The next part of this lecture concerns hybridization and sigma and pi bonding. Sigma and pi bonds are types of covalent bonds, where two or more atoms share electrons. Atoms have orbitals, so the space the electrons occupy in covalent bonds is by the addition of atomic orbitals, those s, p, and d orbitals. So let's consider the simple example.
Hydrogen has one proton and one electron. So the nucleus is represented here by this black dot and the electron probability region is represented by this red circle. So if two hydrogen atoms come together to make H2, the space the electrons occupy is from the addition of the two s orbitals.
So here are the two hydrogen nuclei, and the electron probability region is mostly between the two nuclei. One could also envision this happening with p orbitals. So here is a carbon atom, and here is the nuclei with the p orbital.
Remember that there is a node here, so we're showing part of the electron region here in red, and the other p orbital here in blue. part of the electron region here in blue. So if a carbon with a p orbital met another carbon with a p orbital and they were oriented in such a way that when you brought these two nuclei closer together the red region overlapped, you would wind up with two electrons shared in this covalent bond in this probability region which is represented by the red. between the two nuclei and then small lobes on either side of the nuclei. So these are known as sigma bonds.
Their feature is that they have electron density between the atoms. What that means is electron density is between the nuclei for the hydrogen molecule and the carbon molecule. But what if we have two atoms that come together such that the p orbitals are not oriented toward each other, but rather side by side? Well, if we smoosh those closer together, you notice that we get an electron probability region that exists either above or below the internodal plane, which is defined as the plane between the two nuclei.
So just like individual p orbitals have a node, which is a region of no electron density, this type of bonding interaction also has a node or a region of no electron density. So these are known as pi bonds. The electron density is above and below the atoms, and the two electrons in the bond might be found either above or below the nodal plane.
So how this is different is that the nuclei can see each other. So instead of being the nuclei glued together, it's more like a clasp that goes above and below the nuclei. So how does this impact molecular structure?
If one has bond order one or a single bond between two atoms, that is going to be a sigma bond. The sigma bond is the stronger interaction because it shields the nuclei from each other. It's a direct attachment. So when you have a single bond, the bond order of one, you will have one sigma and no pi bonds.
For the oxygen molecule, the bond order is two. So an oxygen molecule has one sigma bond between the oxygen atoms and one pi bond. That means we have one direct interaction and one top and bottom clasp.
For a triple bond with bond order 3, you will have one sigma bond and two pi bonds. You'll have a clasp on the top and the bottom and side to side. There'll be some pictures soon to show you how this looks in 3D.
The bottom line of this is that every covalent bond starts with one sigma bond. Additional bonds are going to be pi bonds. So here's a question for you.
How many sigma and pi bonds are there in acrylonitrile? So remember, each bond starts with a sigma. Any bond that I highlight in red would be the sigma bonds.
Additional bonds will be pi bonds. So if one takes the theory that bonds are formed when orbitals on different atoms overlap, this would be a prediction that the amine molecule must have bond angles from hydrogen, nitrogen to hydrogen of 90 degrees. That's because p orbitals are perpendicular.
They're at 90 degrees to one another. So if overlap is going to occur with hydrogen atoms, it must be the direction those p orbitals are oriented, 90 degrees. But the experimental reality when hydrogen-nitrogen-hydrogen bonds were measured is that the bond angles were 107 degrees. And if you're recalling earlier lectures, you may say, well, that's... four electron regions, so the bond angle is predicted to be 109, but I know that the lone pair causes the hydrogen-nitrogen-hydrogen bond angles to be a little bit smaller.
So we need to build a new theory on top of quantum mechanics. Atoms by themselves have s and p orbitals and d orbitals and f orbitals. But molecules have bond angles that are 180 degrees, 120 degrees, or 109 degrees apart.
So how does one get from the individual atom to the atom's behavior in molecules? And the answer is hybridization. Hybridization is a theory that accounts for the difference between atomic orbital orientation and molecular shape.
The word hybrid means a mixture. For example, a hybrid car uses both gasoline and electric power. What we're going to do here is mix orbitals. Now we will do this pictorially. This can be done mathematically as well using the equation the Schrödinger model uses to model these electron clouds.
