Chapter 11: Theories of Covalent Bonding

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Ever wondered what actually holds everything together?

I mean, really holds it together.

We're talking about the invisible glue shaping our world from, you know, simple water to the complex proteins in our bodies, chemical bonds.

It's absolutely foundational.

But how do these tiny, energetic atoms actually stick to one another?

Today we're doing a deep dive right into that question, our mission.

To sort of simplify a really crucial chapter from chemistry, the molecular nature of matter and change by Silberberg and Ametest, think of this as your shortcut, maybe, to understanding not just what bonds are, but really how they form, and crucially, why they dictate so much around us.

We'll be pulling back the curtain on two big ideas, valence bond theory, VB theory, and molecular orbital theory, or MO theory.

Yeah, and it's fascinating because no single model perfectly captures everything about chemical bonding.

It's like having different lenses, you know.

Each theory helps us see specific details, and really, together, they give us a much more complete picture.

VB and MO theories, they aren't fighting each other, they're complementary.

Each one is just better at explaining certain things.

Take metric oxide, NO, tiny molecule, really reactive, vital in our bodies, actually.

But it's properties, especially, like its magnetic behavior.

You really need both theories to fully get what's happening there.

Okay, let's start with valence bond theory then, our first lens, it gives a pretty intuitive picture, I think.

Basically, VB theory says a covalent bond forms when atomic orbitals, those electron cloud regions from two atoms, literally overlap in space.

Like picture two clouds just verging into one bigger shared cloud.

Exactly, and in that shared space, a pair of electrons moves in.

But here's the key detail.

They have to have opposite spins,

paired spins.

That comes straight from the Pauli exclusion principle, which basically says no two electrons can be in the exact same state, they need their own unique quantum address.

So for hydrogen forming H2, their ones orbitals overlap, the two electrons pair up with opposite spins and hang out in that shared zone, that's the bond, and the strength of that bond.

Fundamentally, it comes down to how much overlap you get.

More overlap, stronger bond.

Simple as that.

The nuclei are more attracted to that dense electron region between them.

You see it in HF with hydrogen's orbital overlapping fluorine's p orbital, or in F2 with two p orbitals meeting end to end, maximize the overlap.

Okay, that makes sense for simple bonds, H2, F2, HF.

But here's where it gets a bit weird, or at least needs more explanation.

Carbon's p orbitals, they're naturally at 90 degrees to each other, right?

So why is methane CH4 this perfect symmetrical tetrahedron shape with 109 .5 degree angles?

It seems like the atoms are doing some kind of geometry trick.

That's exactly the puzzle Linus Pauling tackled with, well, his brilliant idea of hybridization.

It's a mathematical concept, really.

You take the atom's original orbitals, s, p, sometimes d, and you mathematically mix them, blend them together, and you get these new equivalent hybrid orbitals.

They're not s or p anymore, they're hybrids.

And their shapes and directions in space perfectly match the geometry we actually see in molecules.

And the neat thing is, the number of hybrid orbitals you make always equals the number of atomic orbitals you started with.

So you mix one s and three p's, you get four sp3 hybrids.

And their shapes, they're optimized for the best possible overlap, meaning stronger, more stable bonds, the atom is sort of rearranging its electron clouds to bond better.

So this hybridization, this molecular shape shifting,

how does it explain the shapes we actually see?

Let's walk through the common types.

Okay, first up, mix one s and one p orbital.

What do you get?

You get spa hybridization, two hybrid orbitals pointing 180 degrees apart, that means a linear geometry.

Ah, like in beryllium chloride, BCL2.

The beryllium uses p hybrids, making it linear.

Makes sense.

Okay, next, mix one s and two p orbitals.

Now you've got sp2 hybridization, that gives you three hybrid orbitals, all in a flat plane, 120 degrees apart, think trigonal planar.

Boron trifluoride, bf3, fits that perfectly.

Exactly.

And lone pairs can sit in these hybrid orbitals too, like an ozone 03.

The central oxygen is sp2, but one hybrid holds a lone pair, giving that bent shape.

And the most common one, probably, sp3 hybridization, that's one s and all three p orbitals mixing.

