General Chemistry Advanced Bonding Theories

Hi, welcome back to Educator.com.0000

Today's lesson in general chemistry is going to be advanced bonding theories.0003

We are going to start off with a brief introduction as to why0010

we need these advanced bonding theories from what we already know.0015

That was really Lewis structures.0019

Pretty much the advanced bonding theories that we are going to be talking about are the following.0022

One is what we call valence bond theory.0026

The second one is what we call molecular orbital theory.0030

We will wrap up the session with a brief summary followed by a pair of sample problems.0033

What you and I have already discussed is the representation of valence electrons schematically.0041

Remember that is what we called Lewis structures.0050

We went through a step by step procedure on how to formulate a valid Lewis structure.0052

Lewis structures are sufficient because using VSEPR theory we were able to0058

come up with some predicted geometries strictly off of the Lewis structure.0067

But there exists really two main problems with Lewis theory that we never talked about before.0076

The first main problem has to do with magnetism.0082

If you noticed that all of the Lewis structures that we looked at, all electrons are paired.0087

They are either in a single bond, double bond, or triple bond for electrons.0093

And they are either in a lone pair.0098

If all electrons are paired, then we would expect everything to be diamagnetic.0101

But as we all know, that is not the case.0108

There is definitely more than enough compounds that are paramagnetic,0110

meaning that they do have at least one unpaired electron.0116

Lewis theory does not account for magnetic behavior.0119

A second problem with Lewis theory is the following.0124

Consider all of the compounds that we looked at.0130

For all of the compounds really, the valence shell has been the p orbital.0133

We looked at p orbitals before.0139

They were pretty much three p orbitals per energy level--p_x, p_y, and p_z.0141

We actually graphed them.0148

We saw that because of Cartesian coordinates, the p_x, p_y,0150

and p_z orbitals are going to be perpendicular to each other.0154

If you have nothing but 90 degree angles, how do we get 109.5?0159

How do we get 120, etc?0166

Lewis theory doesn't really account for all of the bond angles that are expected from VSEPR theory.0175

We do need advanced additional bonding theories to make up for the flaws of Lewis theory.0189

Valence bond theory is what we call a localized bonding model.0198

What localized means is the following.0203

It is that an atom's atomic orbitals are going to be0205

centered around that specific atom when forming covalent bonds.0209

In other words, you can think of a specific atom owning0213

those electrons rather than being distributed throughout the entire molecule.0218

Again that is what we call localized bonding model.0224

In order to achieve bond angles that are other than 90 degrees,0227

like 120, like 109.5, what valence bond theory suggests is the following.0231

It is that an atom's valence orbitals begin to overlap each other.0239

When they begin to overlap, they mix.0245

They begin to form these mixtures, these combinations of atomic orbitals which we call hybrids or hybrid orbitals.0248

What we are going to do first is we are going to take a look at one type of hybrid orbital.0260

The first type is what we call an sp3 hybridized carbon atom.0264

We go ahead and look at carbon.0270

What this sp3 means is that we have one s orbital mixing with three of carbon's p orbitals.0272

We can go ahead and show that; let me do that in a different color.0286

If I have a carbon s orbital mixing with a p orbital of carbon, we are going to get a hybrid orbital.0290

A hybrid orbital is going to have both s character and p character.0302

But it is going to be mostly p character because it is one s orbital versus three p's.0307

We are going to get a small lobe representative of the s orbital.0313

We are going to get a much larger lobe that is representative of the p orbital.0319

This is what we call a hybrid orbital.0326

Now that we know what the hybrid orbitals look like, they are going to be centered around the carbon atom.0329

Remember it is what we call a localized bonding model.0335

We are going to have the s orbital right in the middle, closest to the nucleus remember.0338

There is going to be one hybrid here; one hybrid here.0343

One hybrid here; one hybrid just in the back.0347

As you can see the way we have drawn it,0352

if you connect the vertices, we do indeed get a tetrahedron.0355

The concept of hybrid formation allows us to get these bond angles that are predicted by VSEPR theory.0366

Let's go ahead and put that into practice now.0375

Now that we physically have a sense of what a hybrid orbital can quote unquote look like.0378