We'll start with a central atom, this carbon atom, that has two electron regions around it. Here are the valence orbitals of the carbon. There are two s electrons and some two p electrons.
If one has two electron regions, the way to explain the geometry is to mix two of the orbitals, an s and a p orbital. These new hybrid orbitals are called sp orbitals. because they come from the mixing of an s and a p orbital.
So there is an attempt to color code these slides a little bit. The s orbital is blue, the p orbital is red. Blue and red make purple. If two orbitals are mixed, two orbitals come out, and notice they are at intermediate energy. The s orbital is lower in energy, The p orbital is higher in energy.
The sp orbitals are the average energy of the two that are mixed. As a picture of the mathematics, here's what happens. We have an s orbital, we have a p orbital.
If we add the orbitals, blue and red are going to make a purple lobe here that contains most of the electron probability region. If we change the lobe orientation of this p orbital to be the opposite and add, then you notice that the blue and the red will make this purple orbital here. And I hope you notice that these are 180 degrees apart, which explains the bond angle when one has two electron regions.
So this carbon atom in the center has two lobes to it of hybrid orbitals. What about the other p orbitals, the ones that were not included in the hybridization? Well for right now we don't have a use for them. You'll understand the use very soon. I'll leave the px orbital as it is with its nodal plane, and the py orbital would be coming out of the screen and going back into the screen.
So you notice that four orbitals went in and four orbitals come out. the 2-purple, the px orbital, and the py orbital. So that's an important feature of the theory of hybridization. The number of orbitals in is equal to the number of orbitals out. Let's consider this molecule now, which has three electron regions around the carbon.
That carbon has valence s and p orbitals. For three electron regions, one hybridizes three orbitals, and these orbitals are called sp2 orbitals. So once again, very complex math is going to be represented in pictures.
When one makes an sp2 orbital the mixing occurs between one s orbital on the carbon, a p orbital on the carbon, and another p orbital on the carbon. This is more difficult to explain than the sp orbital so I hope you'll trust me in that three orbitals go in, three hybrid orbitals come out, and the main lobe of the hybrid orbitals is oriented at 120 degrees. around the central atom. So what does this look like? Three hybrid orbitals.
And what about PY, which was not in the mixture? PY is oriented above and below the plane. One sees a triangle holding the hybrid orbitals, and the leftover PY orbital is above and below that plane of the triangle. Once again, four orbitals in.
4 orbitals out. So I hope by now you recognize the pattern. When there are 2 electron regions, 2 orbitals are hybridized to give 2 sp orbitals.
When there are 3 electron regions, 3 orbitals are hybridized to give 3 sp2 orbitals. And as you might guess, when there are 4 electron regions, all 4 orbitals about the central atom are hybridized to give us 4 sp3 orbitals. So here are your favorite molecules again. Please count the electron regions and then give the hybridization about the indicated atom. And some more of your favorite molecules.
Once again, please give the hybridization around the indicated atom. So now we're to the connection between hybridization and sigma and pi orbitals. If one has a situation where three electron regions require hybridization of three orbitals to sp2 orbitals, the hybrid orbitals have two functions.
They are used for sigma bonds and lone pairs. The pure orbital, also called the The unhybridized orbital is going to be used for pi bonds. So let's go back to our ammonia molecule. Nitrogen, the atom that's alone, has valence s and p orbitals.
This time I'm going to bring the electrons along for the ride. Nitrogen has five valence electrons. In this compound there are four electron regions, so we'll hybridize four orbitals.
These hybrid orbitals are going to be called sp3 orbitals. They're oriented at 109 degrees and my five electrons are shown here. Now it's time to add the hydrogens.
Hydrogens have electrons in their 1s orbital. There are three hydrogens so each hydrogen has one of these valence orbitals. So now it's time to make some covalent bonds. Our first covalent bond is an interaction between an s and an sp3 orbital and so is our second and so is our third. Here they are shown to you overlapping.
The hybrid orbital is overlapping with the s orbital and the electron density is going to be between the nuclei. So this is a sigma bond. There are three sigma bonds in this molecule. What about the lone pair though? Well, that's hanging out in the last hybrid orbital.
So hybrid orbitals are used for lone pairs and sigma bonds.