.

Double bonds are short.

Single bonds are long.

If that drawing were true, benzene would look lopsided.

A wonky hexagon.

But experimentally, it is a perfect hexagon.

All bond lengths are identical.

So we used to say, oh, it resonates.

It flips back and forth really fast.

Which is a terrible analogy.

It's not flipping.

It's a mule.

A mule?

A mule is a hybrid of a horse and a donkey.

It isn't a horse one second, a donkey the next.

It is a mule all the time.

Benzene is the same.

It isn't flipping between double and single.

It is a hybrid.

How does MO theory explain the hybrid?

Imagine the six carbons.

Each has a p orbital sticking up.

Instead of pairing off A with B, C with the MO theory says, let's combine all six.

A mega orbital.

Yes.

The six p orbitals merge to form a continuous ring of electron density above and below the carbon plane.

Like a donut.

Exactly like a donut sandwich.

A donut of electrons on top, a donut on the bottom.

The electrons are free to run around the entire ring.

They are delocalized.

And being able to roam makes them stable.

Extremely.

Confined electrons are anxious.

Remember, kinetic energy.

Delocalized electrons have room to stretch out.

Their wavelengths get longer.

Their energy drops.

This is why benzene is so chemically bulletproof.

That makes perfect sense.

The smear is more stable than the stick.

Precisely.

And the text notes, this applies to other things too.

Like the nitrate ion in O3 or ozone O3.

The extra electron pairs aren't stuck.

They're smeared across the molecule, which equalizes the bond lengths.

We are in the homestretch here.

Section 11 -7 deals with unresolved issues.

Because science is never actually finished.

The topic is expanded octets.

Oh yes.

The molecules that break the rules.

Take sulfur hexafluoride, SF6.

Sulfur's in the middle.

Six fluorines are attached.

If every bond has two electrons, that's twelve electrons around sulfur.

But the octet rule says eight.

Twelve is definitely not eight.

For decades, the textbook explanation, which I taught for years actually, was that sulfur is in the third period.

It has empty deorbitals.

It uses those deorbitals to store the extra electrons.

But it expands its attic to fit more junk.

This P3D2 hybridization.

That was the story.

But recently, advanced computer modeling has called this a bluff.

The calculations show that deorbitals are way too high in energy.

It would cost sulfur a fortune to actually use them for bonding.

It just doesn't make thermodynamic sense.

So if sulfur isn't using deorbitals, how is it holding onto six fluorines?

The modern view is slightly controversial but compelling.

It suggests we stop looking at it as purely covalent sharing.

Look at figures 1136 and 1137, the electron density maps.

Okay, what are they showing?

They look at bond critical points.

Fluorine is incredibly electronegative.

It pulls electrons like a vacuum.

So maybe the bonds in SF6 are actually significantly ionic.

So it's not sharing twelve electrons.

It's more like a positive sulfur ion surrounded by six negative fluorine ions held together by electrostatic attraction.

With some covalent character, yes.

The text argues that we should start trying to force expanded octets with deorbitals just to make the formal charges look pretty.

The rule of eight, the octet rule is actually very robust.

When it looks like it's broken, it's usually because the bonding is highly polar.

More ionic than we admit.

I find that comforting.

The octet rule is still the king.

It is the rule of two, the pair, and the rule of eight that govern the chemical world.

Everything else is just us trying to force our models onto reality.

Okay, wow.

We have covered a massive amount of ground today.

We went from H2 in a void to the energy well to shaking hands and high -fiving.

We mixed orbitals in a blender.

We solved the magnetic mystery of oxygen.

And finally, we looked at the donut of benzene.

It's a complete journey from the simplest bond to the most complex theories.

For the student listening to this while walking to their exam, what is the big takeaway?

Which theory is actually true?

They are all true in their own domain.

Think of them as maps.

If you want to drive across the country, you use a road map.

That's your Lewis structure.

It shows connections.

If you want to see the terrain, the mountains, and valleys, you use a topographical map.

That's VSPPR and hybridization.

But if you want to drill for oil or understand the magnetic field of the earth, you need a geological survey.

That is molecular orbital theory.

You don't use a geological survey to find the nearest gas station.

Exactly.

The skill of a chemist is not knowing one theory perfectly.

It is knowing which tool to pull out of the toolbox for the problem in front of you.

I love that.

Use the right tool for the job.

Well, thank you for being our guide through the quantum jungle today.

My pleasure.

It's a fascinating place to live.

And to you, the listener, thanks for sticking with us through the nodes and antinodes.

Before we go, just think about this.

If we can map the electron density of simple molecules like SF6 to find out they're more ionic than we thought, what happens when we start applying these computer models to massive proteins in our own bodies?

The maps are only going to get better.

We hope your next chemistry exam feels a little less like a destructive interference and more like a bonding moment.

This has been the Last Minute Lecture Team.

Signing off.

Bye -bye.