Sp3 first, we are going to first start paying attention to what the superscripts mean.0385

The superscript tells us actually a great deal.0391

In sp3, there is a superscript of 1 for the s orbital.0395

There is a superscript of 3 for the p orbital.0400

What that translates to is the following.0403

That one s orbital mixes with three p orbitals to form the0405

sp3 hybrids just like we have seen in the previous slide.0412

But the question is how many hybrids do we form?0416

Again we turn to the sum of the superscripts to help us answer that.0419

Basically the sum of the superscripts equals to the number of hybrid orbitals that are going to form.0426

When you look at sp3, the sum of the superscripts is four.0435

That is why we form four hybrid orbitals.0439

For example, let's go ahead and take a look at water0445

and see how hybridization can help to explain for bonding.0452

Water has the following structure--the central oxygen, H, and two lone pair.0457

Once again the number of electron groups, it is going to be the same as the sum of the superscripts.0467

Here we have four electron groups surrounding oxygen.0491

There is going to be a total of four for the sum of the superscripts.0494

That is going to be sp3.0499

We are going to over other hybridization what we call schemes.0500

Sp3 is the first one; this is sp3 hybridization.0505

We can show this in an energy level diagram; energy.0511

Here the sp3 hybridized atom is going to be the oxygen.0517

Oxygen starts off as 2s and then 2p.0522

Let's go ahead and fill in the electrons now.0527

Oxygen is going to be 2s² and 2p⁴; this is just atomic oxygen by itself.0532

But as soon as oxygen hooks up with those two hydrogens to form water, its atomic orbitals are going to hybridize.0542

Again we are going to form a total of four sp3s.0550

Where are those four going to form?0554

Are they going to form higher in energy than the 2p's?0556

Are they going to be less than the energy of the 2s's?0559

Or are they going to be intermediate?0564

It turns out that we are going to compromise.0567

We are going to have an energy that is going to be intermediate for the entire system.0570

We form four sp3 hybrid orbitals now.0577

When we go ahead now and fill electrons, let's go ahead and fill it.0581

I have a total of six electrons--one, two, three, four, five, and six.0584

When we do this successfully, the overall picture should agree with the Lewis structure.0593

Guess what?--just like the Lewis structure which has two lone pairs around the oxygen,0599

we have one lone pair here and one lone pair here.0604

What do you think these two electrons are?0608

We have two hydrogens bonded to the oxygen.0612

These are going to be bonding electrons with H right here.0616

These electrons go on to form a single bond with the hydrogen; form single bond with H.0629

We now introduce a new terminology.0642

A single bond in terms of valence bond theory is a specific type of bond we call a σ bond; σ bond.0645

When we go ahead and redraw water, H, H, and O, we are going to see that0657

the lone pairs, they are going to exist in sp3 hybrid orbitals of oxygen.0667

We are going to have another sp3 here and another sp3 here, each containing one electron.0676

Those sp3 orbitals are going to overlap and mix with the hydrogen 1s orbitals which also have one electron.0689

Same thing here; that is what we call a σ bond.0698

Again we get the very important term, what we call a σ bond, from valence bond theory.0706

Let's go ahead and look at one more example of an sp3 hybridized atom.0717

The example I would like to look at is ammonia, NH₃.0727

Step one is always do the Lewis structure.0735

Here the Lewis structure for ammonia is going to be here just like that.0742

It is going to be three electron groups plus a lone pair0751

giving you a total of four electron groups around the nitrogen atom.0755

Remember the number of electron groups equals to the sum of the superscripts so this is also sp3.0760

Step two, we are going to now come up with our bonding scheme0771

and show the formation of these hybrids; show hybrid formation.0776

Hopefully again when we are done with this, we can correlate it with the Lewis structure.0785

Draw your energy diagram again; there is energy.0801

Nitrogen, just bare atomic nitrogen, is going to be 2s² and 2p³.0807

But as soon as the nitrogen starts to form bonds with hydrogen to form ammonia, it is going to mix.0818