Yep, that generates four identical tetrahedral hybrid orbitals pointing out at 109 .5 degrees.

Methane, CH4, the classic example, that explains the 109 .5 degree angles perfectly.

And not just methane, this is crucial.

It explains why ammonia, NH3, has angles around 107 degrees and water, H2O, around 104 .5 degrees.

If they just used their unhybridized p orbitals, the angles would be 90 degrees.

Hybridization explains why they're much closer to the tetrahedral angle, even with lone pairs squeezing things a bit.

And for bigger atoms, period three and below.

Alright, they can use d orbitals too, so you get sp3 hybridization, five orbitals pointing towards the corners of a trigonal bipyramid, like in PCL5.

Or even sp3d2 hybridization for six orbitals in an octahedral arrangement, like SF6.

It just extends the idea.

Now, it's important to add a little note here.

Hybridization is an incredibly useful model, really powerful for visualizing shapes.

But it's not, you know, the absolute final word, it's a model.

For example, take hydrogen sulfide, H2S.

Its bond angle is about 92 degrees.

That's actually really close to the 90 degrees between unhybridized p orbitals.

So maybe for some larger hydrides, hybridization isn't the best explanation.

Maybe simple p orbital overlap is closer to the truth.

And there's also some ongoing debate based on more advanced calculations about how much d orbitals really participate in hybridization for those expanded updates.

We still use the sp3d2 models, because they work incredibly well for predicting shapes.

But yeah, it's good to remember models evolve.

That's a really good point.

Models are tools, not absolute reality.

Okay, so hybridization explains how atoms arrange orbitals for shape.

But how do those orbitals actually connect?

Because you said not all overlaps are the same.

Exactly right.

There are two fundamental ways orbitals can overlap, leading to two main types of covalent bonds.

First, sigma bonds, written SU.

These form from end -to -end overlap.

Think of it like a head -on collision.

The main electron density lies directly on the line connecting the two nuclei.

It's like a sausage shape along the bond axis.

All single bonds are sigma bonds.

In ethane, C2H6, that central C -C bond is a sigma bond from sp3 overlap.

And each CH bond is a sigma bond from SICV3's overlap.

Okay, then there are pi bonds written.

These form from side -to -side overlap, usually of unhybridized p orbitals.

Unlike sigma bonds, the electron density in a pi bond isn't on the axis.

It's in two regions, one above the axis and one below it.

Like two clouds sandwiching the sigma bond.

Ah, okay.

So that's how we get multiple bonds.

A double bond must be.

One sigma bond and one pi bond.

Always.

Like in ethylene, C2H4, the carbons are CYSP2 hybridized.

So the C -C connection starts with an sp2 -sp2 sigma bond.

Correct.

And then the leftover unhybridized p orbitals on each carbon, standing perpendicular to the molecular plane, overlap side -to -side.

That's your pi bond.

And a triple bond, like in acetylene, C2H2.

That's one sigma bond plus two pi bonds.

In acetylene, the carbons are CERDI hybridized.

They form a sigma bond using CYSP overlap along the axis.

Then each carbon has two remaining unhybridized p orbitals, perpendicular to each other and to the bond axis.

They overlap side -to -side in pairs.

One pair forms a pi bond above and below.

The other forms a pi bond in front and back.

Wow.

So it makes like a cylinder of electron density around the sigma bond.

Exactly.

Cylindrical symmetry.

Now this difference between sigma and pi bonds, it has huge consequences.

Really important ones.

Sigma bonds.

Because the overlap is end -to -end along the axis, you can usually rotate freely around a single sigma bond.

The overlap isn't really affected.

Think about ethane again.

One CH3 group can spin relative to the other.

Okay.

Yeah, like wheels on an axle.

Right.

But pi bonds, they restrict rotation.

Why?

Because that side -to -side overlap depends on the orbitals being parallel.

If you try to twist the molecule around the double bond axis, you break that parallel alignment.

You break the pi bond.

Wow.

So you can't easily rotate around a double or triple bond.

Precisely.

And that's why we have things like cis and trans isomers for molecules like 1 -F2 -dichloroethylene.