It is going to form again four sp3 hybrid orbitals.0827

Let's go ahead and put the electrons in.0833

I have a total of five electrons--one, two, three, four, and five.0835

Let's go ahead and see if we can correlate it with the Lewis structure.0842

The Lewis structure has one lone pair.0846

The lone pair is right there; that is so far so good.0849

You notice that there is three single bonds with hydrogen.0853

Remember we call the single bond a σ bond.0856

σ here, σ here, and σ here; guess what?0859

We have three electrons that are each going to form a σ bond with the hydrogen.0862

Once again they each form a σ bond with a hydrogen 1s atomic orbital.0870

Good, we have a pretty good understanding now of what we mean by sp3 hybridization.0885

The next bonding type, the next hybridization type is what we call sp2.0893

Again let's look at the sum of the superscripts; that tells us a great deal.0900

Sp2, the sum of the superscripts is a grand total of three which means0906

an atom is going to be sp2 hybridized when it has three electron groups around it.0915

In addition remember that the sum of the superscripts also tells us how many hybrids we are going to form.0923

Here we are going to form exactly three sp2 hybrids.0931

One more thing, the superscripts also tells us the number of each atomic orbital that is going to be used.0940

Here we are going to be having one s orbital mixing with exactly two p orbitals.0948

Let's think about that.0959

We know that every energy we said has a p_x, p_y, and p_z, three p orbitals.0961

But if only two p orbitals are being used out of the three, that tells us the difference.0967

One of the p orbitals remains unused, unhybridized.0974

I am going to put that in; one p orbital is going to be unhybridized.0981

We need to now account for that in our energy diagram.0990

Let's go ahead and do that.0995

A nice example of something that is going to be sp2 hybridized, let's go ahead and look at BF₃.0997

BF₃ here; here is energy.1013

Regular boron itself is going to be 2s² and then just 2p¹.1019

When that goes ahead and mix, we are going to form exactly three sp2s intermediate in energy.1030

Remember that?--always intermediate in energy approximately.1037

This one p orbital that remains unhybridized, if it remains unhybridized, that means1042

it is going to be the same energy as the initial p orbitals.1048

I am going to put that approximately the same just like that.1056

Again we have exactly three sp2s; and we have a 2p orbital that remains unhybridized.1059

We are going to go ahead and fill the electrons now.1066

In BF₃, boron just has three electrons--one, two, and three.1069

Guess what?--there is no lone pairs.1075

There is going to be exactly three σ bonds.1077

When we draw out the Lewis structure for boron trifluoride, that is exactly what we get.1080

Boron has zero lone pairs in this structure and exactly three σ bonds.1087

That looks pretty good right now.1098

But let's go ahead and look at another example.1100

Here we are going to learn now a new type of bonding.1103

An example I want to look at has the following Lewis structure.1106

This is going to be a CH, a double bond, O just like that.1110

This is what we call formaldehyde.1120

Here formaldehyde, the central carbon atom has three electron groups.1125

That is also going to be sp2 hybridized.1131

Let's go ahead and set up the energy level diagram now for the carbon here.1136

Carbon is 2s and 2p; it is going to be 2s² 2p².1140

That is going to hybridize.1148

Again we are going to form exactly three sp2s--one, two, three.1150

We are going to have one of the 2p orbitals remaining unmixed just like that.1154

Let's go ahead and fill electrons now; carbon has four valence electrons.1159

Let's go ahead and populate the orbitals with four--one, two, and three.1163

I am going to put a big asterisk here because this is where we start to deviate.1169

Where do we put the fourth electron?1173

Going by typical Aufbau principle, we would always populate the lower energy1175

orbitals first before proceeding on to the higher atomic orbitals.1182

But in valence bond theory, we are going to go left to right regardless of energy.1187

We are going to go every orbital one time before doubling up.1193

I am going to put my fourth electron here, not in the sp2.1196

That is this special case for valence bond theory is really1202

a big deviation from what we know from Aufbau principle.1207

Please again keep that in mind.1210

When we do this see, it is going to work out because look at the Lewis structure.1214

The Lewis structure has zero lone pairs for the carbon atom.1218

As you can see in our bonding scheme, there is zero lone pairs.1222

We have the following; we have a σ bond here and a σ bond here; σ, σ.1227

And we have a double bond.1234

We have to now discuss what we mean by double bond.1237

A double bond we learned from Lewis theory has exactly four valence electrons.1241