The chlorine atoms are either stuck on the same side, cis or opposite sides, trans, of the double bond.

And those isomers, they can have totally different properties, polarity, boiling points, reactivity, even how they interact in biological systems, all because that pi bond locks the rotation.

It's fundamental to molecular identity and rigidity.

Okay, so V -B theory with hybridization and sigmopy bonds gives us a really good framework for localized bonds and shapes.

It's very visual.

But you mentioned earlier, what about things like, why is liquid oxygen magnetic?

The Lewis structure looks fine.

All electrons seem paired.

Or how do electrons sometimes seem spread out over a whole molecule, not just stuck between two atoms?

V -B theory doesn't handle that so well, does it?

It struggles, yeah.

That's where we need our second lens.

Molecular orbital, or MO theory.

This is a, well, a more sophisticated quantum mechanical approach.

It shifts the whole perspective, the absolute key difference.

V -B theory thinks of electrons as localized in bonds between two atoms, using overlapped atomic or hybrid orbitals.

MO theory says, no, electrons are delocalized.

They occupy molecular orbitals, MOs, that can spread over the entire molecule.

These MOs belong to the molecule as a whole.

Okay, so instead of atomic orbitals overlapping, we're making completely new molecular orbitals.

How does that work?

It's based on combining the wave functions of the original atomic orbitals.

Mathematically, you can add them or subtract them.

When the wave functions add constructively, you get a bonding MO.

This MO has lower energy than the original atomic orbitals, and it has increased electron density between the nuclei.

This pulls the nuclei together, stabilizes the molecule.

By constructive interference of waves.

Exactly.

And when the wave functions subtract or interfere destructively, you get an antibonding MO.

This MO has higher energy, and critically, it has a node, a region of zero electron density, right between the nuclei.

This actually pushes the nuclei apart, destabilizing the molecule.

Destructive interference.

Precisely.

And for every pair of atomic orbitals you combine, you always get two molecular orbitals.

One bonding, lower energy, and one antibonding, higher energy.

Then, once you have your set of molecular orbitals for the molecule, you fill them with the available electrons using the same rules as for atoms.

Aufbau principle, lowest energy first.

Pauli exclusion principle, max two electrons per MO.

Opposite spins.

Hund's rule, fill orbitals of equal energy singly first before pairing them up.

Okay, same filling rules.

And what does that tell us?

It lets us calculate the MO bond order.

It's simple.

Take number of electrons in bonding MOs minus number of electrons in antibonding MOs, and divide by two.

Bond order was half bonding E, antibonding E.

This number predicts if the molecule is stable.

If bond order zero, it should exist.

Higher bond order means a stronger bond.

So it gives a quantitative measure of stability and strength.

Yes, and it works beautifully.

For instance, MO theory correctly predicts why helium gas exists as atoms, not HETO molecules.

The calculation gives HETO a bond order of zero.

Two electrons in bonding, two in antibonding, cancels out.

But what about the HETO plus ion?

Take one electron away.

Now you have two bonding and only one antibonding.

Bond order is URAF2.

Raffalovia is 0 .5.

It's weak, but it can exist.

And it does.

MO theory explains that perfectly.

That is powerful.

So let's apply it.

What about those diatomics from period two, like N2, O2, F2?

Okay, looking at period two.

First, the S block ones.

Lie two.

MO theory gives it a bond order of one.

Stable exists.

B2, bond order zero, doesn't exist.

Matches reality.

Now, moving to the P block, where things get a bit more involved.

The P atomic orbitals combine to form both sigma and pi MOs.

There's actually a neat complication for the lighter ones.

B2, C2, N2.

It's called SP mixing.

The twos and 2P atomic orbitals are close enough in energy that they interact.

And this actually flips the energy order of the sigma 2P and pi 2P molecular orbitals compared to what you might initially expect.

It's a subtle but important effect.

Okay, but oxygen O2, you said MO theory explains its magnetism.

This is the big one.

This is the classic success story for MO theory.

Lewis structures fail here.

VB theory struggles.

But MO theory, it nails it.

When you fill the MO diagram for O2, following Hunn's rule, the last two electrons go into two degenerate, meaning equal energy 2P anti -bonding orbitals.