But what type of bonds?1245

It turns out that a double bond is composed of the following.1248

It is composed of one σ bond and a new type of bond, what we call a π bond.1250

Our σ bond is just going to be the regular σ bond from the hybrid orbitals.1258

Guess what?--this electron that we have right here in the unhybridized atomic orbital,1262

that is going to overlap with oxygen to form a π bond.1268

One σ plus one π is equal to a double bond.1272

We can make a pretty big conclusion right now from these two exercises.1279

Lone pairs and σ bonds are going to come from hybrid orbitals.1288

π bonds are going to come from atomic orbitals that are unhybridized.1300

You may be wondering then what type of bond is stronger, is it σ or π?1311

The lower the energy, the more stable it is going to be.1318

The higher the energy, the more unstable it is going to be.1322

We are going to learn that very soon in our next discussion of thermodynamics.1326

σ bonds are typically going to be stronger than π bonds.1333

The reason why σ bonds are stronger is because once again1341

lower in energy but also we have more overlap of the orbitals.1345

If we have more overlap, the attraction between the nuclei is going to be much stronger.1355

That again is sp2 hybridization.1363

The next one I want to go over with you is what we call sp hybridization.1367

Let's go ahead and take a look at the sum of the superscripts.1372

Here is really s¹ p¹.1375

Remember if you don't see a number, 1 is always implied.1378

That means we are going to have two electron groups around the central atom.1381

Also this tells us that we are going to form a hybrid here by one s mixing with exactly one p.1392

Also we are going to form exactly two hybrid orbitals; two sp hybrids.1404

Let's go ahead and take a look; let's look at hydrogen cyanide; hydrogen cyanide.1415

Step one, it has the following Lewis structure--H, C, triple bond, N.1424

As you can see, carbon is two electron groups; that is going to be sp.1430

Also nitrogen also has two electron groups around it.1436

That too is going to be sp hybridized.1439

Let's first tackle carbon.1441

Then we will tackle nitrogen to see if it agrees with the Lewis structure.1443

Energy; carbon is again 2s 2p.1447

Put in its electrons; carbon is 2s² 2p².1454

That is going to go ahead and mix.1461

Again we are going to form exactly two sp orbitals; two sp hybrids.1463

It tells us that to form the two sp's, it is the mixing of one s and one p.1470

But remember there is three p orbitals per energy level; p_x, p_y, and p_z.1476

If I am only using one of those three, that means I have two remaining unhybridized.1481

We are also going to put that in; where do we put it in?1487

We put it in that it has exactly the same energy level as the initial two p orbitals.1491

Let's fill electrons--one, two, and don't forget this is where we deviate.1497

We go fill left to right all the orbitals first before double up regardless of energy.1502

One electron, two electrons, and now electron number three, and electron number four.1508

So far so good; we don't see any lone pairs at all.1514

The Lewis structure has no lone pairs around the carbon.1518

Let's see what HCN has around carbon; no lone pairs.1523

This bond right here is a σ bond; I am going to label that σ.1531

Now the nature of the triple bond.1535

We saw that a single bond is what we call a σ.1539

We saw that a double bond is one σ and one π.1542

A triple bond is going to be one σ but two π this time.1546

Again a triple bond is going to be one σ and two π.1551

We know that σ comes from hybrid orbitals; there is our σ.1557

We know that π bonds come from unhybridized atomic orbitals right here; π here and π there.1561

As you can see, we have two σ and two π's around carbon which is agreeing with the Lewis structure.1569

Let's see if we can get the same agreement with nitrogen this time.1577

Energy; nitrogen, 2s 2p; nitrogen is 2s² and now 2p³.1582

Again as we already discussed, this nitrogen atom is also sp hybridized.1595

That is going to be one, two.1600

We are going to form two p's right here; exactly two of them unhybridized.1602

Let's go ahead and fill in the electrons.1606

This time it is going to be five--one, two, three, four...1607

OK, now we can double up again with the opposite spin.1611

According to the Lewis structure for nitrogen in HCN, there is going to be one lone pair.1617