And crucially, they go in unpaired with parallel spins.

One electron in each orbital.

Unpaired electrons, that means.

Paramagnetism, exactly.

Because of those two unpaired electrons spinning the same way, O2 interacts strongly with a magnetic field.

It's attracted to it.

Wow, you can actually see liquid oxygen clinging between the poles of a magnet because of where MO theory places those last two electrons.

That's right.

It's a direct observable consequence beautifully explained by the MO diagram.

Now contrast that with N2.

Its MO diagram shows all electrons are paired and the bond order is three.

Explains its incredible stability and triple bond strength and why it's diamagnetic, repelled by magnetic fields.

That's genuinely cool.

Okay, so MO theory clearly works wonders for identical atoms.

What about molecules with different atoms like HF or NO?

Good question.

For these heteronuclear diatomics, the MO diagrams become asymmetric.

Why?

Because the atomic orbitals of different elements start at different energy levels.

A more electronegative atom, like fluorine and HF, has lower energy atomic orbitals than hydrogen.

So when they combine to form MOs, the bonding MO ends up being closer in energy to fluorine's AOs and the antibonding MO is closer to hydrogen's AO energy.

So the diagram itself shows the electron density shift towards the more electronegative atom.

Exactly.

It reflects the polarity of the bond.

And for NO revisiting that one, MO theory gives it a bond order of 2 .5 stronger than a double bond, weaker than a triple, which matches experiments better.

And importantly, it shows one unpaired electron in a patty bonding orbital.

Confirms its paramagnetism and explains its reactivity with that odd electron being located more towards the nitrogen, the less electronegative atom.

And what about really big molecules?

You mentioned benzene, ozone, the ones where VB theory needs resonance structures.

MO theory handles those beautifully, too, through electron delocalization.

It doesn't need multiple resonance drawings.

It just describes extended pi systems.

For benzene, MO theory pictures the six pi electrons occupying molecular orbitals that spread out over the entire ring of six carbon atoms.

You get these donut -shaped electron clouds, one above and one below the plane of the ring.

A single picture instead of two resonance structures flipping back and forth.

Exactly.

Same for ozone.

The pi electrons are delocalized over all three oxygen atoms in specific MOs.

This delocalization inherently explains their extra stability, their bond lengths being intermediate between single and double, and even things like how they absorb UV light.

It's a more unified and arguably more accurate picture for these systems.

Wow.

Okay, so let's recap this journey.

We've really covered a lot of ground here.

You, listening, have just taken a deep dive into, well, the very fabric of how molecules stick together.

We started with valence bond theory, great for visualizing individual bonds as overlaps.

We saw the power of hybridization in explaining molecular shapes, those geometries we see, and how sigma and pi bonds give us single, double, and triple bonds with different properties like rotation.

And then we brought in molecular orbital theory, a different perspective, looking at electrons spread across the whole molecule.

It gave us answers for things VB couldn't easily explain, like oxygen's magnetism, and gave us this elegant idea of delocalization.

And it's crucial to remember, like we said at the start, these aren't competing theories fighting for dominance.

They're complementary.

They're different tools in the chemist's toolkit.

Each gives us unique insights.

VB is often easier to visualize for structure.

MO is often better for energies, magnetism, and delocalized systems.

You use the tool that best fits the question you're asking about the intricate dance of electrons and nuclei.

Absolutely.

And as you continue studying chemistry,

thinking about these models really helps.

It allows us to predict how molecules might react, how we can design new materials with specific properties, even understand the fundamental chemistry of life itself.

It's really foundational stuff.

So maybe a question to leave you with is, how might these models evolve even further?

With increasingly powerful computers, we can do much more complex quantum calculations now.

How might those calculations refine or even challenge our current understanding of bonding, pushing beyond even these sophisticated VB and MO models?

What's the next conceptual leap?

Food for thought, definitely.

Well, thank you so much for joining us on this deep dive into the fascinating world of chemical bonding.

We really hope this has given you a clearer, maybe more engaging perspective on the molecular world all around us.

This has been a deep dive brought to you by the Last Minute Lecture Team.