There is going to be a triple bond around nitrogen which is one σ and two π.1626

Guess what?--it agrees perfectly.1632

Here is our lone pair; here is our one σ; here is the two π's.1636

Again we see that valence bond theory helps us to count for the1645

nature of a single, a double, and now a triple covalent bond.1650

There are two other atomic hybridizations that you should be familiar with.1658

So far we saw that sp3 is going to be for four electron groups.1663

That is going to be a tetrahedral electron geometry.1671

We saw that sp2 is going to be three electron groups.1679

That is going to be a trigonal planar geometry; again electron geometry.1684

We just did sp; we saw that sp was two electron groups.1692

That was a linear electron geometry.1696

Now sp 3d; sp 3d, now we start talking about the d block orbitals.1700

That is a grand total of five electron groups.1708

If you recall, five electron groups was a trigonal bipyramid electron geometry.1712

Finally sp3 d2, that is six electron groups.1722

That is going to be an octahedral electron geometry.1728

Again it depends on your instructor and your textbook.1734

But I will just present to you the five basic atomic hybridization schemes.1739

That is the formation of hybrid orbitals and valence bond theory.1746

Valence bond theory as we just saw is successful in explaining for the observed bond angles predicted by VSEPR theory.1753

However we still have that one issue about magnetism.1764

Take oxygen for example; oxygen's Lewis structure is right here.1768

If you look at this, every electron is paired; we would expect diamagnetism; expected.1776

In other words, if we take molecular oxygen, it should be repelled by a magnetic field.1787

But experimentally when you pour liquid oxygen through a magnet,1794

it actually sticks to the magnet showing that O₂ is actually paramagnetic.1801

Obviously valence bond theory does not always successfully account or predict the actual magnetic behavior of a compound.1814

Then we need yet another bonding theory.1826

This bonding theory is what we call molecular orbital theory, also known as MO theory.1829

Here is the main difference.1840

In contrast to Lewis and valence bond theory, MO theory is a delocalized bonding model; not localized but delocalized.1842

In other words, the electron density is distributed throughout the1853

entire molecule rather than being centered around any individual atom.1857

You remember our discussion about wave functions.1866

It turns out that MO theory is a highly mathematically based theory.1870

If you recall the nature of a wave function, a wave function is representative of atomic orbitals.1878

The actual function if looked at them contain cosine and/or sine trigonometric functions.1883

If we try to think back to that, your basic cosine or sine wave function is a wave.1891

From your early math classes, you learned that these waves have both1901

positive and negative what are called phases; positive and negative phases.1909

Because atomic orbitals are the visual manifestation of a wave function, we can also infer that1923

atomic orbitals also can be represented by different phases, a + phase and a ? phase.1932

For general chemistry, we are only going to limit our discussion to s and p orbitals.1945

Let's first take a look at how s orbitals can interact.1952

I can have an s orbital of this phase mixing with another s orbital of the same phase.1958

When that happens, I form what is called a σ bonding orbital or a σ bonding MO.1970

How does that look like?1980

If here the dots represent the nuclei and if you have exactly two of these s orbitals1982

mixing with each other, we get a smeared out electron density throughout both nuclei.1990

Here is the nuclei.1997

But now we are going to get something that looks like this.1999

Again this is what we call a σ bonding MO.2005

Instead of two separate s orbitals, they now mix and form one entity.2009

As you can see from this diagram, it is completely distributed among both nuclei.2014

This is what we call delocalized.2023

The other possibility can occur.2026

What happens when we have s orbitals mixing that are of opposite phases?2028

To represent opposite phases, I am going to have now shading in one of these s orbitals just like that.2034

Now when I have s orbitals of opposite phases interacting,2044

this is going to be equivalent to destructive interference.2049

Remember we can interpret orbitals as wave-like properties.2056

When we have destructive interference, we actually get the following this time.2062

We are going to get something that looks like this now.2069

This is actually a node.2075

Remember we talked about nodes where we have zero electron probability.2077

This type of MO is not a σ bonding anymore.2085

But it is called a σ anti bonding MO; a σ antibonding MO.2089

For our purposes right now, something you have to remember is that2099

σ bonding will always be lower in energy than σ antibonding.2102

Once again σ bonding is going to lower in energy to σ antibonding.2109

Remember mother nature is always going to favor lower energy.2114

If an orbital is going to result in bonding of the molecule, it is going to be lower in energy.2117

Once again we went over σ bonding and σ antibonding.2124

σ antibonding will typically be represented as a σ*.2129

We talked about s orbitals; let's now talk about p orbitals.2135

P orbitals can interact in one of two ways.2139

They can interact head on or in a parallel fashion.2143

Let's talk about head on first.2152

When I mean head on, if we have a molecule AB like that, the bonding axis is going to be z-axis.2154

I am going to represent this as x; then represent that as y.2166

Once again the z-axis is going to be colinear with the bonding axis.2169

When we have a head on overlap of p orbitals, it is going to be the p_z orbitals.2174

Here is one p_z; here is another p_z interacting head on.2182

We can have the same phases of the p_z orbitals overlapping with each other like that.2189

When that happens, we form a σ bonding orbital.2203

Again we form a σ bonding orbital.2210

The MO is going to be distributed throughout the entire molecule around both nuclei.2214

We are going to get something that looks like this now2221

where the two nuclei are here, here, here, and here.2230

Again this is what we call a σ bonding MO.2238

You may ask then what is the other possibility?2242

The other possibility is for the p_z orbitals now to interact with their opposite phases like that.2244

When the opposite phases interact, it is just like we saw last time with the s orbitals.2266

That is going to be antibonding; this is going to be σ*.2270

That is going to be represented the following way where the two nuclei again are here and here.2276

Let's go ahead and draw the nodes in, shall we?2295

Here you see that there is one node here, one node here.2298

You see here for the antibonding one node, one node, and one node.2302

I want you to compare and contrast.2307

You notice that the antibonding MO for the p orbitals has three nodes2310

while the bonding MO for the p orbitals has two nodes.2316

The same pattern occurs for the s orbitals.2320

You notice that the antibonding MO for the σ has one node2324

while the bonding MO for the σ has zero nodes.2331

The antibonding MOs typically have more nodes than the bonding MOs.2338

Let's go ahead and look at the parallel interaction.2346

Parallel interaction is going to occur for the remaining two p orbitals, basically p_x and p_y.2349

If I have parallel interaction this time, I can have p orbitals occurring like that.2355

When we have parallel interaction, the overlap is not as great.2365

This is not a σ MO anymore.2370

Instead it is going to be a π MO.2372

Because it is the identical phases interacting with each other,2375

this is going to be what is called a π bonding MO.2378

We are going to get an MO that looks like this now distributed among both nuclei just like that.2381

Here we have exactly one node.2395

The other possibility is for parallel interaction but now of opposite phases like that.2401

When we have opposite phases again that is what we call an antibonding MO.2409

This is going to be π*.2413

π* is going to look like this distributed throughout the entire compound.2415

Let me go ahead and erase that.2428

As you can see once again the antibonding MO has more nodes than the corresponding bonding MO.2434

One other possibility is having an s orbital directly combined with a p orbital in a head to head fashion.2448

That is going to be an s orbital combining with the p_z orbital just like that.2455

Again that is going to be σ bonding.2464

Again we can also have s and p opposite phases.2467

That is going to be σ antibonding.2472

We pretty much covered all our bases and the different possibilities of the different types2477

of MOs that can form from s and p and how they look like.2482

Now that we have the combinations down, let's put it all together.2490

Let's go ahead and construct what we call a typical MO diagram.2494

The simplest type of compounds we are going to be looking at again are going to be homonuclear diatomics.2499

Remember two things; σ bonding is going to be less than σ antibonding.2507

Similarly π bonding is going to be less than energy of π antibonding.2518

σ versus π, σ bonding versus π bonding, that is going to become a major issue pretty soon.2527

But let's just go over the small ones first.2535

We will come across this issue here.2540

Hydrogen H₂, molecular H₂, two hydrogen atoms are going to combine.2542

Hydrogen is very simple.2550

We just have the hydrogen 1s orbital here and a hydrogen 1s orbital here.2551

Each of them contains one electron.2555